EMBEDDED FORMULATION OF PRESTRESSED TENDON IN 3D – BRICK ELEMENT

Mohamad Najim Mahmood ,Ayad B Behnam

doi:10.33899/rengj.2010.34783

Abstract

In the present work a formulation of the reinforced bars and prestressed tendons embedded in the brick element is developed and used for the nonlinear analysis of reinforced-prestressed concrete beams. The reinforcement and prestressing bars are represented by an axial 3 nodded bar elements embedded into the 20 nodded isoparametric brick concrete element. Perfect bond is assumed between concrete and prestressing steel bars (or tendons) such that displacements and strains of the bars are assumed to be compatible with those of the concrete element. To verify the applicability of the model two prestressed beams are analyzed and the numerical results show a good agreement with the experimental one. Keywords: Brick element, Embedded bar, Finite element, Nonlinear analysis, Prestressed concrete.

Highlights

The nonlinear analysis of reinforced or prestressed concrete structures requires an efficient modeling that takes into account the stiffness contribution of the steel bars and prestressing tendons to the structural equilibrium equations
The first formulation of the embedded bar to model the reinforcement bars in the nonlinear analysis of axisymmetric concrete structures was presented by Phillips and Zienkiewicz [1] in 1976
The main emphases of the present work is to develop a generalized model for the analysis of prestressed concrete beams, using a three-dimensional brick elements with embedded-curved tendons placed at any orientation and location within the solid brick element which enable the modeling of prestressing tendons at any eccentricity from the neutral axis of the beam and at any orientation

Summary

Introduction

The nonlinear analysis of reinforced or prestressed concrete structures requires an efficient modeling that takes into account the stiffness contribution of the steel bars and prestressing tendons to the structural equilibrium equations. This contribution should consider the prestressing forces carried out by the bars, but it should include the tendon stiffness. Krishnamoorthy and Panneerselvam [2] model the reinforcement bar by embedded two nodes bar elements in the plane stress concrete elements that were used in the nonlinear analysis of reinforced concrete framed structures. These interpolation functions can be used to evaluate the global coordinates at any point (p) along the bar as: xp

Xp yp zp x ei

Where j

Equivalent Nodal Forces and Global Stiffness Matrix

Strains ft

Present Work

Conclusions