sm9 61

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PROBLEM (9.61) The cantilever beam with a rectangular cross section is subjected to loads
P, Q, and R as illustrated in Fig. P9.61. What is the maximum shearing stress max
τ
at point A?
Given: P = 100 kN, Q = 15 kN, R = 10 kN
SOLUTION
At the section that includes points A and B, internal forces and moments (Fig. a):
100 15 10
yz
PkNVkNVkN===
(0.3 0.08) 15(0.22) 3.3
z
M
QkNm=− − =− =− ⋅
(0.3) 10(0.3) 3
y
M
RkNm
=
==⋅
Cross-sectional properties :
2
80 120 9600Amm=× =
364
1(80)(120) 11.52(10 )
12
z
I
mm==
364
1(120)(80) 5.12(10 )
12
y
I
mm==
At point A (Fig. b):
33
66
100(10 ) 3.3(10 )(0.06)
9600(10 ) 11.52(10 )
zA
xz
My
P
AI
σ
−−
=− = +
27.60 kip=
3
6
3 3 10 10 1.563
2 2 9600(10 )
z
xy V
M
Pa
A
τ
−
×
== =
Hence
22 2 2
max ( ) (13.8) (1.563) 13.89
2xxy
M
Pa
σ
ττ
=+= + =
B
Q
z
y
y
M
z
M
P
Figure (a)
C
A
R
Fi
g
ure
(
b
)
x
y
τ
x
σ
A
120 mm
80 mm