Civil Engineering Reference
In-Depth Information
A simple solution for determining the force on the stiffening girder of
linear equation by the classical theory uses the beam-on-elastic-support
analogy (Troitsky 1988). If the shortening of both cables and tower is con-
sidered, the spring constants for the elastic support can be determined by
Equation 2.14 as
1
K
=
(2.14)
)
(
)
(
2
α
+
sin
/
/
H A E
L A E
t
t
t
e
c
c
where:
A
t
,
E
t
, and
H
t
are the area, Young's modulus, and height of the tower,
respectively
A
c
,
E
c
,
L
c
, and α are the area, Young's modulus, length, and inclined
angle of the cable, respectively (Figure 2.38b)
In early analysis of this system, the continuous stiffening girder on elastic
supports is considered as the basic system (Figure 2.38a), and the cable
forces are taken as being redundant.
For the preliminary analysis, a moment diagram may be constructed for
the girder. The cable forces are obtained through the shear forces and then
applied to the tower. The stresses at any section of the bridge system may
be evaluated by computer. Calculation would determine the approximate
cable stresses under dead load on the girder plus live load.
Nonlinear system
—Nonlinearity of cable-stayed bridges generally can
be categorized as the cable, stiffening girders, and towers. The nonlinearity
of the cable is caused by the variation in sag with tensile force. To overcome
this nonlinear effect, Ernst uses the equivalent modulus of elasticity
E
i
to
replace the modulus of elasticity of straight cable, and it will be discussed
more in Chapter 11, which is designated for cable-stayed bridges.
The nonlinearity of the stiffened girders and towers is subjected to the
interaction of compressive axial force and bending moments. The girder
K
L
α
L
w
M
1
M
2
M
3
M
4
M
4
M
3
M
2
M
1
Δ
L
(a)
(b)
Figure 2.38
Basic cable-stayed system: (a) assumption of continuous stiffening girder on
elastic supports; (b) moveable cable.
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