Civil Engineering Reference
In-Depth Information
Example 3.1 outlines the calculation of the geometrical (shift and curvature) effects
on vertical live load forces on right superstructures.
Example 3.1
A ballasted steel through plate girder railway bridge is to be designed with
a6
◦
curvature track across its 70 ft span. The railroad has specified a 5 in.
superelevation based on operating speeds and conditions. The track tie
depth and rail height are taken as 7 in. each and the girders are spaced at
16 ft. Determine the geometrical effects of the curvature on the design live
load shear and bending moment for each girder.
The effect of the offset of the live load center of gravity is (Equation
3.28)
e
s
=[
9.35 in. (from the centerline of the track).
The outside girder forces will be reduced by, and the inside girder
forces increased by,
8
+
(
14
/
12
)
]
(
5
)/(
4.9
)
=
9.74% (Equation 3.29).
The curve mid-ordinate over a 70 ft span (Equation 3.22) is
[
2
(
9.35
)/(
16
)(
12
)
]
(
100
)
=
(
70
)
2
6
8
(
5730
)
=
M
=
0.64 ft
=
7.7 in.
Design for equal shear at the girder ends and use a track offset at the
centerline of
7.7
3
m
1
=
=
2.56, use 2.5 in.
Theeffectofthecurvaturealignment(Equations3.30and3.31)ongirdershear
forces is
1
1
L
2
12
RS
L
2
D
12
(
5730
)S
2
m
1
S
∓
2
m
1
S
∓
±
=
±
1
(
70
)
2
6
12
(
5730
)
16
2
(
2.5
)
(
16
)(
12
)
∓
=
±
=
(
1
±
0.026
∓
0.027
)
=
0.
The effect of the curvature alignment (Equations 3.32 and 3.33) on girder
flexural forces is
1
1
L
2
24
RS
L
2
D
24
(
5730
)S
2
m
1
S
2
m
1
S
±
∓
=
±
∓
1
(
70
)
2
6
24
(
5730
)
16
2
(
2.5
)
(
16
)(
12
)
∓
=
±
=
(
1
±
0.026
∓
0.013
)
.
The outside girder and inside girder forces are multiplied by
(
1
+
0.026
−
0.013
)
=
1.013 and
(
1
−
0.026
+
0.013
)
=
0.987, respectively, to account for the
offset of curved track alignment.
