An Analytical Study on Dynamic Response of Multiple Simply Supported Beam System Subjected to Moving Loads

Based on Euler–Bernoulli beam theory, first, partial differential equations were established for the vibration of multiple simply supported beams subjected to moving loads. Then, integral transforms were conducted on the spatial displacement coordinate and time in the partial differential equations, and the frequency-domain response of multiple simply supported beams subjected to moving loads was obtained. Next, by conducting the corresponding inverse transforms on the displacement frequency-domain responses of multiple simply supported beams, the spatial displacement time-domain responses were obtained. Finally, to validate the analytical method reported in this paper, the dynamic response of a typical double simply supported rail-bridge beam system of high-speed railway in China subjected to a moving load was carried out. The results show that the analytical solution proposed in this paper is consistent with the results obtained from a finite element analysis, validating and rationalizing the analytical solution. Moreover, the system parameters were analyzed for the dynamic response of double simply supported rail-bridge beam system in high-speed railway subjected to a moving load with different speeds; the conclusions can be beneficial for engineering practice

Improved Finite Beam Element Method to Analyze the Natural Vibration of Steel-Concrete Composite Truss Beam

Based on Hamilton’s principle, this study has developed a continuous treatment for the steel-concrete composite truss beam (SCCTB). It has also deduced the SCCTB element stiffness matrix and mass matrix, which include the effects of interface slip, shear deformation, moment of inertia, and many other influencing factors. A finite beam element method (FBEM) program for SCCTB’s natural vibration frequency has been developed and used to calculate the natural vibration frequencies of several SCCTBs with different spans and different degrees of shear connections. The FBEM’s calculation results of several SCCTBs agree well with the results obtained from ANSYS. Based on the results of this study, the following conclusions can be drawn. For the SCCTB with high-order natural vibration frequency and with short span, the effect of the shear deformation is greater. Hence, the effect of the shear deformation on the SCCTB’s high-order natural vibration frequency cannot be ignored. On the other hand, the effect of the interface slip on the SCCTB’s high-order natural vibration frequency is insignificant. However, the effect of the interface slip on the SCCTB’s low-order natural vibration frequency cannot be ignored

Shear Lag Effect and Accordion Effect on Dynamic Characteristics of Composite Box Girder Bridge with Corrugated Steel Webs

This study proposed a dynamic characteristic analytical method (ANM) of a composite box girder bridge with corrugated steel web (CBGCSW) by completely considering the impact of shear lag effect and accordion effect of corrugated steel webs. Based on energy principles and variational principles, a vibration differential equation and the natural boundary conditions of a CBGCSW were developed. The analytical calculation formula for solving the vibration differential equation was then obtained. The results calculated using the ANM agreed well with previous experimental results, which validated the correctness of ANM. To demonstrate the superiority of the ANM, the vibration frequencies of several abstract CBGCSWs with varying ratios of span–width, obtained using the elementary beam theory (EBT) and the finite element method (FEM), were compared with those obtained by ANM. The efficacy of the ANM was verified and some meaningful conclusions were drawn which are helpful to relevant engineering design, such as the observation that a higher natural vibration frequency and smaller span–width ratio significantly magnified the shear lag effect of CBGCSW. The first five-order natural vibration frequencies of the CBGCSW were significantly lower than those of the composite box girder bridge with general steel web (CBGGSW), which indicates that the impact of the accordion effect is significant

Vibration Analysis of Steel-Concrete Composite Box Beams considering Shear Lag and Slip

In order to investigate dynamic characteristics of steel-concrete composite box beams, a longitudinal warping function of beam section considering self-balancing of axial forces is established. On the basis of Hamilton principle, governing differential equations of vibration and displacement boundary conditions are deduced by taking into account coupled influencing of shear lag, interface slip, and shear deformation. The proposed method shows an improvement over previous calculations. The central difference method is applied to solve the differential equations to obtain dynamic responses of composite beams subjected to arbitrarily distributed loads. The results from the proposed method are found to be in good agreement with those from ANSYS through numerical studies. Its validity is thus verified and meaningful conclusions for engineering design can be drawn as follows. There are obvious shear lag effects in the top concrete slab and bottom plate of steel beams under dynamic excitation. This shear lag increases with the increasing degree of shear connections. However, it has little impact on the period and deflection amplitude of vibration of composite box beams. The amplitude of deflection and strains in concrete slab reduce as the degree of shear connections increases. Nevertheless, the influence of shear connections on the period of vibration is not distinct

Distortional Buckling Analysis of Steel-Concrete Composite Girders in Negative Moment Area

Distortional buckling is one of the most important buckling modes of the steel-concrete composite girder under negative moment. In this study, the equivalent lateral and torsional restraints of the bottom flange of a steel-concrete composite girder under negative moments due to variable axial forces are thoroughly investigated. The results show that there is a coupling effect between the applied forces and the lateral and torsional restraint of the bottom flange. Based on the calculation formula of lateral and torsional restraints, the critical buckling stress of I-steel-concrete composite girders and steel-concrete composite box girders under variable axial force is obtained. The critical bending moment of the steel-concrete composite girders can be further calculated. Compared to the traditional calculation methods of elastic foundation beam, the paper introduces an improved method, which considers coupling effect of the external loads and the foundation spring constraints of the bottom flange. Fifteen examples of the steel-concrete composite girders in different conditions are calculated. The calculation results show a good match between the hand calculation and the ANSYS finite element method, which validated that the analytic calculation method proposed in this paper is practical

Dynamic Response Analysis of a Simply Supported Double-Beam System under Successive Moving Loads

The dynamic response of a simply supported double-beam system under moving loads was studied. First, in order to reduce the difficulty of solving the equation, a finite sin-Fourier transform was used to transform the infinite-degree-of-freedom double-beam system into a superimposed two-degrees-of-freedom system. Second, Duhamel’s integral was used to obtain the analytical expression of Fourier amplitude spectrum function considering the initial conditions. Finally, based on finite sin-Fourier inverse transform, the analytical expression of dynamic response of a simply supported double-beam system under moving loads was deduced. The dynamic response under successive moving loads was calculated by the analytical method and the general FEM software ANSYS. The analysis results show that the analytical method calculation results are consistent with ANSYS’ calculation, thus validating the analytical calculation method. The simply supported double-beam system had multiple critical speeds, and the flexural rigidity significantly affected both peak vertical displacement and critical speed

An Analytical Solution for the Geometry of High-Speed Railway CRTS Ⅲ Slab Ballastless Track

To study the mapping relationship between girder deformation and rail deformation for the CRTS Ⅲ slab ballastless track (SBT) multi-span simply supported bridge, this study derived a simplified analytical solution, and the corresponding ANSYS finite element model (AFEM) was established. Compared with the fine analytical model (FAM) and the AFEM, the calculation results of the three models under the conditions of pier settlement and girder vertical fault were compared, which verified the universal properties of the simplified analytical model (SAM). Based on the verified SAM, the influence of pier settlement, fastener stiffness, girder span, and girder vertical fault on rail deformation was studied. The results show that the rail deformation is approximately proportional to pier settlement and girder vertical fault. With the increase in fastener stiffness, the fastener internal force increases, the rail mapping deformation increases, and the length of the rail mapping deformation area decreases. With the increase in girder span, the rail deformation curve becomes smooth, the length of the rail mapping deformation area becomes longer, and the fastener internal force is significantly reduced

Experimental Study and Theoretical Analysis of Steel–Concrete Composite Box Girder Bending Moment–Curvature Restoring Force

A steel–concrete composite box girder has good anti-seismic energy dissipation capacity, absorbs seismic energy, and reduces seismic action. It is very suitable for high-rise and super high-rise mega composite structure systems, which is in accordance with the condition of capital construction. In order to accurately study the elastic–plastic seismic response of the composite structure, the restoring force model of the building structure is the primary problem that needs to be solved. Previous research shows that shear connection degree, force ratio, and web height–thickness ratio are the major factors that influence composite box girder bearing capacity and seismic behavior. In this paper, low cycle vertical load tests of four steel–concrete composite box girders were conducted with different shear connection degrees and ratios of web height to thickness. The seismic behavior of a steel–concrete composite box girder was analyzed in depth, such as the hysteresis law, skeleton curve, and stiffness degradation law, etc. The influence of the shear connection degree and ratio of web height to thickness on seismic performance of the steel–concrete composite box girder was investigated. A three-fold line model of the bending moment–curvature skeleton curve of composite box girders was established. On the basis of experimental data and theoretical analysis, the formula of positive and negative stiffness degradation of composite box girders was obtained. Furthermore, the maximum point orientation hysteresis model of the bending moment–curvature of steel–concrete composite box girders was established. The calculated results of the restoring force model agree well with the experimental results. The accuracy of the proposed method is verified. The calculation method of the model is simple and clear, convenient for hand calculation, and suitable for engineering applications

Earthquake Influence on the Rail Irregularity on High-Speed Railway Bridge

Rail irregularity is the leading cause of enhancing train-track coupling vibration and, therefore, should be studied in detail for safety requirements. In this study, the differences between existing rail irregularities without being subjected to an earthquake between different countries were first studied. Results show that existing power spectrum density and time-domain displacement samples of rail irregularities in the American code are the largest, while the irregularities of the Germany railway are higher than those of China in a specific range of rail wavelengths. Afterward, the effects of earthquake intensity, soil site, and duration on the rail irregularity of a Chinese typical high-speed railway bridge were investigated. For this purpose, a finite element model was established and validated by the shaking table test of a 1/12-scaled high-speed railway bridge experimental specimen. The calculation results indicated that the influences of earthquakes on the rail alignment irregularity were evident