Civil Engineering Reference
In-Depth Information
If FS
3
>
1:
If
E>D
, and
E
is applied in the direction
ψ
e
,
α
e
, or within a certain range encom-
passing this direction, then contact is lost
on both planes and FS
S
Q
(Q
)
2
B((S
)
2
E
2
)
1
/
2
−
E
{
+
−
}
=
0. Terminate
FS
3
=
(S
)
2
E
2
−
calculation.
(III.90)
If
N
1
>
0 and
N
2
<
0, assume contact
on plane 1 only after application of
E
.
Determine
(d)
B
(III.91)
χ
=
+
(
FS
3
)
2
S
x
,
S
y
,
S
z
,
S
a
,
Q
a
,FS
1
from
((
FS
3
)νi
x
−
ρk
x
tan
φ
1
−
µl
x
tan
φ
2
)
equations (III.65) to (III.70) with
E
=
0.
e
x
=−
χ
If FS
1
<
1, terminate computation.
If FS
1
>
1:
(III.92)
((
FS
3
)νi
y
−
ρk
y
tan
φ
1
−
µl
y
tan
φ
2
)
χ
e
y
=−
S
a
Q
a
−
(Q
a
)
2
((S
a
)
2
(III.93)
E
2
)
tan
2
φ
1
}
1
/
2
E
{
+
−
FS
1
=
(S
a
)
2
E
2
−
((
FS
3
)νi
z
−
ρk
z
tan
φ
1
−
µl
z
tan
φ
2
)
(III.84)
e
z
=−
χ
arcsin
S
z
S
a
arctan
tan
φ
1
(
FS
1
)
(III.94)
ψ
e
1
=
−
(III.95)
ψ
e3
=
arcsin
(
−
e
z
)
arctan
e
x
e
y
(III.85)
(III.96)
α
e3
=
arctan
S
x
S
a
180
◦
α
e
1
=
+
(III.86)
Compute
s
e
and
v
e
using
equations
(III.26) and (III.27)
If
N
1
<
0 and
N
2
>
0, assume contact
on plane 2 only after application of
E
.
Determine
(e)
N
1
+
N
1
=
Eρ(r v
e
−
s
e
)
(III.97)
S
x
,
S
y
,
S
z
,
S
b
,
Q
b
,FS
2
from
N
2
+
N
2
=
Eµ(r s
e
−
v
e
)
(III.98)
equations (III.72) to (III.77) with
E
=
0.
If FS
2
<
1, terminate computation.
If FS
2
>
1:
Check that
N
1
0 and
N
2
0
3
Minimum cable or bolt tension T
min
required
to raise the factor of safety to some spe-
cified value
FS.
S
b
Q
b
−
(Q
b
)
2
((S
b
)
2
E
2
)
tan
2
φ
2
1
/
2
E
{
+
−
}
FS
2
=
(S
b
)
2
−
E
2
(III.87)
Evaluate
N
1
,
N
2
,
S
,
Q
by means of equa-
tions (III.61), (III.62), (III.78), (III.79)
with
T
arcsin
S
z
S
b
(a)
arctan
tan
φ
2
(
FS
2
)
ψ
e
2
=
−
=
0.
If
N
2
<
0, contact is lost on plane 2
when
T
(b)
(III.88)
=
0. Assume contact on plane 1
arctan
S
x
S
y
only,
after application on
T
.
Evalu-
180
◦
α
e
2
=
+
(III.89)
ate
S
x
,
S
y
,
S
z
,
S
a
and
Q
a
using equations
(III.65) to (III.69) with
T
=
0.
If
N
1
>
0 and
N
2
>
0, assume contact
on both planes after application of E.
If FS
3
<
1, terminate computation.
(f)
((
FS
)S
a
−
Q
a
)
T
1
=
(
FS
)
2
(III.99)
tan
2
φ
1
+
