Civil Engineering Reference
In-Depth Information
y
6"
¾"
Loading along
z
axis
35 kips
35 kips
7/16"
30½"
x
9'
9'
z
105 kip-in.
T
1890 kip-in.
M
¾"
12"
17.5 kips
V
Cross section in
xy
plane
FIGURE E8.1
The solution of the differential Equation 8.16 is
A
sinh
z
a
B
cosh
z
a
T
2
GJ
z
.
θ =
+
+
C
+
d
2
θ
/
d
z
2
For boundary conditions
θ =
=
0at
z
=
0 and
z
=
L
,
z
a
−
0.40
z
,
T
a
2
GJ
sinh
(z/a)
cosh
(L/
2
a)
sinh
(z/
180
)
1.186
θ =
=
180
−
1
10
−3
1
,
T
2
GJ
d
θ
d
z
=
cosh
(z/a)
cosh
(L/
2
a)
cosh
(z/
180
)
1.186
−
=
2.22
×
−
10
−5
,
d
2
T
2
GJa
θ
d
z
2
=
sinh
(z/a)
cosh
(L/
2
a)
sinh
(z/
180
)
1.186
−
=
1.23
×
−
2
GJa
2
10
−8
.
d
3
T
θ
d
z
3
=
cosh
(z/a)
cosh
(L/
2
a)
cosh
(z/
180
)
1.186
−
=
6.87
×
−
Pure (St. Venant) torsion
(Table E8.1)
:
Gt
d
10
−3
1
θ
d
z
cosh
(z/
180
)
1.186
τ
t
=
=
11,200
(t)
2.22
×
−
24.82
t
1
.
cosh
(z/
180
)
1.186
=
−
