Softened Truss Model for Reinforced Concrete Beams under Torsion Combined with Axial Force

Luís Bernardo,Cátia Taborda

doi:10.3390/applmech1010006

Abstract

The Generalized Softened Variable Angle Truss Model (GSVATM) allows one to compute the global behavior of reinforced concrete (RC) beams under torsion, including the pre- and post-cracking stage. In a previous study, such a model was successfully extended to cover prestressed concrete beams under torsion with longitudinal and uniform prestress. In order to continue to extend the theoretical model for other loading cases, in this article, the GSVATM is extended to cover RC beams under torsion combined with external and centered axial forces. The changes in GSVATM are presented, as well as the modified calculation solution procedure. Some theoretical predictions from the extended GSVATM are compared with numerical results from the non-linear finite element method (FEM), where good agreement is observed for the studied trends.

Highlights

Theoretical models based in Space Truss Analogy (STA) has been widely used for the analysis of the behavior of reinforced concrete (RC) beams under torsion
In order to validate the extended Generalized Softened Variable Angle Truss Model (GSVATM) for RC beams under torsion combined with axial force, this section presents a comparative analysis between some theoretical results from GSVATM with the numerical ones using nonlinear finite element analysis (FEA) by using Abaqus software [19]
The theoretical predictions of the global behavior (MT − θ curves) of a reference RC beam under torsion combined with several external axial stress states, including compressive and tensile, where presented

Summary

Introduction

Theoretical models based in Space Truss Analogy (STA) has been widely used for the analysis of the behavior of reinforced concrete (RC) beams under torsion. Bernardo et al in 2012 proposed the Modified Variable Angle Truss Model (MVATM) [9] and, in 2015, the Generalized Softened Variable Angle Truss Model (GSVATM) [10], both as an extension of the VATM All these improved models incorporate the influence of tensile concrete behavior through an appropriate σ − ε relationship for concrete in tension in the perpendicular direction to the struts. Since torsion is considered to be the primary effect, only cases with low to moderate axial stress states (both compression and tension) are considered This particular loading case is not widely used in current practice, its study will allow one to preliminarily calibrate and check the GSVATM for this combined loading before it can be extended to more complex types. The comparative analysis was performed based on the theoretical and numerical MT − θ curves, namely the shape and some of the key points

Original GSVATM Formulation and Calculation Procedure

Comparative Analysis with Numerical Results

Findings

Conclusions