sm11 14

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PROBLEM (*11.14) A jib crane is made of a rectangular steel bar AB with a width b by depth
h cross section (Fig. P11.14). Determine the buckling load of the column.
Given: b = 2 in., h = 3 in., E = 30 x 106 psi, σy = 36 ksi
*SOLUTION
Refer to Example 11.3. We have axial force in bar AB is P=4W/3.
34
1(3)(2) 2 .
12
y
I
in==, 34
1(2)(3) 4.5 .
12
z
I
in==, 2 (2)(3) 6 .Ai== n
0.577 . 0.866 .
yz
yz
II
rinr
AA
== == in
Buckling in xy-plane ( e
LL
=
).
96 110.9
0.866
z
L
r==
226 3
22
(30 10 )6 4
144.4(10 )
( ) (110.9) 3
cr z
EA W
PLr
ππ ×
== = =
or
Wk 106.3 ips=
Buckling in xz-plane
Line of action of the compressive force again passes through A and thus .
e
LL=
So, 96 166.4
0.577
y
L
r==
Hence
226
22
(30 10 )(6) 4
( ) (166.4) 3
cr y
EA W
PLr
ππ ×
== =
Solving
Wk 48 ips=
ips>
The column will buckle when Wk. 48
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