Semirigid connections show nonlinear behavior even due to small loadings. Therefore linear analysis is not a proper solution algorithm for structures that have such connections; rather a nonlinear analysis should be done. The conventional methods of nonlinear analysis of frames are inherently iterative, and their final results include some small order of approximation. They usually are done through modification of the stiffness matrix of structure and/or load vector. In this paper, a new method of nonlinear analysis has been presented that contrary to iterative methods, it is non-iterative. It does the analysis in one step without change in the initial model and stiffness matrix of the structure or its load vector. Theoretically it does not include approximation and gives exact results. In this method to force internal moments follow their nonlinear moment-rotation curves, some virtual moments (that are primarily unknown) are imposed to the structure at semirigid connections. To find the unknown virtual moments, a quadratic programming problem is formulated and solved. After finding the values of virtual moments, employing superposition principle, exact nonlinear response of structure is obtained and internal forces and moments of members are calculated.
The method is capable to model semirigid connections with multilinear moment-curvature relations. The formulation of the problem for bilinear and trilinear moment-curvature relations has been presented here. Two examples are presented to demonstrate the robustness, capability and validity of the method.