Civil Engineering Reference
In-Depth Information
Table 9.3
Study of a tied-arch bridge with different middle spaces
d
Hanger numbers
Side hanger (1)
Middle hanger (6)
Spacing (ft)
13.4
16.7
25.1
33.4
13.4
16.7
25.1
33.4
Maximum stress (ksi)
46.65
60.83
90.41
121.92
51.78
65.41
96.57
128.08
Minimum stress (ksi)
39.79
51.78
77.40
104.11
42.05
53.77
78.76
104.79
Average stress (ksi)
43.22
56.30
83.90
113.01
46.91
59.59
87.67
116.44
Stress range (ksi)
6.86
9.05
13.01
17.81
9.73
11.64
17.81
23.29
SR ratio
0.758
1.000
1.438
1.970
0.836
1.000
1.530
2.000
9.3.2.2 Space of hangers
The space of hangers is an important parameter that influences the fatigue. In
this example (Figure 9.15), the space
d
is chosen as 4.1 (13.4′), 5.1 (16.7′), 7.7
(25.1′), and 10.2 m (33.4′), respectively. The result is shown in Table 9.3, and
the SR ratio of a spacing is its stress range over that of 5.1 m (16.7′).
Based on Table 9.3, a conclusion could be drawn that a closer spacing of
hangers will benefit hanger fatigues more than a sparse spacing. This can
be understood from the simple fact that the stress ranges due to live loads
are greater in a sparse layout than a finer layout.
9.3.2.3 Distance between side hanger and arch springing
The distance between side hanger and arch springing (
b
shown in Figure 9.15)
will be selected as 2.5 (8.3′), 5.1 (16.7′), 7.7 (25.1′), and 10.2 m (33.4′),
respectively, which means the ratio of this distance to the distance between
other hangers is 0.5:1, 1:1, 1.5:1, and 2:1, respectively. The result is shown in
Table 9.4, and the SR ratio is based on the ratio of
b
to
d
, taking 1:1 as one.
The result in Table 9.4 draws the conclusion that the change of the dis-
tance between the side hanger and springing makes little influence on the
middle hanger but makes great influence on the side hanger.
About the side hanger, either increase or decrease of the distance between the
side hanger and springing will lead to higher stress range. When the distance
is extended, tension in the side hanger as a point to bear the load will increase.
When the distance is too small, however, the side hanger will be short so that
the vertical tensile stiffness will increase and that will also lead to higher stress
range. Hence, to enable the hangers have the most effective work, the distance
between the side hanger and springing should be in a proper range.
The fatigue problem in hangers of a tied-arch bridge is a complicated one
that many factors such as the section area of hangers, flexural rigidity of
hangers, and the impact force of the vehicles will have considerable influ-
ences on the fatigue. Besides, the dimensions of the bridge such as span and
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