Analysis of Longitudinal Force of Beam and Rail of Continuously Welded Rails (CWR) on Railway Bridge

To study the longitudinal force of CWR on viaduct, a track-bridge-pier finite element model is established. Taking a multi-span simply supported beam with a maximum span of 32.7m of an elevated CWR as an example, the additional expansion and contraction forces, displacement between rail and beam and the force of pier are calculated, and whether the rail stress meets the requirements when setting constant resistance fasteners is checked. The results show that: (1) For the left and right lines, the maximum additional expansion forces of single strand rail are both 211.13kN, and the maximum relative displacements between beam and rail are both 6.572mm. (2) The maximum value of the additional expansion and contraction forces and the relative displacement between beam and rail of the same line occur at the same position. The left line is at ZFZ29 pier and the right line is at ZFS31 pier. (3) The maximum force of pier in this section is 500.80kN, and the pier numbers are ZFZ27 and ZFS29. (4) The rail stress is less than the allowable stress of 352MPa, and the rail strength meets the requirements.

Effects of the highway live load on the additional forces of the continuously welded rails of a long-span suspension bridge

High-speed running trains have higher regularity requirements for rail tracks. The track-bridge interaction of long-span bridges for high-speed railways has become a key factor for engineers and researchers in the last decade. However, studies on the track-bridge interaction of long-span bridges are rare because the bridges constructed for high-speed railways are mainly short- or moderate-span bridges, and the effects of the highway live load on the additional forces of continuously welded rails (CWRs) have not been reported. In the present study, the effects of the highway live load on the additional forces of a CWR of a long-span suspension bridge are investigated through numerical simulations. A track-bridge spatial analysis model was established using the principle of the double-layer spring model and the bilinear resistance model. The additional stress and displacement of the rail are calculated, and the effects of the highway live load are analyzed and compared with those without a highway live load. The results show that the highway live load has an obvious effect on the additional forces of a CWR. Under a temperature force, the highway live load increases the maximum tensile stress and compressive stress by 10 and 13%, respectively. Under a bending force, the highway live load increases the maximum compressive rail stress and maximum displacement by 50 and 54%, respectively. Under a rail breaking force, when the highway live load is taken into consideration, the rail displacement at both sides of the broken rail varies by 50 and 42%, respectively. The highway live load must be taken into consideration when calculating the additional forces of rails on highway-railway long-span bridges.

Train-Bridge Dynamic Behaviour of Long-Span Asymmetrical-Stiffness Cable-Stayed Bridge

Long-span cable-stayed bridge (LCB) with unequal-height towers is being designed and constructed in metro lines due to its better adaptability to environment and terrain conditions compared to traditional cable-stayed bridge with equal-height towers. However, the asymmetrical arrangement of towers leads to obvious nonuniformity of the structural stiffness along the longitudinal direction, which intensifies the wheel-rail coupled vibration behaviour, and affects the running safety of operating trains and ride comfort. Therefore, train-bridge dynamic behaviour of long-span asymmetrical-stiffness cable-stayed bridge is deeply investigated in this work. Primarily, considering the comprehensive index of frequency difference and modal assurance criterion (MAC), a nonlinear model updating technique (NMUT) based on penalty function theory is proposed, which can be used to optimize the bridge numerical model. Secondly, on the basis of the train-track-bridge dynamic interaction theory (TDIT), a train-track-bridge coupled dynamic model (TCDM) is established. Finally, a LCB with unequal-height towers is applied as a case to illustrate the influence of asymmetrical stiffness on the train-track-bridge dynamic characteristics. Results show that the proposed NMUT is efficacious and practical. For the LCB with unequal-height towers, a significant difference between the bridge vibration at low tower location and that at high tower location appears. The vertical displacement difference of the main beam on both sides of the bridge increases with the distance from the observation point to the bridge tower increasing. The variation of acceleration difference on both sides of the bridge is influenced by the speed of the train and the position of the observation point simultaneously. In general, vibrations of the main beam at low tower location are larger than those at high tower location.

Stochastic Analysis on the Resonance of Railway Trains Moving over a Series of Simply Supported Bridges

Resonance problems encountered in vehicle-bridge interaction (VBI) have attracted widespread concern over the past decades. Due to system random characteristics, the prediction of resonant speeds and responses will become more complicated. To this end, this study presents stochastic analysis on the resonance of railway trains moving over a series of simply supported bridges with consideration of the randomness of system parameters. A train-slab track-bridge (TSB) vertically coupled dynamics model is established following the basic principle of vehicle-track-coupled dynamics. The railway train is composed of multiple vehicles, and each of them is built by seven rigid parts assigned with a total of 10 degrees of freedom. The rail, track slab, and bridge are considered as Euler–Bernoulli beams, and the vibration equations of which are established by the modal superposition method (MSM). Except for the nonlinear wheel-rail interaction based on the Hertz contact theory, the other coupling relations between each subsystem are assumed to be linear elastic. The number theory method is employed to obtain the representative sample point sets of the random parameters, and the flow trajectories of probabilities for the TSB dynamics system are captured by a probability density evolution method (PDEM). Numerical results indicate that the maximum bridge and vehicle responses are mainly dominated by the primary train-induced resonant speed; the last vehicle of a train will be more seriously excited when the bridges are set in resonance by the train; the resonant speeds and responses are rather sensitive to the system randomness, and the possible maximum amplitudes predicted by the PDEM are significantly underestimated by the traditional deterministic method; optimized parameters of the TSB system are preliminary obtained based on the representative point sets and imposed screening conditions.

Running Safety Assessment of Trains on Bridges under Earthquakes Based on Spectral Intensity Theory

The main goal of this paper is to perform the safety assessment of high-speed trains (HSTs) on the simply supported bridges (SSBs) under low-level earthquakes, which are frequently encountered by HSTs, utilizing spectral intensity (SI) index. First, the HST’s limit displacements, which are calculated by using the multi-body train model with detailed wheel–rail relationship, varying with train speed, frequency and amplitude of a sinusoidal base excitation are obtained. Then, based on the obtained HST’s limit displacements, the spectral intensity limits (SIL) graded by the train’s running speed are calculated, and the relationship between the bridge seismic dynamic responses and the train’s running safety was established. Next, the method that utilizes the SI and the SIL indexes to evaluate the HST’s running safety was proposed and verified by comparing with the evaluation result of the train–track–bridge interaction model. Based on the proposed SI index, the HST’s running safety on the SSBs was evaluated under earthquakes, considering different pier heights and site types. The results showed that the low-frequency components of the ground motions are unfavorable to the HST’s running safety, and the height of bridge piers has a significant impact on running safety.

Dynamic analysis of railway bridges exposed to high-speed trains considering the vehicle–track–bridge–soil interaction

A new semi-analytical approach to analyze the dynamic response of railway bridges subjected to high-speed trains is presented. The bridge is modeled as an Euler–Bernoulli beam on viscoelastic supports that account for the flexibility and damping of the underlying soil. The track is represented by an Euler–Bernoulli beam on viscoelastic bedding. Complex modal expansion of the bridge and track models is performed considering non-classical damping, and coupling of the two subsystems is achieved by component mode synthesis (CMS). The resulting system of equations is coupled with a moving mass–spring–damper (MSD) system of the passing train using a discrete substructuring technique (DST). To validate the presented modeling approach, its results are compared with those of a finite element model. In an application, the influence of the soil–structure interaction, the track subsystem, and geometric imperfections due to track irregularities on the dynamic response of an example bridge is demonstrated.