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

Abstract

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 30~40% 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.

Post-Cracking Shear Stiffness Model of Reinforced Concrete Beams

“…The factor λ MV in Equation ( 13), which can be regard as the shear span-to-depth ratio, has a larger influence on shear deformation than the stirrup ratio ρ v during the pre-cracking stage but less influence during the post-cracking stage [3,6]. This interesting phenomenon is further discussed in the next subsection and in the experimental validation.…”

“…Scholars have developed some empirical or simplified degradation rules to depict the degraded shear stiffness of partially shear-cracked RC beams, such as linear secant stiffness degradation [30], linear tangent stiffness degradation [7], mixed degradation [9], exponential degradation [8], regression fitting degradation [10], adopted Branson's degradation [3], etc. Below are four representative effective shear stiffness models,…”

“…From a practical perspective, current deflection models for RC beams, whether cast in situ or prefabricated, typically ignore the contribution of shear deformations [1,2]. However, some prior shear tests on slender beams revealed that the measured deflections are generally much larger than the prediction-by-code method [3][4][5]. One possible reason for these underestimations may be from the neglect of the contribution of shear deformations, especially the contribution of shear deformation after shear cracking [6][7][8][9][10][11].…”

“…For the shear stiffness degradation criteria, scholars have proposed various rules, such as linear tangent degradation [7], linear secant stiffness degradation [26], hybrid stiffness degradation [9], exponential degradation [8], adopted Branson's degradation [3], etc. However, due to the complex influencing mechanism of shear cracks on shear behavior [27][28][29][30], there is a need for shear stiffness theories that can properly reflect the gradual degradation of shear stiffness with the development of shear cracks.…”

Parametric Investigation of Self-Centering Prestressed Concrete Frame Structures with Variable Friction Dampers

“…P-delta trans formation was used to convert the geometrical coordinates of the columns to take into account the p-delta effect caused by the lateral displacement of the structure. The concrete for the beams and columns was simulated using the Uniaxial Material Concrete 02 consti tutive model, which can consider the tension of concrete [36][37][38][39][40]; Longitudinal reinforced steel bars in beams and columns were modeled using a Steel 02 constitutive model, which was able to capture the hardening effect [41,42]. Prestressed strands were simulated by two Truss elements, which were parallel to the beam.…”