Civil Engineering Reference
In-Depth Information
Figure 2.13
Interaction of shear and torsion on peak plane
Equation (2.92) and noticing that
p
o
2
we obtain a nondimensional interaction relationship for
M
,
V
and
T
in the third mode:
V
V
o
N
b
+
N
t
2
N
t
1
+
R
=
b
v
+
d
v
=
and
2
R
2
d
v
p
o
=
2
T
T
o
2
VT
V
o
T
o
2
1
+
R
+
+
(2.93)
2
R
It should be pointed out that the third mode of failure is independent of the bending moment
M
.
Themi
xed
V
T
term is a function of the shape of the cross-section. For a square section,
√
2 and Equation (2.93) becomes
V
V
o
2
√
2
d
v
/
p
o
=
2
T
T
o
2
√
2
VT
V
o
T
o
1
+
R
+
+
=
(2.94)
2
R
Equation (2.94) represents a series of cylindrical interaction surfaces perpendicular to the
V
T
plane. The intersection of each cylindrical surface with its peak plane will produce
a curve, which is plotted as a solid curve in Figure 2.13. This solid curve, representing
the third interaction surface, is much lower than the corresponding dotted peak interaction
curve formed by the intersection of the first and second interaction surfaces. It can be con-
cluded, therefore, that the third mode of failure will always govern in the vicinity of the peak
planes.
Figure 2.14 illustrates the three interaction surfaces in a perspective manner for the case of
−
R
=
1
/
3. The shaded area in the vicinity of the peak plane is where the third interaction surface
