sm7 90 92

________________________________________________________________________
PROBLEMS (7.90 through 7.92) For the composite beams with cross sections as shown in
Figs. P7.87 through P7.89, determine the maximum permissible bending moments.
Given: (b
σ
)all = 120 MPa, (
s
σ
)all = 140 MPa , Eb = 100 GPa, Es = 200 GPa.
SOLUTION (7.90)
From solution of Prob. 7.87:
2n
=
y
64
0.1443 10
t
I
mm=×
Assume 120 MPa is maximum
allowable stress:
6
63
0.1443 10
120 10 23 10
t
bI
Mc
σ
−
−
×
==× ×
753Nm
=
⋅
The corresponding maximum stress in steel is:
3
6
2(753)(17 10 ) 177 140
0.1443 10
st
nMc
M
Pa MPa
I
σ
−
−
×
== = >
×
Hence,
steel stress controls:
3
66
2 (17 10 )
( ) 140 10 0.1443 10
sall M
σ
−
−
×
=×= ×
from which 594
M
Nm=⋅. Therefore,
594
all
M
Nm=⋅
SOLUTION (7.91)
From solution of Prob. 7.88:
2n
=
64
0.1293 10
t
I
mm=×
Assume 120 MPa is maximum
allowable stress:
6
63
0.1293 10
120 10 22 10
t
bI
Mc
σ
−
−
×
==× ×705 Nm
=
⋅
The corresponding maximum stress in steel is:
3
6
2(705)(18 10 ) 196 140
0.1293 10
st
nMc
M
Pa MPa
I
σ
−
−
×
== = >
×
y
z
20 mm
18 mm
C
z
23 mm C
17 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

Hence,
steel stress controls:
3
66
2 (18 10 )
10 , 503
0.1293 10
M
M
Nm
−
−
×
×= = ⋅
× 140
Thus, 503
all
M
Nm=⋅
SOLUTION (7.92)
From solution of Prob. 7.89:
64
0.1072 10 2.
t
Imm=× = n
Assume 120 Mpa is maximum allowable stress:
6
63
0.1072 10
120 10 20 10 M
−
−
×
=× ×643 Nm
=
⋅
The corresponding maximum stress in steel is
3
6
2(643)(5 10 )
0.1072 10
st
nMc
I
σ
−
−
×
== ×60 140
M
Pa MPa
=
<
Brass stress controls:
M
643
all Nm=⋅
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.