Simplified Evaluation of Shear Stiffness Degradation of Diagonally Cracked Reinforced Concrete Beams

Shear cracking in concrete box-girder bridges, which could cause excessive deflection during the serviceability limit state, cannot be effectively avoided by code-guided design. While elastic shear deformation only accounts for a small proportion of total deformation for un-cracked reinforced concrete (RC) beams, the magnitude of after-cracking shear deformation becomes comparable to flexural deformation for RC beams. However, there is still a lack of practical models to predict the after-cracking shear deformation of RC beams. First, six thin-webbed I beams were tested to investigate the shear stiffness degradation mechanism and the decrease ratio. Then, a very simple truss strut angle formula, which is the crucial parameter for shear stiffness, was established. Furthermore, a stiffness degradation rule for partially cracked beams was proposed considering the influence of concrete tension stiffening, which is essential for predicting the development process of after-cracking shear deformation. Finally, directly measured shear strains were used to validate the proposed shear stiffness model. The results showed that the shear stiffness drops to about 30 similar to 40% of the original stiffness after the first diagonal crack, and the remaining shear stiffness is only about 10% of the original one when the stirrup yields. Increasing the stirrup ratio is a more effective method to control shear stiffness degradation for diagonally cracked RC beams. Also, the proposed shear stiffness model well captures the main features of the shear stiffness degradation, and it provides a relatively accurate prediction of the equivalent shear stiffness at the post-cracking stage.