An Improved Formulation and Analysis of Reddy Beam Model for Framed Structures

MARCOS RODRIGUES; LUIZ FERNANDO MARTHA; J. N. Reddy; Eugenio Ruocco

An Improved Formulation and Analysis of Reddy Beam Model for Framed Structures

Authors

M. A. C. Rodrigues Federal University of Espírito Santo, Department of Civil Engineering, Vitoria, Brazil https://orcid.org/0000-0003-2084-5820
L. F. Martha Pontifical Catholic University of Rio de Janeiro, Department of Civil Engineering, Rio de Janeiro, Brazil https://orcid.org/0000-0002-5783-5151
J. N. Reddy Texas A&M University, College Station, J. Mike Walker ’66 Department of Mechanical Engineering, Texas, USA. https://orcid.org/0000-0002-9739-1639
E. Ruocco University of Campania “L. Vanvitelli”, Department of Engineering, Aversa, Caserta, Italy https://orcid.org/0000-0003-2433-6230

Abstract

A structural analysis of framed structures using the finite element method considering both the Bernoulli- Euler and the Timoshenko beam theories can be performed adopting cubic interpolation functions that yield analytical solutions for the displacements. However, these theories may not provide stress results with sufficient accuracy. In such cases, it is necessary to employ higher order beam formulations, that may require a high level of discretization. Therefore, this study proposes an enhanced Reddy beam element, obtained by considering interpolation functions calculated directly from the solution of the differential equation system. This solution minimizes the impact of structural discretization on the analysis, and framed structures can be effectively modeled considering the minimum number of elements required to describe the geometry. The results obtained by the proposed formulation were compared against classical beam theories and the Reddy beam model adopting conventional shape functions, showing the efficacy of the proposed element in simulating the elastic behavior of framed structures in a FEM-like procedure.

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Published

2024-05-07

Issue

Vol. 21 No. 5 (2024)

Section

Articles

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