Arch bridge structural solution has been known for centuries, in fact the simple
nature of arch that require low tension and shear strength was an advantage as the
simple materials like stone and brick were the only option back in ancient centuries.
By the pass of time especially after industrial revolution, the new materials were
adopted in construction of arch bridges to reach longer spans. Nowadays one long
span arch bridge is made of steel, concrete or combination of these two as "CFST",
as the result of using these high strength materials, very long spans can be achieved.
The current record for longest arch belongs to Chaotianmen bridge over Yangtze
river in China with 552 meters span made of steel and the longest reinforced concrete
type is Wanxian bridge which also cross the Yangtze river through a 420 meters
span. Today the designer is no longer limited by span length as long as arch bridge is the most applicable solution among other approaches, i.e. cable
stayed and suspended bridges are more reasonable if very long span is desired. Like any super structure, the economical and architectural aspects in construction of
a bridge is extremely important, in other words, as a narrower bridge has better
appearance, it also require smaller volume of material which make the design more
economical. Design of such bridge, beside the high strength materials, requires
precise structural analysis approaches capable of integrating the combination of
material behaviour and complex geometry of structure and various types of loads
which may be applied to bridge during its service life. Depend on the design strategy,
analysis may only evaluates the linear elastic behaviour of structure or consider
the nonlinear properties as well. Although most of structures in the past were
designed to act in their elastic range, the rapid increase in computational capacity
allow us to consider different sources of nonlinearities in order to achieve a more
realistic evaluations where the dynamic behaviour of bridge is important especially in
seismic zones where large movements may occur or structure experience P - _ effect
during the earthquake. The above mentioned type of analysis is computationally
expensive and very time consuming. In recent years, several methods were proposed
in order to resolve this problem. Discussion of recent developments on these methods
and their application on long span concrete arch bridges is the main goal of this
research. Accordingly available long span concrete arch bridges have been studied
to gather the critical information about their geometrical aspects and properties
of their materials. Based on concluded information, several concrete arch bridges
were designed for further studies. The main span of these bridges range from 100
to 400 meters. The Structural analysis methods implemented in in this study are
Direct Response History Analysis (DRHA): This method solves the direct
equation of motion over time history of applied acceleration or imposed load
in linear elastic range.
Modal Response History Analysis (MRHA): Similar to DRHA, this method
is also based on time history, but the equation of motion is simplified to single degree of freedom system and calculates the response of each mode
independently. Performing this analysis require less time than DRHA.
Modal Response Spectrum Analysis (MRSA): As it is obvious from its name,
this method calculates the peak response of structure for each mode and combine
them using modal combination rules based on the introduced spectra of
ground motion. This method is expected to be fastest among Elastic analysis.
Nonlinear Response History Analysis (NL-RHA): The most accurate strategy
to address significant nonlinearities in structural dynamics is undoubtedly
the nonlinear response history analysis which is similar to DRHA but extended
to inelastic range by updating the stiffness matrix for every iteration. This
onerous task, clearly increase the computational cost especially for unsymmetrical
buildings that requires to be analyzed in a full 3D model for taking the
torsional effects in to consideration.
Modal Pushover Analysis (MPA): The Modal Pushover Analysis is basically
the MRHA but extended to inelastic stage. After all, the MRHA cannot solve
the system of dynamics because the resisting force fs(u; u_ ) is unknown for
inelastic stage. The solution of MPA for this obstacle is using the previously
recorded fs to evaluate system of dynamics. Extended Modal Pushover Analysis (EMPA): Expanded Modal pushover is
a one of very recent proposed methods which evaluates response of structure
under multi-directional excitation using the modal pushover analysis strategy.
In one specific mode,the original pushover neglect the contribution of the directions
different than characteristic one, this is reasonable in regular symmetric
building but a structure with complex shape like long span arch bridges may
go through strong modal coupling. This method intend to consider modal
coupling while it take same time of computation as MPA.
Coupled Nonlinear Static Pushover Analysis (CNSP): The EMPA includes
the contribution of non-characteristic direction to the formal MPA procedure.
However the static pushovers in EMPA are performed individually for every
mode, accordingly the resulted values from different modes can be combined
but this is only valid in elastic phase; as soon as any element in structure starts
yielding the neutral axis of that section is no longer fixed for both response
during the earthquake, meaning the longitudinal deflection unavoidably affect
the transverse one or vice versa. To overcome this drawback, the CNSP suggests
executing pushover analysis for governing modes of each direction at the
same time. This strategy is estimated to be more accurate than MPA and
EMPA, moreover the calculation time is reduced because only one pushover
analysis is required.
Regardless of the strategy, the accuracy of structural analysis is highly dependent on
modelling and numerical integration approaches used in evaluation of each method.
Therefore the widely used Finite Element Method is implemented in process of all
analysis performed in this research.
In order to address the study, chapter 2, starts with gathered information about
constructed long span arch bridges, this chapter continuous with geometrical and
material definition of new models. Chapter 3 provides the detailed information
about structural analysis strategies; furthermore the step by step description of
procedure of all methods is available in Appendix A. The document ends with the
description of results and conclusion of chapter 4.