此外，2008年日本岩手縣內陸南部發生強震，導致祭畤大橋崩塌。本研究以祭畤大橋為例建立其數值模型進行結構崩塌分析，模擬此橋於強震中崩塌之破壞歷程，重現橋梁破壞過程，分析結果與當時橋梁真實破壞情況一致，驗證本研究所提出之分析方法確實能有效地分析實尺寸橋梁於極限狀態下之動態反應，並評估其於強震下之性能表現，藉以釐清瞭解橋梁破壞機制與緣由，提供未來橋梁規劃與耐震設計之參考。 ;This study presents a dynamic analysis procedure for predicting the responses of large, highly nonlinear, discontinuous structural systems subjected to seismic loading. The concept of equivalent nodal secant stiffness is proposed to diagonalize the conventional stiffness matrix of the structure. With the lumped-mass idealization, the decoupled equilibrium equations of the structure are then solved by the implicit Newmark integration method. Additionally, an incremental-iterative procedure is performed to ensure that the equilibrium conditions are satisfied at the end of each time step. Through extensive applications, the results demonstrate that the proposed procedure is simple and robust for analyzing practical structural systems in terms of computational efficiency and stability.
The concept of equivalent nodal secant damping coefficients is proposed to diagonalize the stiffness-proportional damping matrix. Additionally, a novel method is proposed to rapidly evaluate stiffness-proportional damping nodal forces for nonlinear elements on the element level. With the assumption of lumped-mass idealization an incremental-iterative procedure is performed to solve the decoupled equilibrium equations for damped systems using the implicit Newmark integration scheme and the composite integration scheme. The numerical results reveal that the characteristics of the proposed analysis procedure result in a robust method for solving structural dynamics systems to be achieved.
The dynamic analysis procedure is extended to simulate the seismic-induced collapse of bridges. Nonlinear and discontinuous behavior, such as material yielding, member damage, separation, falling and collision with other members, are considered in the analysis procedure. Additionally, multiple-support excitation is managed by using the equations of motion in the absolute coordinates. The Matsurube Bridge which collapsed in the 2008 Japan Iwate-Miyagi inland earthquake due to not only strong ground excitations but also sliding of underneath rock mass is analyzed for verifying the applicability of the proposed procedure. Through reproducing the in-situ collapse situation, the failure mechanisms of the bridge are identified. The results also demonstrate that the novel implicit dynamic procedure is superior in analyzing the collapse of bridges that exhibit highly nonlinear and discontinuous behaviors under extreme earthquakes.
