マトリックス法による平面骨組の弾塑性解析

抄録

In the present paper, the matrix methods are developed for elastic-plastic analysis of plane framed structures subjected to proportional loading on the basis of the plastic hinge concept :
After the bending moment at a joint reaches the fully plastic moment, the joint behaves as a hinge for the further increase of load. In the case of the force method, the number of redundant forces decreases corresponding to the formation of plastic hinges, and the flexibility matrix for the structure should be modified. The structure collapses when any redundant force cannot be eliminated for the new formation of a plastic hinge. In the case of the displacement method, it is easy to modify the stiffness matrix of the structure by the use of the member stiffness matrix corresponding to the formation of plastic hinges. The structure collapses when the structure stiffness matrix ceases to be positive definite.
The present method can easily be modified to be effective for structures which may yield by axial forces. For a structure subjected to a prescribed loading program, the stress analysis may be conducted by the present method by taking unloading process of plasticity into account.