sm7 15

________________________________________________________________________
PROBLEM (7.15) A simple beam AB of a channel cross section is acted upon by a
concentrated load P at midpoint as shown in Fig. P7.14. Determine the maximum permissible
load P based upon an allowable normal stress all
σ
in the beam.
Given: L = 2 m, b = 400 mm, h = 150 mm, t = 25 mm, all
σ
= 50 MPa
SOLUTION
12
12
22
ii
i
Ay Ay Ay
yAAA
+
==
+
∑
∑
2
y
2(150 25)(75) (350 25)(137.5)
2(150 25) (350 25)
×+×
=
×+ ×
m=m
108.65 mm=
So cm and
1108.65 241.35cm
=
32
1
2[ (25)(150) (25 150)(33.65) ]
12
z
I=+×+
32
1(350)(25) (350 25)(28.85) 30.29(10 )
12 mm+× = 64
11
(2)
22
z
M
MPLp== = =P
Therefore
6
16
(0.10192)
; 50(10 ) , 14.86
30.29(10 )
tz
Mc PPk
I
σ
−
== =
si
6
26
(0.0481)
50(10 ) , 31.49
30.29(10 )
cz
Mc PPk
I
σ
−
== =
N
N
Hence 14.86
all
Pk=
z
y
25
25 25
c1C150 mm
A
A
21
c2
350 mm
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.