Partial Axial Constraints in Frame Analysis Using Braced Analogous Truss

本文推論出剛架之全部或部份桿件之軸向變形受束制的分析之新方法。將原本剛架轉換成類比桁架，再將類比桁架轉換成含側撐的類比桁架，簡稱側撐桁架，剛架之移動自由度可由側撐桁架淬取出。側撐桁架之各桿件單位變形造出各結點之位移向量稱為模態向量。剛架之轉動自由度與桿件之軸向變形束制無關，因此可直接加入於最後的自由度中。將類比桁架另外添加二力桿，用適當的數量，於恰當的位置，作出靜定、穩定之簡單桁架，稱為側撐桁架。對應於側撐桁架之每支實桿件（原有）與虛桿件（後來另外添加）都可計算出對應之模態向量。應用這些模態向量將原本剛架之各剛架元素勁度矩陣及作用力轉換到一個新系統。應用側撐桁架之模態向量作分析，是本文之最大特色。數值計算例題之結果與其他已知方法作比較，因計算步驟最簡短、原理推導最簡潔而可靠，所以顯示出具有正確性與精準性。

關鍵字

部分軸向束制；換向原理；位移模態；直接勁度法；簡單桁架；側撐；類比桁架

並列摘要

This paper describes a newly developed method for analyzing structural frames that considers axial constraints for all members and partial members. This method represents an evolution of an ”analogous truss” approach into an original ”braced analogous truss” approach. The character of the translated degrees of freedom in the transformed structure is extracted under an assumption of axial constraint, named the 'mode shape vector' in this paper. The developed method differs from traditional methods, which only use constraint equations in the original structure. Therefore, this method is both a practical tool in application and an interesting approach to analyzing transformed structures.The braced analogous truss is a modification of the analogous truss. Using virtual members, we were able to transform an unstable analogous truss into a stable simple truss problem. Equivalent nodal loads, the global stiffness matrix and nodal displacements could then be calculated using mode shape vectors. Numerical examples show that highly accurate solutions, under reduced degrees of freedom, are obtainable in structural analysis.

並列關鍵字

partially axial constraint ； contragradient transformation ； mode shape ； direct stiffness method ； simple truss ； brace ； analogous truss

國際替代計量

Partial Axial Constraints in Frame Analysis Using Braced Analogous Truss

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