Civil Engineering Reference
In-Depth Information
TABLE E8.7
Pure Torsion Shear Stress,
τ
t
(ksi)
Element of the Girder
z
=
0 (end)
z
=
L
/
2
=
108 in. (center)
Flange,
t
=
0.625 in.
5.79
0
Web,
t
=
0.375 in.
3.48
0
The solution of the differential equation is (Equation 8.21a)
0.078
1
0.926 sinh
z
66.3
cosh
z
66.3
z
2
8791
+
z
40.70
−
θ =
−
+
−
and its differentials are
10
−3
0.926 cosh
z
66.3
sinh
z
66.3
1.629
,
d
θ
d
z
=
z
66.3
+
1.177
×
−
+
−
10
−5
0.926 sinh
z
66.3
cosh
z
66.3
1
,
d
2
θ
d
z
2
=
1.775
×
−
+
−
10
−7
0.926 cosh
z
a
sinh
z
a
.
d
3
θ
d
z
3
=
2.677
×
−
+
Pure (St. Venant) torsion (Table E8.7)
:
Gt
d
13.18
(t)
0.926 cosh
z
66.3
sinh
z
66.3
1.629
.
θ
d
z
z
66.3
+
τ
t
=
=
−
+
−
Warping torsion (lateral bending of flanges) (Tables E8.8 and
E8.9)
:
d
3
Eb
f
h
16
−
θ
d
z
3
τ
w
=
10
−7
)
0.926 cosh
z
a
sinh
z
a
,
29,000
(
10
)
2
(
12.25
)
16
−
=
(
2.677
×
−
+
0.60
0.926 cosh
z
66.3
sinh
z
66.3
,
τ
w
=
−
+
TABLE E8.8
Warping Torsion Shear Stress,
τ
w
(ksi)
Element of the Girder
z
=
0 (end)
z
=
L
/
2
=
108 in. (center)
Flange,
t
=
0.625 in.
−
0.55
0
