Civil Engineering Reference
In-Depth Information
Figure 14.25
depth equals the full effective depth of the beam.
5
Some designers use other equivalent val-
ues, such as assuming an equivalent T section with flanges of effective widths equal to so
many (say, 2 to 6) times the web width. These equivalent sections can be varied over a
rather wide range without appreciably affecting the final moments.
The ACI Code (8.9.2) states that for such an approximate analysis, only two live-load
combinations need to be considered. These are (1) live load placed on two adjacent spans
and (2) live load placed on alternate spans. Example 14.2 illustrates the application of the
equivalent rigid-frame method to a continuous T beam.
Computer results appear to indicate that the model shown in Figure 14.25 (as permit-
ted by the ACI Code) may not be trustworthy for unsymmetrical loading. Differential col-
umn shortening can completely redistribute the moments obtained from the model (i.e.,
positive moments can become negative moments). As a result, designers should take into
account possible axial deformations in their designs.
EXAMPLE 14.2
Using the equivalent rigid-frame method, draw the shear and moment diagrams for the continuous T
beam of Figure 14.26. The beam is assumed to be framed into 16-in.
16-in. columns and is to sup-
port a service dead load of 2.33 k/ft (including beam weight) and a service live load of 3.19 k/ft. As-
sume that the live load is applied in the center span only. The girders are assumed to have a depth of
24 in. and a web width of 12 in. Assume that the
I
of the T beam equals two times the
I
of its web.
SOLUTION
Computing Fixed-End Moments
w
u
in first and third spans
(1.2)(2.33)
2.8 k/ft
M
u
(2.8)(24)
2
12
134.4 ft- k
w
u
in center span
(1.2)(2.33)
(1.6)(3.19)
7.9 k/ft
M
u
(7.9)(24)
2
12
379.2 ft- k
5
Portland Cement Association, 1959,
Continuity in Concrete Building Frames
, 4th ed. (Chicago), pp. 17-20.
