The free and forced nonlinear vibrations of slender frames with semi-rigid connections are studied in this work. Special attention is given to the influence of static pre-load on the natural frequencies and mode shapes, nonlinear frequency-amplitude relations, and resonance curves. An efficient nonlinear finite element program for buckling and vibration analysis of slender elastic frames with semi-rigid connections is developed. The equilibrium paths are obtained by continuation techniques, in combination with the Newton-Raphson method. The ordinary differential equations of motion of the discretized frame are solved by the Newmark implicit numerical integration method using adaptive time-step strategies. Three structural systems with important practical applications are analyzed: an L-frame, a shallow arch, and a pitched-roof frame. The results highlight the importance of the static preload and the stiffness of the semi-rigid connections on the buckling and vibration characteristics of these structures.
A large part of the numerical procedures for obtaining the equilibrium path or load-displacement curve of structural problems with static nonlinear behavior is based on the Newton-Raphson iterative scheme to which are coupled the path-following methods. In this context, this study uses one technique, referred to as normal flow, in the process of obtaining the approximate nonlinear static response of structural systems. Basically, this technique is an adaptation made with in the Newton-Raphson iterative scheme in an attempt to speed up the nonlinear solution process and/or remove convergence problems. To overcome the critical points and to trace the whole nonlinear equilibrium path, three different strategies are used in association with the normal flow technique: the cylindrical arc-length, the minimum residual displacement norm and the generalized displacement. With this procedure, the performance of these strategies when associated with the normal flow technique is valued. Two arches with highly nonlinear load-displacement curves are used in the study. The results obtained demonstrated that the association of the generalized displacement strategy with the normal flow technique contributes to the improvement of the nonlinear solution methodology.
The present work aims to study the nonlinear behavior of reinforced concrete structures via Refined Plastic Hinge Method (RPHM). Pseudo-springs are used at the finite element ends, where the gradual loss of stiffness is determined by the combination of the normal force and bending moment (NM) in the cross section. The limiting of the uncracked, elastic and plastic regimes is done in the NM diagram. The concrete cracking is explicitly simulated with two approaches to calculate the effective moment of inertia of the cross section. The displacement-based formulation is referenced to the co-rotational system and coupled with continuation strategies to allow to overcome the possible critical points in the equilibrium paths. For validation of the numerical simulations, the results found with the proposed formulation are confronted with experimental and numerical data present in literature.
The design codes for structural design traditionally establish the adoption of partial safety factors to deal with uncertainties. These standards do not allow one to know the real probabilities of failure of a structure. What is needed, from a practical and scientific point of view, is a more consistent approach, based on reliability theory. This article addresses an initial attempt at determining the safety levels of structures based on advanced analysis and design with structural reliability theory. In this context, the authors consider the effects of the geometric nonlinearity and flexibility of connections in the reliability analysis, which aims at setting a certain displacement as the service limit state. For this purpose, a computer program was written called Structural Reliability Module. This program uses a First Order Reliability Method to analyse reliability. To carry out the structural analysis of steel structures, this study uses the program Computational System for Advanced Structural Analysis. Validating the Structural Reliability Module involved comparing the results from other authors with those generated by the program. Results for the structures under study indicate the efficiency of the implemented measures. Results suggest that, when a certain displacement is set as a service limit state, the reliability of the structures under analysis are only slightly influenced by geometric nonlinearity but considerably so by semi-rigid connections.
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