RESUMO: Neste trabalho apresenta-se um conjunto de rotinas do MATLAB para calcular a relação momento-curvatura de seções transversais de concreto armado. Este é um assunto de grande importância para fins acadêmicos e práticos de projeto no contexto da engenharia estrutural. As rotinas computacionais foram desenvolvidas de forma a serem simples, gerais e flexíveis. Isso permite ampla aplicação prática e futuras melhorias e modificações. A conhecida abordagem das lamelas foi utilizada, no entanto também é apresentado um desenvolvimento alternativo do método, que é interessante do ponto de vista conceitual. Por fim, são apresentadas comparações numéricas para validação das rotinas.

ABSTRACT: In this paper we present a set of MATLAB routines for evaluation of the moment-curvature relationship of reinforced concrete cross sections. This is a topic of major importance for both academic and practical design purposes in the context of structural engineering. The computational routines were developed to be simple, general and flexible. This allows wide practical application and future improvements and modifications. The well-known fibers approach is employed, but an alternative development of the method is also presented. This is interesting from the conceptual point of view. Finally, numerical comparisons are presented to validate the routines.

The Generalized Finite Element Method (GFEM) can be viewed as an extension of the Finite Element Method (FEM) where the approximation space is enriched by shape functions appropriately chosen. Many applications of the GFEM can be found in literature, mostly when some information about the solution is known a priori. This paper presents the application of the GFEM to the problem of structural dynamic analysis of bars subject to axial displacements and trusses for the evaluation of the time response of the structure. Since the analytical solution of this problem is composed, in most cases, of a trigonometric series, the enrichment used in this paper is based on sine and cosine functions. Modal Superposition and the Newmark Method are used for the time integration procedure. Five examples are studied and the analytical solution is presented for two of them. The results are compared to the ones obtained with the FEM using linear elements and a Hierarchical Finite Element Method (HFEM) using higher order elements.

This paper presents an approach for the global optimization of truss sizing and geometry that is based on a probabilistic restart procedure coupled with a local search algorithm. The resulting algorithm is able to guarantee local optimality and provides a set of local optima which contain, with an increasing probability as the number of restarts increases, the global solution. The optimization problem searches for a truss structure of minimum volume, subject to stress constraints. The design variables are the bars cross-section areas and some nodal coordinates. Several loading conditions are also considered. Finally, four numerical examples are presented and the main aspects of the approach are discussed.