Civil Engineering Reference
In-Depth Information
compression steel is checked to determine whether or not it has yielded. With the strain
obtained, the compression steel stress
s
)
(
f
is determined, and the value of
A
s
2
is computed
with the following expression:
s
f
s
A
s
2
f
y
A
In addition, it is necessary to compute the strain in the tensile steel (
t
) because if it is
less than 0.005, the value of the bending
will have to be computed inasmuch as it will
be less than its usual 0.90 value. The beam may not be used in the unlikely event that
t
is
less than 0.004.
To determine the value of these strains a quadratic equation is written, which upon solu-
tion will yield the value of
c
and thus the location of the neutral axis. To write this equation,
the nominal tensile strength of the beam is equated to its nominal compressive strength, as
shown at the end of this paragraph. Only one unknown appears in the equation, and that is
c
.
c
d
c
1
cb
A
s
A
s
f
y
0.85
f
(0.003)(29,000)
c
The value of
c
determined enables us to compute the strains in both the compression
and tensile steels and thus their stresses. Even though the writing and solving of this equa-
tion are not too tedious, use of the enclosed computer program, SABLE32, makes short
work of the whole business.
Examples 5.7 and 5.8 illustrate the computation of the design moment strength of
doubly reinforced beams. In the first of these examples the compression steel yields,
while in the second it does not.
EXAMPLE 5.7
Determine the design moment capacity of the beam shown in Figure 5.14 for which
f
y
60,000 psi
and
c
f
3000 psi.
"
d'
=
2
2
2 #9
(2.00 in.
2
)
27"
21
2
"
4 #11
(6.25 in.
2
)
3"
14"
Figure 5.14
