Civil Engineering Reference
In-Depth Information
Figure 7.17
Testing of T-shaped specimen
resulting in a high web reinforcement index
rf
y
of 3.27 MPa (475 psi). In contrast, s
pecimens
B2 an
d B5 we
re designed
by the lim
it desi
gn met
hod using nominal stresses of 0
36
f
c
(MPa)
.
7
f
c
(psi)), respectively. These stresses, in turn, give
corresponding stirrups indices of 1.14 MPa (165 psi) and 0.41 MPa (60 psi), respectively.
Figure 7.18 shows the variation of torque with increase of load
4
f
c
(psi)) and 0
22
f
c
(MPa) (2
(4
.
.
.
w
f
for the three specimens.
It can be seen that all three specimens behave in a reasonably elastic manner up to cracking.
Upon cracking, the torques remain essentially constant while the load is increased. This
confirms the existence of the moment redistribution after cracking. This redistribution of
moments can also be observed in Figure 7.19, showing the torque-twist relationships of the
three test specimens. Before cracking the torque-twist curve is approximately linear. After
cracking, however, the torque-twist curves reach a horizontal plateau, where the angle of twist
increases under a constant torque. In other words, plastic hinges are formed in the spandrel
beam after cracking. When sufficient stirrups were provided, as in specimens B1 and B2, the
plastic hinge in the spandrel beam permitted the floor beam to bend until the longitudinal steel
yielded near midspan.
In specimen B1, where an excessive amount of stirrups was provided, the plastic hinges
in the spandrel beam not only allowed the floor beam to yield, but also allowed the torque
to increase rapidly after the yielding of the floor beam (see Figure 7.18). This phenomenon
can be considered as a redistribution of moments from the floor beam back to the spandrel
beam and is known as the 'second resdistribution of moment after yielding of a floor beam.'
Although this second redistribution of moments may allow us to utilize the ultimate torsional
strength of the web reinforcement in the spandrel beam, Figure 7.18 shows that the increase
of load is small after the yielding of the floor beam. This small gain in load also occurs at very
large angles of twist (as indicated in Figure 7.19) which is undesirable from a serviceability
point of view. In short, from an economic and practical point of view, this second redistribution
