Connecting the ends of girders with a continuous slab-deck to make a multiple-span simply supported girder bridge provides many benefits, but there is no suitable nonlinear analysis model which considers continuous slab-deck cracking under tension and bending. In this article, the rotational spring model is further refined to replace the restraining effects at both ends of the girder by the simplified mechanical model associated with axial stiffness, bending stiffness, and shear stiffness. Then, it is introduced into the analysis of continuous slab-deck. The more accurate rotations and displacements of both ends of continuous slab-deck are obtained to investigate the more precise moment and tension of the continuous slab-deck. Furthermore, this article presents an improved nonlinear analysis model of continuous slab-deck based on a detailed boundary rotational spring model. The displacements of important positions and the strain of key components in continuous slab-deck after cracking are investigated by numerical analysis and full-scale model test to verify the accuracy of the proposed nonlinear analysis model. The result shows that the nonlinear analysis model presented in this article could successfully evaluate the depth of cracks and the stress of rebars in continuous slab-deck, and it is instructional in predicting the cracking state of the continuous slab-deck and the reinforcement design.
A physical perspective of the propagation and attenuation of flexural waves is presented in this paper for the dynamic behaviors of cable stayed beams subjected to a moving load. Based on the method of reverberation-ray matrix (MRRM), the waveform solutions of the wave equations of a simplified beam-cable system subjected to a moving load (hereinafter referred to as a beam-cable system) are given, and the theory is verified by a numerical example. The dynamic response of cable stayed beams is decomposed into nine kinds of flexural waves, including traveling waves, near-field waves, and nondispersive waves, according to the wavenumber characteristics. Numerical examples are analyzed to demonstrate the propagation characteristics of flexural waves through cable stayed beams. Numerical results show that the flexural waves in the cable stayed beams are mainly low-frequency waves whose frequencies are less than 3 times the structural fundamental frequency, which can be used to further improve the computational efficiency of response analysis method based on MRRM, and the proportion of high-frequency components increases gradually with increasing structural stiffness. The near-field wave can be transformed into a traveling shear wave when its frequency is larger than the critical frequency, which decreases with increasing radius of gyration and decreasing elastic modulus of the beam. With the increase in the radius of gyration and the elastic modulus of the beam, the attenuation effect of the near-field wave weakens. The wave velocity and the wave dispersion effect have a positive correlation with the stiffness-related parameters of the beam-cable system. The study of the effect of the beam-cable system parameters on flexural wave propagation characteristics can be applied to achieve a better dynamic design for engineering structures.
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