sm7 96

________________________________________________________________________
PROBLEM (*7.96) An aluminum plate and a steel plate are bonded together to create the
composite beam shown in Fig. P7.96. Find the dimension b of the cross section of the beam for
(a
σ
)all = 80 MPa and (
s
σ
)all =240 MPa.
Given: Ea = 70 GPa, Es = 210 GPa
*SOLUTION
3=
=
as EEn
3n=60 mm
y
Equivalent
aluminum
section
3
60 160 100 20 (10) 48 10 10
60 160 20 480
bb
ybb
××+ ×+
==
×+ +
33
48 10 10 38.4 10 170
180 180 480 480
bb
ybb
×+ ×+
−= − =
++
We have
63 (180 )
( ) 240 10
sall t
M
y
I
σ
−
=×=
6
( ) 80 10
aall t
M
y
I
σ =× =
Divide the first by the second:
3
3
3(180 ) 3(38.4 10 170 )
348 10 10
y
b
y
b
−×+
==
×+
or
, bb 170104.38101048 33 +×=+× mmb 60
=
Then
3
48 10 10(60) 90
480 60
y
mm
×+
==
+
z
’ b
160 mm 180-
y
=90 mm
C
z
y
=90 mm
20 mm
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