sm11 56

________________________________________________________________________
PROBLEM (*11.56) The compressive load P acts with an eccentricity e on the structural steel
tubular column shown in Fig. P11.55. If the horizontal deflection at the top due to loading is vmax ,
calculate:
(a) The eccentricity e.
(b) The maximum stress in the column.
Given: a = 100 mm, b = 80 mm, L =1.8 m, P = 200 kN, vmax = 20 mm, E = 200 GPa
σy = 250 MPa (from Table B.4)
*SOLUTION
22 2 2
100 80 3600Aa b mm=−= − = 2
44 4 4 6
11
( ) (100 80 ) 4.92 10
12 12 4
I
ab mm=−= −=×
2( ) 2(1.8) 3.6 50
e
LL mcm== = =m
22 9 6
22
(200 10 )(4.92 10 ) 749.4
(3.6)
cr e
EI
Pk
L
ππ
−
××
== = N
200 0.267
749.4
cr
P
P==
(a) Equation (11.18):
max [sec( ) 1]
2cr
P
ve P
π
=−
20 [sec( 0.267) 1]
2
e
π
=−, 19.6emm
=
(b) 3
max max
( ) 200(19.6 20)10 7.92
M
Pe v kN m
−
=+ = + = ⋅
33
max
max 36
200 10 7.92 10 (0.05)
36 10 4.92(10 )
Mc
P
AI
σ
−−
××
=+ = +
×86
M
Pa
=
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