Finite element analysis of the thermal interaction of continuously welded rails with simply supported bridges considering nonlinear stiffness

Abstract

The thermal interaction of continuously welded rails with railway bridges has attracted the wide attention of researchers. In this paper, the model of a continuously welded rail and a bridge with longitudinal nonlinear stiffness has been considered. The detailed mechanics equation of the rail on the bridge and the embankment with longitudinal nonlinear stiffness has been presented using the finite element analysis. The validity of the presented model and the compiled program is illustrated. The influences of nonlinear stiffness, span number of the bridge, constant longitudinal restoring force, bridge bearing arrangement, and the span length of the bridge on the additional longitudinal stress and displacement of rails are investigated for multispan simply supported bridges. The results show that (1) the responses of rails for the nonlinear stiffness are less than those for the linear stiffness; (2) when the bridge span reaches a certain number, the maximum additional longitudinal stress and the displacement of the rail tend to be constant; (3) with the increase of the value of the constant longitudinal restoring stress, the maximum additional longitudinal stress and the displacement of the rail increase; (4) the maximum additional longitudinal stress of the rail on multispan simply supported bridges can be reduced by using alternate bearings on one pier; and (5) the maximum additional longitudinal stress and displacement of the rail increase with the increase of the span length of the bridge.

Appropriate Matching Locations of Rail Expansion Regulator and Fixed Bearing of Continuous Beam Considering the Temperature Change of Bridge

“…The track components between rails and bridge, including fasteners, sleepers, and bed, are modeled as coupling shear elements with nonlinear stiffness, as shown in Figure 3. The rail-beam thermal interaction descriptions can be found in [6,7,19]. To facilitate the reading, the main contents are listed here.…”

“…If the absolute value of difference D u is not less than the critical value ũ , the rail slips, relative to its base. The nonlinear relationship in Figure 4 is applied, and the longitudinal restoring force q is a constant q , with (Refernces [6,7]) The whole-mechanics equation for CWR with RER on bridges and embankment can be expressed as (Refernce [19]) If the absolute value of difference u D is not less than the critical value u, the rail slips, relative to its base. The nonlinear relationship in Figure 4 is applied, and the longitudinal restoring force q is a constant q, with (Refernces [6,7])…”

“…The whole-mechanics equation for CWR with RER on bridges and embankment can be expressed as (Refernce [19])…”

“…Yan et al [18] found that installing RER at the end of the bridge can effectively reduce the additional expansion force of rail. Lou et al [19] considered the longitudinal nonlinear stiffness characteristics and studied the influence of some factors on the additional stress of rail. Liu et al [20] studied the influence of the support of a long-span steel bridge on the additional expansion force of rail.…”

Appropriate locations of fixed bearings of continuous beams considering rail-bridge thermal interaction

“…(1), ( 3) and ( 4) can be used in the rail on embankment only by the value of u B with zero. The mechanics equation of CWR track and foundations longitudinal thermal interaction considering nonlinear stiffness can be found in Lou et al, 27 and are omitted here to reduce the length of this paper. The corresponding program for calculating the additional thermal force in rails of the presented model is compiled.…”