Nonlinear analysis of two dimension al structures is performed using the trilinear moment-curvature (M-φ) relationship with strain hardening and strain softening. The trilinear M-φ relationship can be easily replaced by other M-φ relationships, so that analysis can be performed both for steel structures as well as for reinforced concrete structures.
The plastic hinge model is commonly used in the nonlinear analysis of two dimensional structures. Usually, the nonlinear analysis is performed varying the properties of plastic hinges, resulting in lower efficience of analysis, to represent the inelastic behavior of structures.
The Point hinges with elastic properties are used to model the nonlinear behavior of members in the structure. Therefore, the structure with linear spring behaves linearly against external loads and the stiffness matrix of the structure remains unchanged. Nonlinear behavior of this linear model is achieved by the fictitious loads applied to the linear springs at both ends of elastic beam elements, resulting in equivalent nonlinear deformatios. The fictitious loads is calculated using the correction matrix which relates the fictitious loads and the unbalanced moments. The number of iteration can be greatly reduced by utilizing the fact that the unbalanced moments decrease with constant slopes by the fictitious loads as far as the number of plastic hinges remain constant and the efficience of the nonlinear analysis can be enhanced by minimizing the factorization of structural stiffness.
