sm7 21

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PROBLEM (7.21) A beam with a T-cross section is supported and loaded as shown in Fig. P7.20.
Determine the maximum permissible load P based upon an allowable bending stress all
σ
in tension or
compression.
Given: L = 8 ft, a = 2 ft, b = 3 in., b = 1 in., h = 4 in., h1 = 3 in. , all
σ
= 15 ksi
SOLUTION
ii
i
Ay
yA =∑
∑
(3 1)(0.5) (3 1)(2.5) 1.5 .
(3 1) (3 1) in
×+×
==
×+×
and
11.5 .ci= n and n 22.5 .ci=
32
1(3)(1) (3 1)(1)
12
z
I=+×
32
1(1)(3) (3 1)(1)
12
++ ×
=
4
8.5 .in
max 2
( ) (8 2) 1.5
8
Pa
M
La P P
L
=−=−=
Hence
3
max 1 1.5 (1.5)
; 15(10 ) , 56.67
8.5
tz
Mc PPk
I
σ ===
ips
6
max 2 1.5 (2.5)
; 15(10 ) , 34
8.5
cz
Mc PPki
I
σ ===
ps
ps
y
z
y
1 in.
3 in.
c1
C4 in.
c2
A
2
A
13 in.
So
34
all
Pki=
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