Civil Engineering Reference
In-Depth Information
W
TORSIONALLY
FIXED
W
w
l
f
M
+
l
f
2
T
M
K
ts
l
f
K
f
M = 2T
T
l
s
(a)
(b)
Figure 7.15
Test specimen
columns. When a uniform load
is applied on this floor beam, it will produce a rotation at
the ends that in turn induces a torsional moment in the spandrel beams. The interaction of the
floor beam and the spandrel beam can be studied using the T-shaped specimen indicated by
heavy lines. This test specimen includes a spandrel beam between two inflection points and a
floor beam from the joint to the inflection point. The three inflection points, indicated by solid
dots, can be simulated by hinges in the tests.
Figure 7.15(a) shows the T-shaped test specimen resting on three spherical hinges and the
floor beam loaded by a uniform load
w
w
. The ends of the spandrel beams are maintained
torsionally fixed. This condition is more severe, and therefore more conservative, than that
existing in the frame. It is adopted to simplify the analysis and the testing procedures.
The load
acting on the test specimen will create a negative bending moment at the
continuous end of the floor beam due to the torsional restraint of the spandrel beam. If we
separate the floor beam from the spandrel beam, as shown in Figure 7.15(b), this negative
moment is designated as
M
acting on the end of the floor beam. The reaction of this moment
M
becomes a twisting moment acting on the midspan of the spandrel beam, thus creating a
uniform torque
T
in the spandrel beam. The torque
T
is equal to
M
w
2. The bending moment,
shear and torque diagrams are drawn in Figure 7.16 from equilibrium conditions. It can be
seen that all three diagrams can be plotted if the moment
M
is known. This moment will be
called the joint moment.
The joint moment
M
can be determined from the compatibility of rotation at the joint while
neglecting the vertical deflection of the spandrel beam:
/
1
2
f
8
w
M
=
(7.86)
K
f
K
ts
3
16
1
+
where
K
f
=
:
flexural stiffness of the floor beam
=
4
EI
/
f
;
K
ts
=
torsional stiffness of spandrel beam
=
GC
/
s
, where
C
=
St. Venant's torsional
constant.
