マトリックス法による骨組構造物の弾塑性解析

抄録

Recently, the matrix method has become a powerful tool for structural analysis in conjunction with the rapid development of digital computers and the method of elastic analysis of framed structures is almost established. While, the plastic analysis on the structures is performed with the aid of the mechanism method, the moment distribution method or the linear programming method. However, it is impossible by these methods to analyze the elastic-plastic behavior of the framed structures for the entire process of loading.
Jennings and others studied on the elastic-plastic strength of plane frames subjected only to bending and showed a method to analyze the frames by inserting hinges at the yielded sections. This kind of method is not satisfactory to the analysis for framed structures, especially, for space frames, since the interaction is not taken into account and this may produce a serious error in the result of the analysis. The authors contrived a new mechanism of plastic hinge based on the plastic flow theory and established a new method of elastic-plastic analysis of framed structures in two and three dimensions with full consideration of the interaction.
The result of analysis approaches to the exact solution when the increment of external load becomes infinitesimal.
The analysis was made on several kinds of structures including plane frames under combined axial forces and bending and space frame.
The following important informations are obtained.
(1) The new mechanism of plastic hinge is characterized by that the continuity is maintained at yield section through the entire process of elastic-plastic behavior, and the rigidity is reduced automatically by plastification of the section. It should be also noted that a combination of forces and bending (twisting) moment is possible to change at the plastic hinge without violating the yield, condition.
(2) By the new method of analysis, the elastic-plastic behavior of framed structures is investigated, taking into account of the interaction. And the deformation is obtained at each step of loading and the plastic collapse load is evaluated.