sm9 83

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_______________________________________________________________________
PROBLEM (9.83) Design the cross section of a rectangular beam b meters wide by 2b meter,
deep, loaded as shown in Fig. P9.83, if all
σ
= 18 ksi. Use the maximum principal stress theory of
failure.
SOLUTION
0: 10(7.5)(3.75) (4.5) 0
AB
MR=−=
∑, 62.5
B
R
kips
=
0: 12.5
yA
FR kips==
∑
At B at the upper outermost fiber:
33
max
max 3
3
540 10 810 10
1(2 )
12
Mc
Ib
bb
σ
××
== =
Thus,
33
max 3
810 10
;1810
all b
σσ
×
==×, 3.56 .bin
=
At B at the neutral axis axis:
33
max 22
3 3 32.5 10 24.375 10
222
V
Ab b
τ
××
== =
And
max 1 2
τ
σσ ==−
Continued on next slide
3 ft
B
V, kips
x
x
M
, kip⋅in.
2b
A
30
62.5 kips
10 ki
p
s/f
t
b
y
4.5 ft
z
C
-540
12.5
12.5 kips
-32.5

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
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Copyright Act without the permission of the copyright owner is unlawful.
Thus,
33
max 24.375 10
; 18 10 , 1.35 .
all bin
b
τσ
×
==×=
Use a 916
3.in by 18 7.in rectangular beam.