Issue 30

W. Changfeng et alii, Frattura ed Integrità Strutturale, 30 (2014) 486-494; DOI: 10.3221/IGF-ESIS.30.59 489 Moment Curvature crack point yield point damage point Figure 4 : Takeda tri-line hysteresis model. F INITE ELEMENT MODELLING Project background he superstructure of a 60+100+60 m prestressed concrete continuous railway girder bridge was selected as the background project. The pier has a height of 20 m. The cross-section of the pier is rectangular with a dimension of 6.75×2.8 m for side piers and 6.8×4.0m for middle piers. The girder is variable-section boxed girder with single cell box and vertical webs. The girder has a total weight of 14367248 kg. The vertical reaction force for side supports is 8793.74 kN and 63042.5 kN for middle supports. The effect of ground and pier foundation is simplified as foundation springs applied at the cushion cap bottom. The proportionality factor is taken as 20000 kPa/m 2 according to the foundation factor. The spring stiffness is calculated by “m” method [12]. The nonlinearity of ground and pier foundation is ignored and the rotation spring stiffness of the cushion cap bottom is taken as identical for each model. Analytical model Nonlinear Takeda model is used for all bridge piers. Only longitudinal seismic response of the continuous bridge is studied in this research [13]. The length of the plastic hinge of the bridge pier is taken as 1.0 D ( D is the height of calculation of the cross-section) and the plastic hinge is located at the bottom of the pier. The elasto-plasticity of the pier structure is considered within the range of plastic hinge and the nonlinearity is ignored outside the range. The reinforcement ratio of the bridge pier is taken as 0.5% and the control points of the moment-curvature curve of the cross- section of pier bottom are given in Tab. 1. Pier Cracking moment (kN·m) Cracking curvature (rad/m) Yield moment (kN·m) Yield curvature (rad/m) Ultimate moment (kN·m) Ultimate curvature (rad/m) Side pier 33265 0.00014 59050 0.00087 83684 0.03649 middle pier 102917 0.00012 203459 0.00068 237879 0.0081 Table 1 : Control points of the moment-curvature curve for the bottom section of bridge pier. The Beam and piers were simulated by spatial beam element, the beam was separated into 83 elements and each pier was separated into 12 elements. The numerical FE model was shown in Fig. 5. In actual design, the effect of transversal seismic and vertical load is both considered and thus the reinforcing ratio of the fixed pier and middle movable piers are normally identical. Therefore, the same moment-curvature model is used for both middle movable piers and the fixed piers. Five different calculating models are incorporated for different scenarios where the nonlinearity of support is considered or not as well as different installation of restraining devices. (1) Model 1: The nonlinearity of movable supports is ignored. Only the vertical degree of freedom of the movable supports is coupled with the girder, while both the vertical and horizontal degrees of freedom of the fixed supports are linked with the girder. T