sm9 75

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PROBLEM (9.75) A short column constructed of a C 100 x 11 channel section (see Table B.10)
supports an eccentric axial load of P (Fig. P9.75). Determine the largest permissible value of the distance
e, if the maximum compressive stress is not to exceed all
σ
.
Given: P = 20 kN, all
σ
= 40 MPa
SOLUTION
For
62512C×× rolled-steel section (Table B.10):
64 64 32
1.91(10 ) 0.18(10 ) 1.37(10 )
zy
I
mm I mm A mm===
43 102 11.7 8.2
f w
w mm d mm z mm t mm== = =
We have
51
2
Ad
y
mm=− =−
11.7
A
zz mm=− =−
3
20 10
z
M
Pe e=− =− ×
( ) 152
2
w
yp t
M
Pz P z N m
=
=−= ⋅
So
yA
zA
Azy
M
z
MyP
AI I
σ =− − +
or
[]
yA
z
zA
Ay
Mz
IP
MyI A
σ
=− − −
633
66
36 3
1.91 10 (152)( 11.2 10 ) 20 10
[ ( 40 10 )]10
51 10 0.18(10 ) 1.37(10 )
−−
−− −
×−××
=−−−×
−×
607.834 Nm=− ⋅
Hence
3
3
607.834 30.4 10 30.4
20 10
z
M
emmm
P−
−
=− =− = × =
×
y
z
tw
A
P
e d
z