Theoretical And Experimental Study On Shear Deformation Of Reinforced Concrete Beams

The deflection of the reinforced concrete(RC)beam is one of the important parameters which need to be controlled when designing the concrete structures.After the diagonal cracks emerge in the shear span,the shear stiffness degrades significantly leading to a rapid increase of the shear deformation.The current codes for concrete structures provide no expression for estimating the shear deformation after shear cracking.Omitting the contribution of the shear deformation may bring un-conservative design of the concrete structures.The mechanism of the shear deformation after shear cracking changes considerably compared to that at the elastic stage.At present,there still are research gaps that need to be filled in terms of the mechanism,the influence and the computational methods of the post-shear cracking shear deformation.In this thesis,the shear deformation in the shear span of RC beams is investigated in detail from three aspects: experimental work,numerical simulations and theoretical models.In the experimental work,five RC beams with thin webs are tested and the shear deformation in the shear span is successfully separated from the flexure deformation using the Digital Image Correlation(DIC)technique.The influence of the stirrup ratio,the tension reinforcement ratio,the stirrup spacing,the web width and the moment-to-shear ratio on the shear deformation is investigated.Based on the experimental results,the current theoretical models and the Concrete Damage Plasticity(CDP)model,a built-in concrete model provided by the commercial finite element(FE)software Abaqus,are assessed in terms of predicting the shear deformation.Given the defects of the available theoretical and numerical models,a nonlinear concrete numerical model,2D-CONC,is developed and implemented through the subroutine VUMAT provided by Abaqus.The key parameters of the 2D-CONC fixed-crack model are also examined.With the help of the numerical analysis,a practical computational method is proposed.The proposed numerical model and the practical computational method are assessed against the collected experimental results.It demonstrates that the the 2D-CONC fixed-crack model is capable of not only predicting the shear deformation of RC beams,but also accurately reproducing the shear-deformation mechanism after shear cracking.The proposed practical method proves to be a reliable and convenient method for the everyday design of the serviceability of RC beams.The major contributions of the work presented in this thesis are listed:(1)Five RC beams with thin webs are involved in the experimental program.The displacement and strain fields in the shear span are monitored using the DIC measuring system PMLAB which was co-developed by the Optical Mechanics Groups at Southeast University(SEU)and University of Science and Technology of China(USTC).Virtual measuring grids are created to measure the mean shear strain and mean curvature at various locations in the shear span,which allows separating the shear deformation from the flexure deformation.Moreover,the mean vertical strain,the principal compressive strain and the principal compressive strain angle are also experimentally obtained.These deformation results constitute the key parameters representing the shear-deformation mechanism of RC beams after shear cracking(the mean vertical strain reflects the elongation of the stirrup tension tie while the principal compressive strain and the principal compressive strain angle the shortening of the diagonal concrete struts).The current theoretical models fail to reproduce the post-cracking shear-deformation mechanism of the test beams and the calculated shear deformation deviates from the experimental results.(2)A nonlinear concrete numerical model,2D-CONC,which is in the framework of orthotropic theory,is developed and implemented through the subroutine VUMAT provided by Abaqus.Either the rotating-crack model or the fixed-crack model could be selected.The explicit analysis procedure is applied and the convergence difficulty which may be encountered when numerically analyzing the concrete structures is avoided.The definition of the shear response of the crack surface in the 2D-CONC fixed-crack model is discussed by investigating the influence of the shear stiffness and shear capacity of the crack surface on the numerical results.Based on the existing research findings,a shear-slip model of the crack,which is capable of reproducing the shear behavior of RC beams,is presented.(3)The CDP model provided by Abaqus and the developed 2D-CONC model are verified against the element-level tests and the member-level test.In the element-level verification,the experimental results of the RC shear panels are used to verify the numerical models.In the member-level verification,both the overall response(i.e.the total deflections,the flexure-induced deflections and the shear-induced deflections).and the detailed response(i.e.the mean shear strain,the mean vertical strain and principal compression strain angle)are used to verify the numerical models more systematically.It is found that a)the CDP model fail to reproduce the shear-deformation mechanism of RC beams;b)the 2D-CONC rotating-crack model badly underestimate the stiffness of RC beams without stirrups at the higher-level loads;and c)the 2D-CONC fixed-crack model is capable of producing satisfactory results of the shear deformation and the shear capacity.(4)The factors affecting the contribution of the shear-induced deflections to the total deflections are discussed with the validated numerical model.It is found that for the lower longitudinal reinforcement ratio,the lower shear reinforcement ratio,the lower shear span-to-depth ratio and the higher load level,the contribution of shear deformation could be more significant.The numerical results also indicate the influence of the compression reinforcement on the shear deformation after shear cracking is negligible and the concentrated load increases the shear stiffness of the diagonally-cracked section.(5)Based on the parametric analysis with the numerical model,the expression for estimating the tangent shear stiffness after shear cracking,Kt,cr,is proposed.Moreover,a practical computational method for predicting the shear deformation in the shear span of RC beams is developed in the framework of the three-stage model of the shear force-shear strain curve.(6)An experimental database including the deformation results of 32 RC beams is established.The predicted results with either the proposed 2D-CONC fixed-crack model or the practical computational method are in good agreement with the experimental results.