Civil Engineering Reference
In-Depth Information
Calculating
M
n
and
M
n
d
h
f
2
d
a
2
M
n
C
w
C
f
30
8.19
2
30
4
2
(389.8)
(217.6)
16,190 in.- k
1349 ft- k
M
n
(0.90)(1349)
1214 ft- k
5.4
DESIGN OF T BEAMS
For the design of T beams, the flange has normally already been selected in the slab de-
sign, as it is the slab. The size of the web is normally not selected on the basis of moment
requirements but probably is given an area based on shear requirements; that is, a suffi-
cient area is used so as to provide a certain minimum shear capacity, as will be described
in Chapter 8. It is also possible that the width of the web may be selected on the basis of
the width estimated to be needed to put in the reinforcing bars. Sizes may also have been
preselected as previously described in Section 4.4 to simplify formwork, for architectural
requirements, or for deflection reasons. For the examples that follow (5.4 and 5.5), the
values of
h
f
,
d
and
b
w
are given.
The flanges of most T beams are usually so large that the neutral axis probably falls
within the flange and thus the rectangular beam formulas apply. Should the neutral axis
fall within the web, a trial-and-error process is often used for the design. In this process a
lever arm from the center of gravity of the compression block to the center of gravity of
the steel is estimated to equal the larger of 0.9
d
or
d
(
h
f
/2) and from this value called
z
,
a trial steel area is calculated (
A
s
M
n
/
f
y
z
). Then by the process used in Example 5.2, the
value of the estimated lever arm is checked. If there is much difference, the estimated
value of
z
is revised and a new
A
s
determined. This process is continued until the change
in
A
s
is quite small. T beams are designed in Examples 5.4 and 5.5 by this process.
Example 5.6 presents a more direct approach for the case where
a
h
f
. This is the
case where the beam is assumed to be divided into its rectangular parts.
EXAMPLE 5.4
Design a T beam for the floor system shown in Figure 5.9 for which
b
w
and
d
are given.
M
D
80 ft-
c
k,
M
L
100 ft-k,
f
4000 psi,
f
y
60,000 psi, and simple span
20 ft.
Figure 5.9
