Civil Engineering Reference
In-Depth Information
Trial-and-Error Method
A value of
a
can be assumed, the value of
A
s
computed, the value of
a
determined for that
value of
A
s
, another value of
a
assumed, and so on. Alternatively, a value of the lever arm
from
C
to
T
(it's
d
a
/2 for rectangular sections) can be estimated and used in the trial-
and-error procedure.
This method is a general one that will work for all cross sections
with tensile reinforcing.
It is particularly useful for T beams, as will be illustrated in the
next chapter.
EXAMPLE 4.5
The dimensions of the beam shown in Figure 4.5 have been selected for architectural reasons. De-
termine the reinforcing steel area by each of the methods described in this section.
SOLUTION
Using Appendix Tables
M
u
bd
2
(12)(160,000)
(0.9)(16)(21)
2
302.3 psi
from Table A.12
0.0054
A
s
(0.0054)(16)(21)
1.81 in.
2
Use 3 #7 bars (1.80 in.
2
)
Using
Formula
M
u
bd
2
302.3
R
n
(0.85)(3000)
60,000
(2)(302.3)
(0.85)(3000)
1
1
0.0054
Trial-and-Error Method
Here it is necessary to estimate the value of
a
. The student probably has no idea of a reasonable
value for this quantity, but the accuracy of the estimate is not a matter of importance. He or she can
assume some value probably considerably less than
d
2
a
2
and then compute
d
and
A
s
. With this
Figure 4.5
