The design model of reinforced concrete beam formed by the field of cracks directions

Abstract

Now the design of reinforced concrete constructions for static and dynamic loads with regard to the elastoplastic resistance diagrams of materials is widely used. The model of a reinforced concrete beam is proposed, which consists of trapezoidal elements formed by the field of cracks directions. The theoretical angle of inclination of a crack at any point of a beam has been determined on the basis of minimum of external load, necessary for its formation, which has been obtained from the equation of energy balance. The deflections of each point of a beam have been obtained by solving a differential equation of motion at each step the account. The strains in any fiber of normal and inclined sections have been determined according to the hypothesis of bilinear sections. The stresses in concrete and reinforcement have been obtained with the help of the variable elastoplastic stress-strain curves «σ-ε». The failure mechanism of a beam has been determined on a basis of the transverse to longitudinal force ratio in compressed area of concrete. The internal forces have been determined with the help of numerical section height integration of stresses and from the equation of balance of elements above the crack.