sm7 87 89

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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instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other
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Continued on next slide

20 20 30 30 20 10 18
20 20 30 20
ii
i
Ay
y
mm
A
××+××
== =
×+×
∑
∑
42 3
11
(20) 20 20(12) (30)(20) 30 20(8)
12 12
t
I=+×+ +×
2
=×
64
0.1293 10 mm
Thus,
3
max 6
200(22 10 )
() 34
0.1293 10
bt
Mc
M
Pa
I
σ
−
−
×
== =
×
3
max 6
2(200)(18 10 )
( ) 55.7
0.1293 10
st
nMc
M
Pa
I
σ
−
−
×
== =
×
SOLUTION (7.89)
200 2
s
b
E
MNmn
E
=
⋅=
y
=
s
tb
I
InI
=
+
34
20(40) (5) (5)
[]2
12 4 4
ππ
+
4
[]
=−
=×
64
0.1072 10 mm
So,
3
max 6
200(20 10 )
( ) 37.3
0.1072 10
bt
Mc
M
Pa
I
σ
−
−
×
== =
×
3
max 6
2(200)(5 10 )
( ) 18.66
0.1072 10
st
nMc
M
Pa
I
σ
−
−
×
== =
×
Transformed brass section
z
5 m m
Steel Brass 20 mm
20 mm
20 mm
Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or
instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other
reproduction or translation of this work beyond that permitted by Sections 107 or 108 of the 1976 United States
Copyright Act without the permission of the copyright owner is unlawful.
Continued on next slide