ANALYTICAL MODEL FOR SHEAR STIFFNESS OF REINFORCED CONCRETE BEAM WITH STIRRUPS

The calculation of deflection of reinforced concrete (RC) beams generally ignores the contribution of shear deformation. However, diagonal crack will significantly reduce the effective shear stiffness of RC beams, and result in remarkable increase of shear deformation, which should not be neglected in the assessment stage. To evaluate the effective shear stiffness of diagonally cracked RC beams with stirrups, an analytical model of shear stiffness was proposed in the paper. Firstly, the shear stiffness of RC beam at stirrup yielding status was derived based on variable angle truss model. Compared to the elastic shear stiffness, the shear stiffness degradation factor was mainly influenced by the material modulus ratio, stirrup ratio and the inclination angle of strut. Secondly, based on the observed shear stiffness degradation law of shear deformation curve, a constant tangent stiffness degradation mode, which considers the influence of cracking level, was proposed. The shear increment after shear cracking was used as a quantitative indicator for the cracking level. Finally, the analytical formulas of the inclination angle and shear stiffness degradation factor were obtained based on the principle of minimum strain energy. To verify, two thin-webbed concrete beams were tested and corresponding shear deformation were carefully measured. In addition, shear deformation data of fifteen shear segments of RC beams in literature were collected. The comparison results showed that the proposed shear stiffness degradation model gives good prediction of the shear stiffness at stirrup yielding status and reflects the degradation law of shear stiffness at different cracking level.