sm11 84

________________________________________________________________________
PROBLEM (11.84) An S 4 x 7.7 rolled steel (see Table B.8) column of Le = 8 ft
effective length supports an eccentric load P applied e = 1 ¾ in. from the center of the section
measured along the web (Fig. P11.84). Using the interaction formula, determine the maximum
safe value of the load P.
Given: E = 30 x 106 psi, σy = 36 ksi, ( σall )b = 25 ksi
SOLUTION
2
2
cy
E
C
π
σ
=
y
26
3
2(3010)128.3
36 10
π ×
==
×
P
2
2.26 .Ai=n
n
n
3
3.04 .
z
Si=
min 0.581 .
y
rr i
=
=
4
6.08 .
z
I
in=
We have
96 0.581 165.2
ec
Lr C==>
Equation (11.25):
226
22
(30 10 )
( ) 5.65
1.92( ) 1.92(165.2)
all c e
Eksi
Lr
ππ
σ
×
== =
Then, we use
1
()()
all c all b
PA McI
σσ
+≤
Substituting the numerical values:
63
2.26 1.75 (2) 6.08 1
18.27 10 25 10
PP
+≤
××
,
3
(0.078 0.023)10 1P− +≤ 9.9Pkips
≤
Therefore,
max 9.9Pk=ips
3
4
1. in
z
.7
c=2 in.
S 4x7
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