Problem 12.25
Given: Assume that the dimensions of the angle section of the pinnedend column shown are t = 0.635
mm, b = 12.0 mm, and L = 559 mm.
Find:
Show by Figure 12.11 that the column fails as a unit by elastic buckling (not local buckling).
Calculate the average stress in the column at the buckling load and compare it to the stress obtained
experimentally.
Solution:
x
y
b
b
t
t
0.635 mm
⋅
:=
b1
2
m
m
⋅
:=
L
559 mm
⋅
:=
Area of section:
Ab
t
−
()
t
⋅
bt
⋅
+
14.837 mm
2
⋅
=
:=
Centroid location relative to lower left and corner is:
x
c
1
A
−
t
⋅
t
2
⋅
⋅
b
2
⋅
+
⎡
⎣
⎤
⎦
⋅
3.236 mm
⋅
=
:=
y
c
x
c
:=
I
y
−
t
3
12
−
t
⋅
x
c
t
2
−
⎛
⎝
⎞
⎠
2
⋅
+
tb
3
⋅
12
+
⋅
b
2
x
c
−
⎛
⎝
⎞
⎠
2
⋅
+
211.367 mm
4
⋅
=
:=
I
x
I
y
:=
I
xy
−
t
⋅
t
2
x
c
−
⎛
⎝
⎞
⎠
⋅
−
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 Spring '10
 MechanicsofSolids
 Buckling, iy, 23%, 12.0 mm, 0.635 mm, 126.372 mm

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