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This paper presents the fundamentals for prediction of a more realistic behavior of planar steel frames with semi-rigid connections under dynamic loading. The majority of the research in this area concentrates on the nonlinear static analysis of frames with semi-rigid connections. Indeed, few studies have contributed to the nonlinear dynamic and vibration analyses of frames. Therefore, this article first describes the frames' semi-rigid connection behavior under monotonic and cyclic loads, and presents the independent hardening technique adopted to simulate the joint behavior under cyclic excitation. In a finite element context, this paper presents an efficient numerical methodology that is proposed in algorithmic form to obtain the nonlinear transient response of the structural system. The paper also presents, in algorithmic form, a complete description of the adopted connection hysteretic model. Satisfying the equilibrium and compatibility conditions, and assuming only the connection's rotational deformation due to bending as variable, this work obtains the tangent stiffness and mass matrices of the beam-column element with semi-rigid connections at the ends. The study concludes by verifying and validating the proposed numerical approach using four structural steel systems: a L-frame, a two-story frame, a six-story frame, and a four-bay five-story frame. The analyses show that the hysteresis of the semi-rigid connection has a strong effect on the frames' responses and is an important source of damping during the structural vibration.

This paper presents a new procedure for solving structural nonlinear problems by combining the orthogonal residual method (ORM) and normal flow technique (NFT). The perpendicularity condition to the Davidenko flow, introduced by the NFT, which must be satisfied during the iterative process, overcome the difficulties, i.e. the poor convergence and inefficiency of the ORM close to the limit points, particularly the displacement limit points (snap-back behavior). Basically, the idea of the proposed strategy is to adjust the load parameter, which is treated as a variable in the nonlinear incremental-iterative solution process, assuming that the unbalanced forces (residual forces) must be orthogonal to the incremental displacements. This constraint is used together with the NFT perpendicularity condition. The proposed procedure is tested, and its efficiency is corroborated through the analyses of slender shallow and nonshallow arches and an L-frame since they exhibit highly nonlinear behaviors under certain loading conditions. It is concluded that the proposed procedure can overcome the numerical instability problems in the neighborhood of critical points when using only the conventional OR process, and the procedure compares favorably with the arc-length method, minimum residual displacement method, and generalized displacement control method.

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