10-10-2014, 02:21 PM
Cable supported bridges, being flexible in nature, respond more severely due to
ground accelerations than do any other type of bridges. The response is greatly
influenced by many parameters governing the bridge geometry and material.
One of the parameter is the non linear behaviour of the cables and the deck.
Although, the true non linear behaviour of the structure can be both material and
geometric. the geometric non linearitys are more predominant in nature and
affect the response of the structure. This geometric non linear behaviour arises
due to the non linear force deformation relation of the cables. The state of the art
technique in cable supported bridge analysis primarily involves a finite element
modeling of the structure including nonlinear effects.
In this study, an attempt has been made to project the role of geometric non
linear behaviour of suspension bridges on its dynamic response under
earthquake excitations. A finite element model of a cable has been developed
which incorporates geometric non linear features. In this study Both the cables
and the deck- elements have been modeled considering geometric non linear
effects. The effects of material non linearities have not been considered in this
study. The findings of this study indicates that the construction sequences of
suspension bridges induces significance nonlinearities in cable stiffness resulting
a shifting in the dynamic response under seismic excitation. A brief review of the
topics covered in different chapters are indicated below.
A brief review of the work has been presented in Chapter 1. A brief introduction
has been given and the scope and limitations of the works have been indicated.
A critical review of the literatures have been presented in chapter 2. The basic
geometric non linear behaviour of a single cable has been briefly explained. The
various methods available for modeling the bridge super-structure including the
deck an@ cables have been investigated. The use of the beam elements for
modeling the deck of the bridges has been explained. It has been noted in this
chapter that appropriate Placing of the beam elements in the finite element
model is required to depict the exact behavior of the prototype structure. Several
existing methods foifinite element modeling of cables have been discussed. The
advantage of modeling the cable using truss elements and its limitations in
simulating the geometric nonlinear behaviour have been presented in this
chapter. The present. study uses a specially developed spar element which
incorporates the geometric nonlinear behaviour with the idealized modulus of
elasticity. Therefore, a discussion on the cable modeling has bee presented in
this chapter which briefly reviews the existing model for idealized modulus of
elasticity. Various analytical tools available for the geometric nonlinear forced
vibration analysis have been discussed. The various method of simulating the
ground motion acceleration has been explained. Lastly, the use of existing,
strong motion databases for time history analysis has been indicated.
The development of a finite element model of a cable has been discussed in detail
in Chapter 3. The bridge cable undergoes displacements at both the supports
under both static and dynamic loads. Keeping this in mind, the cable element
has been developed from the governing equation of a basic suspended cable
under support displacement assuming the profile to be parabolic. The use of a
idealized straight bar element with lengths equal to the length of the span of the
cable has been discussed. The stress strain law governing the response of the bar
element has been developed from the equilibrium equation for the cable. From
the stress strain law, the idealized tangent modulus of elasticity of the bar
element has been developed. The ability of the idealized modulus of elasticity to
capture the true geometric non linear behaviour of the cable has also been
explained in detail. The advantages and disadvantages of using the tangent
stiffness modulus has been explained. A parametric study examining the
influence of different cable geometric parameters on the stiffness modulus has
also been projected. in this context, a few parameters have been identified which
govern the equation of equilibrium of the cable. This form of idealized modulus
of elasticity has been compared width the existing form and the different
inherent inappropriate assumptions of the later one have been shown. Lastly,
the same idealized tangent modulus has also been developed using the
equilibrium equation of an exact catenary profile of the cable and is used in later
chapters for the modeling.
The free and forced vibration response of the bridge have been projected n
Chapter 4. It is a known fact that the stiffening behaviour of any structure shifts
the natural frequencies of the structure towards the higher end. In this chapter,
one of the source of increase in stiffness, namely, the gradual application of the
deck load as done in construction process has been discussed. The step by step
addition of deck loads in a construction process has been simulated using the
finite element model of the bridge by non linear static analysis. The result of this
simulation has then been validated by comparing with the results obtained by an
analytical simulation of the process using th6 governing equilibrium equation of
the cable which changes with each erection step. General recursive analytical
formulae have been developed for this purpose. After the non linear static
analysis has been per-formed, the free and forced liberation analysis of the
structure has been undertaken starting from the stiffness obtained at the end of
non linear static analysis. The effects of geometric non linear behaviour of the
cable in free and forced vibration analysis have been discussed. Effect of
different erection schemes followed at the construction site on the changes in
stiffness and hence the response of the structure have been discussed.
Finally, chapter 5 based on the study, a broad set of conclusions have been
projected. A few open areas for further research have also been indicated at the
end of the chapter.