Civil Engineering Reference
In-Depth Information
Checking Minimum Reinforcing
min
from Appendix Table A.7
0.00333
A
s
min
(0.00333)(15)(24)
1.20 in.
2
9.58 in.
2
or
OK
Checking values of
t
and
a
3
3.44
6.44 in.
a
6.44
c
1
0.85
7.58 in.
d
c
24
7.58
7.58
t
(0.003)
(0.003)
c
0.00650
0.005
0.90 as assumed
Our procedure for designing T beams has been to assume a value of
z
, compute a trial
steel area of
A
s
, determine
a
for that steel area assuming a rectangular section, and so on.
Should
a
h
f
, we will have a real T beam. A trial-and-error process was used for such a
beam in Example 5.5. It is easily possible, however, to determine
A
s
directly using the
method of Section 5.3 where the member was broken down into its rectangular compo-
nents. For this discussion, reference is made to Figure 5.7.
The compression force provided by the overhanging flange rectangles must be bal-
anced by the tensile force in part of the tensile steel
A
sf
while the compression force in the
web is balanced by the tensile force in the remaining tensile steel
A
sw
.
For the overhanging flange we have
c
(
b
b
w
)(
h
f
)
A
s
f
f
y
0.85
f
from which the required area of steel
A
sf
equals
c
(
b
0.85
f
b
w
)
h
f
A
s
f
f
y
The design strength of these overhanging flanges is
h
f
2
M
uf
A
s
f
f
y
d
The remaining moment to be resisted by the web of the T beam and the steel required
to balance that value are determined next.
M
uw
M
u
M
u
f
The steel required to balance the moment in the rectangular web is obtained by the
usual rectangular beam expression. The value
M
uw
/
b
w
d
2
is computed, and
is deter-
mined from the appropriate Appendix table or the expression for
previously given in
Section 3.4 of this topic. Then
A
sw
b
w
d
A
s
A
sf
A
sw
