Full-scale testing of sheathed cold-formed steel wall stud
systems in axial compression
Vieira, L., Schafer, B.W.
August 2009
A supplemental report for
AISI-COFS Project on
Sheathing Braced Design of Wall Studs
Abstract
A series of twelve full-scale walls (cold-formed steel studs with different sheathing
configurations) were tested under axial compression. This study concentrated on the
different kinds of sheathings attached to the side of the wall, specifically bare (no
sheathing), OSB or Gypsum. Wall sheathing combinations Bare-Bare, OSB-Bare, GypGyp, OSB-Gyp and OSB-OSB were tested. Results revealed that the attachment of
boards to the side of the wall can result in an increase of 91% of strength, when
comparing the case of Bare-Bare to that of OSB-OSB. It was found that the OSB-Bare
walls had no post-buckling reserve. In walls with symmetric sheathing (the OSB-OSB
and Gyp-Gyp cases), the failure mode observed was local buckling, and in both cases it
was identical and predictable. However, the asymmetric sheathing (OSB-Gyp) can result
in different failure modes in some studs.
1
Introduction
This report provides the result of recent research conducted at JHU in association
with AISI on sheathing braced design of walls. The project started with a full literature
review of research focused on sheathing braced design of cold-formed steel walls. An
experimental testing rig (machine) capable of testing full scale walls at different degrees
of freedom was developed. The machine design and construction were successfully
accomplished, and this report provides the results of a series of tests on cold-formed steel
walls, with different sheathing configurations, tested in axial compression.
The walls are composed of a cold-formed steel frame fastened to sheathing. The
sheathing is generally OSB, plywood and/or Gypsum and can play an important
structural role in bracing the cold-formed steel studs. The walls were designed based on
current design practice. The design of the walls was a result of the interaction between
the researchers and the AISI project monitoring task group.
1
2
Background
Winter’s (1960) research into bracing systems for cold-formed steel structures, was
the first to formalize the increase of stud capacity due to its connection to sheathing. In
1962 the AISI design code incorporated the design method developed by Winter, which
focused on flexural buckling of the studs, and a companion experimental method for
determining the lateral restraint stiffness of the connector and sheathing.
Winter (1960) developed a design method based on checking the strength and rigidity
of the connection. Details such as the maximum space between fasteners are checked to
provide adequate lateral bracing to the stud. The research covered only studs connected to
both sides and with the same material on both sides. The requirements, even though
rational, include arbitrary checks, such as considering the buckling length equal to twice
the fastener spacing (known as the “2a” assumption).
Based on a significant amount of work examining sheathing as a shear diaphragm
Simaan and Pekoz (1976) performed tests and developed a design method focusing on
shear deformations in sheathing. The Simaan and Pekoz (1976) design method was used
from 1980 to 2004 by the AISI specification, the method consider the contribution
provided by the board shear stiffness to the flexural, torsional, or torsional-flexural
buckling. The shear diaphragm action is translated to the stud via a rotational spring in
the same plane of the board. The ability of fasteners in traditional materials to provide
bracing support in this manner has been difficult to quantify or verify. As discussed in
Schafer et al. (2008) “The abandonment of the method by AISI in 2004 was justified
practically and theoretically”.
Miller (1994) tested fastener stiffness in Gypsum boards using the same procedure
proposed by Winter (1960). The tests, though limited in scope, provide more information
about the connection behavior and stiffness that is utilized in bracing wall studs. Fiorino
et al. (2006) and Okasha (2004) concentrated their research on the effect of cyclic load.
Iuorio et al. (2008) compiled the lateral and rotational stiffness values that have been
published to date.
AISI-COFS (2007) defines a design methodology based essentially on Winter (1960)
and therefore AISI (1962). Basically the method insures that connection stiffness and
spacing is enough to ensure that the limit state covered by the method is achieved,
regardless of the limit state. The method also does not provide a design approach for
asymmetric sheathing attached to the sides.
3
MDOF
The MDOF (Multi Degree of Freedom) testing rig also called the Big Blue Baby (or
BBB) has a set of seven hydraulic actuators (50kips/actuator). The actuators
concomitantly move a cruciform beam which is attached to the top of the specimen. The
bottom of the specimen is fixed to a steel beam which is connected to the floor.
Four actuators are mainly responsible to move the beam vertically, a fifth actuator can
move the beam horizontally applying a shear force to the wall, and the other two also
move the beam horizontally but perpendicularly to the last one. They are responsible to
twist the beam, thus correcting eventual misalignment.
2
The machine is controlled by a Labview program developed by the authors, the same
program also collects the data as load and displacement.
4
4.1
Wall stud
Design
The studs used in the test are 362S162-68’s (50 ksi) (SSMA/ASTM nomenclature)
throughout. Two types of sheathing are employed: OSB (7/16 in., rated 24/16, exposure
1) and Gypsum (½ in. Sheetrock). Number 6 screws (Simpson #6 x 1 5/8’’) were used to
connect to the Gypsum boards and number 8 screws (Simpson #8 x 1 15/16’’) to connect
to the OSB boards. (The detailed design is shown in Figure 36 and Figure 37).
To construct the walls it was necessary to build a jig. The jig was placed on the floor,
and the studs and tracks are aligned. The gap between the studs and tracks was closed
using a rod clamp nine feet long; the clamp was tightened until the gap was fully closed
(webs of the wall studs were bearing against the web of the track) and then the studs and
tracks were then connected, following the design in Figure 36. After all the studs and
tracks were connected the boards were placed over one side of the steel frame, and they
were marked and screwed following the design showed in Figure 37. After the
installation of the boards on one side, the wall is ready to be installed in the testing rig.
4.2
Installation inside the MDOF
At this point, the wall has a board on only one side, however, for several tests
sheathing was needed on both sides. To install the wall inside the MDOF, first the wall is
placed on the bottom beam, and then the wall is elevated over the bearing plates to insure
only the track and not the wall sheathing may bear, Figure 1. Figure 1 details how the
wall is connected to the top beam of the testing rig (blue), and a similar connection is
used on the bottom. Previous studies (Shifferaw et al. 2009) showed that if the wall
(boards plus studs) is allowed to bear against the loading beam, in addition to the stud, ,
there is an increase of 20% in the strength. In the actual building the continuity of boards
cannot be guaranteed, hence only the steel frame should be loaded, even though this
result in a lower tested capacity. Thus, the installation procedure is designed to insure that
the wall boards never engage in direct bearing.
The cruciform (top) beam is lowered until the distance between top track and the
beam can be measured with the gages available in the lab. The distance can be slightly
different due to misalignment and constructions flaws. To correct this plate that is
connected to the top is shimmed (again see Figure 1). The bearing plate is connected to
the track at every stud through a ½’’ inch bolt.
3
Shim
Plate
Figure 1 – Shim and plate.
4.3
Instrumentation
Position transducers and string pots were utilized to record supplemental
displacements. Depending on the test and the previous data collected, the position
transducer setup and location were changed. A record indicating where the position
transducers (PT) were located was created for each test. Five string pots and eleven
position transducers were installed in each test.
Four string pots were positioned on the top of the upper cruciform beam and one was
placed over the horizontal shear actuator. The string pot data is useful to confirm the
displacement of the actuators and to report eventual accommodation of the joint that
connects the actuator to the beam. To have a “fixed” reference point the string pots were
connected to the ceiling of the lab (which supports a mezzanine area which sees little if
any use and may be regarded as static), see Figure 2a.
The PTs were grouped in different formations. There is a single PT that measures the
out-of-plane displacement, Figure 2b, and a single PT that measures the displacement of
the web (local buckling of the web), Figure 2c. This PT sits on a T aluminum section that
is connected to the board, and the data is collected from the middle of the web, which is
3.5 inches up from the track. There are the groups of three PT that are able to capture
eventual twisting, local and global buckling; one of the PT is placed in the middle and the
other two (edge) are placed right after the outside corner web and flange, Figure 2d. The
groups of two PTs are placed at the same place, but they are only capable of capturing
twisting and global buckling, Figure 2e. In some tests a webcam was placed close to the
single PT that reads the displacement at the end of the stud, Figure 2c.
4
a) String Pot, checking actuator b) PT checking displacement out
displacement
of the wall plane
c) PT checking local buckling at
the end of stud and webcam
d) PT checking flexural, torsional
e) PT checking flexural
and local buckling
and torsional buckling
Figure 2 – String pot, position transducer and webcam installed.
5
Results and Discussion
The load–displacement curves and summary results for each test are provided in the
Appendix (Figure 42). A condensed summary of test results is shown in Table 1. As
expected the ascending order of values for peak load is Bare-Bare, OSB-Bare, Gyp-Gyp,
OSB-Gyp and OSB-OSB. The walls with Gypsum on both sides support more load than
the walls with OSB board on only one side, increasing the peak load 10%. The
attachment of boards on both sides, independently of which kind, (which will be
explained in the next section), is experimentally observed to provide post-buckling
reserve. If the wall has one side OSB and the other Gypsum, there is a boost in the peak
load of 9% compared to the Gyp-Gyp walls, and if both sides are covered with OSB there
is a boost of an additional 3% compared to the OSB-Gyp wall. This means that for the
walls with sheathing on both sides strength varies 12% from the weakest (Gyp-Gyp) to
the strongest (OSB-OSB), additionally relatively stable post-buckling and post-peak
response is observed and the wall gradually lose its capacity to support the load under
deformation controlled load application, unlike the OSB-Bare wall which abruptly fails.
It should be noted that in all cases there is a significant change in the peak load compared
to the Bare-Bare wall.
As shown, the coefficient of variation (COV) was small for the walls with boards on
both sides. Only in the OSB-Bare case there is a bigger variation due to the limit state
5
mode, which basically does not redistribute the load and the wall fails as soon as the first
stud fails.
Table 1 – Condensed summary of test results, ascending order of load.
Specimen
Peak Load (kips) Limit State
Mean
COV
2-BARE-BARE
56.33 FT and F
56.33
12-OSB-BARE
81.57 FT
87.67
0.06
1-OSB-BARE
89.21 FT
6-OSB-BARE
92.23 FT
7-GYP-GYP
94.07 Local
96.39
0.02
11-GYP-GYP
96.66 Local
4-GYP-GYP
98.44 Local
10-OSB-GYP
103.05 Local
104.92
0.02
3-OSB-GYP
105.71 Local
8-OSB-GYP
105.99 Local
5-OSB-OSB
106.04 Local
107.80
0.02
9-OSB-OSB
109.55 Local
5.1
5.1.1
Comments
1-OSB-BARE
Figure 3 shows a side view of the wall being tested as well as a close view of one
set of position transducers and a picture after the wall failed in flexural-torsional
buckling. Figure 4 shows the position transducers (PTs) displacement measurement plot
and their location. The horizontal axis in the graph is relative to the vertical displacement
of the actuators and the vertical axis is the displacement measured by the PTs. As it can
be seen in the “zoomed-in” section of the plot, PT number 7 is observed to have the
greatest increase in displacement, thus best indicating the failure of the wall. PT number
7 is the farthest PT from the board at stud number 7. The difference between PT 7 and 9
gives the rotation of the stud, and the difference between the imaginary line connecting
PT 7 and 9, compared to PT 8, gives the local buckling wave formed.
All of the PTs (Figure 4) followed the same trend (except number 10 which was
measuring the out of plane displacement and as it was predicted PT10 displaced from the
beginning of the test). At approximately 43 kips PT 7 showed an abrupt change in
direction and indicated failure of the wall, at stud 7, in twist. The wall failed in flexuraltorsional buckling with no post-buckling (or post-peak) reserve.
6
b) Position transducers
measuring displacement
a) Side view
c) Wall after test
Figure 3 – 1-OSB-BARE
1-OSB-BARE.txt
3
2.5
2
displacement (in)
1.5
Position Transducer 1
Position Transducer 2
Position Transducer 3
Position Transducer 4
Position Transducer 5
Position Transducer 6
Position Transducer 7
Position Transducer 8
Position Transducer 9
Position Transducer 10
Position Transducer 11
West
1
PT 10
0.5
S6
0
zoom plot
displacement (in)
-0.5
-1
-1.5
-2
0
0.2
S7
S8
S9
PT 9
PT 6
PT 3
PT 8
PT 5
PT 2
PT 7
PT 4
PT 1
S10
0
PT 11
-0.2
0.4
0.1
0.45
position (in)
0.2
0.3
0.5
0.4
position (in)
East
0.5
0.6
0.7
0.8
b) Location of position
transducers, upper view
a) Position transducers plot
Figure 4 – Position transducer for wall 1-OSB-BARE
5.1.2
2-BARE-BARE
Figure 5 shows the test set up and one of the studs undergoing unrestrained
flexural-torsional buckling, Figure 5c. All the positions transducers data is relative from a
fixed point, in this case the ground.
At around 45 kips position transducer number 7, which was placed at stud number
2 (S2), Figure 6, was the first stud to initiate buckling (see inset of Figure 6) in flexuraltorsional buckling. This was followed by stud 4, which also buckled in flexural torsional
buckling (see Figure 6b for stud locations in the wall). The peak load was reached at
56.33 kips, and although the other studs were already showing some deformation
according to the PT data, only after the peak were the other studs (S1, S3, S5) visually
buckling. Stud number 3 and 5 buckled in a pure flexural mode and all the others buckled
7
in a flexural-torsion mode. The test showed that at the length of 8 feet the stud can buckle
in either flexural-torsional or just flexural buckling; the buckling mode is strongly related
to the initial imperfections and how the load is redistributed after one of the studs starts
deforming in relation to the others. The studs were primarily loaded axially, but after they
have different deformations, the stress distribution changes and the stud can be loaded not
only in pure compression but also in bending.
As related in the report by Shifferaw et al. (2009) the single column test resisted
16 kips, if the results are extrapolated to the wall, it should theoretically be able to carry
65 kips (5 studs · 16 kips), however the wall carried only 56.33 kips. It is postulated that
this lower result is because of the lack of redistribution. The weakest of the 5 studs led to
the failure of the entire wall, and after the weakest stud failed the load had to be
redistributed to the other 4 studs – where it could not be carried, immediately leading to
full collapse of the wall.
a) Side view
b) Position Transducers
c) Flexural torsional
buckling
Figure 5 – 2-BARE-BARE
Another important observation is the behavior at the connection between the track
and stud, Figure 7. The track and studs are connected through two screws, one in each
flange. Those two points are fixed and they stay connected throughout the whole test. The
stud is free to lift off the track but it does not have enough strength to penetrate the track.
The restriction, even though unique to the test, can be considered a kind of partial fixity
against twist at the stud ends.
8
2-BARE-BARE.txt
3
2
displacement (in)
1
Position Transducer 1
Position Transducer 2
Position Transducer 3
Position Transducer 4
Position Transducer 5
Position Transducer 6
Position Transducer 7
Position Transducer 8
Position Transducer 9
Position Transducer 10
Position Transducer 11
West
PT 11
0
S1
-1
displacement (in)
-2
zoom plot
0.2
0
S2
S3
0.1
S4
PT 9
PT 6
PT 3
PT 8
PT 5
PT 2
PT 7
PT 4
S5
PT 1
East
-0.2
0.3
-3
0
PT 10
0.35
position (in)
0.2
0.4
0.3
position (in)
0.4
0.5
0.6
b) Location of position
transducers, upper view
a) Position transducers plot
Figure 6 – Position transducer for wall 2-BARE-BARE
b) Contact flange and track
a) Contact web and track
Figure 7 – Contact stud to track
5.1.3
3-OSB-Gyp
Figure 8 shows the test set up and the failure mode. The peak load was 105.71 kips
and the limit state that led to failure was local buckling at the ends, even though the studs
in the field (fasteners at every 12in.) twisted and stud number 14 finally failed in flexuraltorsional buckling. Figure 8b and c shows the cut in the Gypsum board formed by the
fasteners and Figure 8e shows the wall after removing one side of sheathing and the stud
which failed in flexural-torsional buckling.
The studs that were restrained by fasteners every 6 in (edge studs and middle studs)
failed by local buckling because the restrictive force was enough to prevent flexuraltorsional buckling. However one of the studs that was less restrained, stud 14, fasteners
every 12 in (field stud) had enough restriction from the OSB board but not from the
9
Gypsum board, and the fastener was able to tear off the Gypsum board and thus the stud
failed in flexural-torsional buckling,
Figure 9 shows the limit state that led to the failure, which was local buckling at the
end of stud 10. After one of the studs failed the stresses were redistributed and a finite
element model is needed to give more information about the failure’s development.
a) Side view
b) Screw tearing out the
board
c) Closer view of screw
tearing out the board
e) Wall opened after test
d) Local buckling
Figure 8 – 3-OSB-Gyp
10
West
PT 11
3-OSB-GYP.txt
1
0.8
0.6
0.4
displacement (in)
East
Position Transducer 1
Position Transducer 2
Position Transducer 3
Position Transducer 4
Position Transducer 5
Position Transducer 6
Position Transducer 7
Position Transducer 8
Position Transducer 9
Position Transducer 10
Position Transducer 11
b) Location of position transducers, upper view
PT 1
3.5in
PT 3
PT 2
0.2
0
PT 5
-0.2
South
S15
zoom plot
displacement (in)
-0.4
-0.6
-0.8
-1
0
S13
PT 4
S12
S11
North
PT 6
0
-0.02
-0.04
-0.06
-0.08
0.4
0.45
position (in)
0.5
PT 8
0.1
PT 7
S14
0.2
0.3
0.4
0.5
position (in)
0.6
0.7
a) Position transducers plot
0.8
0.9
PT 9
PT 10
1
c) Location of position transducers, side view
Figure 9 – Position transducers for wall 3-OSB-Gyp
5.1.4
4-Gyp-Gyp
Figure 10 shows pictures of the local buckling at the studs’ ends. The peak load
was 98.44 kips, Figure 10b and c shows the wall after being opened, where it is more
clear how the local buckling develops: first the flanges start opening until the yielding
lines at the web are created, at the same time that the stud is opening, a little higher up the
stud starts closing due to the need to keep supporting the load and find a new load path.
Another interesting thing shown in the pictures is how a “bubble” is formed on the
Gypsum board due to the flanges forcing the board. The implication is that when it
happens all the connections in this region are damaged and it cannot hold any load and
therefore is unable to keep restraining the stud.
a) Local buckling at the end
b) Wall opened after the test
c) Local buckling followed by
distortional buckling
Figure 10 – 4-Gyp-Gyp
11
Figure 11 shows in the zoomed plot that stud number 18, the stud in the middle of
the wall, was the one that led the failure due to local buckling at the bottom. However, it
is interesting to note that PT number 3, at the top of stud 17, was also showing signs of
local buckling at the same level of deformation. Although both locations had similar
deformations, likely stud number 18 had greater initial imperfections at the bottom and
this was what triggered the local failure. This will be confirmed later as extensive
measurements of the initial imperfections were conducted.
This test compared to the last test (OSB-Gyp) shows the implications inherent to
the asymmetry of the boards installed to the sides. In the last test, the different stiffness in
each side led to a failure mode other than only local buckling.
West
PT 11
East
b) Location of position transducers, upper view
4-GYP-GYP.txt
0.4
0.3
PT 1
3.5in
PT 3
PT 2
0.2
0
-0.1
Position Transducer 1
Position Transducer 2
Position Transducer 3
Position Transducer 4
Position Transducer 5
Position Transducer 6
Position Transducer 7
Position Transducer 8
Position Transducer 9
Position Transducer 10
Position Transducer 11
-0.2
-0.3
-0.4
-0.5
0
0.1
PT 5
South
displacement (in)
displacement (in)
0.1
0.2
0.3
zoom plot
S20
PT 7
S19
S18
PT 4
S17
S16
North
PT 6
0
-0.05
-0.1
0.6
0.4
0.7
position (in)
0.5
position (in)
0.6
0.8
0.7
a) Position transducers plot
0.8
0.9
1
PT 8
PT 9
PT 10
c) Location of position transducers, side view
Figure 11 – Position Transducer for wall 4-Gyp-Gyp
5.1.5
5-OSB-OSB
Figure 12 shows a side view followed by a picture of the same stud which failed
at the bottom in local buckling. The peak load was 106.04 kips and all studs failed in
local buckling at the bottom. In Figure 13 the zoomed-in plot shows that PTs number 10
and 9 were the first ones to capture the studs failing in local buckling, but stud 22 at the
bottom (PT 10) was the one that showed larger displacements. As stated before, the
symmetry of the boards installed prohibits the studs from twisting.
This test, compared to the previous test: 4-Gyp-Gyp, had a slightly higher peak
load, showing that the OSB board is able to hold axially more load than the Gypsum, but
both were able to restrain the stud thereby failed by local buckling. Hence, the difference
(between OSB-OSB and Gyp-Gyp) is not in how much the boards are able to restrain but
in how much loads the boards are able to carry axially even when not allowed to bear
directly, but still connected to the stud. Thus, some load sharing occurs, although in the
usual model (e.g. Winter 1960) it is presumed that the boards only provide elastic
restraint and do not themselves contribute to the load carrying capacity.
12
a) Side view
b) Local buckling at the
bottom
Figure 12 – 5-OSB-OSB
West
PT 11
East
b) Location of position transducers, upper view
5-OSB-OSB.txt
0.1
PT 1
3.5in
PT 3
PT 2
0
-0.2
PT 5
South
Position Transducer 1
Position Transducer 2
Position Transducer 3
Position Transducer 4
Position Transducer 5
Position Transducer 6
Position Transducer 7
Position Transducer 8
Position Transducer 9
Position Transducer 10
Position Transducer 11
-0.3
-0.4
-0.5
0
0.1
0.2
S25
PT 7
S24
S23
PT 4
displacement (in)
displacement (in)
-0.1
0.3
S22
S21
North
PT 6
zoom plot
0
-0.05
-0.1
0.6
0.4
0.65
position (in)
0.5
position (in)
0.6
0.7
0.7
a) Position transducers plot
0.8
0.9
1
PT 8
PT 9
PT 10
c) Location of position transducers, side view
Figure 13 – Position transducer for wall 5-OSB-OSB
5.1.6
6-OSB-BARE
This test was the one which presented the highest peak load of the OSB-BARE
tests, at 92.23 kips. What occurred during the test was that stud number 27 started to twist
towards the flange side instead of towards the lips side (usual side that buckles), which
probably was the key for the increased peak load. After the stud started to buckle towards
the flange side the stud had to reverse its initial twist before finally twisting to the lip side
and failing. However, stud number 29 led the failure mechanism in the wall, as can be
seen in the PT plot, Figure 15. Figure 14 shows the wall after being tested and the
13
position transducers measuring twisting and local buckling. As in all OSB-BARE tests
there was no post-buckling reserve and the failure was abrupt after the peak load.
If compared to the previous tests, this test has one more piece of data to help
understanding the tests. A PT was placed over the cruciform beam that loaded the
specimen. The discussion about the data collected from this PT is explained in detail after
the comments of each test, but the authors judged it to be necessary to separate specimen
axial deformation from the overall axial deformation (specimen and machine) and this is
the main importance of the position transducers.
c) Position transducers
capturing twist and local
buckling
b) Position transducers
capturing twist
a) Wall after test
Figure 14 – 6-OSB-BARE
West
PT 10
S30
S28
S29
S27
PT 3
PT 6
PT 9
PT 2
PT 5
PT 8
PT 1
PT 4
S26
PT 7
East
b) Location of position transducers, upper view
6-OSB-BARE.txt
0.2
0.1
PT 11
0
Top
-0.2
-0.3
-0.4
-0.5
-0.6
-0.7
-0.8
0
Position Transducer 1
Position Transducer 2
Position Transducer 3
Position Transducer 4
Position Transducer 5
Position Transducer 6
Position Transducer 7
Position Transducer 8
Position Transducer 9
Position Transducer 10
Position Transducer 11
0.1
0.2
displacement (in)
displacement (in)
-0.1
zoom plot
0
South
S30
S29
S28
S27
S26 North
-0.05
-0.1
0.35
0.3
0.4
position (in)
0.4
position (in)
0.45
0.5
0.6
0.7
0.8
Bottom
a) Position transducers plot
c) Location of position transducers, side view
Figure 15 – Positions transducers for wall 6-OSB-BARE
14
5.1.7
7-Gyp-Gyp
Figure 16a, b and c shows pictures after the test, after the wall was opened. It
should be noted that every stud failed in local buckling at the ends except for stud number
32 which failed in distortional buckling. In Figure 16b and c it is clear how the
distortional buckling happened; the fasteners tore out of the Gypsum board which was
not able to restrain the stud from buckling.
The peak load was 94.07 kips. Stud number 35 was the first to buckle locally, but
there was no PT in this place. Stud 34 was the second stud to buckle, which is clear in
Figure 17. After stud 35 buckled there was a drop in the load of the two actuators closer
to the stud but the other two actuators kept loading until the whole wall failed. Figure 16
also shows what the board looks like when the stud buckles locally; it causes the board
paper to separate forming the “bubbles” as shown.
a) Wall after test
b) Distortional buckling
c) Closer view of screw
tearing out the board
d) Bubble forming on the board due
to the stud buckling
e) Buckled flanges tearing
the board
Figure 16 – 7-Gyp-Gyp
Figure 17 also gives an additional piece of data that helps to understand the
results. This time two position transducers were placed over the cruciform beam on the
studs at the edges. The goal was know how much the cruciform beam rotates if each side
is loaded differently, which was the case. Even though it looks like the loading should be
the same, it is not, because the whole machine deforms and the side less loaded has less
machine deformation and at same time the actuator stroke stays constant, and therefore
the points in discussion displace differently.
15
West
PT 9
East
b) Location of position transducers, upper view
7-GYP-GYP.txt
0.5
PT 11
PT 10
3.5in
PT 2
PT 1
displacement (in)
0
-0.5
-1
0
0.1
0.2
displacement (in)
Position Transducer 1
Position Transducer 2
Position Transducer 3
Position Transducer 4
Position Transducer 5
Position Transducer 6
Position Transducer 7
Position Transducer 8
Position Transducer 9
Position Transducer 10
Position Transducer 11
0.3
PT 4
zoom plot
S31
0
S32
PT 3
-0.05
-0.1
0.5
0.4
0.6
position (in)
0.5
position (in)
PT 6
S33
S34
S35
PT 5
0.7
0.6
0.7
0.8
0.9
1
PT 7
a) Position transducers plot
PT 8
c) Location of position transducers, side view
Figure 17 – Position transducers for wall 7-Gyp-Gyp
5.1.8
8-OSB-Gyp
Test 8-OSB-Gyp failed in local buckling at a load of 105.99 kips. Figure 18
shows three different views of what the stud looks like when it fails in local buckling at
the ends and also show the displacement read by the position transducer. The zoom
(inset) plot in Figure 19 shows that PT2 (top of stud 39) and PT8 (bottom of stud 39)
were both moving the same amount, but likely the initial imperfection was determinant
and the stud buckled at the top of the stud. (Again the specific role of initial
imperfections will be investigated further in the future – as individual imperfection
measurements were completed for each stud.)
Another interesting fact is that the wall, even though it had asymmetric boards
installed on the sides, the studs did not show a considerable amount of twist.
a) LB view from the back of stud
b) LB view from the side
c) LB view from inside the stud
Figure 18 – 8-OSB-Gyp
16
West
PT 9
East
b) Location of position transducers, upper view
8-OSB-GYP.txt
0.2
PT 11
PT 10
0.1
0
-0.2
Position Transducer 1
Position Transducer 2
Position Transducer 3
Position Transducer 4
Position Transducer 5
Position Transducer 6
Position Transducer 7
Position Transducer 8
Position Transducer 9
Position Transducer 10
Position Transducer 11
-0.3
-0.4
-0.5
-0.6
-0.7
0
0.1
0.2
displacement (in)
displacement (in)
3.5in
PT 2
PT 1
-0.1
0.3
South
zoom plot
0.05
0
-0.05
0.6
0.4
PT 4
S36
S37
PT 6
S38
PT 3
0.65
position (in)
0.5
position (in)
0.6
S39
North
S40
PT 5
0.7
0.7
0.8
0.9
1
PT 7
a) Position transducers plot
PT 8
c) Location of position transducers, side view
Figure 19 – Position transducers for wall 8-OSB-Gyp
5.1.9
9-OSB-OSB
The 9-OSB-OSB wall failed in local buckling at the top where stud number 44 led
the failure. Similar to the previous test, both top and bottom position transducers at the
same stud had similar displacements but the top was the first to fail, Figure 21.
Figure 20 shows pictures after the wall was tested and opened. The yielding lines
were marked, as shown in the figure. Figure 20a shows the yielding line formed at the
web, Figure 20b shows the yielding lines at the flange. Two yielding lines formed at the
flange; one is a continuation of the local buckling failure in the web and the other, as
already commented before, is an attempt of the stud to keep supporting the load though
another load path.
b) Yielding lines on the flange
a) Yielding line on the web
Figure 20 – 9-OSB-OSB
17
West
PT 9
East
b) Location of position transducers, upper view
9-OSB-OSB.txt
0.1
PT 11
0
PT 10
-0.1
3.5in
PT 2
PT 1
-0.3
-0.4
-0.5
-0.6
-0.7
-0.8
-0.9
-1
0
Position Transducer 1
Position Transducer 2
Position Transducer 3
Position Transducer 4
Position Transducer 5
Position Transducer 6
Position Transducer 7
Position Transducer 8
Position Transducer 9
Position Transducer 10
Position Transducer 11
0.1
0.2
displacement (in)
displacement (in)
-0.2
0.3
zoom plot
S41
0.4
S42
PT 3
-0.05
0.6
PT 4
South
0
PT 6
S43
S44
S45
North
PT 5
0.65
0.7
position (in)
0.5
position (in)
0.6
0.7
0.8
0.9
1
PT 7
a) Position transducers plot
PT 8
c) Location of position transducers, side view
Figure 21 – Position Transducers for wall 9-OSB-OSB
5.1.10 10-OSB-Gyp
The wall 10-OSB-Gyp had a peak load of 103.05 kips. Stud 49, which failed
locally at the top, led the wall to failure, Figure 23. Figure 22a shows the board over stud
49 and Figure 20b shows the same stud after the board was removed. An interesting
observation occurred with stud 47 (field stud, connected every 12 in.); the stud did not
buckle only locally at the end like all the others, it also presented distortional buckling,
Figure 22c. Figure 22d shows the board torn out by the fastener. The distortional
buckling failure probably happened because of the asymmetry of the boards installed; the
OSB board and Gypsum were restraining with different stiffness which led the fastener
tearing off the Gypsum board since the OSB was providing a higher stiffness at the same
location.
18
a) Buckled flanges tearing the
board
b) Local buckling at the top
c) Local buckling followed by
distortional buckling
d) Gypsum was torn out in order
to restrain the stud
Figure 22 – 10-OSB-Gyp
West
PT 9
East
b) Location of position transducers, upper view
10-OSB-GYP.txt
PT 11
0.2
3.5in
PT 2
PT 1
-0.2
-0.4
-0.6
-0.8
0
Position Transducer 1
Position Transducer 2
Position Transducer 3
Position Transducer 4
Position Transducer 5
Position Transducer 6
Position Transducer 7
Position Transducer 8
Position Transducer 9
Position Transducer 10
Position Transducer 11
0.1
0.2
displacement (in)
displacement (in)
0
PT 10
0.3
South
zoom plot
0
PT 4
S46
S47
PT 3
PT 6
S48
S49
S50
North
PT 5
-0.05
-0.1
0.65
0.4
0.7
position (in)
0.5
position (in)
0.75
0.6
0.7
0.8
0.9
1
PT 7
a) Position transducers plot
PT 8
c) Location of position transducers, side view
Figure 23 – Position transducer for wall 10-OSB-Gyp
5.1.11 11-Gyp-Gyp
19
The wall 11-Gyp-Gyp failed in local buckling at the bottom at a load of 96.66
kips, Figure 24. PT 7 and 8 captured the wall failing in local buckling at the same time,
Figure 25. Even though it is not possible to show in a written report the video from the
webcam, for the first time the webcam installed inside the wall was able to capture the
waves forming on the web and evolving to a local failure and yielding.
a) View from the back of studs, local
b) View from the front of studs
buckling on the bottom
Figure 24 – 11-Gyp-Gyp
West
PT 9
East
b) Location of position transducers, upper view
11-GYP-GYP.txt
PT 11
0.1
PT 10
0
3.5in
PT 2
PT 1
-0.1
-0.3
-0.4
-0.5
-0.6
-0.7
-0.8
-0.9
0
Position Transducer 1
Position Transducer 2
Position Transducer 3
Position Transducer 4
Position Transducer 5
Position Transducer 6
Position Transducer 7
Position Transducer 8
Position Transducer 9
Position Transducer 10
Position Transducer 11
0.1
0.2
PT 4
South
displacement (in)
displacement (in)
-0.2
0.3
zoom plot
S51
S52
PT 3
0
PT 6
S53
S54
S55
North
PT 5
-0.05
-0.1
0.65
0.4
0.7
position (in)
0.5
position (in)
0.6
0.75
0.7
a) Position transducers plot
0.8
0.9
1
PT 7
PT 8
c) Location of position transducers, side view
Figure 25 – Position transducers for wall 11-Gyp-Gyp
5.1.12 12-OSB-BARE
The wall 12-OSB-BARE failed in flexural-torsional buckling at a load of 81.57
kips, Figure 26. As in all OSB-BARE walls there was no post buckling reserve and the
failure was abrupt after the peak load. In Figure 27 is clear that stud number 59 first
started to twist and led all the others.
20
Figure 26 – 12-OSB-BARE
West
PT 10
S57
S56
S58
S59
PT 6
PT 9
PT 2
PT 5
PT 8
PT 1
PT 4
PT 3
S60
PT 7
East
b) Location of position transducers, upper view
12-OSB-BARE.txt
PT 11
0.2
Top
0.1
-0.2
-0.3
-0.4
-0.5
0
Position Transducer 1
Position Transducer 2
Position Transducer 3
Position Transducer 4
Position Transducer 5
Position Transducer 6
Position Transducer 7
Position Transducer 8
Position Transducer 9
Position Transducer 10
Position Transducer 11
0.1
displacement (in)
displacement (in)
0
-0.1
0.2
South
zoom plot
0
S56
S57
S58
S59
S60
North
-0.05
-0.1
0.3
0.35
position (in)
0.3
0.4
0.4
0.5
0.6
0.7
position (in)
Bottom
a) Position transducers plot
c) Location of position transducers, side view
Figure 27 – Position transducers for wall 12-OSB-BARE
5.2
Difficulties in collecting and processing the data
Although the difficulty in assessing the axial wall deformation was already
commented on, the authors feel that it should now be explained in better detail, Figure 28
compares all the methods. Usually the position is considered the average of all the builtin LVDTs from the four vertical actuators (plot 11-Gyp-Gyp.txt), nonetheless the
position plotted is actually the displacement of machine and specimen. In order to isolate
only the specimen deformation, two position transducers where placed over the cruciform
21
beam on the edge studs, here called 11-Gyp-Gyp-PT10 and PT11. It can be noted that
those two position transducers give different values. This is because each side of the
specimen does not necessarily have the same deformation. The wisest method would be
plot load versus the average of both position transducers.
The curves were also compared to the single column test (25-Gyp-Gyp). To do this,
the load supported by the wall was divided by five to compare to the single column test.
The single column test, even though it was also tested in the MDOF machine, had less
load applied (only one column) and so less machine deformation, and as it can be seen
the position data is closer to the PT data values. This information is very important to
compare to a FE model. The difference of deformation has to be considered. For
example, at the peak load the position (machine plus specimen) is close to double the
position acquired from the position transducer.
Figure 42 shows the load displacement curves for all the walls tested. The position in
the plot is that of the machine plus wall, since not every test had a position transducer
measuring the vertical displacement.
GYP-GYP 8feet column and w all, w hat is the best variable to plot against load
20
load (kip)
15
10
5
25-GYP-GYP-64S8LTSP-8-T-S-P.dat
11-GYP-GYP.txt
11-GYP-GYP-PT10
11-GYP-GYP-PT11
11-GYP-GYP-mean
0
0
0.2
0.4
0.6
position (in)
0.8
1
Figure 28 – Position assessment.
Another difficulty encountered is in post-processing the data. Figure 29 shows
one example of how the curve fitting was done for a curve of load versus position. The
MDOF machine has a time step control, which means that the actuators move at a
determined speed and stop until it is time to initialize the next time step, and it also does
not start the next time step if one of the actuators did not reach the target position. What
occurs is that during every time step the actuators load a small amount and wait for the
next time step. When the rough data is plotted there is a small amount of noise and a
22
relaxation of the load, a new curve is traced from the rough data and this curve is an
average approximation, but the approximation is small enough to be insignificant.
Figure 29 – Curve fitting of raw load-displacement data
5.3
Coupon Test
Columns and tracks where chosen randomly from the single column specimens
already tested, since they used the same material. Steel plates where roughly cut from the
web and outside the yielded area, the dimension entered in the CNC milling machine to
precisely cut the coupon specimen is showed in Figure 30.
0.38 in.
0.38 in.
1.97 in.
3.18 in.
1.97 in.
0.492 in. *
0.79 in.
R=0.55 in.
gauge length
1.97 in.
*nominal, actual dimension will vary slightly
Figure 30 – Tensile coupon dimensions (Moen (2008)).
23
After cutting the specimens they were immersed in hydrochloride acid,
concentration of 15% per volume (85% distillated water and 15% hydrochloride acid) for
10 minutes. The hydrochloride bath is necessary to remove the zinc coating so that the
specimen dimensions could be measured without the coating. Figure 31 shows the test set
up and one of the specimens after being tested.
Two methods were used to find the yielding stress, the 0.2% offset method and
the autograph method. The 0.2% method considers the yielding stress equal to the stress
where the stiffness line (Young’s modulus = E = 29500ksi) is offset from the origin to the
0.2% engineering strain intersects with the stress-strain curve. The autograph method
uses the same offset technique but the lines are offset to 0.4% and 0.8% of the strain and
the yielding stress is the average value in the range between the two lines.
All the data is presented in Table 2. The authors consider the 0.2% offset method
the most appropriate method to find the yielding stress for the steel used in the studs
because there is no yielding plateau, Figure 38 and Figure 39. However, the steel used in
the track has the yielding plateau and therefore the autograph method is more
appropriate; if the 0.2% method is used to define the yielding stress the value will be a
peak value, Figure 40 and Figure 41.
a) Test set-up
b) Coupon failed
Figure 31 – Tensile coupon test.
6
6.1
General discussions
Bare-Bare
The Bare-Bare wall had its importance in setting a lower bound for the load, Figure
32. In the same figure the load curve from the OSB-OSB walls is also plotted, which
shows the upper bound for the loads. The Bare-Bare walls were also important in helping
to understand the end conditions and how the track restrains the stud. As a next step in
this research the test will be helpful to calibrate the FE models.
The Bare-Bare wall was also important to keep aware of how the load distribution
changes during the test; axial compression versus compression and bending. During the
test the load distribution changes when there is a difference in the behavior of one stud. It
24
was evident in this test because some studs failed in flexural-torsional buckling while
others in just flexural buckling, which is evidence of change in the applied load.
Comparison betw een OSB-OSB and BARE-BARE w alls
120
2-BARE-BARE.txt
5-OSB-OSB.txt
9-OSB-OSB.txt
100
load (kip)
80
60
40
20
0
0
0.2
0.4
0.6
position (in)
0.8
1
1.2
Figure 32 – Bare-Bare
6.2
OSB-Bare
The OSB-Bare walls, Figure 33, were important since they did not have postbuckling reserve, the failure was always abrupt. In order to not allow an abrupt failure,
the common practice is the use of a steel strap to brace the studs. Supposedly the strap
would restrain the studs to each other and the failure would not be determined by
individual failure but by failure of the whole system. Given the nature of the
observations, the adequacy of such a strap is unclear.
25
Comparison betw een OSB-BARE w alls
100
1-OSB-BARE.txt
6-OSB-BARE.txt
12-OSB-BARE.txt
90
80
70
load (kip)
60
50
40
30
20
10
0
0
0.1
0.2
0.3
0.4
0.5
position (in)
0.6
0.7
0.8
Figure 33 – OSB-Bare and OSB-Bare
6.3
Gyp-Gyp
The walls with symmetric boards attached to the sides, Gyp-Gyp and OSB-OSB,
were very predicable, always failing by local buckling at the ends. The local failure at the
ends is most likely a result of the way that the wall is assembled; the ends of the stud had
to be squeezed to fit between the flanges of the track which can create considerable
“fabrication” initial imperfections at the ends (as opposed to “manufacturing”
imperfections).
26
Comparison betw een GYP-GYP w alls
4-GYP-GYP.txt
100
7-GYP-GYP.txt
11-GYP-GYP.txt
load (kip)
80
60
40
20
0
0
0.2
0.4
0.6
position (in)
0.8
1
Figure 34 – Gyp-Gyp
6.4
OSB-Gyp
The OSB-Gyp requires special attention since the asymmetric boards attached to
the sides had an effect in the failure mode, but it needs to be quantified. The first failure
mode encountered was local buckling at the ends, but the field studs had different failure
modes; not only can the asymmetry be responsible for that, but also how the load
distribution acts during the test. The load versus position curve for all the tests are
compared in Figure 35.
27
Comparison betw een OSB-GYP w alls
3-OSB-GYP.txt
8-OSB-GYP.txt
10-OSB-GYP.txt
100
load (kip)
80
60
40
20
0
0
0.2
0.4
0.6
position (in)
0.8
1
Figure 35 – OSB-Gyp
6.5
OSB-OSB
The load versus position curves are compared in Figure 32. The important
conclusion about the OSB-OSB tests is seen when the results are compared with the GypGyp test. Both tests used fully the resistance of the studs, which in both cases failed in
local buckling, but the actual board is what bears more load. OSB, as it was supposed to
be, is able to carry more load and therefore increase the peak load by a small amount.
7
Conclusions
Several conclusions were already commented above, the main conclusions are listed
below: i) how the end conditions behave, ii) the OSB-Bare failure with no post-buckling
reserve, iii) the implications of asymmetric boards and iv) the similarity in the failure
mode and resistance when the boards attached are symmetric. The data collected from
this report as well as the translational stiffness report and the single column test report are
part of the evolution of the larger project that aims to propose a comprehensive and
reliable design method for sheathing-braced walls. Based on the tests results future
research will have concrete data from actual tests to reinforce final conclusions.
8
Future Research
28
The development of a finite element model will be necessary to explore and better
understand the sheathing braced walls. Several questions still remain, such as how the
load distributes, the impact of initial imperfection, and expected reliability.
9
Acknowledgments
The authors are indebted to AISI (American Iron and Steel Institute) for the grants
awarded, Simpson Strong-Tie for the fasteners donated and Nickolay Logvinovsky,
Lauren Thompson and Hannah Blum for all the help and determination during the lab
tests.
10 References
Miller, T., Peköz, T. (1994). “Behavior of Gypsum-Sheathed Cold-Formed Steel Wall
Studs.” ASCE, Journal of Structural Engineering. 120 (5) 1644-1650.
Moen, C. D. (2008). “Direct Strength Design of Cold-Formed Steel Members with
Perforations” Ph.D. Dissertation, Johns Hopkins University, Baltimore, MD.
Shifferaw, Y., Vieira, L., Schafer, B.W. (2009). “Compression Testing of Single Column
Studs with Sheathing Configurations” AISI Progress Report.
Schafer, B. W. , Vieira, L., Iourio, O. (2008) “Notes on AISI Design Methods for
Sheating Braced Design pf Walls Studs in Compression”, Progress Report to AISI-COFS
Project Oversight Committee.
Simaan, A, (1973). “Buckling of Diaphragm-Braced Columns of Unsymmetrical Sections
and Application to Wall Studs Design.” Ph.D. Dissertation, Cornell University, Ithaca,
NY.
Simaan, A. Peköz, T. (1976). “Diaphragm Braced Members and Design of Wall Studs.”
ASCE, Journal of the Structural Division, 102 (ST1) 77-92.
Winter, G. (1960). “Lateral Bracing of Beams and Columns.” ASCE Transactions, Paper
No. 3044, per footnote “published in 1958 in the Journal of the Structural Division”.
29
APPENDIX
953 16 or 95.1875
72.0
48.0
24.0
13
13
Section: 362S162-68
16
or 0.8125
233 16 or 23.1875
24.0
16
or 0.8125
233 16 or 23.1875
24.0
Section: 362T125-68
1.625
1.250
0.500
3.625
3.625
0.0713
0.0713
(in.)
943 8 or 94.375
713 16 or 71.1875
ds
473 16 or 47.1875
15 8 or 1.625
233 16 or 23.1875
13
16
24.0
233 16 or 23.1875
24.0
13
or 0.8125
5
8
16
or 0.8125
or 0.625
24.0
24.0
48.0
96.0
(in.)
Figure 36 – Steel frame detailing
30
3.0
6.0
3.0
6.0
6.0
6.0
6.0
6.0
6.0
2.0
4.0
10.0
6.0
6.0
12.0
6.0
Section: 362S162-68
6.0
Section: 362T125-68
1.625
12.0
1.250
6.0
0.500
6.0
3.625
12.0
3.625
6.0
0.0713
0.0713
6.0
(in.)
12.0
6.0
6.0
12.0
6.0
6.0
12.0
6.0
13
32
or 0.40625
6.0
10.0
13
5
8
16
or 0.8125
or 0.625
24.0
24.0
48.0
96.0
(in.)
Figure 37 – Details of connection between boards and steel frame
31
Table 2 – Data from coupon test and measurements
t bare (in.)
Stud
mean
COV
Track
mean
COV
b bare (in.)
tcoated-average
Specimen
(in.)
1S4L
0.0675
2S4L
0.0675
3S4L
0.0675
1S6L
0.0675
2S6L
0.0675
6S6L*
0.0675
7S6L*
0.0675
61S8L
0.0675
0.0675
0.000
0.0655
0.065
0.0655
0.0655
0.066
0.0655
0.0655
0.0655
0.0655
0.0655
0.0655
0.066
0.0655
0.0655
0.0655
0.0655
0.066
0.0655
0.066
0.0655
0.0655
0.0655
0.0655
0.0655
1T-1S8L*
1T-2S8L*
0.078
0.0775
0.078
0.078
0.077
0.078
0.08
0.08
0.08
0.000
t1
t2
t3
taverage
b1
b2
b3
0.0657
0.0653
0.0657
0.0657
0.0657
0.0655
0.0655
0.0655
0.0656
0.003
0.487
0.4865
0.487
0.487
0.4875
0.487
0.487
0.487
0.487
0.4875
0.4875
0.487
0.487
0.487
0.4875
0.4875
0.487
0.487
0.487
0.4875
0.497
0.4865
0.487
0.4865
0.0777
0.0778
0.0778
0.005
0.487
0.487
0.4875
0.487
0.488
0.488
0.4870
0.4870
0.4872
0.4872
0.4905
0.4868
0.4872
0.4870
0.4875
0.004
fy (0.2% offset)
(ksi)
55.9
54.7
55.6
54.9
55.3
55.3
56.4
56.2
55.54
0.011
fy (autographic method)
(ksi)
57.4
56.1
57.1
56.1
56.4
56
56.7
57
56.6
0.009
0.4875
0.4873
0.4874
0.001
70.7
70.7
70.70
0.000
68.5
69.7
69.1
0.012
baverage
fu (ksi)
Δu (in./in.)
79.38
77.59
78.92
77.99
78.78
79.21
79.69
79.48
78.88
0.009
0.17
0.18
0.16
0.16
0.20
0.24
0.24
0.21
0.19
0.163
77.64
78.39
78.02
0.007
0.24
0.24
0.24
0.001
* Specimen that failed inside the gauge length (length covered by extensometer)
Δu (in./in.) - the big value of COV for Δu is due to the position of the extensometer compared to where it fails. If the crack is in the gauge length, Δu is bigger than if it is outside the gauge length.
32
2S4L.txt
1S6L.txt
80
80
80
80
70
70
70
70
60
50
40
fy (0.2% offset)=55.9 ksi
30
20
60
50
40
fy (0.2% offset)=54.7 ksi
30
20
60
50
40
20
10
10
0
0
0
0.05
0.1
0.15
0.2
Engineering Strain,(in./in.)
0.25
0
0.05
0.1
0.15
0.2
Engineering Strain,(in./in.)
0.25
fy (0.2% offset)=55.6 ksi
30
10
0
Axial Tensile Stress (ksi)
90
Axial Tensile Stress (ksi)
90
2S6L.txt
60
50
40
20
10
0
6S6L.txt
0.05
0.1
0.15
0.2
Engineering Strain,(in./in.)
0
0.25
80
80
80
70
70
70
70
40
fy (0.2% offset)=55.3 ksi
30
20
10
0
50
40
fy (0.2% offset)=55.3 ksi
30
20
10
0
0.05
0.1
0.15
0.2
Engineering Strain,(in./in.)
0.25
0
Axial Tensile Stress (ksi)
80
Axial Tensile Stress (ksi)
90
60
60
50
40
fy (0.2% offset)=56.4 ksi
30
20
10
0
0.05
0.1
0.15
0.2
Engineering Strain,(in./in.)
0.25
0
0.05
0.1
0.15
0.2
Engineering Strain,(in./in.)
0.25
61S8L.txt
90
50
0
7S6L.txt
90
60
fy (0.2% offset)=54.9 ksi
30
90
Axial Tensile Stress (ksi)
Axial Tensile Stress (ksi)
3S4L.txt
90
Axial Tensile Stress (ksi)
Axial Tensile Stress (ksi)
1S4L.txt
90
60
50
40
fy (0.2% offset)=56.2 ksi
30
20
10
0
0.05
0.1
0.15
0.2
Engineering Strain,(in./in.)
0.25
0
0
0.05
0.1
0.15
0.2
Engineering Strain,(in./in.)
0.25
Figure 38 – Yielding stress determined using 0.2% offset method (Studs)
33
2S4L.txt
1S6L.txt
80
80
80
80
60
40
fy (Autographic Method)=57.4 ksi
0
60
40
fy (Autographic Method)=56.1 ksi
20
0
0.05
0.1
0.15
0.2
Engineering Strain (in./in.)
0
0.25
60
40
fy (Autographic Method)=57.1 ksi
Axial Tensile Stress (ksi)
100
Axial Tensile Stress (ksi)
100
20
20
0
2S6L.txt
0.05
0.1
0.15
0.2
Engineering Strain (in./in.)
0
0.25
60
40
fy (Autographic Method)=56.1 ksi
20
0
6S6L.txt
0.05
0.1
0.15
0.2
Engineering Strain (in./in.)
0
0.25
80
80
80
80
40
fy (Autographic Method)=56.4 ksi
20
0
40
fy (Autographic Method)=56 ksi
20
0
0.05
0.1
0.15
0.2
Engineering Strain (in./in.)
0.25
0
60
40
fy (Autographic Method)=56.7 ksi
Axial Tensile Stress (ksi)
100
Axial Tensile Stress (ksi)
100
60
20
0
0.05
0.1
0.15
0.2
Engineering Strain (in./in.)
0.25
0
0.05
0.1
0.15
0.2
Engineering Strain (in./in.)
0.25
61S8L.txt
100
60
0
7S6L.txt
100
Axial Tensile Stress (ksi)
Axial Tensile Stress (ksi)
3S4L.txt
100
Axial Tensile Stress (ksi)
Axial Tensile Stress (ksi)
1S4L.txt
100
60
40
fy (Autographic Method)=57 ksi
20
0
0.05
0.1
0.15
0.2
Engineering Strain (in./in.)
0.25
0
0
0.05
0.1
0.15
0.2
Engineering Strain (in./in.)
0.25
Figure 39 – Yielding stress determined using autographic method (Studs)
34
1T-2S8L.txt
80
80
70
70
60
60
Axial Tensile Stress (ksi)
90
50
40
fy (0.2% offset)=70.7 ksi
30
50
40
20
10
10
0
0
0.05
0.1
0.15
Engineering Strain,(in./in.)
0.2
fy (0.2% offset)=70.7 ksi
30
20
0
0.25
0
0.05
0.1
0.15
Engineering Strain,(in./in.)
0.2
0.25
Figure 40 – Yielding stress determined using 0.2% offset method (Tracks)
1T-1S8L.txt
1T-2S8L.txt
100
100
90
90
80
80
70
70
Axial Tensile Stress (ksi)
Axial Tensile Stress (ksi)
Axial Tensile Stress (ksi)
1T-1S8L.txt
90
60
50
40
fy (Autographic Method)=68.5 ksi
30
60
50
40
20
20
10
10
0
0
0.05
0.1
0.15
Engineering Strain (in./in.)
0.2
fy (Autographic Method)=69.7 ksi
30
0.25
0
0
0.05
0.1
0.15
Engineering Strain (in./in.)
0.2
0.25
Figure 41 – Yielding stress determined using autographic method (Tracks)
35
1-OSB-BARE.txt
2-BARE-BARE.txt
100
4-GYP-GYP.txt
20
0.2
0.4
position (in)
0.6
max P = 98.44 kip
80
80
40
30
60
40
40
10
20
20
0
0.2
5-OSB-OSB.txt
0.4
position (in)
0
0.6
0
0.2
6-OSB-BARE.txt
0.4
0.6
0.8
position (in)
0
1
0.8
1
8-OSB-GYP.txt
max P = 92.23 kip
80
max P = 94.07 kip
80
max P = 105.99 kip
40
60
40
20
20
0
0.2
0.4
0.6
0.8
position (in)
0
1
load (kip)
60
load (kip)
80
load (kip)
80
60
40
20
0
0.2
9-OSB-OSB.txt
0.4
0.6
position (in)
0
0.8
20
0
0.2
10-OSB-GYP.txt
0.4
0.6
0.8
position (in)
0
1
60
40
40
20
20
20
0.5
position (in)
1
0
max P = 81.57 kip
60
40
0
1
60
load (kip)
load (kip)
60
max P = 96.66 kip
80
80
80
0.4
0.6
0.8
position (in)
80
100
max P = 103.05 kip
0.2
12-OSB-BARE.txt
100
max P = 109.55 kip
0
11-GYP-GYP.txt
120
100
60
40
0
0.2
0.4
0.6
0.8
position (in)
1
load (kip)
load (kip)
0.4
0.6
position (in)
100
max P = 106.04 kip
load (kip)
0.2
100
100
0
0
7-GYP-GYP.txt
100
0
60
20
0
0.8
max P = 105.71 kip
load (kip)
40
max P = 56.33 kip
load (kip)
60
0
100
100
50
max P = 89.21 kip
load (kip)
load (kip)
80
0
3-OSB-GYP.txt
60
0
40
20
0
0.2
0.4
0.6
0.8
position (in)
1
0
0
0.2
0.4
position (in)
0.6
Figure 42 – Curve load displacement
36