Civil Engineering Reference
In-Depth Information
Figure 19.15
Work done in a slip fan.
the increment of work done by the internal stresses through the fan is
s
u
R
(
s
u
(
R
δ
W
=
δ
w
δθ
)
+
δθ
)
δ
w
(19.32)
Hence, in the limit,
w
θ
f
0
δ
W
=
2
s
u
R
δ
d
θ
(19.33)
and
δ
W
=
2
s
u
R
δ
w
θ
f
=
2
s
u
R
δ
w
θ
(19.34)
where
θ
f
is the fan angle which is equal to the change
θ
in the direction of the vector
of displacement
w
across slip fan.
We can also consider the change of stress from one region to another across a fan of
discontinuities, as shown in Fig. 19.16. (The fan of stress discontinuities in Fig. 19.16
is not necessarily the same as the fan of slip surfaces in Fig. 19.14.) The fan angle
δ
Figure 19.16
Rotation of the direction of the major principal stress across a stress fan.
