sm9 43

_______________________________________________________________________
PROBLEM (9.43) A simply supported rolled-steel beam of S 250x52 section (see table B.9) is under
a uniform load of intensity w as depicted in Fig. P9.43. What is the maximum tensile stress at point D?
Given: a = 0.4 m, L = 1.8 m, w = 150 kN/m
SOLUTION
y
z
15.1 mm
12.5 mm
D
C d=254 mm
126 mm
0: 135
yAB
FRR===
∑kN
At a section C:
Vk 81 N=
2
1
135(0.4) (150)(0.4)
2
M=−
=⋅ 42 kN m
Table B.9:
64
61.2(10 )
z
I
mm=
254 12.5 114.5
2
D
y
mm=−=
Stress Components:
3
6
42 10 (0.1145) 78.6
61.2(10 )
D
z
My
M
Pa
I
σ
−
×
== =
3
6
81 10 [0.126 0.0125(0.127 0.00625)]
61.2(10 )(0.0151)
z
VQ
Ib
τ
−
×× −
==
16.67
M
Pa=
22
1()
22
σσ
σ
τ =+ +
22
40.41 (39.3) (16.67)=+ + 83.1
M
Pa
=
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