Civil Engineering Reference
In-Depth Information
the midspan of the spandrel beam, while splitting and moving the reaction force
R
to the
two ends of the spandrel beam. When the new set of three diagrams for the spandrel beam
in Figure 7.22(b) is compared with the old set in Figure 7.22(a), it can be seen that they are
identical, except that all the signs are reversed. These reversals of sign are obviously caused
by the interchange of loads and reactions. This interchange of loads and reactions, however,
has not changed the magnitudes of the bending moment, shear force and torsional moment in
the spandrel beam, nor the relationships among them.
The T-shaped test specimen in Figure 7.22(b) is similar to that given in Figure 7.15(a),
except in two aspects. First, an additional concentrated load
P
s
is applied at the midspan of
the spandrel beam, and second, the spandrel beam is much shorter. Both these characteristics
are needed to create large shear stresses in the spandrel beam.
Four T-shaped specimens with concentrated load
P
s
(Figure 7.22b), are taken from series
C of Hsu and Hwang (1977) to demonstrate the interaction of high shear and high torque in
spandrel beams. Each of the four T-shaped specimens C1, C2, C3 and C4 consists of a spandrel
beam and a floor beam. The spandrel beam has a cross section of 152
×
305 mm (6
×
12 in.) and
a span of 1.37 m (4.5 ft). The floor beam has a cross-section of 152
×
229 mm (6
×
9 in.) and a
span of 2.74 m (9 ft). The design floor beam load
w
f
was 114 kN (25.6 kips) and the spandrel
beam load
P
s
was 0 kN (0 kips), 62.3 kN (14.0 kips), 173 kN (38.9 kips) and 110 kN (24.7 kips)
for specimens C1, C2, C3 and C4, respectively. As a result, the longitudinal reinforcement
ratio of the spandrel beams varies from 0.5 to 1.88%, a range normally used in practice.
Specimens C1 a
nd C2 wer
e de
signed b
y the torsional limit design method. A design torsional
stress
33
f
c
(MPa) (4
f
c
(psi)) was assumed for specimen C2, as specified by the
ACI Code. The calculated torsional stirrup was added to the shear stirrup, and the calculated
torsional longitudinal steel was added to the flexural longitudinal steel. An identica
l method
was
used f
or specimen C1, except that a larger design torsional stress
τ
n
of 0
.
50
f
c
(MPa)
τ
n
of 0
.
(6
f
c
(psi)) was used. In order to maintain a design load
w
f
of 114 kN (25.6 kips) and the
same stirrup index as that of C2, the spandrel beam load
P
s
for C1 was reduced to zero.
Specimens C3 and C4 were designed by an alternative method with two characteristics: (1) a
minimum stirrup index
rf
y
of 0.98 MPa (142 psi) is specified for torsion; and (2) no interaction
between torsion requirement and shear requirement. The stirrup index of the spandrel beam is
obtained from the larger of the torsion requirement or the shear requirement.
Specimen C4 was designed by the minimum stirrup index
rf
y
0.98 MPa (142 psi) for
torsion. The stirrup index required by shear is neglected because it is less than that required
by torsion. Specimens C3 was designed by a stirrup index of 186 MPa (270 psi) required by a
large shear force. The minimum stirrup index required by torsion is neglected.
The torque-twist curves for these four specimens are given in Figure 7.23. Specimen C2
behaved as a specimen with optimum web reinforcement in the spandrel beam. After diagonal
cracking in the spandrel beam, a torsional plastic hinge was formed. The large increase of
the angle of twist allowed the moment to be redistributed from the spandrel beam to the floor
beam. Failure was preceded by the yielding of stirrups and longitudinal steel in the spandrel
beam (represented by the circled numbers 2 and 3 in Figure 7.23). This was followed by the
yielding of the bottom longitudinal steel near the midspan of the floor beam (represented by
the circled number 1), and the ductile collapse of the whole specimen. Two observations are
evident: (1) the development of torsional hinges in the spandrel beams was accompanied by
a slight decrease of torque; and (2) the bottom longitudinal reinforcement in the floor beam
just reached its yield strain at collapse. In view of these observations, it can be concluded that
=
