sm7 124

________________________________________________________________________
PROBLEM (*7.124) As shown in Fig. P7.124, a simply supported beam, L meters long,
has a Z section of uniform thickness t for which
33
23 83
yyyz
3
I
tc I tc I tc== =−
Determine the maximum bending stress in the beam if it is subjected to a load P at midspan
and c = 10t.
*SOLUTION
y
z
A
C
N
.A.
t
y’
'
φ
z’
'
p
θ
c
P
c
c
O
yz
I
C
3
5
3tc
2'
p
θ
,
yz
I
I
R
1
I
(33
8
3,tc tc )
33 3
28 10
33
yzyz
I
tc I tc I tc c t== =−=
32 2
11 2
3
R
tc tc=+= 33
3
5
1' 081.3)2( tctcIIz=+==
33
3
5
2' 253.0)2( tctcIIy=−==
1
tan2 ' ' 22.5
1o
pp
θθ ==
PLPLM o
z231.05.22cos25.0
'==
PLPLM o
y096.05.22sin25.0
'−=−=
'
'
tan ' tan( 22.5 ), ' 78.8
oo
z
y
I
I
φφ =− =−
Point A is farthest from N.A. From Example 7.17:
1
'cos'sin'
p
2
AAp
yy t
θ
θ =− + ( )cos22.5 sin 22.5 9.5
22
oo
tt
ct=− + + =−
'sin'cos'
p
2
AAp
t
zy t
θ
θ =− − ( )sin22.5 cos22.5 4.5
22
oo
tt
ct=− + − =−
Thus,
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Continued on next slide

'
'
max ''
'
'yA
zA
Azy
M
z
My
II
σσ ==− +
33
0.231 ( 9.5 ) 0.096 ( 9.5 )
3.081 0.253
PL t PL t
tc tc
−− −
=− +
3
33
2.419 2.419 10
PL PL
ct
−
==×
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.