sm12 42

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PROBLEM (12.42) Using the work-energy method, determine the deflection due to bending at point
B of the cantilever beam shown in Fig. 12.42.
Given:
P = 120 N, E = 200 GPa, h = 2b = 60 mm.
SOLUTION
y
P
60 mm
x
A
O
B
L=0.6 m
x
z
x
=
3b
2bx
L
b
O
z
b = 30 mm
M = − P ( x − 0.3)
2b
z=
x
L
2(30)
=
x
600
x
=
10
0.3 m
0.6 m
1 x
(0.06)3 = 1.8(10−9 ) x m 4
12 10
2
0.9 ( x − 0.3)
0.9
0.09
M 2 dx
dx = 20∫ ( x − 0.6 +
)dx
= 20∫
U =∫
0.3
0.3
x
x
2 EI
Iz =
0.9
x2
= 20
− 0.6 x + 0.09 ln x = 20[0.36 − 0.36 + 0.099] = 1.98 J
2
0.3
Thus,
1
120
U = PvB ;
vB , vB = 33 mm ↓
1.98 =
2
2
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