sm7 105

________________________________________________________________________
PROBLEM (7.105) Determine the value of
α
for which the bending stress in the cantilever beam,
loaded as shown in Fig. P7.105, is a maximum.
Given: b = 6 in., h = 9 in.
SOLUTION
α
cosPLMz−=
α
sinPLM y−=
Maximum value of
Bending stress occurs
at A(or B):
33
cos (4.5) sin (3)
6(9) 12 9(6) 12
yA
zA
Azy
Mz
M y PL PL
II
αα
σ
=− + = +
33
(4.5)sin (3)cos 0
6(9) 12 9(6) 12
A
dPL PL
d
σ
α
α
α
=− + =
or
tan 1.5, 56.3o
αα ==
y
z
9 in.
6 in.
D
B
C
A
P
cos
α
P
sin
α
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