Civil Engineering Reference
In-Depth Information
displacement in direction of the bolt
u
are computed at nodal point
n
of the cell using
x
the transformation:
(18.12)
us
us
u
xn
1
x
xn
1
y
yn
x
s
r
s
y
2
r
y
r
x
Figure 18.8
Local coordinate system
Then the strain in the bolt at nodal point
n
can be computed by:
w
u
()
[
w
u
()
[
w
[
xn
xn
H
(18.13)
xn
w
x
w
[
w
x
where
2(3)
w
[
1
¦
u
(
[
)
N
(
[
)
u
and
(18.14)
xn
i
n
i
w
x
J
i
1
where
x
u
is the displacement in bolt direction at node
i
of the cell and
J
is the Jacobian
of the transformation from
x
,y
to [. The initial stress at node
n
of a cell
c
is computed
by
c
V
(
E
E
)
H
(18.15)
0
xn
Rock
Bolt
xn
R
of the residual vector
^
R
In general the component
due to the “initial stress” is
computed by
RE ı
(18.16)
PQ
,
QdV
i
i
0
V
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