sm7 2

PROBLEM (7.2) An aluminum bar of modulus of elasticity E, width b, depth h , and length
L , is acted upon by bending moments M at its ends so that the midpoint deflection is
δ
(Fig.
P7.2). Determine the maximum longitudinal strain and the bending moment in the bar.
Given: E = 70 GPa, b = 10 mm, h = 30 mm, L = 2 m,
δ
= 10 mm
Assumption: The deflection curve is nearly flat so that the distance between the ends of the bent
bar equals the length of the beam as indicated in the figure.
SOLUTION
3
0.01(0.03)
12
I=
O
94
22.5 10 m
−
=×
From geometry:
2222
max
1 ( ) ( 0.01) 0.02 10v ρρ ρ ρρ
4
−
−= − = − = − +
or
50 m
ρ
=
Equation (7.2), for 2:yh=
max 0.03 300
2 2(50)
h
ε
μ
ρ
== =
Equation (7.6):
99
70 10 (22.5 10 ) 31.5
50
EI
M
Nm
ρ
−
××
== = ⋅
________________________________________________________________________
y
x
M
max
v
y
z
h=30 mm
10 mm
1 m
M
ρ
ρ
1 m
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