Evaluation of minimum reinforcement in flexural members based on fracture mechanics

The minimum flexural reinforcement required in reinforced concrete (RC) beams is affected by the compressive strength of concrete, yield strength of steel reinforcement, fracture toughness and size (depth) of member. This paper reports an analytical investigation carried out to predict the cracking behavior and minimum flexural reinforcement corresponding to limiting crack width. The minimum flexural reinforcement is defined corresponding to the stage where both the maximum surface crack width and the critical crack opening displacement (CODCT) are equal at the yielding of steel reinforcement. An analytical model has been proposed to determine the minimum flexural reinforcement through a parametric study involving several combinations of beam depth, fracture toughness, strength of concrete, and yield strength of steel reinforcement. The proposed model has been validated with the experimental observations reported in the literature on several RC beams of different depth and strength of concrete. The model predicts the minimum flexural reinforcement satisfactorily, agreeing with the experimental observations on various beam depths. The present model looks to be an improvement of several existing models incorporating all the influencing parameters.