模態形狀向量是軸向束制問題的關鍵項目。將原本之剛架結構轉變成類比桁架，再將類比桁架轉變成側撐桁架(屬於靜定桁架類)。因靜定桁架之影響線值，依據Muller_Breslau 原理，會滿足變位諧合條件。而模態形狀向量之計算最困難處在變位諧合條件之成立與否。使用靜定桁架之影響線之計算，可以掌控剛架結構之移動自由度，再拼加與移動自由度互斥的轉動自由度，完整處理剛架結構之所有自由度。 Mode shape matrix is the most important character of axial constrained frame analysis problems. The nodal translational degree of freedoms in frame stress analysis is substituted by mode shape vector. In first step, the frame structure is transformed into a so called analogous truss, because the rotational degree of freedoms is independent on translation degree of freedoms. The new structure is then added some extra members to form a statically determinate stable truss. It is called a restraint truss in this paper. The difficulty of calculation of mode shape matrix is the compatible for all joints and boundaries conditions. There are two methods to calculate influence lines of a statically determinate truss. The use of Muller_Breslau principle is not easy for a truss structure, because it is necessary to satisfy the conditions of compatibility for all joints and boundaries conditions. The calculation of influence lines by the use of the definition of influence lines is more easily than the use of Muller_Breslau principle, but it has the results of satisfying the conditions of compatibility. There thus solve the problem of translational degree of freedom. Add the rotational degree of freedom to independent translational degree of freedom. The total numbers of degree of freedom are under control.
中華民國第九屆結構工程研討會論文集=Proceedings of The 9th National Conference on Structure Engineering，7頁