Square Aluminum Tubes Bent about a Diagonal Axis
Dr. Craig C.
Dr
C Menzemer
Mr. Dave White
The University of Akron
In conjunction with HAPCO
July 2009
Objectives
j
y
Review test data for aluminum tubes
y
S
Summarize
i steps used
d in
i data
d analysis
l i
y
Aluminum Design Manual – terminology, limit states, allowable
stresses
y
Results of data analysis
y
Design Recommendations
Test Data – Square
q
Aluminum Tubes
y
Square tubes with rounded corners; 4 x 0.125 in; 5 x 0.188 in; 6 x
0 25 in,
0.25
in 6.625
6 625 x 0.25
0 25 in
y
Square tubes with sharp corners; 6 x 0.188; 6 x 0.25 in
y
Alloy 6063-T6, welded with 4043 filler and solution heat treated to
T6 condition
d
y
Tubes randomly taken from different lots of material
y
Test specimen
p
lengths
g varied from 16 – 27 ft
y
Square tubular members tested in bending about the diagonal and
geometric axis: 36 tests conducted, 6 on each type
y
29 failed by local buckling,
buckling 2 rounded corner tubes by tensile failure
in HAZ, 4 in casting/weld (3 in sharp corner tube - diagonal), 1
through loading hole
y
Average test results reported
Aluminum Tube Test SetSet-Upp
Test Results - Continued
Tube Size
Test
Direction
Average Moment (ft-lbs)
Failure
4 x 0.125
Diagonal
5909
Buckle
4 x 0.125
Geometric
6131
Buckle
5 x 0.188
0 88
Diagonal
13185
3 8
Buckle
5 x 0.188
Geometric
13024
Buckle
6 x 0.188
Diagonal
23657
Buckle
6 x 0.188
Geometric
24479
Buckle/Hole
6 x 0.25
Diagonal
28310
Buckle
6 x 0.25
0 25
Geometric
27840
Buckle
6.625 x 0.25 Diagonal
31340
Tension
6.625 x 0.25 Geometric
31860
Buckle/Tension
6 x 0.25 S
Diagonal
30490
Base/Weld
6 x 0.25 S
Geometric
32600
Buckle
Analysis
y Procedure and Background
g
y
y
y
y
y
y
y
Evaluate interaction equation and reduce to simple form for specific
test co
conditions
to s
Calculate slenderness of tube elements
Evaluate buckling coefficients for 6063-T6 for minimum guaranteed
yyield strength
g and average
g measured yield
y
strengths
g
Calculate allowable stress as smallest of tension in element bending in
own plane, uniform tension on wall, uniform compression on wall,
compression in element bending in own plane
Calculate design moment for geometric axis based on smallest
allowable stress
Use form of interaction equation to calculate a maximum applied
moment due to wind about diagonal that will result in the allowable
stress on element
Calculate ratio of average test moment to maximum applied moment
about diagonal
Stress Condition for Square Tubes
y
y
Compressed Element
Geometric, 1 Component
Compressed Elements
Diagonal Bending
Analysis
y Assumptions
p
y
Factor of safety for aluminum components on yielding is 1.65 –
building and similar type structures
y
Allowable moments calculated for a geometric axis as for steel
tubes
y
Aluminum D
Al
Design M
Manuall inelastic
l
buckling
b kl coefficients
ff
bbased
d on
tangent modulus concept
y
Approach outlined good for square tubes with slenderness less
than S1 or between S1 and S2
y
Ranges may be considered as “yielding” and “inelastic buckling”
y
Slenderness ggreater than S2 is elastic bucklingg
Inelasstic Buckliing Stress
Inelastic Bucklingg of Aluminum Elements
Bp
Bp - κ D
Dp(b/t)
(b/ )
Slope = Dp
Slenderness, b/t
Note: κ depends on specific conditions
A
Allowable
Stress
Bucklingg of Aluminum Elements
Fcy/n
[[Bp – κDp((b/t)]/n
)]
Euler or post buckling strength
S1
S2
Slenderness, b/t
Interaction Formula
⎛ MX
⎜⎜
⎝ M allowX
α
⎞ ⎛ MY
⎟⎟ + ⎜⎜
⎠ ⎝ M allowY
α
⎞
⎟⎟ = 1
⎠
2
M X = MY =
M applied
2
M allowX = M allowY = M allow
Substitute, reduce
⎛ 2
⎜
M applied
2⎜ 2
⎜ M allow
⎜
⎝
α
⎞
⎟
⎟ =1
⎟
⎟
⎠
Interaction Formula
S ≤ S1
α = 1.6
M allow
M applied =
1.091
S1 < S ≤ S 2
α =1
M applied
l d
M allow
=
1.414
Stress Condition – Bucklingg Coefficients,, Plastic Bendingg
y
Buckling coefficient for uniform vs. gradient;
1 63(b/ )/1 17 (b/t)=
1.63(b/t)/1.17
(b/ ) 1.39
1 39 [Sh
[Sharp 1996].
1996]
y
Condition more severe for considering uniform compression of
element
y
Stress – strain curve for aluminum gives rise to 2 shape factors, one
for yielding and one for ultimate
y
Elastic, pperfectlyy plastic
p
shape
p factor = 1.13. For square
q
aluminum
tubes, Zy = 1.1, Zu = 1.1
Analysis
y Results
4.5
4
Ratio Mexp/Mmaxw
3.5
3
Me/Mmxw 25 ksi
Me/Mmxw 26.9 ksi
Me/Mmxw 31.3 ksi
2.5
2
1.5
1
0.5
0
4 x 1/8
5 x 3/16
6 x 3/16
6 x 1/4
Tube Size
6 5/8 x 1/4
6 x 1/4
Observations
y
The average ratio of the experimental moment to allowable applied
moment ratios for the six types of tubes are all greater than 2.0.
2 0 In
no case was the ratio less than 1.6.
y
Allowable stresses for 6063-T6 were used and incorporated a
factor of safety of 1.65
1 65
y
A mixture of tubes with slenderness in the yielding and inelastic
buckling range were used
y
Calculations using the interaction equation appear to be
conservative
y
Square tubes with sharp corners failed by tension in the base or
weld when loaded about the diagonal
Recommended Specification
p
Provisions
y
Bending of Square Tubes
y
SSquare tubes
b shall
h ll meet the
h design
d i requirements
i
for
f bending
b di about
b
the geometric axes. In addition, tubes shall be designed for bending
about a skewed axis.
Recommended Specification
p
Provisions ((Continued))
y
For tubes with all elements S ≤ S1 α = 1.6
y
Fb = Fcy/n
/ y
y
For tubes with elements S1< S ≤ S2 α = 1.0
y
Fb = Table 6-3