sm9 39

_______________________________________________________________________
PROBLEM (9.39) An overhanging beam of rectangular cross section, 6 in. deep by 4 in. wide,
carries a uniform load of intensity w = 10 kips/in. as shown in Fig. P9.39. Determine the principal
stresses at point D. Sketch the results on a properly oriented element.
SOLUTION
,
0)5.4()75.3)(5.7(10:0 =+−=
∑BA RM kipsRB5.62
=
:0=
∑y
F kipsRA5.12=
1.5 ft
A
B
C
D
3 ft
10 kip/ft
y
3 in.
z
12.5 ki
p
s 62.5 kips 4 in.
D
6 in.
1 in.
3 ft
kipsVD5.175.12)3(10 =−=
3
1
12.5(3) (10)(3) 7.5 90 .
2
D
M
kip ft kip in=− =−⋅=−⋅
34
1(4)(6) 72 .
12
I
in==
3
4(2)2 16 .Qi==n
Therefore,
3
17.5 10 (16) 972
72(4)
DVQ
p
si
Ib
τ
×
== =
3
90 10 (1) 1250
72
DMc
p
si
I
σ
−×
== =− (psi)
τ
625
22
625 972 1160R=+=
psi5356251160
1=−=
σ
psi17856251160
2−=−−=
σ
972
tan2 " , " 28.6
625 o
pp
θθ ==
28.6o
535 psi
1785 psi
D
σ
(psi)
C
1
σ
D
τ
D
σ
(
-1250, -972
)
2
θp"
2
σ
D
O
R
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