Civil Engineering Reference
In-Depth Information
(i)
Effective normal reactions on planes 1
and 2 assuming contact on both planes.
S
x
=
(Tt
x
+
Ee
x
+
N
b
b
x
+
Vf
5
x
+
u
2
A
2
a
x
)
(III.72)
S
y
=
(Tt
y
+
Ee
y
+
N
b
b
y
+
Vf
5
y
+
u
2
A
2
a
y
)
(III.73)
N
1
=
ρ
{
Wk
z
+
T(rv
−
s)
+
E(r v
e
−
s
e
)
+
V(rv
5
−
s
5
)
}
S
z
=
(Tt
z
+
Ee
z
+
N
b
b
z
+
Vf
5
z
−
u
1
A
1
(III.61)
(III.74)
+
u
2
A
2
a
z
)
+
W
N
2
=
µ
{
Wl
z
+
T(rs
−
v)
S
b
=
(S
x
+
S
y
+
S
z
)
1
/
2
(III.75)
+
E(r s
e
−
v
e
)
+
V(rs
5
−
v
5
)
}
(III.76)
Q
b
=
(N
b
−
u
2
A
2
)
tan
φ
2
+
c
2
A
2
Q
b
S
b
−
u
2
A
2
(III.62)
(III.77)
FS
2
=
(j)
Factor of safety when
N
1
<
0 and
N
2
<
0 (contact is lost on both planes).
(m)
If
N
1
>
0 and
N
2
>
0, contact is main-
tained on both planes and the factor of
safety is calculated as follows:
=
FS
0
(III.63)
(k)
If
N
1
>
0 and
N
2
<
0, contact is main-
tained on plane 1 only and the factor of
safety is calculated as follows:
=
ν(Wi
z
−
−
Ew
e
−
S
Tw
Vw
5
)
(III.78)
Q
=
N
1
tan
φ
1
+
N
2
tan
φ
2
N
a
=
Wa
z
−
Ts
−
Es
e
−
Vs
5
−
u
1
A
1
r
(III.64)
+
c
1
A
1
+
c
2
A
2
(III.79)
Q
S
FS
3
=
(III.80)
S
x
=
(Tt
x
+
Ee
x
+
N
a
a
x
+
Vf
5
x
+
u
1
A
1
b
x
)
(III.65)
2
Minimum factor of safety producedwhen load
E of given magnitude is applied in the worst
direction.
S
y
=
(Tt
y
+
Ee
y
+
N
a
a
y
+
Vf
5
y
+
u
1
A
1
b
y
)
(III.66)
Evaluate
N
1
,
N
2
,
S
,
Q
,
FS
3
(a)
by use of
S
z
=
(Tt
z
+
Ee
z
+
N
a
a
z
equations
(III.61),
(III.62),
(III.78),
(III.67)
+
Vf
5
z
+
u
1
A
1
b
z
)
+
W
(III.79) and (III.80) with
E
=
0.
If
N
1
<
0 and
N
2
<
0, even before
E
is applied. Then FS
(b)
S
a
=
(S
x
+
S
y
+
S
z
)
1
/
2
(III.68)
=
0, terminate
computation.
2
mn
|
N
1
N
2
r
(III.69)
Q
a
=
(N
a
−
u
1
A
1
)
tan
φ
1
+
c
1
A
1
(N
1
)
2
(N
2
)
2
(c)
1
/
2
={
+
+
}
D
Q
a
S
a
mn
|
FS
1
=
(III.70)
(III.81)
arcsin
m
|
1
G
N
1
a
z
=
−
·
ψ
e
(l)
If
N
1
<
0 and
N
2
>
0, contact is main-
tained on plane 2 only and the factor of
safety is calculated as follows:
m
|
N
2
b
z
n
|
(III.82)
+
|
·
n
arctan
m
(III.83)
.
N
1
a
x
+
.
N
2
b
x
n
|
n
|
N
b
=
(Wb
z
−
Tv
−
Ev
e
−
Vv
5
−
u
2
A
2
r)
(III.71)
|
m
|
α
e
=
.
N
1
a
y
+
.
N
2
b
y
m
n
|
|
|
|
m
n
