具非線性硬軟化和損傷之多層建築的建模與耐震分析

Abstract

本研究提出一套考慮黏彈塑性行為之非線性結構分析模式，能同時模擬結構進入塑性階段後所產生的非線性硬化／軟化行為，以及因塑性累積導致彈性勁度損傷的現象。在模式的設計上納入兩個水平與一個扭轉自由度，能有效捕捉建築物於地震激振下的多方向反應。研究從柱子的建模出發，並提出該模式的計算策略，進一步探討模式在不同狀態下的反應。在柱模式建構完成後，本研究將其擴展至多層樓系統，透過數值驗證與真實地震歷時模擬，證實本模式算法流程的正確性後，進一步進行地震力的分析，並紀錄不同歷時分析所需的時間得到平均分析每筆歷時所需的時間，顯示本模式具有良好的計算效能。進一步雙線性的模式進行比較，可觀察出在最大層間位移和塑性當量這兩指標下會有低估的情況產生，而在最大層間剪力則是有高估的情形，而本模式可提供更準確的預測。此外，研究亦探討地震入射角對非對稱建築反應的影響，說明不同角度下可能產生顯著的扭轉效應，並據此進行樓層級補強分析，提出針對不同樓層與方向的目標式補強策略。整體而言，本研究建立之分析架構具備高精度、穩定性與延展性，提供一套適用於不對稱建築在多方向地震作用下之耐震評估與補強設計的有效工具。

This study proposes a nonlinear structural analysis model that considers viscoelastoplastic behavior, which can simulate the nonlinear hardening/softening behavior after the structure enters the plastic phase, as well as the phenomenon of elastic stiffness degradation caused by plastic equivalent accumulation. The model is designed with two horizontal and one torsional degrees of freedom, which can effectively capture the multidirectional responses of buildings under seismic excitations. The study starts with the modeling of columns. The computational strategy of the model is proposed, and the responses of the model under different conditions are further investigated. After the model is established, this study extends it to multi-story systems. Through numerical verification and real seismic time history simulation, the correctness of the computational procedure is confirmed. The computation time required for analyzing different time histories is analyzed, proving that our model demonstrates good computational efficiency. Further comparisons with a bilinear model show that under the two indicators of maximum inter-story drift and plastic equivalent, there tends to be underestimation, while maximum inter-story shear tends to be overestimated. Our model provides more accurate predictions. In addition, this study also investigates the influence of seismic incidence angles on the response of asymmetric buildings, illustrating that significant torsional effects may occur under different angles. Based on this, story-level retrofitting analyses are conducted, and target-oriented retrofitting strategies for different stories and directions are proposed. Overall, the analysis framework established in this study possesses high accuracy, stability, and extensibility, providing an effective tool for seismic assessment and retrofitting design of asymmetric buildings under multidirectional seismic actions.