具挫屈影響之塑性極限面

極限分析是現今土木分析方法主流之一，塑性最重要的特徵就是「路徑對路徑」。當材料受不同載重時，內力達到不同降伏點，這些降伏點就會形成一個「初始降伏面」，若繼續加載，則依不同路徑而形成不同「接續降伏面」。最後，當結構或材料達到極限產生靜態崩塌時，各路徑之崩塌點會形成唯一的「塑性極限面」。本文分析方法是多方向、多維度，並且可以直接求得所有崩塌模態，而形成塑性極限面。此種分析方法不需經過繁複冗長的歷時分析，由於為了簡化分析過程，通常只會考慮彎矩變形的影響。在經過前面許多學長的努力下，拓展到軸彎互制，本文將會延續軸彎互制，並且考慮挫屈行為的影響，更能反應結構物真實的情況。本文主要在探討將挫屈行為納入考量之塑性極限面的計算方法，根據整個理論架構，此種方法利用線性代數的運算將具有軸力效應的塑性極限面求出後，再透過穩定分析以及Rankine-Merchant所提出的方法修正塑性極限面，最後會得到一個更保守的塑性極限面。

關鍵字

極限分析；穩定分析；構架；彈塑性；挫屈；軸彎；剪彎

並列摘要

Limit analysis is one of the mainstream analysis methods in civil engineering. The most important feature of plasticity is path versus path, and the displacement and load are path-dependent. When the material is subjected to different loads, the internal force reaches different yield points, these yield points will form an initial yield surface. If the load continues, different subsequent yield surfaces will be formed according to different paths. Finally, when the load reaches the limit state and static collapse occurs, the collapse point of each path will form a unique plastic limit surface. The analysis method in this thesis is multi-directional and multi-dimensional, and all collapse modes can be directly obtained, and the plastic limit surface can be formed. This kind of analysis method does not need to go through a lengthy and time-consuming analysis. Since in order to simplify the analysis process, only the influence of bending moment will be considered. After many previous studies by seniors, it has been extended to the interaction of axial force and bending moment. This thesis carries on the researches on the interaction of axial force and bending moment and will extend to the influence of buckling behavior to reflect the real behavior of the structure . This thesis mainly discusses the calculation method of the plastic limit surface that takes the buckling behavior into consideration. According to the whole theoretical framework, this method calculates the plastic limit surface with the effect of axial force by matrix operation, and then modifies the plastic limit surface through stability analysis and Rankine-Merchant approach. Finally, a more conservative plastic limit surface will be obtained.

並列關鍵字

limit analysis ； stability analysis ； frame ； elasto-plastic ； buckling ； axial or shear-bending

參考文獻

[1]J. Bai and J. Ou. Plastic limit-state design of frame structures based on the strong column weak beam failure mechanism. In 15th World Conference on Earthquake Engineering, Lisboa, Portugal, pages 24–28, 2012.