Beam Stress Ratio: Shear vs. Bending

________________________________________________________________________
PROBLEM (7.72) Determine the ratio of the maximum shearing stress to the largest bending stress
for the simple rectangular beam in Fig.P7.72 subjected to a uniformly distributed load of intensity w.
SOLUTION
w
wL/2
wL/2
L
wL
/
2
x
M
max= wL2/8
V, kN
x
b
M
kN⋅m
h
-wL
/
2
max 3323
22 4
VwL w
Abhb
τ == =
L
h
(1)
22
max 3
8( 2) 3
12 4 2
M
cwL h wL
I
bh bh
σ == = (2)
Thus,
Lh=
maxmax
σ
τ
(3)
For example, if , the above ratio is hL 10=.101
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