Department of Civil Engineering
Sydney NSW 2006
AUSTRALIA
http://www.civil.usyd.edu.au/
Centre for Advanced Structural Engineering
Finite Element Modelling and Design of
Cold-Formed Stainless Steel Sections
Research Report No R845
Maura Lecce, BASc, MASc
Kim JR Rasmussen, MScEng, PhD
April 2005
Department of Civil Engineering
Centre for Advanced Structural Engineering
http://www.civil.usyd.edu.au/
Finite Element Modelling and Design of Cold-Formed
Stainless Steel Sections
Research Report No R845
Maura Lecce, BASc, MASc
Kim Rasmussen, MScEng, PhD
April 2005
Abstract:
This report describes the numerical investigation of cold-formed, thin-walled stainless steel
sections subject to distortional buckling under compression. Austenitic alloy 304 and ferritic
alloys 430 and 3Cr12 were considered. A finite element model calibrated to the data
gathered in a recent experimental programme (Lecce and Rasmussen 2005) shows that
material anisotropy can be ignored and that an accurate calibration model can be achieved
provided nonlinear yielding and enhanced corner properties are included in the model. FE
analyses of more than 570 simple lipped and lipped channels with intermediate stiffeners
covering a distortional buckling slenderness range 0.47 ≤ λd ≤ 3.64 reveal that enhanced
corner properties may become significant for stocky sections with a large corner area (λd <1
with a corner area of at least 10%). The experimental and FE test data were used to evaluate
the Australian, North American and European codes for stainless steel and cold-formed
carbon steel. The evaluation reveals that both the effective width area approach and direct
strength methods are generally inadequate for the design of stainless steel sections. Modified
resistance factors are recommended for the effective width approach of current design codes
to meet limit states design criteria. Direct strength design curves are developed for austenitic
and ferritic stainless steel alloys.
Keywords:
Stainless steel, distortional buckling, cold-formed sections, effective width design, enhanced
corner strength, direct strength method, imperfections, anisotropy, lipped channels,
intermediate stiffeners.
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
Copyright Notice
Department of Civil Engineering, Research Report R845
Finite Element Modelling and Design of Cold-Formed Stainless Steel
Sections
© 2005 Maura Lecce, Kim JR Rasmussen
[email protected]
[email protected]
This publication may be redistributed freely in its entirety and in its original
form without the consent of the copyright owner.
Use of material contained in this publication in any other published works must
be appropriately referenced, and, if necessary, permission sought from the
author.
Published by:
Department of Civil Engineering
The University of Sydney
Sydney NSW 2006
AUSTRALIA
April 2005
This report and other Research Reports published by The Department of Civil
Engineering are available on the Internet:
http://www.civil.usyd.edu.au
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Research Report No R845
2
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
Table of Contents
Table of Contents ..................................................................................................................3
List of Tables .............................................................................................................................4
List of Figures ............................................................................................................................5
Notation......................................................................................................................................7
1
Introduction ......................................................................................................................9
2
Numerical Investigation ...................................................................................................9
2.1
Scope of Numerical Study.......................................................................................9
2.2
Model Calibration ...................................................................................................9
2.2.1
General...........................................................................................................9
2.2.2
Elastic Perfectly Plastic Material Model ..........................................................12
2.2.3
Nonlinear Plastic Material Model based on Flats Only....................................12
2.2.4
Nonlinear Plastic Material Model based on Flats Only with Initial Anisotropy
13
2.2.5
Nonlinear Plastic Material Model with Enhanced Corner Properties ..............15
2.2.6
Calibration Model and All Experimental Tests................................................15
2.3
Simple Lipped Channels vs. Lipped Channels with Intermediate Stiffeners........19
2.4
Modelling Parameters: Further Investigation........................................................21
2.4.1
Investigating Anisotropy ..................................................................................22
2.4.2
Investigating Imperfection Magnitude and Element Type ...............................24
2.5
Modelling Parameters: Further Investigation........................................................27
2.5.1
General..............................................................................................................27
2.5.2
Boundary Conditions and Initial Imperfections ...............................................27
2.5.3
Material Properties ...........................................................................................28
2.5.4
FE Test Results.................................................................................................29
2.6
Conclusions of Numerical Investigation ...............................................................33
3
Evaluation of Current Design Practices..........................................................................33
3.1
General and Scope.................................................................................................33
3.2
Effective Width Approach ....................................................................................34
3.3
Direct Strength Method.........................................................................................44
4
Design Recommendations ..............................................................................................49
4.1
Ultimate Limit States Design Criteria...................................................................49
4.2
EWA Recommendations .......................................................................................49
4.3
Recommended Direct Strength Design Curves.....................................................51
5
Conclusions ....................................................................................................................54
6
References ......................................................................................................................55
Appendix A..............................................................................................................................57
Appendix B ..............................................................................................................................82
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Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
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List of Tables
Table 2. 1. Summary of Model Calibration Results ................................................................18
Table 3. 1. Experimental Tests and EWA Predicted Strengths for Simple Lipped Channels 35
Table 3. 2. Summary of FE Test to EWA Predicted Strengths for Simple Lipped Channels .36
Table 3. 3. Experimental Tests and EWA Evaluation of Lipped Channels with Intermediate
Stiffeners.........................................................................................................................38
Table 3. 4. Summary of FE test to EWA Predicted Strengths for Lipped Channels with
Intermediate Stiffeners ...................................................................................................39
Table 3. 5 Summary of Test to Current Cold-Formed Carbon Steel DSM Predicted Strengths
for Simple Lipped Channels ...........................................................................................47
Table 3. 6. Summary of Test to Current Cold-Formed Carbon Steel DSM Predicted Strengths
for Lipped Channels With Intermediate Stiffeners.........................................................48
Table 4. 1. Proposed φ Factors for EWA AS/NZS 4673: Simple Lipped Channels ...............49
Table 4. 2. Proposed φ Factors for EWA EC3 Part 1-4/1-3: Simple Lipped Channels...........50
Table 4. 3. Proposed φ Factors for AS/NZS 4673 EWA: Lipped Channels with Intermediate
Stiffeners.........................................................................................................................50
Table 4. 4. Proposed φ Factors for EWA EC3 Part 1-4/1-3: Lipped Channels with
Intermediate Stiffeners ...................................................................................................50
Table 4. 5. Summary of Test to Proposed DSM Predicted Strengths......................................53
Table 4. 6. Proposed φ Factors for DSM of Stainless Steel Sections: Simple Lipped Channels
........................................................................................................................................53
Table 4. 7. Proposed φ Factors for DSM of Stainless Steel Sections: Lipped Channels with
Intermediate Stiffeners ...................................................................................................54
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Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
List of Figures
Figure 2. 1. Test Specimens 304D1a (left) and 304D1b (right) for Calibration Model ..........10
Figure 2. 2. Boundary Conditions for Model Calibration FE Analyses ..................................10
Figure 2. 3. Close-up Images of FE Mesh for Model Calibration Analyses from FEMGV 6.4
........................................................................................................................................11
Figure 2. 4. Model Calibration Build-up (inward flange movement) (ABAQUS image at
advanced stages of buckling)..........................................................................................11
Figure 2. 5. Model Calibration Build-up (outward flange movement) (ABAQUS image at
advanced stages of buckling)..........................................................................................12
Figure 2. 6. NLP_ISO Mises Stress Distributions at Ultimate Load for Inward (two left) and
Outward (two right) Flange Movement of a Simple Lipped Channel............................13
Figure 2. 7. Experimental and Calibration FE Load vs. End Shortening Curves for Simple
Lipped Channels .............................................................................................................16
Figure 2. 8. Experimental and Calibration FE Load vs. End Shortening Curves for Lipped
Channels with Intermediate Stiffeners ...........................................................................17
Figure 2. 9. von Mises Membrane Stresses for Simple lipped Channel (top row) and Lipped
Channel with Intermediate Stiffeners (bottom row) at Maximum Load ........................19
Figure 2. 10. Progression of Stress Distributions for a Simple Lipped Channel .....................20
Figure 2. 11. Progression of Stress Distributions in a Lipped Channel with Intermediate
Stiffeners.........................................................................................................................21
Figure 2. 12. Investigating Anisotropy b/t=54.........................................................................22
Figure 2. 13. Distribution of von Mises stresses for Isotropic (left) and 50% Anisotropy
(right) Analyses. (post-buckling end deflection approximately 3mm)..........................23
Figure 2. 14. 50% Anisotropy with (left) and without (right) Orientation (last increment,
post-buckling).................................................................................................................23
Figure 2. 15. Investigating Anisotropy b/t=106.......................................................................24
Figure 2. 16. Investigating Anisotropy b/t=26.5......................................................................24
Figure 2. 17. Effects of Imperfection Magnitude for 304D1...................................................25
Figure 2. 18. Study on Imperfection Values and S4R/S4 Elements .......................................26
Figure 2. 19. Boundary Conditions of FE Tests ......................................................................28
Figure 2. 20. FE and Experimental Results: 304 Simple Lipped Channels.............................29
Figure 2. 21. FE and Experimental Results: 430 Simple Lipped Channels.............................30
Figure 2. 22. FE and Experimental Results: 3Cr12 Simple Lipped Channels.........................30
Figure 2. 23. FE and Experimental Results: 304 Lipped Channels with Intermediate Stiffeners
........................................................................................................................................31
Figure 2. 24. FE Test and Experimental Results: 430 Lipped Channels with Intermediate
Stiffeners.........................................................................................................................31
Figure 2. 25. FE and Experimental Results: 3Cr12 Lipped Channels with Intermediate
Stiffeners.........................................................................................................................32
Figure 2. 26. Austenitic 304 and Ferritic 430 and 3Cr12 Test Results....................................33
Figure 3. 1. Aeff/Ag vs. λd for Alloy 304 (Aeff determined by AS/NZS 4673) ...........................40
Figure 3. 2. 304 Test to AS/NZS 4673 Predicted Strengths vs. Aeff/Ag....................................40
Figure 3. 3. 430/3Cr12 Test to 4673 Predicted Strengths vs. Aeff/Ag .......................................41
Figure 3. 4. 304 Test to EC3 Part 1-4/1-3 Predicted Strengths vs. Aeff/Ag ...............................41
Figure 3. 5. 430/3Cr12 Test to EC3 Part 1-4/1-3 Predicted Strengths vs. Aeff/Ag ....................42
Figure 3. 6. 304 Test to AS/NZS 4673 Predicted Strengths vs. Percent Corner Area.............42
Figure 3. 7. 430/3Cr12 Test to EWA AS/NZS 4673 Predicted Strengths vs. Percent Corner
Area ................................................................................................................................43
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Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
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Figure 3. 8. 304 Test to EWA EC3 Part1-4/1-3 Predicted Strengths vs. Percent Corner Area
........................................................................................................................................43
Figure 3. 9. 430/3Cr12 Test to EC3 Part 1-4/1-3 Predicted Strengths vs. Percent Corner Area
........................................................................................................................................44
Figure 3. 10. 304 Test Data Compared with Current DSM Curves for Cold-Formed Carbon
Steel ................................................................................................................................45
Figure 3. 11. 430 Test Data Compared with Current DSM Curves for Cold-Formed Carbon
Steel ................................................................................................................................45
Figure 3. 12. 3Cr12 Test Data Compared with Current DSM Curves for Cold-Formed Carbon
Steel ................................................................................................................................46
Figure 4. 1. Proposed DSM Distortional Buckling Design Curve for Cold-Formed Austenitic
Stainless Steel Sections ..................................................................................................52
Figure 4. 2. Proposed DSM Distortional Buckling Design Curve for Cold-Formed Ferritic
Stainless Steel Sections ..................................................................................................52
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Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
Notation
Ac
Aeff
Ag
Bf
Bl
Bw
COV
D
Eo
Es
Et
Fm
L
Lcr
LC
LT
Mm
Pn
Pu
Pu,FE
Pu,T
Pu,sc
Vm
Vm
b
d
di
di,w
e
f
fcr
fn
fy
fy,c
fy,f
fu
fu,f
k
kf
m
n
r
ri
t
β
ε
εe
εtp
ε0.01
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
corner area
effective area (total effective area also represented by Ae,t)
gross area
overall flange width
overall lip width
overall web width
coefficient of variation
dead load
initial elastic modulus
secant modulus
tangent modulus
ratio of mean to nominal cross-sectional properties
column length; live load
critical distortional buckling half-wavelength
longitudinal compression
longitudinal tension
ratio of mean to nominal material properties
design strength
distortional test ultimate load (also Pu,t)
finite element distortional test ultimate load
experimental distortional test ultimate load
stub column ultimate load
COV of F
COV of M
element width
section depth
depth of intermediate stiffener
width of intermediate stiffener
parameter used in the modified Ramberg-Osgood equation
stress
critical buckling stress
design strength
yield strength
predicted corner yield strength
specified yield strength of the flats (virgin material)
ultimate strength
specified ultimate capacity of the flats (virgin material)
plate buckling coefficient
plate buckling coefficient of the flange
parameter used in modified Ramberg-Osgood equation
Ramberg-Osgood parameter
centerline radius
inner corner radius
thickness
reliability index for ultimate limit states design criteria
strain
engineering strain
true plastic strain
strain, 0.01%
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April 2005
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
ε0.2
φ
λ
λd
λl
σ
σe
σt
σu
σy
σ0.01
σ0.01,c
σ0.01,f
σ0.2
σ0.2,c
σ0.2,f
ω
ωd
ωl
τ
χd
χd,f
χd,w
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
April 2005
strain, 0.2%
resistance factor
buckling slenderness
distortional buckling slenderness
local buckling slenderness
normal stress
engineering stress
true stress
ultimate stress
yield stress
0.01% proportionality stress
0.01% proportionality stress of corners (cold-worked)
0.01% proportionality stress of flat (virgin material)
0.2% proof stress
0.2% proof stress of corners (cold-worked)
0.2% proof stress of flat (virgin material)
imperfection
measured or recommended imperfection at the flange-lip junction
measured or recommended imperfection at the centre of the web element
shear stress
distortional buckling reduction factor
distortional buckling reduction factor for the flange
distortional buckling reduction factor for the web
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Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
1
April 2005
Introduction
The purpose of this report is to present the numerical investigation of cold-formed stainless
steel sections, based on a recent experimental progamme on cold-formed simple lipped and
lipped channels with intermediate stiffeners made from austenitic 304 and ferritic 430 and
3Cr12 alloys (Lecce and Rasmussen 2005). The experimental and finite element (FE) test
data gathered were used to evaluate current design procedures available for stainless steel.
However, since design codes usually evolve along with cold-formed carbon steel codes, these
were examined also. Finally, design recommendations are made for the design of stainless
steel sections failing in the distortional buckling mode.
2
Numerical Investigation
2.1 Scope of Numerical Study
Numerical studies were carried out to increase the number of data points, or test points, from
which to draw conclusions and recommendations regarding the distortional buckling
behaviour of stainless steel channel sections. First, a model calibration study was conducted
using the 19 experimental distortional buckling tests by considering the experimentally
measured material and geometric properties. Further numerical studies with respect to
anisotropy, imperfections and element type (S4R vs S4) were carried out to confirm that the
calibration model is valid for a greater range of section geometries and material properties.
Following this, a total of 270 simple lipped channels with a distortional buckling slenderness
range of 0.47 ≤ λd ≤ 3.64 and 306 lipped channels with intermediate stiffeners with a
distortional buckling slenderness range of 0.47 ≤ λd ≤ 3.27 were tested by finite element
analyses. To study the effects of enhanced corner properties, typical brake-pressed r/t ratios
of 1 and 2.5 were chosen.
The FE package ABAQUS (2001), Version 6.4, was used for the numerical analyses
and input files were created using the engineering software FEMGV6.4-02 (FEMSYS 2002).
Specific modelling issues are described in the following subsections.
2.2 Model Calibration
2.2.1 General
All data used to develop the calibration model are reported in Lecce and Rasmussen (2005).
Fixed-end boundary conditions with a uniform displacement applied to one end was used in
the model and represented the actual experimental conditions. To save computational time,
symmetrical failure mode was assumed about the mid-web axis and only half of the crosssection was modelled. This assumption is valid because the experimental tests developed
essentially symmetrical distortional buckling deflections as shown in Figure 2.1. The
boundary conditions are shown in Figure 2.2 and are given with respect to the ABAQUS 1-23 axes which correspond to the x,y and z axes. Over 9000 elements, typically 5mm by 5mm
square were used for the model calibration described here. Images of the mesh from different
perspectives are provided in Figure 2.3. The FE models representing the other experimental
tests are similar. Average measured geometric dimensions for test specimens 304D1a and
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Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
304D1b were used in the model (Lecce and Rasmussen 2005). Two sets of analyses were
carried out; one for a positive (+ve) imperfection value, which would trigger inward flange
movement and another for a negative (-ve) imperfection value which would trigger outward
flange movement (as experienced in the experimental test). In the following discussions
these will be referred to as inward model and outward model. The imperfection amplitude,
±0.25mm, is equal to the average of the absolute imperfection values measured at mid-height
of the flange-lip junction of all “304D” test specimens (304D1a, 304D1b, 304D2a and
304D2b), a method adopted by Hasham and Rasmussen (2002). (The imperfection sign
convention used in Lecce and Rasmussen (2005) is opposite to that used in FE modelling).
Figure 2. 1. Test Specimens 304D1a (left) and 304D1b (right) for Calibration Model
Figure 2. 2. Boundary Conditions for Model Calibration FE Analyses
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Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
Figure 2. 3. Close-up Images of FE Mesh for Model Calibration Analyses from FEMGV 6.4
For each set of analyses the material model was constructed by considering nonlinear
stress-strain hardening, initial anisotropy, and enhanced corner properties. The discussions in
the following subsections make reference to Figures 2.4 and 2.5.
125
304D1 Test
(Pu,FE/Pu,T)
PP_(1.23)
NLP_ISO_(1.00)
NLP_ANISO=5%_(1.01)
NLP_EC_ISO_(1.03)
NLP_EC_ANISO=5%_(1.04)
Load (kN)
100
75
50
25
Imperfection=+0.25mm
(flanges move in)
0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
End Shortening (mm)
Figure 2. 4. Model Calibration Build-up (inward flange movement) (ABAQUS image at
advanced stages of buckling)
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Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
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125
304D1 Test
PP_(1.14)
(Pu,FE/Pu,T)
NLP_ISO_(0.94)
NLP_ANISO=5%_(0.95)
NLP_EC_ISO_(1.00)
NLP_EC_ANISO=5%_(1.01)
Load (kN)
100
75
50
25
Imperfection=-0.25mm
(flanges move out)
0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
End Shortening (mm)
Figure 2. 5. Model Calibration Build-up (outward flange movement) (ABAQUS image
at advanced stages of buckling)
2.2.2 Elastic Perfectly Plastic Material Model
The first material model considered was an elastic perfectly-plastic material, labelled PP and
the plastic yield stress was equal to the experimentally measured σ0.2 (242MPa) determined
from the longitudinal compression coupons of the flats (virgin material). Unsurprisingly this
simplistic material model offered a poor match to the experimental test, as shown in Figures
2.4 and 2.5. Studies in the past have also shown that an elastic perfectly-plastic analysis for
stainless steel leads to erroneous results (Rasmussen et al. 2003). The ultimate FE load to
ultimate experimental test load ratios, Pu,FE/Pu,T, (given in the legends of Figures 2.4 and 2.5)
are 1.23 and 1.14 for inward and outward models, respectively. Evidently by simply
changing the sign of the imperfection, different strengths can be obtained. In this example
the ultimate FE load, Pu,FE, for the inward model is 7.4% greater than the outward model.
Extensive studies (Silvestre and Camotim 2004) on this phenomenon for cold-formed carbon
steel have shown that, for simple lipped channels the elastic post-buckling response leads to a
greater ultimate load if the flanges move inwards and the same result is found here with the
PP model.
2.2.3 Nonlinear Plastic Material Model based on Flats Only
The next model included stainless steel material nonlinearity. The true stresses, σt, and true
plastic strains, εtp, as required by ABAQUS, were derived from the longitudinal compression
engineering stress-strain data of the 304 flat material using the following equations:
σ t = σ e (1 + ε e )
ε tp = ln (1 + ε e ) −
(1)
σt
(2)
Eo
where σe and εe are the engineering stresses and strains. For this model, only the “flat”
properties were considered and applied to the entire cross-section. This nonlinear plastic
(NLP) hardening model assumes an initially isotropic (ISO) yield surface described by the
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Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
von Mises criterion and expands, or hardens, isotropically. The resulting load vs. end
shortening NLP_ISO curves for inward and outward models correspond to Pu,FE/Pu,T ratios of
1.00 and 0.94 in Figures 2.4 and 2.5, respectively. Clearly the NLP_ISO model is a
significant improvement from the previous PP model and the imperfection sign used in the
model becomes less important in terms of ultimate load. Nevertheless, the shape of the loadend shortening curve is better described by the outward model. It is interesting to examine
the von Mises stress distributions for the NLP_ISO model at ultimate load and these are
shown in Figure 2.6 for inward and outward flange movement (the contours are scaled with
respect to the ultimate load and deflections are amplified).
Figure 2. 6. NLP_ISO Mises Stress Distributions at Ultimate Load for Inward (two left)
and Outward (two right) Flange Movement of a Simple Lipped Channel
At ultimate load, the section with outward flange movement has achieved greater
deflections compared with the model with inward flange movement. As shown in the
contours, both models show high stresses at the lip but the model with outward flange
movement shows higher stresses at the flange-web corner and is likely a consequence of
attaining greater deflections. Furthermore it is evident that the stresses in flange-lip region of
the inward model is greater and consequently so is the ultimate load.
2.2.4 Nonlinear Plastic Material Model based on Flats Only with Initial
Anisotropy
Another material characteristic considered was the anisotropy. By using ABAQUS’ built-in
modelling tools anisotropy was incorporated in the initial yield surface according to the Hill
criteria described by:
[
2
f (σ ) = F (σ 22 + σ 33 ) 2 + G (σ 33 − σ 11 ) 2 + H (σ 11 − σ 22 ) 2 + 2 Lτ 23
+ 2Mτ 132 + 2 Nτ 122
where F, G, H, L, M and N are given by:
σ 02 ⎛⎜ 1
1
1 ⎞⎟ 1 ⎛⎜ 1
1
1 ⎞⎟
+
−
F=
=
+
−
2
2
2 ⎜⎝ σ 02, 22 σ 02,33 σ 02,11 ⎟⎠ 2 ⎜⎝ R22
R33
R112 ⎟⎠
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]
1/ 2
(3)
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
G=
σ 02 ⎛⎜ 1
1
1
+ 2 − 2
2
2 ⎜⎝ σ 0,33 σ 0,11 σ 0, 22
F=
σ 02 ⎛⎜ 1
1
1 ⎞ 1⎛ 1
1
1 ⎞
+ 2 − 2 ⎟ = ⎜⎜ 2 + 2 − 2 ⎟⎟
2
2 ⎜⎝ σ 0,11 σ 0, 22 σ 0,33 ⎟⎠ 2 ⎝ R11 R22 R33 ⎠
L=
3 ⎛⎜ τ 02
2 ⎜⎝ τ 02, 23
April 2005
⎞ 1⎛ 1
1
1 ⎞
⎟= ⎜
+ 2 − 2 ⎟⎟
2
⎜
⎟ 2 R
⎝ 33 R11 R22 ⎠
⎠
⎞ 3⎛ 1 ⎞
⎟= ⎜
⎟
⎟ 2 ⎜ R2 ⎟
⎝ 23 ⎠
⎠
M=
3 ⎛⎜ τ 02
2 ⎜⎝ τ 02,13
⎞ 3⎛ 1 ⎞
⎟= ⎜
⎟
⎟ 2 ⎜ R2 ⎟
⎝ 13 ⎠
⎠
N=
3 ⎛⎜ τ 02
2 ⎜⎝ τ 02,12
⎞ 3⎛ 1 ⎞
⎟= ⎜
⎟
⎟ 2 ⎜ R2 ⎟
⎝ 12 ⎠
⎠
(4)
where σ0 is the reference yield stress and τ0 is the reference shear yield stress, τ 0 = σ 0 3 .
The yield criterion only has this form when the principal axes of anisotropy are the axes of
reference. That is, for cold-rolled sheets, the principal axes lie in the direction of rolling,
transversely in the plane of the sheet and normal to this plane (Hill 1950). The σ11 is the
stress in the direction of rolling, σ22 is transverse to the direction of rolling and σ33 is normal
(or through-thickness) anisotropy. By default ABAQUS assumes the direction of rolling is in
the global x-1 axis and maintains this alignment unless the user defines otherwise. ABAQUS
requires the user to define the following stress ratios to satisfy the Hill criteria:
σ
σ
σ
R11 = 11 = 1.00; R22 = 22 = 1.05; R33 = 33 = 1.00;
σ0
σ0
σ0
R12 =
τ
τ
τ 12
= 1.01; R13 = 13 = 1.00; R23 = 23 = 1.00
τ0
τ0
τ0
(5)
For the example considered here, the reference stress of the 304 material, σ0 is equal
to the σ0.2 value (242MPa) given by the longitudinal compression coupon tests of the flats.
Since the test specimens were loaded in the longitudinal direction (with respect to rolling),
the σ11 value is equal to σ0, giving R11 = 1.00. The σ22 value is equal to the transverse yield
stress (254MPa) of the compression coupons and thus R22 = 1.05. The through thickness
anisotropy was assumed to be unity (ie; σ33=σ11=σ0) which is reasonable for thin plates; thus
R33 = 1.00. The reference shear yield stress, τ 0 = σ 0 3 and τ 12 = σ 12 3 where σ12 is the
diagonal yield stress (244MPa) and thus R12 = 1.01. The ratios R13 = R23 = 1.00. These
strength ratios are defined under the *PLASTIC card in the ABAQUS input file. The material
model assumes that initial anisotropy remains constant and the plastic hardening, or
expansion of the yield surface occurs isotropically. For a 3D model with multiple surfaces, it
is important to define element orientation to ensure that the anisotropy is aligned correctly for
every element and avoid erroneous results. In ABAQUS, this can be accomplished by using
the *ORIENTATION card following the element definition. For the sections modelled in
this study, it was important to map the local element longitudinal “11” direction axis to
coincide with the global z-3-axis (direction of loading) and the transverse direction “22”
normal to the “11” direction. (Failure to define the orientation can lead to significant errors,
and this is demonstrated in a separate study presented in Section 2.4).
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Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
The results of the nonlinear plastic model with initial anisotropy, NLP_ANISO=5%,
amounted to less than 1% difference in ultimate load compared to the initially isotropic
model, NLP_ISO and the Pu,FE/Pu,T ratios are 1.01 and 0.95 in Figures 2.4 and 2.5,
respectively. These results suggest that material anisotropy has little effect on the ultimate
strength of the sections tested and may be ignored. However, to confirm that this is true also
for sections of different material thicknesses and higher degrees of anisotropy further
investigation was carried out and is described in Section 2.4.
2.2.5 Nonlinear Plastic Material Model with Enhanced Corner Properties
The basic isotropic nonlinear plastic hardening model was modified to include the enhanced
corner properties, which were applied strictly to the corner geometry of the section. The true
stress and true plastic strain properties were derived from the corner coupon stress-strain data
using Eqns. 1 and 2. The NLP_EC_ISO Pu,FE/Pu,T ratios are 1.03 and 1.00 for +ve
imperfection and –ve imperfections, respectively (c.f. Pu,FE/Pu,T = 1.00, Pu,FE/Pu,T = 0.94 for
NLP_ISO). Both sets of NLP_EC_ISO results show good agreement with the test result but
the load versus end shortening behaviour is better described by the outward model which
simulates the actual flange movement of the test. Overall, the sign of imperfection seems to
be less important for the inelastic stainless steel material model compared to the elastic
plastic material model. Finally initial anisotropy was included (NLP_EC_ANISO=5%) and
again results show that the effect of anisotropy is negligible.
2.2.6 Calibration Model and All Experimental Tests
The above discussion shows that material nonlinearity and enhanced corner strengths govern
the ultimate section strength of a stainless steel section and initial anisotropy can be
neglected. Thus the NLP_EC material model was used to evaluate all experimental tests.
The imperfection sign does not have a great impact on the ultimate load but rather shows
more influence in the post-ultimate range as seen in the experimental tests. Nevertheless, the
imperfection sign used for the models simulated the actual flange movement observed during
the tests. For sections which developed both inward and outward flange movement along the
specimen length during the test, the imperfection sign assumed in the model was generally
positive. The load vs. end shortening curves obtained from ABAQUS are shown along with
the experimental plots in Figures 2.7 and 2.8 for simple lipped channels and channels with
intermediate stiffeners, respectively. The ultimate loads are summarized in Table 2.1.
Department of Civil Engineering
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Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
120
80
Load (kN)
Load (kN)
100
60
304D2a (in)
40
304D2b (in)
20
FE_imp=+0.25mm (in)
0
0.5
1.0
1.5
End Shortening (mm)
50
45
40
35
30
25
20
15
10
5
0
2.0
430D2 (out)
FE_imp=-0.10mm (out)
0.0
0.5
1.0
1.5
End Shortening (mm)
45
40
35
30
25
20
15
10
5
0
2.0
Load (kN)
430D1b (in/out)
FE_imp=+0.10mm (in/out)
0.5
1.0
1.5
End Shortening (mm)
45
40
35
30
25
20
15
10
5
0
2.5
160
140
120
100
80
60
40
20
0
430D1a (in/out)
0.0
2.5
Load (kN)
Load (kN)
0.0
April 2005
2.0
2.5
430D3a (in/out)
430D3b (in/out)
FE_imp=+0.10mm (in/out)
0.0
1.0
2.0
End Shortening (mm)
3.0
3Cr12D2 (in/out)
3Cr12D1 (in/out)
FE_imp=+0.36mm (in/out)
0.0
1.0
2.0
3.0
End Shortening (mm)
4.0
Figure 2. 7. Experimental and Calibration FE Load vs. End Shortening Curves for
Simple Lipped Channels
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Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
160
140
120
100
80
60
40
20
0
70
60
40
304DS1a (out)
430DS1 (in/out)
30
304DS1b (in)
FE_imp=+0.22mm (in)
20
FE_imp=-0.22mm (out)
10
FE_imp=-0.23mm (in/out)
0
1.0
2.0
3.0
4.0
End Shortening (mm)
5.0
6.0
0.0
70
70
60
60
50
50
40
2.0
3.0
End Shortening (mm)
40
430DS2 (in)
30
1.0
Load (kN)
Load (kN)
Load (kN)
Load (kN)
50
0.0
4.0
5.0
430DS3 (out)
30
20
20
FE_imp=+0.23mm (in)
10
FE_imp=-0.23mm (out)
10
0
0
1.0
2.0
3.0
End Shortening (mm)
80
70
60
50
40
30
20
10
0
4.0
FE_imp=+0.23mm (in)
1.0
2.0
1.0
2.0
3.0
End Shortening (mm)
4.0
3.0
4.0
End Shortening (mm)
180
160
140
120
100
80
60
40
20
0
430DS4 (in)
0.0
0.0
Load (kN)
0.0
Load (kN)
April 2005
5.0
6.0
3Cr12DS2 (in/out)
3Cr12DS1 (in/out)
FE_imp=+0.16mm (in/out)
0.0
1.0
2.0
3.0
4.0
End Shortening (mm)
5.0
6.0
Figure 2. 8. Experimental and Calibration FE Load vs. End Shortening Curves for
Lipped Channels with Intermediate Stiffeners
Note that the 304DS1a and 304DS1b tests were the only set of experimental twin tests
where one specimen exhibited inward flange movement and the other exhibited outward
flange movement. The test and FE curves for these tests provide a clear example of the
agreement that can be achieved if the correct flange movement is simulated (see Figure 2.8).
From the plots in Figures 2.7 and 2.8 and Table 2.1, it is evident that very good
agreement between the calibration model and experimental tests was achieved, with a mean
Pu,FE/Pu,T ratio of 0.99 and a coefficient of variation (COV) of 0.0263. The same set of FE
analyses were conducted using S4 elements but the differences in ultimate load were less than
0.5% (and at least double the computational time) thus confirming that S4R elements were
adequate for the analyses of the experimental tests.
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Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
Table 2. 1. Summary of Model Calibration Results
ωda
Specimen ID
304D1a
304D1b
304D2a
304D2b
430D1a
430D1b
430D2
430D3a
430D3b
3Cr12D1a
3Cr12D1b
304DS1a
304DS1b
430DS1
430DS2
430DS3
430DS4
3cr12DS1a
3cr12DS1b
mm
-0.25
+0.25
+0.10
-0.10
+0.10
+0.36
-0.22
+0.22
-0.23
+0.23
-0.23
+0.23
+0.16
+0.16
P u,T
kN
102
101
104
104
39
39
45
40
39
138
139
132
134
60
62
64
72
163
161
P u,FE
kN
101
103
40
43
38
140
138
133
58
60
64
69
160
mean
stdv
COV
a
P u,FE /P u,T
0.99
1.00
0.99
0.99
1.02
1.02
0.96
0.94
0.96
1.02
1.01
1.04
0.99
0.96
0.97
1.00
0.96
0.98
0.99
0.99
0.026
0.0263
imperfection amplification applied to the critical distortional buckling
mode. Negative sign means outward flange movement (opposite sign to
experimental data)
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Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
2.3 Simple Lipped Channels vs. Lipped Channels with
Intermediate Stiffeners
By FE modelling, it is easy to plot the stress contours and visualize the development of
stresses and deflections of simple lipped channels compared with those of lipped channels
with intermediate stiffeners. To examine this, two sections are considered: the 304D1a/b
simple lipped channel modelled in Section 2.2 with overall dimensions of Bw = 106mm,
Bf = 90mm, Bl = 12.8mm, (λd = 0.96) and the 304DS1a/b section with similar overall
dimensions of Bw = 122mm, Bf = 90.6mm, Bl = 12.8mm (λd = 0.85). The section length
(800mm) and fixed-end conditions are identical for the two sections. For demonstration
purposes, the material model does not include enhanced corner properties. The von Mises
membrane stress distribution, at ultimate load, is depicted in Figure 2.9 for sections with
inward flange movement.
Figure 2. 9. von Mises Membrane Stresses for Simple lipped Channel (top row) and
Lipped Channel with Intermediate Stiffeners (bottom row) at Maximum Load
From these different views, one can see that the highest membrane stresses are
developed around the flange/lip area for both section types and that intermediate stiffener
provides an obstruction to the spread of stress to the flange-web corner.
Figures 2.10 and 2.11 show the evolution of the mid-surface stresses for the two
different cross-section types through seven images which correspond to the points in the
accompanied load vs. end shortening graph. The contours are scaled with respect to the
stress state of the last increment considered.
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April 2005
120
Load (kN)
100
80
60
40
20
0
0.0
1.0
2.0
3.0
End Shortening (mm)
Figure 2. 10. Progression of Stress Distributions for a Simple Lipped Channel
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4.0
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
140
Load (kN)
120
100
80
60
40
20
0
0.0
1.0
2.0
3.0
End Shortening (mm)
Figure 2. 11. Progression of Stress Distributions in a Lipped Channel with Intermediate
Stiffeners
The first four images show the progression of stresses leading up to the ultimate load
(fifth image) and the last two show the post-peak stress development. By comparing Figures
2.10 and 2.11, it is clear that the simple lipped channel develops a higher concentration of
stresses at the flange-web corner whereas the stresses in the channel with intermediate
stiffeners involve a much larger area. This suggests that the latter is much more effective at
distributing the load and therefore more of the cross-section reaches higher loads. This
agrees with experimental results where channels with intermediate stiffeners exhibited greater
material nonlinearity at ultimate load. Overall, the section corners, including intermediate
stiffeners, are responsible to carry higher loads and for this reason it becomes important to
consider the enhanced corner properties in the evaluation of the section strength.
2.4 Modelling Parameters: Further Investigation
The calibration model developed in Section 2.2 provided excellent agreement experimental
tests and cover a distortional buckling slenderness range of 0.76 ≤ λd ≤ 1.10. This section
will confirm that the FE model also works for a greater range of sections by investigating
further the effects of anisotropy, imperfection value and element type (S4R vs S4).
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Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
2.4.1 Investigating Anisotropy
From the calibration model, it was evident that material anisotropy had little influence on the
ultimate strength. However, the actual measured anisotropy was relatively low (R22=1.05)
and the question remains whether a higher degree of anisotropy would also have negligible
influence. Three sections with thicknesses 1.96mm, 1mm and 4mm were considered with
overall geometric properties of experimental test 304D1a/b. The corresponding b/t ratios are
54, 106 and 26.5. The imperfection value remained constant (-0.25mm) and the thicknesses
were varied [t=1.96mm, (b/t=54); t=1mm, (b/t=106); t=4mm, (b/t=26.5)]. For each section,
two anisotropy values were checked; the measured experimental anisotropy of 5% and an
exaggerated anisotropy of 50%.
The load versus end shortening curve for b/t=54 is given in Figure 2.12. Evidently,
there is negligible difference between the isotropic (ISO) curve and the 5% anisotropy curve
(ANISO=5%) with a marginal difference in ultimate load of approximately 1%. If the
material anisotropy is exaggerated to 50% (ANISO=50%), the maximum increase in ultimate
load is less than approximately 4%. Figure 2.13 displays the von Mises stresses at the midsurface of the shell elements for an isotropic model (left) and a model with 50% anisotropy
(right). The comparison is made in the post-ultimate range where the axial compression is
approximately 3mm and the load has dropped to approximately 65% of the ultimate. The
contour plots show, as expected, that the transverse stresses developed are greater in the
anisotropic model. For the same b/t ratio, material orientation was omitted from the analysis
[see cyan curve for ANISO=50% (No orient.), Figure 2.12] resulting in a significantly
different behaviour with an ultimate load 17% greater than the correctly oriented model. The
von Mises stress distributions in the post-ultimate state for the models ANISO=50% and
ANISO=50% (No orient.) is given in Figure 2.14 and shows the significantly different stress
distributions. This example is given to demonstrate the importance of correct element
orientation when anisotropy is applied.
120
Load (kN)
100
80
60
ISO_t=1.96mm
ANISO=5%_t=1.96mm
40
ANISO=50%_t=1.96mm
20
ANISO=50% (No orient.)_t=1.96mm
0
0.0
1.0
2.0
3.0
4.0
End Shortening (mm)
Figure 2. 12. Investigating Anisotropy b/t=54
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Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
Figure 2. 13. Distribution of von Mises stresses for Isotropic (left) and 50% Anisotropy
(right) Analyses. (post-buckling end deflection approximately 3mm)
Figure 2. 14. 50% Anisotropy with (left) and without (right) Orientation (last
increment, post-buckling)
Figures 2.15 and 2.16 show the results for b/t=106 and b/t=26.5, respectively. The
exaggerated anisotropy generally has the effect of improving material ductility with little
strength benefits.
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Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
35
Load (kN)
30
25
20
15
ISO_t=1mm
10
ANISO=5%_t=1mm
ANISO=50%_t=1mm
5
0
0.0
1.0
2.0
3.0
4.0
End Shortening (mm)
Figure 2. 15. Investigating Anisotropy b/t=106
300
Load (kN)
250
200
150
ISO_t=4mm
100
ANISO=5%_t=4mm
50
ANISO=50%_t=4mm
0
0.0
2.0
4.0
6.0
8.0
End Shortening (mm)
Figure 2. 16. Investigating Anisotropy b/t=26.5
Overall, from a practical design-engineering viewpoint, the simple isotropic
hardening plasticity model suffices for statically loaded stainless steel members. However,
anisotropy is affected by material deformation and cold working and more accurate material
modelling may become important for members under cyclic loading. This was shown by
Olsson (1998) and Gozzi (2004) who developed a material model to account for, among other
phenomenological behaviour, the effects of stainless steel material anisotropy and its
evolution under repeated loading.
2.4.2 Investigating Imperfection Magnitude and Element Type
Another modelling issue to consider in greater detail is the imperfection magnitude used. For
the model calibration described in Section 2.2 (section 304D1a/b), the magnitude of the
imperfection (-0.25mm) was equal to the average of the absolute measured imperfection
values at the flange-lip junction located at mid-height. However, to investigate the sensitivity
to imperfections two other magnitudes were considered including the average of the absolute
maximum measured imperfections at the flange-lip junction (-0.32mm) and a calculated
Department of Civil Engineering
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Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
imperfection value according to the adopted Walker (1975) equation given by
ωd = 0.3t(σ0.2/σcr)0.5, where σcr is the critical elastic distortional buckling stress obtained from
the elastic buckling analysis (σ0.2 = 242MPa, σcr = 263MPa, t = 1.96mm; ωd = -0.56mm).
Figure 2.17 shows the load vs. end shortening results of test specimen 304D1 (used in
the model calibration of Section 2.2) and the FE analyses. Evidently, even if the imperfection
value is doubled, the difference in ultimate load is marginal. It should be noted here that the
distortional buckling slenderness for this fixed ended model is λd = (σ0.2/σcr)0.5 = 0.96.
120
Load (kN)
100
80
304D1
60
NLP_EC_imp=-0.25mm
(average at mid-length)
NLP_EC_imp=-0.32mm
(max average)
NLP_EC_imp=-0.56mm
(walker equation)
40
20
0
0.0
1.0
2.0
3.0
4.0
End Shortening (mm)
Figure 2. 17. Effects of Imperfection Magnitude for 304D1
Of the three imperfection values considered, only the Walker imperfection was
calculated from the material and distortional buckling properties which makes the Walker
equation particularly useful when experimentally measured imperfections are unavailable.
Other methods to estimate initial geometric imperfections have been suggested by Schafer
and Pekoz (1998). In their work, two types of imperfections are defined; Type 1: ωl for local
buckling of the web, and Type 2: ωd for distortional buckling of the flange-lip and are both
directly proportional to the section thickness. In the suggested probabilistic method,
ωl = 0.14t and ωl = 0.66t (ωd = 0.64t and ωd = 1.55t ) respectively correspond to 25% and
75% probability that the imperfections will be less than these maximums and will be referred
to as Schafer_25% and Schafer_75%. Type 1 imperfection magnitudes were comparable
with the experimentally measured imperfections of the flange-lip corners and thus only
ω = 0.14t (Schafer_25%) and ω = 0.66t (Schafer 75%) were considered. According to these
equations, the imperfections are independent of the section slenderness and increase for
increasing section thickness. Therefore, a stockier section, which is conceivably less
susceptible to develop larger initial imperfections, is penalized. This is unlike the Walker
equation where the imperfection amplitude is proportional to the square root of the
distortional buckling slenderness value so that, keeping all other dimensions the same the
imperfections decrease for increasing section thickness.
Three pin-ended sections with λl = 3.122 (local buckling critical), λd = 1.203 and
λd = 0.637 (distortional buckling critical) were modelled. Both S4R and S4 elements were
considered and the results are presented in Figure 2.18.
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Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
7
λ l =3.122
λ d =2.240
6
t=0.5mm
Load (kN)
5
4
3
S4R_Walker_imp=0.44mm
S4R_Schafer_25%_imp=0.07mm
S4R_Schafer_75%_imp=0.33mm
S4_Walker_imp=0.44mm
S4_Schafer_25%_imp=0.07mm
S4_Schafer_75%_imp=0.33mm
2
1
0
0
2
4
6
End Shortening (mm)
8
60
λ l =1.028
λ d =1.203
Load (kN)
50
t=1.5mm
40
30
S4R_Walker_imp=0.52mm
S4R_Schafer_25%_imp=0.21mm
S4R_Schafer_75%_imp=0.99mm
S4_Walker_imp=0.52mm
S4_Schafer_25%_imp=0.21mm
S4_Schafer_75%_imp=0.99mm
20
10
0
0
2
4
6
End Shortening (mm)
8
10
250
λ l =NA
λ d =0.637
Load (kN)
200
t=4.0mm
150
S4R_Walker_imp=0.76mm
S4R_Schafer_25%_imp=0.56mm
S4R_Schafer_75%_imp=2.64mm
S4_Walker_imp=0.76mm
S4_Schafer_25%_imp=0.56mm
S4_Schafer_75%_imp=2.64mm
100
50
0
0
2
4
6
8
10
End Shortening (mm)
12
14
Figure 2. 18. Study on Imperfection Values and S4R/S4 Elements
The Walker and Schafer_25% imperfections produced similar results for all sections
whereas the Schafer_75% became significantly conservative for the stockier section (see plot
where λd = 0.637). The Walker equation is suitable for all sections and conveniently takes
into account the section slenderness and material strength without being overly conservative.
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Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
Finally, the results show that there is no significant advantage to using the S4 elements rather
than the S4R.
2.5 Modelling Parameters: Further Investigation
2.5.1 General
The sections tested by FE analyses were proportioned to fail by distortional buckling and the
geometries generally fell within the limitations outlined by the cold-formed carbon steel code
NAS Appendix 1 (2004). The distortional buckling slenderness values ranged from
0.47 ≤ λd ≤ 3.64 for simple lipped channels and 0.47 ≤ λd ≤ 3.27 for lipped channels with
intermediate stiffeners. Section thickness ranged from 1mm to 8mm and r/t ratios of 1 and
2.5 were considered. The corner area to gross area, Ac /Ag ranged from 1.57% to 47%.
Section geometry and material properties are given in Appendix A.
2.5.2 Boundary Conditions and Initial Imperfections
ThinWall (Papangelis and Hancock 1995) finite strip elastic buckling analyses, which
assumes pinned ends, were conducted for each section to determine the critical elastic
buckling stress and buckling half-wavelength. This information was used to initially
construct an ABAQUS model consisting of a column seven half-wavelengths long with fixedend boundary conditions and intermediate pins at each half-wavelength at the flange-web
corners. The boundary conditions prevented overall buckling, whilst allowing distortional
buckling to develop. The critical distortional failure occurred at the middle of the fourth halfwavelength (half the total column length) essentially under pin-ended conditions and this was
confirmed by the excellent agreement found with the critical buckling stress obtained by
ABAQUS with that determined by ThinWall. To save computational time, distortional
buckling symmetry was assumed for all tests and this allowed one quarter (one half of the
total length and one half of the cross-section) of the model to be analysed with the
appropriate boundary conditions. Figure 2.19 shows an image of a channel with intermediate
stiffeners created in FEMGV6.4-02. As shown in the image, three and a half critical
distortional buckling lengths are modeled and at the fixed end, rotations about all axes are set
to zero and only displacements in the 3-axis (z-axis) direction are allowed. At every
distortional buckling critical length, pins are placed at the web-flange corner and
displacements in the 2-axis are set to zero. At the half-length edge, symmetry is used and the
boundary conditions include zero displacement in the 3-axis direction, and zero rotation
about the 1-axis and 2-axis. The number of elements used varied for each test from
approximately 3000 to over 20,000 elements, with a coarser mesh at the fixed end and a finer
mesh at the half-length end where critical distortional buckling failure occurs.
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Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
Figure 2. 19. Boundary Conditions of FE Tests
Initial imperfections were included in the nonlinear post-buckling Static Riks analysis
as an amplification of the critical elastic distortional buckling mode. The imperfection
amplitude, ωd, was based on the Walker equation (1975) where ωd = 0.3t(fy/fcr)0.5, and fcr is
the critical elastic distortional buckling stress obtained from the FE elastic buckling analyses.
2.5.3 Material Properties
The material properties are based on the longitudinal compression properties for the 304, 430
and 3Cr12 material specified in the AS/NZS 4673 (2001). Enhanced corner properties were
calculated for r/t ratios of 1 and 2.5, where r is the centreline corner radius and t is the section
thickness, and are based on the AS/NZS 4673 (2001) model for predicting corner strength.
The design corner yield strength to design flat yield strength fy,c/fy,f for the 304 material was
2.34 and 1.85 for r/t=1.0 and r/t=2.5, respectively whereas the fy,c/fy,f ratios for the 430 and
3Cr12 material was approximately 1.77 (r/t=1.0) and 1.56 (r/t=2.5). The full-range stressstrain curve proposed by Rasmussen (2003) was used to construct stress-strain data needed
for the material modelling according to the following equations:
n
⎧
⎛ f ⎞
f
⎪
for f ≤ f y
+ 0.002⎜ ⎟
⎜ fy ⎟
⎪⎪ E 0
⎝ ⎠
ε =⎨
m
⎪ f − fy
⎛ f − fy ⎞
⎟ + ε 0.2 for
+ εu ⎜
⎪
⎜ fu − f y ⎟
⎪⎩ E 0.2
⎝
⎠
fy
fu
=
0.2 − 185e
1 − 0.0375(n − 5)
E 0.2 =
(6c)
fy
(6d)
fu
Department of Civil Engineering
Research Report No R845
f > fy
(6b)
E0
1 + 0.002n / e
m = 1 + 3 .5
(6a)
28
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
e=
April 2005
fy
(6e)
E0
True stress and true plastic strains were then calculated using Eqns 1 and 2. Three
sets of FE analyses were carried out for each alloy; the first set used material properties of the
flats only for the entire cross-section and the second and third sets used enhanced material
properties of the corners according to a ratio of r/t=1.0 and r/t=2.5, applied to the corners
only.
2.5.4 FE Test Results
All FE test results are presented in Appendix A. The FE data points have been plotted in
Figures 2.20 to 2.25 in terms of fu/fy versus λd, where fu is the ultimate average stress obtained
by FE or experimental tests, fy is the specified minimum yield strength of the flat (or virgin)
material and λd is the distortional buckling slenderness given by λd = (fy/fcr)0.5. The FE
results are labeled “flats”, “r/t=1”and “r/t=2.5” representing the material properties used in
the model and “Test” represents the experimental test results.
The experimental test sections, which had an r/t ratio of approximately 2.5 are in good
agreement with the FE “r/t=2.5” test results for all alloys. By comparing the FE results for
alloy 304 with those for alloys 430 and 3Cr12, it is evident that the enhanced corner
properties have the greatest impact on 304 stainless steel sections and this is unsurprising
since the corner strength enhancement was greater for this alloy. (The corner to flat yield
strength ratio for the 304 stainless steel was 2.34 and 1.85 for r/t=1.0 and r/t=2.5,
respectively, whereas the ratios were approximately 1.77 and 1.56 for r/t=1.0 and r/t=2.5 of
the ferritic stainless steel). For simple lipped channels, notable strength improvements (up to
12% for alloy 304 and 6% for alloys 430 and 3Cr12) exist for fairly stocky sections (λd <1)
with a corner area of at least 10% whereas sections beyond λd >1 exhibit little to no strength
improvements. (See also Tables A.13-A.15 in Appendix A).
1.40
304 Test
1.20
304 Flats
304 r/t=1
1.00
304 r/t=2.5
fu/f y
0.80
0.60
0.40
0.20
0.00
0.00
0.50
1.00
1.50
λd
2.00
2.50
3.00
3.50
Figure 2. 20. FE and Experimental Results: 304 Simple Lipped Channels
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Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
1.40
430 Test
1.20
430 Flats
430 r/t=1
1.00
430 r/t=2.5
fu/f y
0.80
0.60
0.40
0.20
0.00
0.00
0.50
1.00
1.50
λd
2.00
2.50
3.00
3.50
Figure 2. 21. FE and Experimental Results: 430 Simple Lipped Channels
1.40
3Cr12 Test
1.20
3Cr12 Flats
3Cr12 r/t=1
1.00
3Cr12 r/t=2.5
fu/f y
0.80
0.60
0.40
0.20
0.00
0.00
0.50
1.00
1.50
λd
2.00
2.50
3.00
3.50
Figure 2. 22. FE and Experimental Results: 3Cr12 Simple Lipped Channels
Department of Civil Engineering
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Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
1.40
304 Test
1.20
304 Flats
304 r/t=1
1.00
304 r/t=2.5
fu/f y
0.80
0.60
0.40
0.20
0.00
0.00
0.50
1.00
1.50
λd
2.00
2.50
3.00
3.50
Figure 2. 23. FE and Experimental Results: 304 Lipped Channels with Intermediate
Stiffeners
1.40
430 Test
1.20
430 Flats
430 r/t=1
1.00
430 r/t=2.5
fu/f y
0.80
0.60
0.40
0.20
0.00
0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
λd
Figure 2. 24. FE Test and Experimental Results: 430 Lipped Channels with
Intermediate Stiffeners
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Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
1.40
3Cr12 Test
1.20
3Cr12 Flats
3Cr12 r/t=1
1.00
3Cr12 r/t=2.5
fu/f y
0.80
0.60
0.40
0.20
0.00
0.00
0.50
1.00
1.50
λd
2.00
2.50
3.00
3.50
Figure 2. 25. FE and Experimental Results: 3Cr12 Lipped Channels with Intermediate
Stiffeners
Furthermore, the enhanced corner properties have a greater influence on channels
with intermediate stiffeners and the maximum strength enhancement is 25% for the austenitic
alloy with r/t=2.5 and approximately 16% for the ferritic alloys. Again, the effect of
enhanced corner properties is prevalent for stockier sections with a significant corner area.
(See also Tables A.28-A.30 in Appendix A). It should be noted that the data points which
have reached capacities beyond the yield strength, i.e., fu/fy > 1.00, have been plotted but have
been ignored in the development of direct strength design equations.
All results have been superimposed on one plot shown in Figure 2.26. From this plot
one can see that the austenitic 304 band of results are generally lower than the ferritic 430
and 3Cr12 results apart from those sections which have developed greater strengths due to
enhanced corner properties (approximately λd <1). This can be explained by the fact that
austenitic stainless steels have a lower proportionality yield strength and experiences
significant loss of stiffness compared to the ferritic stainless steels. The higher strengths in
the stocky slenderness range of the austenitic stainless steels can be attributed to a higher
hardening modulus at large strain values compared with the ferritic stainless steels. The
ferritic 430 and 3Cr12 can be grouped together as their material properties are similar.
Department of Civil Engineering
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Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
1.40
Austenitic 304
1.20
Ferritic 430 and
3Cr12
1.00
fu/fy
0.80
0.60
0.40
0.20
0.00
0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
λd
Figure 2. 26. Austenitic 304 and Ferritic 430 and 3Cr12 Test Results
2.6 Conclusions of Numerical Investigation
Several conclusions can be made from the numerical investigations including the following:
- Stainless steel material nonlinearity must be accounted for,
- Numerical analyses should be based on the compressive material properties for
the longitudinal direction,
- Anisotropy can be ignored for statically loaded members,
- Distortional buckling flange movement, instigated by the imperfection sign, may
be ignored as it does not have significant consequences for the ultimate load,
- Section corners and intermediate stiffeners carry significant loads and the
accuracy of a model can be improved by including the enhanced corner properties,
- Enhanced corner properties can cause strength increases of approximately 5% or
greater for sections with approximately λd <1.0 and with at least 10% corner area
and is more significant for austenitic stainless steels.
- A significant amount of data has been gathered in this numerical study and forms
the basis of design code evaluation and the development of recommendations.
3
Evaluation of Current Design Practices
3.1 General and Scope
Current cold-formed stainless steel design codes for distortional buckling, including the
Australian/New Zealand Standard AS/NZS 4673 (2001), the North American ASCE (2002),
and the Eurocode 3 prEN Part 1-4 (2004) in conjunction with prEN Part 1-3 (2004)
(henceforth referred to as EC3 Part 1-4/1-3) have been uncritically based on cold-formed
carbon steel codes and ignore stainless steel material characteristics. It has been unclear
Department of Civil Engineering
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Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
whether current design guidelines for distortional buckling are unconservative or overly
conservative.
The experimental and finite element data presented in Section 2.5 were used to
evaluate the effective width approach (EWA) of the current cold-formed stainless steel codes.
However, because cold-formed stainless steel codes usually evolve along with those for coldformed carbon steel, the EWA and Direct Strength Method (DSM) approaches available in
the AS/NZS 4600 (1996), NAS (2001) and NAS Appendix 1 (2004) were also considered.
3.2 Effective Width Approach
EWA for Simple Lipped Channels
Distortional buckling is treated in the AN/NZS 4673 (2001), ASCE (2002) and the EC3
Part 1-4/1-3 (2004) under the “elements section” of the codes and the design strength is
calculated according to the EWA. The section capacity is based on local plate instability with
allowance for post-buckling strength development. In the Australian and North American
design standards, a flange is partially stiffened if Is/Ia < 1.0 where Is is the moment of inertia
of the lip and Ia is the adequate moment of inertia required for the flange element to behave
as an adequately stiffened element. The lip effective width, treated as an outstand
compression element is reduced according to the ratio Is/Ia, and the flange element plate
buckling coefficient, kf ≤ 4, used to find the flange effective width, takes into account the
distortional buckling. The AS/NZS 4673 (2001) and ASCE (2002) design rules for
distortional buckling are identical and for simple lipped channels are essentially the same as
those provided in the cold-formed carbon steel codes AS/NZS 4600 (1996) and the NAS
(2001).
The EC3 Part 1-4 (2004) for stainless steel distortional buckling refers to the
procedures outlined in the cold-formed carbon steel code, EC3 Part 1-3 (2004), but prescribes
more conservative plate buckling strength curves to take into account stainless steel
nonlinearity (see Appendix B). Aside from this, the design procedures followed are in
accordance with EC3 Part 1-3 (2004). The EC3 Part 1-4/1-3 approach to distortional buckling
differs from that found in the Australian/New Zealand and North American codes in that
rather than using an Is/Ia reduction factors and a reduced flange plate buckling coefficient, a
distortional buckling slenderness reduction factor, χd is used to reduce the area of the edge
stiffener (edge stiffener includes the effective lip and one half of the effective flange elements
which have been already reduced for local buckling). The critical buckling stress of the edge
stiffener, which is required for the calculation of the χd factor, can be found a) by equations
based on the theory of an elastic foundation (Timoshenko and Gere 1961) and is given by
fcr=2(KEIs)0.5/As where K is the spring stiffness of the edge stiffener and Is and As are
geometric properties of the stiffener, or b) from a rational elastic buckling analysis, such as
that provided by ThinWall or ABAQUS. Both methods of determining fcr are considered and
the former will be referred to as the Traditional method and the latter will be referred to as the
Alternative method. The value of χd is optionally refined iteratively (provided that χd < 1)
and is done here only for the EC3 Traditional method. From a design perspective, the EC3
Alternative method is easier to use, particularly when the section geometry becomes
complicated.
The design procedures for simple lipped channels are outlined in Appendix B and
gives reference to the appropriate code clauses. The section effective areas and predicted
loads for all tests are also provided in Appendix B (detailed material and geometric properties
are listed in Appendix A). The results of the EWA for Australian/New Zealand, North
American and European codes for the 304, 430 and 3Cr12 alloys are summarized in Tables
3.1 and 3.2 for experimental and FE tests, respectively. The mean test to predicted load
ratios, Pu,t/Pn, standard deviations (stdv) and coefficient of variations (cov) are shown for
each set of results. Two different predicted design strengths have been calculated; the first
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Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
set of predicted strengths ignores enhanced corner properties (EC Prop.) and is based on the
total effective area times the yield strength of the flats (Pn=fy,f Ae,t) and fall under the heading
“Without EC Prop.”. The second set of predicted design strengths includes enhanced corner
properties and is based on the total effective area of the flats times the yield strength of the
flats plus the effective area of the corners times the yield strength of the corners (Pn=fy,f Ae,f +
fy,c Ae,c) and the results fall under the heading “With EC Prop.”. It should be clarified that the
codes considered do not permit the use of enhanced corner strengths unless a section is fully
effective and is not subject to heat treatment and thus the predicted capacities excluding
enhanced corner properties are apt. However, sections that do actually benefit from enhanced
corner properties (ie experimental and FE r/t=1 and FE r/t=2.5) may partially offset the
detrimental effects of material nonlinearity, making the design strength predictions seem
reasonable. If enhanced corner properties are considered, then the assessment is directed at
determining if the carbon-steel based codes are valid and safe enough to account for stainless
steel material nonlinearity.
Table 3. 1. Experimental Tests and EWA Predicted Strengths for Simple Lipped
Channels
AS/NZS 4673 (2001), ASCE
(2002), (AS/NZS 4600 (1996)
NAS (2001))
Without EC
Prop.
P u,t
Pn
Test ID
304D1a
304D1b
304D2a
304D2b
kN
102
101
104
104
430D1a
430D1b
430D2
430D3a
430D3b
39
39
45
40
39
kN
101
101
101
101
mean
stdv
cov
39
39
41
38
38
mean
stdv
cov
138
138
mean
stdv
cov
3Cr12D1a 138
3Cr12D1b 139
With EC
Prop.
EC3 Part 1-4/1-3 (2004)
Traditional Method
Without EC
Prop.
With EC
Prop.
P u,t /P n P n P u,t /P n P n P u,t /P n P n P u,t /P n
1.01
1.00
1.03
1.03
1.02
0.014
0.014
1.00
0.99
1.10
1.04
1.01
1.03
0.044
0.042
1.00
1.01
1.00
0.005
0.004
kN
121
120
121
121
42
43
45
42
42
155
155
0.84
0.84
0.86
0.86
0.85
0.012
0.014
0.91
0.90
1.00
0.94
0.92
0.93
0.041
0.044
0.89
0.90
0.89
0.004
0.005
kN
86
86
86
86
32
32
34
32
32
115
115
1.19
1.18
1.21
1.21
1.20
0.018
0.015
1.20
1.22
1.33
1.24
1.21
1.24
0.051
0.041
1.20
1.21
1.21
0.006
0.005
kN
100
100
100
100
35
35
37
35
35
127
127
1.02
1.01
1.04
1.04
1.03
0.015
0.015
1.11
1.12
1.22
1.14
1.11
1.14
0.047
0.041
1.09
1.10
1.09
0.006
0.005
EC3 Part 1-4/1-3 (2004)
Alternative Method
Without EC
Prop.
With EC
Prop.
Pn
P u,t /P n P n P u,t /P n
kN
95
95
96
96
kN
112
112
114
114
34
34
35
34
37
123
123
1.08
1.07
1.09
1.09
1.08
0.008
0.008
1.15
1.14
1.28
1.16
1.05
1.16
0.083
0.071
1.12
1.13
1.13
0.006
0.005
37
37
38
37
40
137
137
0.91
0.90
0.92
0.91
0.91
0.007
0.008
1.04
1.04
1.17
1.06
0.96
1.06
0.075
0.071
1.00
1.01
1.01
0.005
0.005
Referring to the experimental results and predicted design strengths in Table 3.1 it can
be seen that for all alloys all codes are conservative as long as enhanced corner properties are
ignored. In fact, the EC3 Part 1-4/1-3 (2004) Traditional method is overly conservative. The
discrepancy between the mean Pu,t/Pn EC3 Traditional and Alternative strength predictions
lies in the model to determine the critical elastic buckling stress. In the Traditional method,
the critical buckling stress does not account for the fixed-end conditions whereas the critical
buckling stress used in the Alternative method is obtained from the ABAQUS elastic buckling
analyses of the fixed-ended experimental test models. As explained in Lecce and Rasmussen
Department of Civil Engineering
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Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
(2005) fixed-ends have the effect of increasing the critical distortional buckling strength
compared to a pin-ended section. Therefore, the distortional buckling slenderness is greater
for the Traditional method evaluation leading to a greater reduction for distortional buckling.
If enhanced corner properties are included in the strength prediction, then all codes become
unconservative except for the EC3 Part 1-4/Part 1-3 (2004) Traditional method.
Considering the FE results shown in Table 3.2 the codes are noticeably less
conservative or unconservative compared with the experimental results shown in Table 3.1,
whether enhanced corner properties are ignored in the design strength predictions or not. The
inconsistency between experimental and FE Pu,t/Pn results are due to the differences in end
conditions of the experimental and FE tests. Furthermore, the FE tests cover a much larger
range of cross-sections resulting in a greater spread of data.
Table 3. 2. Summary of FE Test to EWA Predicted Strengths for Simple Lipped
Channels
AS/NZS 4673 (2001),
ASCE (2002), (AS/NZS
4600 (1996) NAS (2001))
Without EC
With EC
Prop.
Prop.
Alloy/FE Test statistical
Series
variables
mean
304/"flats"
stdv
COV
mean
304/"r/t=1"
stdv
COV
mean
304/"r/t=2.5"
stdv
COV
mean
430/"flats"
stdv
COV
mean
430/"r/t=1"
stdv
COV
mean
430/"r/t=2.5"
stdv
COV
mean
3Cr12/"flats"
stdv
COV
mean
3Cr12/"r/t=1"
stdv
COV
mean
3Cr12/"r/t=2.5"
stdv
COV
EC3 Part 1-4/1-3 (2004)
Traditional Method
EC3 Part 1-4/1-3 (2004)
Alternative Method
Without EC
Prop.
With EC
Prop.
Without EC
Prop.
With EC
Prop.
P u,t /P n
P u,t /P n
P u,t /P n
P u,t /P n
P u,t /P n
P u,t /P n
0.84
0.069
0.082
0.86
0.085
0.099
0.88
0.102
0.117
0.89
0.048
0.054
0.90
0.054
0.060
0.90
0.071
0.080
0.90
0.047
0.053
0.91
0.054
0.059
0.91
0.057
0.062
0.84
0.069
0.082
0.80
0.068
0.085
0.78
0.072
0.093
0.89
0.048
0.054
0.86
0.048
0.056
0.83
0.057
0.070
0.90
0.047
0.053
0.87
0.047
0.054
0.84
0.043
0.051
0.94
0.038
0.041
0.97
0.045
0.047
0.99
0.046
0.046
1.02
0.061
0.060
1.04
0.057
0.055
1.05
0.059
0.056
1.00
0.047
0.047
1.01
0.048
0.047
1.06
0.049
0.046
0.94
0.038
0.041
0.91
0.037
0.040
0.91
0.032
0.035
1.02
0.061
0.060
1.00
0.059
0.059
0.99
0.060
0.061
1.00
0.047
0.047
0.98
0.047
0.048
0.99
0.054
0.055
0.96
0.054
0.057
0.98
0.053
0.054
0.99
0.055
0.055
1.05
0.093
0.089
1.06
0.094
0.089
1.07
0.089
0.084
1.03
0.068
0.066
1.04
0.062
0.060
1.07
0.082
0.077
0.96
0.054
0.057
0.92
0.051
0.056
0.90
0.052
0.058
1.05
0.093
0.089
1.03
0.089
0.087
1.00
0.091
0.092
1.03
0.068
0.066
1.00
0.064
0.064
1.00
0.086
0.087
Looking at the results for the FE 304 study in Table 3.2, it is clear that all codes fail to
adequately predict the section capacity. As long as enhanced corner properties are ignored,
the Pu,t/Pn ratio marginally improves for r/t=1.0 and even more so for r/t=2.5 when compared
to the Pu,t/Pn of the flats. As seen in Section 2, the sections tested which actually benefit from
the enhanced corner properties are relatively few and therefore the Pu,t/Pn ratios improve only
marginally.
Department of Civil Engineering
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Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
For the ferritic 430 and 3Cr12 alloys, the North American and Australian codes
overestimate the section capacities even if enhanced corner properties are ignored and result
in mean Pu,t/Pn ratios less than 1.00. The EC3 Part 1-4/1-3 (2004) methods work reasonably
well for the ferritic stainless steels and becomes increasingly conservative for r/t=1.0 and
r/t=2.5. For example, the mean Pu,t/Pn ratios for the 430 alloy, listed in Table 3.2 under the
EC3 Alternative method, are 1.05, 1.06 and 1.07 for the flats, r/t=1 and r/t=2.5 test sets,
respectively, provided enhanced corner properties are ignored. Nevertheless, the mean test to
predicted strengths are marginally larger than unity and to satisfy limit states design criteria, a
more conservative resistance factor than currently specified would be required.
EWA for Lipped Channels with Intermediate Stiffeners
The AS/NZS 4673 (2001) and ASCE (2002) EWA for lipped channels with intermediate
stiffeners are identical and are similar to the AS/NZS 4600 (1996) and NAS (2001). For
these codes, the intermediate stiffener of a partially stiffened flange element (where kf < 4) is
completely ignored and the flange element is designed as a simple edge-stiffened element.
The justification for ignoring the intermediate stiffener in cases where kf < 4 was given by
research which suggested that the distortional buckling stress is altered by less than ±10%
for sections with flanges that have both intermediate and edge stiffeners compared to those
with just edge stiffeners (NAS Commentary 2002). For cases where kf = 4 the NAS (2001)
allows the designer to take advantage of the added strength given by the intermediate
stiffener. In this case, the effective width for local sub-element buckling and distortional
buckling of the intermediate stiffener are evaluated and the governing buckling mode (local
or distortional) is used to determine the element strength. The treatment of this case differs
from the procedures outlined in the AS/NZS 4673 (2001) where if the intermediate stiffener
satisfies the minimum moment of inertia, an equivalent flange thickness is found and an
effective width is determined by plate local buckling rules. Only a few cross-sections fell
into the case where kf = 4. Example calculations for all cases are provided in Appendix B for
the codes considered.
Only the Alternative method of the EC3 Part 1-4/1-3 (2004) was considered for the
evaluation of the lipped channels with web intermediate stiffeners. The procedures are similar
to those used for the simple lipped channel except that the web elements are also reduced for
distortional buckling of the web intermediate stiffener. Two distortional buckling factors are
calculated, χd,f and χd,w. The flange critical buckling stress is determined from finite element
analyses of the section (as was done for the simple lipped channels). The critical distortional
buckling stress of the web intermediate stiffener, however, is based on a model of the web
element itself with pinned ends and the reduction χd,w applies only to the web intermediate
stiffener plus adjacent effective sub element widths. This procedure completely ignores the
instability of the flange-lip portion and its influence on the stability of the web element.
The results of the code evaluations are provided in Tables 3.3 and 3.4 for
experimental and FE tests. The EWA AS/NZS 4673 (2001) and NAS (2001) results are
identical for the test specimens and seem reasonably conservative as long as enhanced corner
properties are ignored. When the experimental results presented in Table 3.3 are compared
with those in Table 3.1 for simple lipped channels these codes seem more conservative for
channels with intermediate stiffeners. However, the experimental sections in Table 3.3 have
approximately twice the corner area and are stockier compared with simple lipped channels,
contributing to larger Pu,t/Pn ratios. Conversely, the EC3 Part 1-4/1-3 evaluation shows that
the guidelines are unconservative and suggests that the models used to evaluate the effective
widths are inadequate.
Department of Civil Engineering
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Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
Table 3. 3. Experimental Tests and EWA Evaluation of Lipped Channels with
Intermediate Stiffeners
AS/NZS 4673 (2001), ASCE
(2002), (AS/NZS 4600 (1996))
Without EC
Prop.
P u,t
Pn
kN
119
120
mean
stdv
cov
430DS1
60
51
430DS2
62
52
430DS3
64
57
430DS4
72
57
mean
stdv
cov
3Cr12DS1a 163 152
3Cr12DS1b 161 152
mean
stdv
cov
Test ID
304DS1a
304DS2b
kN
132
134
With EC Prop.
P u,t /P n P n
kN
142
142
P u,t /P n
NAS (2001)
Without EC
Prop.
With EC
Prop.
EC Part 1-4/1-3 (2004)
Alternative Method
Without EC
Prop.
With EC
Prop.
P n P u,t /P n P n P u,t /P n
Pn
P u,t /P n P n P u,t /P n
kN
119
120
kN
143
144
kN
180
181
1.11
0.93
1.11
1.12
0.94
1.12
1.11
0.94
1.11
0.0098
0.0083
0.0098
0.0088
0.0089
0.0088
1.17
57
1.05
51 1.17
1.20
58
1.07
52 1.20
1.12
63
1.01
57 1.12
1.27
62
1.15
57 1.27
1.19
1.07
1.19
0.0623
0.0570
0.0623
0.0525
0.0532
0.0525
1.07 171 0.95 152 1.07
1.06 171 0.94 152 1.06
1.07
0.95
1.07
0.0099
0.0085
0.0099
0.0093
0.0090
0.0093
kN
142
142
0.93
0.94
0.94
0.0083
0.0089
57
1.05
58
1.07
63
1.01
62
1.15
1.07
0.0570
0.0532
171 0.95
171 0.94
0.95
0.0085
0.0090
65
67
68
72
174
175
0.92
0.73
0.93
0.74
0.93
0.74
0.0089
0.0069
0.0096
0.0093
0.92
73
0.81
0.92
76
0.81
0.93
77
0.82
1.00
81
0.88
0.94
0.83
0.0378
0.0340
0.0401
0.0408
0.93 205 0.80
0.92 205 0.79
0.93
0.79
0.0097
0.0081
0.0104
0.0102
When the FE test results are considered (see Table 3.4) it is clear that all codes are
more unsafe than those provided for the simple lipped channels and the necessity of capturing
the stainless steel material behaviour becomes even more apparent. The AS/NZS 4673
(2001) and NAS (2001) provide essentially the same results and overall both are comparable
to the results given by the EC3 Part 1-4/1-3 (2004). The spread in data is also significantly
larger for channels with intermediate stiffeners. For example, the AS/NZS 4367 (2001)
evaluation of the 304/”flats” results have a mean Pu,t/Pn=0.84 and COV=0.082 for simple
lipped channels and Pu,t/Pn=0.78 and COV=0.143 for channels with intermediate stiffeners.
Department of Civil Engineering
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Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
Table 3. 4. Summary of FE test to EWA Predicted Strengths for Lipped Channels with
Intermediate Stiffeners
AS/NZS 4673 (2001),
ASCE (2002),(AS/NZS
4600 (1996))
Without EC With EC
Prop.
Prop.
Alloy/FE Test statistical
Series
variables
mean
304/"flats"
stdv
COV
mean
304/"r/t=1"
stdv
COV
mean
304/"r/t=2.5"
stdv
COV
mean
430/"flats"
stdv
COV
mean
430/"r/t=1"
stdv
COV
mean
430/"r/t=2.5"
stdv
COV
mean
3Cr12/"flats"
stdv
COV
mean
3Cr12/"r/t=1"
stdv
COV
mean
3Cr12/"r/t=2.5"
stdv
COV
NAS (2001)
Without EC With EC
Prop.
Prop.
EC3 Part 1-4/1-3 (2004)
Alternative Method
Without EC
Prop.
With EC
Prop.
P u,t /P n
P u,t /P n
P u,t /P n
P u,t /P n
P u,t /P n
P u,t /P n
0.78
0.112
0.143
0.83
0.154
0.185
0.85
0.169
0.199
0.85
0.066
0.077
0.88
0.087
0.099
0.87
0.113
0.129
0.85
0.078
0.092
0.88
0.097
0.111
0.88
0.111
0.126
0.78
0.112
0.143
0.77
0.111
0.144
0.75
0.100
0.133
0.85
0.066
0.077
0.84
0.070
0.083
0.81
0.078
0.096
0.85
0.078
0.092
0.84
0.079
0.094
0.82
0.076
0.093
0.78
0.110
0.142
0.83
0.153
0.184
0.84
0.169
0.201
0.85
0.068
0.080
0.87
0.089
0.101
0.87
0.114
0.131
0.85
0.077
0.091
0.88
0.097
0.111
0.88
0.121
0.137
0.78
0.110
0.142
0.77
0.110
0.143
0.75
0.101
0.135
0.85
0.068
0.080
0.84
0.071
0.085
0.80
0.079
0.098
0.85
0.077
0.091
0.84
0.078
0.093
0.82
0.088
0.108
0.78
0.083
0.107
0.83
0.126
0.152
0.86
0.150
0.175
0.84
0.056
0.067
0.86
0.072
0.084
0.89
0.084
0.095
0.84
0.060
0.071
0.88
0.075
0.086
0.90
0.093
0.103
0.78
0.083
0.107
0.75
0.073
0.098
0.73
0.079
0.108
0.84
0.056
0.067
0.81
0.054
0.067
0.80
0.053
0.067
0.84
0.060
0.071
0.82
0.055
0.067
0.81
0.060
0.074
For alloy 304, the effective area (as determined by the AS/NZS 4673 (2001)) to gross
area ratio, Aeff/Ag, has been plotted against the distortional buckling slenderness, λd in Figure
3.1 (note “IS”=intermediate stiffener). The data points representing the simple lipped
channels generally lie below those for channels with intermediate stiffeners demonstrating
that, for the same distortional buckling slenderness channels with intermediate stiffeners are
more efficient and, for the same distortional buckling slenderness, the calculated Aeff/Ag is
greater than that for a simple lipped channel. However, because channels with intermediate
stiffeners are more efficient sections, and as demonstrated in Section 2, are better at
distributing the load compared to a simple lipped channel, they are also more susceptible to
the detrimental effects of nonlinear material behaviour. (Lecce and Rasmussen (2005)
showed that, at mean ultimate stress, the loss of material stiffness was greater for lipped
channels with intermediate stiffeners compared to simple lipped channels). Bearing in mind
that the EWA methods used to evaluate the design strengths do not account for stainless steel
material nonlinearity, this can help explain why the actual strength to EWA predicted
strength ratios (Pu,t/Pu) for channels with intermediate stiffeners are distinctly lower than
those for simple lipped channels (compare Tables 3.2 and 3.4). The data points that fall
outside the band of results are channels with intermediate stiffeners for which kf = 4 and the
flange intermediate stiffeners were not ignored in the effective width calculations.
Department of Civil Engineering
Research Report No R845
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Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
1
0.9
0.8
0.7
Aeff /Ag
0.6
304 Test
304 r/t=1
304 Flats
304 r/t=2.5
304 Test_IS
304 Flats_IS
304 r/t=1_IS
304 r/t=2.5_IS
0.5
0.4
0.3
0.2
0.1
0
0
0.5
1
1.5
2
2.5
3
3.5
λd
Figure 3. 1. Aeff/Ag vs. λd for Alloy 304 (Aeff determined by AS/NZS 4673)
The test to predicted load ratios are plotted against the effective to gross area ratio in
Figures 3.2-3.5 for the AS/NZS 4673 (2001) and EC3 Part 1-4/1-3 (2004) Alternative method
evaluations. (Note the predicted design strengths do not incorporate enhanced corner
properties but rather assumes a uniform material model). These graphs reveal that the codes
may be adequate as long as the section is nearly fully effective and/or the section develops
increased distortional buckling stress due to the influence of fixed-ends (see the experimental
test points). Interestingly, the trend for the AS/NZS 4673 evaluation shown in Figures 3.2 and
3.3 is that for Aeff/Ag < 1, Pu,t/Pn increases as Aeff/Ag increases whereas Pu,t/Pn decreases as
Aeff/Ag increases for the EC3 Part1-4/1-3 evaluation (Figures 3.4 and 3.5). Therefore, if
Aeff/Ag is considered as an indication of section slenderness, the AS/NZS 4673 seems to work
better for more stockier sections whereas the EC3 Part1-4/1-3 works better for more slender
sections. In all cases if the distortional buckling slenderness is actually increased by fixed
end conditions, as seen with experimental tests, the Pu,t/Pn ratio is generally greater than
unity. Furthermore, in Figures 3.2-3.5, at Aeff/Ag =1.0, Pu,t/Pn can be greater than 1.0. That is,
the ultimate load is greater than the squash load given by Agfy because of the influence of
enhanced corner properties and because the stress exceeds the proof stress in stocky sections.
1.40
1.20
Pu,t /Pn
1.00
304 Test
304 r/t=1
304 Flats
304 r/t=2.5
304 Test_IS
304 Flats_IS
304 r/t=1_IS
304 r/t=2.5_IS
0.80
0.60
0.40
0.20
0.00
0
0.2
0.4
0.6
0.8
1
A eff /A g
Figure 3. 2. 304 Test to AS/NZS 4673 Predicted Strengths vs. Aeff/Ag
Department of Civil Engineering
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Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
1.40
1.20
Pu,t /Pn
1.00
0.80
430/3Cr12_Test
430/3Cr12_Flats
430/3Cr12_r/t=1
430/3Cr12_r/t=2.5
430/3Cr12_Test_IS
430/3Cr12_Flats_IS
430/3Cr12_r/t=1_IS
430/3Cr12_r/t=2.5_IS
0.60
0.40
0.20
0.00
0
0.2
0.4
0.6
0.8
1
A eff /A g (%)
Figure 3. 3. 430/3Cr12 Test to 4673 Predicted Strengths vs. Aeff/Ag
1.40
1.20
Pu,t /Pn
1.00
304 Test
304 r/t=1
304 Flats
304 r/t=2.5
304 Test_IS
304 Flats_IS
304 r/t=1_IS
304 r/t=2.5_IS
0.80
0.60
0.40
0.20
0.00
0
0.2
0.4
0.6
0.8
1
A eff /A g
Figure 3. 4. 304 Test to EC3 Part 1-4/1-3 Predicted Strengths vs. Aeff/Ag
Department of Civil Engineering
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Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
1.40
1.20
Pu,t /Pn
1.00
0.80
0.60
430/3Cr12_Test
430/3Cr12_Flats
430/3Cr12_r/t=1
430/3Cr12_r/t=2.5
430/3Cr12_Test_IS
430/3Cr12_Flats_IS
430/3Cr12_r/t=1_IS
430/3Cr12_r/t=2.5_IS
0.40
0.20
0.00
0
0.2
0.4
0.6
0.8
1
A eff /A g (%)
Figure 3. 5. 430/3Cr12 Test to EC3 Part 1-4/1-3 Predicted Strengths vs. Aeff/Ag
If the Pu,t/Pn ratios are plotted against the percent Ac/Ag, as shown in Figures 3.6-3.9,
one can see that unless Ac/Ag ≥ 40%, the codes can be unsafe.
1.40
1.20
Pu,t /Pn
1.00
304 Test
304 r/t=1
304 Flats
304 r/t=2.5
304 Test_IS
304 Flats_IS
304 r/t=1_IS
304 r/t=2.5_IS
0.80
0.60
0.40
0.20
0.00
0
10
20
30
40
50
A c /A g (%)
Figure 3. 6. 304 Test to AS/NZS 4673 Predicted Strengths vs. Percent Corner Area
Department of Civil Engineering
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Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
1.40
1.20
Pu,t /Pn
1.00
0.80
430/3Cr12_r/t=2.5
430/3Cr12_Test_IS
430/3Cr12_Flats_IS
430/3Cr12_r/t=1_IS
430/3Cr12_r/t=2.5_IS
0.60
0.40
0.20
0.00
0
10
20
30
40
50
A c /A g (%)
Figure 3. 7. 430/3Cr12 Test to EWA AS/NZS 4673 Predicted Strengths vs. Percent
Corner Area
1.40
1.20
Pu,t /Pn
1.00
304 Test
304 Flats
304 r/t=1
304 r/t=2.5
304 Test_IS
304 Flats_IS
304 r/t=1_IS
304 r/t=2.5_IS
0.80
0.60
0.40
0.20
0.00
0
10
20
30
40
50
A c /A g (%)
Figure 3. 8. 304 Test to EWA EC3 Part1-4/1-3 Predicted Strengths vs. Percent Corner
Area
Department of Civil Engineering
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Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
1.40
1.20
Pu,t /Pn
1.00
430/3Cr12_Test
430/3Cr12_Flats
430/3Cr12_r/t=1
430/3Cr12_r/t=2.5
430/3Cr12_Test_IS
430/3Cr12_Flats_IS
430/3Cr12_r/t=1_IS
430/3Cr12_r/t=2.5_IS
0.80
0.60
0.40
0.20
0.00
0
10
20
30
40
50
A c /A g (%)
Figure 3. 9. 430/3Cr12 Test to EC3 Part 1-4/1-3 Predicted Strengths vs. Percent Corner
Area
3.3
Direct Strength Method
Cold-formed carbon steel codes which currently include the DSM guidelines are the AS/NZS
4600 (1996) and the NAS Appendix 1 (2004) and the design curves are provided below;
AS/NZS 4600 (1996);
fn
λ2
= 1− d
fy
4
for λ d < 1.414
fn
2
= 0.055(λ d − 3.6) + 0.237
fy
(7a)
for 1.414 ≤ λ d ≤ 3.605
(7b)
NAS Appendix 1 (2004);
fn
=1
fy
for λ d ≤ 0.561
fn
1
0.25
= 1.2 − 2.4
f y λd
λd
for λ d > 0.561
(8a)
(8b)
and
λd =
fy
f cr
(9)
In the above equations, fn is the design strength so that the capacity of the section is
calculated as fnAg, fy is the specified yield strength (of the flats), fcr is the critical elastic
distortional buckling stress and λd is the distortional buckling slenderness. The curves above,
and the familiar Winter curve for plate buckling, have been plotted with the experimental and
FE test results in Figures 3.10, 3.11 and 3.12 for alloys 304, 430 and 3Cr12 respectively. A
summary of the statistical mean test to predicted strengths are given in Tables 3.5 and 3.6 for
simple lipped channels and channels with intermediate stiffeners. Data points where
fu/fy > 1.0 have been ignored in the statistical evaluations. The plots and tables show that the
DSM curves available in the cold-formed carbon steel codes are unconservative for the
Department of Civil Engineering
44
Research Report No R845
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
austenitic alloy. At first glance the AS/NZS 4600 (1996) seems reasonable for the ferritic
alloys but it actually fails to provide a safe envelope for sections with approximately
0.8 < λd < 1.2 (see Figures 3.11 and 3.12) which is conceivably the common slenderness
range for most practical sections. The NAS Appendix 1 (2004) is generally less conservative
or unconservative for ferritic alloys. Unlike the EWA where the actual to design strength
ratio for channels with intermediate stiffeners were generally lower than that for simple
lipped channels (see Section 3.2), the DSM evaluation leads to a comparable mean fu/fn for
the simple lipped channels and lipped channels with intermediate stiffeners, showing that one
curve will suffice for the two types of cross-sections considered. A new set of design curves
is required for cold-formed stainless steel sections and this is developed in Section 4.
1.40
304 Test
1.20
304 Flats
fn/fy, fu/fy
1.00
304 r/t=1
304 r/t=2.5
0.80
304 Test_IS
304 Flats_IS
0.60
304 r/t=1_IS
0.40
304 r/t=2.5_IS
0.20
AS 4600 DSM
Winter
NAS DSM
0.00
0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
λd
Figure 3. 10. 304 Test Data Compared with Current DSM Curves for Cold-Formed
Carbon Steel
1.40
1.20
430 Test
430 Flats
430 r/t=1
430 Test_IS
430 Flats_IS
430 r/t=1_IS
430 r/t=2.5_IS
Winter
AS 4600 DSM
NAS DSM
fn/fy, fu/fy
1.00
0.80
0.60
0.40
0.20
0.00
0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
λd
Figure 3. 11. 430 Test Data Compared with Current DSM Curves for Cold-Formed
Carbon Steel
Department of Civil Engineering
Research Report No R845
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Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
1.40
1.20
3Cr12 Test
3Cr12 Flats
3Cr12 r/t=1
3Cr12 r/t=2.5
3Cr12 Test_IS
3Cr12 Flats_IS
3Cr12 r/t=1_IS
3Cr12 r/t=2.5_IS
Winter
AS 4600 DSM
NAS DSM
fn/fy, fu/fy
1.00
0.80
0.60
0.40
0.20
0.00
0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
λd
Figure 3. 12. 3Cr12 Test Data Compared with Current DSM Curves for Cold-Formed
Carbon Steel
Department of Civil Engineering
Research Report No R845
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Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
Table 3. 5 Summary of Test to Current Cold-Formed Carbon Steel DSM Predicted
Strengths for Simple Lipped Channels
Alloy/Test Series
304 Experimental
304/"flats"
304/"r/t=1"
304/"r/t=2.5"
430 Experimental
430/"flats"
430/"r/t=1"
430/"r/t=2.5"
3Cr12 Experimental
3Cr12/"flats"
3Cr12/"r/t=1"
3Cr12/"r/t=2.5"
Department of Civil Engineering
Research Report No R845
AS/NZS 4600 (1996)
NAS Appendix 1 (2004)
f u /f n
f u /f n
0.97
0.0046
0.005
0.95
0.0710
0.075
0.97
0.0758
0.078
0.98
0.0783
0.080
1.02
0.0469
0.046
1.03
0.0861
0.083
1.05
0.0880
0.084
1.05
0.0886
0.084
1.00
0.0051
0.005
1.03
0.0858
0.083
1.05
0.0861
0.082
1.06
0.0857
0.081
0.96
0.0040
0.004
0.92
0.0649
0.070
0.94
0.0693
0.074
0.96
0.0717
0.075
1.03
0.0460
0.045
1.02
0.0944
0.093
1.03
0.0951
0.092
1.04
0.0937
0.090
1.00
0.0051
0.005
1.01
0.0894
0.089
1.02
0.0885
0.087
1.04
0.0878
0.085
statistical
variables
mean
stdv
COV
mean
stdv
COV
mean
stdv
COV
mean
stdv
COV
mean
stdv
COV
mean
stdv
COV
mean
stdv
COV
mean
stdv
COV
mean
stdv
COV
mean
stdv
COV
mean
stdv
COV
mean
stdv
COV
47
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
Table 3. 6. Summary of Test to Current Cold-Formed Carbon Steel DSM Predicted
Strengths for Lipped Channels With Intermediate Stiffeners
AS/NZS 4600 (1996)
NAS Appendix 1 (2004)
f u /f n
f u /f n
1.06
0.0113
0.011
0.92
0.0989
0.107
0.95
0.0982
0.103
0.98
0.1003
0.102
1.08
0.0245
0.023
1.04
0.0902
0.087
1.06
0.0908
0.085
1.09
0.0926
0.085
1.08
0.0095
0.009
1.03
0.0919
0.089
1.06
0.0956
0.091
1.08
0.0944
0.088
1.03
0.0109
0.011
0.89
0.0771
0.086
0.93
0.0792
0.086
0.95
0.0798
0.084
1.06
0.0241
0.023
1.00
0.0853
0.085
1.03
0.0823
0.080
1.05
0.0821
0.078
1.07
0.0094
0.009
0.99
0.0840
0.085
1.02
0.0850
0.083
1.05
0.0822
0.079
statistical
Alloy/Test Series
variables
mean
304 Experimental
stdv
COV
mean
304/"flats"
stdv
COV
mean
304/"r/t=1"
stdv
COV
mean
304/"r/t=2.5"
stdv
COV
mean
430 Experimental
stdv
COV
mean
430/"flats"
stdv
COV
mean
430/"r/t=1"
stdv
COV
mean
430/"r/t=2.5"
stdv
COV
mean
3Cr12 Experimental
stdv
COV
mean
3Cr12/"flats"
stdv
COV
mean
3Cr12/"r/t=1"
stdv
COV
mean
3Cr12/"r/t=2.5"
stdv
COV
Department of Civil Engineering
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Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
4
April 2005
Design Recommendations
4.1 Ultimate Limit States Design Criteria
The following design recommendations have been calibrated to the ultimate limit states
design criteria outlined in the ASCE (2002) code for cold-formed stainless steel. Statistical
data including the mean test to predicted strength ratios and coefficient of variations were
used in the first order second moment (FOSM) reliability analysis.
A dead, D, and live, L, load combination was considered where D/L=1/5. The
derivation of resistance factors uses the statistical mean and COV values for material and
cross-section properties set out in the current standards for cold-formed stainless steel and are
in line with those used for cold-formed carbon steel (ASCE 2002, AS/NZS 4673 2001,
AS/NZS 4600 1996, NAS 2001) including Fm=1.00 (ratio of mean to nominal cross-sectional
property), VF=0.05 (COV of F), and Mm=1.10 (ratio of the mean to the nominal material
property) VM=0.10 (COV of M). (The subscript “m” represents the mean value). These
statistical data are based on extensive investigations by Lin et al. (1992);(1988). Resistance
factors have been determined for a target reliability index of β=3.0 and β=2.5. (The ASCE
(2002) specification for cold-formed stainless steel sets β=3.0 which is higher than that set in
cold-formed carbon steel codes where β=2.5).
4.2
EWA Recommendations
From the design evaluations, it is clear that, apart from the EC3 Part1-4/1-3 for simple lipped
channels, the EWA provided in North American, Australian and European codes are
inadequate for stainless steel sections and require modification to provide safe designs. Van
den Berg (2000) is credited for proposing the use of a plasticity reduction factor to modify the
material model (Es/E0 or Et/E0, where appropriate) used in the effective width design
equations to account for stainless steel nonlinearity but this leads to iterative calculations and
may not be suitable for design engineers. As an immediate solution the recommended
strength resistance factor (φ) can be lowered to meet limit states design criteria.
A summary of the statistical mean and coefficient of variation (COV) of the test to
predicted ratios, Pu/Pn, are provided in Tables 4.1 and 4.2 for simple lipped channels and
Tables 4.3 and 4.4 for lipped channels with intermediate stiffeners. (Note the subscript “t”
has been dropped). These values are listed for “all tests” (all experimental and FE analyses)
and for the “flats” only. The latter reflects the case where enhanced corner properties cannot
be used in design (e.g., welded or annealed sections).
Table 4. 1. Proposed φ Factors for EWA AS/NZS 4673: Simple Lipped Channels
P u /P n statistics β =2.5 β =3
data
mean
included
304
all
0.86
304
flats
0.84
430
all
0.90
430
flats
0.89
3Cr12
all
0.91
3Cr12
flats
0.90
alloy
Department of Civil Engineering
Research Report No R845
49
COV
φ
φ
0.105
0.082
0.072
0.054
0.059
0.053
0.72
0.72
0.77
0.77
0.79
0.78
0.63
0.63
0.68
0.69
0.70
0.69
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
Table 4. 2. Proposed φ Factors for EWA EC3 Part 1-4/1-3: Simple Lipped Channels
P u /P n statistics β =2.5 β =3
data
mean
included
304
all
0.98
304
flats
0.96
430
all
1.07
430
flats
1.05
3Cr12
all
1.05
3Cr12
flats
1.03
alloy
COV
φ
φ
0.060
0.057
0.087
0.089
0.070
0.066
0.85
0.83
0.91
0.89
0.90
0.89
0.75
0.74
0.80
0.78
0.80
0.79
Table 4. 3. Proposed φ Factors for AS/NZS 4673 EWA: Lipped Channels with
Intermediate Stiffeners
P u /P n statistics β =2.5 β =3
alloy
304
304
430
430
3Cr12
3Cr12
data
included
all
flats
all
flats
all
flats
mean
COV
φ
φ
0.83
0.78
0.88
0.85
0.87
0.85
0.184
0.143
0.123
0.077
0.114
0.092
0.63
0.62
0.72
0.73
0.72
0.72
0.54
0.54
0.63
0.64
0.63
0.63
Table 4. 4. Proposed φ Factors for EWA EC3 Part 1-4/1-3: Lipped Channels with
Intermediate Stiffeners
P u /P n statistics β =2.5 β =3
alloy
304
304
430
430
3Cr12
3Cr12
data
included
all
flats
all
flats
all
flats
mean
COV
φ
φ
0.82
0.78
0.86
0.84
0.87
0.84
0.152
0.107
0.086
0.067
0.090
0.071
0.65
0.65
0.73
0.72
0.74
0.72
0.56
0.57
0.65
0.64
0.65
0.64
Clearly, the foregoing tables show that a lower φ factor is needed for austenitic 304
material compared to that required by the ferritic 430 and 3Cr12 alloys. Furthermore, to
avoid over conservatism the φ factor would also depend on the cross-section type. For
example, if a target reliability index of β = 2.5 for is considered for the EWA of the AS/NZS
4673 (2001) then the recommended φ factor for the 430/3Cr12 ferritic alloys is 0.8 for simple
lipped channels and 0.7 for channels with intermediate stiffeners.
Department of Civil Engineering
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Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
4.3 Recommended Direct Strength Design Curves
From the experimental and FE studies it is clear that design recommendations can be
developed for two groups – one for austenitic stainless steels and the other for ferritic
stainless steels. The austenitic group requires a more conservative, or lower design curve,
compared to the ferritic group. The following design curves are based on all experimental
and FE results for distortional bucking of simple lipped channels and channels with
intermediate stiffeners.
For Austenitic Stainless Steels:
fn
=1
fy
for
λd ≤ 0.533
f n 0.80 0.15
=
−
f y λd 1.1 λd 2.2
for
(9a)
λd > 0.533
(9b)
For Ferritic Stainless Steels and 3Cr12:
fn
=1
fy
for
λd ≤ 0.533
f n 0.90 0.20
=
−
f y λd 1.1 λd 2.2
for
(10a)
λd > 0.533
(10b)
and,
λd =
fy
(11)
f cr
In the above equations, fn is the design strength, fy is the specified yield strength (of
the flats), fcr is the critical elastic distortional buckling stress and λd is the distortional
buckling slenderness. The two sets of equations are valid for the same range of λd and differ
only with the respect to the constants in the numerators of the equations.
The proposed design curves have been plotted in Figures 4.1 and 4.2 for the austenitic
304 and ferritic 430/3Cr12 alloys, respectively. A summary of the statistical mean, standard
deviation and coefficient of variation of the test to predicted strengths are given in Table 4.5.
Department of Civil Engineering
Research Report No R845
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Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
1.40
304 Test
304 Flats
1.20
304 r/t=1
304 r/t=2.5
1.00
fn/fy, fu/fy
304 Test_IS
304 Flats_IS
0.80
304 r/t=1_IS
304 r/t=2.5_IS
0.60
Proposed Design Curve
0.40
λ d =0.533
0.20
0.00
0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
λd
Figure 4. 1. Proposed DSM Distortional Buckling Design Curve for Cold-Formed
Austenitic Stainless Steel Sections
1.40
430/3Cr12 Test
430/3Cr12 Flats
1.20
430/3Cr12 r/t=1
430/3Cr12 r/t=2.5
fn/fy, fu/fy
1.00
430/3Cr12 Test_IS
430/3Cr12 Flats_IS
0.80
430/3Cr12 r/t=1_IS
430/3Cr12 r/t=2.5_IS
0.60
Proposed Design Curve
0.40
λ d =0.533
0.20
0.00
0.00
0.50
1.00
1.50
λd
2.00
2.50
3.00
3.50
Figure 4. 2. Proposed DSM Distortional Buckling Design Curve for Cold-Formed
Ferritic Stainless Steel Sections
Department of Civil Engineering
Research Report No R845
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Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
Table 4. 5. Summary of Test to Proposed DSM Predicted Strengths
Proposed Design Curves
Simple Lipped Lipped Channels With
Channels
Intermediate Stiffeners
Alloy/Test Series
304 Experimental
304/"flats"
304/"r/t=1"
304/"r/t=2.5"
430 Experimental
430/"flats"
430/"r/t=1"
430/"r/t=2.5"
3Cr12 Experimental
3Cr12/"flats"
3Cr12/"r/t=1"
3Cr12/"r/t=2.5"
statistical
variables
mean
stdv
COV
mean
stdv
COV
mean
stdv
COV
mean
stdv
COV
mean
stdv
COV
mean
stdv
COV
mean
stdv
COV
mean
stdv
COV
mean
stdv
COV
mean
stdv
COV
mean
stdv
COV
mean
stdv
COV
f u /f n
f u /f n
1.10
0.0052
0.005
1.05
0.0708
0.068
1.07
0.0760
0.071
1.09
0.0779
0.071
1.10
0.0501
0.046
1.05
0.0797
0.076
1.07
0.0803
0.075
1.08
0.0810
0.075
1.08
0.0055
0.005
1.05
0.0773
0.074
1.06
0.0755
0.071
1.08
0.0745
0.069
1.17
0.0124
0.011
1.01
0.0842
0.083
1.06
0.0900
0.085
1.09
0.0918
0.084
1.13
0.0266
0.023
1.04
0.0807
0.078
1.07
0.0797
0.075
1.09
0.0800
0.073
1.15
0.0100
0.009
1.03
0.0809
0.078
1.07
0.0808
0.076
1.09
0.0795
0.073
Table 4. 6. Proposed φ Factors for DSM of Stainless Steel Sections: Simple Lipped
Channels
f u /f n statistics β =2.5 β =3
data
mean
included
304
all
1.07
304
flats
1.05
430
all
1.07
430
flats
1.05
3Cr12
all
1.06
3Cr12
flats
1.05
alloy
Department of Civil Engineering
Research Report No R845
53
COV
φ
φ
0.070
0.068
0.074
0.076
0.071
0.074
0.92
0.90
0.92
0.90
0.91
0.90
0.81
0.80
0.81
0.79
0.81
0.80
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
Table 4. 7. Proposed φ Factors for DSM of Stainless Steel Sections: Lipped Channels
with Intermediate Stiffeners
f u /f n statistics β =2.5 β =3
alloy
304
304
430
430
3Cr12
3Cr12
data
included
all
flats
all
flats
all
flats
mean
COV
φ
φ
1.06
1.01
1.07
1.04
1.07
1.03
0.089
0.083
0.076
0.078
0.078
0.078
0.90
0.86
0.92
0.89
0.92
0.88
0.79
0.76
0.81
0.79
0.81
0.78
Tables 4.6 and 4.7 show that if β=2.5, a recommended φ value of 0.90 would be
suitable for all alloys. For sections which are subject to heat treatment or welding it would be
prudent to use a φ factor of 0.85. The resistance factor φ = 0.90 is based on all tests
(experimental plus FE analyses) whereas φ = 0.85 is based on the FE “flats” tests which
represent those sections unaffected by cold working in the corners (i.e., no enhanced corner
properties). By comparison if β =3.0 the recommended φ value is 0.80 (0.75 for sections
subject to heat treatment).
5
Conclusions
The results of the foregoing study shows that the behaviour of stainless steel cross-sections
subject to distortional buckling can be adequately modeled by considering nonlinear yielding
and enhanced corner properties. Anisotropy makes little difference to the ultimate load, even
at high degrees of anisotropy. S4R elements and the Walker equation for determining
geometric imperfection amplitudes provide reliable results for a large range of cross-sections.
The FE study of more than 570 tests show that enhanced corner properties may
become significant for stocky sections λd <1 with at least 10% corner area. The effects of
enhanced corner properties may be ignored for slender sections or sections with a low
percentage of corner area. The effects of nonlinearity are more pronounced for the austenitic
304 alloy sections which achieve lower strength compared with ferritic sections. However,
the strength enhancement for the 304 material is greater than that for ferritic alloys and
consequently, the stocky 304 sections are able to achieve greater strengths.
The effective width evaluation for the experimental tests (fixed-ends) show that the
current codes are reasonably safe. However, if the FE tests (pin-ended) sections are
considered, the codes become unsafe, even if enhanced corner properties are ignored in
design calculations (except for EC3 Part1-4/1-3 for simple lipped channels). Furthermore, the
effective width evaluations of lipped channels with intermediate stiffeners are distinctly more
unsafe than those for simple lipped channels and this accentuates the necessity of capturing
the stainless-steel low proportionality yield stress and early loss of stiffness. Direct strength
methods currently used for cold-formed carbon steel are inadequate for stainless steel.
Design recommendations, which include modified resistance factors for the EWA
methods and DSM design curves for austenitic and ferritic alloys have been proposed.
Department of Civil Engineering
Research Report No R845
54
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
6
April 2005
References
ABAQUS. (2001). "ABAQUS." ABAQUS, Inc., Pawtucket, RI.
AS/NZS:4600. (1996). "Cold-Formed Steel Structures." Australian Standard/New Zealand
Standards 4600:1996, Standards Australia, Sydney, Australia.
AS/NZS:4673. (2001). "Cold-Formed Stainless Steel Structures." Australian Standard/New
Zealand Standard 4673:2001, Standards Australia, Sydney, Australia.
ASCE. (2002). "Specification for the Design of Cold-Formed Stainless Steel Structural
Members." American Society of Civil Engineers, Virginia, USA.
FEMSYS. (2002). "FEMGV." FEMSYS Engineering Software, Leichester, England.
Gozzi, J. (2004). "Plastic Behaviour of Steel: Experimental Investigation and Modelling,"
Lulea University of Technology, Lulea.
Hasham, A. S., and Rasmussen, K. J. R. (2002). "Nonlinear Analysis of Locally Buckled ISection Steel Beam-Columns." Australian Journal of Structural Engineering, 3(3),
171-199.
Hill, R. (1950). "The Mathematical Theory of Plasticity." Oxford Univeristy Press, London.
Lecce, M., and Rasmussen, K. J. R. (2005). "Experimental Investigation of the Distortional
Buckling of Cold-Formed Stainless Steel Sections." Research Report No. 844,
Department of Civil Engineering, University of Sydney, Sydney.
Lin, S. H., Yu, W. W., and Galambos, T. V. (1988). "Load and Resistance Factor Design of
Cold-Formed Stainless Steel - Statistical Analyses of Material Properties and
Development of the LRFD provisions." Fourth Progress Report, University of
Missouri-Rolla, October.
Lin, S. H., Yu, W. W., and Galambos, T. V. (1992). "ASCE LRFD Method for Stainless
Steel Structures." Journal of Structural Engineering, 118(4), 1056-1070.
NAS. (2001). "North American Specification for the Design of Cold-Formed Steel Structural
Members." American Iron and Steel Institute, Washington, D.C.
NAS. (2004). "Appendix 1 Design of Cold-Formed Steel Structural Members with the Direct
Strength Method." American Iron and Steel Institute, Washington, D.C.
Olsson, A. (1998). "Constitutive Modelling of Stainless Steel." Journal of Constructional
Steel Research, 46(1-3), 457.
Papangelis, J. P., and Hancock, G. J. (1995). "Computer Analysis of Thin-Walled Structural
Members." Computers & Structures, 56(1), 157-176.
preEN-1993-Part.1-3. (2004). "Eurocode 3: Design of Steel Structures, Part 1.3: General
Rules Supplementary Rules for Cold-Formed Members and Sheeting." CEN
European Committee for Standardization, Brussels, Belgium.
preEN-1993-Part.1-4. (2004). "Eurocode 3: Design of Steel Structures, Part 1.4: General
Rules Supplementary Rules for Stainless Steels." CEN European Committee for
Standardization, Brussels, Belgium.
Rasmussen, K. J. R. (2003). "Full-Range Stress-Strain Curves for Stainless Steel Alloys."
Journal of Constructional Steel Research, 59(1), 47-61.
Rasmussen, K. J. R., Burns, T., Bezkorovainy, P., and Bambach, M. R. (2003). "Numerical
Modelling of Stainless Steel Plates in Compression." Journal of Constructional Steel
Research, 59(11), 1345-1362.
Schafer, B. W., and Pekoz, T. (1998). "Computational Modeling of Cold-Formed Steel:
Characterizing Geometric Imperfections and Residual Stresses." Journal of
Constructional Steel Research, 47(3), 193-210.
Silvestre, N., and Camotim, D. (2004). "Local-Plate and Distortional Post-Buckling Behavior
of Cold-Formed Steel Lipped Channel Columns with Intermediate Stiffeners." Proc.,
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55
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
17th International Specialty Conference on Cold-Formed Steel Structures, University
of Missouri-Rolla, Orlando, USA, 1-18.
Timoshenko, S. P., and Gere, J. M. (1961). Theory of Elastic Stability, McGraw-Hill Book
Company, Inc., New York.
van den Berg, G. J. (2000). "The Effect of the Non-Linear Stress-Strain Behaviour of
Stainless Steels on Member Capacity." Journal of Constructional Steel Research,
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Walker, A. C. (1975). Design and Analysis of Cold-Formed Sections, International Textbook
Company Ltd., London.
Department of Civil Engineering
Research Report No R845
56
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
Appendix A
This appendix gives the results of the FE ABAQUS analyses. In the following pages, the Test
ID represents the alloy and centreline cross-section geometry in mm in the following form:
Alloy_web_flange_lip_(intermediate stiffener)_thickness_(r/t).
Department of Civil Engineering
Research Report No R845
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Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
Table A. 1. 304 Simple Lipped Channels: Experimental
Material Properties
Test ID
304D1a
304D1b
304D2a
304D2b
Geometric Properties**
Test Results
f pf
fy
Eo
f yc
L, L cr
Bw
Bf
Bl
t
r
Ag
MPa
164
164
164
164
MPa
242
242
242
242
MPa
187000
187000
187000
187000
MPa
565
565
565
565
mm
800
800
600
600
mm
106.3
105.8
105.5
105.6
mm
90.2
90.0
90.0
90.1
mm
12.7
12.5
12.5
12.5
mm
1.96
1.96
1.96
1.96
mm
4.00
4.00
4.00
4.00
mm
2
mm
565
565
565
565
61
61
61
61
A c A c /A g f cr
2
%
11
11
11
11
MPa
264
264
283
283
λd
P u,t
0.96
0.96
0.92
0.92
kN MPa
102 181 0.75
101 179 0.74
104 184 0.76
104 184 0.76
fu
f u /f y
** L and overall dimensions and inner radius given for experimental tests
Table A. 2. 304 Simple Lipped Channels: Flats
Material Properties
Test ID
304_60_60_10_2
304_60_60_10_3
304_60_60_15_2
304_60_60_15_3
304_150_150_30_3
304_150_150_20_3
304_150_150_10_3
304_200_100_15_4
304_200_150_20_3
304_200_150_20_4
304_150_80_5_1
304_50_50_5_1
304_400_400_20_3
304_400_400_20_4
304_400_400_20_5
304_400_400_40_4
304_400_400_40_5
304_400_400_40_6
304_400_400_40_7
304_400_400_40_8
304_300_400_20_3
304_300_400_20_4
304_300_400_20_5
304_400_300_20_3
304_400_300_20_4
304_400_300_20_5
304_400_300_40_5
304_400_300_40_6
304_400_300_40_7
304_400_300_40_8
Geometric Properties**
f pf
fy
Eo
f yc
L, L cr
Bw
Bf
Bl
t
MPa
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
MPa
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
MPa
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
MPa
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
mm
300
270
400
350
1200
900
600
500
800
700
400
250
2000
1800
1600
3000
2300
2300
2000
2000
1800
1600
1400
1600
1400
1200
2000
2000
1800
1600
mm
60
60
60
60
150
150
150
200
200
200
150
50
400
400
400
400
400
400
400
400
300
300
300
400
400
400
400
400
400
400
mm
60
60
60
60
150
150
150
100
150
150
80
50
400
400
400
400
400
400
400
400
400
400
400
300
300
300
300
300
300
300
mm
10
10
15
15
30
20
10
15
20
20
5
5
20
20
20
40
40
40
40
40
20
20
20
20
20
20
40
40
40
40
mm
2.00
3.00
2.00
3.00
3.00
3.00
3.00
4.00
3.00
4.00
1.00
1.00
3.00
4.00
5.00
4.00
5.00
6.00
7.00
8.00
3.00
4.00
5.00
3.00
4.00
5.00
5.00
6.00
7.00
8.00
r
Test Results
Ag
A c A c /A g f cr
2
2
mm mm mm
2.00 393 25
3.00 584 57
2.00 413 25
3.00 614 57
3.00 1514 57
3.00 1454 57
3.00 1394 57
4.00 1692 101
3.00 1604 57
4.00 2132 101
6
1.00 318
6
1.00 158
3.00 3704 57
4.00 4932 101
5.00 6156 157
4.00 5092 101
5.00 6356 157
6.00 7617 226
7.00 8874 308
8.00 10130 402
3.00 3404 57
4.00 4532 101
5.00 5656 157
3.00 3104 57
4.00 4132 101
5.00 5156 157
5.00 5356 157
6.00 6417 226
7.00 7474 308
8.00 8528 402
**centreline dimensions and L cr given for FE tests
Department of Civil Engineering
Research Report No R845
58
%
6.4
9.7
6.1
9.2
3.7
3.9
4.1
5.9
3.5
4.7
2.0
4.0
1.5
2.0
2.6
2.0
2.5
3.0
3.5
4.0
1.7
2.2
2.8
1.8
2.4
3.0
2.9
3.5
4.1
4.7
MPa
402
660
532
844
252
180
102
320
165
233
36
140
22
32
43
62
81
99
120
140
24
34
46
37
53
72
129
160
192
227
λd
P u,t
fu
f u /f y
0.70
0.54
0.61
0.48
0.88
1.04
1.38
0.78
1.09
0.91
2.33
1.18
2.98
2.48
2.14
1.77
1.55
1.40
1.27
1.18
2.85
2.38
2.05
2.30
1.92
1.64
1.23
1.10
1.01
0.93
kN
65
112
74
124
213
183
153
257
191
300
20
18
176
292
443
347
516
727
947
1180
171
293
447
177
294
457
551
766
984
1199
MPa
164
192
178
202
140
126
110
152
119
141
63
117
48
59
72
68
81
95
107
116
50
65
79
57
71
89
103
119
132
141
0.84
0.98
0.91
1.03
0.72
0.64
0.56
0.78
0.61
0.72
0.33
0.60
0.24
0.30
0.37
0.35
0.42
0.49
0.55
0.60
0.26
0.33
0.40
0.29
0.37
0.45
0.53
0.61
0.68
0.72
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
Table A. 3. 304 Simple Lipped Channels: r/t=1
Material Properties
f pf
fy
Eo
f yc
Test ID
MPa MPa MPa MPa
304_60_60_10_2_1
90 195 195000 457
304_60_60_10_3_1
90 195 195000 457
304_60_60_15_2_1
90 195 195000 457
304_60_60_15_3_1
90 195 195000 457
304_150_150_30_3_1 90 195 195000 457
304_150_150_20_3_1 90 195 195000 457
304_150_150_10_3_1 90 195 195000 457
304_200_100_15_4_1 90 195 195000 457
304_200_150_20_3_1 90 195 195000 457
304_200_150_20_4_1 90 195 195000 457
304_150_80_5_1_1
90 195 195000 457
304_50_50_5_1_1
90 195 195000 457
304_400_400_20_3_1 90 195 195000 457
304_400_400_20_4_1 90 195 195000 457
304_400_400_20_5_1 90 195 195000 457
304_400_400_40_4_1 90 195 195000 457
304_400_400_40_5_1 90 195 195000 457
304_400_400_40_6_1 90 195 195000 457
304_400_400_40_7_1 90 195 195000 457
304_400_400_40_8_1 90 195 195000 457
304_300_400_20_3_1 90 195 195000 457
304_300_400_20_4_1 90 195 195000 457
304_300_400_20_5_1 90 195 195000 457
304_400_300_20_3_1 90 195 195000 457
304_400_300_20_4_1 90 195 195000 457
304_400_300_20_5_1 90 195 195000 457
304_400_300_40_5_1 90 195 195000 457
304_400_300_40_6_1 90 195 195000 457
304_400_300_40_7_1 90 195 195000 457
304_400_300_40_8_1 90 195 195000 457
Geometric Properties**
L, L cr
Bw
Bf
Bl
t
mm
300
270
400
350
1200
900
600
500
800
700
400
250
2000
1800
1600
3000
2300
2300
2000
2000
1800
1600
1400
1600
1400
1200
2000
2000
1800
1600
mm
60
60
60
60
150
150
150
200
200
200
150
50
400
400
400
400
400
400
400
400
300
300
300
400
400
400
400
400
400
400
mm
60
60
60
60
150
150
150
100
150
150
80
50
400
400
400
400
400
400
400
400
400
400
400
300
300
300
300
300
300
300
mm
10
10
15
15
30
20
10
15
20
20
5
5
20
20
20
40
40
40
40
40
20
20
20
20
20
20
40
40
40
40
mm
2.00
3.00
2.00
3.00
3.00
3.00
3.00
4.00
3.00
4.00
1.00
1.00
3.00
4.00
5.00
4.00
5.00
6.00
7.00
8.00
3.00
4.00
5.00
3.00
4.00
5.00
5.00
6.00
7.00
8.00
r
Test Results
Ag
A c A c /A g f cr
2
2
mm mm mm
2.00 393 25
3.00 584 57
2.00 413 25
3.00 614 57
3.00 1514 57
3.00 1454 57
3.00 1394 57
4.00 1692 101
3.00 1604 57
4.00 2132 101
6
1.00 318
6
1.00 158
3.00 3704 57
4.00 4932 101
5.00 6156 157
4.00 5092 101
5.00 6356 157
6.00 7617 226
7.00 8874 308
8.00 10130 402
3.00 3404 57
4.00 4532 101
5.00 5656 157
3.00 3104 57
4.00 4132 101
5.00 5156 157
5.00 5356 157
6.00 6417 226
7.00 7474 308
8.00 8528 402
**centreline dimensions and L cr given for FE tests
Department of Civil Engineering
Research Report No R845
59
%
6.4
9.7
6.1
9.2
3.7
3.9
4.1
5.9
3.5
4.7
2.0
4.0
1.5
2.0
2.6
2.0
2.5
3.0
3.5
4.0
1.7
2.2
2.8
1.8
2.4
3.0
2.9
3.5
4.1
4.7
MPa
402
660
532
844
252
180
102
320
165
233
36
140
22
32
43
62
81
99
120
140
24
34
46
37
53
72
129
160
192
227
λd
P u,t
fu
f u /f y
0.70
0.54
0.61
0.48
0.88
1.04
1.38
0.78
1.09
0.91
2.33
1.18
2.98
2.48
2.14
1.77
1.55
1.40
1.27
1.18
2.85
2.38
2.05
2.30
1.92
1.64
1.23
1.10
1.01
0.93
kN
67
120
77
135
217
187
160
266
195
308
21
19
175
296
454
347
525
746
977
1219
175
301
457
176
302
467
558
780
1007
1232
MPa
171
205
187
219
143
129
115
157
121
145
65
120
47
60
74
68
83
98
110
120
51
66
81
57
73
91
104
122
135
144
0.88
1.05
0.96
1.12
0.74
0.66
0.59
0.81
0.62
0.74
0.33
0.62
0.24
0.31
0.38
0.35
0.42
0.50
0.56
0.62
0.26
0.34
0.41
0.29
0.37
0.46
0.53
0.62
0.69
0.74
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
Table A. 4. 304 Simple Lipped Channels: r/t=2.5
Material Properties
f pf
fy
Eo
f yc
Test ID
MPa MPa MPa MPa
304_60_60_10_2_2.5
90 195 195000 360
304_60_60_10_3_2.5
90 195 195000 360
304_60_60_15_2_2.5
90 195 195000 360
304_60_60_15_3_2.5
90 195 195000 360
304_150_150_30_3_2.5 90 195 195000 360
304_150_150_20_3_2.5 90 195 195000 360
304_150_150_10_3_2.5 90 195 195000 360
304_200_100_15_4_2.5 90 195 195000 360
304_200_150_20_3_2.5 90 195 195000 360
304_200_150_20_4_2.5 90 195 195000 360
304_150_80_5_1_2.5
90 195 195000 360
304_50_50_5_1_2.5
90 195 195000 360
304_400_400_20_3_2.5 90 195 195000 360
304_400_400_20_4_2.5 90 195 195000 360
304_400_400_20_5_2.5 90 195 195000 360
304_400_400_40_4_2.5 90 195 195000 360
304_400_400_40_5_2.5 90 195 195000 360
304_400_400_40_6_2.5 90 195 195000 360
304_400_400_40_7_2.5 90 195 195000 360
304_400_400_40_8_2.5 90 195 195000 360
304_300_400_20_3_2.5 90 195 195000 360
304_300_400_20_4_2.5 90 195 195000 360
304_300_400_20_5_2.5 90 195 195000 360
304_400_300_20_3_2.5 90 195 195000 360
304_400_300_20_4_2.5 90 195 195000 360
304_400_300_20_5_2.5 90 195 195000 360
304_400_300_40_5_2.5 90 195 195000 360
304_400_300_40_6_2.5 90 195 195000 360
304_400_300_40_7_2.5 90 195 195000 360
304_400_300_40_8_2.5 90 195 195000 360
Geometric Properties**
L, L cr
Bw
Bf
Bl
t
r
mm
300
270
400
350
1200
900
600
500
800
700
400
250
2000
1800
1600
3000
2300
2300
2000
2000
1800
1600
1400
1600
1400
1200
2000
2000
1800
1600
mm
60
60
60
60
150
150
150
200
200
200
150
50
400
400
400
400
400
400
400
400
300
300
300
400
400
400
400
400
400
400
mm
60
60
60
60
150
150
150
100
150
150
80
50
400
400
400
400
400
400
400
400
400
400
400
300
300
300
300
300
300
300
mm
10
10
15
15
30
20
10
15
20
20
5
5
20
20
20
40
40
40
40
40
20
20
20
20
20
20
40
40
40
40
mm
2.00
3.00
2.00
3.00
3.00
3.00
3.00
4.00
3.00
4.00
1.00
1.00
3.00
4.00
5.00
4.00
5.00
6.00
7.00
8.00
3.00
4.00
5.00
3.00
4.00
5.00
5.00
6.00
7.00
8.00
mm
5.00
7.50
5.00
7.50
7.50
7.50
7.50
10.00
7.50
10.00
2.50
2.50
7.50
10.00
12.50
10.00
12.50
15.00
17.50
20.00
7.50
10.00
12.50
7.50
10.00
12.50
12.50
15.00
17.50
20.00
Test Results
Ag
A c A c /A g f cr
mm2 mm2
**centreline dimensions and L cr given for FE tests
Department of Civil Engineering
Research Report No R845
60
λd
P u,t
% MPa
kN
382 63 16.4 411 0.69 68
561 141 25.2 689 0.53 123
402 63 15.6 542 0.60 78
591 141 23.9 868 0.47 139
1491 141 9.5 257 0.87 218
1431 141 9.9 184 1.03 188
1371 141 10.3 105 1.36 164
1650 251 15.2 328 0.77 268
1581 141 8.9 168 1.08 196
2090 251 12.0 239 0.90 315
5.0
316 16
38 2.28 21
156 16 10.1 142 1.17 19
3681 141 3.8
22 2.96 179
4890 251 5.1
32 2.46 305
6090 393 6.4
43 2.12 458
5050 251 5.0
63 1.76 346
6290 393 6.2
82 1.54 531
7522 565 7.5 106 1.36 755
8745 770 8.8 122 1.26 990
9959 1005 10.1 144 1.16 1234
3381 141 4.2
24 2.82 177
4490 251 5.6
35 2.36 305
5590 393 7.0
48 2.03 464
3081 141 4.6
37 2.28 183
4090 251 6.1
54 1.90 307
5090 393 7.7
74 1.63 477
5290 393 7.4 131 1.22 561
6322 565 8.9 163 1.09 784
7345 770 10.5 197 1.00 1014
8359 1005 12.0 233 0.92 1245
fu
f u /f y
MPa
177
219
194
236
146
131
120
163
124
151
65
124
49
62
75
68
84
100
113
124
52
68
83
59
75
94
106
124
138
149
0.91
1.13
1.00
1.21
0.75
0.67
0.61
0.83
0.64
0.77
0.33
0.63
0.25
0.32
0.39
0.35
0.43
0.51
0.58
0.64
0.27
0.35
0.43
0.30
0.38
0.48
0.54
0.64
0.71
0.76
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
Table A. 5. 430 Simple Lipped Channels: Experimental
Material Properties
f pf
Test ID
430D1a
430D1b
430D2
430D3a
430D3b
fy
MPa MPa
170 271
170 271
170 271
170 271
170 271
Geometric Properties**
Eo
f yc
L,L cr
Bw
Bf
MPa
193000
193000
193000
193000
193000
MPa
452
452
452
452
452
mm
800
800
480
780
782
mm
67.9
67.7
67.5
55.9
55.6
mm mm mm
57.4 8.4 1.13
57.6 8.6 1.13
58.5 10.0 1.13
54.8 8.6 1.13
54.9 8.7 1.13
Bl
Test Results
r
Ag
Ac
mm
2.43
2.50
2.50
2.50
2.50
mm2
211
211
215
188
188
mm2
21
22
22
22
22
t
A c /A g f cr
%
10
10
10
12
12
MPa
224
224
245
254
254
λd
P u,t
fu
f u /f y
1.10
1.10
1.05
1.03
1.03
kN
39
39
45
40
39
MPa
182
185
209
211
206
0.67
0.68
0.77
0.78
0.76
**L and overall dimensions and inner radius given for experimental tests
Table A. 6. 430 Simple Lipped Channels: Flats
Material Properties
f pf
Test ID
430_60_60_10_2
430_60_60_10_3
430_60_60_15_2
430_60_60_15_3
430_150_150_30_3
430_150_150_20_3
430_150_150_10_3
430_200_100_15_4
430_200_150_20_3
430_200_150_20_4
430_150_80_5_1
430_50_50_5_1
430_400_400_20_3
430_400_400_20_4
430_400_400_20_5
430_400_400_40_4
430_400_400_40_5
430_400_400_40_6
430_400_400_40_7
430_400_400_40_8
430_300_400_20_3
430_300_400_20_4
430_300_400_20_5
430_400_300_20_3
430_400_300_20_4
430_400_300_20_5
430_400_300_40_5
430_400_300_40_6
430_400_300_40_7
430_400_300_40_8
fy
MPa MPa
170 275
170 275
170 275
170 275
170 275
170 275
170 275
170 275
170 275
170 275
170 275
170 275
170 275
170 275
170 275
170 275
170 275
170 275
170 275
170 275
170 275
170 275
170 275
170 275
170 275
170 275
170 275
170 275
170 275
170 275
Geometric Properties**
Eo
f yc
L,L cr
Bw
Bf
Bl
t
r
MPa
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
MPa
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
mm
300
270
400
350
1200
900
600
500
800
700
400
250
2000
1800
1600
3000
2300
2300
2000
2000
1800
1600
1400
1600
1400
1200
2000
2000
1800
1600
mm
60
60
60
60
150
150
150
200
200
200
150
50
400
400
400
400
400
400
400
400
300
300
300
400
400
400
400
400
400
400
mm
60
60
60
60
150
150
150
100
150
150
80
50
400
400
400
400
400
400
400
400
400
400
400
300
300
300
300
300
300
300
mm
10
10
15
15
30
20
10
15
20
20
5
5
20
20
20
40
40
40
40
40
20
20
20
20
20
20
40
40
40
40
mm
2.00
3.00
2.00
3.00
3.00
3.00
3.00
4.00
3.00
4.00
1.00
1.00
3.00
4.00
5.00
4.00
5.00
6.00
7.00
8.00
3.00
4.00
5.00
3.00
4.00
5.00
5.00
6.00
7.00
8.00
mm
2.00
3.00
2.00
3.00
3.00
3.00
3.00
4.00
3.00
4.00
1.00
1.00
3.00
4.00
5.00
4.00
5.00
6.00
7.00
8.00
3.00
4.00
5.00
3.00
4.00
5.00
5.00
6.00
7.00
8.00
Test Results
Ag
Ac
mm2 mm2
25
393
57
584
25
413
57
614
57
1514
57
1454
57
1394
1692 101
57
1604
2132 101
6
318
6
158
57
3704
4932 101
6156 157
5092 101
6356 157
7617 226
8874 308
10130 402
57
3404
4532 101
5656 157
57
3104
4132 101
5156 157
5356 157
6417 226
7474 308
8528 402
**centreline dimensions and L cr given for FE tests
Department of Civil Engineering
Research Report No R845
61
A c /A g f cr
%
6.4
9.7
6.1
9.2
3.7
3.9
4.1
5.9
3.5
4.7
2.0
4.0
1.5
2.0
2.6
2.0
2.5
3.0
3.5
4.0
1.7
2.2
2.8
1.8
2.4
3.0
2.9
3.5
4.1
4.7
MPa
381
627
505
801
239
171
97
304
156
221
34
133
21
30
40
59
77
94
114
133
23
33
44
35
50
68
123
152
182
216
λd
P u,t
0.85
0.66
0.74
0.59
1.07
1.27
1.69
0.95
1.33
1.11
2.84
1.44
3.64
3.02
2.61
2.16
1.89
1.71
1.55
1.44
3.47
2.90
2.50
2.80
2.33
2.00
1.50
1.35
1.23
1.13
kN MPa
85
216 0.79
146 250 0.91
96
232 0.84
163 266 0.97
280 185 0.67
240 165 0.60
200 143 0.52
338 200 0.73
244 152 0.55
390 183 0.67
26
83 0.30
24
151 0.55
231
62 0.23
356
72 0.26
579
94 0.34
424
83 0.30
647 102 0.37
950 125 0.45
1226 138 0.50
1531 151 0.55
225
66 0.24
383
85 0.31
579 102 0.37
231
74 0.27
397
96 0.35
594 115 0.42
699 130 0.47
980 153 0.56
1283 172 0.62
1563 183 0.67
fu
f u /f y
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
Table A. 7. 430 Simple Lipped Channels: r/t=1
Material Properties
f pf
Test ID
430_60_60_10_2_1
430_60_60_10_3_1
430_60_60_15_2_1
430_60_60_15_3_1
430_150_150_30_3_1
430_150_150_20_3_1
430_150_150_10_3_1
430_200_100_15_4_1
430_200_150_20_3_1
430_200_150_20_4_1
430_150_80_5_1_1
430_50_50_5_1_1
430_400_400_20_3_1
430_400_400_20_4_1
430_400_400_20_5_1
430_400_400_40_4_1
430_400_400_40_5_1
430_400_400_40_6_1
430_400_400_40_7_1
430_400_400_40_8_1
430_300_400_20_3_1
430_300_400_20_4_1
430_300_400_20_5_1
430_400_300_20_3_1
430_400_300_20_4_1
430_400_300_20_5_1
430_400_300_40_5_1
430_400_300_40_6_1
430_400_300_40_7_1
430_400_300_40_8_1
fy
MPa MPa
170 275
170 275
170 275
170 275
170 275
170 275
170 275
170 275
170 275
170 275
170 275
170 275
170 275
170 275
170 275
170 275
170 275
170 275
170 275
170 275
170 275
170 275
170 275
170 275
170 275
170 275
170 275
170 275
170 275
170 275
Geometric Properties**
Eo
f yc
L,L cr
Bw
Bf
Bl
t
r
MPa
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
MPa
479
479
479
479
479
479
479
479
479
479
479
479
479
479
479
479
479
479
479
479
479
479
479
479
479
479
479
479
479
479
mm
300
270
400
350
1200
900
600
500
800
700
400
250
2000
1800
1600
3000
2300
2300
2000
2000
1800
1600
1400
1600
1400
1200
2000
2000
1800
1600
mm
60
60
60
60
150
150
150
200
200
200
150
50
400
400
400
400
400
400
400
400
300
300
300
400
400
400
400
400
400
400
mm
60
60
60
60
150
150
150
100
150
150
80
50
400
400
400
400
400
400
400
400
400
400
400
300
300
300
300
300
300
300
mm
10
10
15
15
30
20
10
15
20
20
5
5
20
20
20
40
40
40
40
40
20
20
20
20
20
20
40
40
40
40
mm
2.00
3.00
2.00
3.00
3.00
3.00
3.00
4.00
3.00
4.00
1.00
1.00
3.00
4.00
5.00
4.00
5.00
6.00
7.00
8.00
3.00
4.00
5.00
3.00
4.00
5.00
5.00
6.00
7.00
8.00
mm
2.00
3.00
2.00
3.00
3.00
3.00
3.00
4.00
3.00
4.00
1.00
1.00
3.00
4.00
5.00
4.00
5.00
6.00
7.00
8.00
3.00
4.00
5.00
3.00
4.00
5.00
5.00
6.00
7.00
8.00
Test Results
Ag
Ac
mm2 mm2
25
393
57
584
25
413
57
614
57
1514
57
1454
57
1394
1692 101
57
1604
2132 101
6
318
6
158
57
3704
4932 101
6156 157
5092 101
6356 157
7617 226
8874 308
10130 402
57
3404
4532 101
5656 157
57
3104
4132 101
5156 157
5356 157
6417 226
7474 308
8528 402
**centreline dimensions and L cr given for FE tests
Department of Civil Engineering
Research Report No R845
62
A c /A g f cr
%
6.4
9.7
6.1
9.2
3.7
3.9
4.1
5.9
3.5
4.7
2.0
4.0
1.5
2.0
2.6
2.0
2.5
3.0
3.5
4.0
1.7
2.2
2.8
1.8
2.4
3.0
2.9
3.5
4.1
4.7
MPa
381
627
505
801
239
171
97
304
156
221
34
133
21
30
40
59
77
94
114
133
23
33
44
35
50
68
123
152
182
216
λd
P u,t
0.85
0.66
0.74
0.59
1.07
1.27
1.69
0.95
1.33
1.11
2.84
1.44
3.64
3.02
2.61
2.16
1.89
1.71
1.55
1.44
3.47
2.90
2.50
2.80
2.33
2.00
1.50
1.35
1.23
1.13
kN MPa
87
222 0.81
153 261 0.95
98
238 0.87
171 278 1.01
284 188 0.68
243 167 0.61
203 145 0.53
345 204 0.74
246 153 0.56
397 186 0.68
27
83 0.30
24
153 0.55
231
62 0.23
357
72 0.26
586
95 0.35
430
84 0.31
650 102 0.37
953 125 0.46
1234 139 0.51
1547 153 0.56
228
67 0.24
388
86 0.31
586 104 0.38
234
75 0.27
402
97 0.35
601 116 0.42
704 131 0.48
988 154 0.56
1300 174 0.63
1589 186 0.68
fu
f u /f y
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
Table A. 8. 430 Simple Lipped Channels: r/t=2.5
Material Properties
f pf
fy
Test ID
MPa MPa
430_60_60_10_2_2.5
170 275
430_60_60_10_3_2.5
170 275
430_60_60_15_2_2.5
170 275
430_60_60_15_3_2.5
170 275
430_150_150_30_3_2.5 170 275
430_150_150_20_3_2.5 170 275
430_150_150_10_3_2.5 170 275
430_200_100_15_4_2.5 170 275
430_200_150_20_3_2.5 170 275
430_200_150_20_4_2.5 170 275
430_150_80_5_1_2.5
170 275
430_50_50_5_1_2.5
170 275
430_400_400_20_3_2.5 170 275
430_400_400_20_4_2.5 170 275
430_400_400_20_5_2.5 170 275
430_400_400_40_4_2.5 170 275
430_400_400_40_5_2.5 170 275
430_400_400_40_6_2.5 170 275
430_400_400_40_7_2.5 170 275
430_400_400_40_8_2.5 170 275
430_300_400_20_3_2.5 170 275
430_300_400_20_4_2.5 170 275
430_300_400_20_5_2.5 170 275
430_400_300_20_3_2.5 170 275
430_400_300_20_4_2.5 170 275
430_400_300_20_5_2.5 170 275
430_400_300_40_5_2.5 170 275
430_400_300_40_6_2.5 170 275
430_400_300_40_7_2.5 170 275
430_400_300_40_8_2.5 170 275
Geometric Properties**
Test Results
Eo
f yc
L,L cr
Bw
Bf
Bl
t
r
Ag
Ac
MPa
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
MPa
424
424
424
424
424
424
424
424
424
424
424
424
424
424
424
424
424
424
424
424
424
424
424
424
424
424
424
424
424
424
mm
300
270
400
350
1200
900
600
500
800
700
400
250
2000
1800
1600
3000
2300
2300
2000
2000
1800
1600
1400
1600
1400
1200
2000
2000
1800
1600
mm
60
60
60
60
150
150
150
200
200
200
150
50
400
400
400
400
400
400
400
400
300
300
300
400
400
400
400
400
400
400
mm
60
60
60
60
150
150
150
100
150
150
80
50
400
400
400
400
400
400
400
400
400
400
400
300
300
300
300
300
300
300
mm
10
10
15
15
30
20
10
15
20
20
5
5
20
20
20
40
40
40
40
40
20
20
20
20
20
20
40
40
40
40
mm
2.00
3.00
2.00
3.00
3.00
3.00
3.00
4.00
3.00
4.00
1.00
1.00
3.00
4.00
5.00
4.00
5.00
6.00
7.00
8.00
3.00
4.00
5.00
3.00
4.00
5.00
5.00
6.00
7.00
8.00
mm
5.00
7.50
5.00
7.50
7.50
7.50
7.50
10.00
7.50
10.00
2.50
2.50
7.50
10.00
12.50
10.00
12.50
15.00
17.50
20.00
7.50
10.00
12.50
7.50
10.00
12.50
12.50
15.00
17.50
20.00
mm2
382
561
402
591
1491
1431
1371
1650
1581
2090
316
156
3681
4890
6090
5050
6290
7522
8745
9959
3381
4490
5590
3081
4090
5090
5290
6322
7345
8359
mm2
63
141
63
141
141
141
141
251
141
251
16
16
141
251
393
251
393
565
770
1005
141
251
393
141
251
393
393
565
770
1005
**centreline dimensions and L cr given for FE tests
Department of Civil Engineering
Research Report No R845
63
A c /A g f cr
λd
P u,t
fu
f u /f y
% MPa
kN MPa
16.4 390 0.84 87
228 0.83
25.2 654 0.65 154 275 1.00
15.6 514 0.73 99
245 0.89
23.9 823 0.58 173 293 1.07
9.5 243 1.06 286 192 0.70
9.9 175 1.25 244 171 0.62
10.3 100 1.66 205 150 0.54
15.2 311 0.94 346 209 0.76
8.9 160 1.31 247 156 0.57
12.0 226 1.10 399 191 0.69
5.0
36 2.78 26
83 0.30
10.1 135 1.43 24
156 0.57
3.8
21 3.61 236
64 0.23
5.1
31 3.00 343
70 0.25
6.4
41 2.59 586
96 0.35
5.0
60 2.15 437
87 0.31
6.2
78 1.88 650 103 0.38
7.5 100 1.65 953 127 0.46
8.8 116 1.54 1236 141 0.51
10.1 137 1.42 1556 156 0.57
4.2
23 3.44 229
68 0.25
5.6
33 2.87 390
87 0.32
7.0
45 2.47 590 106 0.38
4.6
36 2.78 235
76 0.28
6.1
51 2.31 404
99 0.36
7.7
70 1.98 605 119 0.43
7.4 125 1.49 704 133 0.48
8.9 155 1.33 992 157 0.57
10.5 187 1.21 1306 178 0.65
12.0 221 1.12 1598 191 0.70
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
Table A. 9. 3Cr12 Simple Lipped Channels: Experimental
f pf
Test ID
3Cr12D1a
3Cr12D1b
Material Properties
f yf
Eo
f yc
Bw
Bf
Geometric Properties**
Ag
r
Bl
t
MPa MPa MPa
MPa mm mm mm mm
234 339 208000 606 105.0 85.5 14.7 1.98
234 339 208000 606 105.0 85.4 14.8 1.98
mm
4.00
4.00
Ac
A c /A g
mm2
mm2
555
555
62
62
%
11
11
f cr
λd
Test Results
P u,t
fu
MPa
321 1.03
321 1.03
kN
138
139
MPa
249
251
f u /f y
0.73
0.74
**overall dimensions and inner radius given for experimental tests
Table A. 10. 3Cr12 Simple Lipped Channels: Flats
Material Properties
f pf
Test ID
3Cr12_60_60_10_2
3Cr12_60_60_10_3
3Cr12_60_60_15_2
3Cr12_60_60_15_3
3Cr12_150_150_30_3
3Cr12_150_150_20_3
3Cr12_150_150_10_3
3Cr12_200_100_15_4
3Cr12_200_150_20_3
3Cr12_200_150_20_4
3Cr12_150_80_5_1
3Cr12_50_50_5_1
3Cr12_400_400_20_3
3Cr12_400_400_20_4
3Cr12_400_400_20_5
3Cr12_400_400_40_4
3Cr12_400_400_40_5
3Cr12_400_400_40_6
3Cr12_400_400_40_7
3Cr12_400_400_40_8
3Cr12_300_400_20_3
3Cr12_300_400_20_4
3Cr12_300_400_20_5
3Cr12_400_300_20_3
3Cr12_400_300_20_4
3Cr12_400_300_20_5
3Cr12_400_300_40_5
3Cr12_400_300_40_6
3Cr12_400_300_40_7
3Cr12_400_300_40_8
fy
Eo
Geometric Properties
f yc
MPa MPa MPa
MPa
170 260 210000 260
170 260 210000 260
170 260 210000 260
170 260 210000 260
170 260 210000 260
170 260 210000 260
170 260 210000 260
170 260 210000 260
170 260 210000 260
170 260 210000 260
170 260 210000 260
170 260 210000 260
170 260 210000 260
170 260 210000 260
170 260 210000 260
170 260 210000 260
170 260 210000 260
170 260 210000 260
170 260 210000 260
170 260 210000 260
170 260 210000 260
170 260 210000 260
170 260 210000 260
170 260 210000 260
170 260 210000 260
170 260 210000 260
170 260 210000 260
170 260 210000 260
170 260 210000 260
170 260 210000 260
Department of Civil Engineering
Research Report No R845
Test Results
L,L cr
Bw
Bf
Bl
t
r
Ag
mm
300
270
400
350
1200
900
600
500
800
700
400
250
2000
1800
1600
3000
2300
2300
2000
2000
1800
1600
1400
1600
1400
1200
2000
2000
1800
1600
mm
60
60
60
60
150
150
150
200
200
200
150
50
400
400
400
400
400
400
400
400
300
300
300
400
400
400
400
400
400
400
mm
60
60
60
60
150
150
150
100
150
150
80
50
400
400
400
400
400
400
400
400
400
400
400
300
300
300
300
300
300
300
mm
10
10
15
15
30
20
10
15
20
20
5
5
20
20
20
40
40
40
40
40
20
20
20
20
20
20
40
40
40
40
mm
2.00
3.00
2.00
3.00
3.00
3.00
3.00
4.00
3.00
4.00
1.00
1.00
3.00
4.00
5.00
4.00
5.00
6.00
7.00
8.00
3.00
4.00
5.00
3.00
4.00
5.00
5.00
6.00
7.00
8.00
mm
2.00
3.00
2.00
3.00
3.00
3.00
3.00
4.00
3.00
4.00
1.00
1.00
3.00
4.00
5.00
4.00
5.00
6.00
7.00
8.00
3.00
4.00
5.00
3.00
4.00
5.00
5.00
6.00
7.00
8.00
mm
mm
393
584
413
614
1514
1454
1394
1692
1604
2132
318
158
3704
4932
6156
5092
6356
7617
8874
10130
3404
4532
5656
3104
4132
5156
5356
6417
7474
8528
25
57
25
57
57
57
57
101
57
101
6
6
57
101
157
101
157
226
308
402
57
101
157
57
101
157
157
226
308
402
64
Ac
2
2
A c /A g
f cr
%
6.4
9.7
6.1
9.2
3.7
3.9
4.1
5.9
3.5
4.7
2.0
4.0
1.5
2.0
2.6
2.0
2.5
3.0
3.5
4.0
1.7
2.2
2.8
1.8
2.4
3.0
2.9
3.5
4.1
4.7
MPa
432
711
573
909
272
194
110
345
177
251
39
151
24
34
46
67
87
107
129
151
26
37
50
40
57
78
139
172
207
245
λd
P u,t
0.78
0.60
0.67
0.53
0.98
1.16
1.54
0.87
1.21
1.02
2.59
1.31
3.32
2.76
2.38
1.97
1.73
1.56
1.42
1.31
3.17
2.65
2.28
2.56
2.13
1.83
1.37
1.23
1.12
1.03
kN MPa
83
211 0.81
142 243 0.93
93
226 0.87
157 256 0.98
278 184 0.71
243 167 0.64
201 144 0.56
335 198 0.76
254 158 0.61
389 182 0.70
27
85 0.33
24
155 0.59
237
64 0.25
382
77 0.30
602
98 0.38
444
87 0.34
709 112 0.43
1005 132 0.51
1267 143 0.55
1563 154 0.59
231
68 0.26
395
87 0.34
597 106 0.41
237
76 0.29
409
99 0.38
618 120 0.46
738 138 0.53
1022 159 0.61
1292 173 0.67
1556 182 0.70
fu
f u /f y
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
Table A. 11. 3Cr12 Simple Lipped Channels: r/t=1
Material Properties
f pf
Test ID
3Cr12_60_60_10_2_1
3Cr12_60_60_10_3_1
3Cr12_60_60_15_2_1
3Cr12_60_60_15_3_1
3Cr12_150_150_30_3_1
3Cr12_150_150_20_3_1
3Cr12_150_150_10_3_1
3Cr12_200_100_15_4_1
3Cr12_200_150_20_3_1
3Cr12_200_150_20_4_1
3Cr12_150_80_5_1_1
3Cr12_50_50_5_1_1
3Cr12_400_400_20_3_1
3Cr12_400_400_20_4_1
3Cr12_400_400_20_5_1
3Cr12_400_400_40_4_1
3Cr12_400_400_40_5_1
3Cr12_400_400_40_6_1
3Cr12_400_400_40_7_1
3Cr12_400_400_40_8_1
3Cr12_300_400_20_3_1
3Cr12_300_400_20_4_1
3Cr12_300_400_20_5_1
3Cr12_400_300_20_3_1
3Cr12_400_300_20_4_1
3Cr12_400_300_20_5_1
3Cr12_400_300_40_5_1
3Cr12_400_300_40_6_1
3Cr12_400_300_40_7_1
3Cr12_400_300_40_8_1
fy
Eo
Geometric Properties
f yc
MPa MPa MPa
MPa
170 260 210000 460
170 260 210000 460
170 260 210000 460
170 260 210000 460
170 260 210000 460
170 260 210000 460
170 260 210000 460
170 260 210000 460
170 260 210000 460
170 260 210000 460
170 260 210000 460
170 260 210000 460
170 260 210000 460
170 260 210000 460
170 260 210000 460
170 260 210000 460
170 260 210000 460
170 260 210000 460
170 260 210000 460
170 260 210000 460
170 260 210000 460
170 260 210000 460
170 260 210000 460
170 260 210000 460
170 260 210000 460
170 260 210000 460
170 260 210000 460
170 260 210000 460
170 260 210000 460
170 260 210000 460
Test Results
L,L cr
Bw
Bf
Bl
t
r
Ag
mm
300
270
400
350
1200
900
600
500
800
700
400
250
2000
1800
1600
3000
2300
2300
2000
2000
1800
1600
1400
1600
1400
1200
2000
2000
1800
1600
mm
60
60
60
60
150
150
150
200
200
200
150
50
400
400
400
400
400
400
400
400
300
300
300
400
400
400
400
400
400
400
mm
60
60
60
60
150
150
150
100
150
150
80
50
400
400
400
400
400
400
400
400
400
400
400
300
300
300
300
300
300
300
mm
10
10
15
15
30
20
10
15
20
20
5
5
20
20
20
40
40
40
40
40
20
20
20
20
20
20
40
40
40
40
mm
2.00
3.00
2.00
3.00
3.00
3.00
3.00
4.00
3.00
4.00
1.00
1.00
3.00
4.00
5.00
4.00
5.00
6.00
7.00
8.00
3.00
4.00
5.00
3.00
4.00
5.00
5.00
6.00
7.00
8.00
mm
2.00
3.00
2.00
3.00
3.00
3.00
3.00
4.00
3.00
4.00
1.00
1.00
3.00
4.00
5.00
4.00
5.00
6.00
7.00
8.00
3.00
4.00
5.00
3.00
4.00
5.00
5.00
6.00
7.00
8.00
mm
mm
Ac
393
584
413
614
1514
1454
1394
1692
1604
2132
318
158
3704
4932
6156
5092
6356
7617
8874
10130
3404
4532
5656
3104
4132
5156
5356
6417
7474
8528
25
57
25
57
57
57
57
101
57
101
6
6
57
101
157
101
157
226
308
402
57
101
157
57
101
157
157
226
308
402
2
**centreline dimensions given for FE tests
Department of Civil Engineering
Research Report No R845
65
2
A c /A g
f cr
%
6.4
9.7
6.1
9.2
3.7
3.9
4.1
5.9
3.5
4.7
2.0
4.0
1.5
2.0
2.6
2.0
2.5
3.0
3.5
4.0
1.7
2.2
2.8
1.8
2.4
3.0
2.9
3.5
4.1
4.7
MPa
432
711
573
909
272
194
110
345
177
251
39
151
24
34
46
67
87
107
129
151
26
37
50
40
57
78
139
172
207
245
λd
P u,t
0.78
0.60
0.67
0.53
0.98
1.16
1.54
0.87
1.21
1.02
2.59
1.31
3.32
2.76
2.38
1.97
1.73
1.56
1.42
1.31
3.17
2.65
2.28
2.56
2.13
1.83
1.37
1.23
1.12
1.03
kN MPa
85
217 0.83
148 253 0.97
96
233 0.90
165 269 1.03
283 187 0.72
246 169 0.65
205 147 0.56
343 203 0.78
256 160 0.61
396 186 0.71
27
86 0.33
25
156 0.60
237
64 0.25
383
78 0.30
607
99 0.38
447
88 0.34
710 112 0.43
1009 132 0.51
1277 144 0.55
1581 156 0.60
234
69 0.26
399
88 0.34
603 107 0.41
240
77 0.30
413 100 0.38
621 120 0.46
741 138 0.53
1032 161 0.62
1311 175 0.67
1584 186 0.71
fu
f u /f y
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
Table A. 12. 3Cr12 Simple Lipped Channels: r/t=2.5
Material Properties
f pf
Test ID
3Cr12_60_60_10_2_2.5
3Cr12_60_60_10_3_2.5
3Cr12_60_60_15_2_2.5
3Cr12_60_60_15_3_2.5
3Cr12_150_150_30_3_2.5
3Cr12_150_150_20_3_2.5
3Cr12_150_150_10_3_2.5
3Cr12_200_100_15_4_2.5
3Cr12_200_150_20_3_2.5
3Cr12_200_150_20_4_2.5
3Cr12_150_80_5_1_2.5
3Cr12_50_50_5_1_2.5
3Cr12_400_400_20_3_2.5
3Cr12_400_400_20_4_2.5
3Cr12_400_400_20_5_2.5
3Cr12_400_400_40_4_2.5
3Cr12_400_400_40_5_2.5
3Cr12_400_400_40_6_2.5
3Cr12_400_400_40_7_2.5
3Cr12_400_400_40_8_2.5
3Cr12_300_400_20_3_2.5
3Cr12_300_400_20_4_2.5
3Cr12_300_400_20_5_2.5
3Cr12_400_300_20_3_2.5
3Cr12_400_300_20_4_2.5
3Cr12_400_300_20_5_2.5
3Cr12_400_300_40_5_2.5
3Cr12_400_300_40_6_2.5
3Cr12_400_300_40_7_2.5
3Cr12_400_300_40_8_2.5
fy
Eo
Geometric Properties
f yc
MPa MPa
MPa
MPa
170 260 210000 406
170 260 210000 406
170 260 210000 406
170 260 210000 406
170 260 210000 406
170 260 210000 406
170 260 210000 406
170 260 210000 406
170 260 210000 406
170 260 210000 406
170 260 210000 406
170 260 210000 406
170 260 210000 406
170 260 210000 406
170 260 210000 406
170 260 210000 406
170 260 210000 406
170 260 210000 406
170 260 210000 406
170 260 210000 406
170 260 210000 406
170 260 210000 406
170 260 210000 406
170 260 210000 406
170 260 210000 406
170 260 210000 406
170 260 210000 406
170 260 210000 406
170 260 210000 406
170 260 210000 406
L,L cr
Bw
Bf
Bl
t
mm
300
270
400
350
1200
900
600
500
800
700
400
250
2000
1800
1600
3000
2300
2300
2000
2000
1800
1600
1400
1600
1400
1200
2000
2000
1800
1600
mm
60
60
60
60
150
150
150
200
200
200
150
50
400
400
400
400
400
400
400
400
300
300
300
400
400
400
400
400
400
400
mm
60
60
60
60
150
150
150
100
150
150
80
50
400
400
400
400
400
400
400
400
400
400
400
300
300
300
300
300
300
300
mm
10
10
15
15
30
20
10
15
20
20
5
5
20
20
20
40
40
40
40
40
20
20
20
20
20
20
40
40
40
40
mm
2.00
3.00
2.00
3.00
3.00
3.00
3.00
4.00
3.00
4.00
1.00
1.00
3.00
4.00
5.00
4.00
5.00
6.00
7.00
8.00
3.00
4.00
5.00
3.00
4.00
5.00
5.00
6.00
7.00
8.00
Test Results
r
Ag
Ac
A c /A g
f cr
mm
5.00
7.50
5.00
7.50
7.50
7.50
7.50
10.00
7.50
10.00
2.50
2.50
7.50
10.00
12.50
10.00
12.50
15.00
17.50
20.00
7.50
10.00
12.50
7.50
10.00
12.50
12.50
15.00
17.50
20.00
mm2
mm2
382
561
402
591
1491
1431
1371
1650
1581
2090
316
156
3681
4890
6090
5050
6290
7522
8745
9959
3381
4490
5590
3081
4090
5090
5290
6322
7345
8359
63
141
63
141
141
141
141
251
141
251
16
16
141
251
393
251
393
565
770
1005
141
251
393
141
251
393
393
565
770
1005
%
16.4
25.2
15.6
23.9
9.5
9.9
10.3
15.2
8.9
12.0
5.0
10.1
3.8
5.1
6.4
5.0
6.2
7.5
8.8
10.1
4.2
5.6
7.0
4.6
6.1
7.7
7.4
8.9
10.5
12.0
MPa
443
742
583
935
276
198
113
353
181
257
40
153
24
35
47
68
88
114
132
155
26
38
51
40
58
79
141
176
212
251
**centreline dimensions given for FE tests
Department of Civil Engineering
Research Report No R845
66
λd
P u,t
fu
f u /f y
0.77
0.59
0.67
0.53
0.97
1.15
1.51
0.86
1.20
1.01
2.54
1.30
3.29
2.74
2.36
1.96
1.71
1.51
1.40
1.29
3.14
2.62
2.25
2.54
2.11
1.81
1.36
1.22
1.11
1.02
kN
86
150
97
168
284
248
207
346
257
397
27
25
241
403
608
457
712
1008
1281
1592
235
401
606
240
415
631
739
1036
1316
1592
MPa
224
268
241
285
190
173
151
210
163
190
86
159
66
82
100
91
113
134
146
160
69
89
108
78
101
124
140
164
179
190
0.86
1.03
0.93
1.09
0.73
0.67
0.58
0.81
0.63
0.73
0.33
0.61
0.25
0.32
0.38
0.35
0.44
0.52
0.56
0.61
0.27
0.34
0.42
0.30
0.39
0.48
0.54
0.63
0.69
0.73
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
Table A. 13. FE Test Results Summary: 304 Simple Lipped Channels
Test ID
304_60_60_10_2
304_60_60_10_3
304_60_60_15_2
304_60_60_15_3
304_150_150_30_3
304_150_150_20_3
304_150_150_10_3
304_200_100_15_4
304_200_150_20_3
304_200_150_20_4
304_150_80_5_1
304_50_50_5_1
304_400_400_20_3
304_400_400_20_4
304_400_400_20_5
304_400_400_40_4
304_400_400_40_5
304_400_400_40_6
304_400_400_40_7
304_400_400_40_8
304_300_400_20_3
304_300_400_20_4
304_300_400_20_5
304_400_300_20_3
304_400_300_20_4
304_400_300_20_5
304_400_300_40_5
304_400_300_40_6
304_400_300_40_7
304_400_300_40_8
flats
P flats
kN
65
112
74
124
213
183
153
257
191
300
20
18
176
292
443
347
516
727
947
1180
171
293
447
177
294
457
551
766
984
1199
Department of Civil Engineering
Research Report No R845
A c /A g
%
6.4
9.7
6.1
9.2
3.7
3.9
4.1
5.9
3.5
4.7
2.0
4.0
1.5
2.0
2.6
2.0
2.5
3.0
3.5
4.0
1.7
2.2
2.8
1.8
2.4
3.0
2.9
3.5
4.1
4.7
λd
0.70
0.54
0.61
0.48
0.88
1.04
1.38
0.78
1.09
0.91
2.33
1.18
2.98
2.48
2.14
1.77
1.55
1.40
1.27
1.18
2.85
2.38
2.05
2.30
1.92
1.64
1.23
1.10
1.01
0.93
r/t=1
P r/t=1
kN
67
120
77
135
217
187
160
266
195
308
21
19
175
296
454
347
525
746
977
1219
175
301
457
176
302
467
558
780
1007
1232
67
P r/t=1 /P flats
1.04
1.07
1.05
1.09
1.02
1.02
1.04
1.03
1.02
1.03
1.02
1.03
0.99
1.01
1.03
1.00
1.02
1.03
1.03
1.03
1.03
1.03
1.02
1.00
1.03
1.02
1.01
1.02
1.02
1.03
A c /A g
%
16.4
25.2
15.6
23.9
9.5
9.9
10.3
15.2
8.9
12.0
5.0
10.1
3.8
5.1
6.4
5.0
6.2
7.5
8.8
10.1
4.2
5.6
7.0
4.6
6.1
7.7
7.4
8.9
10.5
12.0
λd
0.69
0.53
0.60
0.47
0.87
1.03
1.36
0.77
1.08
0.90
2.28
1.17
2.96
2.46
2.12
1.76
1.54
1.36
1.26
1.16
2.82
2.36
2.03
2.28
1.90
1.63
1.22
1.09
1.00
0.92
r/t=2.5
P r/t=2.5
kN
68
123
78
139
218
188
164
268
196
315
21
19
179
305
458
346
531
755
990
1234
177
305
464
183
307
477
561
784
1014
1245
P r/t=2.5 /P flats
1.05
1.10
1.06
1.12
1.02
1.03
1.07
1.04
1.03
1.05
1.02
1.04
1.02
1.04
1.03
1.00
1.03
1.04
1.04
1.05
1.04
1.04
1.04
1.04
1.04
1.04
1.02
1.02
1.03
1.04
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
Table A. 14. FE Test Results Summary: 430 Simple Lipped Channels
Test ID
430_60_60_10_2
430_60_60_10_3
430_60_60_15_2
430_60_60_15_3
430_150_150_30_3
430_150_150_20_3
430_150_150_10_3
430_200_100_15_4
430_200_150_20_3
430_200_150_20_4
430_150_80_5_1
430_50_50_5_1
430_400_400_20_3
430_400_400_20_4
430_400_400_20_5
430_400_400_40_4
430_400_400_40_5
430_400_400_40_6
430_400_400_40_7
430_400_400_40_8
430_300_400_20_3
430_300_400_20_4
430_300_400_20_5
430_400_300_20_3
430_400_300_20_4
430_400_300_20_5
430_400_300_40_5
430_400_300_40_6
430_400_300_40_7
430_400_300_40_8
flats
P flats A c /A g
kN
%
6.4
85
9.7
146
6.1
96
9.2
163
3.7
280
3.9
240
4.1
200
5.9
338
3.5
244
4.7
390
2.0
26
4.0
24
1.5
231
2.0
356
2.6
579
2.0
424
2.5
647
3.0
950
3.5
1226
4.0
1531
1.7
225
2.2
383
2.8
579
1.8
231
2.4
397
3.0
594
2.9
699
3.5
980
4.1
1283
4.7
1563
Department of Civil Engineering
Research Report No R845
λd
0.85
0.66
0.74
0.59
1.07
1.27
1.69
0.95
1.33
1.11
2.84
1.44
3.64
3.02
2.61
2.16
1.89
1.71
1.55
1.44
3.47
2.90
2.50
2.80
2.33
2.00
1.50
1.35
1.23
1.13
r/t=1
P r/t=1
kN
87
153
98
171
284
243
203
345
246
397
27
24
231
357
586
430
650
953
1234
1547
228
388
586
234
402
601
704
988
1300
1589
68
P r/t=1 /P flats
1.02
1.04
1.03
1.05
1.01
1.01
1.02
1.02
1.01
1.02
1.01
1.01
1.00
1.00
1.01
1.02
1.00
1.00
1.01
1.01
1.01
1.01
1.01
1.01
1.01
1.01
1.01
1.01
1.01
1.02
A c /A g
%
16.4
25.2
15.6
23.9
9.5
9.9
10.3
15.2
8.9
12.0
5.0
10.1
3.8
5.1
6.4
5.0
6.2
7.5
8.8
10.1
4.2
5.6
7.0
4.6
6.1
7.7
7.4
8.9
10.5
12.0
λd
0.84
0.65
0.73
0.58
1.06
1.25
1.66
0.94
1.31
1.10
2.78
1.43
3.61
3.00
2.59
2.15
1.88
1.65
1.54
1.42
3.44
2.87
2.47
2.78
2.31
1.98
1.49
1.33
1.21
1.12
r/t=2.5
P r/t=2.5
kN
87
154
99
173
286
244
205
346
247
399
26
24
236
343
586
437
650
953
1236
1556
229
390
590
235
404
605
704
992
1306
1598
P r/t=2.5 /P flats
1.03
1.05
1.03
1.06
1.02
1.02
1.03
1.02
1.01
1.02
1.00
1.01
1.02
0.96
1.01
1.03
1.00
1.00
1.01
1.02
1.02
1.02
1.02
1.02
1.02
1.02
1.01
1.01
1.02
1.02
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
Table A. 15. FE Test Results Summary: 3Cr12 Simple Lipped Channels
Test ID
3Cr12_60_60_10_2
3Cr12_60_60_10_3
3Cr12_60_60_15_2
3Cr12_60_60_15_3
3Cr12_150_150_30_3
3Cr12_150_150_20_3
3Cr12_150_150_10_3
3Cr12_200_100_15_4
3Cr12_200_150_20_3
3Cr12_200_150_20_4
3Cr12_150_80_5_1
3Cr12_50_50_5_1
3Cr12_400_400_20_3
3Cr12_400_400_20_4
3Cr12_400_400_20_5
3Cr12_400_400_40_4
3Cr12_400_400_40_5
3Cr12_400_400_40_6
3Cr12_400_400_40_7
3Cr12_400_400_40_8
3Cr12_300_400_20_3
3Cr12_300_400_20_4
3Cr12_300_400_20_5
3Cr12_400_300_20_3
3Cr12_400_300_20_4
3Cr12_400_300_20_5
3Cr12_400_300_40_5
3Cr12_400_300_40_6
3Cr12_400_300_40_7
3Cr12_400_300_40_8
flats
P flats A c /A g
kN
%
6.4
83
9.7
142
6.1
93
9.2
157
3.7
278
3.9
243
4.1
201
5.9
335
3.5
254
4.7
389
2.0
27
4.0
24
1.5
237
2.0
382
2.6
602
2.0
444
2.5
709
3.0
1005
3.5
1267
4.0
1563
1.7
231
2.2
395
2.8
597
1.8
237
2.4
409
3.0
618
2.9
738
3.5
1022
4.1
1292
4.7
1556
Department of Civil Engineering
Research Report No R845
λd
0.78
0.60
0.67
0.53
0.98
1.16
1.54
0.87
1.21
1.02
2.59
1.31
3.32
2.76
2.38
1.97
1.73
1.56
1.42
1.31
3.17
2.65
2.28
2.56
2.13
1.83
1.37
1.23
1.12
1.03
r/t=1
P r/t=1
kN
85
148
96
165
283
246
205
343
256
396
27
25
237
383
607
447
710
1009
1277
1581
234
399
603
240
413
621
741
1032
1311
1584
69
P r/t=1 /P flats
1.03
1.04
1.03
1.05
1.02
1.01
1.02
1.02
1.01
1.02
1.01
1.01
1.00
1.00
1.01
1.01
1.00
1.00
1.01
1.01
1.01
1.01
1.01
1.01
1.01
1.00
1.00
1.01
1.01
1.02
A c /A g
%
16.4
25.2
15.6
23.9
9.5
9.9
10.3
15.2
8.9
12.0
5.0
10.1
3.8
5.1
6.4
5.0
6.2
7.5
8.8
10.1
4.2
5.6
7.0
4.6
6.1
7.7
7.4
8.9
10.5
12.0
λd
0.77
0.59
0.67
0.53
0.97
1.15
1.51
0.86
1.20
1.01
2.54
1.30
3.29
2.74
2.36
1.96
1.71
1.51
1.40
1.29
3.14
2.62
2.25
2.54
2.11
1.81
1.36
1.22
1.11
1.02
r/t=2.5
P r/t=2.5
kN
86
150
97
168
284
248
207
346
257
397
27
25
241
403
608
457
712
1008
1281
1592
235
401
606
240
415
631
739
1036
1316
1592
P r/t=2.5 /P flats
1.03
1.06
1.04
1.07
1.02
1.02
1.03
1.03
1.01
1.02
1.00
1.01
1.02
1.06
1.01
1.03
1.00
1.00
1.01
1.02
1.02
1.02
1.01
1.01
1.01
1.02
1.00
1.01
1.02
1.02
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
Table A. 16. 304 Lipped Channels with Intermediate Stiffeners-Experimental
Material Properties
f pf
Test ID
304DS1a
304DS2b
fy
Eo
f yc
Geometric Properties**
L,L cr
MPa MPa MPa MPa mm
164 242 187000 565 788
164 242 187000 565 785
Bw
Bf
Bl
di
t
mm mm mm mm mm
122.1 90.6 15.0 10.0 1.96
122.2 90.6 15.0 10.0 1.96
Test Results
Ac
A c /A g
r
Ag
mm
3.00
3.00
mm
2
mm
634
634
122
123
2
%
19
19
f cr
λd
MPa
333 0.85
333 0.85
P u,t
fu
f u /f y
kN
132
134
MPa
208
211
0.86
0.87
**L, overall dimensions and inner radius given for experimental tests and di is an approximation used for FE only
Table A. 17. 304 Lipped Channels with Intermediate Stiffeners-Flats
Material Properties
Test ID
304_200_160_25_10_2
304_200_160_25_10_3
304_200_160_25_10_4
304_400_160_25_10_2
304_400_160_25_10_3
304_400_160_25_10_4
304_400_160_25_20_2
304_400_160_25_20_3
304_400_160_25_20_4
304_800_400_40_15_3
304_800_400_40_15_4
304_800_400_40_15_5
304_800_400_40_15_6
304_800_400_40_30_4
304_800_400_40_30_5
304_800_400_40_30_6
304_150_100_10_10_1
304_150_70_15_10_1
304_150_70_15_10_2
304_200_80_15_10_1
304_200_80_15_10_2
304_150_110_15_10_2
304_300_200_20_15_2
304_300_200_20_15_3
304_100_70_20_10_1
304_250_95_20_10_2
304_250_95_20_10_3
304_100_60_10_10_1
304_200_150_15_15_2
304_90_60_10_5_1
304_150_70_15_10_4
304_150_70_15_10_5
304_200_160_35_20_6
304_200_160_35_20_7
Geometric Properties**
Test Results
f pf
fy
Eo
f yc
L,L cr
Bw
Bf
Bl
di
t
r
Ag
Ac
A c /A g
f cr
MPa
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
MPa
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
MPa
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
MPa
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
mm
1400
1200
1000
600
600
500
1800
1600
1200
3500
3000
3000
2500
3500
3000
2500
900
900
600
1000
700
800
1600
1400
900
900
700
600
1000
500
400
400
900
800
mm
200
200
200
400
400
400
400
400
400
800
800
800
800
800
800
800
150
150
150
200
200
150
300
300
100
250
250
100
200
90
150
150
200
200
mm
160
160
160
160
160
160
160
160
160
400
400
400
400
400
400
400
100
70
70
80
80
110
200
200
70
95
95
60
150
60
70
70
160
160
mm
25
25
25
25
25
25
25
25
25
40
40
40
40
40
40
40
10
15
15
15
15
15
20
20
20
20
20
10
15
10
15
15
35
35
mm
10
10
10
10
10
10
20
20
20
15
15
15
15
30
30
30
10
10
10
10
10
10
15
15
10
10
10
10
15
5
10
10
20
20
mm
2.00
3.00
4.00
2.00
3.00
4.00
2.00
3.00
4.00
3.00
4.00
5.00
6.00
4.00
5.00
6.00
1.00
1.00
2.00
1.00
2.00
2.00
2.00
3.00
1.00
2.00
3.00
1.00
2.00
1.00
4.00
5.00
6.00
7.00
mm
2.00
3.00
4.00
2.00
3.00
4.00
2.00
3.00
4.00
3.00
4.00
5.00
6.00
4.00
5.00
6.00
1.00
1.00
2.00
1.00
2.00
2.00
2.00
3.00
1.00
2.00
3.00
1.00
2.00
1.00
4.00
5.00
6.00
7.00
mm2
mm2
1177
1755
2327
1577
2355
3127
1626
2430
3227
5123
6769
8505
10186
6966
8691
10410
392
341
681
412
817
837
1542
2303
302
997
1485
262
1122
239
1327
1643
3721
4318
63
141
251
63
141
251
63
141
251
141
251
393
565
251
393
565
16
16
63
16
63
63
63
141
16
63
141
16
63
16
251
393
565
770
%
5.3
8.1
10.8
4.0
6.0
8.0
3.9
5.8
7.8
2.8
3.7
4.6
5.6
3.6
4.5
5.4
4.0
4.6
9.2
3.8
7.7
7.5
4.1
6.1
5.2
6.3
9.5
6.0
5.6
6.6
18.9
23.9
15.2
17.8
MPa
106
169
238
58
95
138
73
115
165
28
40
52
65
45
58
74
62
111
251
72
164
139
55
88
186
131
214
162
89
189
619
837
527
638
**L cr and centreline dimensions given for FE tests
Department of Civil Engineering
Research Report No R845
70
λd
P u,t
fu
f u /f y
1.35
1.08
0.91
1.83
1.43
1.19
1.64
1.30
1.09
2.63
2.22
1.94
1.73
2.09
1.83
1.63
1.77
1.33
0.88
1.65
1.09
1.19
1.89
1.49
1.02
1.22
0.95
1.10
1.48
1.02
0.56
0.48
0.61
0.55
kN
116
215
328
116
211
328
128
232
355
252
408
577
792
484
683
902
36
32
90
32
90
101
129
235
36
98
182
31
123
27
250
330
669
817
MPa
99
123
141
73
90
105
79
96
110
49
60
68
78
70
79
87
91
94
132
78
110
120
84
102
118
98
123
118
109
113
188
201
180
189
0.51
0.63
0.72
0.38
0.46
0.54
0.40
0.49
0.56
0.25
0.31
0.35
0.40
0.36
0.40
0.44
0.47
0.48
0.68
0.40
0.57
0.62
0.43
0.52
0.60
0.50
0.63
0.61
0.56
0.58
0.97
1.03
0.92
0.97
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
Table A. 18. 304 Lipped Channels with Intermediate Stiffeners: r/t=1
Material Properties
Test ID
304_200_160_25_10_2_1
304_200_160_25_10_3_1
304_200_160_25_10_4_1
304_400_160_25_10_2_1
304_400_160_25_10_3_1
304_400_160_25_10_4_1
304_400_160_25_20_2_1
304_400_160_25_20_3_1
304_400_160_25_20_4_1
304_800_400_40_15_3_1
304_800_400_40_15_4_1
304_800_400_40_15_5_1
304_800_400_40_15_6_1
304_800_400_40_30_4_1
304_800_400_40_30_5_1
304_800_400_40_30_6_1
304_150_100_10_10_1_1
304_150_70_15_10_1_1
304_150_70_15_10_2_1
304_200_80_15_10_1_1
304_200_80_15_10_2_1
304_150_110_15_10_2_1
304_300_200_20_15_2_1
304_300_200_20_15_3_1
304_100_70_20_10_1_1
304_250_95_20_10_2_1
304_250_95_20_10_3_1
304_100_60_10_10_1_1
304_200_150_15_15_2_1
304_90_60_10_5_1_1
304_150_70_15_10_4_1
304_150_70_15_10_5_1
304_200_160_35_20_6_1
304_200_160_35_20_7_1
Geometric Properties**
Test Results
f pf
fy
Eo
f yc
L,L cr
Bw
Bf
Bl
di
t
r
Ag
Ac
A c /A g
f cr
MPa
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
MPa
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
MPa
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
MPa
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
mm
1400
1200
1000
600
600
500
1800
1600
1200
3500
3000
3000
2500
3500
3000
2500
900
900
600
1000
700
800
1600
1400
900
900
700
600
1000
500
400
400
900
800
mm
200
200
200
400
400
400
400
400
400
800
800
800
800
800
800
800
150
150
150
200
200
150
300
300
100
250
250
100
200
90
150
150
200
200
mm
160
160
160
160
160
160
160
160
160
400
400
400
400
400
400
400
100
70
70
80
80
110
200
200
70
95
95
60
150
60
70
70
160
160
mm
25
25
25
25
25
25
25
25
25
40
40
40
40
40
40
40
10
15
15
15
15
15
20
20
20
20
20
10
15
10
15
15
35
35
mm
10
10
10
10
10
10
20
20
20
15
15
15
15
30
30
30
10
10
10
10
10
10
15
15
10
10
10
10
15
5
10
10
20
20
mm
2.00
3.00
4.00
2.00
3.00
4.00
2.00
3.00
4.00
3.00
4.00
5.00
6.00
4.00
5.00
6.00
1.00
1.00
2.00
1.00
2.00
2.00
2.00
3.00
1.00
2.00
3.00
1.00
2.00
1.00
4.00
5.00
6.00
7.00
mm
2.00
3.00
4.00
2.00
3.00
4.00
2.00
3.00
4.00
3.00
4.00
5.00
6.00
4.00
5.00
6.00
1.00
1.00
2.00
1.00
2.00
2.00
2.00
3.00
1.00
2.00
3.00
1.00
2.00
1.00
4.00
5.00
6.00
7.00
mm2
mm2
1177
1755
2327
1577
2355
3127
1626
2430
3227
5123
6769
8505
10186
6966
8691
10410
392
341
681
412
817
837
1542
2303
302
997
1485
262
1122
239
1327
1643
3721
4318
63
141
251
63
141
251
63
141
251
141
251
393
565
251
393
565
16
16
63
16
63
63
63
141
16
63
141
16
63
16
251
393
565
770
%
5.3
8.1
10.8
4.0
6.0
8.0
3.9
5.8
7.8
2.8
3.7
4.6
5.6
3.6
4.5
5.4
4.0
4.6
9.2
3.8
7.7
7.5
4.1
6.1
5.2
6.3
9.5
6.0
5.6
6.6
18.9
23.9
15.2
17.8
MPa
106
169
238
58
95
138
73
115
165
28
40
52
65
45
58
74
62
111
251
72
164
139
55
88
186
131
214
162
89
189
619
837
527
638
**L cr and centreline dimensions given for FE tests
Department of Civil Engineering
Research Report No R845
71
λd
P u,t
fu
f u /f y
1.35
1.08
0.91
1.83
1.43
1.19
1.64
1.30
1.09
2.63
2.22
1.94
1.73
2.09
1.83
1.63
1.77
1.33
0.88
1.65
1.09
1.19
1.89
1.49
1.02
1.22
0.95
1.10
1.48
1.02
0.56
0.48
0.61
0.55
kN
121
227
352
119
221
347
133
244
379
258
423
603
829
503
715
952
37
33
96
33
95
107
133
247
37
102
193
32
128
28
291
408
757
950
MPa
103
129
151
76
94
111
82
100
117
50
62
71
81
72
82
91
94
97
141
81
117
127
86
107
122
103
130
123
114
119
219
249
203
220
0.53
0.66
0.78
0.39
0.48
0.57
0.42
0.51
0.60
0.26
0.32
0.36
0.42
0.37
0.42
0.47
0.48
0.50
0.73
0.41
0.60
0.65
0.44
0.55
0.62
0.53
0.67
0.63
0.59
0.61
1.12
1.28
1.04
1.13
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
Table A. 19. 304 Lipped Channels with Intermediate Stiffeners: r/t=2.5
Material Properties
Test ID
304_200_160_25_10_2_2.5
304_200_160_25_10_3_2.5
304_200_160_25_10_4_2.5
304_400_160_25_10_2_2.5
304_400_160_25_10_3_2.5
304_400_160_25_10_4_2.5
304_400_160_25_20_2_2.5
304_400_160_25_20_3_2.5
304_400_160_25_20_4_2.5
304_800_400_40_15_3_2.5
304_800_400_40_15_4_2.5
304_800_400_40_15_5_2.5
304_800_400_40_15_6_2.5
304_800_400_40_30_4_2.5
304_800_400_40_30_5_2.5
304_800_400_40_30_6_2.5
304_150_100_10_10_1_2.5
304_150_70_15_10_1_2.5
304_150_70_15_10_2_2.5
304_200_80_15_10_1_2.5
304_200_80_15_10_2_2.5
304_150_110_15_10_2_2.5
304_300_200_20_15_2_2.5
304_300_200_20_15_3_2.5
304_100_70_20_10_1_2.5
304_250_95_20_10_2_2.5
304_250_95_20_10_3_2.5
304_100_60_10_10_1_2.5
304_200_150_15_15_2_2.5
304_90_60_10_5_1_2.5
304_150_70_15_10_4_2.5
304_150_70_15_10_5_2.5
304_200_160_35_20_6_2.5
304_200_160_35_20_7_2.5
Geometric Properties**
Bl
di
Test Results
f pf
fy
Eo
f yc
L,L cr
Bw
Bf
MPa
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
MPa
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
MPa
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
195000
MPa
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
mm
1400
1200
1000
600
600
500
1800
1600
1200
3500
3000
3000
2500
3500
3000
2500
900
900
600
1000
700
800
1600
1400
900
900
700
600
1000
500
400
400
900
800
mm
200
200
200
400
400
400
400
400
400
800
800
800
800
800
800
800
150
150
150
200
200
150
300
300
100
250
250
100
200
90
150
150
200
200
mm
mm
mm mm mm mm mm
160 25 10 2.00 5.00 1157 157
160 25 10 3.00 7.50 1711 353
160 25 10 4.00 9.00 2262 565
160 25 10 2.00 5.00 1557 157
160 25 10 3.00 7.50 2311 353
160 25 10 4.00 9.00 3062 565
160 25 20 2.00 5.00 1607 157
160 25 20 3.00 7.50 2386 353
160 25 20 4.00 10.00 3148 628
400 40 15 3.00 7.50 5078 353
400 40 15 4.00 10.00 6739 628
400 40 15 5.00 12.50 8382 982
400 40 15 6.00 12.00 10069 1131
400 40 30 4.00 10.00 6888 628
400 40 30 5.00 12.50 8569 982
400 40 30 6.00 15.00 10234 1414
39
100 10 10 1.00 2.50
387
39
70 15 10 1.00 2.50
337
157
70 15 10 2.00 5.00
657
39
80 15 10 1.00 2.50
407
157
80 15 10 2.00 5.00
797
157
110 15 10 2.00 5.00
817
200 20 15 2.00 5.00 1522 157
200 20 15 3.00 7.50 2258 353
39
70 20 10 1.00 2.50
297
157
95 20 10 2.00 5.00
977
95 20 10 3.00 7.50 1441 353
39
60 10 10 1.00 2.50
257
150 15 15 2.00 5.00 1102 157
39
60 10
5 1.00 2.50
234
70 15 10 4.00 8.50 1268 534
70 15 10 5.00 8.50 1586 668
160 35 20 6.00 15.00 3545 1414
160 35 20 7.00 17.50 4078 1924
t
Ac
Ag
r
2
A c /A g
f cr
%
13.6
20.7
25.0
10.1
15.3
18.5
9.8
14.8
20.0
7.0
9.3
11.7
11.2
9.1
11.5
13.8
10.2
11.7
23.9
9.7
19.7
19.2
10.3
15.6
13.2
16.1
24.5
15.3
14.3
16.8
42.1
42.1
39.9
47.2
MPa
109
174
245
54
87
129
73
115
163
27
38
51
67
45
59
74
63
115
264
74
170
148
56
88
191
133
213
167
92
202
645
866
546
666
2
λd
P u,t
fu
f u /f y
1.34
1.06
0.89
1.90
1.50
1.23
1.64
1.30
1.09
2.69
2.26
1.95
1.71
2.08
1.82
1.62
1.76
1.30
0.86
1.62
1.07
1.15
1.87
1.49
1.01
1.21
0.96
1.08
1.46
0.98
0.55
0.47
0.60
0.54
kN
122
228
356
121
227
360
135
248
384
255
391
590
832
509
721
958
37
34
100
34
98
109
134
249
37
104
196
33
131
29
302
413
793
1009
MPa
105
133
158
78
98
118
84
104
122
50
58
70
83
74
84
94
96
100
152
83
122
133
88
110
126
106
136
129
119
123
238
260
224
247
0.54
0.68
0.81
0.40
0.50
0.60
0.43
0.53
0.63
0.26
0.30
0.36
0.42
0.38
0.43
0.48
0.49
0.51
0.78
0.43
0.63
0.68
0.45
0.57
0.65
0.54
0.70
0.66
0.61
0.63
1.22
1.34
1.15
1.27
**L cr and centreline dimensions given for FE tests
Table A. 20. 430 Lipped Channels with Intermediate Stiffeners: Experimental
Material Properties
Test ID
430DS1
430DS2
430DS3
430DS4
f pf
fy
MPa
170
170
170
170
MPa
271
271
271
271
Eo
Geometric Properties**
f yc
MPa MPa
193000 452
193000 452
193000 452
193000 452
Test Results
L,L cr
Bw
Bf
Bl
di
t
r
Ag
Ac
A c /A g
f cr
mm
875
600
879
600
mm
79.6
79.5
79.6
79.5
mm
70.0
70.2
70.3
70.7
mm
10.5
10.7
14.3
14.2
mm
10.0
10.0
10.0
10.0
mm
1.13
1.13
1.13
1.13
mm
2.43
2.50
2.50
2.50
mm2
269
269
278
278
mm2
53
55
54
54
%
20
20
20
20
MPa
269
335
327
468
λd
P u,t
fu
f u /f y
1.00
0.90
0.91
0.76
kN
60
62
64
72
MPa
222
230
228
258
0.82
0.85
0.84
0.95
**L, overall dimensions and inner radius given for experimental tests and di is an approximation used for FE only
Department of Civil Engineering
Research Report No R845
72
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
Table A. 21. 430 Lipped Channels with Intermediate Stiffeners: Flats
Material Properties
Test ID
430_200_160_25_10_2
430_200_160_25_10_3
430_200_160_25_10_4
430_400_160_25_10_2
430_400_160_25_10_3
430_400_160_25_10_4
430_400_160_25_20_2
430_400_160_25_20_3
430_400_160_25_20_4
430_800_400_40_15_3
430_800_400_40_15_4
430_800_400_40_15_5
430_800_400_40_15_6
430_800_400_40_30_4
430_800_400_40_30_5
430_800_400_40_30_6
430_150_100_10_10_1
430_150_70_15_10_1
430_150_70_15_10_2
430_200_80_15_10_1
430_200_80_15_10_2
430_150_110_15_10_2
430_300_200_20_15_2
430_300_200_20_15_3
430_100_70_20_10_1
430_250_95_20_10_2
430_250_95_20_10_3
430_100_60_10_10_1
430_200_150_15_15_2
430_90_60_10_5_1
430_150_70_15_10_4
430_150_70_15_10_5
430_200_160_35_20_6
430_200_160_35_20_7
Geometric Properties**
f pf
fy
Eo
f yc
L,L cr
Bw
Bf
Bl
di
t
r
MPa
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
MPa
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
MPa
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
MPa
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
mm
1400
1200
1000
600
600
500
1800
1600
1200
3500
3000
3000
2500
3500
3000
2500
900
900
600
1000
700
800
1600
1400
900
900
700
600
1000
500
400
400
900
800
mm
200
200
200
400
400
400
400
400
400
800
800
800
800
800
800
800
150
150
150
200
200
150
300
300
100
250
250
100
200
90
150
150
200
200
mm
160
160
160
160
160
160
160
160
160
400
400
400
400
400
400
400
100
70
70
80
80
110
200
200
70
95
95
60
150
60
70
70
160
160
mm
25
25
25
25
25
25
25
25
25
40
40
40
40
40
40
40
10
15
15
15
15
15
20
20
20
20
20
10
15
10
15
15
35
35
mm
10
10
10
10
10
10
20
20
20
15
15
15
15
30
30
30
10
10
10
10
10
10
15
15
10
10
10
10
15
5
10
10
20
20
mm
2.00
3.00
4.00
2.00
3.00
4.00
2.00
3.00
4.00
3.00
4.00
5.00
6.00
4.00
5.00
6.00
1.00
1.00
2.00
1.00
2.00
2.00
2.00
3.00
1.00
2.00
3.00
1.00
2.00
1.00
4.00
5.00
6.00
7.00
mm
2.00
3.00
4.00
2.00
3.00
4.00
2.00
3.00
4.00
3.00
4.00
5.00
6.00
4.00
5.00
6.00
1.00
1.00
2.00
1.00
2.00
2.00
2.00
3.00
1.00
2.00
3.00
1.00
2.00
1.00
4.00
5.00
6.00
7.00
Test Results
**L cr , centreline dimensions given for FE tests
Department of Civil Engineering
Research Report No R845
73
Ac
Ag
2
2
mm
mm
63
1177
1755 141
2327 251
63
1577
2355 141
3127 251
63
1626
2430 141
3227 251
5123 141
6769 251
8505 393
10186 565
6966 251
8691 393
10410 565
16
392
16
341
63
681
16
412
63
817
63
837
63
1542
2303 141
16
302
63
997
1485 141
16
262
63
1122
16
239
1327 251
1643 393
3721 565
4318 770
A c /A g
f cr
%
5.3
8.1
10.8
4.0
6.0
8.0
3.9
5.8
7.8
2.8
3.7
4.6
5.6
3.6
4.5
5.4
4.0
4.6
9.2
3.8
7.7
7.5
4.1
6.1
5.2
6.3
9.5
6.0
5.6
6.6
18.9
23.9
15.2
17.8
MPa
101
160
226
55
90
131
69
109
157
27
38
49
62
42
55
70
59
105
238
68
156
132
52
84
177
124
203
153
84
125
587
794
500
605
λd
P u,t
fu
f u /f y
1.65
1.31
1.10
2.23
1.75
1.45
2.00
1.59
1.32
3.21
2.71
2.37
2.11
2.55
2.23
1.98
2.16
1.62
1.07
2.01
1.33
1.45
2.30
1.81
1.25
1.49
1.16
1.34
1.81
1.48
0.68
0.59
0.74
0.67
kN
155
284
431
154
282
439
167
312
476
316
527
762
1049
625
907
1198
44
43
118
42
121
134
170
310
48
131
241
41
162
36
322
434
873
1068
MPa
131
162
185
97
120
140
103
128
147
62
78
90
103
90
104
115
112
125
173
102
148
160
110
135
158
131
162
158
145
150
243
264
234
247
0.48
0.59
0.67
0.35
0.44
0.51
0.37
0.47
0.54
0.22
0.28
0.33
0.37
0.33
0.38
0.42
0.41
0.46
0.63
0.37
0.54
0.58
0.40
0.49
0.57
0.48
0.59
0.57
0.53
0.54
0.88
0.96
0.85
0.90
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
Table A. 22. 430 Lipped Channels with Intermediate Stiffeners: r/t=1
Material Properties
Test ID
430_200_160_25_10_2_1
430_200_160_25_10_3_1
430_200_160_25_10_4_1
430_400_160_25_10_2_1
430_400_160_25_10_3_1
430_400_160_25_10_4_1
430_400_160_25_20_2_1
430_400_160_25_20_3_1
430_400_160_25_20_4_1
430_800_400_40_15_3_1
430_800_400_40_15_4_1
430_800_400_40_15_5_1
430_800_400_40_15_6_1
430_800_400_40_30_4_1
430_800_400_40_30_5_1
430_800_400_40_30_6_1
430_150_100_10_10_1_1
430_150_70_15_10_1_1
430_150_70_15_10_2_1
430_200_80_15_10_1_1
430_200_80_15_10_2_1
430_150_110_15_10_2_1
430_300_200_20_15_2_1
430_300_200_20_15_3_1
430_100_70_20_10_1_1
430_250_95_20_10_2_1
430_250_95_20_10_3_1
430_100_60_10_10_1_1
430_200_150_15_15_2_1
430_90_60_10_5_1_1
430_150_70_15_10_4_1
430_150_70_15_10_5_1
430_200_160_35_20_6_1
430_200_160_35_20_7_1
f pf
fy
MPa
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
MPa
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
Eo
Geometric Properties**
f yc
L,L cr
Bw
Bf
Bl
di
t
r
MPa MPa mm
185000 479 1400
185000 479 1200
185000 479 1000
185000 479 600
185000 479 600
185000 479 500
185000 479 1800
185000 479 1600
185000 479 1200
185000 479 3500
185000 479 3000
185000 479 3000
185000 479 2500
185000 479 3500
185000 479 3000
185000 479 2500
185000 479 900
185000 479 900
185000 479 600
185000 479 1000
185000 479 700
185000 479 800
185000 479 1600
185000 479 1400
185000 479 900
185000 479 900
185000 479 700
185000 479 600
185000 479 1000
185000 479 500
185000 479 400
185000 479 400
185000 479 900
185000 479 800
mm
200
200
200
400
400
400
400
400
400
800
800
800
800
800
800
800
150
150
150
200
200
150
300
300
100
250
250
100
200
90
150
150
200
200
mm
160
160
160
160
160
160
160
160
160
400
400
400
400
400
400
400
100
70
70
80
80
110
200
200
70
95
95
60
150
60
70
70
160
160
mm
25
25
25
25
25
25
25
25
25
40
40
40
40
40
40
40
10
15
15
15
15
15
20
20
20
20
20
10
15
10
15
15
35
35
mm
10
10
10
10
10
10
20
20
20
15
15
15
15
30
30
30
10
10
10
10
10
10
15
15
10
10
10
10
15
5
10
10
20
20
mm
2.00
3.00
4.00
2.00
3.00
4.00
2.00
3.00
4.00
3.00
4.00
5.00
6.00
4.00
5.00
6.00
1.00
1.00
2.00
1.00
2.00
2.00
2.00
3.00
1.00
2.00
3.00
1.00
2.00
1.00
4.00
5.00
6.00
7.00
mm
2.00
3.00
4.00
2.00
3.00
4.00
2.00
3.00
4.00
3.00
4.00
5.00
6.00
4.00
5.00
6.00
1.00
1.00
2.00
1.00
2.00
2.00
2.00
3.00
1.00
2.00
3.00
1.00
2.00
1.00
4.00
5.00
6.00
7.00
Test Results
Ag
mm2 mm2
63
1177
1755 141
2327 251
63
1577
2355 141
3127 251
63
1626
2430 141
3227 251
5123 141
6769 251
8505 393
10186 565
6966 251
8691 393
10410 565
16
392
16
341
63
681
16
412
63
817
63
837
63
1542
2303 141
16
302
63
997
1485 141
16
262
63
1122
16
239
1327 251
1643 393
3721 565
4318 770
**L cr , centreline dimensions given for FE tests
Department of Civil Engineering
Research Report No R845
74
Ac
A c /A g
f cr
%
5.3
8.1
10.8
4.0
6.0
8.0
3.9
5.8
7.8
2.8
3.7
4.6
5.6
3.6
4.5
5.4
4.0
4.6
9.2
3.8
7.7
7.5
4.1
6.1
5.2
6.3
9.5
6.0
5.6
6.6
18.9
23.9
15.2
17.8
MPa
101
160
226
55
90
131
69
109
157
27
38
49
62
42
55
70
59
105
238
68
156
132
52
84
177
124
203
153
84
125
587
794
500
605
λd
P u,t
fu
f u /f y
1.65
1.31
1.10
2.23
1.75
1.45
2.00
1.59
1.32
3.21
2.71
2.37
2.11
2.55
2.23
1.98
2.16
1.62
1.07
2.01
1.33
1.45
2.30
1.81
1.25
1.49
1.16
1.34
1.81
1.48
0.68
0.59
0.74
0.67
kN
157
292
448
155
288
452
170
319
491
323
538
780
1075
635
930
1233
48
43
123
42
124
134
144
319
48
134
248
42
167
37
353
491
937
1165
MPa
133
166
193
98
122
145
105
131
152
63
79
92
106
91
107
118
122
127
180
103
152
160
93
139
160
134
167
161
149
153
266
299
252
270
0.49
0.60
0.70
0.36
0.45
0.53
0.38
0.48
0.55
0.23
0.29
0.33
0.38
0.33
0.39
0.43
0.44
0.46
0.66
0.38
0.55
0.58
0.34
0.50
0.58
0.49
0.61
0.59
0.54
0.56
0.97
1.09
0.92
0.98
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
Table A. 23. 430 Lipped Channels with Intermediate Stiffeners: r/t=2.5
Material Properties
f pf
Test ID
fy
MPa MPa
Geometric Properties**
Test Results
f yc
L,L cr
Bw
Bf
Bl
di
t
r
Ag
Ac
A c /A g
f cr
MPa
mm
mm
mm
mm
mm
mm
mm
mm2
mm2
%
MPa
200
160
25
10
2.00
5.00
1157
157
13.6
103
1.63
200
200
400
400
400
400
400
400
800
800
800
800
800
800
800
150
150
150
200
200
150
300
300
100
250
250
100
200
90
150
150
200
200
160
160
160
160
160
160
160
160
400
400
400
400
400
400
400
100
70
70
80
80
110
200
200
70
95
95
60
150
60
70
70
160
160
25
25
25
25
25
25
25
25
40
40
40
40
40
40
40
10
15
15
15
15
15
20
20
20
20
20
10
15
10
15
15
35
35
10
10
10
10
10
20
20
20
15
15
15
15
30
30
30
10
10
10
10
10
10
15
15
10
10
10
10
15
5
10
10
20
20
3.00
4.00
2.00
3.00
4.00
2.00
3.00
4.00
3.00
4.00
5.00
6.00
4.00
5.00
6.00
1.00
1.00
2.00
1.00
2.00
2.00
2.00
3.00
1.00
2.00
3.00
1.00
2.00
1.00
4.00
5.00
6.00
7.00
7.50
9.00
5.00
7.50
9.00
5.00
7.50
10.00
7.50
10.00
12.50
12.00
10.00
12.50
15.00
2.50
2.50
5.00
2.50
5.00
5.00
5.00
7.50
2.50
5.00
7.50
2.50
5.00
2.50
8.50
8.50
15.00
17.50
1711
2262
1557
2311
3062
1607
2386
3148
5078
6739
8382
10069
6888
8569
10234
387
337
657
407
797
817
1522
2258
297
977
1441
257
1102
234
1268
1586
3545
4078
353
565
157
353
565
157
353
628
353
628
982
1131
628
982
1414
39
39
157
39
157
157
157
353
39
157
353
39
157
39
534
668
1414
1924
20.7
25.0
10.1
15.3
18.5
9.8
14.8
20.0
7.0
9.3
11.7
11.2
9.1
11.5
13.8
10.2
11.7
23.9
9.7
19.7
19.2
10.3
15.6
13.2
16.1
24.5
15.3
14.3
16.8
42.1
42.1
39.9
47.2
165
233
51
83
122
69
110
155
26
36
49
63
43
56
70
60
109
251
70
161
140
53
84
181
126
202
159
87
134
612
821
518
632
430_200_160_25_10_2_2.5
170
275
185000
424
430_200_160_25_10_3_2.5
430_200_160_25_10_4_2.5
430_400_160_25_10_2_2.5
430_400_160_25_10_3_2.5
430_400_160_25_10_4_2.5
430_400_160_25_20_2_2.5
430_400_160_25_20_3_2.5
430_400_160_25_20_4_2.5
430_800_400_40_15_3_2.5
430_800_400_40_15_4_2.5
430_800_400_40_15_5_2.5
430_800_400_40_15_6_2.5
430_800_400_40_30_4_2.5
430_800_400_40_30_5_2.5
430_800_400_40_30_6_2.5
430_150_100_10_10_1_2.5
430_150_70_15_10_1_2.5
430_150_70_15_10_2_2.5
430_200_80_15_10_1_2.5
430_200_80_15_10_2_2.5
430_150_110_15_10_2_2.5
430_300_200_20_15_2_2.5
430_300_200_20_15_3_2.5
430_100_70_20_10_1_2.5
430_250_95_20_10_2_2.5
430_250_95_20_10_3_2.5
430_100_60_10_10_1_2.5
430_200_150_15_15_2_2.5
430_90_60_10_5_1_2.5
430_150_70_15_10_4_2.5
430_150_70_15_10_5_2.5
430_200_160_35_20_6_2.5
430_200_160_35_20_7_2.5
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
185000
424
424
424
424
424
424
424
424
424
424
424
424
424
424
424
424
424
424
424
424
424
424
424
424
424
424
424
424
424
424
424
424
424
1400
1200
1000
600
600
500
1800
1600
1200
3500
3000
3000
2500
3500
3000
2500
900
900
600
1000
700
800
1600
1400
900
900
700
600
1000
500
400
400
900
800
**L cr , centreline dimensions given for FE tests
Department of Civil Engineering
Research Report No R845
λd
Eo
MPa
75
P u,t
fu
kN
MPa
f u /f y
157
136
0.49
1.29 294
1.09 452
2.31 157
1.82 288
1.50 465
2.00 169
1.58 321
1.33 492
3.27 322
2.75 523
2.38 753
2.09 1071
2.54 640
2.22 932
1.98 1229
2.15 45
1.59 44
1.05 128
1.98 43
1.31 126
1.40 139
2.28 170
1.81 319
1.23 49
1.48 134
1.17 249
1.32 43
1.78 168
1.43 37
0.67 363
0.58 497
0.73 964
0.66 1207
172
200
101
125
152
105
134
156
63
78
90
106
93
109
120
116
131
194
106
157
170
112
141
165
137
173
167
153
158
286
314
272
296
0.62
0.73
0.37
0.45
0.55
0.38
0.49
0.57
0.23
0.28
0.33
0.39
0.34
0.40
0.44
0.42
0.48
0.71
0.38
0.57
0.62
0.41
0.51
0.60
0.50
0.63
0.61
0.55
0.57
1.04
1.14
0.99
1.08
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
Table A. 24. 3Cr12 Lipped Channels with Intermediate Stiffeners: Experimental
Material Properties
f pf
Test ID
3Cr12DS1a
3Cr12DS1b
fy
Eo
Geometric Properties**
f yc
L,L cr
Bw
Bf
Bl
di
r
Ag
Ac
A c /A g
mm
3.00
3.00
mm2
mm2
565
565
124
124
%
22
22
t
MPa MPa MPa MPa mm
mm mm mm mm mm
234 339 208000 606 1175 110.7 75.5 15.0 10.0 1.98
234 339 208000 606 1176 111.1 75.7 15.0 10.0 1.98
Test Results
f cr
λd
MPa
387 0.94
387 0.94
P u,t
fu
f u /f y
kN MPa
163 288 0.85
161 285 0.84
**L, overall dimensions and inner radius given for experimental tests and di is an approximation used for FE only
Table A. 25. 3Cr12 Lipped Channels with Intermediate Stiffeners: Flats
Material Properties
Test ID
3Cr12_200_160_25_10_2
3Cr12_200_160_25_10_3
3Cr12_200_160_25_10_4
3Cr12_400_160_25_10_2
3Cr12_400_160_25_10_3
3Cr12_400_160_25_10_4
3Cr12_400_160_25_20_2
3Cr12_400_160_25_20_3
3Cr12_400_160_25_20_4
3Cr12_800_400_40_15_3
3Cr12_800_400_40_15_4
3Cr12_800_400_40_15_5
3Cr12_800_400_40_15_6
3Cr12_800_400_40_30_4
3Cr12_800_400_40_30_5
3Cr12_800_400_40_30_6
3Cr12_150_100_10_10_1
3Cr12_150_70_15_10_1
3Cr12_150_70_15_10_2
3Cr12_200_80_15_10_1
3Cr12_200_80_15_10_2
3Cr12_150_110_15_10_2
3Cr12_300_200_20_15_2
3Cr12_300_200_20_15_3
3Cr12_100_70_20_10_1
3Cr12_250_95_20_10_2
3Cr12_250_95_20_10_3
3Cr12_100_60_10_10_1
3Cr12_200_150_15_15_2
3Cr12_90_60_10_5_1
3Cr12_150_70_15_10_4
3Cr12_150_70_15_10_5
3Cr12_200_160_35_20_6
3Cr12_200_160_35_20_7
Geometric Properties**
Test Results
f pf
fy
Eo
f yc
L,L cr
Bw
Bf
Bl
di
t
r
Ag
Ac
A c /A g
f cr
MPa
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
MPa
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
MPa
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
MPa
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
mm
1400
1200
1000
600
600
500
1800
1600
1200
3500
3000
3000
2500
3500
3000
2500
900
900
600
1000
700
800
1600
1400
900
900
700
600
1000
500
400
400
900
800
mm
200
200
200
400
400
400
400
400
400
800
800
800
800
800
800
800
150
150
150
200
200
150
300
300
100
250
250
100
200
90
150
150
200
200
mm
160
160
160
160
160
160
160
160
160
400
400
400
400
400
400
400
100
70
70
80
80
110
200
200
70
95
95
60
150
60
70
70
160
160
mm
25
25
25
25
25
25
25
25
25
40
40
40
40
40
40
40
10
15
15
15
15
15
20
20
20
20
20
10
15
10
15
15
35
35
mm
10
10
10
10
10
10
20
20
20
15
15
15
15
30
30
30
10
10
10
10
10
10
15
15
10
10
10
10
15
5
10
10
20
20
mm
2.00
3.00
4.00
2.00
3.00
4.00
2.00
3.00
4.00
3.00
4.00
5.00
6.00
4.00
5.00
6.00
1.00
1.00
2.00
1.00
2.00
2.00
2.00
3.00
1.00
2.00
3.00
1.00
2.00
1.00
4.00
5.00
6.00
7.00
mm
2.00
3.00
4.00
2.00
3.00
4.00
2.00
3.00
4.00
3.00
4.00
5.00
6.00
4.00
5.00
6.00
1.00
1.00
2.00
1.00
2.00
2.00
2.00
3.00
1.00
2.00
3.00
1.00
2.00
1.00
4.00
5.00
6.00
7.00
mm2
mm2
1177
1755
2327
1577
2355
3127
1626
2430
3227
5123
6769
8505
10186
6966
8691
10410
392
341
681
412
817
837
1542
2303
302
997
1485
262
1122
239
1327
1643
3721
4318
63
141
251
63
141
251
63
141
251
141
251
393
565
251
393
565
16
16
63
16
63
63
63
141
16
63
141
16
63
16
251
393
565
770
%
5.3
8.1
10.8
4.0
6.0
8.0
3.9
5.8
7.8
2.8
3.7
4.6
5.6
3.6
4.5
5.4
4.0
4.6
9.2
3.8
7.7
7.5
4.1
6.1
5.2
6.3
9.5
6.0
5.6
6.6
18.9
23.9
15.2
17.8
MPa
114
182
256
63
102
149
78
124
178
30
43
56
70
48
63
79
67
119
270
77
177
149
59
95
201
141
231
174
95
142
666
901
567
687
**L cr , centreline dimensions given for FE tests
Department of Civil Engineering
Research Report No R845
76
λd
P u,t
fu
f u /f y
1.51
1.20
1.01
2.03
1.60
1.32
1.82
1.45
1.21
2.93
2.47
2.16
1.92
2.33
2.03
1.81
1.97
1.48
0.98
1.83
1.21
1.32
2.10
1.65
1.14
1.36
1.06
1.22
1.65
1.35
0.62
0.54
0.68
0.62
kN
160
287
428
159
290
449
175
316
481
334
551
789
1008
658
929
1224
48
44
120
44
122
133
175
312
49
134
247
41
162
36
312
419
848
1032
MPa
136
164
184
101
123
144
107
130
149
65
81
93
99
94
107
118
122
128
176
107
150
160
114
136
162
135
166
158
145
151
235
255
228
239
0.52
0.63
0.71
0.39
0.47
0.55
0.41
0.50
0.57
0.25
0.31
0.36
0.38
0.36
0.41
0.45
0.47
0.49
0.68
0.41
0.58
0.61
0.44
0.52
0.62
0.52
0.64
0.61
0.56
0.58
0.90
0.98
0.88
0.92
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
Table A. 26. 3Cr12 Lipped Channels with Intermediate Stiffeners: r/t=1
Material Properties
Test ID
3Cr12_200_160_25_10_2_1
3Cr12_200_160_25_10_3_1
3Cr12_200_160_25_10_4_1
3Cr12_400_160_25_10_2_1
3Cr12_400_160_25_10_3_1
3Cr12_400_160_25_10_4_1
3Cr12_400_160_25_20_2_1
3Cr12_400_160_25_20_3_1
3Cr12_400_160_25_20_4_1
3Cr12_800_400_40_15_3_1
3Cr12_800_400_40_15_4_1
3Cr12_800_400_40_15_5_1
3Cr12_800_400_40_15_6_1
3Cr12_800_400_40_30_4_1
3Cr12_800_400_40_30_5_1
3Cr12_800_400_40_30_6_1
3Cr12_150_100_10_10_1_1
3Cr12_150_70_15_10_1_1
3Cr12_150_70_15_10_2_1
3Cr12_200_80_15_10_1_1
3Cr12_200_80_15_10_2_1
3Cr12_150_110_15_10_2_1
3Cr12_300_200_20_15_2_1
3Cr12_300_200_20_15_3_1
3Cr12_100_70_20_10_1_1
3Cr12_250_95_20_10_2_1
3Cr12_250_95_20_10_3_1
3Cr12_100_60_10_10_1_1
3Cr12_200_150_15_15_2_1
3Cr12_90_60_10_5_1_1
3Cr12_150_70_15_10_4_1
3Cr12_150_70_15_10_5_1
3Cr12_200_160_35_20_6_1
3Cr12_200_160_35_20_7_1
Geometric Properties**
Test Results
f pf
fy
Eo
f yc
L,L cr
Bw
Bf
Bl
di
t
r
Ag
Ac
A c /A g
f cr
MPa
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
MPa
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
MPa
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
MPa
460
460
460
460
460
460
460
460
460
460
460
460
460
460
460
460
460
460
460
460
460
460
460
460
460
460
460
460
460
460
460
460
460
460
mm
1400
1200
1000
600
600
500
1800
1600
1200
3500
3000
3000
2500
3500
3000
2500
900
900
600
1000
700
800
1600
1400
900
900
700
600
1000
500
400
400
900
800
mm
200
200
200
400
400
400
400
400
400
800
800
800
800
800
800
800
150
150
150
200
200
150
300
300
100
250
250
100
200
90
150
150
200
200
mm
160
160
160
160
160
160
160
160
160
400
400
400
400
400
400
400
100
70
70
80
80
110
200
200
70
95
95
60
150
60
70
70
160
160
mm
25
25
25
25
25
25
25
25
25
40
40
40
40
40
40
40
10
15
15
15
15
15
20
20
20
20
20
10
15
10
15
15
35
35
mm
10
10
10
10
10
10
20
20
20
15
15
15
15
30
30
30
10
10
10
10
10
10
15
15
10
10
10
10
15
5
10
10
20
20
mm
2.00
3.00
4.00
2.00
3.00
4.00
2.00
3.00
4.00
3.00
4.00
5.00
6.00
4.00
5.00
6.00
1.00
1.00
2.00
1.00
2.00
2.00
2.00
3.00
1.00
2.00
3.00
1.00
2.00
1.00
4.00
5.00
6.00
7.00
mm
2.00
3.00
4.00
2.00
3.00
4.00
2.00
3.00
4.00
3.00
4.00
5.00
6.00
4.00
5.00
6.00
1.00
1.00
2.00
1.00
2.00
2.00
2.00
3.00
1.00
2.00
3.00
1.00
2.00
1.00
4.00
5.00
6.00
7.00
mm2
mm2
1177
1755
2327
1577
2355
3127
1626
2430
3227
5123
6769
8505
10186
6966
8691
10410
392
341
681
412
817
837
1542
2303
302
997
1485
262
1122
239
1327
1643
3721
4318
63
141
251
63
141
251
63
141
251
141
251
393
565
251
393
565
16
16
63
16
63
63
63
141
16
63
141
16
63
16
251
393
565
770
%
5.3
8.1
10.8
4.0
6.0
8.0
3.9
5.8
7.8
2.8
3.7
4.6
5.6
3.6
4.5
5.4
4.0
4.6
9.2
3.8
7.7
7.5
4.1
6.1
5.2
6.3
9.5
6.0
5.6
6.6
18.9
23.9
15.2
17.8
MPa
114
182
256
63
102
149
78
124
178
30
43
56
70
48
63
79
67
119
270
77
177
149
59
95
201
141
231
174
95
142
666
901
567
687
**L cr , centreline dimensions given for FE tests
Department of Civil Engineering
Research Report No R845
77
λd
P u,t
fu
f u /f y
1.51
1.20
1.01
2.03
1.60
1.32
1.82
1.45
1.21
2.93
2.47
2.16
1.92
2.33
2.03
1.81
1.97
1.48
0.98
1.83
1.21
1.32
2.10
1.65
1.14
1.36
1.06
1.22
1.65
1.35
0.62
0.54
0.68
0.62
kN
163
296
448
161
296
462
178
324
495
340
562
806
1106
670
952
1257
49
44
125
45
126
137
178
321
50
137
255
42
167
37
347
479
918
1136
MPa
138
169
193
102
126
148
109
133
153
66
83
95
109
96
110
121
125
130
183
109
154
164
116
139
165
137
172
162
149
154
261
292
247
263
0.53
0.65
0.74
0.39
0.48
0.57
0.42
0.51
0.59
0.26
0.32
0.36
0.42
0.37
0.42
0.46
0.48
0.50
0.70
0.42
0.59
0.63
0.44
0.54
0.63
0.53
0.66
0.62
0.57
0.59
1.01
1.12
0.95
1.01
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
Table A. 27. 3Cr12 Lipped Channels with Intermediate Stiffeners: r/t=2.5
Material Properties
Test ID
3Cr12_200_160_25_10_2_2.5
3Cr12_200_160_25_10_3_2.5
3Cr12_200_160_25_10_4_2.5
3Cr12_400_160_25_10_2_2.5
3Cr12_400_160_25_10_3_2.5
3Cr12_400_160_25_10_4_2.5
3Cr12_400_160_25_20_2_2.5
3Cr12_400_160_25_20_3_2.5
3Cr12_400_160_25_20_4_2.5
3Cr12_800_400_40_15_3_2.5
3Cr12_800_400_40_15_4_2.5
3Cr12_800_400_40_15_5_2.5
3Cr12_800_400_40_15_6_2.5
3Cr12_800_400_40_30_4_2.5
3Cr12_800_400_40_30_5_2.5
3Cr12_800_400_40_30_6_2.5
3Cr12_150_100_10_10_1_2.5
3Cr12_150_70_15_10_1_2.5
3Cr12_150_70_15_10_2_2.5
3Cr12_200_80_15_10_1_2.5
3Cr12_200_80_15_10_2_2.5
3Cr12_150_110_15_10_2_2.5
3Cr12_300_200_20_15_2_2.5
3Cr12_300_200_20_15_3_2.5
3Cr12_100_70_20_10_1_2.5
3Cr12_250_95_20_10_2_2.5
3Cr12_250_95_20_10_3_2.5
3Cr12_100_60_10_10_1_2.5
3Cr12_200_150_15_15_2_2.5
3Cr12_90_60_10_5_1_2.5
3Cr12_150_70_15_10_4_2.5
3Cr12_150_70_15_10_5_2.5
3Cr12_200_160_35_20_6_2.5
3Cr12_200_160_35_20_7_2.5
Geometric Properties**
Test Results
f pf
fy
Eo
f yc
L,L cr
Bw
Bf
Bl
di
t
r
Ag
MPa
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
170
MPa
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
MPa
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
210000
MPa
406
406
406
406
406
406
406
406
406
406
406
406
406
406
406
406
406
406
406
406
406
406
406
406
406
406
406
406
406
406
406
406
406
406
mm
1400
1200
1000
600
600
500
1800
1600
1200
3500
3000
3000
2500
3500
3000
2500
900
900
600
1000
700
800
1600
1400
900
900
700
600
1000
500
400
400
900
800
mm
200
200
200
400
400
400
400
400
400
800
800
800
800
800
800
800
150
150
150
200
200
150
300
300
100
250
250
100
200
90
150
150
200
200
mm
160
160
160
160
160
160
160
160
160
400
400
400
400
400
400
400
100
70
70
80
80
110
200
200
70
95
95
60
150
60
70
70
160
160
mm
25
25
25
25
25
25
25
25
25
40
40
40
40
40
40
40
10
15
15
15
15
15
20
20
20
20
20
10
15
10
15
15
35
35
mm
10
10
10
10
10
10
20
20
20
15
15
15
15
30
30
30
10
10
10
10
10
10
15
15
10
10
10
10
15
5
10
10
20
20
mm
2.00
3.00
4.00
2.00
3.00
4.00
2.00
3.00
4.00
3.00
4.00
5.00
6.00
4.00
5.00
6.00
1.00
1.00
2.00
1.00
2.00
2.00
2.00
3.00
1.00
2.00
3.00
1.00
2.00
1.00
4.00
5.00
6.00
7.00
mm
5.00
7.50
9.00
5.00
7.50
9.00
5.00
7.50
10.00
7.50
10.00
12.50
12.00
10.00
12.50
15.00
2.50
2.50
5.00
2.50
5.00
5.00
5.00
7.50
2.50
5.00
7.50
2.50
5.00
2.50
8.50
8.50
15.00
17.50
mm
mm
1157
1711
2262
1557
2311
3062
1607
2386
3148
5078
6739
8382
10069
6888
8569
10234
387
337
657
407
797
817
1522
2258
297
977
1441
257
1102
234
1268
1586
3545
4078
157
353
565
157
353
565
157
353
628
353
628
982
1131
628
982
1414
39
39
157
39
157
157
157
353
39
157
353
39
157
39
534
668
1414
1924
**centreline dimensions given for FE tests
Department of Civil Engineering
Research Report No R845
78
Ac
2
2
A c /A g
f cr
%
13.6
20.7
25.0
10.1
15.3
18.5
9.8
14.8
20.0
7.0
9.3
11.7
11.2
9.1
11.5
13.8
10.2
11.7
23.9
9.7
19.7
19.2
10.3
15.6
13.2
16.1
24.5
15.3
14.3
16.8
42.1
42.1
39.9
47.2
MPa
117
188
264
58
94
139
78
124
176
29
41
55
72
48
63
80
68
124
285
80
183
159
60
95
206
143
229
180
99
152
694
932
588
717
λd
P u,t
fu
f u /f y
1.49
1.18
0.99
2.11
1.66
1.37
1.82
1.45
1.22
2.99
2.51
2.17
1.90
2.32
2.03
1.80
1.96
1.45
0.96
1.81
1.19
1.28
2.08
1.66
1.12
1.35
1.07
1.20
1.62
1.31
0.61
0.53
0.66
0.60
kN
163
300
454
161
298
478
179
325
497
339
541
776
1110
674
953
1255
49
45
130
45
129
139
179
323
50
138
256
43
168
38
358
485
949
1184
MPa
141
175
201
103
129
156
111
136
158
67
80
93
110
98
111
123
127
135
198
111
161
170
118
143
169
141
178
168
153
160
282
306
268
290
0.54
0.67
0.77
0.40
0.50
0.60
0.43
0.52
0.61
0.26
0.31
0.36
0.42
0.38
0.43
0.47
0.49
0.52
0.76
0.43
0.62
0.65
0.45
0.55
0.65
0.54
0.68
0.65
0.59
0.62
1.09
1.18
1.03
1.12
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
Table A. 28. FE Test Results Summary: 304 Lipped Channels with Intermediate Stiffeners
Test ID
304_200_160_25_10_2
304_200_160_25_10_3
304_200_160_25_10_4
304_400_160_25_10_2
304_400_160_25_10_3
304_400_160_25_10_4
304_400_160_25_20_2
304_400_160_25_20_3
304_400_160_25_20_4
304_800_400_40_15_3
304_800_400_40_15_4
304_800_400_40_15_5
304_800_400_40_15_6
304_800_400_40_30_4
304_800_400_40_30_5
304_800_400_40_30_6
304_150_100_10_10_1
304_150_70_15_10_1
304_150_70_15_10_2
304_200_80_15_10_1
304_200_80_15_10_2
304_150_110_15_10_2
304_300_200_20_15_2
304_300_200_20_15_3
304_100_70_20_10_1
304_250_95_20_10_2
304_250_95_20_10_3
304_100_60_10_10_1
304_200_150_15_15_2
304_90_60_10_5_1
304_150_70_15_10_4
304_150_70_15_10_5
304_200_160_35_20_6
304_200_160_35_20_7
Department of Civil Engineering
Research Report No R845
flats
P flats
kN
116
215
328
116
211
328
128
232
355
252
408
577
792
484
683
902
36
32
90
32
90
101
129
235
36
98
182
31
123
27
250
330
669
817
A c /A g
%
5.3
8.1
10.8
4.0
6.0
8.0
3.9
5.8
7.8
2.8
3.7
4.6
5.6
3.6
4.5
5.4
4.0
4.6
9.2
3.8
7.7
7.5
4.1
6.1
5.2
6.3
9.5
6.0
5.6
6.6
18.9
23.9
15.2
17.8
λd
1.35
1.08
0.91
1.83
1.43
1.19
1.64
1.30
1.09
2.63
2.22
1.94
1.73
2.09
1.83
1.63
1.77
1.33
0.88
1.65
1.09
1.19
1.89
1.49
1.02
1.22
0.95
1.10
1.48
1.02
0.56
0.48
0.61
0.55
r/t=1
P r/t=1
kN
121
227
352
119
221
347
133
244
379
258
423
603
829
503
715
952
37
33
96
33
95
107
133
247
37
102
193
32
128
28
291
408
757
950
79
P r/t=1 /P flats
1.04
1.06
1.07
1.03
1.05
1.06
1.03
1.05
1.07
1.03
1.04
1.04
1.05
1.04
1.05
1.06
1.03
1.03
1.07
1.03
1.06
1.06
1.03
1.05
1.03
1.05
1.06
1.05
1.05
1.05
1.16
1.24
1.13
1.16
A c /A g
%
13.6
20.7
25.0
10.1
15.3
18.5
9.8
14.8
20.0
7.0
9.3
11.7
11.2
9.1
11.5
13.8
10.2
11.7
23.9
9.7
19.7
19.2
10.3
15.6
13.2
16.1
24.5
15.3
14.3
16.8
42.1
42.1
39.9
47.2
λd
1.34
1.06
0.89
1.90
1.50
1.23
1.64
1.30
1.09
2.69
2.26
1.95
1.71
2.08
1.82
1.62
1.76
1.30
0.86
1.62
1.07
1.15
1.87
1.49
1.01
1.21
0.96
1.08
1.46
0.98
0.55
0.47
0.60
0.54
r/t=2.5
P r/t=2.5
kN
122
228
356
121
227
360
135
248
384
255
391
590
832
509
721
958
37
34
100
34
98
109
134
249
37
104
196
33
131
29
302
413
793
1009
P r/t=2.5 /P flats
1.05
1.06
1.09
1.04
1.08
1.10
1.05
1.07
1.08
1.01
0.96
1.02
1.05
1.05
1.06
1.06
1.05
1.06
1.11
1.05
1.08
1.08
1.04
1.06
1.05
1.06
1.07
1.07
1.07
1.07
1.21
1.25
1.19
1.23
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
Table A. 29. FE Test Results Summary: 430 Lipped Channels with Intermediate Stiffeners
Test ID
430_200_160_25_10_2
430_200_160_25_10_3
430_200_160_25_10_4
430_400_160_25_10_2
430_400_160_25_10_3
430_400_160_25_10_4
430_400_160_25_20_2
430_400_160_25_20_3
430_400_160_25_20_4
430_800_400_40_15_3
430_800_400_40_15_4
430_800_400_40_15_5
430_800_400_40_15_6
430_800_400_40_30_4
430_800_400_40_30_5
430_800_400_40_30_6
430_150_100_10_10_1
430_150_70_15_10_1
430_150_70_15_10_2
430_200_80_15_10_1
430_200_80_15_10_2
430_150_110_15_10_2
430_300_200_20_15_2
430_300_200_20_15_3
430_100_70_20_10_1
430_250_95_20_10_2
430_250_95_20_10_3
430_100_60_10_10_1
430_200_150_15_15_2
430_90_60_10_5_1
430_150_70_15_10_4
430_150_70_15_10_5
430_200_160_35_20_6
430_200_160_35_20_7
Department of Civil Engineering
Research Report No R845
flats
P flats A c /A g
kN
%
5.3
155
8.1
284
10.8
431
4.0
154
6.0
282
8.0
439
3.9
167
5.8
312
7.8
476
2.8
316
3.7
527
4.6
762
5.6
1049
3.6
625
4.5
907
5.4
1198
4.0
44
4.6
43
9.2
118
3.8
42
7.7
121
7.5
134
4.1
170
6.1
310
5.2
48
6.3
131
9.5
241
6.0
41
5.6
162
6.6
36
18.9
322
23.9
434
15.2
873
1068 17.8
λd
1.65
1.31
1.10
2.23
1.75
1.45
2.00
1.59
1.32
3.21
2.71
2.37
2.11
2.55
2.23
1.98
2.16
1.62
1.07
2.01
1.33
1.45
2.30
1.81
1.25
1.49
1.16
1.34
1.81
1.48
0.68
0.59
0.74
0.67
r/t=1
P r/t=1
kN
157
292
448
155
288
452
170
319
491
323
538
780
1075
635
930
1233
48
43
123
42
124
134
171
319
48
134
248
42
167
37
353
491
937
1165
80
P r/t=1 /P flats
1.02
1.03
1.04
1.01
1.02
1.03
1.02
1.02
1.03
1.02
1.02
1.02
1.03
1.02
1.03
1.03
1.09
1.02
1.04
1.02
1.03
1.00
1.01
1.03
1.01
1.02
1.03
1.02
1.03
1.02
1.10
1.13
1.07
1.09
A c /A g
%
13.6
20.7
25.0
10.1
15.3
18.5
9.8
14.8
20.0
7.0
9.3
11.7
11.2
9.1
11.5
13.8
10.2
11.7
23.9
9.7
19.7
19.2
10.3
15.6
13.2
16.1
24.5
15.3
14.3
16.8
42.1
42.1
39.9
47.2
λd
1.63
1.29
1.09
2.31
1.82
1.50
2.00
1.58
1.33
3.27
2.75
2.38
2.09
2.54
2.22
1.98
2.15
1.59
1.05
1.98
1.31
1.40
2.28
1.81
1.23
1.48
1.17
1.32
1.78
1.43
0.67
0.58
0.73
0.66
r/t=2.5
P r/t=2.5
kN
157
294
452
157
288
465
169
321
492
322
523
753
1071
640
932
1229
45
44
128
43
126
139
170
319
49
134
249
43
168
37
363
497
964
1207
P r/t=2.5 /P flats
1.01
1.03
1.05
1.02
1.02
1.06
1.01
1.03
1.03
1.02
0.99
0.99
1.02
1.02
1.03
1.03
1.02
1.03
1.08
1.03
1.04
1.04
1.00
1.03
1.02
1.03
1.04
1.04
1.04
1.03
1.13
1.15
1.10
1.13
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
Table A. 30. FE Test Results Summary: 3Cr12 Lipped Channels with Intermediate Stiffeners
Test ID
3Cr12_200_160_25_10_2
3Cr12_200_160_25_10_3
3Cr12_200_160_25_10_4
3Cr12_400_160_25_10_2
3Cr12_400_160_25_10_3
3Cr12_400_160_25_10_4
3Cr12_400_160_25_20_2
3Cr12_400_160_25_20_3
3Cr12_400_160_25_20_4
3Cr12_800_400_40_15_3
3Cr12_800_400_40_15_4
3Cr12_800_400_40_15_5
3Cr12_800_400_40_15_6
3Cr12_800_400_40_30_4
3Cr12_800_400_40_30_5
3Cr12_800_400_40_30_6
3Cr12_150_100_10_10_1
3Cr12_150_70_15_10_1
3Cr12_150_70_15_10_2
3Cr12_200_80_15_10_1
3Cr12_200_80_15_10_2
3Cr12_150_110_15_10_2
3Cr12_300_200_20_15_2
3Cr12_300_200_20_15_3
3Cr12_100_70_20_10_1
3Cr12_250_95_20_10_2
3Cr12_250_95_20_10_3
3Cr12_100_60_10_10_1
3Cr12_200_150_15_15_2
3Cr12_90_60_10_5_1
3Cr12_150_70_15_10_4
3Cr12_150_70_15_10_5
3Cr12_200_160_35_20_6
3Cr12_200_160_35_20_7
Department of Civil Engineering
Research Report No R845
flats
P flats A c /A g
kN
%
5.3
160
8.1
287
10.8
428
4.0
159
6.0
290
8.0
449
3.9
175
5.8
316
7.8
481
2.8
334
3.7
551
4.6
789
5.6
1008
3.6
658
4.5
929
5.4
1224
4.0
48
4.6
44
9.2
120
3.8
44
7.7
122
7.5
133
4.1
175
6.1
312
5.2
49
6.3
134
9.5
247
6.0
41
5.6
162
6.6
36
18.9
312
23.9
419
15.2
848
1032 17.8
λd
1.51
1.20
1.01
2.03
1.60
1.32
1.82
1.45
1.21
2.93
2.47
2.16
1.92
2.33
2.03
1.81
1.97
1.48
0.98
1.83
1.21
1.32
2.10
1.65
1.14
1.36
1.06
1.22
1.65
1.35
0.62
0.54
0.68
0.62
81
r/t=1
P r/t=1
kN
163
296
448
161
296
462
178
324
495
340
562
806
1106
670
952
1257
49
44
125
45
126
137
178
321
50
137
255
42
167
37
347
479
918
1136
P r/t=1 /P flats
1.01
1.03
1.05
1.01
1.02
1.03
1.02
1.02
1.03
1.02
1.02
1.02
1.10
1.02
1.02
1.03
1.02
1.02
1.04
1.02
1.03
1.03
1.02
1.03
1.02
1.02
1.03
1.03
1.03
1.02
1.11
1.14
1.08
1.10
A c /A g
%
13.6
20.7
25.0
10.1
15.3
18.5
9.8
14.8
20.0
7.0
9.3
11.7
11.2
9.1
11.5
13.8
10.2
11.7
23.9
9.7
19.7
19.2
10.3
15.6
13.2
16.1
24.5
15.3
14.3
16.8
42.1
42.1
39.9
47.2
λd
1.49
1.18
0.99
2.11
1.66
1.37
1.82
1.45
1.22
2.99
2.51
2.17
1.90
2.32
2.03
1.80
1.96
1.45
0.96
1.81
1.19
1.28
2.08
1.66
1.12
1.35
1.07
1.20
1.62
1.31
0.61
0.53
0.66
0.60
r/t=2.5
P r/t=2.5
kN
163
300
454
161
298
478
179
325
497
339
541
776
1110
674
953
1255
49
45
130
45
129
139
179
323
50
138
256
43
168
38
358
485
949
1184
P r/t=2.5 /P flats
1.02
1.04
1.06
1.01
1.03
1.06
1.02
1.03
1.03
1.01
0.98
0.98
1.10
1.02
1.03
1.03
1.03
1.04
1.09
1.02
1.05
1.04
1.02
1.03
1.03
1.02
1.04
1.05
1.04
1.04
1.15
1.16
1.12
1.15
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
Appendix B
This appendix shows the evaluation of current design codes for simple lipped channels and
channels with intermediate stiffeners. The stainless steel codes considered are the AS/NZS
4673 (2001) which is equivalent to the ASCE (2002) and the Eurocode 3 Part1-4 (2004)/Part 13 (2004). The cold-formed carbon steel codes AS/NZS 4600 (1996) and NAS (2001) and NAS
Appendix 1 (2004) are also considered and references to applicable clauses are provided. The
general notation used in the following pages are shown below. NOTE that EC3 code uses
centreline dimensions in calculations. Also, the sections used for FE analyses are defined at the
centreline (see Appendix A).
Bl
Bf
rm
id
t
Bw
r
Figure B. 1. General Cross-Section Notation for Simple Lipped Channels*
f
Bl
0.5Bf
0.5Bw
di
Bw
rmid
rmid
r
2di
Figure B. 2. General Cross-Section Notation for Lipped Channels with Intermediate Stiffeners*
*NB: ABAQUS cross-section dimensions given in APPENDIX A are centreline dimensions
Department of Civil Engineering
Research Report No R845
82
April 2005
bw2
bw
Bw
bw
Bw
bw1
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
Figure B. 3. General Symbols used for Web Elements*
*NB: EC3 uses centreline widths
Bf
bf1
bl
Bl
bl
Bl
bf
bf2
bf
Bf
Figure B. 4. General Symbols used for Flange and Lip Elements*
*NB: EC3 uses centreline widths
Department of Civil Engineering
Research Report No R845
83
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
EFFECTIVE WIDTH CALCULATIONS FOR SIMPLE LIPPED
CHANNELS: AS/NZS 4673 (EQUIVALENT TO ASCE
2002)
Cross-section and Material Properties
Thickness
Inner Corner Radius
Centerline Corner Radius
Web overall width
Flange Overall width
Lip Overall length
0.2% Yield Stress of flats
0.2% Yield Stress of corners
Initial Modulus of Elasticity
WEB
t := 1.96mm
r := 4mm
rmid := 4.98mm
Bw := 106.3 ⋅mm
Bf := 90.2 ⋅mm
Bl := 12.7 ⋅mm
fy := 242 ⋅MPa
fycrns := 565MPa
E0 := 187000 ⋅MPa
(CL 2.2.1)
bw := Bw − 2( t + r)
bw = 94.38 mm
kw := 4
1.052 ⋅
λ w :=
bw
t
⋅
fy
E0
kw
⎡⎢
⎛ 1 − 0.22 ⎞ ⎥⎤
⎜
λw ⎠ ⎥
⎢
⎝
ρ w := if λ w < 0.673 , 1 ,
⎢
⎥
λw
⎣
⎦
bew := ρ w ⋅bw
λ w = 0.911
Eqn. 2.2.1.2(4).
ρ w = 0.833
Eqn. 2.2.1.2(3)
bew = 78.572 mm Eqn. 2.2.1.2(2)
FLANGES (CL 2.4.3)
S := 1.28 ⋅
E0
fy
Department of Civil Engineering
Research Report No R845
S = 35.581
Eqn. 2.4.1(3)
84
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
bf := Bf − 2 ⋅( t + r)
April 2005
bf = 78.28 mm
bf
= 39.939
t
bl := Bl − ( t + r)
θ := 90 ⋅
Ia :=
bl = 6.74 mm
π
180
3
Is := bl ⋅t ⋅
bf
0 if
4
Is = 50.01 mm
12
S
3
≤
t
( sin( θ ) ) 2
3
4
Ia = 1.979 × 10 mm
3
⎞
⎛ bf
⎜ t
ku
bf
bf
S
4
399 ⋅⎜
−
⋅t if
< S∧
>
3
4 ⎠
t
t
⎝ S
⎡⎡
⎛ bf ⎞ ⎤ ⎤
⎜
⎢⎢
⎥ ⎥
⎢⎢115 ⋅ ⎝ t ⎠ + 5⎥ ⋅t4⎥ otherwise
S
⎣⎣
⎦ ⎦
⎛ Is
C2 := min⎜
,1
⎞
C2 = 0.025
⎝ Ia ⎠
⎡
kf :=
4 if
⎛ bl ⎞ ⎤
, 4⎥
⎝ bf ⎠ ⎦
ka := min⎢5.25 − 5 ⋅⎜
ku := 0.43
⎣
bf
t
≤
ka = 4
S
3
( C2) 0.5⋅( ka − ku) + ku
kf = 1.479
bf
⎛ bf
S⎞
< S∧
>
t
3⎠
⎝ t
if ⎜
⎡⎣( C2) 0.333⋅( ka − ku) + ku⎤⎦ otherwise
1.052 ⋅
λ f :=
bf
t
⋅
fy
E0
λ f = 1.243
kf
⎡⎢
⎛ 1 − 0.22 ⎞ ⎥⎤
⎜
λf ⎠ ⎥
⎢
⎝
ρ f := if λ f < 0.673 , 1 ,
⎢
⎥
λf
⎣
⎦
Department of Civil Engineering
Research Report No R845
ρ f = 0.662
85
Eqn. 2.2.1.2(4).
Eqn. 2.2.1.2(3)
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
bef := ρ f ⋅bf
April 2005
bef = 51.835 mm Eqn. 2.2.1.2(2)
LIP (CL 2.4.3)
bl := Bl − ( r + t)
bl = 6.74 mm
kl := 0.5
1.052 ⋅
λ l :=
bl
t
⋅
fy
E0
λ l = 0.184
kl
⎡⎢
⎛ 1 − 0.22 ⎞ ⎤⎥
⎜
λl ⎠ ⎥
⎢
⎝
ρ l := if λ l < 0.673 , 1 ,
⎢
⎥
λl
⎣
⎦
bele := ρ l⋅bl
bel :=
Eqn. 2.2.1.2(4).
ρl = 1
bele = 6.74 mm
bele if
bf
t
≤
S
3
bel = 0.17 mm
bf
⎛ bf
S⎞
< S∧
>
t
3⎠
⎝ t
C2 ⋅bele if ⎜
C2 ⋅bele otherwise
TOTAL EFFECTIVE AREA
Aeflats := t ⋅( bew + 2 ⋅bef + 2 ⋅bel)
⎛
⎝
Aecrns := 2π t ⋅⎜ r +
t⎞
2⎠
Aetotal := Aeflats + Aecrns
2
Aeflats = 357.9 mm
2
Aecrns = 61.3 mm
2
Aetotal = 419.2 mm
PREDICTED LOADS
Without Enhanced Corner Properties
Pn := Aetotal ⋅fy
Pn = 101.4 kN
With Enhanced Corner Properties
Department of Civil Engineering
Research Report No R845
86
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
Pn := Aeflats ⋅fy + Aecrns ⋅fycrns
Department of Civil Engineering
Research Report No R845
Pn = 121.3 kN
87
April 2005
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
EFFECTIVE WIDTH CALCULATIONS FOR SIMPLE LIPPED
CHANNELS: NAS (2001)
Cross-section and Material Properties
Thickness
Inner Corner Radius
Centerline Corner Radius
Web overall width
Flange Overall width
Lip Overall length
0.2% Yield Stress of flats
0.2% Yield Stress of corners
Initial Modulus of Elasticity
WEB
t := 1.96mm
r := 4mm
rmid := 4.98mm
Bw := 106.3 ⋅mm
Bf := 90.2 ⋅mm
Bl := 12.7 ⋅mm
fy := 242 ⋅MPa
fycrns := 565MPa
E0 := 187000 ⋅MPa
(CL B2.1)
bw := Bw − 2( t + r)
bw = 94.38 mm
kw := 4
1.052 ⋅
λ w :=
bw
t
⋅
fy
E0
kw
⎡⎢
⎛ 1 − 0.22 ⎞ ⎥⎤
⎜
λw ⎠ ⎥
⎢
⎝
ρ w := if λ w < 0.673 , 1 ,
⎢
⎥
λw
⎣
⎦
bew := ρ w ⋅bw
λ w = 0.911
Eqns. B2.1-4&B2.1-5
ρ w = 0.833
Eqn. B2.1-3
bew = 78.572 mm
Eqn. B2.1-2
FLANGES (CL B4.2)
S := 1.28 ⋅
E0
fy
bf := Bf − 2 ⋅( t + r)
Department of Civil Engineering
Research Report No R845
S = 35.581
Eqn. B4-1
bf = 78.28 mm
88
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
bf
= 39.939
t
bl := Bl − ( t + r)
θ := 90 ⋅
Ia :=
bl = 6.74 mm
π
180
3
Is := bl ⋅t ⋅
bf
0 if
( sin( θ ) ) 2
4
Is = 50.01 mm
12
Eqn. B4-2
3
≤ 0.328S
t
4
Ia = 1.979 × 10 mm
3
⎡⎡
bf
⎛ bf
⎞ ⎤⎥ ⎛
⎢⎢
⎜ t
⎜
t
4 4
min⎢ ⎢399 ⋅⎜
− 0.327 ⋅t ⎥ , t ⎜ 5 + 115 ⋅
S
⎣⎣
⎝ S
⎠ ⎦ ⎝
⎞ ⎤⎥
bf
⎥ if
> 0.328S
t
⎠⎦
Eqns. B4.2-1&B4-2-10
bf ⎞
⎤
⎡⎛
⎢⎜
1⎥
t
n := max⎢⎜ 0.582 −
, ⎥
4S ⎠ 3 ⎦
⎣⎝
⎛ Is
R1 := min⎜
⎝ Ia
kf :=
,1
⎞
⎠
(
n
min 3.57 ⋅R1 + 0.43 , 4
⎡⎡⎛
Bl ⎞
⎣⎣⎝
bf ⎠
min⎢⎢⎜ 4.82 − 5
1.052 ⋅
λ f :=
bf
t
⋅
)
if
Bl
bf
n
≤ 0.25
n = 0.333
Eqn. B4-2-11
R1 = 0.025
Eqn. B4.2-9
kf = 1.478
⎤ ⎤
Bl
⎦ ⎦
bf
R1 + 0.43⎥ , 4⎥ if 0.25 <
Table B4.2
≤ 0.8
fy
E0
λ f = 1.243
kf
⎡⎢
⎛ 1 − 0.22 ⎞ ⎥⎤
⎜
λf ⎠ ⎥
⎢
⎝
ρ f := if λ f < 0.673 , 1 ,
⎢
⎥
λf
⎣
⎦
bef := ρ f ⋅bf
ρ f = 0.662
Eqn. B2.1-3
bef = 51.835 mm
Eqn. B2.1-2
LIP (CL B4.2)
bl := Bl − ( r + t)
Department of Civil Engineering
Research Report No R845
bl = 6.74 mm
89
Eqns. B2.1-4&B2.1-5
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
kl := 0.43
1.052 ⋅
λ l :=
bl
t
⋅
fy
E0
kl
⎡⎢
⎛ 1 − 0.22 ⎞ ⎤⎥
⎜
λl ⎠ ⎥
⎢
⎝
ρ l := if λ l < 0.673 , 1 ,
⎢
⎥
λl
⎣
⎦
bele := ρ l⋅bl
bel :=
bele if
bf
t
≤ 0.328S
λ l = 0.198
Eqns. B2.1-4&B2.1-5
ρl = 1
Eqn. B2.1-3
bele = 6.74 mm
Eqn. B2.1-2
bel = 0.17 mm
Eqns. B4.2-3&B4.2-7
⎛ bf
⎞
> 0.328S
⎝ t
⎠
R1⋅bele if ⎜
TOTAL EFFECTIVE AREA
Aeflats := t ⋅( bew + 2 ⋅bef + 2 ⋅bel)
⎛
⎝
Aecrns := 2π t ⋅⎜ r +
t⎞
2⎠
Aetotal := Aeflats + Aecrns
2
Aeflats = 357.8 mm
2
Aecrns = 61.3 mm
2
Aetotal = 419.1 mm
PREDICTED LOADS
Without Enhanced Corner Properties
Pn := Aetotal ⋅fy
Pn = 101.4 kN
With Enhanced Corner Properties
Pn := Aeflats ⋅fy + Aecrns ⋅fycrns
Department of Civil Engineering
Research Report No R845
Pn = 121.2 kN
90
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
EFFECTIVE WIDTH CALCULATIONS FOR SIMPLE LIPPED
CHANNELS: EUROCODE 3 PART 1-4/PART 1-3
Cross-section and Material Properties
Thickness
Inner Corner Radius
Centerline Corner Radius
Web overall width
Flange Overall width
Lip Overall length
0.2% Yield Stress of flats
0.2% Yield Stress of corners
Initial Modulus of Elasticity
Poisson’s Ratio
t := 1.96mm
r := 4mm
t
rmid := r +
2
rmid := 4.98mm
Bw := 106.3mm
Bf := 90.2mm
Bl := 12.7mm
fy := 242 ⋅ MPa
fycrn := 565 ⋅ MPa
E0 := 187000 ⋅ MPa
υ := 0.3
Notional Dimensions taking into account rounded corners CL 5.1 Part 1-3
1 ⎞ ⎤
⎡
⎛
bf := if⎢ r ≤ 5t ∧ r ≤ 0.1 ⋅ ( Bf − t) , ( Bf − t) , Bf − ( rmid) ⋅ ⎜ 1 −
⋅ 2⎥
bf = 88.2 mm
2⎠ ⎦
⎣
⎝
⎡
⎣
⎛
⎝
bw := if⎢ r ≤ 5t ∧ r ≤ 0.1 ⋅ ( Bw − t) , ( Bw − t) , Bw − ( rmid) ⋅ ⎜ 1 −
⎡
⎣
⎛
⎝
bl := if⎢ r ≤ 5t ∧ r ≤ 0.1 ⋅ ⎜ Bl −
1 ⎞
2⎠
⎤
⎦
⋅ 2⎥
t⎞ ⎛
t⎞
1 ⎞⎤
⎛
, ⎜ Bl −
, ( Bl) − ( rmid) ⋅ ⎜ 1 −
⎥
2⎠ ⎝
2⎠
2⎠⎦
⎝
bw = 104.3 mm
bl = 11.2 mm
Estimated Gross Area
A := ( 2 ⋅ bl + 2bf + bw) ⋅ t
Department of Civil Engineering
Research Report No R845
2
A = 594 mm
91
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
WEB (CL 5.5.2 Part 1-3)
⎛ 235 ⋅ E ⎞
⎝ fy ⋅ 210000 ⎠
λ p.w :=
.5
ε := ⎜
kw := 4
bw
t
⋅
1
λ p.w = 1.007
28.4 ⋅ ε ⋅ kw
⎡⎢
⎛⎜ 0.772 − 0.125 ⎞⎤⎥
λ p.w ⎟⎥
⎢
⎜
ρ w := if λ p.w < 0.673 , 1 ,
⎢
⎜
⎥
λ p.w
⎣
⎝
⎠⎦
ρ w = 0.643
bew := ρ w ⋅ bw
bew1 := 0.5 ⋅ bew
bew = 67.118 mm
bew2 := 0.5 ⋅ bew
bew2 = 33.6 mm
bew1 = 33.6 mm
Initial Effective-Width Calculations assuming flanges are doubly supported CL
5.5.3.2 (3) Part 1-3 with λ and ρ from CL 5.2.3 Part 1-4
FLANGES (CL 5.2.3 Part 1-4)
⎛ 235 ⋅ E ⎞
⎝ fy ⋅ 210000 ⎠
.5
ε := ⎜
λ p.f :=
bf
t
⋅
kf := 4
1
λ p.f = 0.852
28.4 ⋅ ε ⋅ kf
⎡⎢
⎛⎜ 0.772 − 0.125 ⎞⎤⎥
λ p.f ⎟⎥
⎢
⎜
ρ f := if λ p.f < 0.673 , 1 ,
⎢
⎜
⎥
λ p.f
⎣
⎝
⎠⎦
ρ f = 0.734
bef := ρ f ⋅ bf
bef1 := 0.5 ⋅ bef
bef = 64.739 mm
bef2 := 0.5 ⋅ bef
bef2 = 32.4 mm
Department of Civil Engineering
Research Report No R845
bef1 = 32.4 mm
92
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
LIPS (CL 5.5.3.2 (5) Part 1-3 and 5.2.3 Part 1-4)
⎛ 235 ⋅ E ⎞
⎝ fy ⋅ 210000 ⎠
.5
ε := ⎜
2⎤
⎡⎢
⎥
3
⎛ bl
⎞ ⎥
⎢ bl
kl := if
⎢ bf < 0.35 , 0.5 , 0.5 + 0.83 ⋅ ⎜ bf − 0.35 ⎥
⎣
⎝
⎠ ⎦
λ p.l :=
bl
t
⋅
1
kl = 0.5
λ p.l = 0.307
28.4 ⋅ ε ⋅ kl
⎡⎢
⎛⎜ 1.0 − 0.231 ⎞⎤⎥
λ p.l ⎟⎥
⎢
⎜
ρ l := if λ p.l < 0.673 , 1 ,
⎢
⎜
⎥
λ p.l
⎣
⎝
⎠⎦
ρl = 1
bel := ρ l ⋅ bl
bel = 11.2 mm
Initial effective area of stiffeners CL 5.5.3.2 (6) Part 1-3
As1 := t ⋅ ( bef2 + bel)
2
As1 = 85.5 mm
Spring Stiffness and Critical Stress Calculation for Edge Stiffener CL 5.5.3.1 Part 1-3
2
(
bef2 + bel ⋅ t)
x1 :=
x1 = 12.27 mm
2 ⋅ ( bef2 + bel)
y1 :=
( bel2 + bef2 ⋅ t)
y1 = 2.18 mm
2 ⋅ ( bef2 + bel)
B1 = 75.97 mm
B1 := bf − x1
kf1 := 1
3
K1 :=
E0 ⋅ t
(
4⋅ 1 − υ
)
2
⋅
1
2
3
2
B1 ⋅ bw + B1 + 0.5 ⋅ B1 ⋅ bw ⋅ kf1
Department of Civil Engineering
Research Report No R845
93
K1 = 0.2883
N
2
mm
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
⎛ bel
⎞
t
t⎞
3 t
⎛
+ bel ⋅
+ bef2 ⋅ t ⋅ ⎜ y1 −
+ bel ⋅ t ⋅ ⎜
− y1
12
12
2⎠
⎝
⎝ 2
⎠
3
Is1 := bef2 ⋅
April 2005
2
2
4
Is1 = 605 mm
Elastic Critical Buckling Stress
σ cr.s1 :=
2 ⋅ K1 ⋅ E0 ⋅ Is1
σ cr.s1 = 134
As1
N
2
mm
Initial Reduction factor for distortional buckling CL 5.5.3.1 (7) Part 1-3
λ d1 :=
χ d1 :=
fy
λ d1 = 1.346
σ cr.s1
1 if λ d1 ≤ 0.65
( 1.47 − 0.723 ⋅ λ d1)
0.66
λ d1
if 0.65 < λ d1 < 1.38
if λ d1 ≥ 1.38
χ d1 = 0.497
Iterate for reduction factor -Stiffener CL 5.5.3.2 Part 1-3
Department of Civil Engineering
Research Report No R845
94
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
( )
x χ d1 :=
April 2005
λ p.f.red1 ← λ p.f ⋅ χ d1
0.125
⎡⎢
⎤⎥
0.772 −
λ
λ
−
λ
(
)
p.f.red1
p.f
p.f.red1 ⎥
⎢
ρ f ← if λ p.f.red1 < 0.673 , 1 ,
+ 0.18 ⋅
⎢
λ p.f.red1
( λ p.f − 0.6) ⎥⎦
⎣
bef ← ρ f ⋅ bf
bef2 ← 0.5 ⋅ bef
λ p.l.red1 ← λ p.l ⋅ χ d1
0.231
⎡⎢
⎤⎥
1.0 −
λ
λ
−
λ
(
)
p.l.red1
p.l
p.l.red1 ⎥
⎢
+ 0.18 ⋅
ρ l ← if λ p.l.red1 < 0.673 , 1 ,
⎢
λ
λ
−
( p.l 0.6) ⎥⎦
p.l.red1
⎣
bel ← bl ⋅ ρ l
x1 ←
( bef22 + bel ⋅ t)
2 ⋅ ( bef2 + bel)
2
(
bel + bef2 ⋅ t)
y1 ←
2 ⋅ ( bef2 + bel)
As1 ← t ⋅ ( bef2 + bel)
⎞
⎛ bel
t
t⎞
3 t
⎛
+ bel ⋅
+ bef2 ⋅ t ⋅ ⎜ y1 −
+ bel ⋅ t ⋅ ⎜
− y1
12
12
2⎠
⎝
⎝ 2
⎠
3
Is1 ← bef2 ⋅
2⋅
σ cr.s1 ←
λ d1 ←
χ d1 ←
2
( K1 ⋅ E0 ⋅ Is1)
As1
fy
σ cr.s1
1 if λ d1 ≤ 0.65
( 1.47 − 0.723 ⋅ λ d1)
0.66
λ d1
ans :=
if 0.65 < λ d1 < 1.38
if λ d1 ≥ 1.38
( )
χ d1 ← x χ d1
( )
χ d1 ← x( χ d1)
while χ d1 − x χ d1
( )
> 0.001 ∧ χ d1 < x χ d1
χ d1
χ d1 := ans
Department of Civil Engineering
Research Report No R845
χ d1 = 0.441
95
2
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
(
)
bef2temp λ p.f , χ d1 :=
April 2005
λ p.f.red1 ← λ p.f ⋅ χ d1
.125
⎡⎢
⎤⎥
0.772 −
λ
λ
−
λ
(
)
p.f.red1
p.f
p.f.red1 ⎥
⎢
ρ f ← if λ p.f.red1 < 0.673 , 1 ,
+ 0.18 ⋅
⎢
λ p.f.red1
( λ p.f − 0.6) ⎥⎦
⎣
bef ← ρ f ⋅ bf
bef2 ← 0.5 ⋅ bef
(
)
bef2temp λ p.f , χ d1 = 44.1 mm
(
bef2 := bef2temp λ p.f , χ d1
(
)
beltemp λ p.l , χ d1 :=
)
bef2 = 44.12 mm
λ p.c.red1 ← λ p.l ⋅ χ d1
0.231
⎡⎢
⎤⎥
1.0 −
λ p.c.red1
( λ p.l − λ p.c.red1) ⎥
⎢
ρ l ← if λ p.c.red1 < 0.673 , 1 ,
+ 0.18 ⋅
⎢
λ p.c.red1
( λ p.l − 0.6) ⎥⎦
⎣
bel ← bl ⋅ ρ l
(
)
beltemp λ p.l , χ d1 = 11.2 mm
bel := beltemp λ p.l , χ d1
(
)
bel = 11.241 mm
TOTAL EFFECTIVE AREA
Aetotal := t ⋅ ⎡⎣ bew + 2bef1 + 2( bef2 + bel) ⋅ χ d1 ⎤⎦
Aetotal = 354.1 mm
Aecrns := ⎡⎣π ⋅ t ⋅ ( rmid)⎤⎦ ⋅ χ d1 + π ⋅ t ⋅ ( rmid)
Aecrns = 44.2 mm
Aeflats := Aetotal − Aecrns
Aeflats = 309.9 mm
2
2
2
PREDICTED LOADS
Without Enhanced Corner Properties
Pn := Aetotal ⋅ fy
Pn = 85.7 kN
With Enhanced Corner Properties
Pn := Aeflats ⋅ fy + Aecrns ⋅ fycrn
Department of Civil Engineering
Research Report No R845
Pn = 100.0 kN
96
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
EFFECTIVE WIDTH CALCULATIONS FOR LIPPED
CHANNELS WITH INTERMEDIATE STIFFENERS : AS/NZS
4673 (2001), ASCE (2002)
(k f < 4; FLANGE IS NOT ADEQUATELY EDGE - STIFFENED )
Cross-section and Material Properties
Thickness
Inner Corner Radius
Centerline Corner Radius
t := 1.96 mm
r := 3 mm
t
rmid := r +
2
r mid = 3.98 mm
Web overall width
B w := 122.2 mm
Flange Overall width
B f := 90.6 mm
Lip Overall length
B l := 15 mm
Intermediate Stiffener height
d i := 9.7 mm
NOTE: according to the nominal geometric proportions, the stiffener width, di,w , di,w=2di but
measured dimensions of the experimental test specimens show that better agreement is given if
di,w=(2di + r). This adjustment is reflected in the calculations. For all FE analyses, di,w=2di.
0.2% Yield Stress of flats
0.2% Yield Stress of corners
Initial Modulus of Elasticity
Total Corner Area
fy := 242 ⋅MPa
fycrns := 565MPa
E0 := 187000 ⋅MPa
Acrns := 2.5 ⋅ ⎡⎣2 ⋅ π ⋅ t ⋅ ( rmid)⎤⎦
2
Acrns = 122.5 mm
Measured Gross Area
WEB
2
Ag := 634mm
(CL 2.4.2)
Moment of Inertia of Intermediate stiffener
I s := 377 mm
4
Total Area of Intermediate stiffener
A s := 57 mm
2
Corner Area of Intermediate stiffener
Ascrns := π t ⋅ rmid
A scrns = 24.507 mm
Flat Area of Intermediate stiffener
Asflats := As − Ascrns
A sflats = 32.493 mm
Department of Civil Engineering
Research Report No R845
97
2
2
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
S := 1.28 ⋅
April 2005
E0
fy
S = 35.581
Eqn. 2.4.1 (3)
web element
b w = 112.28 mm
bw := Bw − 2 ⋅ ( t + r)
web sub element
bw
b w1 :=
2
− (di + r ) −
π⋅r
8
b w1 = 42.262 mm
Determine effectiveness of Web Intermediate Stiffener
bw
t
= 57.286
Ia :=
0 if
bw
4
≤ S
t
Ia = 450.108 mm
Eqn. 2.4.2.2(3), (6)
bw
⎞
⎛
1 bw
⋅
− 50 if S <
< 3S
S t
t
⎝
⎠
bw
⎞
1 bw
4 ⎛
t ⋅ ⎜ 128 ⋅
− 285 if
≥ 3⋅S
S t
t
⎝
⎠
t ⋅ ⎜ 50 ⋅
4
n :=
1
2
1
3
bw
if S <
if
bw
⎛ Is
C2 := min⎜
n = 0.5
< 3S
≥ 3S
t
,1
t
⎞
C2 = 0.838
⎝ Ia ⎠
(
n
kw := min 3 ⋅ C2 + 1 , 4
)
kw = 3.746
Eqn. 2.4.2.2(7)
2
Aes := C2 ⋅ As
A es = 47.742 mm
Aescrns := C2 Ascrns
A escrns = 20.526 mm
Aesflats := C2 ⋅ Asflats
A esflats = 27.215 mm
2
2
Determine effectiveness of Web sub element CL 2.4.2
1.052 ⋅
λ w :=
bw1
t
⋅
fy
E0
kw
⎡⎢
⎛ 1 − 0.22 ⎞ ⎥⎤
⎜
λw ⎠ ⎥
⎢
⎝
ρ w := if λ w < 0.673 , 1 ,
⎢
⎥
λw
⎣
⎦
Department of Civil Engineering
Research Report No R845
98
λw = 0.422
Eqn. 2.2.1.2(4)
ρw = 1
Eqn. 2.2.1.2(3)
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
bw1e := bw1 ⋅ ρ w
b w1e = 42.262 mm
bw2e := bw1e
b w2e = 42.262 mm
bew := bw1e + bw2e
b ew = 84.524 mm
Aewflats := bew ⋅ t + Aesflats
2
A ewflats = 192.882 mm
2
Aewcrns := Aescrns
A ewcrns = 20.526 mm
FLANGES (CL 2.4.3)
bf := Bf − 2 ⋅ ( t + r)
bf
t
bf = 80.68 mm
= 41.163
b f1 :=
bf
2
caseA :=
− (di + r ) −
1 if
2 if
3 if
bf
t
S
3
bf
t
≤
<
π⋅r
8
S
3
bf
t
b f1 = 26.462 mm
caseA = 2
≤ S
> S
CaseA=2 or 3: Flange is Not Fully Effective, temporarily ignore intermediate
stiffener and find kf according to CL 2.4.3
FLANGES (CL 2.4.3) (continued)
bf := Bf − 2 ⋅ ( t + r)
bf = 80.68 mm
bl := Bl − ( t + r)
bl = 10.04 mm
Is :=
3
bl ⋅ t
12
ku := 0.43
4
Is = 165.301 mm
3
⎡
⎞ ⎤⎥
⎛ bf
⎢
⎜ t
ku
bf
S
4
Ia := ⎢399 ⋅ ⎜
−
⋅ t ⎥ if
<
< S
4 ⎠
3
t
⎣
⎝ S
⎦
bf ⎞
⎛
⎜
bf
t
4
t if
≥ S
⎜ 5 + 115 ⋅
S ⎠
t
⎝
Department of Civil Engineering
Research Report No R845
3
4
Ia = 2.037 × 10 mm
99
Eqns. 2.4.3.2(4) (11)
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
n :=
bf
1
S
if
<
< S
2
3
t
April 2005
n = 0.333
bf
1
if
≥ S
3
t
⎛ Is
C2 := min⎜
⎞
,1
C2 = 0.081
⎝ Ia ⎠
Bl ⎞ ⎤
⎡⎛
ka := min⎢⎜ 5.25 − 5 ⋅
, 4⎥
bf ⎠ ⎦
⎣⎝
Eqn. 2.4.3.2(5)
ka = 4
ku = 0.43
kf := C2 ( ka − ku ) + ku
n
kf = 1.976
caseB := if( kf < 4 , 21 , 22)
Eqn. 2.4.3.2(8)
caseB = 21
CaseB=2-1: Flange is Not Fully Effective, kf <4 completely ignore intermediate
stiffener and find effective areas according to CL 2.4.3
FLANGES (CL 2.4.3) (continued)
bf := Bf − 2 ⋅ ( t + r)
1.052 ⋅
λ f :=
bf
⋅
t
bf = 80.68 mm
fy
E0
kf
λ f = 1.108
kf = 1.976
⎡⎢
⎛ 1 − 0.22 ⎞ ⎥⎤
⎜
λf ⎠ ⎥
⎢
⎝
ρ f := if λ f < 0.673 , 1 ,
⎢
⎥
λf
⎣
⎦
Eqn. 2.2.1.2(4)
ρ f = 0.723
Eqn. 2.2.1.2(3)
bef := bf ⋅ ρ f
bef = 58.345 mm
Aefflats := t ⋅ bef
Aefflats = 114.356 mm
2
LIP (CL 2.4.3)
bl := Bl − ( t + r)
bl = 10.04 mm
kl := 0.43
1.052 ⋅
λ l :=
bl
t
⋅
fy
E0
λ l = 0.296
kl
Department of Civil Engineering
Research Report No R845
100
Eqn. 2.2.1.2(4)
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
⎡⎢
⎛ 1 − 0.22 ⎞ ⎤⎥
⎜
λl ⎠ ⎥
⎢
⎝
ρ l := if λ l < 0.673 , 1 ,
⎢
⎥
λl
⎣
⎦
April 2005
ρl = 1
Eqn. 2.2.1.2(3)
bele := bl ⋅ ρ l
bele = 10.04 mm
bel := bele ⋅ C2
bel = 0.815 mm
Aelflats := t ⋅ bel
Aelflats = 1.597 mm
2
TOTAL EFFECTIVE AREAS (INTERMEDIATE STIFFENERS OF FLANGES
IGNORED)
From WEB
From FLANGE
2
A ewflats = 192.882 mm
2
A ewcrns = 20.526 mm
From LIP
2
2
Aefflats = 114.356 mm
Aelflats = 1.597 mm
2
Aefcrns := 0mm
2
Aeflats := Aewflats + 2Aefflats + 2Aelflats
A eflats = 424.79 mm
Aecrns := Aewcrns + 2Aefcrns + 2πt ⋅ rmid
A ecrns = 69.54 mm
Aetotal := Aecrns + Aeflats
A etotal = 494.328 mm
2
2
PREDICTED LOAD
Without enhanced corner properties (kf<4)
Pn := ( Aeflats + Aecrns ) ⋅ fy
With enhanced corner properties (kf<4)
Pn := Aeflats ⋅ fy + Aecrns ⋅ fycrn
Department of Civil Engineering
Research Report No R845
101
P n = 119.627 kN
P n = 142.089 kN
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
EFFECTIVE WIDTH CALCULATIONS FOR LIPPED
CHANNELS WITH INTERMEDIATE STIFFENERS : AS/NZS
4673 (2001), ASCE (2002)
(k f = 4; FLANGE IS NOT ADEQUATELY EDGE - STIFFENED )
Cross-Section and Material Properties
Thickness
Centerline Corner Radius
Centerline Web Width
Centerline Flange Width
Centerline Lip Length
Intermediate Stiffener height
(width =2*di)
0.2% Yield Stress of flats
0.2% Yield Stress of corners
Initial Modulus of Elasticity
Total Corner Area
t := 1mm
rmid := 1mm
Bw := 150mm
Bf := 70mm
Bl := 15mm
di := 10mm
fy := 195MPa
fycrn := 457MPa
E0 := 195000 MPa
A crns := 2.5 ⋅ ⎡⎣2 ⋅ π ⋅ t ⋅ ( rmid)⎤⎦
2
A crns = 15.7mm
2
A g := 341mm
Gross Area
WEB
(CL 2.4.2)
4
Moment of Inertia of Intermediate stiffener
Is := 267mm
Total Area of Intermediate stiffener
A s := 29mm
Corner Area of Intermediate stiffener
Ascrns := π t ⋅ rmid
A scrns = 3.142 mm
Flat Area of Intermediate stiffener
Asflats := As − Ascrns
A sflats = 25.858 mm
S := 1.28 ⋅
2
E0
fy
S = 40.477
web element
b w := Bw − 2 ⋅ ( rmid)
b w = 148mm
web sub element
b w1 :=
bw
2
− di −
π ⋅ rmid
8
Department of Civil Engineering
Research Report No R845
b w1 = 63.607mm
102
Eqn. 2.4.1 (3)
2
2
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
Determine effectiveness of Web Intermediate Stiffener
bw
t
= 148
Ia :=
0 if
bw
4
≤ S
t
Ia = 183.017mm
Eqn. 2.4.2.2(3), (6)
bw
⎛
⎞
1 bw
⋅
− 50 if S <
< 3S
S t
t
⎝
⎠
bw
⎞
1 bw
4 ⎛
t ⋅ ⎜ 128 ⋅
− 285 if
≥ 3⋅S
S t
t
⎝
⎠
t ⋅ ⎜ 50 ⋅
4
n :=
bw
1
if S <
< 3S
2
t
1
3
if
bw
⎛ Is
C2 := min⎜
≥ 3S
t
,1
n = 0.333
⎞
C2 = 1
⎝ Ia ⎠
(
n
kw := min 3 ⋅ C2 + 1 , 4
)
kw = 4
Eqn. 2.4.2.2(7)
2
Aes := C2 ⋅ As
A es = 29mm
Aescrns := C2 Ascrns
A escrns = 3.142 mm
Aesflats := C2 ⋅ Asflats
A esflats = 25.858 mm
2
2
Determine effectiveness of Web sub element CL 2.4.2
1.052 ⋅
λ w :=
bw1
t
⋅
fy
E0
kw
⎡⎢
⎛ 1 − 0.22 ⎞ ⎥⎤
⎜
λw ⎠ ⎥
⎢
⎝
ρ w := if λ w < 0.673 , 1 ,
⎢
⎥
λw
⎣
⎦
λw = 1.058
Eqn. 2.2.1.2(4)
ρ w = 0.749
Eqn. 2.2.1.2(3)
bw1e := bw1 ⋅ ρ w
b w1e = 47.618mm
bw2e := bw1e
b w2e = 47.618mm
bew := bw1e + bw2e
b ew = 95.237mm
Aewflats := bew ⋅ t + Aesflats
2
A ewflats = 121.095mm
2
Aewcrns := Aescrns
Department of Civil Engineering
Research Report No R845
A ewcrns = 3.142mm
103
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
FLANGES (CL 2.4.3)
b f := Bf − 2 ⋅ ( rmid )
bf
t
April 2005
b f = 68mm
= 41.163
b f1 :=
bf
2
caseA :=
π ⋅ rmid
− di −
1 if
2 if
3 if
8
bf
t
≤
S
3
b f1 = 23.607mm
caseA = 3
bf
S
<
≤ S
3
t
bf
t
> S
CaseA=2 or 3: Flange is Not Fully Effective, temporarily ignore intermediate
stiffener and find kf according to CL 2.4.3
FLANGES (CL 2.4.3) (continued)
b f := Bf − 2 ⋅ ( rmid )
b f = 68mm
b l := Bl − ( rmid )
b l = 14mm
3
Is :=
bl ⋅ t
12
ku := 0.43
4
Is = 228.667mm
3
⎡
⎞ ⎤⎥
⎛ bf
⎢
⎜ t
ku
bf
S
4
Ia := ⎢399 ⋅ ⎜
−
⋅ t ⎥ if
<
< S
4 ⎠
3
t
⎣
⎝ S
⎦
bf ⎞
⎛
⎜
bf
t
4
t if
≥ S
⎜ 5 + 115 ⋅
S ⎠
t
⎝
n :=
bf
1
S
if
<
< S
t
2
3
n = 0.333
bf
1
if
≥ S
t
3
Department of Civil Engineering
Research Report No R845
4
Ia = 198.195mm
104
Eqns. 2.4.3.2(4) (11)
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
⎛ Is
C2 := min⎜
,1
⎞
April 2005
C2 = 1
⎝ Ia ⎠
Bl ⎞ ⎤
⎡⎛
ka := min⎢⎜ 5.25 − 5 ⋅
, 4⎥
bf ⎠ ⎦
⎣⎝
Eqn. 2.4.3.2(5)
ka = 4
ku = 0.43
kf := C2 ( ka − ku ) + ku
n
kf = 4
caseB := if( kf < 4 , 21 , 22)
Eqn. 2.4.3.2(8)
caseB = 22
CaseB=2-2: Flange kf =4; flange is adequately EDGE STIFFENED, include
intermediate stiffener and find effective areas according to CL 2.5
FLANGES (CL 2.5) (continued)
Moment of Inertia Flange and Intermediate Stiffener Isf := 717.2mm4
Moment of Inertia Intermediate Stiffener only Is := 267mm4
2
⎤
⎤
⎡⎡
0.119 ⋅ E0 4⎥
⎢⎢
⎛ b f1 ⎞
4⎥
Imin := max⎢⎢( 3.66) ⋅ ⎜
−
⋅ t ⎥ , 18.4 ⋅ t ⎥
fy
⎝ t ⎠
⎣⎣
⎦
⎦
4
Imin = 76.625mm
Eqns. 2.5(1)
Determine effectiveness of Flange sub element CL 2.5
bf
b f1 :=
2
− di −
π ⋅ rmid
8
b f1 = 23.607mm
kf := 4
1.052 ⋅
λf :=
b f1
t
⋅
fy
E0
kf
λf = 0.393
⎡⎢
⎛ 1 − 0.22⎞ ⎥⎤
⎜
λf ⎠ ⎥
⎢
⎝
ρ f := if λf < 0.673, 1 ,
⎢
⎥
λf
⎣
⎦
Eqn. 2.4.3.2(5)
ρf = 1
b ef1 := ρ f ⋅ b f1
b ef1 = 23.607mm
b ef2 := b ef1
b ef2 = 23.607mm
Flange sub element is fully effective, calculate equivalent thickness for
flange/intermediate stiffener element CL 2.5(c)
Department of Civil Engineering
Research Report No R845
105
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
ts :=
t if Is < Imin ∧ ρ f < 1
3
12
Isf
if Is ≥ Imin ∧ ρ f
bf
bf
1.052 ⋅
ts
λf :=
April 2005
ts = 5.021mm
Eqn. 2.5(2)
1
fy
⋅
E0
λf = 0.225
kf
⎡⎢
⎛ 1 − 0.22⎞ ⎤⎥
⎜
λf ⎠ ⎥
⎢
⎝
ρ f := if λf < 0.673, 1 ,
⎢⎣
⎥⎦
λf
ρf = 1
b ef := ρ f ⋅ b f
b ef = 68mm
A efflats := ( b ef1 + b ef2 ) ⋅ t + A sflats
A efflats = 73.073mm
A efcrns := A scrns
A efcrns = 3.142mm
2
2
LIP (CL 2.4.3)
b l := Bl − ( rmid)
kl := 0.5
1.052 ⋅
λ l :=
bl
t
⋅
b l = 14mm
fy
E0
kl
⎡⎢
⎛ 1 − 0.22 ⎞ ⎤⎥
⎜
λl ⎠ ⎥
⎢
⎝
ρ l := if λ l < 0.673 , 1 ,
⎢
⎥
λl
⎣
⎦
λl = 0.659
Eqn. 2.2.1.2(4)
ρl = 1
Eqn. 2.2.1.2(3)
b ele := b l ⋅ ρ l
C2 = 1
b ele = 14mm
bel := bele ⋅ C2
bel = 14mm
A elflats := t ⋅ b el
A elflats = 14mm
2
TOTAL EFFECTIVE AREAS
From WEB
From FLANGE
2
A ewflats = 121.095mm
2
A ewcrns = 3.142mm
A efflats = 73.073mm
2
A elflats = 14mm
2
A efcrns = 3.142mm
2
A eflats = 295.241mm
A eflats := A ewflats + 2A efflats + 2A elflats
Department of Civil Engineering
Research Report No R845
From LIP
2
106
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
2
A ecrns = 15.708mm
A ecrns := A ewcrns + 2A efcrns + 2πrmid ⋅ t
PREDICTED LOAD
Without enhanced corner properties (kf=4)
Pn := ( Aeflats + Aecrns ) ⋅ fy
With enhanced corner properties (kf=4)
Pn := Aeflats ⋅ fy + Aecrns ⋅ fycrn
Department of Civil Engineering
Research Report No R845
107
Pn = 60.635kN
Pn = 64.751kN
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
EFFECTIVE
WIDTH
April 2005
CALCULATIONS
FOR
CHANNELS WITH INTERMEDIATE STIFFENERS:
LIPPED
NAS
(2001)
(k f < 4; FLANGE IS NOT ADEQUATELY EDGE - STIFFENED )
Cross-section and Material Properties
Thickness
Inner Corner Radius
Centerline Corner Radius
t := 1.96mm
r := 3mm
t
rmid := r +
2
rmid = 3.98 mm
Web overall width
Bw := 122.2mm
Flange Overall width
Bf := 90.6mm
Lip Overall length
Bl := 15mm
Intermediate Stiffener height
d i := 9.7 mm
NOTE: according to the nominal geometric proportions, the stiffener width, di,w , di,w=2di but
measured dimensions of the experimental test specimens show that better agreement is given if
di,w=(2di + r). This adjustment is reflected in the calculations. For all FE analyses, di,w=2di
0.2% Yield Stress of flats
0.2% Yield Stress of corners
Initial Modulus of Elasticity
Total Corner Area
fy := 242 ⋅MPa
fycrns := 565MPa
E0 := 187000 ⋅MPa
Acrns := 2.5 ⋅ ⎡⎣2 ⋅ π ⋅ t ⋅ ( rmid)⎤⎦
2
Acrns = 122.5 mm
Measured Gross Area
WEB
2
Ag := 634mm
(CL B2.1)
Moment of Inertia of Intermediate stiffener
I s := 377 mm
4
Total Area of Intermediate stiffener
A s := 57 mm
2
Corner Area of Intermediate stiffener
Ascrns := π t ⋅ rmid
A scrns = 24.507 mm
Flat Area of Intermediate stiffener
Asflats := As − Ascrns
A sflats = 32.493 mm
Department of Civil Engineering
Research Report No R845
108
2
2
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
E0
S := 1.28 ⋅
fy
S = 35.581
web element
bw := Bw − 2 ⋅ ( t + r)
bw = 112.28 mm
web sub element
b w1 :=
bw
2
π⋅r
− (di + r ) −
8
b w1 = 42.262 mm
Determine effectiveness of Web Intermediate Stiffener
bw
t
= 57.286
Ia :=
bw
4
Ia = 450.108 mm
Eqn. B4.1-7 B4.1-8
n = 0.449
Eqn. B4.1-4
R1 = 0.838
Eqn. B4.1-6
kw := 3 ⋅ R1 + 1
kw = 3.771
Eqn. B4.1-5
Aes := R1 ⋅ As
A es = 47.742mm
Aescrns := R1 Ascrns
A escrns = 20.526mm
Aesflats := R1 ⋅ Asflats
A esflats = 27.215mm
0 if
t
≤ S
bw
⎞
⎛
1 bw
⋅
− 50 if S <
< 3S
S t
t
⎝
⎠
bw
⎞
1 bw
4 ⎛
− 285 if
≥ 3⋅S
t ⋅ ⎜ 128 ⋅
S t
t
⎝
⎠
t ⋅ ⎜ 50 ⋅
4
⎡⎛
⎣⎝
n := max⎢⎜ 0.583 −
⎛ Is
R1 := min⎜
⎝ Ia
,1
bw ⎞ 1 ⎤
, ⎥
12 ⋅ S t ⎠ 3 ⎦
1
⋅
⎞
⎠
n
2
2
2
Determine effectiveness of Web sub element (see figure B4-1) CL B2.1
1.052 ⋅
λ w :=
bw1
t
⋅
fy
E0
λw = 0.42 Eqn. B2.1-4 B2.1-5
kw
⎡⎢
⎛ 1 − 0.22 ⎞ ⎥⎤
⎜
λw ⎠ ⎥
⎢
⎝
ρ w := if λ w < 0.673 , 1 ,
⎢
⎥
λw
⎣
⎦
Department of Civil Engineering
Research Report No R845
ρw = 1
109
Eqn. B2.1-3
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
bw1e := bw1 ⋅ ρ w
b w1e = 42.262 mm
bw2e := bw1e
b w2e = 42.262 mm
bew := bw1e + bw2e
b ew = 84.524 mm
Aewflats := bew ⋅ t + Aesflats
Eqn. B2.1-2
2
A ewflats = 192.882 mm
2
Aewcrns := Aescrns
A ewcrns = 20.526 mm
FLANGES (CL B5.2)
bf := Bf − 2 ⋅ ( t + r)
bf
t
bf = 80.68 mm
= 41.163
b f1 :=
bf
2
π⋅r
− (di + r ) −
b f1 = 26.462mm
8
⎛ bf
⎞
≤ 0.328S , 1 , 2
t
⎝
⎠
caseA := if⎜
caseA = 2
CaseA=2: Flange is Not Fully Effective, completely ignore intermediate stiffener and
find kf according to B4.2
FLANGES (CL B4.2) (continued)
bf := Bf − 2 ⋅ ( t + r)
bf = 80.68 mm
bl := Bl − ( t + r)
bl = 10.04 mm
3
Is :=
bl ⋅ t
4
Is = 165.301 mm
12
ku := 0.43
3
⎡⎡
bf
⎛ bf
⎞ ⎤⎥ ⎛
⎢⎢
⎜ t
⎜
t
4 4
Ia := min⎢ ⎢399 ⋅ ⎜
− 0.327 ⋅ t ⎥ , t ⎜ 5 + 115 ⋅
S
⎣⎣
⎝ S
⎠ ⎦ ⎝
⎡⎛
⎣⎝
n := max⎢⎜ 0.582 −
⎛ Is
R1 := min⎜
,1
bf ⎞ 1 ⎤
, ⎥
4 ⋅ S t ⎠ 3⎦
1
⋅
⎞
⎝ Ia ⎠
Department of Civil Engineering
Research Report No R845
110
⎞ ⎤⎥
⎥
⎠⎦
3
4
Ia = 2.037 × 10 mm
Eqn B4.2-10
n = 0.333
Eqn. B4.2-11
R1 = 0.081
Eqn. B4.2-9
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
kf :=
(
n
min 3.57 ⋅ R1 + 0.43 , 4
⎡⎡⎛
Bl ⎞
⎣⎣⎝
bf ⎠
min⎢⎢⎜ 4.82 − 5
)
if
n
Bl
bf
April 2005
≤ 0.25
kf = 1.976
⎤ ⎤
Bl
⎦ ⎦
bf
R1 + 0.43⎥ , 4⎥ if 0.25 <
Table B4.2
≤ 0.8
caseB := if( kf < 4 , 21 , 22)
caseB = 21
CaseB=2-1: Flange is Not Fully Effective, kf <4 completely ignore intermediate
stiffener and find effective areas according to CL B4.2
FLANGES (CL B4.2) (continued)
bf := Bf − 2 ⋅ ( t + r)
1.052 ⋅
λ f :=
bf
⋅
t
bf = 80.68 mm
fy
E0
kf
λ f = 1.108
kf = 1.976
⎡⎢
⎛ 1 − 0.22 ⎞ ⎥⎤
⎜
λf ⎠ ⎥
⎢
⎝
ρ f := if λ f < 0.673 , 1 ,
⎢
⎥
λf
⎣
⎦
ρ f = 0.723
bef := bf ⋅ ρ f
bef = 58.345 mm
Aefflats := t ⋅ bef
Aefflats = 114.356 mm
2
LIP (CL B4.2)
bl := Bl − ( t + r)
bl = 10.04 mm
kl := 0.43
1.052 ⋅
λ l :=
bl
t
⋅
fy
E0
kl
⎡⎢
⎛ 1 − 0.22 ⎞ ⎤⎥
⎜
λl ⎠ ⎥
⎢
⎝
ρ l := if λ l < 0.673 , 1 ,
⎢
⎥
λl
⎣
⎦
λ l = 0.296
Eqn. B2.1-4 B2.1-5
ρl = 1
Eqn. B2.1-3
bele := bl ⋅ ρ l
bele = 10.04 mm Eqn. B2.1-2
bel := bele ⋅ R1
bel = 0.815 mm
Aelflats := t ⋅ bel
Aelflats = 1.597 mm
Department of Civil Engineering
Research Report No R845
2
111
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
TOTAL EFFECTIVE AREAS (INTERMEDIATE STIFFENERS OF FLANGES
IGNORED)
From WEB
From FLANGES
2
A ewflats = 192.882 mm
2
A ewcrns = 20.526 mm
From LIP
2
2
Aefflats = 114.356 mm
Aelflats = 1.597 mm
2
Aefcrns := 0mm
2
Aeflats := Aewflats + 2Aefflats + 2Aelflats
A eflats = 424.787 mm
Aecrns := Aewcrns + 2π t ⋅ rmid
A ecrns = 69.54 mm
Aetotal := Aecrns + Aeflats
A etotal = 494.328mm
2
2
PREDICTED LOAD
without enhanced corner properties (kf<4)
Pn := ( Aeflats + Aecrns ) ⋅ fy
with enhanced corner properties (kf<4)
Pn := Aeflats ⋅ fy + Aecrns ⋅ fycrn
Department of Civil Engineering
Research Report No R845
112
Pn = 119.627kN
Pn = 142.089kN
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
EFFECTIVE WIDTH CALCULATIONS FOR LIPPED
CHANNELS WITH INTERMEDIATE STIFFNERS: NAS
2001
(k f = 4; FLANGE IS NOT ADEQUATELY EDGE - STIFFENED )
Cross-Section and Material Properties
Thickness
Centerline Corner Radius
Centerline Web Width
Centerline Flange Width
Centerline Lip Length
Intermediate Stiffener height
(width =2*di)
0.2% Yield Stress of flats
0.2% Yield Stress of corners
Initial Modulus of Elasticity
Total Corner Area
t := 1mm
rmid := 1mm
Bw := 150mm
Bf := 70mm
Bl := 15mm
di := 10mm
fy := 195MPa
fycrn := 457MPa
E0 := 195000 MPa
A crns := 2.5 ⋅ ⎡⎣2 ⋅ π ⋅ t ⋅ ( rmid)⎤⎦
2
A crns = 15.7mm
2
A g := 341mm
Gross Area
WEB
(CL B4.1)
4
Moment of Inertia of Intermediate stiffener
Is := 267mm
Total Area of Intermediate stiffener
A s := 29mm
Corner Area of Intermediate stiffener
Ascrns := π t ⋅ rmid
A scrns = 3.142 mm
Flat Area of Intermediate stiffener
Asflats := As − Ascrns
A sflats = 25.858 mm
S := 1.28 ⋅
2
E0
fy
S = 40.477
web element
b w := Bw − 2 ⋅ ( rmid)
b w = 148mm
web sub element
b w1 :=
bw
2
− di −
π ⋅ rmid
8
Department of Civil Engineering
Research Report No R845
b w1 = 63.607mm
113
Eqn. B4-1
2
2
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
Determine effectiveness of Web Intermediate Stiffener
bw
t
= 148
Ia :=
0 if
bw
t
4
Ia = 183.017mm
≤ S
Eqns. B4.1-1, B4.1-7, B4.1-8
bw
⎛
⎞
1 bw
⋅
− 50 if S <
< 3S
S t
t
⎝
⎠
bw
⎞
1 bw
4 ⎛
− 285 if
≥ 3⋅S
t ⋅ ⎜ 128 ⋅
S t
t
⎝
⎠
t ⋅ ⎜ 50 ⋅
4
⎡⎛
⎣⎝
n := max⎢⎜ 0.583 −
1
12 ⋅ S
⋅
b w ⎞ 1⎤
, ⎥
t ⎠ 3⎦
n = 0.333
⎛ Is ⎞
R1 := min⎜
,1
R1 = 1
⎝ Ia ⎠
n
kw := 3 ⋅ R1 + 1
Eqns. B4.1-6
kw = 4
Eqns. B4.1-5
2
A es := R1 ⋅ A s
A es = 29mm
A escrns := R1 A scrns
A escrns = 3.142 mm
A esflats := R1 ⋅ A sflats
A esflats = 25.858 mm
2
2
Determine effectiveness of Web sub element CL 2.4.2
1.052 ⋅
λ w :=
bw1
t
⋅
fy
E0
kw
⎡⎢
⎛ 1 − 0.22 ⎞ ⎥⎤
⎜
λw ⎠ ⎥
⎢
⎝
ρ w := if λ w < 0.673 , 1 ,
⎢
⎥
λw
⎣
⎦
λw = 1.058
Eqns. B2.1-4, B2.1-5
ρ w = 0.749
Eqn. B2.1-3
bw1e := bw1 ⋅ ρ w
b w1e = 47.618mm
bw2e := bw1e
b w2e = 47.618mm
bew := bw1e + bw2e
b ew = 95.237mm
Aewflats := bew ⋅ t + Aesflats
2
A ewflats = 121.095mm
2
A ewcrns = 3.142mm
Aewcrns := Aescrns
Department of Civil Engineering
Research Report No R845
114
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
FLANGES (CL 2.4.3)
b f := Bf − 2 ⋅ ( rmid)
bf
t
April 2005
b f = 68mm
= 41.163
b f1 :=
bf
2
− di −
π ⋅ rmid
b f1 = 23.607mm
8
⎛ bf
⎞
≤ 0.328 ⋅ S , 1 , 2
⎝ t
⎠
caseA := if ⎜
caseA = 2
CaseA=2 or 3: Flange is Not Fully Effective, temporarily ignore intermediate
stiffener and find kf according to CL B4.2
FLANGES (CL B4.2) (continued)
b f := Bf − 2 ⋅ ( rmid)
b f = 68mm
b l := Bl − ( rmid)
b l = 14mm
3
Is :=
bl ⋅ t
4
Is = 228.667mm
12
ku := 0.43
3
⎡⎢ ⎡⎢
⎤
bf ⎞ ⎥
⎛ bf
⎞
⎥⎤ ⎛
⎜ t
⎜
⎢⎢
t ⎥
4⎥ 4
Ia := min⎢ ⎢399 ⋅ ⎜
− 0.327 ⋅ t ⎥ , t ⎜ 5 + 115 ⋅
⎥
S ⎠⎦
⎣⎣
⎝ S
⎠
⎦ ⎝
b f ⎞ 1⎤
1
⎡⎛
⋅
, ⎥
4⋅ S
t ⎠ 3⎦
⎣⎝
⎛ Is ⎞
R1 := min⎜ , 1
⎝ Ia ⎠
Bl
n
kf := min⎛⎝ 3.57 ⋅ R1 + 0.43, 4⎞⎠ if
≤ 0.25
b
n := max⎢⎜ 0.582 −
4
Ia = 198.195mm
Eqn. B4.2-10
n = 0.333
Eqn. B4.2-11
R1 = 1
Eqn. B4.2-9
kf = 4
f
⎡⎡⎛
Bl ⎞
⎣⎣⎝
bf
min⎢⎢⎜ 4.82 − 5
⎠
n
⎤ ⎤
Bl
⎦ ⎦
bf
R1 + 0.43⎥ , 4⎥ if 0.25 <
caseB := if( kf < 4 , 21 , 22)
Table B4.2
≤ 0.8
caseB = 22
CaseB=2-2: Flange kf =4; flange is adequately EDGE STIFFENED, include
intermediate stiffener and find effective areas according to CL B5
Department of Civil Engineering
Research Report No R845
115
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
FLANGES (CL B.5.1.1)
Moment of Inertia Intermediate Stiffener only Isp := 267mm4
Number of intermediate stiffeners
n s := 1
Determine effectiveness of Flange sub element CL B5.1.1
1
δ :=
As
γ :=
bf ⋅ t
bf ⋅ t
kloc := 4 ⋅ ( n s + 1)
kd :=
10.92 ⋅ Isp
3
2
(1 + β 2)2 + γ ⋅ (1 + ns)
β ⋅ ⎡⎣ 1 + δ ⋅ ( n s + 1) ⎤⎦
2
bf ⎞ ⎤
⎡⎛
⎢ ⎜ 11 − b
⎥
l⎠
⎝
⎢
R := min
, 1⎥
5
⎣
⎦
kfa := min( kloc , R ⋅ kd)
1.052 ⋅
bf
t
λf :=
⋅
β := ⎡⎣ 1 + γ ⋅ ( n s + 1)⎤⎦
Eqns. B5.1.1-1
kd = 11.133
Eqns. B5.1.1-2
R =1
Eqns. B5.1.1-8 and CL B5.2
kfa = 11.133
Eqns. B5.1-6
λf = 0.678
Eqns. B5.1-5, B5.1-4
fy
E0
kfa
A gsf
t
Eqns. B5.1.1-5, B5.1.1-3, B5.1.1-3
kloc = 16
⎡⎢
⎛ 1 − 0.22⎞ ⎤⎥
⎜
λf ⎠ ⎥
⎢
⎝
ρ f := if λf < 0.673, 1 ,
⎢⎣
⎥⎦
λf
b efp :=
4
⋅ ρf
ρ f = 0.996
Eqn. B5.1-3
b efp = 75.936mm
Eqn. B5.1-1
2
A efcrns := ρ f ⋅ A scrns
A efcrns = 3.13mm
A esflats := A sflats ⋅ ρ f
A esflats = 25.764mm
A efflats := A gsf ⋅ ρ f − A efcrns
A efflats = 72.806mm
2
2
LIP (CL B3)
Department of Civil Engineering
Research Report No R845
116
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
b l := Bl − ( rmid)
April 2005
b l = 14mm
kl := 0.43
1.052 ⋅
λ l :=
bl
t
⋅
fy
E0
λl = 0.71
kl
⎡⎢
⎛ 1 − 0.22 ⎞ ⎤⎥
⎜
λl ⎠ ⎥
⎢
⎝
ρ l := if λ l < 0.673 , 1 ,
⎢
⎥
λl
⎣
⎦
ρ l = 0.972
b ele := b l ⋅ ρ l
b ele = 13.606mm
R1 = 1
b el := b ele ⋅ R1
b el = 13.606mm
A elflats := t ⋅ b el
A elflats = 13.606mm
2
TOTAL EFFECTIVE AREAS
From WEB
From FLANGE
2
A ewflats = 121.095mm
2
A ewcrns = 3.142mm
From LIP
2
2
A efflats = 72.806mm
A elflats = 13.606mm
2
A efcrns = 3.13mm
2
A eflats := A ewflats + 2A efflats + 2A elflats
A eflats = 293.919mm
A ecrns := A ewcrns + 2A efcrns + 2πrmid ⋅ t
A ecrns = 15.685mm
2
PREDICTED LOAD
Without enhanced corner properties (kf=4)
Pn := ( Aeflats + Aecrns ) ⋅ fy
With enhanced corner properties (kf=4)
Pn := Aeflats ⋅ fy + Aecrns ⋅ fycrn
Department of Civil Engineering
Research Report No R845
117
Pn = 60.373kN
Pn = 64.482kN
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
EFFECTIVE WIDTH CALCULATIONS FOR LIPPED
CHANNELS
WITH
INTERMEDIATE
STIFFNERS:
EUROCODE 3 PART1-4/1-3 (2004)
Cross-Section and Material Properties
Thickness
Centerline Corner Radius
Centerline Web Width
Centerline Flange Width
Centerline Lip Length
Intermediate Stiffener height
(width =2*di)
0.2% Yield Stress of flats
0.2% Yield Stress of corners
Initial Modulus of Elasticity
Total Corner Area
t := 1mm
r mid := 1mm
B w := 150 mm
B f := 70 mm
B l := 15 mm
di := 10mm
fy := 195MPa
fycrn := 457MPa
E0 := 195000 MPa
A crns := 2.5 ⋅ ⎡⎣2 ⋅ π ⋅ t ⋅ ( rmid)⎤⎦
2
A crns = 15.7mm
2
A g := 341mm
Gross Area
Notional Dimensions taking into account rounded corners CL 5.1 Part 1-3
⎞ ⋅ 2⎤ b = 70 mm
⎥ f
⎦
b f := if ⎡⎢ r ≤ 5t ∧ r ≤ 0.1 ⋅ ( Bf ) , ( Bf ) , ( Bf ) − ( rmid) ⋅ ⎛⎜ 1 −
1
b w := if ⎡⎢ r ≤ 5t ∧ r ≤ 0.1 ⋅ ( Bw) , ( Bw) , Bw − ( rmid) ⋅ ⎛⎜ 1 −
1
⎣
⎝
⎣
⎝
b l := if ⎡⎢ r ≤ 5t ∧ r ≤ 0.1 ⋅ ( Bl) , ( Bl) , ( Bl) − ( rmid) ⋅ ⎛⎜ 1 −
⎣
⎝
WEB (CL 5.5.3.3 Part 1-3)
Sub Element 1 – reduction for local buckling
⎛ 235 ⋅ E0 ⎞
ε := ⎜
⎝ fy ⋅ 210000⎠
b w1 :=
bw
2
2⎠
− di −
.5
kw1 := 4
π ⋅ rmid
8
Department of Civil Engineering
Research Report No R845
b w1 = 64.607 mm
118
⎞ ⋅ 2⎤ b = 150 mm
⎥ w
⎦
2⎠
⎞⎤
⎥
2 ⎠⎦
1
b l = 15 mm
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
b w1
λp.w1 :=
t
⋅
1
28.4 ⋅ ε ⋅
kw1
April 2005
λp.w1 = 1.075
⎡⎢
⎛⎜ 0.772 − 0.125 ⎞⎤⎥
λp.w1 ⎟⎥
⎢
⎜
ρ w1 := if λp.w1 < 0.673, 1 ,
⎢⎣
⎜⎝
λp.w1
⎠⎥⎦
ρ w1 = 0.61
b ew1 := ρ w1 ⋅ b w1
b ew1 = 39.401 mm
b ew11 := 0.5 ⋅ b ew1
b ew12 := 0.5 ⋅ b ew1
b ew11 = 19.701 mm
b ew12 = 19.701 mm
Sub Element 2 (identical to sub element 1 ) – reduction for local buckling
λp.w2 := λp.w1
ρ w2 := ρ w1
λp.w2 = 1.075
b w2 := b w1
b ew2 := ρ w2 ⋅ b w2
b ew21 := 0.5 ⋅ b ew2
b ew21 = 19.701mm
b ew22 := 0.5 ⋅ b ew2
b ew22 = 19.701mm
ρ w2 = 0.61
b ew2 = 39.401 mm
Find distortional buckling reduction factor for web intermediate stiffener (critical
elastic buckling stress for an independent web element with pinned ends – from
ThinWall)
σcr.sw = 182MPa
fy
λd1w :=
λd1w = 1.035
σcr.sw
χ d1w :=
1 if λd1w ≤ 0.65
(1.47 − 0.723 ⋅ λd1w)
0.66
λd1w
χ d1w = 0.722
if 0.65 < λd1w < 1.38
if λd1w ≥ 1.38
FLANGE (CL 5.5.2 Part 1-3)
Sub Element 1 –reduction for local buckling
b f1 :=
bf
− di −
2
π ⋅ rmid
⎛ 235 ⋅ E0 ⎞
ε := ⎜
⎝ fy ⋅ 210000⎠
λp.f1 :=
b f1
t
⋅
b f1 = 24.607 mm
8
.5
kf1 := 4
1
28.4 ⋅ ε ⋅
Department of Civil Engineering
Research Report No R845
kf1
λp.f1 = 0.41
119
CL 5.5.3.1 (7)
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
⎡⎢
⎛⎜ 0.772 − 0.125 ⎞⎥⎤
λp.f1 ⎟⎥
⎢
⎜
ρ f1 := if λp.f1 < 0.673, 1 ,
⎢⎣
⎜⎝
λp.f1
⎠⎥⎦
April 2005
ρ f1 = 1
b ef1 := ρ f1 ⋅ b f1
b ef1 = 24.607 mm
b ef11 := 0.5 ⋅ b ef1
b ef11 = 12.304 mm
b ef12 := 0.5 ⋅ b ef1
b ef12 = 12.304 mm
Sub Element 2 (identical to sub element 1) – reduction for local bucking
λp.f2 := λp.f1
λp.f2 = 0.41
ρ f2 := ρ f1
b f2 := b f1
ρ f2 = 1
b ef21 := 0.5 ⋅ b ef2
b ef22 := 0.5 ⋅ b ef2
b ef21 = 12.304 mm
b ef2 := ρ f2 ⋅ b f2
b ef2 = 24.607 mm
b ef22 = 12.304 mm
Find distortional buckling reduction factor for flange-lip stiffener (critical
distortional buckling stress of the cross-section – from ABAQUS)
σcr.sf = 111MPa
χ d1f :=
λd1f :=
fy
λd1f = 1.325
σcr.sf
1 if λd1f ≤ 0.65
(
1.47 − 0.723 ⋅ λd1f
0.66
λd1f
χ d1f = 0.512
)
if 0.65 < λd1f < 1.38
if λd1f ≥ 1.38
LIP (CL 5.5.2 Part 1-3)
reduction for local buckling
2⎤
⎡
⎢
⎥
3
⎢ bl
⎛ bl
⎞ ⎥
kl := if ⎢
< 0.35, 0.5, 0.5 + 0.83 ⋅ ⎜
− 0.35 ⎥
⎣ bf
⎝ bf
⎠ ⎦
λp.l :=
bl
t
⋅
1
28.4 ⋅ ε ⋅
kl
Department of Civil Engineering
Research Report No R845
λp.l = 0.706
120
kl = 0.5
CL 5.5.3.1 (7)
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
⎡⎢
⎛⎜ 1.0 − 0.231 ⎞⎥⎤
λp.l ⎟⎥
⎢
⎜
ρ l := if λp.l < 0.673, 1 ,
⎢⎣
⎜⎝ λp.l ⎠⎥⎦
b el := ρ l ⋅ b l
April 2005
ρ l = 0.953
b el = 14.294 mm
TOTAL EFFECTIVE AREAS
From WEB
χ d1w = 0.722
A ewflats := ( b ew11 + b ew22 − 2 ⋅ rmid) ⋅ t + ( b ew12 + b ew21 ) ⋅ t ⋅ χ d1w + A sflats ⋅ χ d1w
2
A ewflats = 84.494mm
2
A ewcrns := A scrns ⋅ χ d1w
A ewcrns = 2.267mm
From FLANGE (one flange)
A efflats := ( b ef11 + b ef12 − rmid ) ⋅ t + 0.5A sflats + ( b ef21 + b ef22 − rmid ) ⋅ t ⋅ χ d1f + 0.5A sflats ⋅ χ d1f
2
A efflats = 55.233mm
A efcrns := 0.5 ⋅ A scrns ⋅ χ d1f + 0.5A scrns
2
A efcrns = 2.375mm
From LIP (one lip)
A elflats := ( b el − rmid) ⋅ t ⋅ χ d1f
2
A elflats = 6.803mm
Outer corners of the cross-section not included above:
A e_4crns := ⎡⎣π ⋅ t ⋅ ( rmid)⎤⎦ ⋅ χ d1f + π ⋅ t ⋅ ( rmid)
(flange lip corners are reduced by χ d1f )
2
A eflats := A ewflats + 2 ⋅ A efflats + 2 ⋅ A elflats
A eflats = 208.565mm
A ecrns := A ewcrns + 2 ⋅ A efcrns + A e_4crns
A ecrns = 11.765mm
A etotal := A eflats + A ecrns
A etotal = 220.3mm
2
2
PREDICTED LOAD
Without enhanced corner properties
Pn := A etotal ⋅ fy
Pn = 43.0kN
With enhanced corner properties
Pn := A eflats ⋅ fy + A ecrns ⋅ fycrn
Department of Civil Engineering
Research Report No R845
Pn = 46.0kN
121
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
ASCE (2002), AS/NZS 4673 (2001)
(AS/NZS 4600 (1996) NAS (2001))
Material
Properties
Test ID
304D1a
304D1b
304D2a
304D2b
Geometry
Effective Areas
Without EC Prop. With EC Prop.
f y,f
f y,c
Ag
Ac
A c /A g
P u,t
A e,f
A e,c
A e,t
Pn
P u,t /P n
Pn
MPa
242
242
242
242
MPa
565
565
565
565
mm2
565
565
565
565
mm2
61
61
61
61
%
11
11
11
11
kN
102
101
104
104
mm2
356
355
356
356
mm2
61
61
61
61
mm2
418
416
417
417
kN
101
1.01
101
1.00
101
1.03
101
1.03
mean 1.02
stdv 0.0143
cov 0.0140
kN
121
120
121
121
experimental
P u,t /P n
0.84
0.84
0.86
0.86
0.85
0.0118
0.0139
ASCE (2002), AS/NZS 4673 (2001)
(AS/NZS 4600 (1996) NAS (2001))
Material
Properties
f y,f
Test ID
304_60_60_10_2
304_60_60_10_3
304_60_60_15_2
304_60_60_15_3
304_150_150_30_3
304_150_150_20_3
304_150_150_10_3
304_200_100_15_4
304_200_150_20_3
304_200_150_20_4
304_150_80_5_1
304_50_50_5_1
304_400_400_20_3
304_400_400_20_4
304_400_400_20_5
304_400_400_40_4
304_400_400_40_5
304_400_400_40_6
304_400_400_40_7
304_400_400_40_8
304_300_400_20_3
304_300_400_20_4
304_300_400_20_5
304_400_300_20_3
304_400_300_20_4
304_400_300_20_5
304_400_300_40_5
304_400_300_40_6
304_400_300_40_7
304_400_300_40_8
f y,c
Geometry
Ag
Ac
2
MPa MPa mm
195 195
393
195 195
584
195 195
413
195 195
614
195 195 1514
195 195 1454
195 195 1394
195 195 1692
195 195 1604
195 195 2132
195 195
318
195 195
158
195 195 3704
195 195 4932
195 195 6156
195 195 5092
195 195 6356
195 195 7617
195 195 8874
195 195 10130
195 195 3404
195 195 4532
195 195 5656
195 195 3104
195 195 4132
195 195 5156
195 195 5356
195 195 6417
195 195 7474
195 195 8528
Effective Areas
A c /A g
2
mm
25
57
25
57
57
57
57
101
57
101
6
6
57
101
157
101
157
226
308
402
57
101
157
57
101
157
157
226
308
402
%
6
10
6
9
4
4
4
6
4
5
2
4
2
2
3
2
2
3
3
4
2
2
3
2
2
3
3
4
4
5
P u,t
kN
65
112
74
124
213
183
153
257
191
300
20
18
176
292
443
347
516
727
947
1180
171
293
447
177
294
457
551
766
984
1199
A e,f
2
A e,c
2
mm mm
345
25
528
57
388
25
558
57
1185 57
1034 57
883
57
1460 101
1072 57
1604 101
120
6
107
6
1141 57
1875 101
2742 157
2268 101
3249 157
4357 226
5566 308
6854 402
1123 57
1831 101
2654 157
1148 57
1876 101
2729 157
3225 157
4288 226
5437 308
6418 402
flats
Department of Civil Engineering
Research Report No R845
122
Without EC Prop. With EC Prop.
A e,t
2
mm
370
585
413
615
1242
1090
940
1561
1129
1705
126
113
1198
1976
2899
2369
3406
4583
5874
7256
1179
1931
2811
1205
1976
2886
3382
4514
5745
6820
Pn
P u,t /P n
kN
72
0.90
114
0.98
81
0.91
120
1.03
242
0.88
213
0.86
183
0.84
304
0.84
220
0.87
332
0.90
25
0.82
22
0.84
234
0.76
385
0.76
565
0.78
462
0.75
664
0.78
894
0.81
1145
0.83
1415
0.83
230
0.74
377
0.78
548
0.81
235
0.75
385
0.76
563
0.81
659
0.84
880
0.87
1120
0.88
1330
0.90
mean 0.84
stdv 0.0687
cov 0.0821
Pn
kN
72
114
81
120
242
213
183
304
220
332
25
22
234
385
565
462
664
894
1145
1415
230
377
548
235
385
563
659
880
1120
1330
P u,t /P n
0.90
0.98
0.91
1.03
0.88
0.86
0.84
0.84
0.87
0.90
0.82
0.84
0.76
0.76
0.78
0.75
0.78
0.81
0.83
0.83
0.74
0.78
0.81
0.75
0.76
0.81
0.84
0.87
0.88
0.90
0.84
0.0687
0.0821
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
ASCE (2002), AS/NZS 4673 (2001)
(AS/NZS 4600 (1996) NAS (2001))
Material
Properties
f y,f
Test ID
304_60_60_10_2_1
304_60_60_10_3_1
304_60_60_15_2_1
304_60_60_15_3_1
304_150_150_30_3_1
304_150_150_20_3_1
304_150_150_10_3_1
304_200_100_15_4_1
304_200_150_20_3_1
304_200_150_20_4_1
304_150_80_5_1_1
304_50_50_5_1_1
304_400_400_20_3_1
304_400_400_20_4_1
304_400_400_20_5_1
304_400_400_40_4_1
304_400_400_40_5_1
304_400_400_40_6_1
304_400_400_40_7_1
304_400_400_40_8_1
304_300_400_20_3_1
304_300_400_20_4_1
304_300_400_20_5_1
304_400_300_20_3_1
304_400_300_20_4_1
304_400_300_20_5_1
304_400_300_40_5_1
304_400_300_40_6_1
304_400_300_40_7_1
304_400_300_40_8_1
f y,c
Geometry
Ag
MPa MPa mm2
195 457
393
195 457
584
195 457
413
195 457
614
195 457 1514
195 457 1454
195 457 1394
195 457 1692
195 457 1604
195 457 2132
195 457
318
195 457
158
195 457 3704
195 457 4932
195 457 6156
195 457 5092
195 457 6356
195 457 7617
195 457 8874
195 457 10130
195 457 3404
195 457 4532
195 457 5656
195 457 3104
195 457 4132
195 457 5156
195 457 5356
195 457 6417
195 457 7474
195 457 8528
Effective Areas
Ac
A c /A g
P u,t
A e,f
A e,c
mm2
25
57
25
57
57
57
57
101
57
101
6
6
57
101
157
101
157
226
308
402
57
101
157
57
101
157
157
226
308
402
%
6
10
6
9
4
4
4
6
4
5
2
4
2
2
3
2
2
3
3
4
2
2
3
2
2
3
3
4
4
5
kN
67
120
77
135
217
187
160
266
195
308
21
19
175
296
454
347
525
746
977
1219
175
301
457
176
302
467
558
780
1007
1232
mm2 mm2
345
25
528
57
388
25
558
57
1185 57
1034 57
883
57
1460 101
1072 57
1604 101
120
6
107
6
1141 57
1875 101
2742 157
2268 101
3249 157
4357 226
5566 308
6854 402
1123 57
1831 101
2654 157
1148 57
1876 101
2729 157
3225 157
4288 226
5437 308
6418 402
r/t=1
Department of Civil Engineering
Research Report No R845
123
A e,t
mm2
370
585
413
615
1242
1090
940
1561
1129
1705
126
113
1198
1976
2899
2369
3406
4583
5874
7256
1179
1931
2811
1205
1976
2886
3382
4514
5745
6820
Without EC Prop. With EC Prop.
Pn
P u,t /P n
kN
72
0.93
114
1.05
81
0.96
120
1.12
242
0.90
213
0.88
183
0.87
304
0.87
220
0.88
332
0.93
25
0.84
22
0.86
234
0.75
385
0.77
565
0.80
462
0.75
664
0.79
894
0.83
1145
0.85
1415
0.86
230
0.76
377
0.80
548
0.83
235
0.75
385
0.78
563
0.83
659
0.85
880
0.89
1120
0.90
1330
0.93
mean 0.86
stdv 0.0851
cov 0.0989
Pn
kN
79
129
87
135
257
227
198
331
235
359
26
24
248
412
607
488
705
953
1226
1520
245
403
589
250
412
604
701
939
1201
1435
P u,t /P n
0.85
0.93
0.88
1.00
0.85
0.82
0.81
0.80
0.83
0.86
0.78
0.80
0.70
0.72
0.75
0.71
0.74
0.78
0.80
0.80
0.72
0.75
0.78
0.70
0.73
0.77
0.80
0.83
0.84
0.86
0.80
0.0682
0.0852
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
ASCE (2002), AS/NZS 4673 (2001)
(AS/NZS 4600 (1996) NAS (2001))
Material
Properties
f y,f
Test ID
304_60_60_10_2_2.5
304_60_60_10_3_2.5
304_60_60_15_2_2.5
304_60_60_15_3_2.5
304_150_150_30_3_2.5
304_150_150_20_3_2.5
304_150_150_10_3_2.5
304_200_100_15_4_2.5
304_200_150_20_3_2.5
304_200_150_20_4_2.5
304_150_80_5_1_2.5
304_50_50_5_1_2.5
304_400_400_20_3_2.5
304_400_400_20_4_2.5
304_400_400_20_5_2.5
304_400_400_40_4_2.5
304_400_400_40_5_2.5
304_400_400_40_6_2.5
304_400_400_40_7_2.5
304_400_400_40_8_2.5
304_300_400_20_3_2.5
304_300_400_20_4_2.5
304_300_400_20_5_2.5
304_400_300_20_3_2.5
304_400_300_20_4_2.5
304_400_300_20_5_2.5
304_400_300_40_5_2.5
304_400_300_40_6_2.5
304_400_300_40_7_2.5
304_400_300_40_8_2.5
f y,c
MPa MPa
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
Geometry
Effective Areas
Ag
Ac
A c /A g
P u,t
A e,f
A e,c
mm2
382
561
402
591
1491
1431
1371
1650
1581
2090
316
156
3681
4890
6090
5050
6290
7522
8745
9959
3381
4490
5590
3081
4090
5090
5290
6322
7345
8359
mm2
63
141
63
141
141
141
141
251
141
251
16
16
141
251
393
251
393
565
770
1005
141
251
393
141
251
393
393
565
770
1005
%
16
25
16
24
9
10
10
15
9
12
5
10
4
5
6
5
6
8
9
10
4
6
7
5
6
8
7
9
10
12
kN
68
123
78
139
218
188
164
268
196
315
21
19
179
305
458
346
531
755
990
1234
177
305
464
183
307
477
561
784
1014
1245
mm2 mm2
303
63
420 141
340
63
450 141
1094 141
956 141
775 141
1323 251
999 141
1463 251
111
16
98
16
1075 141
1736 251
2490 393
2146 251
3057 393
4065 565
5139 770
6250 1005
1055 141
1688 251
2394 393
1080 141
1735 251
2477 393
3028 393
3997 565
4694 770
5850 1005
A e,t
mm2
366
561
403
591
1235
1098
917
1574
1141
1714
127
113
1216
1987
2883
2397
3450
4630
5908
7256
1197
1939
2786
1222
1986
2870
3421
4563
5464
6856
r/t=2.5
All Tests
Without EC Prop. With EC Prop.
Pn
P u,t /P n
kN
71
0.95
109
1.12
79
0.99
115
1.21
241
0.90
214
0.88
179
0.92
307
0.87
222
0.88
334
0.94
25
0.83
22
0.87
237
0.75
388
0.79
562
0.81
467
0.74
673
0.79
903
0.84
1152
0.86
1415
0.87
233
0.76
378
0.81
543
0.85
238
0.77
387
0.79
560
0.85
667
0.84
890
0.88
1065
0.95
1337
0.93
mean 0.88
stdv 0.1022
cov 0.1167
Pn
kN
82
133
89
139
264
237
202
348
246
376
27
25
260
429
627
509
738
996
1279
1581
257
420
608
262
429
624
732
983
1192
1503
mean 0.86
stdv 0.0911
cov 0.1053
P u,t /P n
0.83
0.93
0.88
1.00
0.82
0.79
0.81
0.77
0.80
0.84
0.75
0.78
0.69
0.71
0.73
0.68
0.72
0.76
0.77
0.78
0.69
0.73
0.76
0.70
0.71
0.76
0.77
0.80
0.85
0.83
0.78
0.0723
0.0925
0.81
0.0718
0.0889
EC3 Part 1-4/1-3 (2004) Traditional Method
Material
Properties
f y,f
Test ID
304D1a
304D1b
304D2a
304D2b
f y,c
MPa MPa
242 565
242 565
242 565
242 565
Geometry
Effective Areas
Ag
Ac
A c /A g
P u,t
A e,f
A e,c
A e,t
mm2
565
565
565
565
mm2
61
61
61
61
%
11
11
11
11
kN
102
101
104
104
mm2 mm2 mm2
310
44
354
310
44
354
310
44
354
310
44
354
experimental
Department of Civil Engineering
Research Report No R845
124
Without EC Prop. With EC Prop.
Pn
P u,t /P n
kN
86
86
86
86
mean
stdv
cov
1.19
1.18
1.21
1.21
1.20
0.0175
0.0146
Pn
kN
100
100
100
100
P u,t /P n
1.02
1.01
1.04
1.04
1.03
0.0150
0.0146
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
EC3 Part 1-4/1-3 (2004) Traditional Method
Material
Properties
f y,f
Test ID
304_60_60_10_2
304_60_60_10_3
304_60_60_15_2
304_60_60_15_3
304_150_150_30_3
304_150_150_20_3
304_150_150_10_3
304_200_100_15_4
304_200_150_20_3
304_200_150_20_4
304_150_80_5_1
304_50_50_5_1
304_400_400_20_3
304_400_400_20_4
304_400_400_20_5
304_400_400_40_4
304_400_400_40_5
304_400_400_40_6
304_400_400_40_7
304_400_400_40_8
304_300_400_20_3
304_300_400_20_4
304_300_400_20_5
304_400_300_20_3
304_400_300_20_4
304_400_300_20_5
304_400_300_40_5
304_400_300_40_6
304_400_300_40_7
304_400_300_40_8
f y,c
Geometry
Ag
MPa MPa mm2
195 195
393
195 195
584
195 195
413
195 195
614
195 195 1514
195 195 1454
195 195 1394
195 195 1692
195 195 1604
195 195 2132
195 195
318
195 195
158
195 195 3704
195 195 4932
195 195 6156
195 195 5092
195 195 6356
195 195 7617
195 195 8874
195 195 10130
195 195 3404
195 195 4532
195 195 5656
195 195 3104
195 195 4132
195 195 5156
195 195 5356
195 195 6417
195 195 7474
195 195 8528
Effective Areas
Ac
A c /A g
P u,t
A e,f
A e,c
mm2
25
57
25
57
57
57
57
101
57
101
6
6
57
101
157
101
157
226
308
402
57
101
157
57
101
157
157
226
308
402
%
6
10
6
9
4
4
4
6
4
5
2
4
2
2
3
2
2
3
3
4
2
2
3
2
2
3
3
4
4
5
kN
65
112
74
124
213
183
153
257
191
300
20
18
176
292
443
347
516
727
947
1180
171
293
447
177
294
457
551
766
984
1199
mm2 mm2
356
23
541
55
390
25
573
57
1069 50
930
43
809
38
1328 90
926
42
1620 83
100
4
96
5
939
33
1622 60
2416 95
1792 67
2702 106
3755 155
4876 214
6171 288
935
34
1608 61
2392 96
946
35
1601 63
2384 101
2722 113
3703 168
4899 241
6481 334
flats
Department of Civil Engineering
Research Report No R845
125
A e,t
mm2
379
596
415
630
1119
973
847
1418
968
1703
104
101
972
1682
2511
1859
2808
3910
5090
6459
969
1669
2488
981
1664
2485
2835
3871
5140
6815
Without EC Prop. With EC Prop.
Pn
kN
74
116
81
123
218
190
165
277
189
332
20
20
190
328
490
362
548
762
993
1260
189
325
485
191
324
485
553
755
1002
1329
mean
stdv
cov
P u,t /P n
0.87
0.96
0.91
1.01
0.97
0.96
0.93
0.93
1.01
0.90
1.00
0.94
0.93
0.89
0.90
0.96
0.94
0.95
0.95
0.94
0.90
0.90
0.92
0.92
0.91
0.94
1.00
1.01
0.98
0.90
0.94
0.0385
0.0408
Pn
kN
74
116
81
123
218
190
165
277
189
332
20
20
190
328
490
362
548
762
993
1260
189
325
485
191
324
485
553
755
1002
1329
P u,t /P n
0.87
0.96
0.91
1.01
0.97
0.96
0.93
0.93
1.01
0.90
1.00
0.94
0.93
0.89
0.90
0.96
0.94
0.95
0.95
0.94
0.90
0.90
0.92
0.92
0.91
0.94
1.00
1.01
0.98
0.90
0.94
0.0385
0.0408
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
EC3 Part 1-4/1-3 (2004) Traditional Method
Material
Properties
f y,f
Test ID
304_60_60_10_2_1
304_60_60_10_3_1
304_60_60_15_2_1
304_60_60_15_3_1
304_150_150_30_3_1
304_150_150_20_3_1
304_150_150_10_3_1
304_200_100_15_4_1
304_200_150_20_3_1
304_200_150_20_4_1
304_150_80_5_1_1
304_50_50_5_1_1
304_400_400_20_3_1
304_400_400_20_4_1
304_400_400_20_5_1
304_400_400_40_4_1
304_400_400_40_5_1
304_400_400_40_6_1
304_400_400_40_7_1
304_400_400_40_8_1
304_300_400_20_3_1
304_300_400_20_4_1
304_300_400_20_5_1
304_400_300_20_3_1
304_400_300_20_4_1
304_400_300_20_5_1
304_400_300_40_5_1
304_400_300_40_6_1
304_400_300_40_7_1
304_400_300_40_8_1
f y,c
Geometry
Ag
MPa MPa mm2
195 457
393
195 457
584
195 457
413
195 457
614
195 457 1514
195 457 1454
195 457 1394
195 457 1692
195 457 1604
195 457 2132
195 457
318
195 457
158
195 457 3704
195 457 4932
195 457 6156
195 457 5092
195 457 6356
195 457 7617
195 457 8874
195 457 10130
195 457 3404
195 457 4532
195 457 5656
195 457 3104
195 457 4132
195 457 5156
195 457 5356
195 457 6417
195 457 7474
195 457 8528
Effective Areas
Ac
A c /A g
P u,t
A e,f
A e,c
mm2
25
57
25
57
57
57
57
101
57
101
6
6
57
101
157
101
157
226
308
402
57
101
157
57
101
157
157
226
308
402
%
6
10
6
9
4
4
4
6
4
5
2
4
2
2
3
2
2
3
3
4
2
2
3
2
2
3
3
4
4
5
kN
67
120
77
135
217
187
160
266
195
308
21
19
175
296
454
347
525
746
977
1219
175
301
457
176
302
467
558
780
1007
1232
mm2 mm2
356
23
541
55
390
25
573
57
1069 50
930
43
809
38
1328 90
926
42
1620 83
100
4
96
5
939
33
1622 60
2416 95
1792 67
2702 106
3755 155
4876 214
6171 288
935
34
1608 61
2392 96
946
35
1601 63
2384 101
2722 113
3703 168
4899 241
6481 334
r/t=1
Department of Civil Engineering
Research Report No R845
126
A e,t
mm2
379
596
415
630
1119
973
847
1418
968
1703
104
101
972
1682
2511
1859
2808
3910
5090
6459
969
1669
2488
981
1664
2485
2835
3871
5140
6815
Without EC Prop. With EC Prop.
Pn
kN
74
116
81
123
218
190
165
277
189
332
20
20
190
328
490
362
548
762
993
1260
189
325
485
191
324
485
553
755
1002
1329
mean
stdv
cov
P u,t /P n
0.91
1.03
0.95
1.10
1.00
0.99
0.97
0.96
1.03
0.93
1.02
0.97
0.92
0.90
0.93
0.96
0.96
0.98
0.98
0.97
0.93
0.92
0.94
0.92
0.93
0.96
1.01
1.03
1.00
0.93
0.97
0.0451
0.0466
Pn
kN
80
131
87
138
231
201
175
300
200
354
21
21
198
344
515
380
575
803
1049
1335
198
341
510
200
341
511
583
799
1065
1416
P u,t /P n
0.84
0.92
0.88
0.98
0.94
0.93
0.91
0.89
0.97
0.87
0.97
0.91
0.88
0.86
0.88
0.91
0.91
0.93
0.93
0.91
0.89
0.88
0.90
0.88
0.89
0.91
0.96
0.98
0.95
0.87
0.91
0.0366
0.0402
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
EC3 Part 1-4/1-3 (2004) Traditional Method
Material
Properties
f y,f
Test ID
304_60_60_10_2_2.5
304_60_60_10_3_2.5
304_60_60_15_2_2.5
304_60_60_15_3_2.5
304_150_150_30_3_2.5
304_150_150_20_3_2.5
304_150_150_10_3_2.5
304_200_100_15_4_2.5
304_200_150_20_3_2.5
304_200_150_20_4_2.5
304_150_80_5_1_2.5
304_50_50_5_1_2.5
304_400_400_20_3_2.5
304_400_400_20_4_2.5
304_400_400_20_5_2.5
304_400_400_40_4_2.5
304_400_400_40_5_2.5
304_400_400_40_6_2.5
304_400_400_40_7_2.5
304_400_400_40_8_2.5
304_300_400_20_3_2.5
304_300_400_20_4_2.5
304_300_400_20_5_2.5
304_400_300_20_3_2.5
304_400_300_20_4_2.5
304_400_300_20_5_2.5
304_400_300_40_5_2.5
304_400_300_40_6_2.5
304_400_300_40_7_2.5
304_400_300_40_8_2.5
f y,c
MPa MPa
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
Geometry
Effective Areas
Ag
Ac
A c /A g
P u,t
A e,f
A e,c
mm2
382
561
402
591
1491
1431
1371
1650
1581
2090
316
156
3681
4890
6090
5050
6290
7522
8745
9959
3381
4490
5590
3081
4090
5090
5290
6322
7345
8359
mm2
63
141
63
141
141
141
141
251
141
251
16
16
141
251
393
251
393
565
770
1005
141
251
393
141
251
393
393
565
770
1005
%
16
25
16
24
9
10
10
15
9
12
5
10
4
5
6
5
6
8
9
10
4
6
7
5
6
8
7
9
10
12
kN
68
123
78
139
218
188
164
268
196
315
21
19
179
305
458
346
531
755
990
1234
177
305
464
183
307
477
561
784
1014
1245
mm2 mm2
313
57
443 136
350
62
484 141
989 123
853 106
739
93
1162 220
856 104
1457 203
93
9
88
11
885
83
1515 149
2240 236
1685 166
2535 263
3492 383
4515 532
5636 709
881
84
1501 150
2209 237
889
86
1484 156
2197 249
2529 282
3425 416
4472 592
5820 811
A e,t
mm2
370
579
412
625
1112
959
832
1382
960
1660
102
99
968
1664
2476
1851
2798
3875
5047
6345
965
1651
2446
975
1640
2446
2811
3841
5064
6631
r/t=2.5
All Tests
Department of Civil Engineering
Research Report No R845
127
Without EC Prop. With EC Prop.
Pn
P u,t /P n
kN
72
113
80
122
217
187
162
269
187
324
20
19
189
324
483
361
546
756
984
1237
188
322
477
190
320
477
548
749
987
1293
mean
stdv
cov
0.94
1.09
0.97
1.14
1.00
1.01
1.01
1.00
1.05
0.97
1.03
1.00
0.95
0.94
0.95
0.96
0.97
1.00
1.01
1.00
0.94
0.95
0.97
0.96
0.96
1.00
1.02
1.05
1.03
0.96
0.99
0.0461
0.0464
mean
stdv
cov
0.98
0.0663
0.0678
Pn
kN
82
135
90
145
237
204
178
306
204
357
22
21
202
349
522
388
589
819
1072
1354
202
347
516
204
345
518
595
818
1085
1427
P u,t /P n
0.83
0.91
0.86
0.96
0.92
0.92
0.92
0.88
0.96
0.88
0.95
0.91
0.88
0.87
0.88
0.89
0.90
0.92
0.92
0.91
0.88
0.88
0.90
0.90
0.89
0.92
0.94
0.96
0.93
0.87
0.91
0.0316
0.0350
0.92
0.0440
0.0476
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
EC3 Part 1-4/1-3 (2004) Alternative Method
Material
Properties
f y,f
Test ID
304D1a
304D1b
304D2a
304D2b
f y,c
MPa MPa
242 565
242 565
242 565
242 565
Geometry
Ag
Ac
2
mm
565
565
565
565
A c /A g
P u,t
A e,f
%
11
11
11
11
kN
102
101
104
104
mm
337
336
341
341
2
mm
61
61
61
61
Without EC
Prop.
Effective Areas
2
A e,c
2
mm
54
54
55
55
A e,t
2
mm
391
391
396
396
experimental
Pn
With EC Prop.
P u,t /P n
Pn
kN
95
1.08
95
1.07
96
1.09
96
1.09
mean 1.08
stdv 0.0082
cov 0.0076
kN
112
112
114
114
P u,t /P n
0.91
0.90
0.92
0.91
0.91
0.0068
0.0075
EC3 Part 1-4/1-3 (2004) Alternative Method
Material
Properties
f y,f
Test ID
304_60_60_10_2
304_60_60_10_3
304_60_60_15_2
304_60_60_15_3
304_150_150_30_3
304_150_150_20_3
304_150_150_10_3
304_200_100_15_4
304_200_150_20_3
304_200_150_20_4
304_150_80_5_1
304_50_50_5_1
304_400_400_20_3
304_400_400_20_4
304_400_400_20_5
304_400_400_40_4
304_400_400_40_5
304_400_400_40_6
304_400_400_40_7
304_400_400_40_8
304_300_400_20_3
304_300_400_20_4
304_300_400_20_5
304_400_300_20_3
304_400_300_20_4
304_400_300_20_5
304_400_300_40_5
304_400_300_40_6
304_400_300_40_7
304_400_300_40_8
f y,c
Geometry
Ag
MPa MPa mm2
195 195
393
195 195
584
195 195
413
195 195
614
195 195 1514
195 195 1454
195 195 1394
195 195 1692
195 195 1604
195 195 2132
195 195
318
195 195
158
195 195 3704
195 195 4932
195 195 6156
195 195 5092
195 195 6356
195 195 7617
195 195 8874
195 195 10130
195 195 3404
195 195 4532
195 195 5656
195 195 3104
195 195 4132
195 195 5156
195 195 5356
195 195 6417
195 195 7474
195 195 8528
Department of Civil Engineering
Research Report No R845
Effective Areas
Ac
A c /A g
P u,t
A e,f
mm2
25
57
25
57
57
57
57
101
57
101
6
6
57
101
157
101
157
226
308
402
57
101
157
57
101
157
157
226
308
402
%
6
10
6
9
4
4
4
6
4
5
2
4
2
2
3
2
2
3
3
4
2
2
3
2
2
3
3
4
4
5
kN
65
112
74
124
213
183
153
257
191
300
20
18
176
292
443
347
516
727
947
1180
171
293
447
177
294
457
551
766
984
1199
mm2 mm2
370
25
543
57
395
25
573
57
1051 52
952
49
820
42
1373 96
957
48
1722 91
94
4
99
5
852
35
1497 64
2311 103
1640 69
2528 112
3583 166
4875 238
6330 325
847
35
1482 64
2279 104
870
36
1526 68
2351 110
2665 124
3807 189
5094 268
6862 362
128
A e,c
A e,t
Without EC
Prop.
Pn
P u,t /P n
mm2 kN
395
77
0.84
600 117
0.96
420
82
0.90
630 123
1.01
1103 215
0.99
1000 195
0.94
861 168
0.91
1469 286
0.90
1005 196
0.97
1813 353
0.85
98
19
1.05
104
20
0.91
886 173
1.02
1561 304
0.96
2413 471
0.94
1709 333
1.04
2640 515
1.00
3749 731
0.99
5113 997
0.95
6656 1298
0.91
881 172
0.99
1546 301
0.97
2383 465
0.96
906 177
1.00
1594 311
0.95
2461 480
0.95
2789 544
1.01
3996 779
0.98
5362 1046
0.94
7224 1409
0.85
mean 0.96
flats
stdv 0.0543
cov 0.0568
With EC Prop.
Pn
kN
77
117
82
123
215
195
168
286
196
353
19
20
173
304
471
333
515
731
997
1298
172
301
465
177
311
480
544
779
1046
1409
P u,t /P n
0.84
0.96
0.90
1.01
0.99
0.94
0.91
0.90
0.97
0.85
1.05
0.91
1.02
0.96
0.94
1.04
1.00
0.99
0.95
0.91
0.99
0.97
0.96
1.00
0.95
0.95
1.01
0.98
0.94
0.85
0.96
0.0543
0.0568
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
EC3 Part 1-4/1-3 (2004) Alternative Method
Material
Properties
f y,f
Test ID
304_60_60_10_2_1
304_60_60_10_3_1
304_60_60_15_2_1
304_60_60_15_3_1
304_150_150_30_3_1
304_150_150_20_3_1
304_150_150_10_3_1
304_200_100_15_4_1
304_200_150_20_3_1
304_200_150_20_4_1
304_150_80_5_1_1
304_50_50_5_1_1
304_400_400_20_3_1
304_400_400_20_4_1
304_400_400_20_5_1
304_400_400_40_4_1
304_400_400_40_5_1
304_400_400_40_6_1
304_400_400_40_7_1
304_400_400_40_8_1
304_300_400_20_3_1
304_300_400_20_4_1
304_300_400_20_5_1
304_400_300_20_3_1
304_400_300_20_4_1
304_400_300_20_5_1
304_400_300_40_5_1
304_400_300_40_6_1
304_400_300_40_7_1
304_400_300_40_8_1
f y,c
Geometry
Ag
MPa MPa mm2
195 457
393
195 457
584
195 457
413
195 457
614
195 457 1514
195 457 1454
195 457 1394
195 457 1692
195 457 1604
195 457 2132
195 457
318
195 457
158
195 457 3704
195 457 4932
195 457 6156
195 457 5092
195 457 6356
195 457 7617
195 457 8874
195 457 10130
195 457 3404
195 457 4532
195 457 5656
195 457 3104
195 457 4132
195 457 5156
195 457 5356
195 457 6417
195 457 7474
195 457 8528
Department of Civil Engineering
Research Report No R845
Effective Areas
Ac
A c /A g
P u,t
A e,f
mm2
25
57
25
57
57
57
57
101
57
101
6
6
57
101
157
101
157
226
308
402
57
101
157
57
101
157
157
226
308
402
%
6
10
6
9
4
4
4
6
4
5
2
4
2
2
3
2
2
3
3
4
2
2
3
2
2
3
3
4
4
5
kN
67
120
77
135
217
187
160
266
195
308
21
19
175
296
454
347
525
746
977
1219
175
301
457
176
302
467
558
780
1007
1232
mm2 mm2
370
25
543
57
395
25
573
57
1051 52
952
49
820
42
1373 96
957
48
1722 91
94
4
99
5
852
35
1497 64
2311 103
1640 69
2528 112
3583 166
4875 238
6330 325
847
35
1482 64
2279 104
870
36
1526 68
2351 110
2665 124
3807 189
5094 268
6862 362
129
A e,c
A e,t
Without EC
Prop.
Pn
P u,t /P n
mm2 kN
395
77
0.87
600 117
1.03
420
82
0.94
630 123
1.10
1103 215
1.01
1000 195
0.96
861 168
0.95
1469 286
0.93
1005 196
0.99
1813 353
0.87
98
19
1.07
104
20
0.94
886 173
1.01
1561 304
0.97
2413 471
0.97
1709 333
1.04
2640 515
1.02
3749 731
1.02
5113 997
0.98
6656 1298
0.94
881 172
1.02
1546 301
1.00
2383 465
0.98
906 177
1.00
1594 311
0.97
2461 480
0.97
2789 544
1.03
3996 779
1.00
5362 1046
0.96
7224 1409
0.87
mean 0.98
r/t=1
stdv 0.0530
cov 0.0541
With EC Prop.
Pn
kN
83
132
88
138
229
208
179
311
208
377
20
22
182
321
498
351
544
775
1059
1383
181
318
492
186
328
509
576
829
1116
1504
P u,t /P n
0.81
0.91
0.87
0.98
0.95
0.90
0.89
0.85
0.93
0.82
1.02
0.88
0.96
0.92
0.91
0.99
0.97
0.96
0.92
0.88
0.97
0.95
0.93
0.94
0.92
0.92
0.97
0.94
0.90
0.82
0.92
0.0510
0.0555
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
EC3 Part 1-4/1-3 (2004) Alternative Method
Material
Properties
f y,f
Test ID
304_60_60_10_2_2.5
304_60_60_10_3_2.5
304_60_60_15_2_2.5
304_60_60_15_3_2.5
304_150_150_30_3_2.5
304_150_150_20_3_2.5
304_150_150_10_3_2.5
304_200_100_15_4_2.5
304_200_150_20_3_2.5
304_200_150_20_4_2.5
304_150_80_5_1_2.5
304_50_50_5_1_2.5
304_400_400_20_3_2.5
304_400_400_20_4_2.5
304_400_400_20_5_2.5
304_400_400_40_4_2.5
304_400_400_40_5_2.5
304_400_400_40_6_2.5
304_400_400_40_7_2.5
304_400_400_40_8_2.5
304_300_400_20_3_2.5
304_300_400_20_4_2.5
304_300_400_20_5_2.5
304_400_300_20_3_2.5
304_400_300_20_4_2.5
304_400_300_20_5_2.5
304_400_300_40_5_2.5
304_400_300_40_6_2.5
304_400_300_40_7_2.5
304_400_300_40_8_2.5
f y,c
MPa MPa
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
195 360
Geometry
Effective Areas
Ag
Ac
A c /A g
P u,t
A e,f
A e,c
mm2
382
561
402
591
1491
1431
1371
1650
1581
2090
316
156
3681
4890
6090
5050
6290
7522
8745
9959
3381
4490
5590
3081
4090
5090
5290
6322
7345
8359
mm2
63
141
63
141
141
141
141
251
141
251
16
16
141
251
393
251
393
565
770
1005
141
251
393
141
251
393
393
565
770
1005
%
16
25
16
24
9
10
10
15
9
12
5
10
4
5
6
5
6
8
9
10
4
6
7
5
6
8
7
9
10
12
kN
68
123
78
139
218
188
164
268
196
315
21
19
179
305
458
346
531
755
990
1234
177
305
464
183
307
477
561
784
1014
1245
mm2 mm2
334
62
459 141
357
63
489 141
976 130
882 122
760 105
1232 240
889 120
1590 228
89
10
91
13
801
86
1403 159
2159 257
1538 173
2365 280
3366 421
4537 599
5870 819
795
87
1387 161
2127 260
816
91
1427 169
2190 276
2486 312
3536 475
4708 674
6339 909
A e,t
mm2
396
600
420
630
1106
1004
865
1472
1008
1818
99
104
887
1563
2416
1711
2645
3787
5136
6688
882
1548
2387
908
1596
2466
2798
4011
5381
7248
r/t=2.5
All Tests
Without EC
Prop.
Pn
P u,t /P n
kN
77
0.88
117
1.05
82
0.95
123
1.13
216
1.01
196
0.96
169
0.97
287
0.93
197
1.00
355
0.89
19
1.07
20
0.95
173
1.03
305
1.00
471
0.97
334
1.04
516
1.03
738
1.02
1002
0.99
1304
0.95
172
1.03
302
1.01
466
1.00
177
1.03
311
0.98
481
0.99
546
1.03
782
1.00
1049
0.97
1413
0.88
mean 0.99
stdv 0.0548
cov 0.0553
With EC Prop.
Pn
kN
87
140
92
146
237
216
186
327
216
392
21
22
187
331
514
362
562
808
1100
1439
186
328
508
192
339
526
597
861
1160
1563
mean 0.98
stdv 0.0583
cov 0.0595
P u,t /P n
0.78
0.88
0.85
0.95
0.92
0.87
0.88
0.82
0.91
0.80
0.98
0.86
0.96
0.92
0.89
0.96
0.95
0.93
0.90
0.86
0.95
0.93
0.91
0.95
0.90
0.91
0.94
0.91
0.87
0.80
0.90
0.0517
0.0576
0.92
0.0559
0.0605
ASCE (2002), AS/NZS 4673 (2001), (AS/NZS 4600
(1996) NAS (2001))
Material
Properties
`
Test ID
430D1a
430D1b
430D2
430D3a
430D3b
f y,f
f y,c
MPa MPa
271 452
271 452
271 452
271 452
271 452
Geometry
Effective Areas
Ag
Ac
A c /A g
P u,t
A e,f
A e,c
A e,t
Pn
P u,t /P n
Pn
mm2
211
211
215
188
188
mm2
21
22
22
22
22
%
10
10
10
12
12
kN
39
39
45
40
39
mm2
121
123
129
119
119
mm2
21
22
22
22
22
mm2
142
145
151
141
141
kN
39
1.00
39
0.99
41
1.10
38
1.04
38
1.01
mean 1.03
stdv 0.0437
cov 0.0425
kN
42
43
45
42
42
experimental
Department of Civil Engineering
Research Report No R845
Without EC Prop. With EC Prop.
130
P u,t /P n
0.91
0.90
1.00
0.94
0.92
0.93
0.0412
0.0441
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
ASCE (2002), AS/NZS 4673 (2001), (AS/NZS 4600
(1996) NAS (2001))
Material
Properties
`
Test ID
430_60_60_10_2
430_60_60_10_3
430_60_60_15_2
430_60_60_15_3
430_150_150_30_3
430_150_150_20_3
430_150_150_10_3
430_200_100_15_4
430_200_150_20_3
430_200_150_20_4
430_150_80_5_1
430_50_50_5_1
430_400_400_20_3
430_400_400_20_4
430_400_400_20_5
430_400_400_40_4
430_400_400_40_5
430_400_400_40_6
430_400_400_40_7
430_400_400_40_8
430_300_400_20_3
430_300_400_20_4
430_300_400_20_5
430_400_300_20_3
430_400_300_20_4
430_400_300_20_5
430_400_300_40_5
430_400_300_40_6
430_400_300_40_7
430_400_300_40_8
f y,f
f y,c
Geometry
Ag
MPa MPa mm2
275 275
393
275 275
584
275 275
413
275 275
614
275 275 1514
275 275 1454
275 275 1394
275 275 1692
275 275 1604
275 275 2132
275 275
318
275 275
158
275 275 3704
275 275 4932
275 275 6156
275 275 5092
275 275 6356
275 275 7617
275 275 8874
275 275 10130
275 275 3404
275 275 4532
275 275 5656
275 275 3104
275 275 4132
275 275 5156
275 275 5356
275 275 6417
275 275 7474
275 275 8528
Effective Areas
Ac
A c /A g
P u,t
A e,f
A e,c
A e,t
mm2
25
57
25
57
57
57
57
101
57
101
6
6
57
101
157
101
157
226
308
402
57
101
157
57
101
157
157
226
308
402
%
6
10
6
9
4
4
4
6
4
5
2
4
2
2
3
2
2
3
3
4
2
2
3
2
2
3
3
4
4
5
kN
85
146
96
163
280
240
200
338
244
390
26
24
231
356
579
424
647
950
1226
1531
225
383
579
231
397
594
699
980
1283
1563
mm2
301
497
353
558
1016
882
752
1305
908
1434
99
91
939
1553
2286
1877
2707
3656
4706
5839
926
1523
2227
947
1559
2285
2708
3632
4647
5736
mm2
25
57
25
57
57
57
57
101
57
101
6
6
57
101
157
101
157
226
308
402
57
101
157
57
101
157
157
226
308
402
mm2
326
554
378
615
1072
939
808
1406
965
1535
106
98
995
1653
2443
1977
2864
3882
5013
6241
983
1623
2384
1004
1659
2442
2865
3858
4955
6138
flats
Department of Civil Engineering
Research Report No R845
131
Without EC Prop. With EC Prop.
Pn
P u,t /P n
kN
90
0.95
152
0.96
104
0.92
169
0.97
295
0.95
258
0.93
222
0.90
387
0.87
265
0.92
422
0.92
29
0.90
27
0.89
274
0.84
455
0.78
672
0.86
544
0.78
788
0.82
1068
0.89
1379
0.89
1716
0.89
270
0.83
446
0.86
656
0.88
276
0.84
456
0.87
672
0.88
788
0.89
1061
0.92
1363
0.94
1688
0.93
mean 0.89
stdv 0.0480
cov 0.0539
Pn
kN
90
152
104
169
295
258
222
387
265
422
29
27
274
455
672
544
788
1068
1379
1716
270
446
656
276
456
672
788
1061
1363
1688
P u,t /P n
0.95
0.96
0.92
0.97
0.95
0.93
0.90
0.87
0.92
0.92
0.90
0.89
0.84
0.78
0.86
0.78
0.82
0.89
0.89
0.89
0.83
0.86
0.88
0.84
0.87
0.88
0.89
0.92
0.94
0.93
0.89
0.0480
0.0539
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
ASCE (2002), AS/NZS 4673 (2001), (AS/NZS 4600
(1996) NAS (2001))
Material
Properties
`
Test ID
430_60_60_10_2_1
430_60_60_10_3_1
430_60_60_15_2_1
430_60_60_15_3_1
430_150_150_30_3_1
430_150_150_20_3_1
430_150_150_10_3_1
430_200_100_15_4_1
430_200_150_20_3_1
430_200_150_20_4_1
430_150_80_5_1_1
430_50_50_5_1_1
430_400_400_20_3_1
430_400_400_20_4_1
430_400_400_20_5_1
430_400_400_40_4_1
430_400_400_40_5_1
430_400_400_40_6_1
430_400_400_40_7_1
430_400_400_40_8_1
430_300_400_20_3_1
430_300_400_20_4_1
430_300_400_20_5_1
430_400_300_20_3_1
430_400_300_20_4_1
430_400_300_20_5_1
430_400_300_40_5_1
430_400_300_40_6_1
430_400_300_40_7_1
430_400_300_40_8_1
f y,f
f y,c
Geometry
Ag
MPa MPa mm2
275 479
393
275 479
584
275 479
413
275 479
614
275 479 1514
275 479 1454
275 479 1394
275 479 1692
275 479 1604
275 479 2132
275 479
318
275 479
158
275 479 3704
275 479 4932
275 479 6156
275 479 5092
275 479 6356
275 479 7617
275 479 8874
275 479 10130
275 479 3404
275 479 4532
275 479 5656
275 479 3104
275 479 4132
275 479 5156
275 479 5356
275 479 6417
275 479 7474
275 479 8528
Effective Areas
Ac
A c /A g
P u,t
A e,f
A e,c
mm2
25
57
25
57
57
57
57
101
57
101
6
6
57
101
157
101
157
226
308
402
57
101
157
57
101
157
157
226
308
402
%
6
10
6
9
4
4
4
6
4
5
2
4
2
2
3
2
2
3
3
4
2
2
3
2
2
3
3
4
4
5
kN
87
153
98
171
284
243
203
345
246
397
27
24
230
357
586
430
650
953
1234
1547
228
388
586
234
402
601
704
988
1300
1589
mm2 mm2
301
25
497
57
353
25
558
57
1016 57
882
57
752
57
1305 101
908
57
1434 101
99
6
91
6
939
57
1553 101
2286 157
1877 101
2707 157
3656 226
4706 308
5839 402
926
57
1523 101
2227 157
947
57
1559 101
2285 157
2708 157
3632 226
4647 308
5736 402
r/t=1
Department of Civil Engineering
Research Report No R845
132
A e,t
mm2
326
554
378
615
1072
939
808
1406
965
1535
106
98
995
1653
2443
1977
2864
3882
5013
6241
983
1623
2384
1004
1659
2442
2865
3858
4955
6138
Without EC Prop. With EC Prop.
Pn
P u,t /P n
kN
90
0.97
152
1.00
104
0.95
169
1.01
295
0.96
258
0.94
222
0.91
387
0.89
265
0.93
422
0.94
29
0.91
27
0.90
274
0.84
455
0.78
672
0.87
544
0.79
788
0.83
1068
0.89
1379
0.89
1716
0.90
270
0.84
446
0.87
656
0.89
276
0.85
456
0.88
672
0.89
788
0.89
1061
0.93
1363
0.95
1688
0.94
mean 0.90
stdv 0.0543
cov 0.0602
Pn
kN
95
164
109
181
306
270
234
407
277
443
30
28
285
475
704
564
820
1114
1441
1798
282
467
688
288
477
704
820
1107
1426
1770
P u,t /P n
0.92
0.93
0.90
0.94
0.93
0.90
0.87
0.85
0.89
0.90
0.88
0.86
0.81
0.75
0.83
0.76
0.79
0.86
0.86
0.86
0.81
0.83
0.85
0.81
0.84
0.85
0.86
0.89
0.91
0.90
0.86
0.0479
0.0556
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
ASCE (2002), AS/NZS 4673 (2001), (AS/NZS 4600
(1996) NAS (2001))
Material
Properties
`
Test ID
430_60_60_10_2_2.5
430_60_60_10_3_2.5
430_60_60_15_2_2.5
430_60_60_15_3_2.5
430_150_150_30_3_2.5
430_150_150_20_3_2.5
430_150_150_10_3_2.5
430_200_100_15_4_2.5
430_200_150_20_3_2.5
430_200_150_20_4_2.5
430_150_80_5_1_2.5
430_50_50_5_1_2.5
430_400_400_20_3_2.5
430_400_400_20_4_2.5
430_400_400_20_5_2.5
430_400_400_40_4_2.5
430_400_400_40_5_2.5
430_400_400_40_6_2.5
430_400_400_40_7_2.5
430_400_400_40_8_2.5
430_300_400_20_3_2.5
430_300_400_20_4_2.5
430_300_400_20_5_2.5
430_400_300_20_3_2.5
430_400_300_20_4_2.5
430_400_300_20_5_2.5
430_400_300_40_5_2.5
430_400_300_40_6_2.5
430_400_300_40_7_2.5
430_400_300_40_8_2.5
f y,f
f y,c
MPa MPa
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
Geometry
Effective Areas
A e,c
Without EC Prop. With EC Prop.
Ag
Ac
A c /A g
P u,t
A e,f
A e,t
Pn
mm2
382
561
402
591
1491
1431
1371
1650
1581
2090
316
156
3681
4890
6090
5050
6290
7522
8745
9959
3381
4490
5590
3081
4090
5090
5290
6322
7345
8359
mm2
63
141
63
141
141
141
141
251
141
251
16
16
141
251
393
251
393
565
770
1005
141
251
393
141
251
393
393
565
770
1005
%
16
25
16
24
9
10
10
15
9
12
5
10
4
5
6
5
6
8
9
10
4
6
7
5
6
8
7
9
10
12
kN
87
154
99
173
286
244
205
346
247
399
26
24
236
343
586
437
650
953
1236
1556
229
390
590
235
404
605
704
992
1306
1598
mm2 mm2 mm2
264
63
327
406 141 547
314
63
376
450 141 591
941 141 1083
819 141 960
664 141 806
1162 251 1413
847 141 989
1206 251 1457
92
16
108
83
16
99
885 141 1027
1441 251 1692
2083 393 2476
1777 251 2028
2550 393 2943
3417 565 3982
4354 770 5124
5342 1005 6347
872 141 1013
1408 251 1660
2018 393 2411
892 141 1033
1444 251 1696
2079 393 2472
2545 393 2938
3390 565 3955
4298 770 5068
4822 1005 5828
r/t=2.5
P u,t /P n
kN
90
0.97
151
1.02
104
0.95
163
1.06
298
0.96
264
0.92
222
0.93
389
0.89
272
0.91
401
1.00
30
0.89
27
0.89
282
0.83
465
0.74
681
0.86
558
0.78
809
0.80
1095
0.87
1409
0.88
1746
0.89
279
0.82
456
0.85
663
0.89
284
0.83
466
0.87
680
0.89
808
0.87
1088
0.91
1394
0.94
1603
1.00
mean 0.90
stdv 0.0715
cov 0.0797
Pn
kN
99
172
113
184
319
285
243
426
293
438
32
30
303
503
739
595
868
1179
1524
1895
300
494
721
305
504
738
866
1172
1508
1752
mean 0.90
stdv 0.0647
cov 0.0716
All Tests
P u,t /P n
0.88
0.90
0.87
0.94
0.90
0.86
0.85
0.81
0.84
0.91
0.82
0.82
0.78
0.68
0.79
0.73
0.75
0.81
0.81
0.82
0.76
0.79
0.82
0.77
0.80
0.82
0.81
0.85
0.87
0.91
0.83
0.0575
0.0696
0.86
0.0588
0.0681
EC3 Part 1-4/1-3 (2004) Traditional Method
Material
Properties
`
Test ID
430D1a
430D1b
430D2
430D3a
430D3b
f y,f
f y,c
MPa MPa
271 452
271 452
271 452
271 452
271 452
Geometry
Ag
Ac
2
mm
211
211
215
188
188
Effective Areas
A c /A g
2
mm
21
22
22
22
22
%
10
10
10
12
12
P u,t
kN
39
39
45
40
39
A e,f
2
mm
103
103
109
102
102
A e,c
2
mm
15
15
16
16
16
A e,t
133
2
mm
118
118
125
118
118
experimental
Department of Civil Engineering
Research Report No R845
Without EC Prop. With EC Prop.
Pn
P u,t /P n
Pn
kN
32
1.20
32
1.22
34
1.33
32
1.24
32
1.21
mean 1.24
stdv 0.0506
cov 0.0408
kN
35
35
37
35
35
P u,t /P n
1.11
1.12
1.22
1.14
1.11
1.14
0.0469
0.0411
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
EC3 Part 1-4/1-3 (2004) Traditional Method
Material
Properties
`
Test ID
430_60_60_10_2
430_60_60_10_3
430_60_60_15_2
430_60_60_15_3
430_150_150_30_3
430_150_150_20_3
430_150_150_10_3
430_200_100_15_4
430_200_150_20_3
430_200_150_20_4
430_150_80_5_1
430_50_50_5_1
430_400_400_20_3
430_400_400_20_4
430_400_400_20_5
430_400_400_40_4
430_400_400_40_5
430_400_400_40_6
430_400_400_40_7
430_400_400_40_8
430_300_400_20_3
430_300_400_20_4
430_300_400_20_5
430_400_300_20_3
430_400_300_20_4
430_400_300_20_5
430_400_300_40_5
430_400_300_40_6
430_400_300_40_7
430_400_300_40_8
f y,f
f y,c
Geometry
Ag
MPa MPa mm2
275 275
393
275 275
584
275 275
413
275 275
614
275 275 1514
275 275 1454
275 275 1394
275 275 1692
275 275 1604
275 275 2132
275 275
318
275 275
158
275 275 3704
275 275 4932
275 275 6156
275 275 5092
275 275 6356
275 275 7617
275 275 8874
275 275 10130
275 275 3404
275 275 4532
275 275 5656
275 275 3104
275 275 4132
275 275 5156
275 275 5356
275 275 6417
275 275 7474
275 275 8528
Effective Areas
Ac
A c /A g
P u,t
A e,f
A e,c
A e,t
mm2
25
57
25
57
57
57
57
101
57
101
6
6
57
101
157
101
157
226
308
402
57
101
157
57
101
157
157
226
308
402
%
6
10
6
9
4
4
4
6
4
5
2
4
2
2
3
2
2
3
3
4
2
2
3
2
2
3
3
4
4
5
kN
85
146
96
163
280
240
200
338
244
390
26
24
231
356
579
424
647
950
1226
1531
225
383
579
231
397
594
699
980
1283
1563
mm2
336
517
372
566
876
770
680
1172
772
1276
84
81
768
1331
2025
1466
2222
3111
4080
5173
766
1323
2006
774
1336
1984
2248
3089
4030
5102
mm2
22
52
23
55
45
40
36
83
39
74
4
4
33
59
96
64
101
148
203
271
33
59
93
34
61
97
107
157
219
295
mm2
358
569
395
621
921
810
716
1255
811
1350
88
85
801
1390
2121
1530
2323
3259
4283
5444
799
1382
2099
808
1397
2081
2355
3246
4249
5397
flats
Department of Civil Engineering
Research Report No R845
134
Without EC Prop. With EC Prop.
Pn
P u,t /P n
kN
98
0.86
156
0.93
109
0.88
171
0.96
253
1.11
223
1.08
197
1.01
345
0.98
223
1.09
371
1.05
24
1.09
23
1.02
220
1.05
382
0.93
583
0.99
421
1.01
639
1.01
896
1.06
1178
1.04
1497
1.02
220
1.02
380
1.01
577
1.00
222
1.04
384
1.03
572
1.04
648
1.08
893
1.10
1168
1.10
1484
1.05
mean 1.02
stdv 0.0612
cov 0.0599
Pn
kN
98
156
109
171
253
223
197
345
223
371
24
23
220
382
583
421
639
896
1178
1497
220
380
577
222
384
572
648
893
1168
1484
P u,t /P n
0.86
0.93
0.88
0.96
1.11
1.08
1.01
0.98
1.09
1.05
1.09
1.02
1.05
0.93
0.99
1.01
1.01
1.06
1.04
1.02
1.02
1.01
1.00
1.04
1.03
1.04
1.08
1.10
1.10
1.05
1.02
0.0612
0.0599
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
EC3 Part 1-4/1-3 (2004) Traditional Method
Material
Properties
`
Test ID
430_60_60_10_2_1
430_60_60_10_3_1
430_60_60_15_2_1
430_60_60_15_3_1
430_150_150_30_3_1
430_150_150_20_3_1
430_150_150_10_3_1
430_200_100_15_4_1
430_200_150_20_3_1
430_200_150_20_4_1
430_150_80_5_1_1
430_50_50_5_1_1
430_400_400_20_3_1
430_400_400_20_4_1
430_400_400_20_5_1
430_400_400_40_4_1
430_400_400_40_5_1
430_400_400_40_6_1
430_400_400_40_7_1
430_400_400_40_8_1
430_300_400_20_3_1
430_300_400_20_4_1
430_300_400_20_5_1
430_400_300_20_3_1
430_400_300_20_4_1
430_400_300_20_5_1
430_400_300_40_5_1
430_400_300_40_6_1
430_400_300_40_7_1
430_400_300_40_8_1
f y,f
f y,c
Geometry
Ag
MPa MPa mm2
275 479
393
275 479
584
275 479
413
275 479
614
275 479 1514
275 479 1454
275 479 1394
275 479 1692
275 479 1604
275 479 2132
275 479
318
275 479
158
275 479 3704
275 479 4932
275 479 6156
275 479 5092
275 479 6356
275 479 7617
275 479 8874
275 479 10130
275 479 3404
275 479 4532
275 479 5656
275 479 3104
275 479 4132
275 479 5156
275 479 5356
275 479 6417
275 479 7474
275 479 8528
Effective Areas
Ac
A c /A g
P u,t
A e,f
A e,c
A e,t
mm2
25
57
25
57
57
57
57
101
57
101
6
6
57
101
157
101
157
226
308
402
57
101
157
57
101
157
157
226
308
402
%
6
10
6
9
4
4
4
6
4
5
2
4
2
2
3
2
2
3
3
4
2
2
3
2
2
3
3
4
4
5
kN
87
153
98
171
284
243
203
345
246
397
27
24
230
357
586
430
650
953
1234
1547
228
388
586
234
402
601
704
988
1300
1589
mm2
336
517
372
566
876
770
680
1172
772
1276
84
81
768
1331
2025
1466
2222
3111
4080
5173
766
1323
2006
774
1336
1984
2248
3089
4030
5102
mm2
22
52
23
55
45
40
36
83
39
74
4
4
33
59
96
64
101
148
203
271
33
59
93
34
61
97
107
157
219
295
mm2
358
569
395
621
921
810
716
1255
811
1350
88
85
801
1390
2121
1530
2323
3259
4283
5444
799
1382
2099
808
1397
2081
2355
3246
4249
5397
r/t=1
Department of Civil Engineering
Research Report No R845
135
Without EC Prop. With EC Prop.
Pn
P u,t /P n
kN
98
0.88
156
0.97
109
0.90
171
1.00
253
1.12
223
1.09
197
1.03
345
1.00
223
1.10
371
1.07
24
1.10
23
1.03
220
1.04
382
0.93
583
1.00
421
1.02
639
1.02
896
1.06
1178
1.05
1497
1.03
220
1.04
380
1.02
577
1.01
222
1.05
384
1.05
572
1.05
648
1.09
893
1.11
1168
1.11
1484
1.07
mean 1.04
stdv 0.0574
cov 0.0554
Pn
kN
103
167
114
182
262
231
204
362
231
386
25
24
227
394
603
434
659
926
1219
1552
226
392
596
229
397
592
670
925
1213
1544
P u,t /P n
0.85
0.91
0.87
0.94
1.08
1.05
0.99
0.95
1.06
1.03
1.07
0.99
1.01
0.91
0.97
0.99
0.99
1.03
1.01
1.00
1.01
0.99
0.98
1.02
1.01
1.01
1.05
1.07
1.07
1.03
1.00
0.0587
0.0588
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
EC3 Part 1-4/1-3 (2004) Traditional Method
Material
Properties
`
Test ID
430_60_60_10_2_2.5
430_60_60_10_3_2.5
430_60_60_15_2_2.5
430_60_60_15_3_2.5
430_150_150_30_3_2.5
430_150_150_20_3_2.5
430_150_150_10_3_2.5
430_200_100_15_4_2.5
430_200_150_20_3_2.5
430_200_150_20_4_2.5
430_150_80_5_1_2.5
430_50_50_5_1_2.5
430_400_400_20_3_2.5
430_400_400_20_4_2.5
430_400_400_20_5_2.5
430_400_400_40_4_2.5
430_400_400_40_5_2.5
430_400_400_40_6_2.5
430_400_400_40_7_2.5
430_400_400_40_8_2.5
430_300_400_20_3_2.5
430_300_400_20_4_2.5
430_300_400_20_5_2.5
430_400_300_20_3_2.5
430_400_300_20_4_2.5
430_400_300_20_5_2.5
430_400_300_40_5_2.5
430_400_300_40_6_2.5
430_400_300_40_7_2.5
430_400_300_40_8_2.5
f y,f
f y,c
MPa MPa
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
Geometry
Effective Areas
Ag
Ac
A c /A g
P u,t
A e,f
A e,c
A e,t
mm2
382
561
402
591
1491
1431
1371
1650
1581
2090
316
156
3681
4890
6090
5050
6290
7522
8745
9959
3381
4490
5590
3081
4090
5090
5290
6322
7345
8359
mm2
63
141
63
141
141
141
141
251
141
251
16
16
141
251
393
251
393
565
770
1005
141
251
393
141
251
393
393
565
770
1005
%
16
25
16
24
9
10
10
15
9
12
5
10
4
5
6
5
6
8
9
10
4
6
7
5
6
8
7
9
10
12
kN
87
154
99
173
286
244
205
346
247
399
26
24
236
343
586
437
650
953
1236
1556
229
390
590
235
404
605
704
992
1306
1598
mm2
296
423
334
476
802
703
615
1015
707
1143
77
73
716
1230
1847
1364
2059
2872
3740
4683
713
1221
1844
720
1231
1810
2075
2829
3667
4571
mm2
53
128
58
138
112
99
89
200
98
181
9
10
81
145
229
159
252
367
504
688
81
146
230
84
151
239
267
391
544
725
mm2
349
551
392
614
914
802
704
1215
805
1324
86
83
797
1375
2076
1523
2311
3239
4244
5371
794
1367
2074
804
1382
2049
2342
3220
4211
5296
r/t=2.5
All Tests
Department of Civil Engineering
Research Report No R845
136
Without EC Prop. With EC Prop.
Pn
P u,t /P n
kN
96
0.91
152
1.02
108
0.92
169
1.02
251
1.14
221
1.11
194
1.06
334
1.03
221
1.11
364
1.10
24
1.11
23
1.06
219
1.08
378
0.91
571
1.03
419
1.04
636
1.02
891
1.07
1167
1.06
1477
1.05
218
1.05
376
1.04
570
1.03
221
1.06
380
1.06
563
1.07
644
1.09
885
1.12
1158
1.13
1456
1.10
mean 1.05
stdv 0.0587
cov 0.0557
mean 1.05
stdv 0.0746
cov 0.0712
Pn
kN
104
171
116
189
268
235
207
364
236
391
25
24
231
400
605
443
673
945
1242
1580
230
398
605
234
403
599
684
944
1239
1564
P u,t /P n
0.84
0.90
0.85
0.91
1.07
1.04
0.99
0.95
1.05
1.02
1.05
0.99
1.02
0.86
0.97
0.99
0.97
1.01
1.00
0.99
0.99
0.98
0.98
1.01
1.00
1.01
1.03
1.05
1.05
1.02
0.99
0.0600
0.0608
1.01
0.0678
0.0672
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
EC3 Part 1-4/1-3 (2004) Alternative Method
Material
Properties
`
Test ID
430D1a
430D1b
430D2
430D3a
430D3b
f y,f
f y,c
MPa MPa
271 452
271 452
271 452
271 452
271 452
Geometry
Effective Areas
Without EC Prop. With EC Prop.
Ag
Ac
A c /A g
P u,t
A e,f
A e,c
A e,t
Pn
P u,t /P n
Pn
mm2
211
211
215
188
188
mm2
21
22
22
22
22
%
10
10
10
12
12
kN
39
39
45
40
39
mm2
106
108
112
108
118
mm2
18
18
18
18
18
mm2
124
126
130
126
136
kN
34
1.15
34
1.14
35
1.28
34
1.16
37
1.05
mean 1.16
stdv 0.0825
cov 0.0714
kN
37
37
38
37
40
experimental
P u,t /P n
1.04
1.04
1.17
1.06
0.96
1.06
0.0750
0.0711
EC3 Part 1-4/1-3 (2004) Alternative Method
Material
Properties
`
Test ID
430_60_60_10_2
430_60_60_10_3
430_60_60_15_2
430_60_60_15_3
430_150_150_30_3
430_150_150_20_3
430_150_150_10_3
430_200_100_15_4
430_200_150_20_3
430_200_150_20_4
430_150_80_5_1
430_50_50_5_1
430_400_400_20_3
430_400_400_20_4
430_400_400_20_5
430_400_400_40_4
430_400_400_40_5
430_400_400_40_6
430_400_400_40_7
430_400_400_40_8
430_300_400_20_3
430_300_400_20_4
430_300_400_20_5
430_400_300_20_3
430_400_300_20_4
430_400_300_20_5
430_400_300_40_5
430_400_300_40_6
430_400_300_40_7
430_400_300_40_8
f y,f
f y,c
Geometry
Ag
MPa MPa mm2
275 275
393
275 275
584
275 275
413
275 275
614
275 275 1514
275 275 1454
275 275 1394
275 275 1692
275 275 1604
275 275 2132
275 275
318
275 275
158
275 275 3704
275 275 4932
275 275 6156
275 275 5092
275 275 6356
275 275 7617
275 275 8874
275 275 10130
275 275 3404
275 275 4532
275 275 5656
275 275 3104
275 275 4132
275 275 5156
275 275 5356
275 275 6417
275 275 7474
275 275 8528
Effective Areas
Ac
A c /A g
P u,t
A e,f
A e,c
A e,t
mm2
25
57
25
57
57
57
57
101
57
101
6
6
57
101
157
101
157
226
308
402
57
101
157
57
101
157
157
226
308
402
%
6
10
6
9
4
4
4
6
4
5
2
4
2
2
3
2
2
3
3
4
2
2
3
2
2
3
3
4
4
5
kN
85
146
96
163
280
240
200
338
244
390
26
24
231
356
579
424
647
950
1226
1531
225
383
579
231
397
594
699
980
1283
1563
mm2
354
542
384
573
853
757
672
1229
755
1332
77
79
691
1216
1882
1324
2045
2905
3907
5034
687
1206
1861
704
1239
1914
2108
2997
4087
5753
mm2
23
56
24
57
48
44
39
90
43
84
4
5
33
61
98
66
106
157
219
293
34
62
99
35
64
104
113
169
244
332
mm2
377
598
409
630
901
801
712
1318
797
1415
81
83
724
1278
1980
1389
2151
3062
4127
5327
721
1268
1960
739
1303
2018
2221
3166
4331
6085
flats
Department of Civil Engineering
Research Report No R845
137
Without EC Prop. With EC Prop.
Pn
P u,t /P n
kN
104
0.82
164
0.89
112
0.85
173
0.94
248
1.13
220
1.09
196
1.02
363
0.93
219
1.11
389
1.00
22
1.18
23
1.05
199
1.16
351
1.01
545
1.06
382
1.11
591
1.09
842
1.13
1135
1.08
1465
1.04
198
1.13
349
1.10
539
1.07
203
1.14
358
1.11
555
1.07
611
1.14
871
1.13
1191
1.08
1673
0.93
mean 1.05
stdv 0.0933
cov 0.0885
Pn
kN
104
164
112
173
248
220
196
363
219
389
22
23
199
351
545
382
591
842
1135
1465
198
349
539
203
358
555
611
871
1191
1673
P u,t /P n
0.82
0.89
0.85
0.94
1.13
1.09
1.02
0.93
1.11
1.00
1.18
1.05
1.16
1.01
1.06
1.11
1.09
1.13
1.08
1.04
1.13
1.10
1.07
1.14
1.11
1.07
1.14
1.13
1.08
0.93
1.05
0.0933
0.0885
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
EC3 Part 1-4/1-3 (2004) Alternative Method
Material
Properties
`
Test ID
430_60_60_10_2_1
430_60_60_10_3_1
430_60_60_15_2_1
430_60_60_15_3_1
430_150_150_30_3_1
430_150_150_20_3_1
430_150_150_10_3_1
430_200_100_15_4_1
430_200_150_20_3_1
430_200_150_20_4_1
430_150_80_5_1_1
430_50_50_5_1_1
430_400_400_20_3_1
430_400_400_20_4_1
430_400_400_20_5_1
430_400_400_40_4_1
430_400_400_40_5_1
430_400_400_40_6_1
430_400_400_40_7_1
430_400_400_40_8_1
430_300_400_20_3_1
430_300_400_20_4_1
430_300_400_20_5_1
430_400_300_20_3_1
430_400_300_20_4_1
430_400_300_20_5_1
430_400_300_40_5_1
430_400_300_40_6_1
430_400_300_40_7_1
430_400_300_40_8_1
f y,f
f y,c
Geometry
Ag
MPa MPa mm2
275 479
393
275 479
584
275 479
413
275 479
614
275 479 1514
275 479 1454
275 479 1394
275 479 1692
275 479 1604
275 479 2132
275 479
318
275 479
158
275 479 3704
275 479 4932
275 479 6156
275 479 5092
275 479 6356
275 479 7617
275 479 8874
275 479 10130
275 479 3404
275 479 4532
275 479 5656
275 479 3104
275 479 4132
275 479 5156
275 479 5356
275 479 6417
275 479 7474
275 479 8528
Effective Areas
Ac
A c /A g
P u,t
A e,f
A e,c
A e,t
mm2
25
57
25
57
57
57
57
101
57
101
6
6
57
101
157
101
157
226
308
402
57
101
157
57
101
157
157
226
308
402
%
6
10
6
9
4
4
4
6
4
5
2
4
2
2
3
2
2
3
3
4
2
2
3
2
2
3
3
4
4
5
kN
87
153
98
171
284
243
203
345
246
397
27
24
230
357
586
430
650
953
1234
1547
228
388
586
234
402
601
704
988
1300
1589
mm2
354
542
384
573
853
757
672
1229
755
1332
77
79
691
1216
1882
1324
2045
2905
3907
5034
687
1206
1861
704
1239
1914
2108
2997
4087
5753
mm2
23
56
24
57
48
44
39
90
43
84
4
5
33
61
98
66
106
157
219
293
34
62
99
35
64
104
113
169
244
332
mm2
377
598
409
630
901
801
712
1318
797
1415
81
83
724
1278
1980
1389
2151
3062
4127
5327
721
1268
1960
739
1303
2018
2221
3166
4331
6085
r/t=1
Department of Civil Engineering
Research Report No R845
138
Without EC Prop. With EC Prop.
Pn
P u,t /P n
kN
104
0.84
164
0.93
112
0.88
173
0.98
248
1.15
220
1.10
196
1.04
363
0.95
219
1.12
389
1.02
22
1.20
23
1.05
199
0.87
351
1.02
545
1.08
382
1.13
591
1.10
842
1.13
1135
1.09
1465
1.06
198
1.15
349
1.11
539
1.09
203
1.15
358
1.12
555
1.08
611
1.15
871
1.13
1191
1.09
1673
0.95
mean 1.06
stdv 0.0938
cov 0.0886
Pn
kN
108
176
117
185
257
229
204
381
228
406
23
24
206
364
565
395
613
874
1180
1525
205
361
559
210
372
576
634
905
1241
1741
P u,t /P n
0.80
0.87
0.84
0.92
1.10
1.06
0.99
0.91
1.08
0.98
1.16
1.01
1.12
0.98
1.04
1.09
1.06
1.09
1.05
1.01
1.11
1.07
1.05
1.11
1.08
1.04
1.11
1.09
1.05
0.91
1.03
0.0894
0.0871
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
EC3 Part 1-4/1-3 (2004) Alternative Method
Material
Properties
`
Test ID
430_60_60_10_2_2.5
430_60_60_10_3_2.5
430_60_60_15_2_2.5
430_60_60_15_3_2.5
430_150_150_30_3_2.5
430_150_150_20_3_2.5
430_150_150_10_3_2.5
430_200_100_15_4_2.5
430_200_150_20_3_2.5
430_200_150_20_4_2.5
430_150_80_5_1_2.5
430_50_50_5_1_2.5
430_400_400_20_3_2.5
430_400_400_20_4_2.5
430_400_400_20_5_2.5
430_400_400_40_4_2.5
430_400_400_40_5_2.5
430_400_400_40_6_2.5
430_400_400_40_7_2.5
430_400_400_40_8_2.5
430_300_400_20_3_2.5
430_300_400_20_4_2.5
430_300_400_20_5_2.5
430_400_300_20_3_2.5
430_400_300_20_4_2.5
430_400_300_20_5_2.5
430_400_300_40_5_2.5
430_400_300_40_6_2.5
430_400_300_40_7_2.5
430_400_300_40_8_2.5
f y,f
f y,c
MPa MPa
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
275 424
Geometry
Effective Areas
Without EC Prop. With EC Prop.
Ag
Ac
A c /A g
P u,t
A e,f
A e,c
A e,t
Pn
mm2
382
561
402
591
1491
1431
1371
1650
1581
2090
316
156
3681
4890
6090
5050
6290
7522
8745
9959
3381
4490
5590
3081
4090
5090
5290
6322
7345
8359
mm2
63
141
63
141
141
141
141
251
141
251
16
16
141
251
393
251
393
565
770
1005
141
251
393
141
251
393
393
565
770
1005
%
16
25
16
24
9
10
10
15
9
12
5
10
4
5
6
5
6
8
9
10
4
6
7
5
6
8
7
9
10
12
kN
87
154
99
173
286
244
205
346
247
399
26
24
236
343
586
437
650
953
1236
1556
229
390
590
235
404
605
704
992
1306
1598
mm2
320
459
348
489
783
695
615
1097
694
1211
71
72
641
1125
1735
1227
1889
2688
3586
4606
637
1115
1714
653
1143
1760
1941
2757
3739
5276
mm2
59
141
61
141
120
110
99
225
107
210
10
11
84
153
246
164
265
396
550
737
84
155
249
87
162
262
284
426
613
836
mm2
378
600
409
630
904
805
714
1322
802
1421
81
83
725
1279
1982
1391
2154
3084
4136
5343
722
1270
1963
740
1305
2022
2225
3182
4352
6112
r/t=2.5
P u,t /P n
kN
104
0.84
165
0.93
113
0.88
173
1.00
249
1.15
221
1.10
196
1.05
364
0.95
220
1.12
391
1.02
22
1.19
23
1.06
199
1.18
352
0.97
545
1.07
382
1.14
592
1.10
848
1.12
1137
1.09
1469
1.06
198
1.15
349
1.12
540
1.09
204
1.16
359
1.12
556
1.09
612
1.15
875
1.13
1197
1.09
1681
0.95
mean 1.07
stdv 0.0893
cov 0.0835
Pn
kN
113
186
122
194
266
238
211
397
236
422
24
25
212
375
582
407
632
907
1219
1579
211
372
577
217
383
595
654
939
1288
1805
mean 1.07
stdv 0.0930
cov 0.0873
All Tests
P u,t /P n
0.77
0.83
0.81
0.89
1.07
1.03
0.97
0.87
1.04
0.95
1.11
0.99
1.11
0.92
1.01
1.07
1.03
1.05
1.01
0.99
1.09
1.05
1.02
1.09
1.05
1.02
1.08
1.06
1.01
0.89
1.00
0.0912
0.0916
1.03
0.0925
0.0900
ASCE (2002), AS/NZS 4673 (2001), (AS/NZS 4600
(1996) NAS (2001))
Material
Properties
f y,f
Test ID
3Cr12D1a
3Cr12D1b
f y,c
MPa MPa
339 606
339 606
Geometry
Ag
Ac
2
mm
555
555
Effective Areas
A c /A g
2
mm
62
62
%
11
11
P u,t
kN
138
139
A e,f
2
mm
345
346
A e,c
2
mm
62
62
A e,t
139
2
mm
407
408
experimental
Department of Civil Engineering
Research Report No R845
Without EC Prop. With EC Prop.
Pn
P u,t /P n
Pn
kN
138
1.00
138
1.01
mean 1.00
stdv 0.0045
cov 0.0045
kN
155
155
P u,t /P n
0.89
0.90
0.89
0.0041
0.0046
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
ASCE (2002), AS/NZS 4673 (2001), (AS/NZS 4600
(1996) NAS (2001))
Material
Properties
f y,f
Test ID
3Cr12_60_60_10_2
3Cr12_60_60_10_3
3Cr12_60_60_15_2
3Cr12_60_60_15_3
3Cr12_150_150_30_3
3Cr12_150_150_20_3
3Cr12_150_150_10_3
3Cr12_200_100_15_4
3Cr12_200_150_20_3
3Cr12_200_150_20_4
3Cr12_150_80_5_1
3Cr12_50_50_5_1
3Cr12_400_400_20_3
3Cr12_400_400_20_4
3Cr12_400_400_20_5
3Cr12_400_400_40_4
3Cr12_400_400_40_5
3Cr12_400_400_40_6
3Cr12_400_400_40_7
3Cr12_400_400_40_8
3Cr12_300_400_20_3
3Cr12_300_400_20_4
3Cr12_300_400_20_5
3Cr12_400_300_20_3
3Cr12_400_300_20_4
3Cr12_400_300_20_5
3Cr12_400_300_40_5
3Cr12_400_300_40_6
3Cr12_400_300_40_7
3Cr12_400_300_40_8
f y,c
Geometry
Ag
Ac
2
MPa MPa mm
260 260
393
260 260
584
260 260
413
260 260
614
260 260 1514
260 260 1454
260 260 1394
260 260 1692
260 260 1604
260 260 2132
260 260
318
260 260
158
260 260 3704
260 260 4932
260 260 6156
260 260 5092
260 260 6356
260 260 7617
260 260 8874
260 260 10130
260 260 3404
260 260 4532
260 260 5656
260 260 3104
260 260 4132
260 260 5156
260 260 5356
260 260 6417
260 260 7474
260 260 8528
Effective Areas
A c /A g
2
mm
25
57
25
57
57
57
57
101
57
101
6
6
57
101
157
101
157
226
308
402
57
101
157
57
101
157
157
226
308
402
%
6
10
6
9
4
4
4
6
4
5
2
4
2
2
3
2
2
3
3
4
2
2
3
2
2
3
3
4
4
5
P u,t
kN
83
142
93
157
278
243
201
335
254
389
27
24
237
382
602
444
709
1005
1267
1563
231
395
597
237
409
618
738
1022
1292
1556
A e,f
2
mm
326
510
371
558
1093
951
811
1400
982
1435
108
98
1028
1695
2488
2050
2948
3969
5091
6297
1013
1659
2417
1036
1699
2483
2939
3927
5005
5741
A e,c
2
mm
25
57
25
57
57
57
57
101
57
101
6
6
57
101
157
101
157
226
308
402
57
101
157
57
101
157
157
226
308
402
flats
Department of Civil Engineering
Research Report No R845
140
Without EC Prop. With EC Prop.
A e,t
2
mm
351
567
396
615
1149
1007
867
1500
1038
1536
115
105
1084
1795
2645
2150
3105
4195
5399
6699
1069
1759
2574
1092
1799
2640
3096
4153
5313
6143
Pn
P u,t /P n
kN
91
0.91
147
0.96
103
0.91
160
0.98
299
0.93
262
0.93
226
0.89
390
0.86
270
0.94
399
0.97
30
0.91
27
0.90
282
0.84
467
0.82
688
0.88
559
0.79
807
0.88
1091
0.92
1404
0.90
1742
0.90
278
0.83
457
0.86
669
0.89
284
0.83
468
0.87
686
0.90
805
0.92
1080
0.95
1381
0.94
1597
0.97
mean 0.90
stdv 0.0473
cov 0.0526
Pn
kN
91
147
103
160
299
262
226
390
270
399
30
27
282
467
688
559
807
1091
1404
1742
278
457
669
284
468
686
805
1080
1381
1597
P u,t /P n
0.91
0.96
0.91
0.98
0.93
0.93
0.89
0.86
0.94
0.97
0.91
0.90
0.84
0.82
0.88
0.79
0.88
0.92
0.90
0.90
0.83
0.86
0.89
0.83
0.87
0.90
0.92
0.95
0.94
0.97
0.90
0.0473
0.0526
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
ASCE (2002), AS/NZS 4673 (2001), (AS/NZS 4600
(1996) NAS (2001))
Material
Properties
f y,f
Test ID
3Cr12_60_60_10_2_1
3Cr12_60_60_10_3_1
3Cr12_60_60_15_2_1
3Cr12_60_60_15_3_1
3Cr12_150_150_30_3_1
3Cr12_150_150_20_3_1
3Cr12_150_150_10_3_1
3Cr12_200_100_15_4_1
3Cr12_200_150_20_3_1
3Cr12_200_150_20_4_1
3Cr12_150_80_5_1_1
3Cr12_50_50_5_1_1
3Cr12_400_400_20_3_1
3Cr12_400_400_20_4_1
3Cr12_400_400_20_5_1
3Cr12_400_400_40_4_1
3Cr12_400_400_40_5_1
3Cr12_400_400_40_6_1
3Cr12_400_400_40_7_1
3Cr12_400_400_40_8_1
3Cr12_300_400_20_3_1
3Cr12_300_400_20_4_1
3Cr12_300_400_20_5_1
3Cr12_400_300_20_3_1
3Cr12_400_300_20_4_1
3Cr12_400_300_20_5_1
3Cr12_400_300_40_5_1
3Cr12_400_300_40_6_1
3Cr12_400_300_40_7_1
3Cr12_400_300_40_8_1
f y,c
Geometry
Ag
Ac
2
MPa MPa mm
260 460
393
260 460
584
260 460
413
260 460
614
260 460 1514
260 460 1454
260 460 1394
260 460 1692
260 460 1604
260 460 2132
260 460
318
260 460
158
260 460 3704
260 460 4932
260 460 6156
260 460 5092
260 460 6356
260 460 7617
260 460 8874
260 460 10130
260 460 3404
260 460 4532
260 460 5656
260 460 3104
260 460 4132
260 460 5156
260 460 5356
260 460 6417
260 460 7474
260 460 8528
Effective Areas
A c /A g
2
mm
25
57
25
57
57
57
57
101
57
101
6
6
57
101
157
101
157
226
308
402
57
101
157
57
101
157
157
226
308
402
%
6
10
6
9
4
4
4
6
4
5
2
4
2
2
3
2
2
3
3
4
2
2
3
2
2
3
3
4
4
5
P u,t
kN
85
148
96
165
283
246
205
343
256
396
27
25
237
383
607
447
710
1009
1277
1581
234
399
603
240
413
621
741
1032
1311
1584
A e,f
2
mm
326
510
371
558
1093
951
811
1400
982
1435
108
98
1028
1695
2488
2050
2948
3969
5091
6297
1013
1659
2417
1036
1699
2483
2939
3927
5005
5741
A e,c
2
mm
25
57
25
57
57
57
57
101
57
101
6
6
57
101
157
101
157
226
308
402
57
101
157
57
101
157
157
226
308
402
r/t=1
Department of Civil Engineering
Research Report No R845
141
Without EC Prop. With EC Prop.
A e,t
2
mm
351
567
396
615
1149
1007
867
1500
1038
1536
115
105
1084
1795
2645
2150
3105
4195
5399
6699
1069
1759
2574
1092
1799
2640
3096
4153
5313
6143
Pn
P u,t /P n
kN
91
0.93
147
1.00
103
0.94
160
1.03
299
0.95
262
0.94
226
0.91
390
0.88
270
0.95
399
0.99
30
0.92
27
0.91
282
0.84
467
0.82
688
0.88
559
0.80
807
0.88
1091
0.92
1404
0.91
1742
0.91
278
0.84
457
0.87
669
0.90
284
0.84
468
0.88
686
0.90
805
0.92
1080
0.96
1381
0.95
1597
0.99
mean 0.91
stdv 0.0542
cov 0.0594
Pn
kN
96
159
108
171
310
273
237
410
281
419
31
28
293
487
719
579
839
1136
1465
1822
289
478
701
295
488
718
836
1125
1443
1678
P u,t /P n
0.89
0.93
0.89
0.96
0.91
0.90
0.86
0.84
0.91
0.94
0.88
0.87
0.81
0.79
0.84
0.77
0.85
0.89
0.87
0.87
0.81
0.84
0.86
0.81
0.85
0.87
0.89
0.92
0.91
0.94
0.87
0.0474
0.0543
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
f y,f
Test ID
3Cr12_60_60_10_2_2.5
3Cr12_60_60_10_3_2.5
3Cr12_60_60_15_2_2.5
3Cr12_60_60_15_3_2.5
3Cr12_150_150_30_3_2.5
3Cr12_150_150_20_3_2.5
3Cr12_150_150_10_3_2.5
3Cr12_200_100_15_4_2.5
3Cr12_200_150_20_3_2.5
3Cr12_200_150_20_4_2.5
3Cr12_150_80_5_1_2.5
3Cr12_50_50_5_1_2.5
3Cr12_400_400_20_3_2.5
3Cr12_400_400_20_4_2.5
3Cr12_400_400_20_5_2.5
3Cr12_400_400_40_4_2.5
3Cr12_400_400_40_5_2.5
3Cr12_400_400_40_6_2.5
3Cr12_400_400_40_7_2.5
3Cr12_400_400_40_8_2.5
3Cr12_300_400_20_3_2.5
3Cr12_300_400_20_4_2.5
3Cr12_300_400_20_5_2.5
3Cr12_400_300_20_3_2.5
3Cr12_400_300_20_4_2.5
3Cr12_400_300_20_5_2.5
3Cr12_400_300_40_5_2.5
3Cr12_400_300_40_6_2.5
3Cr12_400_300_40_7_2.5
3Cr12_400_300_40_8_2.5
f y,c
MPa MPa
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
Ag
Ac
2
mm
382
561
402
591
1491
1431
1371
1650
1581
2090
316
156
3681
4890
6090
5050
6290
7522
8745
9959
3381
4490
5590
3081
4090
5090
5290
6322
7345
8359
A c /A g
2
mm
63
141
63
141
141
141
141
251
141
251
16
16
141
251
393
251
393
565
770
1005
141
251
393
141
251
393
393
565
770
1005
%
16
25
16
24
9
10
10
15
9
12
5
10
4
5
6
5
6
8
9
10
4
6
7
5
6
8
7
9
10
12
P u,t
kN
86
150
97
168
284
248
207
346
257
397
27
25
241
403
608
457
712
1008
1281
1592
235
401
606
240
415
631
739
1036
1316
1592
April 2005
A e,f
2
mm
285
413
329
477
1018
882
714
1267
917
1319
101
90
969
1571
2263
1945
2779
3709
4709
5754
953
1532
2185
975
1573
2256
2767
3667
4629
5276
A e,c
2
mm
63
141
63
141
141
141
141
251
141
251
16
16
141
251
393
251
393
565
770
1005
141
251
393
141
251
393
393
565
770
1005
r/t=2.5
All Tests
Department of Civil Engineering
Research Report No R845
142
A e,t
2
mm
348
555
392
618
1159
1023
856
1518
1058
1570
116
106
1110
1822
2656
2196
3172
4274
5478
6760
1094
1784
2578
1117
1824
2649
3159
4233
5399
6282
Pn
P u,t /P n
kN
90
0.95
144
1.04
102
0.95
161
1.05
301
0.94
266
0.93
223
0.93
395
0.88
275
0.94
408
0.97
30
0.90
27
0.90
289
0.84
474
0.85
691
0.88
571
0.80
825
0.86
1111
0.91
1424
0.90
1758
0.91
285
0.83
464
0.87
670
0.90
290
0.83
474
0.87
689
0.92
821
0.90
1101
0.94
1404
0.94
1633
0.97
mean 0.91
stdv 0.0568
cov 0.0625
mean 0.91
stdv 0.0539
cov 0.0592
Pn
kN
100
165
111
181
322
287
243
431
296
445
33
30
309
511
748
608
882
1194
1537
1904
305
500
728
311
511
746
879
1183
1516
1780
P u,t /P n
0.86
0.91
0.87
0.93
0.88
0.86
0.85
0.80
0.87
0.89
0.83
0.83
0.78
0.79
0.81
0.75
0.81
0.84
0.83
0.84
0.77
0.80
0.83
0.77
0.81
0.85
0.84
0.88
0.87
0.89
0.84
0.0431
0.0514
0.87
0.0514
0.0591
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
EC3 Part 1-4/1-3 (2004) Traditional Method
Material
Properties
f y,f
Test ID
3Cr12D1a
3Cr12D1b
f y,c
MPa MPa
339 606
339 606
Geometry
Effective Areas
A e,c
Without EC Prop. With EC Prop.
Ag
Ac
A c /A g
P u,t
A e,f
A e,t
mm2
555
555
mm2
62
62
%
11
11
kN
138
139
mm2 mm2 mm2
293
45
338
293
45
338
experimental
Pn
P u,t /P n
Pn
kN
115
1.20
115
1.21
mean 1.21
stdv 0.0062
cov 0.0051
kN
127
127
P u,t /P n
1.09
1.10
1.09
0.0056
0.0051
EC3 Part 1-4/1-3 (2004) Traditional Method
Material
Properties
f y,f
Test ID
3Cr12_60_60_10_2
3Cr12_60_60_10_3
3Cr12_60_60_15_2
3Cr12_60_60_15_3
3Cr12_150_150_30_3
3Cr12_150_150_20_3
3Cr12_150_150_10_3
3Cr12_200_100_15_4
3Cr12_200_150_20_3
3Cr12_200_150_20_4
3Cr12_150_80_5_1
3Cr12_50_50_5_1
3Cr12_400_400_20_3
3Cr12_400_400_20_4
3Cr12_400_400_20_5
3Cr12_400_400_40_4
3Cr12_400_400_40_5
3Cr12_400_400_40_6
3Cr12_400_400_40_7
3Cr12_400_400_40_8
3Cr12_300_400_20_3
3Cr12_300_400_20_4
3Cr12_300_400_20_5
3Cr12_400_300_20_3
3Cr12_400_300_20_4
3Cr12_400_300_20_5
3Cr12_400_300_40_5
3Cr12_400_300_40_6
3Cr12_400_300_40_7
3Cr12_400_300_40_8
f y,c
Geometry
Ag
Ac
2
MPa MPa mm
260 260
393
260 260
584
260 260
413
260 260
614
260 260 1514
260 260 1454
260 260 1394
260 260 1692
260 260 1604
260 260 2132
260 260
318
260 260
158
260 260 3704
260 260 4932
260 260 6156
260 260 5092
260 260 6356
260 260 7617
260 260 8874
260 260 10130
260 260 3404
260 260 4532
260 260 5656
260 260 3104
260 260 4132
260 260 5156
260 260 5356
260 260 6417
260 260 7474
260 260 8528
Effective Areas
A c /A g
2
mm
25
57
25
57
57
57
57
101
57
101
6
6
57
101
157
101
157
226
308
402
57
101
157
57
101
157
157
226
308
402
%
6
10
6
9
4
4
4
6
4
5
2
4
2
2
3
2
2
3
3
4
2
2
3
2
2
3
3
4
4
5
P u,t
kN
83
142
93
157
278
243
201
335
254
389
27
24
237
382
602
444
709
1005
1267
1563
231
395
597
237
409
618
738
1022
1292
1556
A e,f
2
A e,c
2
mm mm
345
23
528
54
381
24
573
57
964
47
835
41
738
37
1245 87
840
40
1403 78
91
4
88
4
843
33
1458 59
2193 94
1609 65
2435 103
3404 151
4427 208
5617 279
840
33
1448 60
2176 95
849
34
1452 62
2161 99
2463 110
3362 162
4376 226
5612 311
flats
Department of Civil Engineering
Research Report No R845
143
Without EC Prop. With EC Prop.
A e,t
2
mm
368
582
405
630
1011
876
775
1332
880
1481
95
92
876
1517
2287
1674
2538
3555
4635
5896
873
1508
2271
883
1514
2260
2573
3524
4602
5923
Pn
P u,t /P n
kN
96
0.89
151
0.97
105
0.91
164
1.00
263
1.07
228
1.06
202
0.99
346
0.98
229
1.07
385
1.01
25
1.07
24
1.00
228
1.01
395
0.90
595
0.97
435
0.97
660
0.98
924
1.03
1205
1.02
1533
1.00
227
0.99
392
0.98
590
0.98
230
1.01
394
1.01
588
1.01
669
1.04
916
1.07
1197
1.07
1540
1.02
mean 1.00
stdv 0.0472
cov 0.0471
Pn
kN
96
151
105
164
263
228
202
346
229
385
25
24
228
395
595
435
660
924
1205
1533
227
392
590
230
394
588
669
916
1197
1540
P u,t /P n
0.89
0.97
0.91
1.00
1.07
1.06
0.99
0.98
1.07
1.01
1.07
1.00
1.01
0.90
0.97
0.97
0.98
1.03
1.02
1.00
0.99
0.98
0.98
1.01
1.01
1.01
1.04
1.07
1.07
1.02
1.00
0.0472
0.0471
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
EC3 Part 1-4/1-3 (2004) Traditional Method
Material
Properties
f y,f
Test ID
3Cr12_60_60_10_2_1
3Cr12_60_60_10_3_1
3Cr12_60_60_15_2_1
3Cr12_60_60_15_3_1
3Cr12_150_150_30_3_1
3Cr12_150_150_20_3_1
3Cr12_150_150_10_3_1
3Cr12_200_100_15_4_1
3Cr12_200_150_20_3_1
3Cr12_200_150_20_4_1
3Cr12_150_80_5_1_1
3Cr12_50_50_5_1_1
3Cr12_400_400_20_3_1
3Cr12_400_400_20_4_1
3Cr12_400_400_20_5_1
3Cr12_400_400_40_4_1
3Cr12_400_400_40_5_1
3Cr12_400_400_40_6_1
3Cr12_400_400_40_7_1
3Cr12_400_400_40_8_1
3Cr12_300_400_20_3_1
3Cr12_300_400_20_4_1
3Cr12_300_400_20_5_1
3Cr12_400_300_20_3_1
3Cr12_400_300_20_4_1
3Cr12_400_300_20_5_1
3Cr12_400_300_40_5_1
3Cr12_400_300_40_6_1
3Cr12_400_300_40_7_1
3Cr12_400_300_40_8_1
f y,c
Geometry
Ag
MPa MPa mm2
260 460
393
260 460
584
260 460
413
260 460
614
260 460 1514
260 460 1454
260 460 1394
260 460 1692
260 460 1604
260 460 2132
260 460
318
260 460
158
260 460 3704
260 460 4932
260 460 6156
260 460 5092
260 460 6356
260 460 7617
260 460 8874
260 460 10130
260 460 3404
260 460 4532
260 460 5656
260 460 3104
260 460 4132
260 460 5156
260 460 5356
260 460 6417
260 460 7474
260 460 8528
Effective Areas
Ac
A c /A g
P u,t
A e,f
A e,c
mm2
25
57
25
57
57
57
57
101
57
101
6
6
57
101
157
101
157
226
308
402
57
101
157
57
101
157
157
226
308
402
%
6
10
6
9
4
4
4
6
4
5
2
4
2
2
3
2
2
3
3
4
2
2
3
2
2
3
3
4
4
5
kN
85
148
96
165
283
246
205
343
256
396
27
25
237
383
607
447
710
1009
1277
1581
234
399
603
240
413
621
741
1032
1311
1584
mm2 mm2
345
23
528
54
381
24
573
57
964
47
835
41
738
37
1245 87
840
40
1403 78
91
4
88
4
843
33
1458 59
2193 94
1609 65
2435 103
3404 151
4427 208
5617 279
840
33
1448 60
2176 95
849
34
1452 62
2161 99
2463 110
3362 162
4376 226
5612 311
r/t=1
Department of Civil Engineering
Research Report No R845
144
A e,t
mm2
368
582
405
630
1011
876
775
1332
880
1481
95
92
876
1517
2287
1674
2538
3555
4635
5896
873
1508
2271
883
1514
2260
2573
3524
4602
5923
Without EC Prop. With EC Prop.
Pn
P u,t /P n
kN
96
0.91
151
1.01
105
0.93
164
1.04
263
1.08
228
1.07
202
1.01
346
1.00
229
1.07
385
1.03
25
1.08
24
1.00
228
0.94
395
0.90
595
0.99
435
0.99
660
0.99
924
1.03
1205
1.02
1533
1.01
227
1.00
392
0.99
590
0.99
230
1.02
394
1.02
588
1.02
669
1.05
916
1.08
1197
1.09
1540
1.03
mean 1.01
stdv 0.0477
cov 0.0471
Pn
kN
100
162
110
175
272
236
209
364
237
401
25
25
234
406
613
448
681
955
1247
1589
234
404
609
236
406
607
691
949
1242
1602
P u,t /P n
0.87
0.94
0.89
0.97
1.04
1.03
0.97
0.95
1.04
0.99
1.04
0.97
0.91
0.88
0.96
0.96
0.96
1.00
0.99
0.97
0.98
0.96
0.96
0.99
0.99
0.99
1.02
1.04
1.05
0.99
0.98
0.0471
0.0482
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
EC3 Part 1-4/1-3 (2004) Traditional Method
Material
Properties
f y,f
Test ID
3Cr12_60_60_10_2_2.5
3Cr12_60_60_10_3_2.5
3Cr12_60_60_15_2_2.5
3Cr12_60_60_15_3_2.5
3Cr12_150_150_30_3_2.5
3Cr12_150_150_20_3_2.5
3Cr12_150_150_10_3_2.5
3Cr12_200_100_15_4_2.5
3Cr12_200_150_20_3_2.5
3Cr12_200_150_20_4_2.5
3Cr12_150_80_5_1_2.5
3Cr12_50_50_5_1_2.5
3Cr12_400_400_20_3_2.5
3Cr12_400_400_20_4_2.5
3Cr12_400_400_20_5_2.5
3Cr12_400_400_40_4_2.5
3Cr12_400_400_40_5_2.5
3Cr12_400_400_40_6_2.5
3Cr12_400_400_40_7_2.5
3Cr12_400_400_40_8_2.5
3Cr12_300_400_20_3_2.5
3Cr12_300_400_20_4_2.5
3Cr12_300_400_20_5_2.5
3Cr12_400_300_20_3_2.5
3Cr12_400_300_20_4_2.5
3Cr12_400_300_20_5_2.5
3Cr12_400_300_40_5_2.5
3Cr12_400_300_40_6_2.5
3Cr12_400_300_40_7_2.5
3Cr12_400_300_40_8_2.5
f y,c
MPa MPa
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
Geometry
Effective Areas
Ag
Ac
A c /A g
P u,t
A e,f
A e,c
mm2
382
561
402
591
1491
1431
1371
1650
1581
2090
316
156
3681
4890
6090
5050
6290
7522
8745
9959
3381
4490
5590
3081
4090
5090
5290
6322
7345
8359
mm2
63
141
63
141
141
141
141
251
141
251
16
16
141
251
393
251
393
565
770
1005
141
251
393
141
251
393
393
565
770
1005
%
16
25
16
24
9
10
10
15
9
12
5
10
4
5
6
5
6
8
9
10
4
6
7
5
6
8
7
9
10
12
kN
86
150
97
168
284
248
207
346
257
397
27
25
241
403
608
457
712
1008
1281
1592
235
401
606
240
415
631
739
1036
1316
1592
mm2 mm2
304
55
433 132
342
60
484 141
887 117
767 102
670
91
1084 210
773 100
1246 188
84
9
80
11
790
82
1355 147
2019 232
1505 162
2268 257
3159 374
4080 516
5107 686
787
83
1344 148
1999 233
794
85
1338 153
1982 243
2284 273
3093 402
3999 560
4985 751
Without EC Prop. With EC Prop.
A e,t
mm2
359
565
402
625
1004
869
761
1294
873
1434
93
91
872
1502
2251
1667
2525
3533
4596
5793
870
1492
2232
879
1491
2225
2557
3495
4559
5736
r/t=2.5
Pn
P u,t /P n
kN
93
0.92
147
1.02
105
0.93
163
1.03
261
1.09
226
1.10
198
1.05
336
1.03
227
1.13
373
1.06
24
1.12
24
1.05
227
1.06
391
1.03
585
1.04
433
1.05
657
1.08
919
1.10
1195
1.07
1506
1.06
226
1.04
388
1.03
580
1.04
229
1.05
388
1.07
579
1.09
665
1.11
909
1.14
1185
1.11
1491
1.07
mean 1.06
stdv 0.0489
cov 0.0462
Pn
kN
101
166
113
183
278
241
211
367
242
400
26
25
239
412
619
457
694
973
1270
1606
238
410
614
241
410
614
705
967
1267
1601
mean 1.03
stdv 0.0595
cov 0.0578
All Tests
P u,t /P n
0.85
0.90
0.86
0.92
1.02
1.03
0.98
0.94
1.06
0.99
1.06
0.99
1.01
0.98
0.98
1.00
1.03
1.04
1.01
0.99
0.99
0.98
0.99
1.00
1.01
1.03
1.05
1.07
1.04
0.99
0.99
0.0542
0.0547
0.99
0.0519
0.0523
EC3 Part 1-4/1-3 (2004) Alternative Method
Material
Properties
f y,f
Test ID
3Cr12D1a
3Cr12D1b
f y,c
MPa MPa
339 606
339 606
Effective Areas
Geometry
Ag
Ac
2
mm
555
555
A c /A g
2
mm
62
62
%
11
11
P u,t
kN
138
139
A e,f
2
mm
309
309
A e,c
2
mm
54
54
A e,t
145
2
mm
363
363
experimental
Department of Civil Engineering
Research Report No R845
Without EC Prop. With EC Prop.
Pn
P u,t /P n
Pn
kN
123
1.12
123
1.13
mean 1.13
stdv 0.0055
cov 0.0049
kN
137
137
P u,t /P n
1.00
1.01
1.01
0.0050
0.0049
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
EC3 Part 1-4/1-3 (2004) Alternative Method
Material
Properties
f y,f
Test ID
3Cr12_60_60_10_2
3Cr12_60_60_10_3
3Cr12_60_60_15_2
3Cr12_60_60_15_3
3Cr12_150_150_30_3
3Cr12_150_150_20_3
3Cr12_150_150_10_3
3Cr12_200_100_15_4
3Cr12_200_150_20_3
3Cr12_200_150_20_4
3Cr12_150_80_5_1
3Cr12_50_50_5_1
3Cr12_400_400_20_3
3Cr12_400_400_20_4
3Cr12_400_400_20_5
3Cr12_400_400_40_4
3Cr12_400_400_40_5
3Cr12_400_400_40_6
3Cr12_400_400_40_7
3Cr12_400_400_40_8
3Cr12_300_400_20_3
3Cr12_300_400_20_4
3Cr12_300_400_20_5
3Cr12_400_300_20_3
3Cr12_400_300_20_4
3Cr12_400_300_20_5
3Cr12_400_300_40_5
3Cr12_400_300_40_6
3Cr12_400_300_40_7
3Cr12_400_300_40_8
f y,c
Effective Areas
Geometry
Ag
MPa MPa mm2
260 260
393
260 260
584
260 260
413
260 260
614
260 260 1514
260 260 1454
260 260 1394
260 260 1692
260 260 1604
260 260 2132
260 260
318
260 260
158
260 260 3704
260 260 4932
260 260 6156
260 260 5092
260 260 6356
260 260 7617
260 260 8874
260 260 10130
260 260 3404
260 260 4532
260 260 5656
260 260 3104
260 260 4132
260 260 5156
260 260 5356
260 260 6417
260 260 7474
260 260 8528
Ac
A c /A g
P u,t
A e,f
A e,c
mm2
25
57
25
57
57
57
57
101
57
101
6
6
57
101
157
101
157
226
308
402
57
101
157
57
101
157
157
226
308
402
%
6
10
6
9
4
4
4
6
4
5
2
4
2
2
3
2
2
3
3
4
2
2
3
2
2
3
3
4
4
5
kN
83
142
93
157
278
243
201
335
254
389
27
24
237
382
602
444
709
1005
1267
1563
231
395
597
237
409
618
738
1022
1292
1556
mm2 mm2
362
24
543
57
392
25
573
57
943
50
845
46
737
40
1296 93
846
45
1468 87
84
4
87
5
761
34
1339 62
2069 100
1461 67
2256 109
3201 161
4300 226
5581 306
757
34
1327 63
2044 101
777
36
1364 66
2105 107
2324 116
3362 179
4543 256
5847 347
flats
Department of Civil Engineering
Research Report No R845
146
A e,t
mm2
386
600
417
630
993
891
777
1388
891
1555
88
92
795
1401
2170
1528
2364
3362
4526
5887
791
1390
2145
812
1430
2212
2441
3541
4799
6194
Without EC Prop. With EC Prop.
Pn
P u,t /P n
kN
100
0.85
156
0.94
108
0.88
164
1.00
258
1.09
232
1.04
202
0.99
361
0.94
232
1.05
404
0.96
23
1.14
24
1.00
207
1.12
364
0.98
564
1.03
397
1.07
615
1.05
874
1.09
1177
1.04
1531
1.00
206
1.09
361
1.06
558
1.04
211
1.09
372
1.07
575
1.03
635
1.10
921
1.06
1248
1.03
1611
0.97
mean 1.03
stdv 0.0677
cov 0.0659
Pn
kN
100
156
108
164
258
232
202
361
232
404
23
24
207
364
564
397
615
874
1177
1531
206
361
558
211
372
575
635
921
1248
1611
P u,t /P n
0.85
0.94
0.88
1.00
1.09
1.04
0.99
0.94
1.05
0.96
1.14
1.00
1.12
0.98
1.03
1.07
1.05
1.09
1.04
1.00
1.09
1.06
1.04
1.09
1.07
1.03
1.10
1.06
1.03
0.97
1.03
0.0677
0.0659
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
EC3 Part 1-4/1-3 (2004) Alternative Method
Material
Properties
f y,f
Test ID
3Cr12_60_60_10_2_1
3Cr12_60_60_10_3_1
3Cr12_60_60_15_2_1
3Cr12_60_60_15_3_1
3Cr12_150_150_30_3_1
3Cr12_150_150_20_3_1
3Cr12_150_150_10_3_1
3Cr12_200_100_15_4_1
3Cr12_200_150_20_3_1
3Cr12_200_150_20_4_1
3Cr12_150_80_5_1_1
3Cr12_50_50_5_1_1
3Cr12_400_400_20_3_1
3Cr12_400_400_20_4_1
3Cr12_400_400_20_5_1
3Cr12_400_400_40_4_1
3Cr12_400_400_40_5_1
3Cr12_400_400_40_6_1
3Cr12_400_400_40_7_1
3Cr12_400_400_40_8_1
3Cr12_300_400_20_3_1
3Cr12_300_400_20_4_1
3Cr12_300_400_20_5_1
3Cr12_400_300_20_3_1
3Cr12_400_300_20_4_1
3Cr12_400_300_20_5_1
3Cr12_400_300_40_5_1
3Cr12_400_300_40_6_1
3Cr12_400_300_40_7_1
3Cr12_400_300_40_8_1
f y,c
Effective Areas
Geometry
Ag
MPa MPa mm2
260 460
393
260 460
584
260 460
413
260 460
614
260 460 1514
260 460 1454
260 460 1394
260 460 1692
260 460 1604
260 460 2132
260 460
318
260 460
158
260 460 3704
260 460 4932
260 460 6156
260 460 5092
260 460 6356
260 460 7617
260 460 8874
260 460 10130
260 460 3404
260 460 4532
260 460 5656
260 460 3104
260 460 4132
260 460 5156
260 460 5356
260 460 6417
260 460 7474
260 460 8528
Ac
A c /A g
P u,t
A e,f
A e,c
mm2
25
57
25
57
57
57
57
101
57
101
6
6
57
101
157
101
157
226
308
402
57
101
157
57
101
157
157
226
308
402
%
6
10
6
9
4
4
4
6
4
5
2
4
2
2
3
2
2
3
3
4
2
2
3
2
2
3
3
4
4
5
kN
85
148
96
165
283
246
205
343
256
396
27
25
237
383
607
447
710
1009
1277
1581
234
399
603
240
413
621
741
1032
1311
1584
mm2 mm2
362
24
543
57
392
25
573
57
943
50
845
46
737
40
1296 93
846
45
1468 87
84
4
87
5
761
34
1339 62
2069 100
1461 67
2256 109
3201 161
4300 226
5581 306
757
34
1327 63
2044 101
777
36
1364 66
2105 107
2324 116
3362 179
4543 256
5847 347
r/t=1
Department of Civil Engineering
Research Report No R845
147
A e,t
mm2
386
600
417
630
993
891
777
1388
891
1555
88
92
795
1401
2170
1528
2364
3362
4526
5887
791
1390
2145
812
1430
2212
2441
3541
4799
6194
Without EC Prop. With EC Prop.
Pn
P u,t /P n
kN
100
0.87
156
0.98
108
0.91
164
1.04
258
1.10
232
1.05
202
1.00
361
0.96
232
1.06
404
0.98
23
1.15
24
1.01
207
1.04
364
0.98
564
1.04
397
1.08
615
1.06
874
1.09
1177
1.05
1531
1.01
206
1.11
361
1.07
558
1.05
211
1.11
372
1.08
575
1.04
635
1.11
921
1.07
1248
1.04
1611
0.99
mean 1.04
stdv 0.0620
cov 0.0597
Pn
kN
105
167
113
175
268
241
210
379
241
422
24
25
213
377
584
411
636
906
1222
1592
212
374
578
218
385
596
658
956
1299
1680
P u,t /P n
0.83
0.91
0.87
0.97
1.06
1.01
0.96
0.91
1.02
0.94
1.12
0.97
1.00
0.95
1.00
1.05
1.02
1.05
1.01
0.97
1.07
1.04
1.01
1.07
1.05
1.01
1.07
1.03
1.00
0.95
1.00
0.0641
0.0642
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
EC3 Part 1-4/1-3 (2004) Alternative Method
Material
Properties
f y,f
Test ID
3Cr12_60_60_10_2_2.5
3Cr12_60_60_10_3_2.5
3Cr12_60_60_15_2_2.5
3Cr12_60_60_15_3_2.5
3Cr12_150_150_30_3_2.5
3Cr12_150_150_20_3_2.5
3Cr12_150_150_10_3_2.5
3Cr12_200_100_15_4_2.5
3Cr12_200_150_20_3_2.5
3Cr12_200_150_20_4_2.5
3Cr12_150_80_5_1_2.5
3Cr12_50_50_5_1_2.5
3Cr12_400_400_20_3_2.5
3Cr12_400_400_20_4_2.5
3Cr12_400_400_20_5_2.5
3Cr12_400_400_40_4_2.5
3Cr12_400_400_40_5_2.5
3Cr12_400_400_40_6_2.5
3Cr12_400_400_40_7_2.5
3Cr12_400_400_40_8_2.5
3Cr12_300_400_20_3_2.5
3Cr12_300_400_20_4_2.5
3Cr12_300_400_20_5_2.5
3Cr12_400_300_20_3_2.5
3Cr12_400_300_20_4_2.5
3Cr12_400_300_20_5_2.5
3Cr12_400_300_40_5_2.5
3Cr12_400_300_40_6_2.5
3Cr12_400_300_40_7_2.5
3Cr12_400_300_40_8_2.5
f y,c
MPa MPa
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
260 406
Effective Areas
Geometry
Ag
Ac
A c /A g
P u,t
A e,f
A e,c
mm2
382
561
402
591
1491
1431
1371
1650
1581
2090
316
156
3681
4890
6090
5050
6290
7522
8745
9959
3381
4490
5590
3081
4090
5090
5290
6322
7345
8359
mm2
63
141
63
141
141
141
141
251
141
251
16
16
141
251
393
251
393
565
770
1005
141
251
393
141
251
393
393
565
770
1005
%
16
25
16
24
9
10
10
15
9
12
5
10
4
5
6
5
6
8
9
10
4
6
7
5
6
8
7
9
10
12
kN
86
150
97
168
284
248
207
346
257
397
27
25
241
403
608
457
712
1008
1281
1592
235
401
606
240
415
631
739
1036
1316
1592
mm2 mm2
326
60
459 141
355
62
489 141
870 125
779 116
679 101
1160 232
782 113
1342 219
79
10
80
12
711
85
1247 156
1921 251
1362 168
2096 272
2982 406
3971 566
5149 771
706
86
1234 157
1895 254
724
89
1267 165
1948 268
2158 293
3107 450
4176 642
5347 871
A e,t
mm2
387
600
418
630
995
895
780
1392
895
1561
89
92
795
1403
2172
1530
2368
3388
4537
5920
792
1391
2149
813
1432
2216
2451
3557
4819
6218
r/t=2.5
All Tests
Department of Civil Engineering
Research Report No R845
148
Without EC Prop. With EC Prop.
Pn
P u,t /P n
kN
101
0.85
156
0.96
109
0.89
164
1.03
259
1.10
233
1.06
203
1.02
362
0.96
233
1.11
406
0.98
23
1.18
24
1.03
207
1.17
365
1.11
565
1.08
398
1.15
616
1.16
881
1.14
1180
1.09
1539
1.03
206
1.14
362
1.11
559
1.08
211
1.14
372
1.11
576
1.10
637
1.16
925
1.12
1253
1.05
1617
0.98
mean 1.07
stdv 0.0818
cov 0.0765
mean 1.05
stdv 0.0727
cov 0.0695
Pn
kN
109
177
118
184
277
250
218
396
249
438
24
26
219
387
601
422
655
940
1262
1652
218
385
596
224
396
615
680
990
1347
1744
P u,t /P n
0.78
0.85
0.82
0.91
1.02
0.99
0.95
0.88
1.03
0.91
1.11
0.96
1.10
1.04
1.01
1.08
1.09
1.07
1.01
0.96
1.08
1.04
1.02
1.07
1.05
1.03
1.09
1.05
0.98
0.91
1.00
0.0862
0.0865
1.01
0.0730
0.0725
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
ASCE (2002), AS/NZS 4673 (2001)
Material
Properties
f y,f
Test ID
304DS1a
304DS2b
f y,c
MPa MPa
242 565
242 565
Geometry
Ag
Ac
2
mm
634
634
Effective Areas
A c /A g
2
%
19
19
mm
122
123
P u,t
kN
132
134
A e,f
2
mm
423
425
A e,c
2
mm
69
70
Without EC Prop. With EC Prop.
A e,t
2
mm
493
494
experimental
Pn
P u,t /P n
Pn
kN
119
1.11
120
1.12
mean 1.11
stdv 0.0098
cov 0.0088
kN
142
142
P u,t /P n
0.93
0.94
0.94
0.0083
0.0089
ASCE (2002), AS/NZS 4673 (2001)
Material
Properties
Test ID
304_200_160_25_10_2
304_200_160_25_10_3
304_200_160_25_10_4
304_400_160_25_10_2
304_400_160_25_10_3
304_400_160_25_10_4
304_400_160_25_20_2
304_400_160_25_20_3
304_400_160_25_20_4
304_800_400_40_15_3
304_800_400_40_15_4
304_800_400_40_15_5
304_800_400_40_15_6
304_800_400_40_30_4
304_800_400_40_30_5
304_800_400_40_30_6
304_150_100_10_10_1
304_150_70_15_10_1
304_150_70_15_10_2
304_200_80_15_10_1
304_200_80_15_10_2
304_150_110_15_10_2
304_300_200_20_15_2
304_300_200_20_15_3
304_100_70_20_10_1
304_250_95_20_10_2
304_250_95_20_10_3
304_100_60_10_10_1
304_200_150_15_15_2
304_90_60_10_5_1
304_150_70_15_10_4
304_150_70_15_10_5
304_200_160_35_20_6
304_200_160_35_20_7
Geometry
Effective Areas
f y,f
f y,c
Ag
Ac
A c /A g
P u,t
A e,f
A e,c
MPa
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
MPa
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
mm2
1177
1755
2327
1577
2355
3127
1626
2430
3227
5123
6769
8505
10186
6966
8691
10410
392
341
681
412
817
837
1542
2303
302
997
1485
262
1122
239
1327
1643
3721
4318
mm2
63
141
251
63
141
251
63
141
251
141
251
393
565
251
393
565
16
16
63
16
63
63
63
141
16
63
141
16
63
16
251
393
565
770
%
5
8
11
4
6
8
4
6
8
3
4
5
6
4
5
5
4
5
9
4
8
8
4
6
5
6
10
6
6
7
19
24
15
18
kN
116
215
328
116
211
328
128
232
355
252
408
577
792
484
683
902
36
32
90
32
90
101
129
235
36
98
182
31
123
27
250
330
669
817
mm2 mm2
760
32
1257 68
1713 130
763
26
1418 59
2053 104
903
35
1616 75
2340 126
1709 58
2694 103
3887 160
5269 231
3014 118
4289 180
5777 258
210
9
294
16
580
37
313
15
614
32
595
37
775
33
1415 71
229
9
703
30
1217 63
192
9
710
38
173
8
1127 151
1250 393
3221 339
3677 462
flats
Department of Civil Engineering
Research Report No R845
149
A e,t
mm2
792
1325
1844
789
1477
2157
938
1691
2466
1768
2797
4047
5500
3131
4468
6035
220
310
617
328
646
631
808
1486
239
732
1281
202
748
181
1278
1643
3561
4139
Without EC Prop. With EC Prop.
Pn
P u,t /P n
kN
154
0.75
258
0.83
360
0.91
154
0.75
288
0.73
421
0.78
183
0.70
330
0.70
481
0.74
345
0.73
545
0.75
789
0.73
1073
0.74
611
0.79
871
0.78
1177
0.77
43
0.83
60
0.53
120
0.75
64
0.50
126
0.72
123
0.82
158
0.82
290
0.81
47
0.76
143
0.68
250
0.73
39
0.79
146
0.84
35
0.76
249
1.00
320
1.03
694
0.96
807
1.01
mean 0.78
stdv 0.1116
cov 0.1430
Pn
kN
154
258
360
154
288
421
183
330
481
345
545
789
1073
611
871
1177
43
60
120
64
126
123
158
290
47
143
250
39
146
35
249
320
694
807
P u,t /P n
0.75
0.83
0.91
0.75
0.73
0.78
0.70
0.70
0.74
0.73
0.75
0.73
0.74
0.79
0.78
0.77
0.83
0.53
0.75
0.50
0.72
0.82
0.82
0.81
0.76
0.68
0.73
0.79
0.84
0.76
1.00
1.03
0.96
1.01
0.78
0.1116
0.1430
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
ASCE (2002), AS/NZS 4673 (2001)
Material
Properties
Test ID
304_200_160_25_10_2_1
304_200_160_25_10_3_1
304_200_160_25_10_4_1
304_400_160_25_10_2_1
304_400_160_25_10_3_1
304_400_160_25_10_4_1
304_400_160_25_20_2_1
304_400_160_25_20_3_1
304_400_160_25_20_4_1
304_800_400_40_15_3_1
304_800_400_40_15_4_1
304_800_400_40_15_5_1
304_800_400_40_15_6_1
304_800_400_40_30_4_1
304_800_400_40_30_5_1
304_800_400_40_30_6_1
304_150_100_10_10_1_1
304_150_70_15_10_1_1
304_150_70_15_10_2_1
304_200_80_15_10_1_1
304_200_80_15_10_2_1
304_150_110_15_10_2_1
304_300_200_20_15_2_1
304_300_200_20_15_3_1
304_100_70_20_10_1_1
304_250_95_20_10_2_1
304_250_95_20_10_3_1
304_100_60_10_10_1_1
304_200_150_15_15_2_1
304_90_60_10_5_1_1
304_150_70_15_10_4_1
304_150_70_15_10_5_1
304_200_160_35_20_6_1
304_200_160_35_20_7_1
Geometry
Effective Areas
f y,f
f y,c
Ag
Ac
A c /A g
P u,t
A e,f
A e,c
MPa
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
MPa
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
mm2
1177
1755
2327
1577
2355
3127
1626
2430
3227
5123
6769
8505
10186
6966
8691
10410
392
341
681
412
817
837
1542
2303
302
997
1485
262
1122
239
1327
1643
3721
4318
mm2
63
141
251
63
141
251
63
141
251
141
251
393
565
251
393
565
16
16
63
16
63
63
63
141
16
63
141
16
63
16
251
393
565
770
%
5
8
11
4
6
8
4
6
8
3
4
5
6
4
5
5
4
5
9
4
8
8
4
6
5
6
10
6
6
7
19
24
15
18
kN
121
227
352
119
221
347
133
244
379
258
423
603
829
503
715
952
37
33
96
33
95
107
133
247
37
102
193
32
128
28
291
408
757
950
mm2 mm2
760
32
1257 68
1713 130
763
26
1418 59
2053 104
903
35
1616 75
2340 126
1709 58
2694 103
3887 160
5269 231
3014 118
4289 180
5777 258
210
9
294
16
580
37
313
15
614
32
595
37
775
33
1415 71
229
9
703
30
1217 63
192
9
710
38
173
8
1127 151
1250 393
3221 339
3677 462
r/t=1
Department of Civil Engineering
Research Report No R845
150
A e,t
mm2
792
1325
1844
789
1477
2157
938
1691
2466
1768
2797
4047
5500
3131
4468
6035
220
310
617
328
646
631
808
1486
239
732
1281
202
748
181
1278
1643
3561
4139
Without EC Prop. With EC Prop.
Pn
P u,t /P n
kN
154
0.78
258
0.88
360
0.98
154
0.78
288
0.77
421
0.83
183
0.73
330
0.74
481
0.79
345
0.75
545
0.77
789
0.76
1073
0.77
611
0.82
871
0.82
1177
0.81
43
0.85
60
0.55
120
0.80
64
0.52
126
0.76
123
0.87
158
0.84
290
0.85
47
0.79
143
0.72
250
0.77
39
0.82
146
0.88
35
0.80
249
1.17
320
1.28
694
1.09
807
1.18
mean 0.83
stdv 0.1539
cov 0.1847
Pn
kN
163
276
394
161
304
448
192
349
514
360
572
831
1133
641
918
1245
45
65
130
68
134
133
166
309
49
151
266
42
156
37
289
423
783
928
P u,t /P n
0.74
0.82
0.89
0.74
0.73
0.77
0.69
0.70
0.74
0.72
0.74
0.72
0.73
0.78
0.78
0.76
0.81
0.51
0.74
0.49
0.71
0.80
0.80
0.80
0.75
0.68
0.73
0.77
0.83
0.76
1.01
0.97
0.97
1.02
0.77
0.1113
0.1443
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
ASCE (2002), AS/NZS 4673 (2001)
Material
Properties
Test ID
304_200_160_25_10_2_2.5
304_200_160_25_10_3_2.5
304_200_160_25_10_4_2.5
304_400_160_25_10_2_2.5
304_400_160_25_10_3_2.5
304_400_160_25_10_4_2.5
304_400_160_25_20_2_2.5
304_400_160_25_20_3_2.5
304_400_160_25_20_4_2.5
304_800_400_40_15_3_2.5
304_800_400_40_15_4_2.5
304_800_400_40_15_5_2.5
304_800_400_40_15_6_2.5
304_800_400_40_30_4_2.5
304_800_400_40_30_5_2.5
304_800_400_40_30_6_2.5
304_150_100_10_10_1_2.5
304_150_70_15_10_1_2.5
304_150_70_15_10_2_2.5
304_200_80_15_10_1_2.5
304_200_80_15_10_2_2.5
304_150_110_15_10_2_2.5
304_300_200_20_15_2_2.5
304_300_200_20_15_3_2.5
304_100_70_20_10_1_2.5
304_250_95_20_10_2_2.5
304_250_95_20_10_3_2.5
304_100_60_10_10_1_2.5
304_200_150_15_15_2_2.5
304_90_60_10_5_1_2.5
304_150_70_15_10_4_2.5
304_150_70_15_10_5_2.5
304_200_160_35_20_6_2.5
304_200_160_35_20_7_2.5
Geometry
Effective Areas
f y,f
f y,c
Ag
Ac
A c /A g
P u,t
A e,f
A e,c
MPa
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
MPa
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
mm2
1157
1711
2262
1557
2311
3062
1607
2386
3148
5078
6739
8382
10069
6888
8569
10234
387
337
657
407
797
817
1522
2258
297
977
1441
257
1102
234
1268
1586
3545
4078
mm2
157
353
565
157
353
565
157
353
628
353
628
982
1131
628
982
1414
39
39
157
39
157
157
157
353
39
157
353
39
157
39
534
668
1414
1924
%
14
21
25
10
15
18
10
15
20
7
9
12
11
9
11
14
10
12
24
10
20
19
10
16
13
16
25
15
14
17
42
42
40
47
kN
122
228
356
121
227
360
135
248
384
255
391
590
832
509
721
958
37
34
100
34
98
109
134
249
37
104
196
33
131
29
302
413
793
1009
mm2 mm2
720
85
1138 182
1529 339
729
67
1357 150
1966 237
874
94
1556 201
2232 339
1646 148
2593 259
3720 403
5131 465
2917 305
4137 466
5539 674
198
24
231
24
515
94
237
23
588
85
535
94
750
88
1348 191
218
24
658
78
1130 164
175
24
649
94
160
22
734 534
918 668
2562 848
2823 1155
A e,t
Without EC
Prop.
With EC Prop.
Pn
Pn
P u,t /P n
mm2 kN
805 157
0.78
1321 258
0.89
1868 364
0.98
796 155
0.78
1508 294
0.77
2203 429
0.84
967 189
0.71
1758 343
0.72
2571 501
0.77
1794 350
0.73
2853 556
0.70
4123 804
0.73
5596 1091 0.76
3222 628
0.81
4604 898
0.80
6214 1212 0.79
222
43
0.86
255
50
0.68
609 119
0.84
260
51
0.66
672 131
0.74
629 123
0.89
838 163
0.82
1539 300
0.83
242
47
0.79
736 143
0.72
1294 252
0.78
199
39
0.85
744 145
0.90
183
36
0.81
1268 247
1.22
1586 309
1.34
3410 665
1.19
3978 776
1.30
mean 0.85
r/t=2.5
stdv 0.1689
cov 0.1994
kN
171
288
420
166
319
469
204
376
557
374
599
870
1168
679
975
1323
47
54
134
55
145
138
178
332
51
156
279
43
161
39
335
419
805
966
P u,t /P n
0.71
0.79
0.85
0.73
0.71
0.77
0.66
0.66
0.69
0.68
0.65
0.68
0.71
0.75
0.74
0.72
0.79
0.63
0.75
0.62
0.67
0.79
0.75
0.75
0.73
0.66
0.70
0.78
0.81
0.73
0.90
0.98
0.99
1.04
0.75
0.1004
0.1334
mean 0.83 mean 0.77
stdv 0.1522
stdv 0.1089
cov 0.1843
cov 0.1412
All Tests
NAS (2001)
Material
Properties
f y,f
Test ID
304DS1a
304DS2b
f y,c
MPa MPa
242 565
242 565
Department of Civil Engineering
Research Report No R845
Effective Areas
Geometry
Without EC
Prop.
Ag
Ac
A c /A g
P u,t
A e,f
A e,c
A e,t
Pn
mm2
634
634
mm2
122
123
%
19
19
kN
132
134
mm2
424
425
mm2
69
70
mm2
493
494
kN
119
120
151
P u,t /P n
1.11
1.12
1.11
0.0098
0.0088
With EC Prop.
Pn
kN
142
142
P u,t /P n
0.93
0.94
0.94
0.0083
0.0089
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
NAS (2001)
Material
Properties
Test ID
304_200_160_25_10_2
304_200_160_25_10_3
304_200_160_25_10_4
304_400_160_25_10_2
304_400_160_25_10_3
304_400_160_25_10_4
304_400_160_25_20_2
304_400_160_25_20_3
304_400_160_25_20_4
304_800_400_40_15_3
304_800_400_40_15_4
304_800_400_40_15_5
304_800_400_40_15_6
304_800_400_40_30_4
304_800_400_40_30_5
304_800_400_40_30_6
304_150_100_10_10_1
304_150_70_15_10_1
304_150_70_15_10_2
304_200_80_15_10_1
304_200_80_15_10_2
304_150_110_15_10_2
304_300_200_20_15_2
304_300_200_20_15_3
304_100_70_20_10_1
304_250_95_20_10_2
304_250_95_20_10_3
304_100_60_10_10_1
304_200_150_15_15_2
304_90_60_10_5_1
304_150_70_15_10_4
304_150_70_15_10_5
304_200_160_35_20_6
304_200_160_35_20_7
Geometry
Effective Areas
f y,f
f y,c
Ag
Ac
A c /A g
P u,t
A e,f
A e,c
MPa
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
MPa
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
mm2
1177
1755
2327
1577
2355
3127
1626
2430
3227
5123
6769
8505
10186
6966
8691
10410
392
341
681
412
817
837
1542
2303
302
997
1485
262
1122
239
1327
1643
3721
4318
mm2
63
141
251
63
141
251
63
141
251
141
251
393
565
251
393
565
16
16
63
16
63
63
63
141
16
63
141
16
63
16
251
393
565
770
%
5
8
11
4
6
8
4
6
8
3
4
5
6
4
5
5
4
5
9
4
8
8
4
6
5
6
10
6
6
7
19
24
15
18
kN
116
215
328
116
211
328
128
232
355
252
408
577
792
484
683
902
36
32
90
32
90
101
129
235
36
98
182
31
123
27
250
330
669
817
mm2
765
1257
1796
763
1418
2196
903
1616
2443
1709
2694
3887
5269
3014
4289
5777
210
294
580
300
634
595
775
1427
228
703
1231
192
710
173
1127
1250
3221
3677
mm2
32
68
130
26
59
104
35
75
126
58
103
160
231
118
180
258
9
16
37
15
32
37
33
71
9
30
63
9
38
8
151
393
339
462
Department of Civil Engineering
Research Report No R845
152
A e,t
Without EC
Prop.
Pn
P u,t /P n
mm2 kN
797 155
0.75
1325 258
0.83
1926 376
0.87
789 154
0.75
1477 288
0.73
2300 449
0.73
938 183
0.70
1691 330
0.70
2570 501
0.71
1768 345
0.73
2797 545
0.75
4047 789
0.73
5500 1073
0.74
3131 611
0.79
4468 871
0.78
6035 1177
0.77
220
43
0.83
309
60
0.53
617 120
0.75
315
61
0.53
666 130
0.69
631 123
0.82
808 158
0.82
1498 292
0.80
237
46
0.77
732 143
0.68
1294 252
0.72
202
39
0.79
748 146
0.84
181
35
0.76
1278 249
1.00
1643 320
1.03
3561 694
0.96
4139 807
1.01
mean 0.78
flats
stdv 0.1100
cov 0.1417
With EC Prop.
Pn
kN
155
258
376
154
288
449
183
330
501
345
545
789
1073
611
871
1177
43
60
120
61
130
123
158
292
46
143
252
39
146
35
249
320
694
807
P u,t /P n
0.75
0.83
0.87
0.75
0.73
0.73
0.70
0.70
0.71
0.73
0.75
0.73
0.74
0.79
0.78
0.77
0.83
0.53
0.75
0.53
0.69
0.82
0.82
0.80
0.77
0.68
0.72
0.79
0.84
0.76
1.00
1.03
0.96
1.01
0.78
0.1100
0.1417
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
NAS (2001)
Material
Properties
Test ID
304_200_160_25_10_2_1
304_200_160_25_10_3_1
304_200_160_25_10_4_1
304_400_160_25_10_2_1
304_400_160_25_10_3_1
304_400_160_25_10_4_1
304_400_160_25_20_2_1
304_400_160_25_20_3_1
304_400_160_25_20_4_1
304_800_400_40_15_3_1
304_800_400_40_15_4_1
304_800_400_40_15_5_1
304_800_400_40_15_6_1
304_800_400_40_30_4_1
304_800_400_40_30_5_1
304_800_400_40_30_6_1
304_150_100_10_10_1_1
304_150_70_15_10_1_1
304_150_70_15_10_2_1
304_200_80_15_10_1_1
304_200_80_15_10_2_1
304_150_110_15_10_2_1
304_300_200_20_15_2_1
304_300_200_20_15_3_1
304_100_70_20_10_1_1
304_250_95_20_10_2_1
304_250_95_20_10_3_1
304_100_60_10_10_1_1
304_200_150_15_15_2_1
304_90_60_10_5_1_1
304_150_70_15_10_4_1
304_150_70_15_10_5_1
304_200_160_35_20_6_1
304_200_160_35_20_7_1
Geometry
Effective Areas
f y,f
f y,c
Ag
Ac
A c /A g
P u,t
A e,f
A e,c
MPa
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
MPa
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
mm2
1177
1755
2327
1577
2355
3127
1626
2430
3227
5123
6769
8505
10186
6966
8691
10410
392
341
681
412
817
837
1542
2303
302
997
1485
262
1122
239
1327
1643
3721
4318
mm2
63
141
251
63
141
251
63
141
251
141
251
393
565
251
393
565
16
16
63
16
63
63
63
141
16
63
141
16
63
16
251
393
565
770
%
5
8
11
4
6
8
4
6
8
3
4
5
6
4
5
5
4
5
9
4
8
8
4
6
5
6
10
6
6
7
19
24
15
18
kN
121
227
352
119
221
347
133
244
379
258
423
603
829
503
715
952
37
33
96
33
95
107
133
247
37
102
193
32
128
28
291
408
757
950
mm2
765
1257
1796
763
1418
2196
903
1616
2443
1709
2694
3887
5269
3014
4289
5777
210
294
580
300
634
595
775
1427
228
703
1231
192
710
173
1127
1250
3221
3677
mm2
32
68
130
26
59
104
35
75
126
58
103
160
231
118
180
258
9
16
37
15
32
37
33
71
9
30
63
9
38
8
151
393
339
462
Department of Civil Engineering
Research Report No R845
153
A e,t
Without EC
Prop.
Pn
P u,t /P n
mm2 kN
797 155
0.78
1325 258
0.88
1926 376
0.94
789 154
0.78
1477 288
0.77
2300 449
0.77
938 183
0.73
1691 330
0.74
2570 501
0.76
1768 345
0.75
2797 545
0.77
4047 789
0.76
5500 1073
0.77
3131 611
0.82
4468 871
0.82
6035 1177
0.81
220
43
0.85
309
60
0.55
617 120
0.80
315
61
0.54
666 130
0.73
631 123
0.87
808 158
0.84
1498 292
0.84
237
46
0.79
732 143
0.72
1294 252
0.77
202
39
0.82
748 146
0.88
181
35
0.80
1278 249
1.17
1643 320
1.28
3561 694
1.09
4139 807
1.18
mean 0.83
r/t=1
stdv 0.1526
cov 0.1841
With EC Prop.
Pn
kN
164
276
410
161
304
476
192
349
534
360
572
831
1133
641
918
1245
45
64
130
65
138
133
166
311
49
151
269
42
156
38
289
423
783
928
P u,t /P n
0.74
0.82
0.86
0.74
0.73
0.73
0.69
0.70
0.71
0.72
0.74
0.72
0.73
0.78
0.78
0.76
0.81
0.51
0.74
0.51
0.69
0.80
0.80
0.79
0.75
0.68
0.72
0.77
0.83
0.76
1.01
0.97
0.97
1.02
0.77
0.1097
0.1429
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
NAS (2001)
Material
Properties
Test ID
304_200_160_25_10_2_2.5
304_200_160_25_10_3_2.5
304_200_160_25_10_4_2.5
304_400_160_25_10_2_2.5
304_400_160_25_10_3_2.5
304_400_160_25_10_4_2.5
304_400_160_25_20_2_2.5
304_400_160_25_20_3_2.5
304_400_160_25_20_4_2.5
304_800_400_40_15_3_2.5
304_800_400_40_15_4_2.5
304_800_400_40_15_5_2.5
304_800_400_40_15_6_2.5
304_800_400_40_30_4_2.5
304_800_400_40_30_5_2.5
304_800_400_40_30_6_2.5
304_150_100_10_10_1_2.5
304_150_70_15_10_1_2.5
304_150_70_15_10_2_2.5
304_200_80_15_10_1_2.5
304_200_80_15_10_2_2.5
304_150_110_15_10_2_2.5
304_300_200_20_15_2_2.5
304_300_200_20_15_3_2.5
304_100_70_20_10_1_2.5
304_250_95_20_10_2_2.5
304_250_95_20_10_3_2.5
304_100_60_10_10_1_2.5
304_200_150_15_15_2_2.5
304_90_60_10_5_1_2.5
304_150_70_15_10_4_2.5
304_150_70_15_10_5_2.5
304_200_160_35_20_6_2.5
304_200_160_35_20_7_2.5
Geometry
Effective Areas
f y,f
f y,c
Ag
Ac
A c /A g
P u,t
A e,f
A e,c
MPa
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
MPa
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
mm2
1157
1711
2262
1557
2311
3062
1607
2386
3148
5078
6739
8382
10069
6888
8569
10234
387
337
657
407
797
817
1522
2258
297
977
1441
257
1102
234
1268
1586
3545
4078
mm2
157
353
565
157
353
565
157
353
628
353
628
982
1131
628
982
1414
39
39
157
39
157
157
157
353
39
157
353
39
157
39
534
668
1414
1924
%
14
21
25
10
15
18
10
15
20
7
9
12
11
9
11
14
10
12
24
10
20
19
10
16
13
16
25
15
14
17
42
42
40
47
kN
122
228
356
121
227
360
135
248
384
255
391
590
832
509
721
958
37
34
100
34
98
109
134
249
37
104
196
33
131
29
302
413
793
1009
mm2 mm2
723
85
1138 182
1610 339
729
67
1357 150
2102 237
874
94
1556 201
2323 339
1646 148
2593 259
3720 403
5131 465
2917 305
4137 466
5539 674
198
24
231
24
515
94
237
23
605
85
535
94
750
88
1353 191
217
24
668
78
1139 164
175
24
649
94
160
22
734 534
918 668
2560 848
2823 1155
A e,t
Without EC
Prop.
Pn
P u,t /P n
mm2 kN
808 158
0.77
1321 258
0.89
1949 380
0.94
796 155
0.78
1508 294
0.77
2338 456
0.79
967 189
0.71
1758 343
0.72
2663 519
0.74
1794 350
0.73
2853 556
0.70
4123 804
0.73
5596 1091
0.76
3222 628
0.81
4604 898
0.80
6214 1212
0.79
222
43
0.86
255
50
0.68
609 119
0.84
260
51
0.66
690 135
0.72
629 123
0.89
838 163
0.82
1545 301
0.83
240
47
0.80
746 145
0.71
1304 254
0.77
199
39
0.85
744 145
0.90
183
36
0.81
1268 247
1.22
1586 309
1.34
3408 665
1.19
3978 776
1.30
mean 0.84
r/t=2.5
stdv 0.1695
cov 0.2011
With EC Prop.
Pn
kN
172
288
436
166
319
495
204
376
575
374
599
870
1168
679
975
1323
47
54
134
55
149
138
178
333
51
158
281
43
161
39
335
419
804
966
mean 0.82
stdv 0.1517
cov 0.1846
All Tests
P u,t /P n
0.71
0.79
0.82
0.73
0.71
0.73
0.66
0.66
0.67
0.68
0.65
0.68
0.71
0.75
0.74
0.72
0.79
0.63
0.75
0.62
0.66
0.79
0.75
0.75
0.74
0.65
0.70
0.78
0.81
0.73
0.90
0.98
0.99
1.04
0.75
0.1009
0.1347
0.77
0.1081
0.1409
EC3 Part 1-4/1-3 (2004) Alternative Method
Material
Properties
f y,f
Test ID
304DS1a
304DS2b
f y,c
MPa MPa
242 565
242 565
Department of Civil Engineering
Research Report No R845
Geometry
Ag
Ac
2
mm
634
634
Effective Areas
A c /A g
2
mm
122
123
%
19
19
154
P u,t
kN
132
134
A e,f
2
mm
478
478
A e,c
2
mm
115
115
Without EC Prop. With EC Prop.
A e,t
2
mm
592
593
Pn
P u,t /P n
Pn
kN
143
0.92
144
0.93
mean 0.93
stdv 0.0089
cov 0.0096
kN
180
181
P u,t /P n
0.73
0.74
0.74
0.0069
0.0093
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
EC3 Part 1-4/1-3 (2004) Alternative Method
Material
Properties
Test ID
304_200_160_25_10_2
304_200_160_25_10_3
304_200_160_25_10_4
304_400_160_25_10_2
304_400_160_25_10_3
304_400_160_25_10_4
304_400_160_25_20_2
304_400_160_25_20_3
304_400_160_25_20_4
304_800_400_40_15_3
304_800_400_40_15_4
304_800_400_40_15_5
304_800_400_40_15_6
304_800_400_40_30_4
304_800_400_40_30_5
304_800_400_40_30_6
304_150_100_10_10_1
304_150_70_15_10_1
304_150_70_15_10_2
304_200_80_15_10_1
304_200_80_15_10_2
304_150_110_15_10_2
304_300_200_20_15_2
304_300_200_20_15_3
304_100_70_20_10_1
304_250_95_20_10_2
304_250_95_20_10_3
304_100_60_10_10_1
304_200_150_15_15_2
304_90_60_10_5_1
304_150_70_15_10_4
304_150_70_15_10_5
304_200_160_35_20_6
304_200_160_35_20_7
Geometry
f y,f
f y,c
Ag
Ac
MPa
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
MPa
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
mm
1177
1755
2327
1577
2355
3127
1626
2430
3227
5123
6769
8505
10186
6966
8691
10410
392
341
681
412
817
837
1542
2303
302
997
1485
262
1122
239
1327
1643
3721
4318
2
2
mm
63
141
251
63
141
251
63
141
251
141
251
393
565
251
393
565
16
16
63
16
63
63
63
141
16
63
141
16
63
16
251
393
565
770
Effective Areas
A c /A g
P u,t
A e,f
%
5
8
11
4
6
8
4
6
8
3
4
5
6
4
5
5
4
5
9
4
8
8
4
6
5
6
10
6
6
7
19
24
15
18
kN
116
215
328
116
211
328
128
232
355
252
408
577
792
484
683
902
36
32
90
32
90
101
129
235
36
98
182
31
123
27
250
330
669
817
mm mm
796
47
1410 122
1939 233
684
38
1224 94
1927 187
780
41
1449 105
2284 208
1512 77
2568 144
4017 235
5201 353
2933 151
4372 248
5679 373
232
11
207
12
577
58
196
10
578
52
665
53
783
41
1529 103
250
14
591
47
1173 122
220
14
793
48
196
14
1078 251
1253 393
3160 565
3555 770
2
A e,c
2
flats
Department of Civil Engineering
Research Report No R845
155
Without EC Prop. With EC Prop.
A e,t
2
mm
843
1532
2172
722
1318
2114
821
1554
2492
1589
2712
4252
5555
3085
4620
6052
243
219
635
206
629
718
824
1632
264
638
1296
234
841
209
1329
1643
3725
4324
Pn
P u,t /P n
kN
164
0.71
299
0.72
423
0.77
141
0.82
257
0.82
412
0.80
160
0.80
303
0.77
486
0.73
310
0.81
529
0.77
829
0.70
1083
0.73
602
0.81
901
0.76
1180
0.76
47
0.75
43
0.75
124
0.73
40
0.80
123
0.73
140
0.72
161
0.80
318
0.74
52
0.69
124
0.79
253
0.72
46
0.68
164
0.75
41
0.66
259
0.96
321
1.03
726
0.92
843
0.97
mean 0.78
stdv 0.0834
cov 0.1071
Pn
kN
164
299
423
141
257
412
160
303
486
310
529
829
1083
602
901
1180
47
43
124
40
123
140
161
318
52
124
253
46
164
41
259
321
726
843
P u,t /P n
0.71
0.72
0.77
0.82
0.82
0.80
0.80
0.77
0.73
0.81
0.77
0.70
0.73
0.81
0.76
0.76
0.75
0.75
0.73
0.80
0.73
0.72
0.80
0.74
0.69
0.79
0.72
0.68
0.75
0.66
0.96
1.03
0.92
0.97
0.78
0.0834
0.1071
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
EC3 Part 1-4/1-3 (2004) Alternative Method
Material
Properties
Test ID
304_200_160_25_10_2_1
304_200_160_25_10_3_1
304_200_160_25_10_4_1
304_400_160_25_10_2_1
304_400_160_25_10_3_1
304_400_160_25_10_4_1
304_400_160_25_20_2_1
304_400_160_25_20_3_1
304_400_160_25_20_4_1
304_800_400_40_15_3_1
304_800_400_40_15_4_1
304_800_400_40_15_5_1
304_800_400_40_15_6_1
304_800_400_40_30_4_1
304_800_400_40_30_5_1
304_800_400_40_30_6_1
304_150_100_10_10_1_1
304_150_70_15_10_1_1
304_150_70_15_10_2_1
304_200_80_15_10_1_1
304_200_80_15_10_2_1
304_150_110_15_10_2_1
304_300_200_20_15_2_1
304_300_200_20_15_3_1
304_100_70_20_10_1_1
304_250_95_20_10_2_1
304_250_95_20_10_3_1
304_100_60_10_10_1_1
304_200_150_15_15_2_1
304_90_60_10_5_1_1
304_150_70_15_10_4_1
304_150_70_15_10_5_1
304_200_160_35_20_6_1
304_200_160_35_20_7_1
Effective Areas
Geometry
f y,f
f y,c
Ag
Ac
MPa
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
MPa
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
457
mm
1177
1755
2327
1577
2355
3127
1626
2430
3227
5123
6769
8505
10186
6966
8691
10410
392
341
681
412
817
837
1542
2303
302
997
1485
262
1122
239
1327
1643
3721
4318
2
2
mm
63
141
251
63
141
251
63
141
251
141
251
393
565
251
393
565
16
16
63
16
63
63
63
141
16
63
141
16
63
16
251
393
565
770
A c /A g
P u,t
A e,f
%
5
8
11
4
6
8
4
6
8
3
4
5
6
4
5
5
4
5
9
4
8
8
4
6
5
6
10
6
6
7
19
24
15
18
kN
121
227
352
119
221
347
133
244
379
258
423
603
829
503
715
952
37
33
96
33
95
107
133
247
37
102
193
32
128
28
291
408
757
950
mm mm
796
47
1410 122
1939 233
684
38
1224 94
1927 187
780
41
1449 105
2284 208
1512 77
2568 144
4017 235
5201 353
2933 151
4372 248
5679 373
232
11
207
12
577
58
196
10
578
52
665
53
783
41
1529 103
250
14
591
47
1173 122
220
14
793
48
196
14
1078 251
1253 393
3160 565
3555 770
2
A e,c
2
r/t=1
Department of Civil Engineering
Research Report No R845
156
Without EC Prop. With EC Prop.
A e,t
2
mm
843
1532
2172
722
1318
2114
821
1554
2492
1589
2712
4252
5555
3085
4620
6052
243
219
635
206
629
718
824
1632
264
638
1296
234
841
209
1329
1643
3725
4324
Pn
P u,t /P n
kN
164
0.74
299
0.76
423
0.83
141
0.85
257
0.86
412
0.84
160
0.83
303
0.80
486
0.78
310
0.83
529
0.80
829
0.73
1083
0.77
602
0.84
901
0.79
1180
0.81
47
0.77
43
0.77
124
0.78
40
0.83
123
0.78
140
0.76
161
0.83
318
0.78
52
0.71
124
0.82
253
0.77
46
0.71
164
0.78
41
0.70
259
1.12
321
1.27
726
1.04
843
1.13
mean 0.83
stdv 0.1259
cov 0.1518
Pn
kN
177
331
484
151
282
461
171
330
540
330
567
891
1176
641
966
1278
50
46
139
43
136
154
171
345
55
137
285
49
176
44
325
424
875
1045
P u,t /P n
0.69
0.69
0.73
0.79
0.79
0.75
0.78
0.74
0.70
0.78
0.75
0.68
0.71
0.79
0.74
0.74
0.73
0.72
0.69
0.77
0.70
0.69
0.78
0.71
0.66
0.75
0.68
0.66
0.73
0.64
0.89
0.96
0.87
0.91
0.75
0.0731
0.0980
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
EC3 Part 1-4/1-3 (2004) Alternative Method
Material
Properties
Test ID
304_200_160_25_10_2_2.5
304_200_160_25_10_3_2.5
304_200_160_25_10_4_2.5
304_400_160_25_10_2_2.5
304_400_160_25_10_3_2.5
304_400_160_25_10_4_2.5
304_400_160_25_20_2_2.5
304_400_160_25_20_3_2.5
304_400_160_25_20_4_2.5
304_800_400_40_15_3_2.5
304_800_400_40_15_4_2.5
304_800_400_40_15_5_2.5
304_800_400_40_15_6_2.5
304_800_400_40_30_4_2.5
304_800_400_40_30_5_2.5
304_800_400_40_30_6_2.5
304_150_100_10_10_1_2.5
304_150_70_15_10_1_2.5
304_150_70_15_10_2_2.5
304_200_80_15_10_1_2.5
304_200_80_15_10_2_2.5
304_150_110_15_10_2_2.5
304_300_200_20_15_2_2.5
304_300_200_20_15_3_2.5
304_100_70_20_10_1_2.5
304_250_95_20_10_2_2.5
304_250_95_20_10_3_2.5
304_100_60_10_10_1_2.5
304_200_150_15_15_2_2.5
304_90_60_10_5_1_2.5
304_150_70_15_10_4_2.5
304_150_70_15_10_5_2.5
304_200_160_35_20_6_2.5
304_200_160_35_20_7_2.5
Effective Areas
Geometry
f y,f
f y,c
Ag
Ac
MPa
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
MPa
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
360
mm
1157
1711
2262
1557
2311
3062
1607
2386
3148
5078
6739
8382
10069
6888
8569
10234
387
337
657
407
797
817
1522
2258
297
977
1441
257
1102
234
1268
1586
3545
4078
2
2
mm
157
353
565
157
353
565
157
353
628
353
628
982
1131
628
982
1414
39
39
157
39
157
157
157
353
39
157
353
39
157
39
534
668
1414
1924
A c /A g
P u,t
A e,f
%
14
21
25
10
15
18
10
15
20
7
9
12
11
9
11
14
10
12
24
10
20
19
10
16
13
16
25
15
14
17
42
42
40
47
kN
122
228
356
121
227
360
135
248
384
255
391
590
832
509
721
958
37
34
100
34
98
109
134
249
37
104
196
33
131
29
302
413
793
1009
mm mm
718 118
1197 306
1596 526
611
94
1049 232
1633 414
708 102
1267 261
1918 518
1382 191
2325 358
3595 587
4794 708
2686 379
3938 620
5027 933
213
27
189
30
475 146
179
26
489 131
577 133
717 103
1349 258
226
35
510 118
951 306
196
34
713 120
173
34
739 534
924 668
2143 1414
2170 1924
2
A e,c
2
r/t=2.5
All Tests
Department of Civil Engineering
Research Report No R845
157
Without EC Prop. With EC Prop.
A e,t
2
mm
837
1503
2122
706
1281
2047
810
1528
2436
1574
2683
4182
5502
3065
4558
5960
240
218
621
204
620
710
820
1607
261
628
1257
231
833
207
1273
1591
3556
4094
Pn
P u,t /P n
kN
163
0.75
293
0.78
414
0.86
138
0.88
250
0.91
399
0.90
158
0.85
298
0.83
475
0.81
307
0.83
523
0.75
815
0.72
1073
0.78
598
0.85
889
0.81
1162
0.82
47
0.79
43
0.79
121
0.83
40
0.85
121
0.81
138
0.79
160
0.84
313
0.79
51
0.73
122
0.85
245
0.80
45
0.74
162
0.81
40
0.71
248
1.22
310
1.33
693
1.14
798
1.26
mean 0.86
stdv 0.1503
cov 0.1749
mean 0.82
stdv 0.1259
cov 0.1527
Pn
kN
183
344
501
153
288
467
175
341
560
338
582
912
1190
660
991
1316
51
47
145
44
142
160
177
356
57
142
295
51
182
46
336
420
927
1116
P u,t /P n
0.67
0.66
0.71
0.79
0.79
0.77
0.77
0.73
0.69
0.75
0.67
0.65
0.70
0.77
0.73
0.73
0.72
0.71
0.69
0.77
0.68
0.68
0.76
0.70
0.66
0.73
0.66
0.65
0.72
0.62
0.90
0.98
0.86
0.90
0.73
0.0793
0.1080
0.75
0.0794
0.1055
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
ASCE (2002), AS/NZS 4673 (2001)
Material
Properties
f y,f
Test ID
430DS1
430DS2
430DS3
430DS4
f y,c
MPa MPa
271 452
271 452
271 452
271 452
Geometry
Effective Areas
Without EC Prop With EC Prop
Ag
Ac
A c /A g
P u,t
A e,f
A e,c
A e,t
Pn
P u,t /P n
Pn
mm2
269
269
278
278
mm2
53
55
54
54
%
20
20
20
20
kN
60
62
64
72
mm2
157
158
177
176
mm2
32
33
33
33
mm2
189
191
209
209
kN
51
1.17
52
1.20
57
1.12
57
1.27
mean 1.19
stdv 0.0623
cov 0.0525
kN
57
58
63
62
experimental
P u,t /P n
1.05
1.07
1.01
1.15
1.07
0.0570
0.0532
ASCE (2002), AS/NZS 4673 (2001)
Material
Properties
f y,f
Test ID
430_200_160_25_10_2
430_200_160_25_10_3
430_200_160_25_10_4
430_400_160_25_10_2
430_400_160_25_10_3
430_400_160_25_10_4
430_400_160_25_20_2
430_400_160_25_20_3
430_400_160_25_20_4
430_800_400_40_15_3
430_800_400_40_15_4
430_800_400_40_15_5
430_800_400_40_15_6
430_800_400_40_30_4
430_800_400_40_30_5
430_800_400_40_30_6
430_150_100_10_10_1
430_150_70_15_10_1
430_150_70_15_10_2
430_200_80_15_10_1
430_200_80_15_10_2
430_150_110_15_10_2
430_300_200_20_15_2
430_300_200_20_15_3
430_100_70_20_10_1
430_250_95_20_10_2
430_250_95_20_10_3
430_100_60_10_10_1
430_200_150_15_15_2
430_90_60_10_5_1
430_150_70_15_10_4
430_150_70_15_10_5
430_200_160_35_20_6
430_200_160_35_20_7
f y,c
Geometry
Ag
Ac
2
MPa MPa mm
275 275 1177
275 275 1755
275 275 2327
275 275 1577
275 275 2355
275 275 3127
275 275 1626
275 275 2430
275 275 3227
275 275 5123
275 275 6769
275 275 8505
275 275 10186
275 275 6966
275 275 8691
275 275 10410
275 275
392
275 275
341
275 275
681
275 275
412
275 275
817
275 275
837
275 275 1542
275 275 2303
275 275
302
275 275
997
275 275 1485
275 275
262
275 275 1122
275 275
239
275 275 1327
275 275 1643
275 275 3721
275 275 4318
Effective Areas
A c /A g
2
mm
63
141
251
63
141
251
63
141
251
141
251
393
565
251
393
565
16
16
63
16
63
63
63
141
16
63
141
16
63
16
251
393
565
770
%
5
8
11
4
6
8
4
6
8
3
4
5
6
4
5
5
4
5
9
4
8
8
4
6
5
6
10
6
6
7
19
24
15
18
P u,t
kN
155
284
431
154
282
439
167
312
476
316
527
762
1049
625
907
1198
44
43
118
42
121
134
170
310
48
131
241
41
162
36
322
434
873
1068
A e,f
2
mm
631
1110
1601
626
1172
1786
733
1317
2027
1388
2200
3184
4325
2449
3497
4714
178
211
498
200
527
528
626
1175
205
581
1018
171
619
145
1078
1351
2988
3478
A e,c
2
mm
30
64
113
26
58
103
32
67
119
58
102
159
229
113
172
245
9
9
33
8
30
33
30
67
9
28
61
9
38
8
151
236
339
462
flats
Department of Civil Engineering
Research Report No R845
158
Without EC Prop With EC Prop
A e,t
2
mm
661
1174
1714
652
1230
1889
765
1384
2147
1446
2302
3343
4554
2562
3669
4960
188
221
531
208
557
561
656
1242
214
609
1080
181
657
152
1228
1587
3327
3940
Pn
P u,t /P n
kN
182
0.85
323
0.88
471
0.91
179
0.86
338
0.83
520
0.85
210
0.79
381
0.82
590
0.81
398
0.80
633
0.83
919
0.83
1252
0.84
705
0.89
1009
0.90
1364
0.88
52
0.85
61
0.71
146
0.81
57
0.73
153
0.79
154
0.87
180
0.94
342
0.91
59
0.81
167
0.78
297
0.81
50
0.83
181
0.90
42
0.85
338
0.95
436
1.00
915
0.95
1084
0.99
mean 0.85
stdv 0.0658
cov 0.0771
Pn
kN
182
323
471
179
338
520
210
381
590
398
633
919
1252
705
1009
1364
52
61
146
57
153
154
180
342
59
167
297
50
181
42
338
436
915
1084
P u,t /P n
0.85
0.88
0.91
0.86
0.83
0.85
0.79
0.82
0.81
0.80
0.83
0.83
0.84
0.89
0.90
0.88
0.85
0.71
0.81
0.73
0.79
0.87
0.94
0.91
0.81
0.78
0.81
0.83
0.90
0.85
0.95
1.00
0.95
0.99
0.85
0.0658
0.0771
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
ASCE (2002), AS/NZS 4673 (2001)
Material
Properties
f y,f
Test ID
430_200_160_25_10_2_1
430_200_160_25_10_3_1
430_200_160_25_10_4_1
430_400_160_25_10_2_1
430_400_160_25_10_3_1
430_400_160_25_10_4_1
430_400_160_25_20_2_1
430_400_160_25_20_3_1
430_400_160_25_20_4_1
430_800_400_40_15_3_1
430_800_400_40_15_4_1
430_800_400_40_15_5_1
430_800_400_40_15_6_1
430_800_400_40_30_4_1
430_800_400_40_30_5_1
430_800_400_40_30_6_1
430_150_100_10_10_1_1
430_150_70_15_10_1_1
430_150_70_15_10_2_1
430_200_80_15_10_1_1
430_200_80_15_10_2_1
430_150_110_15_10_2_1
430_300_200_20_15_2_1
430_300_200_20_15_3_1
430_100_70_20_10_1_1
430_250_95_20_10_2_1
430_250_95_20_10_3_1
430_100_60_10_10_1_1
430_200_150_15_15_2_1
430_90_60_10_5_1_1
430_150_70_15_10_4_1
430_150_70_15_10_5_1
430_200_160_35_20_6_1
430_200_160_35_20_7_1
f y,c
Geometry
Ag
MPa MPa mm2
275 479 1177
275 479 1755
275 479 2327
275 479 1577
275 479 2355
275 479 3127
275 479 1626
275 479 2430
275 479 3227
275 479 5123
275 479 6769
275 479 8505
275 479 10186
275 479 6966
275 479 8691
275 479 10410
275 479
392
275 479
341
275 479
681
275 479
412
275 479
817
275 479
837
275 479 1542
275 479 2303
275 479
302
275 479
997
275 479 1485
275 479
262
275 479 1122
275 479
239
275 479 1327
275 479 1643
275 479 3721
275 479 4318
Effective Areas
Ac
A c /A g
P u,t
A e,f
A e,c
A e,t
mm2
63
141
251
63
141
251
63
141
251
141
251
393
565
251
393
565
16
16
63
16
63
63
63
141
16
63
141
16
63
16
251
393
565
770
%
5
8
11
4
6
8
4
6
8
3
4
5
6
4
5
5
4
5
9
4
8
8
4
6
5
6
10
6
6
7
19
24
15
18
kN
157
292
448
155
288
452
170
319
491
323
538
780
1075
635
930
1233
48
43
123
42
124
134
144
319
48
134
248
42
167
37
353
491
937
1165
mm2
631
1110
1601
626
1172
1786
733
1317
2027
1388
2200
3184
4325
2449
3497
4714
178
211
498
200
527
528
626
1175
205
581
1018
171
619
145
1078
1351
2988
3478
mm2
30
64
113
26
58
103
32
67
119
58
102
159
229
113
172
245
9
9
33
8
30
33
30
67
9
28
61
9
38
8
151
236
339
462
mm2
661
1174
1714
652
1230
1889
765
1384
2147
1446
2302
3343
4554
2562
3669
4960
188
221
531
208
557
561
656
1242
214
609
1080
181
657
152
1228
1587
3327
3940
r/t=1
Department of Civil Engineering
Research Report No R845
159
Without EC Prop With EC Prop
Pn
P u,t /P n
kN
182
0.86
323
0.90
471
0.95
179
0.87
338
0.85
520
0.87
210
0.81
381
0.84
590
0.83
398
0.81
633
0.85
919
0.85
1252
0.86
705
0.90
1009
0.92
1364
0.90
52
0.93
61
0.72
146
0.84
57
0.74
153
0.81
154
0.87
180
0.80
342
0.93
59
0.82
167
0.80
297
0.84
50
0.85
181
0.92
42
0.87
338
1.04
436
1.13
915
1.02
1084
1.08
mean 0.88
stdv 0.0870
cov 0.0990
Pn
kN
188
336
494
185
350
541
217
394
615
409
654
952
1299
728
1044
1414
53
63
153
59
159
161
187
355
61
173
309
52
188
43
369
484
984
1178
P u,t /P n
0.84
0.87
0.91
0.84
0.82
0.84
0.78
0.81
0.80
0.79
0.82
0.82
0.83
0.87
0.89
0.87
0.89
0.69
0.80
0.72
0.78
0.83
0.77
0.90
0.79
0.77
0.80
0.82
0.88
0.84
0.96
1.01
0.95
0.99
0.84
0.0698
0.0829
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
ASCE (2002), AS/NZS 4673 (2001)
Material
Properties
Test ID
430_200_160_25_10_2_2.5
430_200_160_25_10_3_2.5
430_200_160_25_10_4_2.5
430_400_160_25_10_2_2.5
430_400_160_25_10_3_2.5
430_400_160_25_10_4_2.5
430_400_160_25_20_2_2.5
430_400_160_25_20_3_2.5
430_400_160_25_20_4_2.5
430_800_400_40_15_3_2.5
430_800_400_40_15_4_2.5
430_800_400_40_15_5_2.5
430_800_400_40_15_6_2.5
430_800_400_40_30_4_2.5
430_800_400_40_30_5_2.5
430_800_400_40_30_6_2.5
430_150_100_10_10_1_2.5
430_150_70_15_10_1_2.5
430_150_70_15_10_2_2.5
430_200_80_15_10_1_2.5
430_200_80_15_10_2_2.5
430_150_110_15_10_2_2.5
430_300_200_20_15_2_2.5
430_300_200_20_15_3_2.5
430_100_70_20_10_1_2.5
430_250_95_20_10_2_2.5
430_250_95_20_10_3_2.5
430_100_60_10_10_1_2.5
430_200_150_15_15_2_2.5
430_90_60_10_5_1_2.5
430_150_70_15_10_4_2.5
430_150_70_15_10_5_2.5
430_200_160_35_20_6_2.5
430_200_160_35_20_7_2.5
Geometry
f y,f
f y,c
Ag
Ac
MPa
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
MPa mm2 mm2
424 1157 157
424 1711 353
424 2262 565
424 1557 157
424 2311 353
424 3062 565
424 1607 157
424 2386 353
424 3148 628
424 5078 353
424 6739 628
424 8382 982
424 10069 1131
424 6888 628
424 8569 982
424 10234 1414
424
387
39
424
337
39
424
657
157
424
407
39
424
797
157
424
817
157
424 1522 157
424 2258 353
424
297
39
424
977
157
424 1441 353
424
257
39
424 1102 157
424
234
39
424 1268 534
424 1586 668
424 3545 1414
424 4078 1924
Effective Areas
A c /A g
P u,t
A e,f
A e,c
A e,t
%
14
21
25
10
15
18
10
15
20
7
9
12
11
9
11
14
10
12
24
10
20
19
10
16
13
16
25
15
14
17
42
42
40
47
kN
157
294
452
157
288
465
169
321
492
322
523
753
1071
640
932
1229
45
44
128
43
126
139
170
319
49
134
249
43
168
37
363
497
964
1207
mm2
601
1030
1447
598
1121
1705
709
1267
1937
1338
2117
3047
4209
2371
3374
4522
170
198
459
192
503
485
606
1125
197
554
966
158
573
138
783
918
2408
2665
mm2
79
166
265
66
146
234
85
176
315
146
257
399
460
289
441
628
24
24
90
21
79
90
79
177
24
71
157
24
94
20
320
668
848
1155
mm2
679
1196
1712
664
1268
1939
793
1443
2252
1484
2374
3446
4668
2660
3815
5150
193
222
549
213
582
575
685
1303
221
625
1123
182
667
158
1103
1586
3257
3819
r/t=2.5
All Tests
Department of Civil Engineering
Research Report No R845
160
Without EC Prop With EC Prop
Pn
P u,t /P n
kN
187
0.84
329
0.89
471
0.96
183
0.86
349
0.83
533
0.87
218
0.78
397
0.81
619
0.79
408
0.79
653
0.80
948
0.79
1284
0.83
732
0.87
1049
0.89
1416
0.87
53
0.84
61
0.72
151
0.85
59
0.73
160
0.78
158
0.88
188
0.90
358
0.89
61
0.80
172
0.78
309
0.81
50
0.86
183
0.92
44
0.85
303
1.20
436
1.14
896
1.08
1050
1.15
mean 0.87
stdv 0.1128
cov 0.1294
mean 0.88
stdv 0.1082
cov 0.1229
Pn
kN
199
354
510
192
370
568
231
423
666
430
691
1007
1352
775
1115
1510
57
65
164
62
172
171
200
385
64
183
332
54
197
47
351
536
1022
1222
P u,t /P n
0.79
0.83
0.89
0.82
0.78
0.82
0.73
0.76
0.74
0.75
0.76
0.75
0.79
0.83
0.84
0.81
0.79
0.68
0.78
0.70
0.73
0.81
0.85
0.83
0.76
0.73
0.75
0.80
0.85
0.79
1.03
0.93
0.94
0.99
0.81
0.0778
0.0964
0.84
0.0857
0.1016
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
NAS (2001)
Material
Properties
f y,f
Test ID
430DS1
430DS2
430DS3
430DS4
f y,c
MPa MPa
271 452
271 452
271 452
271 452
Geometry
Effective Areas
Without EC Prop
With EC Prop
Ag
Ac
A c /A g
P u,t
A e,f
A e,c
A e,t
Pn
P u,t /P n
Pn
mm2
269
269
278
278
mm2
53
55
54
54
%
20
20
20
20
kN
60
62
64
72
mm2
157
158
177
176
mm2
32
33
33
33
mm2
189
191
209
209
kN
51
1.17
52
1.20
57
1.12
57
1.27
mean 1.19
stdv 0.0623
cov 0.0525
kN
57
58
63
62
experimental
P u,t /P n
1.05
1.07
1.01
1.15
1.07
0.0570
0.0532
NAS (2001)
Material
Properties
f y,f
Test ID
430_200_160_25_10_2
430_200_160_25_10_3
430_200_160_25_10_4
430_400_160_25_10_2
430_400_160_25_10_3
430_400_160_25_10_4
430_400_160_25_20_2
430_400_160_25_20_3
430_400_160_25_20_4
430_800_400_40_15_3
430_800_400_40_15_4
430_800_400_40_15_5
430_800_400_40_15_6
430_800_400_40_30_4
430_800_400_40_30_5
430_800_400_40_30_6
430_150_100_10_10_1
430_150_70_15_10_1
430_150_70_15_10_2
430_200_80_15_10_1
430_200_80_15_10_2
430_150_110_15_10_2
430_300_200_20_15_2
430_300_200_20_15_3
430_100_70_20_10_1
430_250_95_20_10_2
430_250_95_20_10_3
430_100_60_10_10_1
430_200_150_15_15_2
430_90_60_10_5_1
430_150_70_15_10_4
430_150_70_15_10_5
430_200_160_35_20_6
430_200_160_35_20_7
Department of Civil Engineering
Research Report No R845
f y,c
Geometry
Ag
MPa MPa mm2
275 275 1177
275 275 1755
275 275 2327
275 275 1577
275 275 2355
275 275 3127
275 275 1626
275 275 2430
275 275 3227
275 275 5123
275 275 6769
275 275 8505
275 275 10186
275 275 6966
275 275 8691
275 275 10410
275 275
392
275 275
341
275 275
681
275 275
412
275 275
817
275 275
837
275 275 1542
275 275 2303
275 275
302
275 275
997
275 275 1485
275 275
262
275 275 1122
275 275
239
275 275 1327
275 275 1643
275 275 3721
275 275 4318
Effective Areas
Without EC Prop
Ac
A c /A g
P u,t
A e,f
A e,c
A e,t
Pn
mm2
63
141
251
63
141
251
63
141
251
141
251
393
565
251
393
565
16
16
63
16
63
63
63
141
16
63
141
16
63
16
251
393
565
770
%
5
8
11
4
6
8
4
6
8
3
4
5
6
4
5
5
4
5
9
4
8
8
4
6
5
6
10
6
6
7
19
24
15
18
kN
155
284
431
154
282
439
167
312
476
316
527
762
1049
625
907
1198
44
43
118
42
121
134
170
310
48
131
241
41
162
36
322
434
873
1068
mm2
640
1119
1601
625
1172
1868
732
1317
2069
1385
2200
3184
4325
2449
3497
4714
178
210
517
199
537
530
626
1198
203
581
1068
171
619
146
1078
1351
2987
3477
mm2
30
64
113
26
58
103
32
67
119
58
102
159
229
113
172
245
9
9
33
8
30
33
30
67
9
28
61
9
38
8
151
236
339
462
mm2
670
1183
1714
651
1230
1971
764
1384
2188
1443
2302
3343
4554
2562
3669
4960
188
220
550
207
567
563
656
1265
213
609
1130
181
657
154
1228
1587
3327
3938
kN
184
325
471
179
338
542
210
381
602
397
633
919
1252
705
1009
1364
52
60
151
57
156
155
180
348
59
167
311
50
181
42
338
436
915
1083
161
P u,t /P n
0.84
0.87
0.91
0.86
0.83
0.81
0.80
0.82
0.79
0.80
0.83
0.83
0.84
0.89
0.90
0.88
0.85
0.71
0.78
0.74
0.77
0.86
0.94
0.89
0.81
0.78
0.77
0.83
0.90
0.84
0.95
1.00
0.95
0.99
0.85
0.0677
0.0797
With EC Prop
Pn
kN
184
325
471
179
338
542
210
381
602
397
633
919
1252
705
1009
1364
52
60
151
57
156
155
180
348
59
167
311
50
181
42
338
436
915
1083
P u,t /P n
0.84
0.87
0.91
0.86
0.83
0.81
0.80
0.82
0.79
0.80
0.83
0.83
0.84
0.89
0.90
0.88
0.85
0.71
0.78
0.74
0.77
0.86
0.94
0.89
0.81
0.78
0.77
0.83
0.90
0.84
0.95
1.00
0.95
0.99
0.85
0.0677
0.0797
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
NAS (2001)
Material
Properties
f y,f
Test ID
430_200_160_25_10_2_1
430_200_160_25_10_3_1
430_200_160_25_10_4_1
430_400_160_25_10_2_1
430_400_160_25_10_3_1
430_400_160_25_10_4_1
430_400_160_25_20_2_1
430_400_160_25_20_3_1
430_400_160_25_20_4_1
430_800_400_40_15_3_1
430_800_400_40_15_4_1
430_800_400_40_15_5_1
430_800_400_40_15_6_1
430_800_400_40_30_4_1
430_800_400_40_30_5_1
430_800_400_40_30_6_1
430_150_100_10_10_1_1
430_150_70_15_10_1_1
430_150_70_15_10_2_1
430_200_80_15_10_1_1
430_200_80_15_10_2_1
430_150_110_15_10_2_1
430_300_200_20_15_2_1
430_300_200_20_15_3_1
430_100_70_20_10_1_1
430_250_95_20_10_2_1
430_250_95_20_10_3_1
430_100_60_10_10_1_1
430_200_150_15_15_2_1
430_90_60_10_5_1_1
430_150_70_15_10_4_1
430_150_70_15_10_5_1
430_200_160_35_20_6_1
430_200_160_35_20_7_1
f y,c
Geometry
Ag
MPa MPa mm2
275 479 1177
275 479 1755
275 479 2327
275 479 1577
275 479 2355
275 479 3127
275 479 1626
275 479 2430
275 479 3227
275 479 5123
275 479 6769
275 479 8505
275 479 10186
275 479 6966
275 479 8691
275 479 10410
275 479
392
275 479
341
275 479
681
275 479
412
275 479
817
275 479
837
275 479 1542
275 479 2303
275 479
302
275 479
997
275 479 1485
275 479
262
275 479 1122
275 479
239
275 479 1327
275 479 1643
275 479 3721
275 479 4318
Effective Areas
Ac
A c /A g
P u,t
A e,f
A e,c
A e,t
Pn
mm2
63
141
251
63
141
251
63
141
251
141
251
393
565
251
393
565
16
16
63
16
63
63
63
141
16
63
141
16
63
16
251
393
565
770
%
5
8
11
4
6
8
4
6
8
3
4
5
6
4
5
5
4
5
9
4
8
8
4
6
5
6
10
6
6
7
19
24
15
18
kN
157
292
448
155
288
452
170
319
491
323
538
780
1075
635
930
1233
48
43
123
42
124
134
144
319
48
134
248
42
167
37
353
491
937
1165
mm2
640
1119
1601
625
1172
1868
732
1317
2069
1385
2200
3184
4325
2449
3497
4714
178
210
517
199
537
530
626
1198
203
581
1068
171
619
146
1078
1351
2987
3477
mm2
30
64
113
26
58
103
32
67
119
58
102
159
229
113
172
245
9
9
33
8
30
33
30
67
9
28
61
9
38
8
151
236
339
462
mm2
670
1183
1714
651
1230
1971
764
1384
2188
1443
2302
3343
4554
2562
3669
4960
188
220
550
207
567
563
656
1265
213
609
1130
181
657
154
1228
1587
3327
3938
kN
184
325
471
179
338
542
210
381
602
397
633
919
1252
705
1009
1364
52
60
151
57
156
155
180
348
59
167
311
50
181
42
338
436
915
1083
r/t=1
Department of Civil Engineering
Research Report No R845
Without EC Prop
162
P u,t /P n
0.85
0.90
0.95
0.87
0.85
0.83
0.81
0.84
0.82
0.81
0.85
0.85
0.86
0.90
0.92
0.90
0.93
0.72
0.81
0.75
0.80
0.86
0.80
0.92
0.83
0.80
0.80
0.85
0.92
0.86
1.04
1.13
1.02
1.08
0.87
0.0885
0.1013
With EC Prop
Pn
kN
190
338
494
184
350
563
217
394
626
409
654
952
1299
728
1044
1414
53
62
158
58
162
162
187
362
60
173
323
52
188
44
369
484
984
1177
P u,t /P n
0.83
0.86
0.91
0.84
0.82
0.80
0.79
0.81
0.78
0.79
0.82
0.82
0.83
0.87
0.89
0.87
0.89
0.70
0.78
0.73
0.77
0.83
0.77
0.88
0.80
0.77
0.77
0.82
0.88
0.83
0.96
1.01
0.95
0.99
0.84
0.0713
0.0851
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
NAS (2001)
Material
Properties
Test ID
430_200_160_25_10_2_2.5
430_200_160_25_10_3_2.5
430_200_160_25_10_4_2.5
430_400_160_25_10_2_2.5
430_400_160_25_10_3_2.5
430_400_160_25_10_4_2.5
430_400_160_25_20_2_2.5
430_400_160_25_20_3_2.5
430_400_160_25_20_4_2.5
430_800_400_40_15_3_2.5
430_800_400_40_15_4_2.5
430_800_400_40_15_5_2.5
430_800_400_40_15_6_2.5
430_800_400_40_30_4_2.5
430_800_400_40_30_5_2.5
430_800_400_40_30_6_2.5
430_150_100_10_10_1_2.5
430_150_70_15_10_1_2.5
430_150_70_15_10_2_2.5
430_200_80_15_10_1_2.5
430_200_80_15_10_2_2.5
430_150_110_15_10_2_2.5
430_300_200_20_15_2_2.5
430_300_200_20_15_3_2.5
430_100_70_20_10_1_2.5
430_250_95_20_10_2_2.5
430_250_95_20_10_3_2.5
430_100_60_10_10_1_2.5
430_200_150_15_15_2_2.5
430_90_60_10_5_1_2.5
430_150_70_15_10_4_2.5
430_150_70_15_10_5_2.5
430_200_160_35_20_6_2.5
430_200_160_35_20_7_2.5
Geometry
f y,f
f y,c
Ag
Ac
MPa
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
MPa mm2 mm2
424 1157 157
424 1711 353
424 2262 565
424 1557 157
424 2311 353
424 3062 565
424 1607 157
424 2386 353
424 3148 628
424 5078 353
424 6739 628
424 8382 982
424 10069 1131
424 6888 628
424 8569 982
424 10234 1414
424
387
39
424
337
39
424
657
157
424
407
39
424
797
157
424
817
157
424 1522 157
424 2258 353
424
297
39
424
977
157
424 1441 353
424
257
39
424 1102 157
424
234
39
424 1268 534
424 1586 668
424 3545 1414
424 4078 1924
Effective Areas
A c /A g
P u,t
A e,f
A e,c
%
14
21
25
10
15
18
10
15
20
7
9
12
11
9
11
14
10
12
24
10
20
19
10
16
13
16
25
15
14
17
42
42
40
47
kN
157
294
452
157
288
465
169
321
492
322
523
753
1071
640
932
1229
45
44
128
43
126
139
170
319
49
134
249
43
168
37
363
497
964
1207
mm2 mm2
608
79
1030 166
1447 265
598
66
1121 146
1780 234
709
85
1267 176
1964 315
1338 146
2117 257
3047 399
4209 460
2371 289
3374 441
4522 628
170
24
198
24
474
90
191
21
510
79
485
90
606
79
1141 177
196
24
554
71
1008 157
158
24
573
94
139
20
783 320
918 668
2408 848
2664 1155
r/t=2.5
All Tests
Department of Civil Engineering
Research Report No R845
163
Without EC Prop With EC Prop
A e,t
Pn
mm2
686
1196
1712
664
1268
2014
793
1443
2279
1484
2374
3446
4668
2660
3815
5150
193
221
564
213
589
575
685
1318
219
625
1165
182
667
159
1103
1586
3256
3818
kN
189
329
471
183
349
554
218
397
627
408
653
948
1284
732
1049
1416
53
61
155
58
162
158
188
362
60
172
320
50
183
44
303
436
895
1050
P u,t /P n
0.83
0.89
0.96
0.86
0.83
0.84
0.78
0.81
0.79
0.79
0.80
0.79
0.83
0.87
0.89
0.87
0.84
0.72
0.82
0.74
0.78
0.88
0.90
0.88
0.81
0.78
0.78
0.86
0.92
0.84
1.20
1.14
1.08
1.15
0.87
0.1140
0.1313
0.88
0.1098
0.1253
Pn
kN
200
354
510
192
370
589
231
423
674
430
691
1007
1352
775
1115
1510
57
64
168
62
174
171
200
389
64
183
344
54
197
47
351
536
1022
1222
P u,t /P n
0.78
0.83
0.89
0.82
0.78
0.79
0.73
0.76
0.73
0.75
0.76
0.75
0.79
0.83
0.84
0.81
0.79
0.69
0.76
0.70
0.72
0.81
0.85
0.82
0.77
0.73
0.72
0.80
0.85
0.79
1.03
0.93
0.94
0.99
0.80
0.0789
0.0982
0.84
0.0871
0.1038
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
EC3 Part 1-4/1-3 Alternative Method
Material
Properties
f y,f
Test ID
430DS1
430DS2
430DS3
430DS4
f y,c
MPa MPa
271 452
271 452
271 452
271 452
Geometry
Effective Areas
Without EC Prop With EC Prop
Ag
Ac
A c /A g
P u,t
A e,f
A e,c
A e,t
Pn
P u,t /P n
Pn
mm2
269
269
278
278
mm2
53
55
54
54
%
20
20
20
20
kN
60
62
64
72
mm2
191
197
202
212
mm2
47
51
50
53
mm2
239
247
252
265
kN
65
0.92
67
0.92
68
0.93
72
1.00
mean 0.94
stdv 0.0378
cov 0.0401
kN
73
76
77
81
experimental
P u,t /P n
0.81
0.81
0.82
0.88
0.83
0.0340
0.0408
EC3 Part 1-4/1-3 Alternative Method
Material
Properties
f y,f
Test ID
430_200_160_25_10_2
430_200_160_25_10_3
430_200_160_25_10_4
430_400_160_25_10_2
430_400_160_25_10_3
430_400_160_25_10_4
430_400_160_25_20_2
430_400_160_25_20_3
430_400_160_25_20_4
430_800_400_40_15_3
430_800_400_40_15_4
430_800_400_40_15_5
430_800_400_40_15_6
430_800_400_40_30_4
430_800_400_40_30_5
430_800_400_40_30_6
430_150_100_10_10_1
430_150_70_15_10_1
430_150_70_15_10_2
430_200_80_15_10_1
430_200_80_15_10_2
430_150_110_15_10_2
430_300_200_20_15_2
430_300_200_20_15_3
430_100_70_20_10_1
430_250_95_20_10_2
430_250_95_20_10_3
430_100_60_10_10_1
430_200_150_15_15_2
430_90_60_10_5_1
430_150_70_15_10_4
430_150_70_15_10_5
430_200_160_35_20_6
430_200_160_35_20_7
Department of Civil Engineering
Research Report No R845
f y,c
Geometry
Ag
Ac
2
MPa MPa mm
275 275 1177
275 275 1755
275 275 2327
275 275 1577
275 275 2355
275 275 3127
275 275 1626
275 275 2430
275 275 3227
275 275 5123
275 275 6769
275 275 8505
275 275 10186
275 275 6966
275 275 8691
275 275 10410
275 275
392
275 275
341
275 275
681
275 275
412
275 275
817
275 275
837
275 275 1542
275 275 2303
275 275
302
275 275
997
275 275 1485
275 275
262
275 275 1122
275 275
239
275 275 1327
275 275 1643
275 275 3721
275 275 4318
Effective Areas
A c /A g
2
mm
63
141
251
63
141
251
63
141
251
141
251
393
565
251
393
565
16
16
63
16
63
63
63
141
16
63
141
16
63
16
251
393
565
770
164
%
5
8
11
4
6
8
4
6
8
3
4
5
6
4
5
5
4
5
9
4
8
8
4
6
5
6
10
6
6
7
19
24
15
18
P u,t
kN
155
284
431
154
282
439
167
312
476
316
527
762
1049
625
907
1198
44
43
118
42
121
134
170
310
48
131
241
41
162
36
322
434
873
1068
A e,f
2
mm
636
1272
1800
555
1074
1632
689
1220
1903
1239
2084
3176
4637
2437
3604
5022
180
176
532
173
481
605
639
1335
207
496
944
182
704
151
1070
1253
3080
3531
A e,c
2
mm
43
109
215
36
87
167
38
93
183
73
134
221
330
142
232
347
10
11
53
10
46
47
38
94
13
42
110
12
44
11
249
393
550
764
Without EC Prop With EC Prop
A e,t
2
mm
679
1381
2015
591
1161
1799
727
1313
2086
1313
2219
3397
4967
2579
3835
5369
190
187
586
182
526
652
677
1429
220
538
1054
194
748
162
1319
1643
3630
4296
Pn
kN
187
380
554
162
319
495
200
361
574
361
610
934
1366
709
1055
1476
52
51
161
50
145
179
186
393
61
148
290
53
206
45
363
453
998
1181
P u,t /P n
0.83
0.75
0.78
0.95
0.88
0.89
0.84
0.86
0.83
0.88
0.86
0.82
0.77
0.88
0.86
0.81
0.84
0.83
0.73
0.83
0.83
0.75
0.91
0.79
0.79
0.88
0.83
0.77
0.79
0.80
0.89
0.96
0.87
0.90
0.84
0.0557
0.0665
Pn
kN
187
380
554
162
319
495
200
361
574
361
610
934
1366
709
1055
1476
52
51
161
50
145
179
186
393
61
148
290
53
206
45
363
453
998
1181
P u,t /P n
0.83
0.75
0.78
0.95
0.88
0.89
0.84
0.86
0.83
0.88
0.86
0.82
0.77
0.88
0.86
0.81
0.84
0.83
0.73
0.83
0.83
0.75
0.91
0.79
0.79
0.88
0.83
0.77
0.79
0.80
0.89
0.96
0.87
0.90
0.84
0.0557
0.0665
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
EC3 Part 1-4/1-3 Alternative Method
Material
Properties
f y,f
Test ID
430_200_160_25_10_2_2.5
430_200_160_25_10_3_2.5
430_200_160_25_10_4_2.5
430_400_160_25_10_2_2.5
430_400_160_25_10_3_2.5
430_400_160_25_10_4_2.5
430_400_160_25_20_2_2.5
430_400_160_25_20_3_2.5
430_400_160_25_20_4_2.5
430_800_400_40_15_3_2.5
430_800_400_40_15_4_2.5
430_800_400_40_15_5_2.5
430_800_400_40_15_6_2.5
430_800_400_40_30_4_2.5
430_800_400_40_30_5_2.5
430_800_400_40_30_6_2.5
430_150_100_10_10_1_2.5
430_150_70_15_10_1_2.5
430_150_70_15_10_2_2.5
430_200_80_15_10_1_2.5
430_200_80_15_10_2_2.5
430_150_110_15_10_2_2.5
430_300_200_20_15_2_2.5
430_300_200_20_15_3_2.5
430_100_70_20_10_1_2.5
430_250_95_20_10_2_2.5
430_250_95_20_10_3_2.5
430_100_60_10_10_1_2.5
430_200_150_15_15_2_2.5
430_90_60_10_5_1_2.5
430_150_70_15_10_4_2.5
430_150_70_15_10_5_2.5
430_200_160_35_20_6_2.5
430_200_160_35_20_7_2.5
f y,c
Effective Areas
Geometry
Ag
Ac
A c /A g
P u,t
A e,f
%
14
21
25
10
15
18
10
15
20
7
9
12
11
9
11
14
10
12
24
10
20
19
10
16
13
16
25
15
14
17
42
42
40
47
kN
157
294
452
157
288
465
169
321
492
322
523
753
1071
640
932
1229
45
44
128
43
126
139
170
319
49
134
249
43
168
37
363
497
964
1207
mm2 mm2 mm2
568 108 675
1083 275 1358
1485 486 1971
493
89
581
912 216 1128
1377 372 1748
622
95
717
1056 234 1289
1579 455 2034
1117 183 1300
1860 334 2194
2808 552 3360
4253 662 4916
2206 356 2562
3495 579 4074
4413 867 5281
164
25
189
158
27
185
439 135 573
156
24
180
404 115 519
523 119 642
579
95
673
1170 236 1406
187
32
218
423 104 528
750 274 1024
162
31
193
629 111 740
132
29
160
736 531 1267
924 668 1591
2097 1382 3479
2164 1919 4083
MPa MPa mm2 mm2
275 424 1157 157
275 424 1711 353
275 424 2262 565
275 424 1557 157
275 424 2311 353
275 424 3062 565
275 424 1607 157
275 424 2386 353
275 424 3148 628
275 424 5078 353
275 424 6739 628
275 424 8382 982
275 424 10069 1131
275 424 6888 628
275 424 8569 982
275 424 10234 1414
275 424
387
39
275 424
337
39
275 424
657
157
275 424
407
39
275 424
797
157
275 424
817
157
275 424 1522 157
275 424 2258 353
275 424
297
39
275 424
977
157
275 424 1441 353
275 424
257
39
275 424 1102 157
275 424
234
39
275 424 1268 534
275 424 1586 668
275 424 3545 1414
275 424 4078 1924
A e,c
r/t=2.5
All Tests
Department of Civil Engineering
Research Report No R845
165
A e,t
Without EC Prop With EC Prop
Pn
kN
186
373
542
160
310
481
197
355
559
357
603
924
1352
705
1120
1452
52
51
158
50
143
177
185
387
60
145
281
53
204
44
348
438
957
1123
P u,t /P n
0.84
0.79
0.83
0.98
0.93
0.97
0.86
0.90
0.88
0.90
0.87
0.82
0.79
0.91
0.83
0.85
0.86
0.87
0.81
0.87
0.88
0.79
0.92
0.83
0.81
0.92
0.89
0.81
0.83
0.84
1.04
1.14
1.01
1.08
0.89
0.0837
0.0945
0.86
0.0739
0.0855
Pn
kN
202
414
614
173
342
536
211
389
627
385
653
1006
1450
758
1207
1581
56
55
178
53
160
194
199
422
65
161
322
58
220
48
428
537
1163
1409
P u,t /P n
0.78
0.71
0.74
0.91
0.84
0.87
0.80
0.82
0.78
0.84
0.80
0.75
0.74
0.84
0.77
0.78
0.81
0.80
0.72
0.81
0.79
0.71
0.85
0.76
0.75
0.83
0.77
0.74
0.76
0.76
0.85
0.93
0.83
0.86
0.80
0.0534
0.0669
0.82
0.0558
0.0684
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
EC3 Part 1-4/1-3 Alternative Method
Material
Properties
f y,f
f y,c
Geometry
Ag
MPa MPa mm2
275 479 1177
275 479 1755
275 479 2327
275 479 1577
275 479 2355
275 479 3127
275 479 1626
275 479 2430
275 479 3227
275 479 5123
275 479 6769
275 479 8505
275 479 10186
275 479 6966
275 479 8691
275 479 10410
275 479
392
275 479
341
275 479
681
275 479
412
275 479
817
275 479
837
275 479 1542
275 479 2303
275 479
302
275 479
997
275 479 1485
275 479
262
275 479 1122
275 479
239
275 479 1327
275 479 1643
275 479 3721
275 479 4318
Test ID
430_200_160_25_10_2_1
430_200_160_25_10_3_1
430_200_160_25_10_4_1
430_400_160_25_10_2_1
430_400_160_25_10_3_1
430_400_160_25_10_4_1
430_400_160_25_20_2_1
430_400_160_25_20_3_1
430_400_160_25_20_4_1
430_800_400_40_15_3_1
430_800_400_40_15_4_1
430_800_400_40_15_5_1
430_800_400_40_15_6_1
430_800_400_40_30_4_1
430_800_400_40_30_5_1
430_800_400_40_30_6_1
430_150_100_10_10_1_1
430_150_70_15_10_1_1
430_150_70_15_10_2_1
430_200_80_15_10_1_1
430_200_80_15_10_2_1
430_150_110_15_10_2_1
430_300_200_20_15_2_1
430_300_200_20_15_3_1
430_100_70_20_10_1_1
430_250_95_20_10_2_1
430_250_95_20_10_3_1
430_100_60_10_10_1_1
430_200_150_15_15_2_1
430_90_60_10_5_1_1
430_150_70_15_10_4_1
430_150_70_15_10_5_1
430_200_160_35_20_6_1
430_200_160_35_20_7_1
Effective Areas
Without EC Prop With EC Prop
Ac
A c /A g
P u,t
A e,f
A e,c
A e,t
Pn
mm2
63
141
251
63
141
251
63
141
251
141
251
393
565
251
393
565
16
16
63
16
63
63
63
141
16
63
141
16
63
16
251
393
565
770
%
5
8
11
4
6
8
4
6
8
3
4
5
6
4
5
5
4
5
9
4
8
8
4
6
5
6
10
6
6
7
19
24
15
18
kN
157
292
448
155
288
452
170
319
491
323
538
780
1075
635
930
1233
48
43
123
42
124
134
144
319
48
134
248
42
167
37
353
491
937
1165
mm2
636
1272
1800
555
1074
1632
689
1220
1903
1239
2084
3176
4637
2437
3604
5022
180
176
532
173
481
605
639
1335
207
496
944
182
704
151
1070
1253
3080
3531
mm2
43
109
215
36
87
167
38
93
183
73
134
221
330
142
232
347
10
11
53
10
46
47
38
94
13
42
110
12
44
11
249
393
550
764
mm2
679
1381
2015
591
1161
1799
727
1313
2086
1313
2219
3397
4967
2579
3835
5369
190
187
586
182
526
652
677
1429
220
538
1054
194
748
162
1319
1643
3630
4296
kN
187
380
554
162
319
495
200
361
574
361
610
934
1366
709
1055
1476
52
51
161
50
145
179
186
393
61
148
290
53
206
45
363
453
998
1181
r/t=1
P u,t /P n
0.84
0.77
0.81
0.96
0.90
0.91
0.85
0.88
0.86
0.89
0.88
0.84
0.79
0.90
0.88
0.84
0.92
0.85
0.76
0.85
0.86
0.75
0.77
0.81
0.80
0.90
0.86
0.79
0.81
0.82
0.97
1.09
0.94
0.99
0.86
0.0721
0.0837
Pn
kN
196
402
598
170
337
529
208
380
611
376
637
979
1433
738
1102
1547
54
54
172
52
154
189
194
412
63
156
312
56
215
47
413
533
1111
1337
P u,t /P n
0.80
0.73
0.75
0.91
0.85
0.85
0.82
0.84
0.80
0.86
0.84
0.80
0.75
0.86
0.84
0.80
0.88
0.81
0.71
0.82
0.81
0.71
0.74
0.77
0.77
0.85
0.80
0.75
0.78
0.78
0.85
0.92
0.84
0.87
0.81
0.0542
0.0668
ASCE (2002), AS/NZS 4673 (2001)
Material
Properties
f y,f
Test ID
3Cr12DS1a
3Cr12DS2b
f y,c
MPa MPa
339 606
339 606
Department of Civil Engineering
Research Report No R845
Geometry
Ag
Ac
2
mm
565
565
Effective Areas
A c /A g
2
mm
124
124
%
22
22
166
P u,t
kN
163
161
A e,f
2
mm
379
379
A e,c
2
mm
70
70
Without EC Prop With EC Prop
A e,t
2
mm
448
449
Pn
P u,t /P n
Pn
kN
152
1.07
152
1.06
mean 1.07
stdv 0.0099
cov 0.0093
kN
171
171
P u,t /P n
0.95
0.94
0.95
0.0085
0.0090
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
ASCE (2002), AS/NZS 4673 (2001)
Material
Properties
Test ID
3Cr12_200_160_25_10_2
3Cr12_200_160_25_10_3
3Cr12_200_160_25_10_4
3Cr12_400_160_25_10_2
3Cr12_400_160_25_10_3
3Cr12_400_160_25_10_4
3Cr12_400_160_25_20_2
3Cr12_400_160_25_20_3
3Cr12_400_160_25_20_4
3Cr12_800_400_40_15_3
3Cr12_800_400_40_15_4
3Cr12_800_400_40_15_5
3Cr12_800_400_40_15_6
3Cr12_800_400_40_30_4
3Cr12_800_400_40_30_5
3Cr12_800_400_40_30_6
3Cr12_150_100_10_10_1
3Cr12_150_70_15_10_1
3Cr12_150_70_15_10_2
3Cr12_200_80_15_10_1
3Cr12_200_80_15_10_2
3Cr12_150_110_15_10_2
3Cr12_300_200_20_15_2
3Cr12_300_200_20_15_3
3Cr12_100_70_20_10_1
3Cr12_250_95_20_10_2
3Cr12_250_95_20_10_3
3Cr12_100_60_10_10_1
3Cr12_200_150_15_15_2
3Cr12_90_60_10_5_1
3Cr12_150_70_15_10_4
3Cr12_150_70_15_10_5
3Cr12_200_160_35_20_6
3Cr12_200_160_35_20_7
Geometry
f y,f
f y,c
Ag
MPa
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
MPa mm2
260 1177
260 1755
260 2327
260 1577
260 2355
260 3127
260 1626
260 2430
260 3227
260 5123
260 6769
260 8505
260 10186
260 6966
260 8691
260 10410
260 392
260 341
260 681
260 412
260 817
260 837
260 1542
260 2303
260 302
260 997
260 1485
260 262
260 1122
260 239
260 1327
260 1643
260 3721
260 4318
Effective Areas
Ac
A c /A g
P u,t
A e,f
A e,c
A e,t
mm2
63
141
251
63
141
251
63
141
251
141
251
393
565
251
393
565
16
16
63
16
63
63
63
141
16
63
141
16
63
16
251
393
565
770
%
5
8
11
4
6
8
4
6
8
3
4
5
6
4
5
5
4
5
9
4
8
8
4
6
5
6
10
6
6
7
19
24
15
18
kN
160
287
428
159
290
449
175
316
481
334
551
789
1008
658
929
1224
48
44
120
44
122
133
175
312
49
134
247
41
162
36
312
419
848
1032
mm2
689
1188
1678
686
1280
1936
807
1446
2198
1530
2417
3492
4738
2696
3843
5176
194
285
538
221
570
559
690
1282
217
634
1128
182
660
157
1127
1250
3064
3639
mm2
31
65
118
26
58
104
33
70
122
58
103
160
230
115
175
250
9
16
34
8
31
34
31
69
9
28
62
9
38
8
151
393
339
462
mm2
719
1253
1796
712
1339
2040
840
1516
2321
1588
2519
3652
4968
2811
4018
5426
203
301
572
229
601
593
722
1351
226
663
1190
191
698
165
1278
1643
3404
4101
flats
Department of Civil Engineering
Research Report No R845
167
Without EC Prop With EC Prop
Pn
P u,t /P n
kN
187
0.86
326
0.88
467
0.92
185
0.86
348
0.83
530
0.85
218
0.80
394
0.80
603
0.80
413
0.81
655
0.84
949
0.83
1292
0.78
731
0.90
1045
0.89
1411
0.87
53
0.91
78
0.56
149
0.80
60
0.74
156
0.78
154
0.87
188
0.93
351
0.89
59
0.83
172
0.78
310
0.80
50
0.83
182
0.89
43
0.84
332
0.94
427
0.98
885
0.96
1066
0.97
mean 0.85
stdv 0.0778
cov 0.0918
Pn
kN
187
326
467
185
348
530
218
394
603
413
655
949
1292
731
1045
1411
53
78
149
60
156
154
188
351
59
172
310
50
182
43
332
427
885
1066
P u,t /P n
0.86
0.88
0.92
0.86
0.83
0.85
0.80
0.80
0.80
0.81
0.84
0.83
0.78
0.90
0.89
0.87
0.91
0.56
0.80
0.74
0.78
0.87
0.93
0.89
0.83
0.78
0.80
0.83
0.89
0.84
0.94
0.98
0.96
0.97
0.85
0.0778
0.0918
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
ASCE (2002), AS/NZS 4673 (2001)
Material
Properties
f y,f
Test ID
3Cr12_200_160_25_10_2_1
3Cr12_200_160_25_10_3_1
3Cr12_200_160_25_10_4_1
3Cr12_400_160_25_10_2_1
3Cr12_400_160_25_10_3_1
3Cr12_400_160_25_10_4_1
3Cr12_400_160_25_20_2_1
3Cr12_400_160_25_20_3_1
3Cr12_400_160_25_20_4_1
3Cr12_800_400_40_15_3_1
3Cr12_800_400_40_15_4_1
3Cr12_800_400_40_15_5_1
3Cr12_800_400_40_15_6_1
3Cr12_800_400_40_30_4_1
3Cr12_800_400_40_30_5_1
3Cr12_800_400_40_30_6_1
3Cr12_150_100_10_10_1_1
3Cr12_150_70_15_10_1_1
3Cr12_150_70_15_10_2_1
3Cr12_200_80_15_10_1_1
3Cr12_200_80_15_10_2_1
3Cr12_150_110_15_10_2_1
3Cr12_300_200_20_15_2_1
3Cr12_300_200_20_15_3_1
3Cr12_100_70_20_10_1_1
3Cr12_250_95_20_10_2_1
3Cr12_250_95_20_10_3_1
3Cr12_100_60_10_10_1_1
3Cr12_200_150_15_15_2_1
3Cr12_90_60_10_5_1_1
3Cr12_150_70_15_10_4_1
3Cr12_150_70_15_10_5_1
3Cr12_200_160_35_20_6_1
3Cr12_200_160_35_20_7_1
MPa
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
f y,c
Geometry
Ag
MPa mm2
460 1177
460 1755
460 2327
460 1577
460 2355
460 3127
460 1626
460 2430
460 3227
460 5123
460 6769
460 8505
460 10186
460 6966
460 8691
460 10410
460 392
460 341
460 681
460 412
460 817
460 837
460 1542
460 2303
460 302
460 997
460 1485
460 262
460 1122
460 239
460 1327
460 1643
460 3721
460 4318
Effective Areas
Ac
A c /A g
P u,t
A e,f
A e,c
A e,t
mm2
63
141
251
63
141
251
63
141
251
141
251
393
565
251
393
565
16
16
63
16
63
63
63
141
16
63
141
16
63
16
251
393
565
770
%
5
8
11
4
6
8
4
6
8
3
4
5
6
4
5
5
4
5
9
4
8
8
4
6
5
6
10
6
6
7
19
24
15
18
kN
163
296
448
161
296
462
178
324
495
340
562
806
1106
670
952
1257
49
44
125
45
126
137
178
321
50
137
255
42
167
37
347
479
918
1136
mm2
689
1188
1678
686
1280
1936
807
1446
2198
1530
2417
3492
4738
2696
3843
5176
194
285
538
221
570
559
690
1282
217
634
1128
182
660
157
1127
1250
3064
3639
mm2
31
65
118
26
58
104
33
70
122
58
103
160
230
115
175
250
9
16
34
8
31
34
31
69
9
28
62
9
38
8
151
393
339
462
mm2
719
1253
1796
712
1339
2040
840
1516
2321
1588
2519
3652
4968
2811
4018
5426
203
301
572
229
601
593
722
1351
226
663
1190
191
698
165
1278
1643
3404
4101
r/t=1
Department of Civil Engineering
Research Report No R845
168
Without EC Prop With EC Prop
Pn
P u,t /P n
kN
187
0.87
326
0.91
467
0.96
185
0.87
348
0.85
530
0.87
218
0.81
394
0.82
603
0.82
413
0.82
655
0.86
949
0.85
1292
0.86
731
0.92
1045
0.91
1411
0.89
53
0.92
78
0.57
149
0.84
60
0.75
156
0.81
154
0.89
188
0.95
351
0.91
59
0.84
172
0.80
310
0.82
50
0.85
182
0.92
43
0.86
332
1.04
427
1.12
885
1.04
1066
1.07
mean 0.88
stdv 0.0974
cov 0.1108
Pn
kN
193
339
491
190
360
551
225
408
628
424
675
981
1338
754
1080
1461
55
81
156
61
162
161
194
365
61
178
322
52
189
45
362
506
953
1159
P u,t /P n
0.84
0.87
0.91
0.85
0.82
0.84
0.79
0.79
0.79
0.80
0.83
0.82
0.83
0.89
0.88
0.86
0.89
0.55
0.80
0.73
0.78
0.85
0.92
0.88
0.82
0.77
0.79
0.82
0.88
0.83
0.96
0.95
0.96
0.98
0.84
0.0789
0.0939
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
ASCE (2002), AS/NZS 4673 (2001)
Material
Properties
Test ID
3Cr12_200_160_25_10_2_2.5
3Cr12_200_160_25_10_3_2.5
3Cr12_200_160_25_10_4_2.5
3Cr12_400_160_25_10_2_2.5
3Cr12_400_160_25_10_3_2.5
3Cr12_400_160_25_10_4_2.5
3Cr12_400_160_25_20_2_2.5
3Cr12_400_160_25_20_3_2.5
3Cr12_400_160_25_20_4_2.5
3Cr12_800_400_40_15_3_2.5
3Cr12_800_400_40_15_4_2.5
3Cr12_800_400_40_15_5_2.5
3Cr12_800_400_40_15_6_2.5
3Cr12_800_400_40_30_4_2.5
3Cr12_800_400_40_30_5_2.5
3Cr12_800_400_40_30_6_2.5
3Cr12_150_100_10_10_1_2.5
3Cr12_150_70_15_10_1_2.5
3Cr12_150_70_15_10_2_2.5
3Cr12_200_80_15_10_1_2.5
3Cr12_200_80_15_10_2_2.5
3Cr12_150_110_15_10_2_2.5
3Cr12_300_200_20_15_2_2.5
3Cr12_300_200_20_15_3_2.5
3Cr12_100_70_20_10_1_2.5
3Cr12_250_95_20_10_2_2.5
3Cr12_250_95_20_10_3_2.5
3Cr12_100_60_10_10_1_2.5
3Cr12_200_150_15_15_2_2.5
3Cr12_90_60_10_5_1_2.5
3Cr12_150_70_15_10_4_2.5
3Cr12_150_70_15_10_5_2.5
3Cr12_200_160_35_20_6_2.5
3Cr12_200_160_35_20_7_2.5
Geometry
f y,f
f y,c
Ag
Ac
MPa
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
MPa mm2 mm2
406 1157 157
406 1711 353
406 2262 565
406 1557 157
406 2311 353
406 3062 565
406 1607 157
406 2386 353
406 3148 628
406 5078 353
406 6739 628
406 8382 982
406 10069 1131
406 6888 628
406 8569 982
406 10234 1414
406
387
39
406
337
39
406
657
157
406
407
39
406
797
157
406
817
157
406 1522 157
406 2258 353
406
297
39
406
977
157
406 1441 353
406
257
39
406 1102 157
406
234
39
406 1268 534
406 1586 668
406 3545 1414
406 4078 1924
Effective Areas
A c /A g
P u,t
A e,f
A e,c
%
14
21
25
10
15
18
10
15
20
7
9
12
11
9
11
14
10
12
24
10
20
19
10
16
13
16
25
15
14
17
42
42
40
47
kN
163
300
454
161
298
478
179
325
497
339
541
776
1110
674
953
1255
49
45
130
45
129
139
179
323
50
138
256
43
168
38
358
485
949
1184
mm2 mm2
654
81
1078 172
1410 284
656
67
1225 148
1745 235
781
88
1392 185
1997 325
1473 147
2326 258
3342 401
4612 462
2609 296
3707 450
4964 644
182
24
213
24
490
94
212
22
524
81
510
94
668
83
1225 183
209
24
605
74
1063 160
168
24
610
94
149
21
918 320
918 668
2451 848
2763 1155
A e,t
mm2
735
1250
1694
722
1373
1980
869
1577
2321
1619
2583
3742
5073
2905
4158
5608
206
237
584
234
605
604
750
1408
232
678
1223
192
704
170
1239
1586
3299
3917
r/t=2.5
Without EC Prop With EC Prop
Pn
P u,t /P n
kN
191
0.85
325
0.92
440
1.03
188
0.86
357
0.84
515
0.93
226
0.79
410
0.79
604
0.82
421
0.80
672
0.80
973
0.80
1319
0.84
755
0.89
1081
0.88
1458
0.86
54
0.92
62
0.74
152
0.86
61
0.74
157
0.82
157
0.88
195
0.92
366
0.88
60
0.83
176
0.78
318
0.81
50
0.87
183
0.92
44
0.85
322
1.11
412
1.18
858
1.11
1019
1.16
mean 0.88
stdv 0.1112
cov 0.1256
Pn
kN
203
350
482
197
379
549
239
437
651
442
709
1031
1387
798
1147
1552
57
65
166
64
169
171
207
393
64
187
341
53
197
47
369
510
982
1187
mean 0.87
stdv 0.0996
cov 0.1140
All Tests
P u,t /P n
0.80
0.86
0.94
0.81
0.79
0.87
0.75
0.74
0.76
0.77
0.76
0.75
0.80
0.84
0.83
0.81
0.86
0.70
0.78
0.71
0.76
0.81
0.86
0.82
0.79
0.74
0.75
0.81
0.86
0.79
0.97
0.95
0.97
1.00
0.82
0.0760
0.0929
0.84
0.0786
0.0939
NAS (2001)
Material
Properties
f y,f
Test ID
3Cr12DS1a
3Cr12DS2b
f y,c
MPa MPa
339 606
339 606
Geometry
Effective Areas
Ag
Ac
A c /A g
P u,t
A e,f
A e,c
A e,t
mm2
565
565
mm2
124
124
%
22
22
kN
163
161
mm2
379
379
mm2
70
70
mm2
448
449
experimental
Department of Civil Engineering
Research Report No R845
169
Without EC
Prop
Pn
With EC Prop
P u,t /P n
Pn
kN
152
1.07
152
1.06
mean 1.07
stdv 0.0099
cov 0.0093
kN
171
171
P u,t /P n
0.95
0.94
0.95
0.0085
0.0090
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
NAS (2001)
Material
Properties
f y,f
Test ID
3Cr12_200_160_25_10_2
3Cr12_200_160_25_10_3
3Cr12_200_160_25_10_4
3Cr12_400_160_25_10_2
3Cr12_400_160_25_10_3
3Cr12_400_160_25_10_4
3Cr12_400_160_25_20_2
3Cr12_400_160_25_20_3
3Cr12_400_160_25_20_4
3Cr12_800_400_40_15_3
3Cr12_800_400_40_15_4
3Cr12_800_400_40_15_5
3Cr12_800_400_40_15_6
3Cr12_800_400_40_30_4
3Cr12_800_400_40_30_5
3Cr12_800_400_40_30_6
3Cr12_150_100_10_10_1
3Cr12_150_70_15_10_1
3Cr12_150_70_15_10_2
3Cr12_200_80_15_10_1
3Cr12_200_80_15_10_2
3Cr12_150_110_15_10_2
3Cr12_300_200_20_15_2
3Cr12_300_200_20_15_3
3Cr12_100_70_20_10_1
3Cr12_250_95_20_10_2
3Cr12_250_95_20_10_3
3Cr12_100_60_10_10_1
3Cr12_200_150_15_15_2
3Cr12_90_60_10_5_1
3Cr12_150_70_15_10_4
3Cr12_150_70_15_10_5
3Cr12_200_160_35_20_6
3Cr12_200_160_35_20_7
MPa
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
f y,c
Geometry
Ag
MPa mm2
260 1177
260 1755
260 2327
260 1577
260 2355
260 3127
260 1626
260 2430
260 3227
260 5123
260 6769
260 8505
260 10186
260 6966
260 8691
260 10410
260
392
260
341
260
681
260
412
260
817
260
837
260 1542
260 2303
260
302
260
997
260 1485
260
262
260 1122
260
239
260 1327
260 1643
260 3721
260 4318
Ac
A c /A g
P u,t
A e,f
%
5
8
11
4
6
8
4
6
8
3
4
5
6
4
5
5
4
5
9
4
8
8
4
6
5
6
10
6
6
7
19
24
15
18
kN
160
287
428
159
290
449
175
316
481
334
551
789
1008
658
929
1224
48
44
120
44
122
133
175
312
49
134
247
41
162
36
312
419
848
1032
mm
696
1188
1678
686
1280
2008
807
1446
2230
1528
2417
3492
4738
2696
3843
5176
194
276
549
220
578
559
690
1300
215
634
1157
182
660
158
1127
1250
3063
3635
2
mm
63
141
251
63
141
251
63
141
251
141
251
393
565
251
393
565
16
16
63
16
63
63
63
141
16
63
141
16
63
16
251
393
565
770
2
A e,c
2
mm
31
65
118
26
58
104
33
70
122
58
103
160
230
115
175
250
9
15
34
8
31
34
31
69
9
28
62
9
38
8
151
393
339
462
flats
Department of Civil Engineering
Research Report No R845
170
Without EC
Prop
Effective Areas
A e,t
2
mm
727
1253
1796
712
1339
2111
840
1516
2352
1586
2519
3652
4968
2811
4018
5426
203
291
583
228
609
593
722
1369
225
663
1219
191
698
166
1278
1643
3402
4097
Pn
P u,t /P n
kN
189
0.85
326
0.88
467
0.92
185
0.86
348
0.83
549
0.82
218
0.80
394
0.80
612
0.79
412
0.81
655
0.84
949
0.83
1292
0.78
731
0.90
1045
0.89
1411
0.87
53
0.91
76
0.58
152
0.79
59
0.75
158
0.77
154
0.87
188
0.93
356
0.88
58
0.84
172
0.78
317
0.78
50
0.83
182
0.89
43
0.84
332
0.94
427
0.98
885
0.96
1065
0.97
mean 0.85
stdv 0.0768
cov 0.0909
With EC Prop
Pn
kN
189
326
467
185
348
549
218
394
612
412
655
949
1292
731
1045
1411
53
76
152
59
158
154
188
356
58
172
317
50
182
43
332
427
885
1065
P u,t /P n
0.85
0.88
0.92
0.86
0.83
0.82
0.80
0.80
0.79
0.81
0.84
0.83
0.78
0.90
0.89
0.87
0.91
0.58
0.79
0.75
0.77
0.87
0.93
0.88
0.84
0.78
0.78
0.83
0.89
0.84
0.94
0.98
0.96
0.97
0.85
0.0768
0.0909
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
NAS (2001)
Material
Properties
f y,f
Test ID
3Cr12_200_160_25_10_2_1
3Cr12_200_160_25_10_3_1
3Cr12_200_160_25_10_4_1
3Cr12_400_160_25_10_2_1
3Cr12_400_160_25_10_3_1
3Cr12_400_160_25_10_4_1
3Cr12_400_160_25_20_2_1
3Cr12_400_160_25_20_3_1
3Cr12_400_160_25_20_4_1
3Cr12_800_400_40_15_3_1
3Cr12_800_400_40_15_4_1
3Cr12_800_400_40_15_5_1
3Cr12_800_400_40_15_6_1
3Cr12_800_400_40_30_4_1
3Cr12_800_400_40_30_5_1
3Cr12_800_400_40_30_6_1
3Cr12_150_100_10_10_1_1
3Cr12_150_70_15_10_1_1
3Cr12_150_70_15_10_2_1
3Cr12_200_80_15_10_1_1
3Cr12_200_80_15_10_2_1
3Cr12_150_110_15_10_2_1
3Cr12_300_200_20_15_2_1
3Cr12_300_200_20_15_3_1
3Cr12_100_70_20_10_1_1
3Cr12_250_95_20_10_2_1
3Cr12_250_95_20_10_3_1
3Cr12_100_60_10_10_1_1
3Cr12_200_150_15_15_2_1
3Cr12_90_60_10_5_1_1
3Cr12_150_70_15_10_4_1
3Cr12_150_70_15_10_5_1
3Cr12_200_160_35_20_6_1
3Cr12_200_160_35_20_7_1
MPa
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
f y,c
Ag
MPa mm2
460 1177
460 1755
460 2327
460 1577
460 2355
460 3127
460 1626
460 2430
460 3227
460 5123
460 6769
460 8505
460 10186
460 6966
460 8691
460 10410
460
392
460
341
460
681
460
412
460
817
460
837
460 1542
460 2303
460
302
460
997
460 1485
460
262
460 1122
460
239
460 1327
460 1643
460 3721
460 4318
Ac
A c /A g
P u,t
A e,f
%
5
8
11
4
6
8
4
6
8
3
4
5
6
4
5
5
4
5
9
4
8
8
4
6
5
6
10
6
6
7
19
24
15
18
kN
163
296
448
161
296
462
178
324
495
340
562
806
1106
670
952
1257
49
44
125
45
126
137
178
321
50
137
255
42
167
37
347
479
918
1136
mm mm
696
31
1188 65
1678 118
686
26
1280 58
2008 104
807
33
1446 70
2230 122
1528 58
2417 103
3492 160
4738 230
2696 115
3843 175
5176 250
194
9
276
15
549
34
220
8
578
31
559
34
690
31
1300 69
215
9
634
28
1157 62
182
9
660
38
158
8
1127 151
1250 393
3063 339
3635 462
2
mm
63
141
251
63
141
251
63
141
251
141
251
393
565
251
393
565
16
16
63
16
63
63
63
141
16
63
141
16
63
16
251
393
565
770
2
A e,c
2
r/t-1
Department of Civil Engineering
Research Report No R845
171
Without EC
Prop
Effective Areas
Geometry
A e,t
2
mm
727
1253
1796
712
1339
2111
840
1516
2352
1586
2519
3652
4968
2811
4018
5426
203
291
583
228
609
593
722
1369
225
663
1219
191
698
166
1278
1643
3402
4097
Pn
kN
189
326
467
185
348
549
218
394
612
412
655
949
1292
731
1045
1411
53
76
152
59
158
154
188
356
58
172
317
50
182
43
332
427
885
1065
P u,t /P n
0.86
0.91
0.96
0.87
0.85
0.84
0.81
0.82
0.81
0.83
0.86
0.85
0.86
0.92
0.91
0.89
0.92
0.59
0.82
0.76
0.80
0.89
0.95
0.90
0.85
0.80
0.80
0.85
0.92
0.85
1.04
1.12
1.04
1.07
0.88
0.0969
0.1105
With EC Prop
Pn
kN
195
339
491
190
360
570
225
408
636
424
675
981
1338
754
1080
1461
55
79
158
61
164
161
194
370
60
178
329
52
189
45
362
506
952
1158
P u,t /P n
0.83
0.87
0.91
0.85
0.82
0.81
0.79
0.79
0.78
0.80
0.83
0.82
0.83
0.89
0.88
0.86
0.89
0.56
0.79
0.74
0.77
0.85
0.92
0.87
0.82
0.77
0.77
0.82
0.88
0.82
0.96
0.95
0.96
0.98
0.84
0.0779
0.0929
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
NAS (2001)
Material
Properties
f y,f
Test ID
3Cr12_200_160_25_10_2_2.5
3Cr12_200_160_25_10_3_2.5
3Cr12_200_160_25_10_4_2.5
3Cr12_400_160_25_10_2_2.5
3Cr12_400_160_25_10_3_2.5
3Cr12_400_160_25_10_4_2.5
3Cr12_400_160_25_20_2_2.5
3Cr12_400_160_25_20_3_2.5
3Cr12_400_160_25_20_4_2.5
3Cr12_800_400_40_15_3_2.5
3Cr12_800_400_40_15_4_2.5
3Cr12_800_400_40_15_5_2.5
3Cr12_800_400_40_15_6_2.5
3Cr12_800_400_40_30_4_2.5
3Cr12_800_400_40_30_5_2.5
3Cr12_800_400_40_30_6_2.5
3Cr12_150_100_10_10_1_2.5
3Cr12_150_70_15_10_1_2.5
3Cr12_150_70_15_10_2_2.5
3Cr12_200_80_15_10_1_2.5
3Cr12_200_80_15_10_2_2.5
3Cr12_150_110_15_10_2_2.5
3Cr12_300_200_20_15_2_2.5
3Cr12_300_200_20_15_3_2.5
3Cr12_100_70_20_10_1_2.5
3Cr12_250_95_20_10_2_2.5
3Cr12_250_95_20_10_3_2.5
3Cr12_100_60_10_10_1_2.5
3Cr12_200_150_15_15_2_2.5
3Cr12_90_60_10_5_1_2.5
3Cr12_150_70_15_10_4_2.5
3Cr12_150_70_15_10_5_2.5
3Cr12_200_160_35_20_6_2.5
3Cr12_200_160_35_20_7_2.5
MPa
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
f y,c
Geometry
Ag
Ac
Effective Areas
A c /A g
P u,t
A e,f
%
14
21
25
10
15
18
10
15
20
7
9
12
11
9
11
14
10
12
24
10
20
19
10
16
13
16
25
15
14
17
42
42
40
47
kN
163
300
454
161
298
478
179
325
497
339
541
776
1110
674
953
1255
49
45
130
45
129
139
179
323
50
138
256
43
168
38
358
485
949
1184
mm2 mm2
659
81
1078 172
1516 284
656
67
1225 148
1917 235
781
88
1392 185
2120 325
1473 147
2326 258
3342 401
4612 462
2609 296
3707 450
4964 644
182
24
213
24
500
94
211
22
551
81
510
94
668
83
1236 183
207
24
605
74
1081 160
168
24
610
94
150
21
901 214
918 668
2450 848
2760 1155
MPa mm2 mm2
406 1157 157
406 1711 353
406 2262 565
406 1557 157
406 2311 353
406 3062 565
406 1607 157
406 2386 353
406 3148 628
406 5078 353
406 6739 628
406 8382 982
406 10069 1131
406 6888 628
406 8569 982
406 10234 1414
406
387
39
406
337
39
406
657
157
406
407
39
406
797
157
406
817
157
406 1522 157
406 2258 353
406
297
39
406
977
157
406 1441 353
406
257
39
406 1102 157
406
234
39
406 1268 534
406 1586 668
406 3545 1414
406 4078 1924
A e,c
r/t=2.5
All Tests
Department of Civil Engineering
Research Report No R845
172
A e,t
mm2
740
1250
1800
722
1373
2152
869
1577
2445
1619
2583
3742
5073
2905
4158
5608
206
237
595
233
632
604
750
1419
231
678
1240
192
704
171
1115
1586
3298
3914
Without EC
Prop
Pn
P u,t /P n
kN
192
0.85
325
0.92
468
0.97
188
0.86
357
0.84
559
0.85
226
0.79
410
0.79
636
0.78
421
0.80
672
0.80
973
0.80
1319
0.84
755
0.89
1081
0.88
1458
0.86
54
0.92
61
0.74
155
0.84
61
0.75
164
0.78
157
0.88
195
0.92
369
0.88
60
0.84
176
0.78
323
0.80
50
0.87
183
0.92
44
0.84
290
1.24
412
1.18
858
1.11
1018
1.16
mean 0.88
stdv 0.1205
cov 0.1367
mean 0.87
stdv 0.1027
cov 0.1179
With EC Prop
Pn
kN
204
350
509
197
379
594
239
437
683
442
709
1031
1387
798
1147
1552
57
65
168
64
176
171
207
396
63
187
346
53
197
48
321
510
981
1186
P u,t /P n
0.80
0.86
0.89
0.81
0.79
0.80
0.75
0.74
0.73
0.77
0.76
0.75
0.80
0.84
0.83
0.81
0.86
0.70
0.77
0.71
0.73
0.81
0.86
0.82
0.79
0.74
0.74
0.81
0.86
0.79
1.12
0.95
0.97
1.00
0.82
0.0879
0.1076
0.84
0.0819
0.0980
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
EC3 Part 1-4/1-3 (2004) Alternative Method
Material
Properties
f y,f
Test ID
3Cr12DS1a
3Cr12DS2b
f y,c
MPa MPa
339 606
339 606
Geometry
Without EC
Prop
Effective Areas
Ag
Ac
A c /A g
P u,t
A e,f
A e,c
A e,t
mm2
565
565
mm2
124
124
%
22
22
kN
163
161
mm2
401
402
mm2
113
113
mm2
514
516
experimental
Pn
With EC Prop
P u,t /P n
Pn
kN
174
0.93
175
0.92
mean 0.93
stdv 0.0097
cov 0.0104
kN
205
205
P u,t /P n
0.80
0.79
0.79
0.0081
0.0102
EC3 Part 1-4/1-3 (2004) Alternative Method
Material
Properties
f y,f
Test ID
3Cr12_200_160_25_10_2
3Cr12_200_160_25_10_3
3Cr12_200_160_25_10_4
3Cr12_400_160_25_10_2
3Cr12_400_160_25_10_3
3Cr12_400_160_25_10_4
3Cr12_400_160_25_20_2
3Cr12_400_160_25_20_3
3Cr12_400_160_25_20_4
3Cr12_800_400_40_15_3
3Cr12_800_400_40_15_4
3Cr12_800_400_40_15_5
3Cr12_800_400_40_15_6
3Cr12_800_400_40_30_4
3Cr12_800_400_40_30_5
3Cr12_800_400_40_30_6
3Cr12_150_100_10_10_1
3Cr12_150_70_15_10_1
3Cr12_150_70_15_10_2
3Cr12_200_80_15_10_1
3Cr12_200_80_15_10_2
3Cr12_150_110_15_10_2
3Cr12_300_200_20_15_2
3Cr12_300_200_20_15_3
3Cr12_100_70_20_10_1
3Cr12_250_95_20_10_2
3Cr12_250_95_20_10_3
3Cr12_100_60_10_10_1
3Cr12_200_150_15_15_2
3Cr12_90_60_10_5_1
3Cr12_150_70_15_10_4
3Cr12_150_70_15_10_5
3Cr12_200_160_35_20_6
3Cr12_200_160_35_20_7
MPa
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
f y,c
Geometry
Ag
MPa mm2
260 1177
260 1755
260 2327
260 1577
260 2355
260 3127
260 1626
260 2430
260 3227
260 5123
260 6769
260 8505
260 10186
260 6966
260 8691
260 10410
260
392
260
341
260
681
260
412
260
817
260
837
260 1542
260 2303
260
302
260
997
260 1485
260
262
260 1122
260
239
260 1327
260 1643
260 3721
260 4318
Ac
A c /A g
P u,t
A e,f
%
5
8
11
4
6
8
4
6
8
3
4
5
6
4
5
5
4
5
9
4
8
8
4
6
5
6
10
6
6
7
19
24
15
18
kN
160
287
428
159
290
449
175
316
481
334
551
789
1008
658
929
1224
48
44
120
44
122
133
175
312
49
134
247
41
162
36
312
419
848
1032
mm
740
1338
1870
643
1138
1750
729
1311
2077
1358
2308
3467
4878
2652
4103
5301
197
190
553
183
525
629
697
1421
223
529
1023
196
743
161
1078
1253
3136
3555
2
mm
63
141
251
63
141
251
63
141
251
141
251
393
565
251
393
565
16
16
63
16
63
63
63
141
16
63
141
16
63
16
251
393
565
770
2
A e,c
2
mm
45
115
224
37
90
174
39
98
195
75
139
227
340
146
239
358
10
11
56
10
49
49
39
98
13
43
116
13
46
12
251
393
561
770
flats
Department of Civil Engineering
Research Report No R845
173
Without EC
Prop
Effective Areas
A e,t
2
mm
785
1453
2093
679
1228
1924
768
1409
2271
1433
2447
3694
5218
2798
4342
5658
208
201
609
192
573
679
737
1520
237
572
1138
209
789
172
1329
1643
3697
4324
Pn
P u,t /P n
kN
204
0.79
378
0.76
544
0.79
177
0.90
319
0.91
500
0.90
200
0.87
366
0.86
591
0.82
373
0.90
636
0.87
960
0.82
1357
0.74
728
0.90
1129
0.82
1471
0.83
54
0.89
52
0.84
158
0.76
50
0.88
149
0.82
176
0.76
191
0.92
395
0.79
62
0.79
149
0.90
296
0.83
54
0.76
205
0.79
45
0.81
346
0.90
428
0.98
961
0.88
1124
0.92
mean 0.84
stdv 0.0596
cov 0.0706
With EC Prop
Pn
kN
204
378
544
177
319
500
200
366
591
373
636
960
1357
728
1129
1471
54
52
158
50
149
176
191
395
62
149
296
54
205
45
346
428
961
1124
P u,t /P n
0.79
0.76
0.79
0.90
0.91
0.90
0.87
0.86
0.82
0.90
0.87
0.82
0.74
0.90
0.82
0.83
0.89
0.84
0.76
0.88
0.82
0.76
0.92
0.79
0.79
0.90
0.83
0.76
0.79
0.81
0.90
0.98
0.88
0.92
0.84
0.0596
0.0706
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
EC3 Part 1-4/1-3 (2004) Alternative Method
Material
Properties
f y,f
Test ID
3Cr12_200_160_25_10_2_1
3Cr12_200_160_25_10_3_1
3Cr12_200_160_25_10_4_1
3Cr12_400_160_25_10_2_1
3Cr12_400_160_25_10_3_1
3Cr12_400_160_25_10_4_1
3Cr12_400_160_25_20_2_1
3Cr12_400_160_25_20_3_1
3Cr12_400_160_25_20_4_1
3Cr12_800_400_40_15_3_1
3Cr12_800_400_40_15_4_1
3Cr12_800_400_40_15_5_1
3Cr12_800_400_40_15_6_1
3Cr12_800_400_40_30_4_1
3Cr12_800_400_40_30_5_1
3Cr12_800_400_40_30_6_1
3Cr12_150_100_10_10_1_1
3Cr12_150_70_15_10_1_1
3Cr12_150_70_15_10_2_1
3Cr12_200_80_15_10_1_1
3Cr12_200_80_15_10_2_1
3Cr12_150_110_15_10_2_1
3Cr12_300_200_20_15_2_1
3Cr12_300_200_20_15_3_1
3Cr12_100_70_20_10_1_1
3Cr12_250_95_20_10_2_1
3Cr12_250_95_20_10_3_1
3Cr12_100_60_10_10_1_1
3Cr12_200_150_15_15_2_1
3Cr12_90_60_10_5_1_1
3Cr12_150_70_15_10_4_1
3Cr12_150_70_15_10_5_1
3Cr12_200_160_35_20_6_1
3Cr12_200_160_35_20_7_1
MPa
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
f y,c
Geometry
Ag
MPa mm2
460 1177
460 1755
460 2327
460 1577
460 2355
460 3127
460 1626
460 2430
460 3227
460 5123
460 6769
460 8505
460 10186
460 6966
460 8691
460 10410
460
392
460
341
460
681
460
412
460
817
460
837
460 1542
460 2303
460
302
460
997
460 1485
460
262
460 1122
460
239
460 1327
460 1643
460 3721
460 4318
Ac
A c /A g
P u,t
A e,f
%
5
8
11
4
6
8
4
6
8
3
4
5
6
4
5
5
4
5
9
4
8
8
4
6
5
6
10
6
6
7
19
24
15
18
kN
163
296
448
161
296
462
178
324
495
340
562
806
1106
670
952
1257
49
44
125
45
126
137
178
321
50
137
255
42
167
37
347
479
918
1136
mm
740
1338
1870
643
1138
1750
729
1311
2077
1358
2308
3467
4878
2652
4103
5301
197
190
553
183
525
629
697
1421
223
529
1023
196
743
161
1078
1253
3136
3555
2
mm
63
141
251
63
141
251
63
141
251
141
251
393
565
251
393
565
16
16
63
16
63
63
63
141
16
63
141
16
63
16
251
393
565
770
2
A e,c
2
mm
45
115
224
37
90
174
39
98
195
75
139
227
340
146
239
358
10
11
56
10
49
49
39
98
13
43
116
13
46
12
251
393
561
770
r/t=1
Department of Civil Engineering
Research Report No R845
174
Without EC
Prop
Effective Areas
A e,t
2
mm
785
1453
2093
679
1228
1924
768
1409
2271
1433
2447
3694
5218
2798
4342
5658
208
201
609
192
573
679
737
1520
237
572
1138
209
789
172
1329
1643
3697
4324
Pn
P u,t /P n
kN
204
0.80
378
0.78
544
0.82
177
0.91
319
0.93
500
0.92
200
0.89
366
0.88
591
0.84
373
0.91
636
0.88
960
0.84
1357
0.81
728
0.92
1129
0.84
1471
0.85
54
0.90
52
0.85
158
0.79
50
0.90
149
0.85
176
0.78
191
0.93
395
0.81
62
0.81
149
0.92
296
0.86
54
0.78
205
0.81
45
0.82
346
1.00
428
1.12
961
0.96
1124
1.01
mean 0.88
stdv 0.0748
cov 0.0855
With EC Prop
Pn
kN
213
401
589
184
337
535
208
386
629
387
664
1006
1425
757
1177
1543
56
54
169
52
159
186
199
415
64
157
319
57
214
47
396
506
1074
1278
P u,t /P n
0.76
0.74
0.76
0.88
0.88
0.86
0.86
0.84
0.79
0.88
0.85
0.80
0.78
0.89
0.81
0.81
0.87
0.82
0.74
0.86
0.79
0.74
0.89
0.77
0.77
0.87
0.80
0.75
0.78
0.78
0.88
0.95
0.86
0.89
0.82
0.0551
0.0670
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
April 2005
EC3 Part 1-4/1-3 (2004) Alternative Method
Material
Properties
f y,f
Test ID
3Cr12_200_160_25_10_2_2.5
3Cr12_200_160_25_10_3_2.5
3Cr12_200_160_25_10_4_2.5
3Cr12_400_160_25_10_2_2.5
3Cr12_400_160_25_10_3_2.5
3Cr12_400_160_25_10_4_2.5
3Cr12_400_160_25_20_2_2.5
3Cr12_400_160_25_20_3_2.5
3Cr12_400_160_25_20_4_2.5
3Cr12_800_400_40_15_3_2.5
3Cr12_800_400_40_15_4_2.5
3Cr12_800_400_40_15_5_2.5
3Cr12_800_400_40_15_6_2.5
3Cr12_800_400_40_30_4_2.5
3Cr12_800_400_40_30_5_2.5
3Cr12_800_400_40_30_6_2.5
3Cr12_150_100_10_10_1_2.5
3Cr12_150_70_15_10_1_2.5
3Cr12_150_70_15_10_2_2.5
3Cr12_200_80_15_10_1_2.5
3Cr12_200_80_15_10_2_2.5
3Cr12_150_110_15_10_2_2.5
3Cr12_300_200_20_15_2_2.5
3Cr12_300_200_20_15_3_2.5
3Cr12_100_70_20_10_1_2.5
3Cr12_250_95_20_10_2_2.5
3Cr12_250_95_20_10_3_2.5
3Cr12_100_60_10_10_1_2.5
3Cr12_200_150_15_15_2_2.5
3Cr12_90_60_10_5_1_2.5
3Cr12_150_70_15_10_4_2.5
3Cr12_150_70_15_10_5_2.5
3Cr12_200_160_35_20_6_2.5
3Cr12_200_160_35_20_7_2.5
MPa
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
260
f y,c
Ag
Ac
A c /A g
P u,t
A e,f
%
14
21
25
10
15
18
10
15
20
7
9
12
11
9
11
14
10
12
24
10
20
19
10
16
13
16
25
15
14
17
42
42
40
47
kN
163
300
454
161
298
478
179
325
497
339
541
776
1110
674
953
1255
49
45
130
45
129
139
179
323
50
138
256
43
168
38
358
485
949
1184
mm mm mm
664 112 776
1137 290 1426
1541 506 2047
573
91
664
970 223 1193
1472 385 1856
659
98
758
1140 244 1384
1732 485 2217
1232 186 1419
2074 347 2421
3378 566 3944
4484 682 5166
2415 366 2781
3685 597 4282
4673 895 5568
181
26
207
171
28
199
456 140 596
166
25
190
442 122 565
547 126 672
635
98
733
1249 246 1496
201
34
235
454 109 563
818 289 1107
174
33
207
666 115 781
142
30
172
739 534 1273
924 668 1591
2134 1408 3542
2170 1924 4094
MPa mm2 mm2
406 1157 157
406 1711 353
406 2262 565
406 1557 157
406 2311 353
406 3062 565
406 1607 157
406 2386 353
406 3148 628
406 5078 353
406 6739 628
406 8382 982
406 10069 1131
406 6888 628
406 8569 982
406 10234 1414
406
387
39
406
337
39
406
657
157
406
407
39
406
797
157
406
817
157
406 1522 157
406 2258 353
406
297
39
406
977
157
406 1441 353
406
257
39
406 1102 157
406
234
39
406 1268 534
406 1586 668
406 3545 1414
406 4078 1924
2
A e,c
2
r/t=2.5
All Tests
Department of Civil Engineering
Research Report No R845
Without EC
Prop
Effective Areas
Geometry
175
A e,t
2
Pn
P u,t /P n
kN
202
0.81
371
0.81
532
0.85
173
0.93
310
0.96
483
0.99
197
0.91
360
0.90
577
0.86
369
0.92
629
0.86
1026
0.76
1343
0.83
723
0.93
1113
0.86
1448
0.87
54
0.91
52
0.88
155
0.84
50
0.91
147
0.88
175
0.79
190
0.94
389
0.83
61
0.82
146
0.94
288
0.89
54
0.80
203
0.83
45
0.84
331
1.08
414
1.17
921
1.03
1064
1.11
mean 0.90
stdv 0.0927
cov 0.1031
mean 0.87
stdv 0.0790
cov 0.0904
With EC Prop
Pn
kN
218
413
606
186
343
539
211
396
647
396
680
1108
1443
776
1200
1578
58
56
175
53
165
193
205
425
66
162
330
59
220
49
409
511
1126
1345
P u,t /P n
0.75
0.73
0.75
0.86
0.87
0.89
0.84
0.82
0.77
0.86
0.79
0.70
0.77
0.87
0.79
0.80
0.85
0.81
0.74
0.85
0.78
0.72
0.87
0.76
0.76
0.85
0.78
0.74
0.77
0.76
0.88
0.95
0.84
0.88
0.81
0.0598
0.0740
0.82
0.0591
0.0718
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
fy
Test ID
304D1a
304D1b
304D2a
304D2b
Geometric
Properties
A g A c A c /A g f cr
2
2
MPa mm mm
242 565 61
242 565 61
242 565 61
242 565 61
%
11
11
11
11
MPa
264
264
283
283
Test Results
AS 4600 (1996)
λd
P u,t
0.96
0.96
0.92
0.92
kN MPa
102 181 0.75
101 179 0.74
104 184 0.76
104 184 0.76
fu
April 2005
f u /f y f n,4600 /f y f u /f n,4600
0.77
0.77
0.79
0.79
mean
COV
fy
Test ID
304_60_60_10_2
304_60_60_10_3
304_60_60_15_2
304_60_60_15_3
304_150_150_30_3
304_150_150_20_3
304_150_150_10_3
304_200_100_15_4
304_200_150_20_3
304_200_150_20_4
304_150_80_5_1
304_50_50_5_1
304_400_400_20_3
304_400_400_20_4
304_400_400_20_5
304_400_400_40_4
304_400_400_40_5
304_400_400_40_6
304_400_400_40_7
304_400_400_40_8
304_300_400_20_3
304_300_400_20_4
304_300_400_20_5
304_400_300_20_3
304_400_300_20_4
304_400_300_20_5
304_400_300_40_5
304_400_300_40_6
304_400_300_40_7
304_400_300_40_8
2
2
MPa mm mm
195 393 25
195 584 57
195 413 25
195 614 57
195 1514 57
195 1454 57
195 1394 57
195 1692 101
195 1604 57
195 2132 101
6
195 318
6
195 158
195 3704 57
195 4932 101
195 6156 157
195 5092 101
195 6356 157
195 7617 226
195 8874 308
195 10130 402
195 3404 57
195 4532 101
195 5656 157
195 3104 57
195 4132 101
195 5156 157
195 5356 157
195 6417 226
195 7474 308
195 8528 402
%
6.4
9.7
6.1
9.2
3.7
3.9
4.1
5.9
3.5
4.7
2.0
4.0
1.5
2.0
2.6
2.0
2.5
3.0
3.5
4.0
1.7
2.2
2.8
1.8
2.4
3.0
2.9
3.5
4.1
4.7
MPa
402
660
532
844
252
180
102
320
165
233
36
140
22
32
43
62
81
99
120
140
24
34
46
37
53
72
129
160
192
227
Test Results
λd
P u,t
fu
0.70
0.54
0.61
0.48
0.88
1.04
1.38
0.78
1.09
0.91
2.33
1.18
2.98
2.48
2.14
1.77
1.55
1.40
1.27
1.18
2.85
2.38
2.05
2.30
1.92
1.64
1.23
1.10
1.01
0.93
kN
65
112
74
124
213
183
153
257
191
300
20
18
176
292
443
347
516
727
947
1180
171
293
447
177
294
457
551
766
984
1199
MPa
164
192
178
202
140
126
110
152
119
141
63
117
48
59
72
68
81
95
107
116
50
65
79
57
71
89
103
119
132
141
flats
176
0.005
AS 4600 (1996)
f u /f y f n,4600 /f y f u /f n,4600
0.84
0.98
0.91
1.03
0.72
0.64
0.56
0.78
0.61
0.72
0.33
0.60
0.24
0.30
0.37
0.35
0.42
0.49
0.55
0.60
0.26
0.33
0.40
0.29
0.37
0.45
0.53
0.61
0.68
0.72
0.88
0.93
0.91
na
0.81
0.73
0.52
0.85
0.70
0.79
0.33
0.65
0.26
0.31
0.35
0.42
0.47
0.51
0.59
0.65
0.27
0.32
0.37
0.33
0.39
0.45
0.62
0.69
0.75
0.79
0.96
1.06
1.01
na
0.89
0.88
1.08
0.92
0.87
0.91
1.00
0.92
0.95
0.99
1.04
0.83
0.89
0.96
0.92
0.91
0.96
1.04
1.10
0.88
0.93
1.02
0.85
0.88
0.90
0.92
mean
0.95
0.96
0.95
0.95
0.95
0.96
0.67
0.67
0.69
0.69
1.11
1.10
1.10
1.10
1.10
0.0040
0.0052
0.004
0.005
NAS Appendix 1
PROPOSED
(2004)
f n,NAS /f y f u /f n,NAS f n,prop. /f y f u /f n,prop.
0.95
1.00
0.99
na
0.83
0.73
0.56
0.89
0.70
0.80
0.33
0.65
0.25
0.31
0.36
0.44
0.50
0.56
0.61
0.65
0.26
0.32
0.38
0.33
0.41
0.47
0.63
0.69
0.75
0.80
0.89
0.98
0.92
na
0.87
0.89
1.00
0.87
0.87
0.90
0.99
0.92
0.97
0.98
1.02
0.79
0.83
0.88
0.90
0.92
0.97
1.03
1.07
0.87
0.90
0.96
0.84
0.89
0.91
0.91
0.86
0.99
0.94
na
0.72
0.63
0.49
0.79
0.60
0.70
0.29
0.56
0.23
0.27
0.32
0.38
0.44
0.48
0.52
0.56
0.24
0.29
0.33
0.30
0.36
0.41
0.54
0.60
0.65
0.69
0.98
0.99
0.97
na
1.00
1.03
1.16
0.98
1.01
1.03
1.11
1.06
1.08
1.11
1.16
0.91
0.96
1.02
1.04
1.06
1.08
1.16
1.22
0.99
1.03
1.10
0.97
1.03
1.05
1.04
0.92
1.05
st dev 0.0710
0.0649
0.0708
0.075
0.070
0.068
COV
Department of Civil Engineering
Research Report No R845
0.78
0.78
0.80
0.80
st dev 0.0046
experimental tests
Geometric
Properties
A g A c A c /A g f cr
0.97
0.96
0.97
0.97
0.97
NAS Appendix 1
PROPOSED
(2004)
f n,NAS /f y f u /f n,NAS f n,prop. /f y f u /f n,prop.
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
fy
Geometric
Properties
A g A c A c /A g f cr
2
2
Test ID
MPa mm mm
304_60_60_10_2_1
195 393 25
304_60_60_10_3_1
195 584 57
304_60_60_15_2_1
195 413 25
304_60_60_15_3_1
195 614 57
304_150_150_30_3_1 195 1514 57
304_150_150_20_3_1 195 1454 57
304_150_150_10_3_1 195 1394 57
304_200_100_15_4_1 195 1692 101
304_200_150_20_3_1 195 1604 57
304_200_150_20_4_1 195 2132 101
6
304_150_80_5_1_1
195 318
6
304_50_50_5_1_1
195 158
304_400_400_20_3_1 195 3704 57
304_400_400_20_4_1 195 4932 101
304_400_400_20_5_1 195 6156 157
304_400_400_40_4_1 195 5092 101
304_400_400_40_5_1 195 6356 157
304_400_400_40_6_1 195 7617 226
304_400_400_40_7_1 195 8874 308
304_400_400_40_8_1 195 10130 402
304_300_400_20_3_1 195 3404 57
304_300_400_20_4_1 195 4532 101
304_300_400_20_5_1 195 5656 157
304_400_300_20_3_1 195 3104 57
304_400_300_20_4_1 195 4132 101
304_400_300_20_5_1 195 5156 157
304_400_300_40_5_1 195 5356 157
304_400_300_40_6_1 195 6417 226
304_400_300_40_7_1 195 7474 308
304_400_300_40_8_1 195 8528 402
%
6.4
9.7
6.1
9.2
3.7
3.9
4.1
5.9
3.5
4.7
2.0
4.0
1.5
2.0
2.6
2.0
2.5
3.0
3.5
4.0
1.7
2.2
2.8
1.8
2.4
3.0
2.9
3.5
4.1
4.7
MPa
402
660
532
844
252
180
102
320
165
233
36
140
22
32
43
62
81
99
120
140
24
34
46
37
53
72
129
160
192
227
Test Results
λd
P u,t
fu
0.70
0.54
0.61
0.48
0.88
1.04
1.38
0.78
1.09
0.91
2.33
1.18
2.98
2.48
2.14
1.77
1.55
1.40
1.27
1.18
2.85
2.38
2.05
2.30
1.92
1.64
1.23
1.10
1.01
0.93
kN
67
120
77
135
217
187
160
266
195
308
21
19
175
296
454
347
525
746
977
1219
175
301
457
176
302
467
558
780
1007
1232
MPa
171
205
187
219
143
129
115
157
121
145
65
120
47
60
74
68
83
98
110
120
51
66
81
57
73
91
104
122
135
144
r/t=1
April 2005
AS 4600 (1996)
f u /f y f n,4600 /f y f u /f n,4600
0.88
1.05
0.96
1.12
0.74
0.66
0.59
0.81
0.62
0.74
0.33
0.62
0.24
0.31
0.38
0.35
0.42
0.50
0.56
0.62
0.26
0.34
0.41
0.29
0.37
0.46
0.53
0.62
0.69
0.74
0.88
na
0.91
na
0.81
0.73
0.52
0.85
0.70
0.79
0.33
0.65
0.26
0.31
0.35
0.42
0.47
0.51
0.59
0.65
0.27
0.32
0.37
0.33
0.39
0.45
0.62
0.69
0.75
0.79
1.00
na
1.05
na
0.91
0.90
1.13
0.95
0.88
0.94
1.02
0.95
0.94
1.01
1.07
0.83
0.91
0.99
0.95
0.94
0.98
1.07
1.12
0.88
0.95
1.04
0.86
0.90
0.93
0.94
mean
0.97
177
0.95
na
0.99
na
0.83
0.73
0.56
0.89
0.70
0.80
0.33
0.65
0.25
0.31
0.36
0.44
0.50
0.56
0.61
0.65
0.26
0.32
0.38
0.33
0.41
0.47
0.63
0.69
0.75
0.80
0.93
na
0.96
na
0.89
0.91
1.04
0.90
0.89
0.92
1.01
0.95
0.97
1.00
1.05
0.79
0.84
0.90
0.93
0.95
1.00
1.06
1.10
0.87
0.92
0.98
0.85
0.90
0.93
0.93
0.86
na
0.94
na
0.72
0.63
0.49
0.79
0.60
0.70
0.29
0.56
0.23
0.27
0.32
0.38
0.44
0.48
0.52
0.56
0.24
0.29
0.33
0.30
0.36
0.41
0.54
0.60
0.65
0.69
1.02
na
1.02
na
1.02
1.05
1.21
1.02
1.03
1.06
1.14
1.10
1.07
1.12
1.19
0.91
0.97
1.05
1.08
1.10
1.11
1.19
1.25
0.98
1.05
1.13
0.98
1.04
1.07
1.07
0.94
1.07
st dev 0.0758
0.0693
0.0760
0.078
0.074
0.071
COV
Department of Civil Engineering
Research Report No R845
NAS Appendix 1
PROPOSED
(2004)
f n,NAS /f y f u /f n,NAS f n,prop. /f y f u /f n,prop.
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
fy
Test ID
304_60_60_10_2_2.5
304_60_60_10_3_2.5
304_60_60_15_2_2.5
304_60_60_15_3_2.5
304_150_150_30_3_2.5
304_150_150_20_3_2.5
304_150_150_10_3_2.5
304_200_100_15_4_2.5
304_200_150_20_3_2.5
304_200_150_20_4_2.5
304_150_80_5_1_2.5
304_50_50_5_1_2.5
304_400_400_20_3_2.5
304_400_400_20_4_2.5
304_400_400_20_5_2.5
304_400_400_40_4_2.5
304_400_400_40_5_2.5
304_400_400_40_6_2.5
304_400_400_40_7_2.5
304_400_400_40_8_2.5
304_300_400_20_3_2.5
304_300_400_20_4_2.5
304_300_400_20_5_2.5
304_400_300_20_3_2.5
304_400_300_20_4_2.5
304_400_300_20_5_2.5
304_400_300_40_5_2.5
304_400_300_40_6_2.5
304_400_300_40_7_2.5
304_400_300_40_8_2.5
MPa
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
Geometric
Properties
A g A c A c /A g f cr
2
mm
AS 4600 (1996)
Test Results
λd
P u,t
2
mm
fu
% MPa
kN
382 63 16.4 411 0.69 68
561 141 25.2 689 0.53 123
402 63 15.6 542 0.60 78
591 141 23.9 868 0.47 139
1491 141 9.5 257 0.87 218
1431 141 9.9 184 1.03 188
1371 141 10.3 105 1.36 164
1650 251 15.2 328 0.77 268
1581 141 8.9 168 1.08 196
2090 251 12.0 239 0.90 315
316 16 5.0
38 2.28 21
156 16 10.1 142 1.17 19
3681 141 3.8
22 2.96 179
4890 251 5.1
32 2.46 305
6090 393 6.4
43 2.12 458
5050 251 5.0
63 1.76 346
6290 393 6.2
82 1.54 531
7522 565 7.5 106 1.36 755
8745 770 8.8 122 1.26 990
9959 1005 10.1 144 1.16 1234
3381 141 4.2
24 2.82 177
4490 251 5.6
35 2.36 305
5590 393 7.0
48 2.03 464
3081 141 4.6
37 2.28 183
4090 251 6.1
54 1.90 307
5090 393 7.7
74 1.63 477
5290 393 7.4 131 1.22 561
6322 565 8.9 163 1.09 784
7345 770 10.5 197 1.00 1014
8359 1005 12.0 233 0.92 1245
April 2005
f u /f y f n,4600 /f y f u /f n,4600
MPa
177
219
194
236
146
131
120
163
124
151
65
124
49
62
75
68
84
100
113
124
52
68
83
59
75
94
106
124
138
149
0.91
1.13
1.00
1.21
0.75
0.67
0.61
0.83
0.64
0.77
0.33
0.63
0.25
0.32
0.39
0.35
0.43
0.51
0.58
0.64
0.27
0.35
0.43
0.30
0.38
0.48
0.54
0.64
0.71
0.76
r/t=2.5
all tests
0.88
na
0.91
na
0.81
0.74
0.54
0.85
0.71
0.80
0.33
0.66
0.26
0.31
0.36
0.42
0.47
0.54
0.60
0.66
0.27
0.32
0.37
0.33
0.40
0.45
0.63
0.70
0.75
0.79
1.03
na
1.09
na
0.92
0.92
1.14
0.98
0.90
0.97
1.00
0.97
0.96
1.04
1.08
0.83
0.92
0.95
0.96
0.96
0.99
1.08
1.14
0.92
0.97
1.06
0.86
0.91
0.94
0.97
mean
0.98
fy
Test ID
430D1a
430D1b
430D2
430D3a
430D3b
Ag
2
MPa mm
271 211
271 211
271 215
271 188
271 188
Ac
mm2
21
22
22
22
22
Test Results
A c /A g f cr
%
10
10
10
12
12
MPa
224
224
245
254
254
λ d P u,t
1.10
1.10
1.05
1.03
1.03
fu
experimental tests
Department of Civil Engineering
Research Report No R845
178
0.96
na
1.00
na
0.90
0.92
1.07
0.93
0.90
0.95
0.99
0.97
0.98
1.03
1.06
0.79
0.85
0.90
0.95
0.96
1.01
1.07
1.11
0.90
0.94
1.00
0.86
0.91
0.94
0.95
0.87
na
0.94
na
0.73
0.63
0.49
0.80
0.61
0.71
0.30
0.57
0.23
0.28
0.32
0.39
0.44
0.50
0.53
0.57
0.24
0.29
0.34
0.30
0.36
0.42
0.55
0.60
0.65
0.70
1.05
na
1.06
na
1.03
1.06
1.24
1.04
1.04
1.09
1.12
1.12
1.09
1.16
1.20
0.91
0.99
1.04
1.10
1.12
1.12
1.21
1.27
1.02
1.07
1.15
0.99
1.06
1.08
1.09
1.09
st dev 0.0783
0.0717
0.0779
COV
0.080
0.075
0.071
mean
0.96
0.94
1.07
st dev 0.0737
0.0679
0.0748
0.076
0.072
0.070
AS 4600 (1996)
f u /f y f n,4600 /f y f u /f n,4600
kN MPa
39 182 0.67
39 185 0.68
45 209 0.77
40 211 0.78
39 206 0.76
0.95
na
0.99
na
0.83
0.73
0.57
0.90
0.71
0.81
0.34
0.66
0.25
0.31
0.36
0.44
0.51
0.57
0.61
0.66
0.27
0.33
0.38
0.34
0.41
0.48
0.63
0.70
0.75
0.80
0.96
COV
Geometric Properties
NAS Appendix 1
PROPOSED
(2004)
f n,NAS /f y f u /f n,NAS f n,prop. /f y f u /f n,prop.
NAS Appendix 1
PROPOSED
(2004)
f n,NAS /f y f u /f n,NAS f n,prop. /f y f u /f n,prop.
0.69
0.69
0.72
0.73
0.73
0.97
0.98
1.07
1.06
1.04
1.03
0.65
0.65
0.67
0.68
0.68
1.04
1.05
1.15
1.14
1.11
1.10
0.70
0.70
0.72
0.73
0.73
mean
0.97
0.98
1.07
1.06
1.04
1.02
st dev
0.0469
0.0460
0.0501
COV
0.046
0.045
0.046
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
Geometric Properties
fy
Test ID
430_60_60_10_2
430_60_60_10_3
430_60_60_15_2
430_60_60_15_3
430_150_150_30_3
430_150_150_20_3
430_150_150_10_3
430_200_100_15_4
430_200_150_20_3
430_200_150_20_4
430_150_80_5_1
430_50_50_5_1
430_400_400_20_3
430_400_400_20_4
430_400_400_20_5
430_400_400_40_4
430_400_400_40_5
430_400_400_40_6
430_400_400_40_7
430_400_400_40_8
430_300_400_20_3
430_300_400_20_4
430_300_400_20_5
430_400_300_20_3
430_400_300_20_4
430_400_300_20_5
430_400_300_40_5
430_400_300_40_6
430_400_300_40_7
430_400_300_40_8
MPa
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
Ag
Ac
2
mm
393
584
413
614
1514
1454
1394
1692
1604
2132
318
158
3704
4932
6156
5092
6356
7617
8874
10130
3404
4532
5656
3104
4132
5156
5356
6417
7474
8528
Test Results
A c /A g f cr
2
mm
25
57
25
57
57
57
57
101
57
101
6
6
57
101
157
101
157
226
308
402
57
101
157
57
101
157
157
226
308
402
%
6.4
9.7
6.1
9.2
3.7
3.9
4.1
5.9
3.5
4.7
2.0
4.0
1.5
2.0
2.6
2.0
2.5
3.0
3.5
4.0
1.7
2.2
2.8
1.8
2.4
3.0
2.9
3.5
4.1
4.7
MPa
381
627
505
801
239
171
97
304
156
221
34
133
21
30
40
59
77
94
114
133
23
33
44
35
50
68
123
152
182
216
λd
P u,t
fu
0.85
0.66
0.74
0.59
1.07
1.27
1.69
0.95
1.33
1.11
2.84
1.44
3.64
3.02
2.61
2.16
1.89
1.71
1.55
1.44
3.47
2.90
2.50
2.80
2.33
2.00
1.50
1.35
1.23
1.13
kN
85
146
96
163
280
240
200
338
244
390
26
24
231
356
579
424
647
950
1226
1531
225
383
579
231
397
594
699
980
1283
1563
MPa
216
250
232
266
185
165
143
200
152
183
83
151
62
72
94
83
102
125
138
151
66
85
102
74
96
115
130
153
172
183
flats
Department of Civil Engineering
Research Report No R845
179
April 2005
AS 4600 (1996)
f u /f y f n,4600 /f y f u /f n,4600
0.79
0.91
0.84
0.97
0.67
0.60
0.52
0.73
0.55
0.67
0.30
0.55
0.23
0.26
0.34
0.30
0.37
0.45
0.50
0.55
0.24
0.31
0.37
0.27
0.35
0.42
0.47
0.56
0.62
0.67
0.82
0.89
0.86
0.91
0.71
0.60
0.44
0.77
0.56
0.69
0.27
0.49
0.24
0.26
0.29
0.35
0.40
0.43
0.47
0.49
0.24
0.26
0.30
0.27
0.33
0.38
0.48
0.55
0.62
0.68
0.96
1.02
0.98
1.06
0.94
1.00
1.19
0.94
0.99
0.97
1.12
1.12
0.96
1.03
1.17
0.86
0.93
1.05
1.08
1.11
1.01
1.17
1.23
0.99
1.07
1.11
0.99
1.02
1.00
0.98
NAS Appendix 1
PROPOSED
(2004)
f n,NAS /f y f u /f n,NAS f n,prop. /f y f u /f n,prop.
0.85
0.97
0.92
1.00
0.71
0.61
0.46
0.78
0.59
0.69
0.27
0.54
0.20
0.25
0.29
0.36
0.41
0.46
0.50
0.54
0.21
0.26
0.31
0.27
0.33
0.39
0.52
0.58
0.63
0.68
0.93
0.94
0.91
0.97
0.95
0.98
1.13
0.93
0.95
0.97
1.13
1.02
1.13
1.06
1.17
0.85
0.90
0.99
1.00
1.01
1.13
1.19
1.22
1.01
1.06
1.08
0.91
0.96
0.99
0.98
0.79
0.92
0.87
0.97
0.66
0.57
0.44
0.73
0.55
0.64
0.27
0.51
0.21
0.25
0.29
0.35
0.40
0.44
0.48
0.51
0.22
0.26
0.30
0.27
0.32
0.38
0.50
0.54
0.59
0.63
1.00
0.99
0.97
0.99
1.02
1.05
1.18
1.00
1.00
1.04
1.13
1.07
1.10
1.05
1.18
0.87
0.93
1.04
1.05
1.07
1.11
1.18
1.23
1.01
1.08
1.11
0.96
1.02
1.06
1.05
mean
1.03
1.02
1.05
st dev
0.0861
0.0944
0.0797
COV
0.083
0.093
0.076
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
Geometric Properties
fy
Test ID
430_60_60_10_2_1
430_60_60_10_3_1
430_60_60_15_2_1
430_60_60_15_3_1
430_150_150_30_3_1
430_150_150_20_3_1
430_150_150_10_3_1
430_200_100_15_4_1
430_200_150_20_3_1
430_200_150_20_4_1
430_150_80_5_1_1
430_50_50_5_1_1
430_400_400_20_3_1
430_400_400_20_4_1
430_400_400_20_5_1
430_400_400_40_4_1
430_400_400_40_5_1
430_400_400_40_6_1
430_400_400_40_7_1
430_400_400_40_8_1
430_300_400_20_3_1
430_300_400_20_4_1
430_300_400_20_5_1
430_400_300_20_3_1
430_400_300_20_4_1
430_400_300_20_5_1
430_400_300_40_5_1
430_400_300_40_6_1
430_400_300_40_7_1
430_400_300_40_8_1
MPa
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
Ag
Ac
2
mm
393
584
413
614
1514
1454
1394
1692
1604
2132
318
158
3704
4932
6156
5092
6356
7617
8874
10130
3404
4532
5656
3104
4132
5156
5356
6417
7474
8528
Test Results
A c /A g f cr
2
mm
25
57
25
57
57
57
57
101
57
101
6
6
57
101
157
101
157
226
308
402
57
101
157
57
101
157
157
226
308
402
%
6.4
9.7
6.1
9.2
3.7
3.9
4.1
5.9
3.5
4.7
2.0
4.0
1.5
2.0
2.6
2.0
2.5
3.0
3.5
4.0
1.7
2.2
2.8
1.8
2.4
3.0
2.9
3.5
4.1
4.7
MPa
381
627
505
801
239
171
97
304
156
221
34
133
21
30
40
59
77
94
114
133
23
33
44
35
50
68
123
152
182
216
λd
P u,t
fu
0.85
0.66
0.74
0.59
1.07
1.27
1.69
0.95
1.33
1.11
2.84
1.44
3.64
3.02
2.61
2.16
1.89
1.71
1.55
1.44
3.47
2.90
2.50
2.80
2.33
2.00
1.50
1.35
1.23
1.13
kN
87
153
98
171
284
243
203
345
246
397
27
24
231
357
586
430
650
953
1234
1547
228
388
586
234
402
601
704
988
1300
1589
MPa
222
261
238
278
188
167
145
204
153
186
83
153
62
72
95
84
102
125
139
153
67
86
104
75
97
116
131
154
174
186
r/t=1.0
Department of Civil Engineering
Research Report No R845
180
April 2005
AS 4600 (1996)
f u /f y f n,4600 /f y f u /f n,4600
0.81
0.95
0.87
1.01
0.68
0.61
0.53
0.74
0.56
0.68
0.30
0.55
0.23
0.26
0.35
0.31
0.37
0.46
0.51
0.56
0.24
0.31
0.38
0.27
0.35
0.42
0.48
0.56
0.63
0.68
0.82
0.89
0.86
na
0.71
0.60
0.44
0.77
0.56
0.69
0.27
0.49
0.24
0.26
0.29
0.35
0.40
0.43
0.47
0.49
0.24
0.26
0.30
0.27
0.33
0.38
0.48
0.55
0.62
0.68
0.98
1.07
1.00
na
0.96
1.02
1.21
0.96
0.99
0.98
1.13
1.12
0.96
1.03
1.19
0.88
0.94
1.05
1.08
1.12
1.02
1.18
1.24
1.01
1.09
1.12
0.99
1.02
1.01
0.99
NAS Appendix 1
PROPOSED
(2004)
f n,NAS /f y f u /f n,NAS f n,prop. /f y f u /f n,prop.
0.85
0.97
0.92
na
0.71
0.61
0.46
0.78
0.59
0.69
0.27
0.54
0.20
0.25
0.29
0.36
0.41
0.46
0.50
0.54
0.21
0.26
0.31
0.27
0.33
0.39
0.52
0.58
0.63
0.68
0.95
0.98
0.94
na
0.96
1.00
1.14
0.95
0.95
0.99
1.14
1.02
1.13
1.06
1.19
0.86
0.91
1.00
1.01
1.02
1.15
1.20
1.23
1.02
1.08
1.09
0.92
0.97
1.01
1.00
0.79
0.92
0.87
na
0.66
0.57
0.44
0.73
0.55
0.64
0.27
0.51
0.21
0.25
0.29
0.35
0.40
0.44
0.48
0.51
0.22
0.26
0.30
0.27
0.32
0.38
0.50
0.54
0.59
0.63
1.02
1.03
1.00
na
1.03
1.06
1.19
1.02
1.01
1.05
1.14
1.08
1.10
1.06
1.20
0.88
0.94
1.04
1.06
1.08
1.13
1.20
1.25
1.02
1.10
1.13
0.97
1.03
1.07
1.07
mean
1.05
1.03
1.07
st dev
0.0880
0.0951
0.0803
COV
0.084
0.092
0.075
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
Geometric Properties
fy
Ag
Ac
2
Test Results
λd
A c /A g f cr
P u,t
2
AS 4600 (1996)
fu
Test ID
MPa mm mm
% MPa
kN
63 16.4 390 0.84 87
430_60_60_10_2_2.5
275 382
430_60_60_10_3_2.5
275 561 141 25.2 654 0.65 154
63 15.6 514 0.73 99
430_60_60_15_2_2.5
275 402
430_60_60_15_3_2.5
275 591 141 23.9 823 0.58 173
430_150_150_30_3_2.5 275 1491 141 9.5 243 1.06 286
430_150_150_20_3_2.5 275 1431 141 9.9 175 1.25 244
430_150_150_10_3_2.5 275 1371 141 10.3 100 1.66 205
430_200_100_15_4_2.5 275 1650 251 15.2 311 0.94 346
430_200_150_20_3_2.5 275 1581 141 8.9 160 1.31 247
430_200_150_20_4_2.5 275 2090 251 12.0 226 1.10 399
16
5.0
430_150_80_5_1_2.5
275 316
36 2.78 26
16 10.1 135 1.43 24
430_50_50_5_1_2.5
275 156
430_400_400_20_3_2.5 275 3681 141 3.8
21 3.61 236
430_400_400_20_4_2.5 275 4890 251 5.1
31 3.00 343
430_400_400_20_5_2.5 275 6090 393 6.4
41 2.59 586
430_400_400_40_4_2.5 275 5050 251 5.0
60 2.15 437
430_400_400_40_5_2.5 275 6290 393 6.2
78 1.88 650
430_400_400_40_6_2.5 275 7522 565 7.5 100 1.65 953
430_400_400_40_7_2.5 275 8745 770 8.8 116 1.54 1236
430_400_400_40_8_2.5 275 9959 1005 10.1 137 1.42 1556
430_300_400_20_3_2.5 275 3381 141 4.2
23 3.44 229
430_300_400_20_4_2.5 275 4490 251 5.6
33 2.87 390
430_300_400_20_5_2.5 275 5590 393 7.0
45 2.47 590
430_400_300_20_3_2.5 275 3081 141 4.6
36 2.78 235
430_400_300_20_4_2.5 275 4090 251 6.1
51 2.31 404
430_400_300_20_5_2.5 275 5090 393 7.7
70 1.98 605
430_400_300_40_5_2.5 275 5290 393 7.4 125 1.49 704
430_400_300_40_6_2.5 275 6322 565 8.9 155 1.33 992
430_400_300_40_7_2.5 275 7345 770 10.5 187 1.21 1306
430_400_300_40_8_2.5 275 8359 1005 12.0 221 1.12 1598
f u /f y f n,4600 /f y f u /f n,4600
MPa
228
275
245
293
192
171
150
209
156
191
83
156
64
70
96
87
103
127
141
156
68
87
106
76
99
119
133
157
178
191
0.83
1.00
0.89
1.07
0.70
0.62
0.54
0.76
0.57
0.69
0.30
0.57
0.23
0.25
0.35
0.31
0.38
0.46
0.51
0.57
0.25
0.32
0.38
0.28
0.36
0.43
0.48
0.57
0.65
0.70
r/t=2.5
all tests
Geometric Properties
Test ID
3Cr12D1a
3Cr12D1b
fy
Ag
Ac
A c /A g
MPa
339
339
mm2
mm2
555
555
62
62
%
11
11
Test Results
f cr
λd
P u,t
April 2005
fu
0.82
na
0.87
na
0.72
0.61
0.44
0.78
0.57
0.70
0.27
0.50
0.24
0.26
0.29
0.35
0.40
0.45
0.47
0.50
0.24
0.27
0.31
0.27
0.33
0.38
0.48
0.56
0.63
0.69
1.01
na
1.03
na
0.97
1.02
1.23
0.98
1.00
1.00
1.11
1.14
0.98
0.99
1.19
0.89
0.94
1.03
1.09
1.14
1.03
1.19
1.25
1.01
1.09
1.13
1.00
1.03
1.02
1.01
0.80
na
0.87
na
0.67
0.58
0.45
0.73
0.56
0.65
0.27
0.52
0.21
0.25
0.29
0.35
0.40
0.45
0.48
0.52
0.22
0.26
0.31
0.27
0.33
0.38
0.50
0.55
0.60
0.64
1.04
na
1.02
na
1.05
1.07
1.21
1.04
1.02
1.07
1.12
1.10
1.12
1.02
1.20
0.90
0.94
1.02
1.06
1.09
1.13
1.20
1.26
1.02
1.10
1.14
0.97
1.04
1.08
1.09
1.05
1.04
1.08
0.0886
0.0937
0.0810
COV
0.084
0.090
0.075
mean
1.04
1.03
1.07
st dev
0.0852
0.0917
0.0789
COV
0.082
0.089
0.074
0.74
0.74
1.00
1.00
mean
1.00
NAS Appendix 1
PROPOSED
(2004)
f n,NAS /f y f u /f n,NAS f n,prop. /f y f u /f n,prop.
0.73
0.73
1.00
1.01
0.69
0.69
1.07
1.08
1.00
1.08
st dev 0.0051
0.0051
0.0055
0.005
0.005
0.005
COV
181
0.97
na
0.96
na
0.98
1.01
1.16
0.97
0.96
1.00
1.12
1.04
1.15
1.02
1.19
0.88
0.91
0.98
1.01
1.03
1.15
1.21
1.24
1.02
1.08
1.10
0.92
0.98
1.02
1.02
mean
f u /f y f n,4600 /f y f u /f n,4600
MPa
kN MPa
321 1.03 138 249 0.73
321 1.03 139 251 0.74
0.85
na
0.93
na
0.71
0.62
0.47
0.79
0.59
0.69
0.27
0.55
0.20
0.25
0.29
0.36
0.41
0.47
0.51
0.55
0.21
0.26
0.31
0.27
0.33
0.39
0.53
0.58
0.64
0.68
st dev
AS 4600 (1996)
experimental
Department of Civil Engineering
Research Report No R845
NAS Appendix 1
PROPOSED
(2004)
f n,NAS /f y f u /f n,NAS f n,prop. /f y f u /f n,prop.
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
Geometric Properties
fy
Test ID
3Cr12_60_60_10_2
3Cr12_60_60_10_3
3Cr12_60_60_15_2
3Cr12_60_60_15_3
3Cr12_150_150_30_3
3Cr12_150_150_20_3
3Cr12_150_150_10_3
3Cr12_200_100_15_4
3Cr12_200_150_20_3
3Cr12_200_150_20_4
3Cr12_150_80_5_1
3Cr12_50_50_5_1
3Cr12_400_400_20_3
3Cr12_400_400_20_4
3Cr12_400_400_20_5
3Cr12_400_400_40_4
3Cr12_400_400_40_5
3Cr12_400_400_40_6
3Cr12_400_400_40_7
3Cr12_400_400_40_8
3Cr12_300_400_20_3
3Cr12_300_400_20_4
3Cr12_300_400_20_5
3Cr12_400_300_20_3
3Cr12_400_300_20_4
3Cr12_400_300_20_5
3Cr12_400_300_40_5
3Cr12_400_300_40_6
3Cr12_400_300_40_7
3Cr12_400_300_40_8
Test Results
Ag
Ac
A c /A g
f cr
λd
P u,t
fu
mm2
mm2
%
6.4
9.7
6.1
9.2
3.7
3.9
4.1
5.9
3.5
4.7
2.0
4.0
1.5
2.0
2.6
2.0
2.5
3.0
3.5
4.0
1.7
2.2
2.8
1.8
2.4
3.0
2.9
3.5
4.1
4.7
MPa
432
711
573
909
272
194
110
345
177
251
39
151
24
34
46
67
87
107
129
151
26
37
50
40
57
78
139
172
207
245
0.78
0.60
0.67
0.53
0.98
1.16
1.54
0.87
1.21
1.02
2.59
1.31
3.32
2.76
2.38
1.97
1.73
1.56
1.42
1.31
3.17
2.65
2.28
2.56
2.13
1.83
1.37
1.23
1.12
1.03
kN
83
142
93
157
278
243
201
335
254
389
27
24
237
382
602
444
709
1005
1267
1563
231
395
597
237
409
618
738
1022
1292
1556
MPa
211
243
226
256
184
167
144
198
158
182
85
155
64
77
98
87
112
132
143
154
68
87
106
76
99
120
138
159
173
182
MPa
25
260 393
57
260 584
25
260 413
57
260 614
260 1514 57
260 1454 57
260 1394 57
260 1692 101
260 1604 57
260 2132 101
6
260 318
6
260 158
260 3704 57
260 4932 101
260 6156 157
260 5092 101
260 6356 157
260 7617 226
260 8874 308
260 10130 402
260 3404 57
260 4532 101
260 5656 157
260 3104 57
260 4132 101
260 5156 157
260 5356 157
260 6417 226
260 7474 308
260 8528 402
flats
April 2005
AS 4600 (1996)
f u /f y f n,4600 /f y f u /f n,4600
0.81
0.93
0.87
0.98
0.71
0.64
0.56
0.76
0.61
0.70
0.33
0.59
0.25
0.30
0.38
0.34
0.43
0.51
0.55
0.59
0.26
0.34
0.41
0.29
0.38
0.46
0.53
0.61
0.67
0.70
0.85
0.91
0.89
0.93
0.76
0.67
0.47
0.81
0.63
0.74
0.29
0.57
0.24
0.28
0.32
0.38
0.43
0.47
0.50
0.57
0.25
0.29
0.33
0.30
0.36
0.41
0.53
0.62
0.69
0.73
0.96
1.03
0.98
1.06
0.93
0.97
1.18
0.94
0.96
0.95
1.12
1.05
1.02
1.08
1.18
0.88
1.00
1.09
1.10
1.04
1.06
1.17
1.22
0.99
1.07
1.13
0.99
0.98
0.97
0.96
mean
1.03
182
0.90
0.99
0.96
1.00
0.76
0.66
0.51
0.83
0.64
0.74
0.29
0.59
0.22
0.27
0.32
0.39
0.45
0.50
0.55
0.59
0.23
0.29
0.34
0.30
0.36
0.43
0.57
0.63
0.68
0.73
0.91
0.94
0.90
0.98
0.93
0.97
1.10
0.91
0.95
0.95
1.12
1.01
1.10
1.09
1.17
0.85
0.95
1.01
1.00
1.00
1.11
1.17
1.20
0.99
1.05
1.08
0.93
0.98
0.97
0.96
0.84
0.96
0.91
1.00
0.71
0.62
0.48
0.78
0.60
0.69
0.29
0.56
0.23
0.27
0.32
0.38
0.43
0.48
0.52
0.56
0.24
0.28
0.33
0.29
0.35
0.41
0.54
0.59
0.64
0.68
0.97
0.97
0.95
0.98
0.99
1.03
1.15
0.98
1.02
1.02
1.13
1.07
1.09
1.09
1.19
0.88
0.99
1.07
1.06
1.06
1.10
1.18
1.23
1.00
1.08
1.12
0.99
1.04
1.04
1.03
1.01
1.05
st dev 0.0858
0.0894
0.0773
0.083
0.089
0.074
COV
Department of Civil Engineering
Research Report No R845
NAS Appendix 1
PROPOSED
(2004)
f n,NAS /f y f u /f n,NAS f n,prop. /f y f u /f n,prop.
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
Geometric Properties
fy
Test ID
3Cr12_60_60_10_2_1
3Cr12_60_60_10_3_1
3Cr12_60_60_15_2_1
3Cr12_60_60_15_3_1
3Cr12_150_150_30_3_1
3Cr12_150_150_20_3_1
3Cr12_150_150_10_3_1
3Cr12_200_100_15_4_1
3Cr12_200_150_20_3_1
3Cr12_200_150_20_4_1
3Cr12_150_80_5_1_1
3Cr12_50_50_5_1_1
3Cr12_400_400_20_3_1
3Cr12_400_400_20_4_1
3Cr12_400_400_20_5_1
3Cr12_400_400_40_4_1
3Cr12_400_400_40_5_1
3Cr12_400_400_40_6_1
3Cr12_400_400_40_7_1
3Cr12_400_400_40_8_1
3Cr12_300_400_20_3_1
3Cr12_300_400_20_4_1
3Cr12_300_400_20_5_1
3Cr12_400_300_20_3_1
3Cr12_400_300_20_4_1
3Cr12_400_300_20_5_1
3Cr12_400_300_40_5_1
3Cr12_400_300_40_6_1
3Cr12_400_300_40_7_1
3Cr12_400_300_40_8_1
Test Results
Ag
Ac
A c /A g
f cr
λd
P u,t
fu
mm2
mm2
%
6.4
9.7
6.1
9.2
3.7
3.9
4.1
5.9
3.5
4.7
2.0
4.0
1.5
2.0
2.6
2.0
2.5
3.0
3.5
4.0
1.7
2.2
2.8
1.8
2.4
3.0
2.9
3.5
4.1
4.7
MPa
432
711
573
909
272
194
110
345
177
251
39
151
24
34
46
67
87
107
129
151
26
37
50
40
57
78
139
172
207
245
0.78
0.60
0.67
0.53
0.98
1.16
1.54
0.87
1.21
1.02
2.59
1.31
3.32
2.76
2.38
1.97
1.73
1.56
1.42
1.31
3.17
2.65
2.28
2.56
2.13
1.83
1.37
1.23
1.12
1.03
kN
85
148
96
165
283
246
205
343
256
396
27
25
237
383
607
447
710
1009
1277
1581
234
399
603
240
413
621
741
1032
1311
1584
MPa
217
253
233
269
187
169
147
203
160
186
86
156
64
78
99
88
112
132
144
156
69
88
107
77
100
120
138
161
175
186
MPa
25
260 393
57
260 584
25
260 413
57
260 614
260 1514 57
260 1454 57
260 1394 57
260 1692 101
260 1604 57
260 2132 101
6
260 318
6
260 158
260 3704 57
260 4932 101
260 6156 157
260 5092 101
260 6356 157
260 7617 226
260 8874 308
260 10130 402
260 3404 57
260 4532 101
260 5656 157
260 3104 57
260 4132 101
260 5156 157
260 5356 157
260 6417 226
260 7474 308
260 8528 402
r/t=1
April 2005
AS 4600 (1996)
f u /f y f n,4600 /f y f u /f n,4600
0.83
0.97
0.90
1.03
0.72
0.65
0.56
0.78
0.61
0.71
0.33
0.60
0.25
0.30
0.38
0.34
0.43
0.51
0.55
0.60
0.26
0.34
0.41
0.30
0.38
0.46
0.53
0.62
0.67
0.71
0.85
0.91
0.89
na
0.76
0.67
0.47
0.81
0.63
0.74
0.29
0.57
0.24
0.28
0.32
0.38
0.43
0.47
0.50
0.57
0.25
0.29
0.33
0.30
0.36
0.41
0.53
0.62
0.69
0.73
0.98
1.07
1.01
na
0.94
0.98
1.20
0.96
0.97
0.96
1.13
1.06
1.02
1.08
1.19
0.88
1.00
1.09
1.11
1.05
1.07
1.18
1.23
1.00
1.08
1.13
1.00
0.99
0.98
0.97
mean
1.05
183
0.90
0.99
0.96
na
0.76
0.66
0.51
0.83
0.64
0.74
0.29
0.59
0.22
0.27
0.32
0.39
0.45
0.50
0.55
0.59
0.23
0.29
0.34
0.30
0.36
0.43
0.57
0.63
0.68
0.73
0.93
0.98
0.93
na
0.94
0.98
1.11
0.93
0.96
0.96
1.13
1.02
1.10
1.09
1.18
0.86
0.95
1.02
1.01
1.01
1.12
1.18
1.22
1.00
1.06
1.09
0.93
0.98
0.99
0.98
0.84
0.96
0.91
na
0.71
0.62
0.48
0.78
0.60
0.69
0.29
0.56
0.23
0.27
0.32
0.38
0.43
0.48
0.52
0.56
0.24
0.28
0.33
0.29
0.35
0.41
0.54
0.59
0.64
0.68
0.99
1.01
0.98
na
1.01
1.05
1.17
1.00
1.03
1.03
1.14
1.08
1.09
1.09
1.19
0.89
0.99
1.07
1.06
1.08
1.11
1.19
1.24
1.01
1.09
1.13
0.99
1.05
1.06
1.04
1.02
1.06
st dev 0.0861
0.0885
0.0755
0.082
0.087
0.071
COV
Department of Civil Engineering
Research Report No R845
NAS Appendix 1
PROPOSED
(2004)
f n,NAS /f y f u /f n,NAS f n,prop. /f y f u /f n,prop.
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
Geometric Properties
fy
Ag
Ac
2
mm
Test ID
MPa
3Cr12_60_60_10_2_2.5
260
3Cr12_60_60_10_3_2.5
260
3Cr12_60_60_15_2_2.5
260
3Cr12_60_60_15_3_2.5
260
3Cr12_150_150_30_3_2.5 260
3Cr12_150_150_20_3_2.5 260
3Cr12_150_150_10_3_2.5 260
3Cr12_200_100_15_4_2.5 260
3Cr12_200_150_20_3_2.5 260
3Cr12_200_150_20_4_2.5 260
3Cr12_150_80_5_1_2.5
260
3Cr12_50_50_5_1_2.5
260
3Cr12_400_400_20_3_2.5 260
3Cr12_400_400_20_4_2.5 260
3Cr12_400_400_20_5_2.5 260
3Cr12_400_400_40_4_2.5 260
3Cr12_400_400_40_5_2.5 260
3Cr12_400_400_40_6_2.5 260
3Cr12_400_400_40_7_2.5 260
3Cr12_400_400_40_8_2.5 260
3Cr12_300_400_20_3_2.5 260
3Cr12_300_400_20_4_2.5 260
3Cr12_300_400_20_5_2.5 260
3Cr12_400_300_20_3_2.5 260
3Cr12_400_300_20_4_2.5 260
3Cr12_400_300_20_5_2.5 260
3Cr12_400_300_40_5_2.5 260
3Cr12_400_300_40_6_2.5 260
3Cr12_400_300_40_7_2.5 260
3Cr12_400_300_40_8_2.5 260
2
mm
63
382
561 141
63
402
591 141
1491 141
1431 141
1371 141
1650 251
1581 141
2090 251
16
316
16
156
3681 141
4890 251
6090 393
5050 251
6290 393
7522 565
8745 770
9959 1005
3381 141
4490 251
5590 393
3081 141
4090 251
5090 393
5290 393
6322 565
7345 770
8359 1005
Test Results
A c /A g
f cr
λd
P u,t
fu
%
16.4
25.2
15.6
23.9
9.5
9.9
10.3
15.2
8.9
12.0
5.0
10.1
3.8
5.1
6.4
5.0
6.2
7.5
8.8
10.1
4.2
5.6
7.0
4.6
6.1
7.7
7.4
8.9
10.5
12.0
MPa
443
742
583
935
276
198
113
353
181
257
40
153
24
35
47
68
88
114
132
155
26
38
51
40
58
79
141
176
212
251
0.77
0.59
0.67
0.53
0.97
1.15
1.51
0.86
1.20
1.01
2.54
1.30
3.29
2.74
2.36
1.96
1.71
1.51
1.40
1.29
3.14
2.62
2.25
2.54
2.11
1.81
1.36
1.22
1.11
1.02
kN
86
150
97
168
284
248
207
346
257
397
27
25
241
403
608
457
712
1008
1281
1592
235
401
606
240
415
631
739
1036
1316
1592
MPa
224
268
241
285
190
173
151
210
163
190
86
159
66
82
100
91
113
134
146
160
69
89
108
78
101
124
140
164
179
190
April 2005
AS 4600 (1996)
f u /f y f n,4600 /f y f u /f n,4600
0.86
1.03
0.93
1.09
0.73
0.67
0.58
0.81
0.63
0.73
0.33
0.61
0.25
0.32
0.38
0.35
0.44
0.52
0.56
0.61
0.27
0.34
0.42
0.30
0.39
0.48
0.54
0.63
0.69
0.73
r/t=2.5
all tests
0.85
na
0.89
na
0.76
0.67
0.48
0.82
0.64
0.75
0.30
0.57
0.24
0.28
0.32
0.38
0.43
0.48
0.51
0.58
0.25
0.29
0.34
0.30
0.36
0.41
0.54
0.63
0.69
0.74
mean
f yf
Test ID
304DS1a
304DS2b
Ag
2
MPa mm
242 634
242 634
Ac
A c /A g
mm2
%
19
19
122
123
Test Results
f cr
λd
MPa
333 0.85
333 0.85
P u,t
fu
kN
132
134
MPa
208
211
experimental tests
Department of Civil Engineering
Research Report No R845
184
0.95
na
0.96
na
0.95
0.99
1.13
0.96
0.97
0.98
1.10
1.03
1.12
1.15
1.18
0.88
0.96
1.00
1.02
1.03
1.13
1.19
1.22
1.00
1.07
1.11
0.94
0.99
1.00
0.99
1.04
0.85
na
0.92
na
0.72
0.63
0.49
0.78
0.60
0.70
0.30
0.56
0.23
0.28
0.32
0.38
0.44
0.49
0.52
0.56
0.24
0.29
0.33
0.30
0.36
0.41
0.54
0.60
0.64
0.69
1.02
na
1.01
na
1.02
1.06
1.19
1.03
1.04
1.05
1.11
1.09
1.11
1.15
1.20
0.91
1.00
1.05
1.07
1.09
1.12
1.20
1.25
1.01
1.09
1.15
0.99
1.06
1.07
1.06
1.08
0.0878
0.0745
COV
0.081
0.085
0.069
mean
1.04
1.02
1.06
st dev 0.0846
0.0872
0.0750
0.081
0.085
0.071
AS 4600 (1996)
f u /f y f n,4600 /f y f u /f n,4600
0.86
0.87
0.90
na
0.96
na
0.77
0.67
0.52
0.84
0.64
0.75
0.30
0.60
0.22
0.28
0.32
0.40
0.46
0.52
0.55
0.60
0.24
0.29
0.34
0.30
0.37
0.43
0.57
0.63
0.69
0.74
st dev 0.0857
COV
Geometric Properties
1.01
na
1.04
na
0.96
0.99
1.22
0.99
0.98
0.98
1.11
1.07
1.04
1.14
1.19
0.90
1.01
1.08
1.11
1.06
1.08
1.19
1.24
1.00
1.09
1.15
0.99
1.00
0.99
0.99
1.06
NAS Appendix 1
PROPOSED
(2004)
f n,NAS /f y f u /f n,NAS f n,prop. /f y f u /f n,prop.
NAS Appendix 1
PROPOSED
(2004)
f n,NAS /f y f u /f n,NAS f n,prop. /f y f u /f n,prop.
0.84
0.84
1.02
1.03
1.03
0.74
0.74
1.16
1.18
1.17
0.82
0.82
mean
1.05
1.07
1.06
st dev
0.0113
0.0109
0.0124
COV
0.011
0.011
0.011
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
Geometric Properties
Test ID
304_200_160_25_10_2
304_200_160_25_10_3
304_200_160_25_10_4
304_400_160_25_10_2
304_400_160_25_10_3
304_400_160_25_10_4
304_400_160_25_20_2
304_400_160_25_20_3
304_400_160_25_20_4
304_800_400_40_15_3
304_800_400_40_15_4
304_800_400_40_15_5
304_800_400_40_15_6
304_800_400_40_30_4
304_800_400_40_30_5
304_800_400_40_30_6
304_150_100_10_10_1
304_150_70_15_10_1
304_150_70_15_10_2
304_200_80_15_10_1
304_200_80_15_10_2
304_150_110_15_10_2
304_300_200_20_15_2
304_300_200_20_15_3
304_100_70_20_10_1
304_250_95_20_10_2
304_250_95_20_10_3
304_100_60_10_10_1
304_200_150_15_15_2
304_90_60_10_5_1
304_150_70_15_10_4
304_150_70_15_10_5
304_200_160_35_20_6
304_200_160_35_20_7
Test Results
f yf
Ag
Ac
A c /A g
f cr
MPa
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
mm2
mm2
1177
1755
2327
1577
2355
3127
1626
2430
3227
5123
6769
8505
10186
6966
8691
10410
392
341
681
412
817
837
1542
2303
302
997
1485
262
1122
239
1327
1643
3721
4318
63
141
251
63
141
251
63
141
251
141
251
393
565
251
393
565
16
16
63
16
63
63
63
141
16
63
141
16
63
16
251
393
565
770
%
5.3
8.1
10.8
4.0
6.0
8.0
3.9
5.8
7.8
2.8
3.7
4.6
5.6
3.6
4.5
5.4
4.0
4.6
9.2
3.8
7.7
7.5
4.1
6.1
5.2
6.3
9.5
6.0
5.6
6.6
18.9
23.9
15.2
17.8
MPa
106
169
238
58
95
138
73
115
165
28
40
52
65
45
58
74
62
111
251
72
164
139
55
88
186
131
214
162
89
189
619
837
527
638
λd
P u,t
fu
1.35
1.08
0.91
1.83
1.43
1.19
1.64
1.30
1.09
2.63
2.22
1.94
1.73
2.09
1.83
1.63
1.77
1.33
0.88
1.65
1.09
1.19
1.89
1.49
1.02
1.22
0.95
1.10
1.48
1.02
0.56
0.48
0.61
0.55
kN
116
215
328
116
211
328
128
232
355
252
408
577
792
484
683
902
36
32
90
32
90
101
129
235
36
98
182
31
123
27
250
330
669
817
MPa
99
123
141
73
90
105
79
96
110
49
60
68
78
70
79
87
91
94
132
78
110
120
84
102
118
98
123
118
109
113
188
201
180
189
flats
Department of Civil Engineering
Research Report No R845
185
April 2005
AS 4600 (1996)
f u /f y f n,4600 /f y f u /f n,4600
0.51
0.63
0.72
0.38
0.46
0.54
0.40
0.49
0.56
0.25
0.31
0.35
0.40
0.36
0.40
0.44
0.47
0.48
0.68
0.40
0.57
0.62
0.43
0.52
0.60
0.50
0.63
0.61
0.56
0.58
0.97
1.03
0.92
0.97
0.54
0.71
0.79
0.41
0.49
0.65
0.45
0.58
0.71
0.29
0.34
0.39
0.43
0.36
0.41
0.45
0.42
0.56
0.81
0.45
0.70
0.65
0.40
0.48
0.74
0.63
0.77
0.70
0.48
0.74
0.92
na
0.91
0.92
0.94
0.88
0.91
0.92
0.93
0.83
0.90
0.85
0.80
0.87
0.90
0.90
0.93
0.98
0.98
0.99
1.10
0.86
0.84
0.90
0.81
0.95
1.08
1.08
0.82
0.80
0.82
0.87
1.16
0.78
1.05
na
1.02
1.05
NAS Appendix 1
PROPOSED
(2004)
f n,NAS /f y f u /f n,NAS f n,prop. /f y f u /f n,prop.
0.57
0.71
0.81
0.43
0.54
0.65
0.48
0.60
0.70
0.29
0.35
0.40
0.45
0.37
0.43
0.48
0.44
0.58
0.83
0.47
0.70
0.65
0.41
0.52
0.74
0.63
0.78
0.69
0.53
0.74
1.00
na
0.99
1.00
0.88
0.89
0.89
0.88
0.84
0.83
0.85
0.82
0.81
0.87
0.89
0.87
0.88
0.96
0.95
0.93
1.06
0.82
0.82
0.85
0.81
0.95
1.04
1.00
0.82
0.80
0.81
0.87
1.07
0.78
0.97
na
0.93
0.97
0.50
0.61
0.71
0.37
0.47
0.56
0.41
0.52
0.61
0.26
0.31
0.35
0.39
0.33
0.37
0.42
0.38
0.51
0.72
0.41
0.60
0.56
0.36
0.45
0.64
0.55
0.68
0.60
0.46
0.64
0.98
na
0.93
0.98
1.02
1.03
1.02
1.01
0.98
0.96
0.98
0.95
0.93
0.98
1.01
0.99
1.02
1.09
1.08
1.07
1.21
0.95
0.94
0.98
0.94
1.10
1.19
1.15
0.95
0.92
0.93
1.01
1.23
0.90
0.99
na
0.99
0.99
mean
0.92
0.89
1.01
st dev
0.0989
0.0771
0.0842
COV
0.107
0.086
0.083
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
Geometric Properties
Test ID
304_200_160_25_10_2_1
304_200_160_25_10_3_1
304_200_160_25_10_4_1
304_400_160_25_10_2_1
304_400_160_25_10_3_1
304_400_160_25_10_4_1
304_400_160_25_20_2_1
304_400_160_25_20_3_1
304_400_160_25_20_4_1
304_800_400_40_15_3_1
304_800_400_40_15_4_1
304_800_400_40_15_5_1
304_800_400_40_15_6_1
304_800_400_40_30_4_1
304_800_400_40_30_5_1
304_800_400_40_30_6_1
304_150_100_10_10_1_1
304_150_70_15_10_1_1
304_150_70_15_10_2_1
304_200_80_15_10_1_1
304_200_80_15_10_2_1
304_150_110_15_10_2_1
304_300_200_20_15_2_1
304_300_200_20_15_3_1
304_100_70_20_10_1_1
304_250_95_20_10_2_1
304_250_95_20_10_3_1
304_100_60_10_10_1_1
304_200_150_15_15_2_1
304_90_60_10_5_1_1
304_150_70_15_10_4_1
304_150_70_15_10_5_1
304_200_160_35_20_6_1
304_200_160_35_20_7_1
Test Results
fy
Ag
Ac
A c /A g
f cr
MPa
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
195
mm2
mm2
1177
1755
2327
1577
2355
3127
1626
2430
3227
5123
6769
8505
10186
6966
8691
10410
392
341
681
412
817
837
1542
2303
302
997
1485
262
1122
239
1327
1643
3721
4318
63
141
251
63
141
251
63
141
251
141
251
393
565
251
393
565
16
16
63
16
63
63
63
141
16
63
141
16
63
16
251
393
565
770
%
5.3
8.1
10.8
4.0
6.0
8.0
3.9
5.8
7.8
2.8
3.7
4.6
5.6
3.6
4.5
5.4
4.0
4.6
9.2
3.8
7.7
7.5
4.1
6.1
5.2
6.3
9.5
6.0
5.6
6.6
18.9
23.9
15.2
17.8
MPa
106
169
238
58
95
138
73
115
165
28
40
52
65
45
58
74
62
111
251
72
164
139
55
88
186
131
214
162
89
189
619
837
527
638
λd
P u,t
fu
1.35
1.08
0.91
1.83
1.43
1.19
1.64
1.30
1.09
2.63
2.22
1.94
1.73
2.09
1.83
1.63
1.77
1.33
0.88
1.65
1.09
1.19
1.89
1.49
1.02
1.22
0.95
1.10
1.48
1.02
0.56
0.48
0.61
0.55
kN
121
227
352
119
221
347
133
244
379
258
423
603
829
503
715
952
37
33
96
33
95
107
133
247
37
102
193
32
128
28
291
408
757
950
MPa
103
129
151
76
94
111
82
100
117
50
62
71
81
72
82
91
94
97
141
81
117
127
86
107
122
103
130
123
114
119
219
249
203
220
r/t=1
Department of Civil Engineering
Research Report No R845
186
April 2005
AS 4600 (1996)
f u /f y f n,4600 /f y f u /f n,4600
0.53
0.66
0.78
0.39
0.48
0.57
0.42
0.51
0.60
0.26
0.32
0.36
0.42
0.37
0.42
0.47
0.48
0.50
0.73
0.41
0.60
0.65
0.44
0.55
0.62
0.53
0.67
0.63
0.59
0.61
1.12
1.28
1.04
1.13
0.54
0.71
0.79
0.41
0.49
0.65
0.45
0.58
0.71
0.29
0.34
0.39
0.43
0.36
0.41
0.45
0.42
0.56
0.81
0.45
0.70
0.65
0.40
0.48
0.74
0.63
0.77
0.70
0.48
0.74
na
na
na
na
0.98
0.93
0.98
0.95
0.97
0.88
0.93
0.89
0.85
0.90
0.94
0.94
0.97
1.02
1.03
1.04
1.14
0.89
0.90
0.93
0.85
1.01
1.11
1.14
0.84
0.84
0.86
0.91
1.22
0.82
na
na
na
na
NAS Appendix 1
PROPOSED
(2004)
f n,NAS /f y f u /f n,NAS f n,prop. /f y f u /f n,prop.
0.57
0.71
0.81
0.43
0.54
0.65
0.48
0.60
0.70
0.29
0.35
0.40
0.45
0.37
0.43
0.48
0.44
0.58
0.83
0.47
0.70
0.65
0.41
0.52
0.74
0.63
0.78
0.69
0.53
0.74
na
na
na
na
0.92
0.94
0.96
0.91
0.89
0.88
0.88
0.86
0.86
0.90
0.92
0.91
0.93
1.00
0.99
0.98
1.09
0.85
0.88
0.87
0.86
1.01
1.07
1.05
0.85
0.83
0.86
0.91
1.12
0.82
na
na
na
na
0.50
0.61
0.71
0.37
0.47
0.56
0.41
0.52
0.61
0.26
0.31
0.35
0.39
0.33
0.37
0.42
0.38
0.51
0.72
0.41
0.60
0.56
0.36
0.45
0.64
0.55
0.68
0.60
0.46
0.64
na
na
na
na
1.06
1.09
1.10
1.04
1.03
1.02
1.01
1.00
0.99
1.00
1.04
1.04
1.06
1.14
1.13
1.12
1.25
0.98
1.01
1.00
0.99
1.17
1.23
1.21
0.98
0.97
0.99
1.06
1.29
0.95
na
na
na
na
mean
0.95
0.93
1.06
st dev
0.0982
0.0792
0.0900
COV
0.103
0.086
0.085
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
Geometric Properties
fy
Test ID
304_200_160_25_10_2_2.5
304_200_160_25_10_3_2.5
304_200_160_25_10_4_2.5
304_400_160_25_10_2_2.5
304_400_160_25_10_3_2.5
304_400_160_25_10_4_2.5
304_400_160_25_20_2_2.5
304_400_160_25_20_3_2.5
304_400_160_25_20_4_2.5
304_800_400_40_15_3_2.5
304_800_400_40_15_4_2.5
304_800_400_40_15_5_2.5
304_800_400_40_15_6_2.5
304_800_400_40_30_4_2.5
304_800_400_40_30_5_2.5
304_800_400_40_30_6_2.5
304_150_100_10_10_1_2.5
304_150_70_15_10_1_2.5
304_150_70_15_10_2_2.5
304_200_80_15_10_1_2.5
304_200_80_15_10_2_2.5
304_150_110_15_10_2_2.5
304_300_200_20_15_2_2.5
304_300_200_20_15_3_2.5
304_100_70_20_10_1_2.5
304_250_95_20_10_2_2.5
304_250_95_20_10_3_2.5
304_100_60_10_10_1_2.5
304_200_150_15_15_2_2.5
304_90_60_10_5_1_2.5
304_150_70_15_10_4_2.5
304_150_70_15_10_5_2.5
304_200_160_35_20_6_2.5
304_200_160_35_20_7_2.5
Ag
2
MPa mm
AS 4600 (1996)
Test Results
λd
fu
kN
MPa
f u /f y f n,4600 /f y f u /f n,4600
Ac
A c /A g
f cr
%
MPa
13.6
20.7
25.0
10.1
15.3
18.5
9.8
14.8
20.0
7.0
9.3
11.7
11.2
9.1
11.5
13.8
10.2
11.7
23.9
9.7
19.7
19.2
10.3
15.6
13.2
16.1
24.5
15.3
14.3
16.8
42.1
42.1
39.9
47.2
109
1.34
122
105
0.54
0.55
0.98
0.58
174
245
54
87
129
73
115
163
27
38
51
67
45
59
74
63
115
264
74
170
148
56
88
191
133
213
167
92
202
645
866
546
666
1.06 228
0.89 356
1.90 121
1.50 227
1.23 360
1.64 135
1.30 248
1.09 384
2.69 255
2.26 391
1.95 590
1.71 832
2.08 509
1.82 721
1.62 958
1.76 37
1.30 34
0.86 100
1.62 34
1.07 98
1.15 109
1.87 134
1.49 249
1.01 37
1.21 104
0.96 196
1.08 33
1.46 131
0.98 29
0.55 302
0.47 413
0.60 793
0.54 1009
133
158
78
98
118
84
104
122
50
58
70
83
74
84
94
96
100
152
83
122
133
88
110
126
106
136
129
119
123
238
260
224
247
0.68
0.81
0.40
0.50
0.60
0.43
0.53
0.63
0.26
0.30
0.36
0.42
0.38
0.43
0.48
0.49
0.51
0.78
0.43
0.63
0.68
0.45
0.57
0.65
0.54
0.70
0.66
0.61
0.63
1.22
1.34
1.15
1.27
0.72
0.80
0.40
0.48
0.62
0.45
0.58
0.70
0.28
0.34
0.39
0.43
0.36
0.41
0.45
0.42
0.58
0.82
0.45
0.71
0.67
0.40
0.48
0.74
0.63
0.77
0.71
0.49
0.76
na
na
na
na
0.95
1.01
1.00
1.05
0.97
0.96
0.92
0.89
0.91
0.89
0.93
0.98
1.04
1.05
1.06
1.16
0.89
0.96
0.94
0.88
1.02
1.13
1.17
0.87
0.86
0.90
0.93
1.24
0.83
na
na
na
na
0.72
0.82
0.41
0.52
0.63
0.48
0.60
0.70
0.28
0.34
0.40
0.46
0.37
0.43
0.48
0.44
0.60
0.84
0.48
0.71
0.67
0.42
0.52
0.74
0.64
0.78
0.70
0.53
0.76
na
na
na
na
r/t=2.5
all tests
Geometric Properties
Test ID
430DS1
430DS2
430DS3
430DS4
fy
Ag
MPa
271
271
271
271
mm
269
269
278
278
Ac
2
2
mm
53
55
54
54
Test Results
A c /A g
f cr
%
20
20
20
20
MPa
269
335
327
468
λd
P u,t
fu
1.00
0.90
0.91
0.76
kN
60
62
64
72
MPa
222
230
228
258
experimental tests
Department of Civil Engineering
Research Report No R845
NAS Appendix 1
PROPOSED
(2004)
f n,NAS /f y f u /f n,NAS f n,prop. /f y f u /f n,prop.
mm2
195 1157
157
195 1711 353
195 2262 565
195 1557 157
195 2311 353
195 3062 565
195 1607 157
195 2386 353
195 3148 628
195 5078 353
195 6739 628
195 8382 982
195 10069 1131
195 6888 628
195 8569 982
195 10234 1414
39
195 387
39
195 337
157
195 657
39
195 407
157
195 797
157
195 817
195 1522 157
195 2258 353
39
195 297
157
195 977
195 1441 353
39
195 257
195 1102 157
39
195 234
195 1268 534
195 1586 668
195 3545 1414
195 4078 1924
P u,t
April 2005
187
0.93
0.96
0.99
0.97
0.97
0.96
0.90
0.89
0.90
0.91
0.87
0.91
0.93
1.02
1.01
1.00
1.11
0.86
0.93
0.88
0.88
1.02
1.09
1.08
0.87
0.85
0.90
0.94
1.14
0.83
na
na
na
na
0.50
0.62
0.71
0.36
0.45
0.54
0.41
0.52
0.60
0.25
0.30
0.35
0.40
0.33
0.37
0.42
0.39
0.51
0.74
0.42
0.61
0.58
0.36
0.45
0.64
0.55
0.67
0.61
0.46
0.66
na
na
na
na
1.08
1.10
1.13
1.11
1.11
1.11
1.04
1.03
1.04
1.02
0.99
1.03
1.07
1.16
1.16
1.15
1.28
1.00
1.06
1.02
1.02
1.19
1.25
1.25
1.00
0.99
1.03
1.09
1.31
0.95
na
na
na
na
mean
0.98
0.95
1.09
st dev
0.1003
0.0798
0.0918
COV
0.102
0.084
0.084
mean
0.95
0.92
1.06
st dev
0.1009
0.0821
0.0940
COV
0.106
0.089
0.089
AS 4600 (1996)
NAS Appendix 1
(2004)
PROPOSED
f u /f y f n,4600 /f y f u /f n,4600 f n,NAS /f y f u /f n,NAS f n,prop. /f y f u /f n,prop.
0.82
0.85
0.84
0.95
0.75
0.81
0.81
0.91
1.09
1.04
1.05
1.05
1.06
0.70
0.76
0.75
0.85
1.17
1.12
1.12
1.12
1.13
0.75
0.80
0.79
0.86
mean
1.09
1.06
1.06
1.11
1.08
st dev
0.0245
0.0241
0.0266
COV
0.023
0.023
0.023
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
Geometric Properties
fy
Test ID
430_200_160_25_10_2
430_200_160_25_10_3
430_200_160_25_10_4
430_400_160_25_10_2
430_400_160_25_10_3
430_400_160_25_10_4
430_400_160_25_20_2
430_400_160_25_20_3
430_400_160_25_20_4
430_800_400_40_15_3
430_800_400_40_15_4
430_800_400_40_15_5
430_800_400_40_15_6
430_800_400_40_30_4
430_800_400_40_30_5
430_800_400_40_30_6
430_150_100_10_10_1
430_150_70_15_10_1
430_150_70_15_10_2
430_200_80_15_10_1
430_200_80_15_10_2
430_150_110_15_10_2
430_300_200_20_15_2
430_300_200_20_15_3
430_100_70_20_10_1
430_250_95_20_10_2
430_250_95_20_10_3
430_100_60_10_10_1
430_200_150_15_15_2
430_90_60_10_5_1
430_150_70_15_10_4
430_150_70_15_10_5
430_200_160_35_20_6
430_200_160_35_20_7
Ag
Ac
2
2
MPa mm mm
275 1177 63
275 1755 141
275 2327 251
275 1577 63
275 2355 141
275 3127 251
275 1626 63
275 2430 141
275 3227 251
275 5123 141
275 6769 251
275 8505 393
275 10186 565
275 6966 251
275 8691 393
275 10410 565
16
275 392
16
275 341
63
275 681
16
275 412
63
275 817
63
275 837
275 1542 63
275 2303 141
16
275 302
63
275 997
275 1485 141
16
275 262
275 1122 63
16
275 239
275 1327 251
275 1643 393
275 3721 565
275 4318 770
Test Results
A c /A g
f cr
%
5.3
8.1
10.8
4.0
6.0
8.0
3.9
5.8
7.8
2.8
3.7
4.6
5.6
3.6
4.5
5.4
4.0
4.6
9.2
3.8
7.7
7.5
4.1
6.1
5.2
6.3
9.5
6.0
5.6
6.6
18.9
23.9
15.2
17.8
MPa
101
160
226
55
90
131
69
109
157
27
38
49
62
42
55
70
59
105
238
68
156
132
52
84
177
124
203
153
84
125
587
794
500
605
P u,t
1.65
1.31
1.10
2.23
1.75
1.45
2.00
1.59
1.32
3.21
2.71
2.37
2.11
2.55
2.23
1.98
2.16
1.62
1.07
2.01
1.33
1.45
2.30
1.81
1.25
1.49
1.16
1.34
1.81
1.48
0.68
0.59
0.74
0.67
kN MPa
155 131 0.48
284 162 0.59
431 185 0.67
154
97 0.35
282 120 0.44
439 140 0.51
167 103 0.37
312 128 0.47
476 147 0.54
316
62 0.22
527
78 0.28
762
90 0.33
1049 103 0.37
625
90 0.33
907 104 0.38
1198 115 0.42
44
112 0.41
43
125 0.46
118 173 0.63
42
102 0.37
121 148 0.54
134 160 0.58
170 110 0.40
310 135 0.49
48
158 0.57
131 131 0.48
241 162 0.59
41
158 0.57
162 145 0.53
36
150 0.54
322 243 0.88
434 264 0.96
873 234 0.85
1068 247 0.90
flats
Department of Civil Engineering
Research Report No R845
AS 4600 (1996)
λd
fu
188
April 2005
NAS Appendix 1
(2004)
PROPOSED
f u /f y f n,4600 /f y f u /f n,4600 f n,NAS /f y f u /f n,NAS f n,prop. /f y f u /f n,prop.
0.45
0.57
0.70
0.34
0.43
0.49
0.38
0.46
0.56
0.25
0.28
0.32
0.36
0.30
0.34
0.38
0.35
0.45
0.71
0.38
0.56
0.49
0.33
0.41
0.61
0.48
0.66
0.55
0.41
0.48
0.88
0.91
0.86
0.89
1.07
1.03
0.97
1.04
1.02
1.04
0.99
1.01
0.95
0.92
1.01
1.02
1.04
1.10
1.12
1.10
1.16
1.01
0.89
0.98
0.96
1.18
1.21
1.19
0.94
0.99
0.89
1.04
1.27
1.12
1.00
1.05
0.99
1.01
0.47
0.59
0.69
0.35
0.45
0.54
0.39
0.49
0.59
0.23
0.28
0.32
0.37
0.30
0.35
0.39
0.36
0.48
0.71
0.39
0.58
0.54
0.33
0.43
0.62
0.52
0.66
0.58
0.43
0.53
0.96
1.00
0.92
0.96
1.01
0.99
0.97
1.02
0.98
0.95
0.96
0.95
0.91
0.97
1.01
1.01
1.02
1.09
1.10
1.07
1.14
0.95
0.89
0.96
0.92
1.08
1.20
1.14
0.93
0.91
0.89
0.99
1.22
1.03
0.92
0.96
0.93
0.94
0.45
0.56
0.65
0.34
0.43
0.51
0.38
0.47
0.55
0.23
0.28
0.32
0.36
0.30
0.34
0.38
0.35
0.46
0.66
0.37
0.55
0.51
0.33
0.41
0.58
0.50
0.62
0.55
0.41
0.50
0.91
0.97
0.86
0.91
1.06
1.05
1.04
1.05
1.02
1.00
0.99
0.99
0.97
0.96
1.02
1.02
1.05
1.10
1.12
1.10
1.17
0.99
0.95
0.99
0.98
1.14
1.22
1.18
0.99
0.96
0.95
1.05
1.27
1.09
0.97
0.99
0.99
0.99
mean
1.04
1.00
1.04
st dev
0.0902
0.0853
0.0807
COV
0.087
0.085
0.078
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
Geometric Properties
fy
Test ID
430_200_160_25_10_2_1
430_200_160_25_10_3_1
430_200_160_25_10_4_1
430_400_160_25_10_2_1
430_400_160_25_10_3_1
430_400_160_25_10_4_1
430_400_160_25_20_2_1
430_400_160_25_20_3_1
430_400_160_25_20_4_1
430_800_400_40_15_3_1
430_800_400_40_15_4_1
430_800_400_40_15_5_1
430_800_400_40_15_6_1
430_800_400_40_30_4_1
430_800_400_40_30_5_1
430_800_400_40_30_6_1
430_150_100_10_10_1_1
430_150_70_15_10_1_1
430_150_70_15_10_2_1
430_200_80_15_10_1_1
430_200_80_15_10_2_1
430_150_110_15_10_2_1
430_300_200_20_15_2_1
430_300_200_20_15_3_1
430_100_70_20_10_1_1
430_250_95_20_10_2_1
430_250_95_20_10_3_1
430_100_60_10_10_1_1
430_200_150_15_15_2_1
430_90_60_10_5_1_1
430_150_70_15_10_4_1
430_150_70_15_10_5_1
430_200_160_35_20_6_1
430_200_160_35_20_7_1
Ag
Ac
2
2
MPa mm mm
275 1177 63
275 1755 141
275 2327 251
275 1577 63
275 2355 141
275 3127 251
275 1626 63
275 2430 141
275 3227 251
275 5123 141
275 6769 251
275 8505 393
275 10186 565
275 6966 251
275 8691 393
275 10410 565
16
275 392
16
275 341
63
275 681
16
275 412
63
275 817
63
275 837
275 1542 63
275 2303 141
16
275 302
63
275 997
275 1485 141
16
275 262
275 1122 63
16
275 239
275 1327 251
275 1643 393
275 3721 565
275 4318 770
Test Results
A c /A g
f cr
%
5.3
8.1
10.8
4.0
6.0
8.0
3.9
5.8
7.8
2.8
3.7
4.6
5.6
3.6
4.5
5.4
4.0
4.6
9.2
3.8
7.7
7.5
4.1
6.1
5.2
6.3
9.5
6.0
5.6
6.6
18.9
23.9
15.2
17.8
MPa
101
160
226
55
90
131
69
109
157
27
38
49
62
42
55
70
59
105
238
68
156
132
52
84
177
124
203
153
84
125
587
794
500
605
P u,t
1.65
1.31
1.10
2.23
1.75
1.45
2.00
1.59
1.32
3.21
2.71
2.37
2.11
2.55
2.23
1.98
2.16
1.62
1.07
2.01
1.33
1.45
2.30
1.81
1.25
1.49
1.16
1.34
1.81
1.48
0.68
0.59
0.74
0.67
kN MPa
157 133 0.49
292 166 0.60
448 193 0.70
155
98 0.36
288 122 0.45
452 145 0.53
170 105 0.38
319 131 0.48
491 152 0.55
323
63 0.23
538
79 0.29
780
92 0.33
1075 106 0.38
635
91 0.33
930 107 0.39
1233 118 0.43
48
122 0.44
43
127 0.46
123 180 0.66
42
103 0.38
124 152 0.55
134 160 0.58
144
93 0.34
319 139 0.50
48
160 0.58
134 134 0.49
248 167 0.61
42
161 0.59
167 149 0.54
37
153 0.56
353 266 0.97
491 299 1.09
937 252 0.92
1165 270 0.98
r/t=1.0
Department of Civil Engineering
Research Report No R845
AS 4600 (1996)
λd
fu
189
April 2005
NAS Appendix 1
(2004)
PROPOSED
f u /f y f n,4600 /f y f u /f n,4600 f n,NAS /f y f u /f n,NAS f n,prop. /f y f u /f n,prop.
0.45
0.57
0.70
0.34
0.43
0.49
0.38
0.46
0.56
0.25
0.28
0.32
0.36
0.30
0.34
0.38
0.35
0.45
0.71
0.38
0.56
0.49
0.33
0.41
0.61
0.48
0.66
0.55
0.41
0.48
0.88
na
0.86
0.89
1.09
1.06
1.01
1.05
1.05
1.07
1.01
1.04
0.99
0.93
1.03
1.04
1.07
1.11
1.14
1.13
1.27
1.02
0.92
1.00
0.99
1.18
1.03
1.22
0.95
1.01
0.92
1.06
1.31
1.15
1.09
na
1.06
1.11
0.47
0.59
0.69
0.35
0.45
0.54
0.39
0.49
0.59
0.23
0.28
0.32
0.37
0.30
0.35
0.39
0.36
0.48
0.71
0.39
0.58
0.54
0.33
0.43
0.62
0.52
0.66
0.58
0.43
0.53
0.96
na
0.92
0.96
1.03
1.02
1.01
1.03
1.00
0.98
0.98
0.97
0.94
0.99
1.03
1.03
1.05
1.11
1.13
1.10
1.24
0.96
0.93
0.97
0.95
1.08
1.02
1.17
0.94
0.93
0.92
1.01
1.26
1.06
1.01
na
1.00
1.02
0.45
0.56
0.65
0.34
0.43
0.51
0.38
0.47
0.55
0.23
0.28
0.32
0.36
0.30
0.34
0.38
0.35
0.46
0.66
0.37
0.55
0.51
0.33
0.41
0.58
0.50
0.62
0.55
0.41
0.50
0.91
na
0.86
0.91
1.07
1.08
1.08
1.06
1.04
1.03
1.01
1.02
1.00
0.98
1.04
1.05
1.07
1.12
1.15
1.14
1.27
1.01
0.99
1.00
1.00
1.14
1.03
1.22
1.00
0.98
0.98
1.07
1.30
1.11
1.07
na
1.06
1.08
mean
1.06
1.03
1.07
st dev
0.0908
0.0823
0.0797
COV
0.085
0.080
0.075
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
Geometric Properties
Test Results
λd
fy
Ag
Ac
A c /A g
f cr
Test ID
MPa
mm2
mm2
%
MPa
430_200_160_25_10_2_2.5
275
1157
157
13.6
103 1.63
430_200_160_25_10_3_2.5
430_200_160_25_10_4_2.5
430_400_160_25_10_2_2.5
430_400_160_25_10_3_2.5
430_400_160_25_10_4_2.5
430_400_160_25_20_2_2.5
430_400_160_25_20_3_2.5
430_400_160_25_20_4_2.5
430_800_400_40_15_3_2.5
430_800_400_40_15_4_2.5
430_800_400_40_15_5_2.5
430_800_400_40_15_6_2.5
430_800_400_40_30_4_2.5
430_800_400_40_30_5_2.5
430_800_400_40_30_6_2.5
430_150_100_10_10_1_2.5
430_150_70_15_10_1_2.5
430_150_70_15_10_2_2.5
430_200_80_15_10_1_2.5
430_200_80_15_10_2_2.5
430_150_110_15_10_2_2.5
430_300_200_20_15_2_2.5
430_300_200_20_15_3_2.5
430_100_70_20_10_1_2.5
430_250_95_20_10_2_2.5
430_250_95_20_10_3_2.5
430_100_60_10_10_1_2.5
430_200_150_15_15_2_2.5
430_90_60_10_5_1_2.5
430_150_70_15_10_4_2.5
430_150_70_15_10_5_2.5
430_200_160_35_20_6_2.5
430_200_160_35_20_7_2.5
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
275
1711
2262
1557
2311
3062
1607
2386
3148
5078
6739
8382
10069
6888
8569
10234
387
337
657
407
797
817
1522
2258
297
977
1441
257
1102
234
1268
1586
3545
4078
353
565
157
353
565
157
353
628
353
628
982
1131
628
982
1414
39
39
157
39
157
157
157
353
39
157
353
39
157
39
534
668
1414
1924
20.7
25.0
10.1
15.3
18.5
9.8
14.8
20.0
7.0
9.3
11.7
11.2
9.1
11.5
13.8
10.2
11.7
23.9
9.7
19.7
19.2
10.3
15.6
13.2
16.1
24.5
15.3
14.3
16.8
42.1
42.1
39.9
47.2
165
233
51
83
122
69
110
155
26
36
49
63
43
56
70
60
109
251
70
161
140
53
84
181
126
202
159
87
134
612
821
518
632
AS 4600 (1996)
Test ID
3Cr12DS1a
3Cr12DS1b
MPa
339
339
mm2
mm2
565
565
124
124
%
22
22
f cr
f u /f y f n,4600 /f y f u /f n,4600 f n,NAS /f y f u /f n,NAS f n,prop. /f y f u /f n,prop.
kN
MPa
157
136
0.49
0.45
1.10
0.48
1.03
0.46
1.08
1.29 294
1.09 452
2.31 157
1.82 288
1.50 465
2.00 169
1.58 321
1.33 492
3.27 322
2.75 523
2.38 753
2.09 1071
2.54 640
2.22 932
1.98 1229
2.15 45
1.59 44
1.05 128
1.98 43
1.31 126
1.40 139
2.28 170
1.81 319
1.23 49
1.48 134
1.17 249
1.32 43
1.78 168
1.43 37
0.67 363
0.58 497
0.73 964
0.66 1207
172
200
101
125
152
105
134
156
63
78
90
106
93
109
120
116
131
194
106
157
170
112
141
165
137
173
167
153
158
286
314
272
296
0.62
0.73
0.37
0.45
0.55
0.38
0.49
0.57
0.23
0.28
0.33
0.39
0.34
0.40
0.44
0.42
0.48
0.71
0.38
0.57
0.62
0.41
0.51
0.60
0.50
0.63
0.61
0.55
0.57
1.04
1.14
0.99
1.08
0.58
0.70
0.33
0.41
0.48
0.38
0.46
0.56
0.24
0.28
0.32
0.36
0.30
0.34
0.38
0.35
0.46
0.73
0.38
0.57
0.51
0.33
0.41
0.62
0.48
0.66
0.57
0.42
0.50
na
na
0.87
na
1.07
1.03
1.12
1.10
1.15
1.01
1.06
1.02
0.95
1.02
1.03
1.07
1.13
1.16
1.14
1.19
1.04
0.97
1.01
1.00
1.21
1.22
1.25
0.96
1.03
0.95
1.07
1.32
1.16
na
na
1.14
na
0.60
0.70
0.33
0.43
0.52
0.39
0.49
0.58
0.23
0.27
0.32
0.37
0.30
0.35
0.39
0.36
0.49
0.72
0.39
0.59
0.56
0.34
0.43
0.63
0.53
0.66
0.59
0.44
0.54
na
na
0.93
na
1.04
1.04
1.10
1.06
1.06
0.99
0.99
0.98
1.02
1.03
1.01
1.04
1.12
1.14
1.11
1.17
0.97
0.98
0.98
0.96
1.11
1.21
1.20
0.95
0.94
0.96
1.03
1.27
1.05
na
na
1.07
na
0.57
0.65
0.33
0.41
0.49
0.38
0.47
0.55
0.23
0.27
0.32
0.36
0.30
0.34
0.38
0.35
0.47
0.67
0.38
0.56
0.53
0.33
0.41
0.59
0.50
0.62
0.56
0.42
0.52
na
na
0.87
na
1.10
1.11
1.12
1.10
1.12
1.02
1.04
1.03
1.00
1.03
1.03
1.07
1.14
1.17
1.15
1.20
1.02
1.05
1.01
1.02
1.17
1.23
1.24
1.02
0.99
1.02
1.09
1.32
1.11
na
na
1.13
na
Test Results
P u,t f u
λd
MPa
387 0.94
387 0.94
190
mean
1.09
1.05
1.09
st dev
0.0926
0.0821
0.0800
COV
0.085
0.078
0.073
mean
1.06
1.03
1.07
st dev
0.0907
0.0837
0.0818
COV
0.085
0.082
0.076
AS 4600 (1996)
NAS Appendix 1
PROPOSED
f u /f y f n,4600 /f y f u /f n,4600 f n,NAS /f y f u /f n,NAS f n,prop. /f y f u /f n,prop.
kN MPa
163 288 0.85
161 285 0.84
experimental
Department of Civil Engineering
Research Report No R845
PROPOSED
fu
all tests
Geometric Propertie
Ag
A c A c /A g
NAS Appendix 1
(2004)
P u,t
r/t=2.5
fy
April 2005
0.78
0.78
1.09
1.08
0.79
0.79
1.08
1.06
0.74
0.74
1.16
1.14
mean
1.08
1.07
1.15
st dev
0.0095
0.0094
0.0100
COV
0.009
0.009
0.009
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
Geometric Propertie
fy
Test ID
3Cr12_200_160_25_10_2
3Cr12_200_160_25_10_3
3Cr12_200_160_25_10_4
3Cr12_400_160_25_10_2
3Cr12_400_160_25_10_3
3Cr12_400_160_25_10_4
3Cr12_400_160_25_20_2
3Cr12_400_160_25_20_3
3Cr12_400_160_25_20_4
3Cr12_800_400_40_15_3
3Cr12_800_400_40_15_4
3Cr12_800_400_40_15_5
3Cr12_800_400_40_15_6
3Cr12_800_400_40_30_4
3Cr12_800_400_40_30_5
3Cr12_800_400_40_30_6
3Cr12_150_100_10_10_1
3Cr12_150_70_15_10_1
3Cr12_150_70_15_10_2
3Cr12_200_80_15_10_1
3Cr12_200_80_15_10_2
3Cr12_150_110_15_10_2
3Cr12_300_200_20_15_2
3Cr12_300_200_20_15_3
3Cr12_100_70_20_10_1
3Cr12_250_95_20_10_2
3Cr12_250_95_20_10_3
3Cr12_100_60_10_10_1
3Cr12_200_150_15_15_2
3Cr12_90_60_10_5_1
3Cr12_150_70_15_10_4
3Cr12_150_70_15_10_5
3Cr12_200_160_35_20_6
3Cr12_200_160_35_20_7
Ag
2
MPa mm
260 1177
260 1755
260 2327
260 1577
260 2355
260 3127
260 1626
260 2430
260 3227
260 5123
260 6769
260 8505
260 10186
260 6966
260 8691
260 10410
260
392
260
341
260
681
260
412
260
817
260
837
260 1542
260 2303
260
302
260
997
260 1485
260
262
260 1122
260
239
260 1327
260 1643
260 3721
260 4318
Test Results
Ac
A c /A g
f cr
mm2
%
5.3
8.1
10.8
4.0
6.0
8.0
3.9
5.8
7.8
2.8
3.7
4.6
5.6
3.6
4.5
5.4
4.0
4.6
9.2
3.8
7.7
7.5
4.1
6.1
5.2
6.3
9.5
6.0
5.6
6.6
18.9
23.9
15.2
17.8
MPa
114
182
256
63
102
149
78
124
178
30
43
56
70
48
63
79
67
119
270
77
177
149
59
95
201
141
231
174
95
142
666
901
567
687
63
141
251
63
141
251
63
141
251
141
251
393
565
251
393
565
16
16
63
16
63
63
63
141
16
63
141
16
63
16
251
393
565
770
λd
P u,t
fu
1.51
1.20
1.01
2.03
1.60
1.32
1.82
1.45
1.21
2.93
2.47
2.16
1.92
2.33
2.03
1.81
1.97
1.48
0.98
1.83
1.21
1.32
2.10
1.65
1.14
1.36
1.06
1.22
1.65
1.35
0.62
0.54
0.68
0.62
kN
160
287
428
159
290
449
175
316
481
334
551
789
1008
658
929
1224
48
44
120
44
122
133
175
312
49
134
247
41
162
36
312
419
848
1032
MPa
136
164
184
101
123
144
107
130
149
65
81
93
99
94
107
118
122
128
176
107
150
160
114
136
162
135
166
158
145
151
235
255
228
239
flats
Department of Civil Engineering
Research Report No R845
191
April 2005
AS 4600 (1996)
f u /f y f n,4600 /f y f u /f n,4600
0.52
0.63
0.71
0.39
0.47
0.55
0.41
0.50
0.57
0.25
0.31
0.36
0.38
0.36
0.41
0.45
0.47
0.49
0.68
0.41
0.58
0.61
0.44
0.52
0.62
0.52
0.64
0.61
0.56
0.58
0.90
0.98
0.88
0.92
NAS Appendix 1
PROPOSED
(2004)
f n,NAS /f y f u /f n,NAS f n,prop. /f y f u /f n,prop.
0.52
0.64
0.75
0.38
0.49
0.59
0.43
0.54
0.64
0.26
0.31
0.36
0.40
0.33
0.38
0.43
0.39
0.53
0.76
0.42
0.64
0.59
0.37
0.47
0.67
0.57
0.71
0.63
0.47
0.57
0.99
1.00
0.96
0.99
1.01
0.98
0.95
1.02
0.97
0.94
0.97
0.93
0.90
0.98
1.01
1.00
0.94
1.10
1.08
1.05
1.19
0.93
0.89
0.97
0.91
1.04
1.19
1.10
0.93
0.91
0.90
0.96
1.18
1.01
0.92
0.98
0.91
0.93
0.99
0.49
0.60
0.70
0.37
0.47
0.55
0.41
0.51
0.60
0.26
0.31
0.35
0.39
0.32
0.37
0.41
0.38
0.50
0.71
0.41
0.60
0.55
0.36
0.45
0.63
0.54
0.67
0.59
0.45
0.54
0.95
1.00
0.91
0.95
1.06
1.04
1.02
1.05
1.02
1.00
1.00
0.98
0.96
0.97
1.02
1.02
0.97
1.12
1.11
1.09
1.23
0.98
0.95
1.01
0.96
1.11
1.22
1.16
0.99
0.96
0.96
1.02
1.23
1.07
0.95
0.98
0.96
0.96
1.03
0.48
0.64
0.75
0.37
0.46
0.56
0.41
0.49
0.63
0.26
0.31
0.35
0.39
0.33
0.37
0.41
0.38
0.48
0.76
0.41
0.63
0.57
0.36
0.45
0.68
0.54
0.72
0.63
0.45
0.54
0.90
0.93
0.89
0.91
mean
1.10
0.98
0.95
1.04
1.03
0.98
1.01
1.02
0.90
0.96
1.02
1.02
0.97
1.11
1.11
1.09
1.23
1.02
0.89
1.01
0.91
1.09
1.21
1.17
0.92
0.97
0.89
0.97
1.25
1.07
1.00
1.06
0.99
1.02
1.03
st dev
0.0919
0.0840
0.0809
COV
0.089
0.085
0.078
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
Geometric Propertie
fy
Test ID
3Cr12_200_160_25_10_2_1
3Cr12_200_160_25_10_3_1
3Cr12_200_160_25_10_4_1
3Cr12_400_160_25_10_2_1
3Cr12_400_160_25_10_3_1
3Cr12_400_160_25_10_4_1
3Cr12_400_160_25_20_2_1
3Cr12_400_160_25_20_3_1
3Cr12_400_160_25_20_4_1
3Cr12_800_400_40_15_3_1
3Cr12_800_400_40_15_4_1
3Cr12_800_400_40_15_5_1
3Cr12_800_400_40_15_6_1
3Cr12_800_400_40_30_4_1
3Cr12_800_400_40_30_5_1
3Cr12_800_400_40_30_6_1
3Cr12_150_100_10_10_1_1
3Cr12_150_70_15_10_1_1
3Cr12_150_70_15_10_2_1
3Cr12_200_80_15_10_1_1
3Cr12_200_80_15_10_2_1
3Cr12_150_110_15_10_2_1
3Cr12_300_200_20_15_2_1
3Cr12_300_200_20_15_3_1
3Cr12_100_70_20_10_1_1
3Cr12_250_95_20_10_2_1
3Cr12_250_95_20_10_3_1
3Cr12_100_60_10_10_1_1
3Cr12_200_150_15_15_2_1
3Cr12_90_60_10_5_1_1
3Cr12_150_70_15_10_4_1
3Cr12_150_70_15_10_5_1
3Cr12_200_160_35_20_6_1
3Cr12_200_160_35_20_7_1
Ag
2
MPa mm
260 1177
260 1755
260 2327
260 1577
260 2355
260 3127
260 1626
260 2430
260 3227
260 5123
260 6769
260 8505
260 10186
260 6966
260 8691
260 10410
260
392
260
341
260
681
260
412
260
817
260
837
260 1542
260 2303
260
302
260
997
260 1485
260
262
260 1122
260
239
260 1327
260 1643
260 3721
260 4318
Test Results
Ac
A c /A g
f cr
mm2
%
5.3
8.1
10.8
4.0
6.0
8.0
3.9
5.8
7.8
2.8
3.7
4.6
5.6
3.6
4.5
5.4
4.0
4.6
9.2
3.8
7.7
7.5
4.1
6.1
5.2
6.3
9.5
6.0
5.6
6.6
18.9
23.9
15.2
17.8
MPa
114
182
256
63
102
149
78
124
178
30
43
56
70
48
63
79
67
119
270
77
177
149
59
95
201
141
231
174
95
142
666
901
567
687
63
141
251
63
141
251
63
141
251
141
251
393
565
251
393
565
16
16
63
16
63
63
63
141
16
63
141
16
63
16
251
393
565
770
λd
P u,t
fu
1.51
1.20
1.01
2.03
1.60
1.32
1.82
1.45
1.21
2.93
2.47
2.16
1.92
2.33
2.03
1.81
1.97
1.48
0.98
1.83
1.21
1.32
2.10
1.65
1.14
1.36
1.06
1.22
1.65
1.35
0.62
0.54
0.68
0.62
kN
163
296
448
161
296
462
178
324
495
340
562
806
1106
670
952
1257
49
44
125
45
126
137
178
321
50
137
255
42
167
37
347
479
918
1136
MPa
138
169
193
102
126
148
109
133
153
66
83
95
109
96
110
121
125
130
183
109
154
164
116
139
165
137
172
162
149
154
261
292
247
263
r/t=1
Department of Civil Engineering
Research Report No R845
192
April 2005
AS 4600 (1996)
f u /f y f n,4600 /f y f u /f n,4600
0.53
0.65
0.74
0.39
0.48
0.57
0.42
0.51
0.59
0.26
0.32
0.36
0.42
0.37
0.42
0.46
0.48
0.50
0.70
0.42
0.59
0.63
0.44
0.54
0.63
0.53
0.66
0.62
0.57
0.59
1.01
1.12
0.95
1.01
NAS Appendix 1
PROPOSED
(2004)
f n,NAS /f y f u /f n,NAS f n,prop. /f y f u /f n,prop.
0.52
0.64
0.75
0.38
0.49
0.59
0.43
0.54
0.64
0.26
0.31
0.36
0.40
0.33
0.38
0.43
0.39
0.53
0.76
0.42
0.64
0.59
0.37
0.47
0.67
0.57
0.71
0.63
0.47
0.57
na
na
0.96
na
1.03
1.01
0.99
1.03
0.99
0.97
0.98
0.95
0.92
1.00
1.03
1.02
1.03
1.12
1.11
1.08
1.22
0.95
0.93
0.99
0.93
1.07
1.21
1.14
0.94
0.92
0.92
0.99
1.21
1.03
na
na
0.99
na
1.02
0.49
0.60
0.70
0.37
0.47
0.55
0.41
0.51
0.60
0.26
0.31
0.35
0.39
0.32
0.37
0.41
0.38
0.50
0.71
0.41
0.60
0.55
0.36
0.45
0.63
0.54
0.67
0.59
0.45
0.54
na
na
0.91
na
1.08
1.07
1.06
1.06
1.03
1.03
1.02
1.00
0.98
0.99
1.04
1.04
1.07
1.14
1.14
1.12
1.25
1.00
0.99
1.03
0.99
1.14
1.24
1.19
1.00
0.98
0.99
1.05
1.26
1.10
na
na
1.04
na
1.07
0.48
0.64
0.75
0.37
0.46
0.56
0.41
0.49
0.63
0.26
0.31
0.35
0.39
0.33
0.37
0.41
0.38
0.48
0.76
0.41
0.63
0.57
0.36
0.45
0.68
0.54
0.72
0.63
0.45
0.54
na
na
0.89
na
mean
1.11
1.01
0.99
1.06
1.05
1.01
1.02
1.04
0.93
0.98
1.04
1.04
1.07
1.13
1.13
1.12
1.25
1.03
0.93
1.03
0.94
1.12
1.23
1.20
0.94
0.98
0.92
0.99
1.28
1.10
na
na
1.07
na
1.06
st dev
0.0956
0.0850
0.0808
COV
0.091
0.083
0.076
Finite Element Modelling and Design of Cold-Formed Stainless Steel Sections
Geometric Propertie
fy
Test ID
3Cr12_200_160_25_10_2_2.5
3Cr12_200_160_25_10_3_2.5
3Cr12_200_160_25_10_4_2.5
3Cr12_400_160_25_10_2_2.5
3Cr12_400_160_25_10_3_2.5
3Cr12_400_160_25_10_4_2.5
3Cr12_400_160_25_20_2_2.5
3Cr12_400_160_25_20_3_2.5
3Cr12_400_160_25_20_4_2.5
3Cr12_800_400_40_15_3_2.5
3Cr12_800_400_40_15_4_2.5
3Cr12_800_400_40_15_5_2.5
3Cr12_800_400_40_15_6_2.5
3Cr12_800_400_40_30_4_2.5
3Cr12_800_400_40_30_5_2.5
3Cr12_800_400_40_30_6_2.5
3Cr12_150_100_10_10_1_2.5
3Cr12_150_70_15_10_1_2.5
3Cr12_150_70_15_10_2_2.5
3Cr12_200_80_15_10_1_2.5
3Cr12_200_80_15_10_2_2.5
3Cr12_150_110_15_10_2_2.5
3Cr12_300_200_20_15_2_2.5
3Cr12_300_200_20_15_3_2.5
3Cr12_100_70_20_10_1_2.5
3Cr12_250_95_20_10_2_2.5
3Cr12_250_95_20_10_3_2.5
3Cr12_100_60_10_10_1_2.5
3Cr12_200_150_15_15_2_2.5
3Cr12_90_60_10_5_1_2.5
3Cr12_150_70_15_10_4_2.5
3Cr12_150_70_15_10_5_2.5
3Cr12_200_160_35_20_6_2.5
3Cr12_200_160_35_20_7_2.5
Ag
Ac
2
mm2
MPa mm
260 1157 157
260 1711 353
260 2262 565
260 1557 157
260 2311 353
260 3062 565
260 1607 157
260 2386 353
260 3148 628
260 5078 353
260 6739 628
260 8382 982
260 10069 1131
260 6888 628
260 8569 982
260 10234 1414
39
260
387
39
260
337
157
260
657
39
260
407
157
260
797
157
260
817
260 1522 157
260 2258 353
39
260
297
157
260
977
260 1441 353
39
260
257
260 1102 157
39
260
234
260 1268 534
260 1586 668
260 3545 1414
260 4078 1924
AS 4600 (1996)
Test Results
A c /A g
f cr
%
13.6
20.7
25.0
10.1
15.3
18.5
9.8
14.8
20.0
7.0
9.3
11.7
11.2
9.1
11.5
13.8
10.2
11.7
23.9
9.7
19.7
19.2
10.3
15.6
13.2
16.1
24.5
15.3
14.3
16.8
42.1
42.1
39.9
47.2
MPa
117
188
264
58
94
139
78
124
176
29
41
55
72
48
63
80
68
124
285
80
183
159
60
95
206
143
229
180
99
152
694
932
588
717
λd
P u,t
fu
1.49
1.18
0.99
2.11
1.66
1.37
1.82
1.45
1.22
2.99
2.51
2.17
1.90
2.32
2.03
1.80
1.96
1.45
0.96
1.81
1.19
1.28
2.08
1.66
1.12
1.35
1.07
1.20
1.62
1.31
0.61
0.53
0.66
0.60
kN
163
300
454
161
298
478
179
325
497
339
541
776
1110
674
953
1255
49
45
130
45
129
139
179
323
50
138
256
43
168
38
358
485
949
1184
MPa
141
175
201
103
129
156
111
136
158
67
80
93
110
98
111
123
127
135
198
111
161
170
118
143
169
141
178
168
153
160
282
306
268
290
f u /f y f n,4600 /f y f u /f n,4600
r/t=2.5
all tests
Department of Civil Engineering
Research Report No R845
193
April 2005
0.54
0.67
0.77
0.40
0.50
0.60
0.43
0.52
0.61
0.26
0.31
0.36
0.42
0.38
0.43
0.47
0.49
0.52
0.76
0.43
0.62
0.65
0.45
0.55
0.65
0.54
0.68
0.65
0.59
0.62
1.09
1.18
1.03
1.12
NAS Appendix 1
PROPOSED
(2004)
f n,NAS /f y f u /f n,NAS f n,prop. /f y f u /f n,prop.
0.52
0.65
0.75
0.37
0.47
0.57
0.43
0.54
0.63
0.25
0.30
0.36
0.41
0.33
0.38
0.43
0.40
0.54
0.78
0.43
0.65
0.61
0.37
0.47
0.68
0.58
0.71
0.64
0.48
0.59
na
na
na
na
1.03
1.03
1.02
1.08
1.06
1.05
1.00
0.97
0.96
1.02
1.02
1.00
1.04
1.14
1.12
1.09
1.23
0.96
0.98
0.99
0.96
1.08
1.22
1.17
0.96
0.94
0.96
1.01
1.22
1.04
na
na
na
na
1.05
0.50
0.61
0.70
0.36
0.45
0.54
0.41
0.51
0.60
0.25
0.30
0.35
0.39
0.33
0.37
0.42
0.38
0.51
0.73
0.41
0.61
0.57
0.36
0.45
0.64
0.54
0.67
0.60
0.46
0.56
na
na
na
na
1.09
1.10
1.10
1.11
1.11
1.12
1.04
1.03
1.02
1.02
1.03
1.03
1.07
1.16
1.15
1.14
1.27
1.02
1.05
1.03
1.02
1.15
1.25
1.22
1.02
1.00
1.03
1.07
1.28
1.10
na
na
na
na
1.09
0.48
0.65
0.75
0.36
0.44
0.53
0.41
0.49
0.63
0.26
0.30
0.35
0.40
0.33
0.37
0.41
0.38
0.49
0.77
0.41
0.65
0.59
0.36
0.44
0.68
0.54
0.72
0.64
0.45
0.57
na
na
na
na
mean
1.12
1.03
1.02
1.11
1.12
1.13
1.04
1.07
0.96
1.00
1.02
1.02
1.07
1.15
1.15
1.14
1.27
1.05
0.99
1.03
0.96
1.10
1.24
1.24
0.95
1.00
0.96
1.01
1.30
1.08
na
na
na
na
1.08
st dev
0.0944
0.0822
0.0795
COV
0.088
0.079
0.073
mean
1.05
1.02
1.07
st dev
0.0943
0.0854
0.0834
COV
0.090
0.084
0.078