sm7 31

________________________________________________________________________
PROBLEM (*7.31) An overhanging beam is loaded as shown in Fig. P7.31. The allowable
stresses in tension and compression are ( t
σ
)all and ( c
σ
)all , respectively. Determine the maximum
permissible value of the load w.
Given: (t
σ
)all = 7 ksi, ( c
σ
)all = 18 ksi
*SOLUTION
y
2
1
4.5 (3.75)
2
C
M
ww=− +
2.53w
=
11
1
3 ft
C
B
V
x
2
2(1 4 2) 1.5 1 0.5 1.763 .
2(1 4) 1 1.5
y
in
×× + ×+
==
×+×
33
22
14 1.51
2[ 1 4(0.237) ] 1.5 1(1.263)
12 12
I×× =+× ++×
4
13.63 .in=
At section A
3
7 10 (13.63)
( ) 42.65 .
2.237
At I
M
kip in
c
σ ×
== = ⋅
3
18 10 (13.63)
( ) 139.2 .
1.763
AC I
M
kip in
c
σ ×
== = ⋅
Tension governs. Hence,
3
4.5 42.65 10 12, 790w w lb ft=× =
At section C
3
7 10 (13.63)
( ) 54.12 .
1.763
Ct I
M
kip in
c
σ ×
== = ⋅
3
18 10 (13.63)
( ) 109.7 .
2.273
Cc I
M
kip in
c
σ ×
== = ⋅
16wL
x
M
3
A
w
3
-3
7.5 f
t
w lb/f
t
1.5
3 ft
z
y
2.237
C=1.763
-4.5w -4.5w
2.53w
3.75
.75
R
=6.75w
R
B=6.75w
A
-3
Dimensions are in inches
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Continued on next slide

Tension governs:
3
2.53 54.12 10 12, 1783w w lb ft=× =
Allowable safe load is thus
790
all
wlbft
=
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.