sm7 14

________________________________________________________________________
PROBLEM (7.14) A simply supported channel AB carries a concentrated load P at the
midpoint, as shown in Fig.P7.14. Compute the maximum tensile stress t
σ
and largest
compressive stress c
σ
in the member.
Given: L = 10 ft, b = 14 in., h = 6 in., t = 0.5 in., P = 5 kips
SOLUTION
12
12
22
ii
i
Ay Ay Ay
yAAA
+
==
+
∑
∑
2
2(61)(3) (121)(5.5)
2(6 1) (12 1)
×+×
=
×+ ×
in=n
y
z
y
1 in.
1 in. 1 in.
c1C6
c2
A
2
A
1
12
4.25 .in=
So c and
14.25 . 21.75 .ci=
32
1
2[ (1)(6) (6 1)(1.25) ]
12
z
I=+×+
32
1(12)(1) (12 1)(1.25) 74.5 .
12 in+× = 4
11
(5)(10 12) 300 .
42
z
M
M PL kip in== = × = ⋅
1300(4.25) 17.11
74.5
tz
Mc ksi
I
σ == =
2300(1.75) 7.05
74.5
cz
Mc ksi
I
σ =− =− =−
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