Civil Engineering Reference
In-Depth Information
TABLE E8.1
Pure Torsion Shear Stress,
τ
t
(ksi)
Element of the Girder
z
=
0 (end)
z
=
L
/
2
=
108 in. (center)
Flange,
t
=
0.75 in.
2.92
0
Web,
t
=
0.44 in.
1.70
0
Warping torsion (lateral bending of the flanges) (Tables E8.2 and E8.3)
:
d
3
10
−8
Eb
f
h
16
29,000
(
12
)
2
(
31.25
)
16
−
θ
d
z
3
−
cosh
(z/
180
)
1.186
τ
w
=
=
6.87
×
−
0.472 cosh
z
180
,
=
d
2
10
−5
Eb
f
h
4
θ
d
z
2
29,000
(
12
)(
31.25
)
4
sinh
(z/
180
)
1.186
σ
w
=
=
1.23
×
−
28.20 sinh
z
180
.
=−
Flexure of the girder
(
Tables E8.4
and
E8.5)
:
M
=
35
(
216
)/
4
=
1890 kip-in.,
σ
b
(
0
)
=
0,
σ
b
L
2
1890
339
=±
=±
5.58 ksi,
V
=
35
/
2
=
17.5 k,
32
−
0.75
135.5 in.
3
,
Q
flange
=[
(
12
−
0.44
)(
0.75
)
]
=
2
TABLE E8.2
Warping Torsion Shear Stress,
τ
w
(ksi)
Element of the Girder
z
=
0 (end)
z
=
L
/
2
=
108 in. (center)
Flange,
t
=
0.75 in.
0.47
0.56
TABLE E8.3
Warping Torsion Normal Stress,
σ
w
(ksi)
Element of the Girder
z
=
0 (end)
z
=
L
/
2
=
108 in. (center)
Flanges,
t
=
0.75 in.
0
−
17.95
