Cantilever Beam Stress Analysis: Eccentric Axial Load

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PROBLEM (9.64) A rolled steel cantilever beam of S12 x 50 section (see Table B.9) is
subjected to an eccentric axial load P at its free end (Fig. P9.64). What is the largest permissible
value of P if the allowable stress is limited to all
σ
= 15 ksi.
SOLUTION
From Table B.9:
2
14.7 .Ain=
4
2305 .
I
in=
4
15.7 .
y
I
in=
0.659 .
f
tin=
We have (see Fig. P9.64):
5.7 2
zy
M
PM P==−
1
6 . 0.3295 .
2
AB A B f
y
yinzzt in==− =−= =
Then
5.7 ( 6) 2 (0.3295)
14.7 305 14.7
yA
zA
Azy
Mz
MyPPPP
AI I
σ
−
=− + = − −
0.0680 0.1121 0.0448 0.1353PPPP=+−=
0.0680 0.1121 0.0448 0.225
BPPPP
σ
=++=
Hence
; 15 0.8369
all B all
P
σ
σ
=
=, 66.7Pkips
=
z
C
B
y
y
M
z
M
P
A