Influence Of Diagonal Cracking On Shear Behaviors Of Concrete Beam Bridges

Diagonal cracking has a significant influence on the shear capacity and shear stiffness of concrete beam bridges.However,at present,the calculation methods of shear strength are still not unified as the calculation of flexural strength in main design codes.In addition,the shear stiffness calculation is rarely mentioned in codes.In this paper,a detailed study was performed on the influence of diagonal cracking on shear behaviors of concrete beam bridges.The main work includes formulation of shear capacity model,measurement of after-cracking shear deformation and theoretical research of shear stiffness degradation and other aspects,as listed below:(1)Based on ACI-DAfStb shear database of reinforced concrete(RC)slender beam,the distribution of main shear parameters were analyzed,and the influence of each shear parameter on shear capacity was studied.The results showed that:The shear strength of RC slender beams were mainly affected by concrete strength fc',shear span ratio ?,the longitudinal reinforcement ratio ?,stirrup intensity pvfyv and effective height of section d.It increases nonlinearly with fc'.Besides,it decreases with ?,but the descending rate become slower for ?>4.In addition,it increases with p and tre-nds to constant for large ?.Moreover,it increases with stirrup intensity ?vfyv,but the magnitude is limited by the compressive strength of concrete.Furthermore,it decreases with increase of d.This size effect becomes particularly significant for small size specimen and becomes unapparent for specimen with web reinforcement.Specimens with large size,high strength concrete and low longitudinal reinforcement ratio were still inadequate,which differs from engineering practice.(2)The advantages and disadvantages of shear design method of popular design codes as well as their theoretical foundation were summarized.Then,the possible shear failure modes and their corresponding damage control point were analyzed,based on which the transition mechanism between different shear failure modes was discussed.To overcome the limitation of popular specifications that their shear design formula cannot make smooth transition between different shear failure modes,shear models were established based on flexural-shear cracking failure mode and web-shear cracking failure mode respectively.(3)For flexural-shear cracking failure mode,a refined analysis model based on compression zone for slender RC beams without stirrups was established.This model divides concrete compression zone into two parts:shear compression zone and diagonal tension zone,for which the failure criterion of principal compression stress and failure criterion of tensile stress were adopted to calculate their shear contributions respectively.Then,the theoretical formula for shear capacity of slender RC beams without stirrups was established.Further,Taken the contribution of shear stirrups into account,the theoretical formula for shear capacity of slender RC beams with stirrups was obtained.The proposed theoretical formula gives smooth transition of strength prediction from shear compression failure mode to diagonal tension failure model.In addition,the proposed formula reflects the influence rules of concrete strength fc',longitudinal reinforcement ratio p,shear span ratio ?,stirrup intensity ?vfyv and effective height d.Test verification with ACI-DAfStb shear database showed that the prediction accuracy and stability of proposed formulas were increased compared to code's methods.(4)For web-shear cracking failure mode,the variable angle truss model(VATM)was recommended to calculate the shear capacity of RC beams,and two kinds of theoretical formulas of strut angle for VATM were derived.Based on test results analysis,it is found that the strut angle rotation can be divided into two stages:namely the stable cracking stage and the plastic rotating stage.It is pointed out that the synergistic effect of concrete and stirrups has not worked yet during the stable cracking stage,and the shear contribution of concrete should be accounted independently.While during the plastic rotating stage,the synergistic effect already worked,the concrete contribution need not included in.To calculate the strut angle,the minimum strain energy principle and the plastic theory were applied to stable cracking stage and plastic rotating stage,respectively.Finally,two theoretical calculation formulas for strut angle were obtained,and corresponding shear capacity formulas was established for the two stages.The ACI-DAfStb shear database was used for test verification.The results showed that the two proposed simplified formulas can reflect the influence rules of concrete strength fc',longitudinal reinforcement ratio ?,shear span ratio ?,stirrup intensity ?vfyv and effective height d,and that the prediction accuracy and stability of proposed simplified formulas were improved compared to code's methods.(5)For beams with inflection point,variable cross-section or prestress,their influence on shear transfer mechanism were analyzed.Modified shear capacity calculating method were proposed and compared with experimental results.(6)Six large size thin-webbed restrained RC beams were tested to investigate the shear stiffness degradation after diagonal cracking.The strain before and after diagonal cracking were continuously measured based on strain measuring grid,which was made of mechanical strain gauge with large base length.The after cracking shear deformation and bending deformation of variable depth beams were obtained directly with the isoparametric transformation method.The test results show that:For specimens with lower stirrup ratio,diagonal crack developing and stirrups yielding are the two turning points of load deformation curve.The residual shear stiffness after cracking can be improved by increasing both concrete strength and stirrup ratio.However,increasing stirrup ratio gives better control of after-cracking shear deformation.(7)A shear stiffness theoretical degradation model was proposed to evaluate the effective shear stiffness of RC beams after diagonal cracking.Firstly,the equivalent shear stiffness at stirrup yielding state was derived with VATM.Secondly,to consider the influence of cracking degree on stiffness degradation,constant tangent stiffness degradation mode was proposed according to experimental law.Different test data were collected for comparison,and the results showed that the proposed model gives good evaluation of shear stiffness degradation of diagonal cracked RC beams.(8)To give quantitatively assessment of shear stiffness of diagonal cracked beam bridges,a simplified evaluation method are proposed based on experimental and theoretical study.Diagonal cracking grading was used to describe the cracking level,and the after-cracking shear stiffness was assumed to decrease linearly with diagonal cracking grading.As a practical and conservative method,it was applied to an actual bridge for rapid and quantitative assessment of shear stiffness.