Softening in reinforced concrete beams and frames

The softening postpeak load-deflection relation for cracking reinforced concrete beams and frames is analyzed by layered finite elements. Concrete is assumed to exhibit strain softening in both tension and compression, and the steel reinforcement is elastic-plastic. The bending theory assumptions are used and bond slip of reinforcement is neglected. It is shown that the model can satisfactorily approximate the existing test results for softening beams and frames. At the same time, the constitutive laws with strain softening, including those of continuum damage mechanics, are shown to lead to spurious sensitivity of results to the chosen finite element size, similar to that documented before for other strain-softening problems. In analogy to the finite element crack-band model, this problem can be overcome if the minimum admissible element size is specified as a cross section property; its suitable value appears to be equal to the beam depth.