Rigidity of reinforced concrete elements with inclined cracks under the action of transversal force and torsion

Abstract

A method for determining the dowel forces in the longitudinal and transverse reinforcement of RCE with flexural cracks subjected to transverse force and torques is presented.

It is shown that the external transverse force is perceived by the shear force in the compressed zone of concrete, the sum of the forces in stirrups and transverse (dowel) force in the longitudinal reinforcement. It is assumed that the external transverse force is perceived in proportion to the stiffnesses of these three components. The shear stiffness of compressed zone of concrete is defined as the product of the area of the compressed zone and the shear modulus of concrete. The axial stiffness of transverse reinforcement within the calculated inclined section is defined as the product of the Young modulus of the rebar by the total area of all transverse rebars in this section. The shear stiffness of the longitudinal reinforcement is determined by the empirical formula for the anchor displacement in the transverse direction due to the force acting perpendicular to its axis. In torsion, the dowel force in the longitudinal reinforcement has horizontal and vertical components.

The axial force and a horizontal component of the dowel force arise in the transverse reinforcement. To determine all components of the axial and dowel forces in the longitudinal and transverse reinforcement, the compatibility conditions should be composed in the places of the cut of the longitudinal and transverse rebars. In addition to displacements from external and internal forces, these conditions also include displacements due to local deformation in the places of cut of reinforcement. As a result, a system of four equations is derived for determining the vertical and horizontal components of forces in the longitudinal and transverse reinforcement.

After determining all the dowel forces in the longitudinal and transverse reinforcement, the mutual displacement of the sides of the inclined cracks is defined as the sum of displacements caused by external load and dowel forces. Having dowel and longitudinal forces, the torsional stiffness of an element with an inclined crack should be determined according to the method developed by the authors of this article previously.