________________________________________________________________________
PROBLEM (*11.87) A W 410 x 85 steel column ( Table B. 8) of Le =5-m effective length
supports an eccentric load of P = 400 kN at a distance e from the center of the section measured
along the web (Fig. P11.87). Employ the interaction formula to determine the maximum allowable
value of e.
Given: ( σall )b = 140 MPa, E = 210 MPa
*SOLUTION
2
2.26 .Ai=n
64
316 10
z
I
mm=×
y
32
10.8 10Am=× m
417 2 208.5cmm
=
=
171
z
rm
e
P
m
=
min 40.6rmm
=
min 123.2
e
Lr
=
410x85
z
417 mm
W
Equation (11.25):
229
22
min
(210 10 )
( ) 71.12
1.92( ) 1.92(123.2)
all c e
E
M
Pa
Lr
ππ
σ
×
===
Interaction formula:
1
()()
all c all b
PA McI
σσ
+≤; 2
66
() 1
7.12 10 140 10 z
PAecr
PA
+
≤
××
3
36 2
400 10 1 (0.2085)
[]
10.8 10 (10 ) 71.12 (0.17) (140)
e
−
×1
+
≤
×
2
(0.2085) 0.127 0.0141
(140)(0.171)
e≤−
or
2
0.0129(140)(0.171) 0.253
0.2085
em≤≤
Thus,
em 253 m=
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