sm7 73

________________________________________________________________________
PROBLEM (7.73) Determine the ratio of the largest shear stress to the maximum bending
stress for a simply supported beam of circular cross section carrying a concentrated load P at
its midspan (Fig. P7.73).
SOLUTION
L/
2
L/
2
P
h=2c
L
P/
2
P/
2
4
From solution of Prob. 7.64:
max 22
4422
33 3
VP P
Ac
τ
c
π
π
== =
Also
max 33
4
M
cMPL
I
cc
σ
π
π
== =
Thus, LhLc 332
maxmax
=
=
σ
τ
For example, if , the above quotient is
hL 10=301 .
4
c
I
π
=
M
kN⋅m
P/
2
x
P
L
/
4-
P
/2
x
V, kN
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