Civil Engineering Reference
In-Depth Information
(Hsu, 1968a). Figure 7.10 shows beams B1-B6 with increasing percentage of reinforcement,
and the balanced percentage lies in between beams B3 and B4. The thickness ratios
t
d
/
t
do
for
B3 and B4 are 0.77 and 0.82, respectively, calculated from the computer program. Taking a
close average of 0.8 for these two beams gives the maximum thickness
t
d
,
max
as:
8
A
c
p
c
t
d
,
max
=
0
.
8
t
do
=
0
.
(7.85)
The validity of Equation (7.85) can be observed in Figure 7.11 by the dotted curve connecting
the test points B1 and B5. The dotted curve crosses from the under-reinforced region into the
over-reinforced region at about 0
.
8
t
do
. Series B is quite representative of the other series of
test points.
7.2.5 Compatibility Torsion in Spandrel Beams
The ACI Code provides a so-called compatibility torsion for the design of spandrel beams
in a statically indeterminate structure, when the torsional moment in the spandrel beam can
be redistributed to other adjoining members after the formation of plastic hinges. Utilizing
the limit design concept, this torsional plastic hinge can maintain a much smaller moment
than that calculated by elastic analysis, thus resulting in a cost-effective, and yet very simple,
design. This compatibility torsion, which is first introduced in Section 2.3.4.1, will now be
studied in a more detailed and systematic manner.
7.2.5.1 Moment Redistribution
The redistribution of moment from a spandrel beam after torsional cracking to the adjoining
floor systems will be illustrated by a three-dimensional structural frame, shown in Figure 7.14.
The portion of the frame shown includes four columns, two spandrel beams and three floor
beams. The floor beam at the center is supported by the two spandrel beams, rather than the
COLUMNS
W
I.P
FLOOR BEAMS
I.P
SPANDREL
BEAM
I.P
Figure 7.14
Space frame showing the test specimen
