Keywords: softening, beams, cracks, damage, plastic hinge, parametric study, non-linear, dynamic, numerical analysis.

Cracking in concrete occurs in the tension face of a beam when concrete stresses, due to applied loadings, exceed tensile strength. As load increases, bending moment and tensile stresses increase leading to more cracks in underside of the beam while compressive stress is yet to reach fullstrength and stress distribution is linear. This stage of behavior is known as post-cracking, service load behaviour [1].

At overload, the compressive concrete is highly stressed and the concrete begins to behave in a non-linear manner. As the moment increases, strain in top fibre increases while stress begins to decrease and peak stress moves away from extreme fibre and into the compression zone whereby the neutral axis moves downward indicating a case of softening in compressive concrete zone. As softening of the concrete takes place, stiffness and moment of resistance are dramatically reduced in the beam.

A softening study enables the production of design data such as the ultimate moment of resistance , cracking moment, yield and ultimate curvature, plastic hinge length, and vertical deflection. These are important in defining the strength of a beam and the ductility of the beam which is reflected by values of yield and ultimate curvature and plastic hinge length.

In this study, numerical analysis was performed for several beams of a research program conducted at Monash University, Melbourne Australia [2] to study the softening of beam. The Abaqus software was used for numerical three-dimensional volumetric elements modeling the beams. Appropriete non-linear stress-strain relationships of concrete and steel material were used [3].

The results obtained from analyzed beams will be used to assess the behavior of beams in cracks, ultimate and post-ultimate (softening) stages.

A brief illustration on the different aspects of design data, parametric study, and comparisons that can be obtained from the proposed analysis is presented. Conclusions and recomnendations that summarize the different output are presented.

1

R.F. Warner, B.V. Rangan, A.S. Hall, "Reinforced Concrete", 3rd Edition, Longman Cheshire Pty Limited, Melbourne, Australia, 1989.

2

P. Le Darvall, D. Tse, "Softening hinges in reinforced concrete beams", First National Civil Engineering Conference, Melbourne, Australia, 1987.

3

C. Pontirolli, "Comportement au souffle des structures en beton arme, analyse experimentale et modelisation", Thèse de l'ENS Cachan, France, 1995.

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