sm7 102

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PROBLEM (*7.102) Determine the maximum permissible value of P for the simply
supported reinforced concrete beam, loaded as shown in Fig.P7.102.
Given: (c
σ
)all = 8.4 MPa, (
s
σ
)all = 140 MPa, n = 8
*SOLUTION
nAs=32x103 mm2
y
z
300
60
d=310
50
kd=180.3
d(1-k)=129.7
100
Dimensions are
in millimeters
We have:
max 28MPn==
3
0.06
0: (0.3) ( 0.06)(0.1) 32 10 (0.31 )
22
zkd kd
Qkd kd k
−d
−
=−− =×
∑−
0
2=−+ kdkd
Simplifying,
( (1) 101.0)(38.0)
Solving Eq. (1):
2
1,2 0.38 (0.38) 0.404 0.38 0.741
()
22
kd −± + −± ==
m mm d k mm== −=−=
Use
kd 0.1803 180.3 , (1 ) 310 180.3 129.7
Referring to the figure:
3
300(180.3) 300 180.3(90.15)
12
t
I=+×
323
100(120.3)
[ 100(120.3)(60.15) ] 32 10 (129.7)
12
−+ +×
2
64
631.7 10 mm=×
Therefore,
36
max 6
2 (180.3 10 )
() 8.4 10
631.7 10
ct
Mc P
I
σ
−
−
×
== =×
×
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Continued on next slide

from which
14.72Pk=N
Similarly,
36
max 6
8(2 )(129.7 10 )
( ) 140 10
631.7 10
st
nMc P
I
σ
−
−
×
== =×
×
N
N
or
42.6Pk=
Thus,
14.72
all
Pk=
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.