Civil Engineering Reference
In-Depth Information
obtain the same information is to refer to Graph 1 which is also located in Appendix A.
The user, however, will have some difficulty in reading this small-scale graph accu-
rately. This expression for
is also very useful for tensilely reinforced rectangular sec-
tions that do not fall into the tables.
3.5
STRAINS IN FLEXURAL MEMBERS
As previously mentioned, Section 10.2.2 of the Code states that the strains in concrete
members and their reinforcement are to be assumed to vary directly with distances from
their neutral axes. (This assumption is not applicable to deep flexural members whose
depths over their clear spans are greater than 0.25.) Furthermore, in Section 10.2.3 the
Code states that the maximum usable strain in the extreme compression fibers of a flexural
member is to be 0.003. Finally, Section 10.3.3 states that for Grade 60 reinforcement and
for all prestressed reinforcement we may set the strain in the steel equal to 0.002 at the
f
y
E
s
60,000
29
balanced condition. (Theoretically, for 60,000-psi steel it equals
0.00207.)
10
6
In Section 3.4 a value was derived for
a
, the depth of the equivalent stress block of a
beam. It can be related to
c
with the factor
.
A
s
f
y
0.85
f
a
c
b
1
c
Then the distance
c
from the extreme concrete compression fibers to the neutral
axis is
a
1
c
In Example 3.1 the values of
a
and
c
are determined for the beam previously consid-
ered in Example 2.6, and by straight-line proportions the strain in the reinforcing
t
is
computed.
EXAMPLE 3.1
c
Determine the values of
a
,
c
, and
t
for the beam shown in Figure 3.4.
f
y
60,000 psi and
f
3000 psi.
A
s
f
y
0.85
f
(3.00)(60)
(0.85)(3)(14)
SOLUTION
a
c
b
5.04
1
0.85 for 3000 psi concrete
c
a
1
5.04
0.85
5.93
t
d
c
21
5.93
5.93
(0.003)
(0.003)
0.00762
c
