Reinforced Concrete Beam Stress Calculation

________________________________________________________________________
PROBLEM (7.101) A reinforced concrete beam of the cross section shown in Fig. P7.101 is
acted upon a by bending moment M about the z axis. Calculate:
(a) The stress in the steel.
(b) The maximum stress in the concrete.
Given: Ec = 3.75 x 106 psi, Es = 30 x 106 psi, M = 5 kip
⋅
in., b = 10 in., d = 16 in.,
As = 4 in.
SOLUTION
2
30 8, (8)(4) 32 .
3.75
ss
c
E
nnA
E
== = = =in
y
Locate the N.A. Use Eq.(7.43a):
222 () () 0
ss
nn
kd kd A dA
bb
+−=
) 6.4( ) 102.4 0kd kd+−=
Substituting the data
(
2
Solving,
2
6.4 (6.4) 4(1)( 102.4) 7.413 .
2in
−+ − −
==
d in−=
kd
and
dk 8.587 .
Equation(7.43b):
32
1 7.413
(10)(7.413) (10 7.413)( ) 0 (32)(8.587)
12 2
t
I=+×++
2
+=
=+
4
339.469 1,018.408 2359.6 3717.4 .in
(a) 3
8(5 10 )(8.587) 92.4
3717.4
st
nMc ksi
I
σ
×
== =
(b) 3
max (5 10 )(7.413)
( ) 9.97
3717.4
ct
Mc
p
si
I
σ
×
== =
2 in.
nA
s
=32 in.2
z
b=10 in.
kd
d(1-k)
d=16 in.
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