Taking arch bridges, including deck, half-through, and through arch bridges (short for DAB, HTAB, and TAB) as examples, mechanics analysis models of longitudinal interaction between continuously welded rails (short for CWRs) and arch bridges are established. Based on the finite element method (FEM), the longitudinal interaction calculation software of CWR on arch bridges has been developed. Focusing on an HTAB, the tension, compression, and deflection conditions are calculated and analyzed. The results show that the mechanics analysis models of three types of arch bridges can truly reflect the real state of the structure; the calculation software can be used for systematic research of the CWR on arch bridge; as for HTAB, temperature difference of arch rib has a small effect on rail tension/compression, and arch bridge can be simplified as a continuous beam for rail tension/compression additional force calculation; in calculation of deflection conditions of HTAB, it is suggested that train loads are arranged on half span and full span and take the direction of load entering bridge into account. Additionally, the deflection additional force variation of CFST basket handle arch bridge is different from that of ordinary bridge.

Over the years, continuous welded rail (CWR) was usually laid on common simply supported beams or continuous beam bridge structure in China [

Up to now, the related technology of CWR on ordinary bridge structure is relatively mature. Many scholars have started researches on the mechanics problems of the railway bridge under the load of moving vehicles and have obtained a lot of valuable results, including the Green’s functions method for both infinite and finite elastic structures [

Three types of arch bridges and ordinary bridge have common basic assumptions [

The arch foot and the underlying connection of DAB and HTAB are fully constrained, without considering underlying displacements.

Lateral stiffness of arch ring structure is not considered, only considering vertical stiffness.

For piers of DAB, only longitudinal stiffness is considered; pier’s bottom and the upper arch ring are fixed together.

Hangers of HTAB, TAB, and arch ring connected nodes are on the arch axis.

Essentially, analysis of CWR longitudinal force on bridge is based on the rail/beam interaction [

The mechanics model of DAB is shown in Figure

The mechanics model of track/girder/pier of DAB.

The model of track/girder/pier of HTAB is shown in Figure

The mechanics model of track/girder/pier of HTAB.

TAB is very common in the construction of urban rail transit. It is usually built to meet the needs of urban landscape and large span, generally divided into simple supported beam arch or continuous beam arch. Now TAB is often simplified into a normal simple supported beam or continuous beam in calculation. The calculation of longitudinal force and the results can meet the accuracy requirements. The mechanics model of track/girder/pier of TAB is shown in Figure

The mechanics model of track/girder/pier of TAB.

In these mechanics models, arch span and both ends of main arch can be made up with any number and the span of simply supported beams, continuous beams, or rigid frame bridge. And the entire girder can be considered as uniform section beam or beams with variable section. The horizontal stiffness of piers has embodied the pier structure type and its connection with girder at both ends of the main arch span. Piers and suspenders stiffness are reflected by their cross-section parameters. The types of arch rib structures, such as reinforced concrete arch, concrete filled steel tubular arch, steel box arch and steel truss arch, can be simplified as beam elements. Three arch axis line forms, such as the arc line, quadratic parabola, and catenary, are considered in these calculation models. Moreover, structure parameters and resistance type of track components are variable in the calculation model.

The calculation models of CWR on arch bridge mentioned above are established and solved by means of secondary development based on a large finite element software ANSYS. Reasonable element selection of the structural parts is particularly important to the calculation results, and the selections are as follows.

BEAM54 element.

Most structures of the three types of arch bridges are similar, but the local structure is slightly different. This paper used the combined method of FORTRAN language, the finite element software ANSYS, and Parametric Design Language (APDL) to program the general-purpose computing software of longitudinal interaction of CWR track on arch bridge (LICAB). This software uses executable programs (by Fortran language) to read input parameters file and preprocess the data and uses source files compiled by APDL to read the relevant parameters of the arch bridge structure automatically. After that, it calculates a variety of conditions (including the conditions of tension/compression force, deflection force, the braking force, and the broken rail force) in ANSYS environment and generates the corresponding calculation results file. Figure

Mechanics model of three types of arch bridges.

Deck arch bridge

Half-through arch bridge

Through arch bridge

LICAB’s calculation results were compared with the results given in [

Here, taking the HTAB as an example, tension/compression and deflection conditions (the rail intensity control conditions) are analyzed.

A new double-track railway large span arch bridge: its main span is 351 m, with a vector height of 64.5 m; the arch axis is quadratic parabola, and 18 suspenders with spacing of 12 m are set. The span of side beam is 24.6 m, and its arch rib has a structure of steel-concrete composite truss basket arch structure; its main span adopts the prestressed concrete box girder. Bridge span arrangement is shown in Figure

Span arrangement of bridge (unit: m).

In calculation of tension/compression condition, beam temperature difference is 15°C, and temperature difference of arch rib in turn is 0, 15, 20, and 25°C. Rail tension/compression additional force calculation results are shown in Figure

Rail tension/compression additional force results.

In Figure

Result of simplified model.

Simplified model of HTAB.

Figure

In calculation of deflection conditions, the train loads (Chinese live load) are separately arranged on 1/4, 1/2, 3/4, and full span of arch bridge from the left side to the other side. Rail deflection force calculation results are shown in Figure

Rail deflection force calculations.

Figure

A long span concrete filled steel tubular (CFST) basket handle arch bridge is applied in newly constructed double-track railway. The calculated span is 380 m, and the vector height of the bridge’s arch ring is 76 m. Within the vault height of 77 m, concrete rigid frame with type “

Bridge structure diagram.

For this model, it is assumed that the arch foot pier in the left is the origin of coordinates. In order to reduce the influence of boundary conditions, 6 spans from both sides of the arch ring center are taken as calculation sections according to the actual bridge arrangement.

Existing specification only specifies the conventional beam temperature differences, not involving temperature difference values of bridges with special types. In calculation of expansion force, two conditions were considered, that is, the arch ring temperature difference and no arch ring temperature difference. The temperature difference of concrete beam is taken as ±15°C. The temperature difference of arch ring is considered as ±15°C. Figure

Rail tension/compression additional force.

Beam/rail relative displacements.

As shown in Figures

China railway standard live load is used, and the load moves from left to right into the bridge. The calculation considers two load distributions, that is, the full-span load and a half-span load. The deflection additional force of rail result is shown in Figure

Rail deflection additional force.

Beam/rail relative displacements.

As seen from Figures

China railway standard live load brakes from the left to the right into the bridge. The calculation considers two load distributions, that is, the full-span load and a half-span load. Figure

Rail braking additional force.

Beam/rail fast relative displacements.

As seen from Figures

In tension/compression condition, the maximal rail expansion additional force is increased by 1.31 times when the temperature difference of arch ring is considered. The distribution of expansion additional force changed a lot, which means the temperature variation has a great influence on the stress of track structure.

The calculation results in deflection condition show that deflection additional force is small when the load is set on full span, because the deflection of arch ring is symmetric, and the beam/rail relative displacement is small. When the load is only set on half span, the arch ring occurred approximation anti-symmetric deformation, and the beam/rail relative displacement is big, which results in big deflection additional force.

In braking condition, the beam/rail fast relative displacement is big when the braking load is distributed in full span, and the results can be used in the stability checking calculation of ballast bed.

In summary, this paper analyzed the characteristics of CWR on arch bridges, created DAB, HTAB, and TAB mechanics analysis models, and developed the calculation software for longitudinal interaction of CWR on arch bridges (LICABs). Taking an HTAB as an example, the results can be concluded as follows:

mechanics analysis models of three types of arch bridges can truly reflect the real state of the structure;

using the LICAB software, systematic research can be realized for the force and deformation law of the CWR on arch bridge;

as for HTAB, temperature difference of arch rib has a small effect on rail tension/compression, and arch bridge can be simplified as a continuous beam for rail tension/compression calculation;

it is suggested that train loads are arranged on 1/2 span and full span and take the direction of load entering bridge into account in calculation of deflection conditions of HTAB;

the deflection additional force variation of CFST basket handle arch bridge is different from that of ordinary bridge. The deformation of arch ring has big influence on the deflection additional force of rail. Usually, when the load is set on half of the span, the deflection additional force is the worst. For ordinary bridge, its deflection additional force is much less than the tension/compression additional force, so it is not used as the controlling factor. But the deflection additional force of the basket handle arch bridge is big, close to the tension/compression additional force, so attention should be paid to its check calculation.

This work is financially supported by the National Natural Science Foundation of China under Grant no. 51078320 and no. 51008256. And it was also supported by the Scientific Research and Development Program of Chinese Ministry of Railways under Grant no. 2011G009.