Arch bridges - Computational Analysis and Design of Bridge Structures - page 281

q

p

y

y

x

H x H

0

V = ql /2 V = ql /2

l /2 l /2

l

Figure 9.14 Perfect arch shape under a uniform symmetric load.

Substituting x and y with l 2 and f, respectively, at the crown, the horizon-
tal thrust H can be obtained as

2

ql
f

H = (9.2)

8

Substituting Equation 9.2 into Equation 9.1, the perfect arch shape can be
derived as

f
l

x
l

4

y = x − (9.3)

1

From Equation 9.3, it can be seen that the perfect axis for an arch under
uniform dead load is a parabola. In most arch bridges, the dead loads along
the bridge axis do not vary much and can be assumed as uniformed, which
is the reason that the parabola arch axis is commonly used. In addition
to parabola, catenary and circularity can also be used as an arch axis.
It should be noted that when perfect arch axis is referred it implies that the
arch is under a uniform dead load.
From Equation 9.2, a common fact of arch bridges is proved that the
horizontal thrust is inversely proportional to the arch rise.

9.3.2 fatigue analysis and affecting factors
Long-span arch bridge provides a favorable driving condition for the vehi-
cles. However, the repeated action of traffic to the bridge will lead fatigue
damage to the members of the arch structure, especially the hangers in
the tied-arch bridge. Most bridges were damaged not because of the load
beyond capacity but because certain hangers lost the strength due to fatigue
damage.