sm7 87

PROBLEMS (7.87 through 7.89) The composite beams of Figs. P7.87 through P7.89 are
fabricated by bonding a steel bar and a brass bar and are subjected to the bending moment M = 200
N⋅m. Dimensions are in millimeters. Determine the maximum bending stress in the brass and steel.
Given: Es = 200 GPa, Eb = 100 GPa
SOLUTION (7.87)
200
M
Nm
=
⋅
2
s
b
E
nE
=
=
Equivalent brass section
’
y
z
20n=40 mm
20 30 25 40 10 5 17
20 30 40 10
ii
i
Ay
y
mm
A
××+××
== =
×+×
∑
∑
32
1
()
2
t
I
bh Ad=+
∑
32 3
11
(20)(30) 20 30(8) (40)(10) 40 10(12)
12 12 2
×++×=+
=×
64
0.1443 10 mm
Thus,
3
max 6
200(23 10 )
() 0.1443 10
bt
Mc
I
σ
−
−
×
== ×31.9
M
Pa
=
3
max 6
2(200)(17 10 )
() 0.1443 10
st
nMc
I
σ
−
−
×
== ×47.1
M
Pa
=
SOLUTION (7.88)
200
M
Nm
=
⋅
2
s
b
E
nE
=
=
Equivalent brass section
z
20 mm
3 mm 0 40-
y
=23
C
y
=17 mm
10 mm
y
z
’
20 mm
z
5+n(10)+5=30 mm
20 mm 40-
y
=22 mm
C
y
=18 mm
20 mm
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