Fracture of Reinforced Concrete Beams Subjected to Three Point Bending

The present paper investigates deformation of three point bent reinforced concrete (RC) beams analytically (using fracture mechanics), computationally (using finite element method) and experimentally. As the applied force increases the crack is initially trapped by the reinforcement. The debonding of the reinforcement is attributed to the horizontal crack. Simultaneously, the vertical crack propagates driven by the externally applied force. The reinforcement behaves as elasto-plastic spring that decreases the stress intensity factor. The developed analytic model provides estimates of the collapse load, crack length and crack opening displacement. The ultimate loading is estimated by the numerical smeared crack model, incorporated in nonlinear finite element code DIANA. Experimental measurements are used to verify theoretically and numerically obtained results. Special attention is focused on the determination of vertical crack size using graphite and optical fibers.