Civil Engineering Reference
In-Depth Information
Figure 2.11
Shear flow due to shear and torsion in a box section
the four walls are:
V
2
d
v
T
2
A
o
q
w
=
+
(2.74)
V
2
d
v
T
2
A
o
q
r
w
=−
+
(2.75)
T
2
A
o
q
t
w
=
q
b
w
=
(2.76)
The steel cage of the box section is simplified as shown in Figure 2.12. It is assumed that
the centroids of the four longitudinal corner bars are located at the intersection points of the
center line of the hoop bars. It is also assumed that the center line of shear flow coincides with
the center line of the hoop bars, as well as the center line of the longitudinal bars. The angle
α
r
of the concrete struts should also be different in the four walls. According to Equation (2.5)
the value of
α
r
is:
q
n
t
tan
α
r
=
(2.77)
Substituting the four
q
's from Equations (2.74)-(2.76) into Equation (2.77) we have
V
2
d
v
1
n
t
T
2
A
o
tan
α
w
=
+
(2.78)
1
n
t
V
2
d
v
T
2
A
o
tan
α
r
w
=
−
+
(2.79)
T
2
A
o
1
n
t
tan
α
t
w
=
tan
α
b
w
=
(2.80)
These four angles are also shown in Fig. 2.12.
A rectangular box section subjected to shear, torsion and bending may fail in three modes.
They are presented in the following three sections.
