Francis T.K. Au

Vibration of railway bridges under a moving train by using bridge-track-vehicle element

During the last two decades, much attention has been paid to various vibration problems associated with railways. They include the dynamic response of railway bridges and railway tracks at grade under the action of moving trains. However, studies on the role of track structures on the vibration of railway bridges are rather limited. In this paper, a new element called bridge-track-vehicle element is proposed for investigating the interactions among a moving train, and its supporting railway track structure and bridge structure. The moving train is modelled as a series of two-degree-of-freedom mass-spring-damper systems at the axle locations. A bridge-track-vehicle element consists of vehicles modelled as mass-spring-damper systems, an upper beam element to model the rails and a lower beam element to model the bridge deck. The two beam elements are interconnected by a series of springs and dampers to model the rail bed. The investigation shows that the effect of track structure on the dynamic response of bridge structure is insignificant. However, the effect of the bridge structure on the dynamic response of the track structure is considerable.

Impact study of cable-stayed railway bridges with random rail irregularities

Abstract This paper describes a study of the vibration of cable-stayed bridges under moving railway trains. The moving train comprises a number of cars, each of which is modelled as a four-axle system possessing 10 degrees of freedom. The cable-stayed bridge is modelled as a planar system. As the rail irregularities are random in nature, sample profiles to model them are generated using a suitable power spectral density function of rail roughness. The behaviour of such a vehicle–bridge interaction problem is investigated using a typical cable-stayed bridge. The aspects studied include the effects of number of random samples, damping, class of railway track quality and initial motion of train vehicles.

Determination of initial cable forces in prestressed concrete cable-stayed bridges for given design deck profiles using the force equilibrium method

Abstract The determination of initial cable forces in a prestressed concrete cable-stayed bridge for a given vertical profile of deck under its dead load is an important but difficult task that affects the overall design of the bridge. A new method utilizing the idea of force equilibrium is presented in this paper for their determination. The method can easily account for the effect of prestressing and the additional bending moments due to the vertical profile of the bridge deck. It is much more rational and simple than the traditional “zero displacement” method, and it is able to achieve bending moments in the bridge deck approaching those in a continuous beam over rigid simple supports.

Numerical modelling for temperature distribution in steel bridges

Abstract Steel bridges may undergo significant temperature changes under the combined influence of solar radiation, daily air temperature variation and wind speed. In some circumstances, these temperature changes can induce thermal stresses that are comparable to the stresses induced by dead and live loads. As steel has a high conductivity, the bridges usually respond to the change of environmental conditions more readily. Therefore, an investigation of the thermal behaviour of steel bridges is important. This paper describes a numerical model developed for the analysis of temperature distribution in steel bridges and the computed results are compared with those obtained from scaled models. Sensitivity analysis has been carried out to study the effects of various parameters on the temperature distribution. In addition, a least square method is also suggested for backfiguring best values for the input parameters, if they are not available.

Identification of vehicles moving on continuous bridges with rough surface

Abstract This paper describes the parameter identification of vehicles moving on multi-span continuous bridges taking into account the surface roughness. Each moving vehicle is modelled as a two-degree-of-freedom system that comprises five components: a lower mass and an upper mass, which are connected together by a damper and a spring, together with another spring to represent the contact stiffness between the tyres and the bridge deck. The corresponding parameters of these five components, namely, the equivalent values of the two masses, the damping coefficient, and the two spring stiffnesses together with the roughness parameters are identified based on dynamic simulation of the vehicle–bridge system. In the study, the accelerations at selected measurement stations are simulated from the dynamic analysis of a continuous beam under moving vehicles taking into account randomly generated bridge surface roughness, together with the addition of artificially generated measurement noise. The identification is realized through a robust multi-stage optimization scheme based on genetic algorithms, which searches for the best estimates of parameters by minimizing the errors between the measured accelerations and the reconstructed accelerations from the identified parameters. Starting from the very wide initial variable domains, this multi-stage optimization scheme reduces the variable search domains stage by stage using the identified results of the previous stage. A few test cases are carried out to verify the efficiency of the multi-stage optimization procedure. The identified parameters are also used to estimate the time-varying contact forces between the vehicles and the bridge.

Temperature monitoring of steel bridges

The temperature monitoring of Tsing Ma Bridge is performed by the Wind and Structural Health Monitoring System on the Lantau Link as one of its functions. The system consists of over 90 platinum resistance type detectors on Tsing Ma Bridge installed at 4 selected cross-sections. Since May 1997, temperature measurements have been continuously recorded. The University of Hong Kong has been assisting in the analysis of these field measurements. This paper describes the instrumentation and data analysis related to the study. In parallel with this, experimental segmental steel sections under the influence of solar radiation have been set up on the university campus and temperature measurements have been recorded since 1993. Correlation results of observed data have shown that the temperature of steel sections mainly depends on the solar intensity and shade air temperature. Based on the theory of heat transfer, finite element models for different structural components of the bridge deck have been developed for prediction of temperature distribution. Good agreement with field data was observed. Comparison of positive temperature gradients among different structures has shown that they can generally be classified into two categories depending on the number of web faces exposed to the environment.

Estimation of Shrinkage Effects on Reinforced Concrete Podiums

The shrinkage of concrete often creates cracking problems in large podium structures. The long-term effects of shrinkage and creep in a concrete structure may be estimated by analysing it as a plane stress problem with the supporting walls and columns modelled as springs having suitable stiffnesses. The variation of stresses and strains may be obtained by time integration based on the conventional creep coefficient, time-dependent concrete modulus and shrinkage strain. Using a simplified one-dimensional model, the effects of structure size, support stiffness and stage construction on the induced stresses are investigated. Results show that the magnitude of induced stress normally increases with the member length and support stiffness. The rate of stress increase also depends on the support stiffness. An extensive parametric study is carried out to investigate the use of stage construction in controlling shrinkage stresses particularly focusing on the effect of time-lag and size of late-cast strip. Design charts are prepared for estimation of shrinkage stresses for simple cases. Examples of rough estimation of shrinkage stresses in two-dimensional cases are presented. Recommendations are also given for provision of reinforcement for crack control.

Modong Hongshui River Bridge, China

The Modong Hongshui River Bridge forms a vital component of the dual three-lane expressway between Nanning and Liuzhou, Guangxi Province in the south-western part of China. It is a reinforced concrete arch bridge with a main span of 180 m. The arch ribs were built using precast concrete segments erected by cantilever construction method with tiebacks. This technique has been well tried in the construction of cable-stayed bridges. As the tiebacks are temporary and therefore recoverable, the method is considered very economical.

Experimental and numerical investigation of post-tensioned concrete flat slabs in fire

Purpose This paper aims to understand the structural fire performance of two-way post-tensioned flat slabs, particularly their deformations and load-carrying mechanisms in fire, and to explore the behaviour of post-tensioned high-strength self-compacting concrete flat slabs with unbonded tendons in fire. Design/methodology/approach Four tests of post-tensioned high-strength self-compacting concrete flat slabs were conducted under fire conditions. Numerical modelling using the commercial package ABAQUS was conducted to help interpret the test results. Findings Two of the specimens with lower moisture contents demonstrated excellent fire resistance performance, while the others with slightly higher moisture contents experienced severe concrete spalling. Originality/value The test results were discussed in respect of thermal profiles, deflections, crack patterns and concrete spalling. The performance of post-tensioned high-strength self-compacting concrete flat slabs with unbonded tendons under fire conditions was better understood.

Early Age Temperature Rise and Thermal Stresses Induced in Concrete Bridge Pier

Heat generation of concrete during hardening causes early age temperature rise, and if the associated tendency of volume change is restrained, thermal stresses would be induced and early thermal cracking would result. This issue should be duly considered in concrete bridge construction as the bridge piers as well as other structural members are typically mass concrete members. In this paper, a real-life bridge pier is selected for study. The pier was instrumented to measure its early age temperature rise on site. Finite element analysis was conducted to evaluate the time variations of temperature distributions and thermal stresses induced in the bridge pier. The measurement and analysis results threw light on the evaluation of risk of thermal cracking and planning of temperature control measures in similar projects.