THEORETICAL, EXPERIMENTAL AND NUMERICAL APPROACH TO FRACTURE OF REINFORCED CONCRETE BEAMS IN BENDING

摘要

In the previous papers theoretical and experimental investigations were presented for failure analysis of reinforced concrete beams, using Fracture Mechanics Concept. Theoretical approach was based on Carpinteri's model in which main crack propagation was considered. This crack was actually artificial crack, which was representing main crack, process zone in front of main crack and surrounding damage. The crack was bridged by reinforcement, which was crack arrester. Experimental investigation was performed on two series of specimens. Both series were three point bending reinforced concrete beams with the length of 1.5m, width of 15 cm and height of 20 cm. First series of specimens were with the reinforcement made from mild steel while second were with the reinforcement with ribs (high yield steel). The quality of concrete was MB 30. The main problem in experimental investigation was to record simultaneously intensity of force and the length of the crack. This goal was reached by embedment of graphite and optical fibers in front of main crack. At the moment when graphite and optical fibers were broken (electrical resistance jumps to infinity in case of graphite fibers, and intensity of light disappears in the case of optical fibers) the crack tip position is at they are place. Main part of this paper is numerical approach to Fracture of reinforced concrete beams. The nonlinear Finite Element Method is applied, with material nonlinearity for both materials: concrete and reinforcement. Concrete is modeled as nonlinear in compression and brittle elastic in tension. Reinforcement is represented as elasto-plastic material without hardening. Also small deformation incremental and iterative procedure, using Newton-Raphson model of integration is employed.