The Study On Shear And Cracking Performence Of Reinforced Concrete Haunched Cantilever Beams

Reinforced concrete haunched cantilever members are widely applied in buildings and bridges,The quality accidents of cantilever members cracking and collapsing occurred now and then in recent years which reveal the defect of the design code and the deficiency of related research.The experimental study of shear and cracking performance of hauched cantilever beam will help to provide a clear design method for shear design and crack width caculation of the fixed end,So as to improve the safety and durability of the members.Following studies were mainly made.1.A static test of 20 haunched cantilever beams without stirrups and 16 hauched cantilever beams with stirrups was designed and carried out under concentrated load,during which the T-shaped specimens with columns and reverted loading modes were adopted.Main shear factors included the inclined angle of haunch,longitudinal reinforcement ratio,stirrups ratio and shear span-depth ratio.Main cracking factors included the longitudinal bar diameter,anchorage length of longitudinal bar,the strength of concrete.The test results of beams without stirrups showed that the inclined angle of haunch has remarkable impact on the on the location of the diagonal crack.The nominal shear strength of cantilever end has remarkble correlation with the inclined angle of haunch.The nominal shear strength of the cantilever end increases with the increase of the inclined angle of haunch.Adopting Zararis' s critical diagonal crack model,A linear relationship between the shear span-depth ratio of the critical section and the inclined angle of haunch was established,Based on the experimental data of hauched beams in this paper and referenced papers,a formula for calculating the shear capacity of haunched beams without stirrups was proposed,and the predicted values calculated by this formula are in good agreement with the test value and results of 22 nonlinear finite element models.The test results of beams with stirrups showed that the inclined angle of haunch has remarkable impact on the on the location of the diagonal crack.The inclined angle of critical diagonal crack increases with the increase of the inclined angle of haunch.There are more flexural-shear cracks in the beam web when the stirrup ratio is high,whereas the change of stirrup ratio has no obvious influence on the angle and position of the critical diagonal crack.The inclination angle of critical diagonal cracks were measured and counted,and the coefficient of stirrup was determined by truss model.The calculation formula of shear capacity of hauched beam with stirrups was proposed by considering the formula for calculating the shear capacity of haunched beams without stirrups as the concrete term.This formula is in good agreement with the formula in Code for design of concrete structures GB50010-2010(hereinafter referred to as China's code)and the predicted values of the formula are also in good agreement with the test value in this paper and reference papers.The relationship between the accuracy of the formula in China's code formula and the reinforcement ratio was analyzed based on 984 shear tests of beams without web reinforcement under concentrated loads collected and screened from foreign experimental data,which turned out that it was not safe if the formula in China's code does not adopt the reinforcement ratio coefficient in the interval of low reinforcement ratio and the formula adopting reinforcement ratio coefficient could accurately reflect the effect of reinforcement ratio on shear bearing capacity.The relationship between the accuracy of the formula in China's code and the reinforcement ratio was analyzed based on 257 shear tests of beams with web reinforcement under concentrated load collected and screened from foreign experimental data,which turned out that reliability index of China's code formula without adopting reinforcement ratio coefficient failed to meet the specification requirements of 3.7 when the reinforcement ratio was less than 2%.Whereas the shear span-depth ratio coefficient is adopted in the stirrup term in the formula in China's code based on statistical analysis,the calculation formula of shear strength of beams with web reinforcement is proposed adopting reinforcement ratio coefficient and it turns out that this formula meets the code requirements of 3.7 when the reinforcement ratio is less than 2%.All the test beams were modeled and analyzed with the Nonlinear Finite Element software ABAQUS.The outcomes of ABAQUS included that the load bearing capacity,formation and propagation of cracks,load-deflection curves,load-stress of steel bar as well as load-stress of concrete compression zone.Compared with the test results,the simulation accurately reflected the major force and deformation characteristics of the test beams,and revealed their failure mechanism.The nonlinear finite element analysis of principal compressive stress indicated that the shear mechanism of variable depth beams without web reinforcement can be idealized as an arch of two sections.Within the first section,the shear force transfer along a slope from the beam bottom beside the support up to the edge of the compression zone;with the second section,the shear force is parallel to the compressed edge till to the fixed end of the cantilever beam.Greater inclined angle ? corresponds to greater shear transferred by the arch.Tests of beams with the inclinations of the inclined angle ? ranging from 0~0.07 and 0.24~0.3 are fail to be seen.So nonlinear finite element models of 22 variable depth beams was established to fill up the deficiency in the data within the two intervals.More diagonal cracks occurred in the web of variable depth cantilever beams with stirrups.Shear resistance mechanism of truss formed in the beam web.The test results showed that greater inclined angle ? of haunch means greater angle of critical oblique cracks.The truss model was used to evaluate the shear resistant action of stirrup.The angle of critical diagonal cracks in beams with web reinforcement was measured and counted in the test for determining the coefficient of the stirrup item.In this paper,shear capacity of variable depth beams without web reinforcement was adopted in the calculation formula concerning concrete properties.A calculation formula concerning shear capacity of variable depth beams with web reinforcement was established,and this formula fit in well with the formulas in China's code.The experimental data in this paper and foreign literatures indicated that the predicted values of the variable depth cantilever beams comply well with the test results.In the test,flexural crack widths of the fixed ends of 24 beams on 12 tested specimens were measured in their serviceability limit states.It was found that the measured value is greater than that calculated by the formula in China's code.According to a statistical analysis,the anchorage length of longitudinal reinforcement embedded in the columns is related to the width of the cracks.In the ABAQUS model,the bond stress-slip relationship of steel and concrete was simulated by nonlinear springs.The relationship between anchorage length and slippage was analyzed.The fixed end crack width was regarded as the summation of the slippage in the anchorage zone and the slippage inside the beam of the opposite side.As to the fixed end cracks,an adjustment coefficient was added to the flexural crack width formula in China's code,thus taking into account the influence of the anchorage zone length on the crack width.