sm7 100

________________________________________________________________________
PROBLEM (7.100) The cross section of a bimetallic beam consists of strips of aluminum and
copper bonded together, as depicted in Fig. P7.100. Under the action of bending moment M
about the z axis, determine:
(a) The maximum stress in the aluminum strip.
(b) The maximum stress in the copper strip.
Given: Ec = 105 GPa, Ea = 75 GPa, M = 40kN
⋅
m
SOLUTION
We have 105 1.4
75
c
a
E
nE == =
Equivalent aluminum section:
8 mm
3 m
m
1.4x(20)=28 mm
y
z
5.162 mm=
y
20 mm
(28)(8)(4) (20)(3)(9.5) 5.162
(28 8) (20 3)
y
mm
+
==
×+ ×
32
1(28)(8) (28 8)(1.162)
12
t
I=+×+
32
1(20)(3) (20 3)(4.338) 2.67(10 )
12 mm+× = 34
(a) 3
9
(40)( 5.162 10 ) 77.33
2.67(10 )
at
My
M
Pa
I
σ
−
−
−×
=− =− =
(b) 3
9
(1.4)(40)(5.838 10 ) 122.4
2.67(10 )
ct
nMy
M
Pa
I
σ
−
−
×
=− =− =−
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