The Calculating Method Of The Crack Width Of Flexural Members Of UHPC Beams With Ultra-high-strength Steel Bars

Ultra-high performance concrete(UHPC)is a new type of cementitious composite material with ultra-high compressive strength,good toughness and excellent durability.The reason why the combination of HRB600 grade reinforcement and UHPC has been applied less is that there is still a lack of systematic research and quantitative analysis of the influence of key design parameters on the ultimate load carrying capacity and crack width of high-strength reinforced UHPC structures in China.Therefore,this paper derives the crack width calculation formulae for reinforced UHPC beams based on the bond-slip theory;conducts flexural performance tests on UHPC beams configured with HRB600 grade reinforcement to study the effects of various design parameters on the beam load carrying capacity and crack width;and establishes a numerical calculation model for the crack width of high-strength reinforced UHPC beams.The main work and conclusions of this paper are as follows:(1)On the basis of the basic mechanical property tests on UHPC materials,four-point bending performance tests were conducted on three UHPC beams with HRB600-grade high-strength reinforcement and one UHPC beam with HRB400-grade ordinary reinforcement to measure the cracking load,yield load,reinforcement strain,crack width,crack location,crack spacing and crack height,etc.The test results show that when HRB600 grade high-strength reinforcement is used as the tensile longitudinal reinforcement,the reinforcement and UHPC can work together better and the high compressive strength of UHPC can be better utilised;the crack development of reinforced UHPC beams can be roughly divided into three processes,namely the initial cracking stage,the stable crack development stage and the rapid crack development stage;the flexural crack pattern can be roughly divided into primary cracks,longitudinal cracks and secondary cracks according to the crack height.The distribution of cracks is generally dense and fine.(2)According to the test results,the influence of reinforcement type,reinforcement rate and protective layer thickness on the bearing capacity and crack width of UHPC beams was analysed.The results show that the ultimate load carrying capacity of UHPC beams increases by 5.98% when the reinforcement rate increases from 1.27% to 1.67%under the case of reinforcement strength grade HRB600,and the larger the reinforcement rate the smaller the crack width of the beam under the same load;the ultimate load carrying capacity of HRB600 grade UHPC beams increases by 10.7%compared with HRB400 grade UHPC beams under the same reinforcement rate.The ultimate load carrying capacity of UHPC beams is increased by 10.7% compared with that of HRB400 grade UHPC beams under the same load,and the crack width under the same load is approximately the same;the ultimate load carrying capacity of UHPC beams is increased by 7.4% when the thickness of the protective layer is reduced from30 mm to 20 mm with the same reinforcement rate and the strength grade of HRB600 and the thickness of the protective layer is reduced from 30 mm to 20 mm,and the crack width under the same load is larger.(3)Based on the bond-slip theory,the influence of the bridging action of steel fibres in the cracked UHPC section on the stress of the reinforcement is considered,and the residual tensile strength of UHPC between the cracked sections is assumed to be a certain value,and it is assumed that the strains of the reinforcement and UHPC within the crack transmission length conform to the ideal triangular function distribution,and the crack width calculation formula for reinforced steel fibre UHPC axial ties is theoretically derived.The accuracy of the formula is verified and the results show that the theoretically calculated maximum crack width values are in good agreement with the experimental measured values,especially when the load is in the range of 0.6 to0.7Mu,which can predict the maximum crack width of UHPC beams better.(4)Based on the comprehensive consideration of the tensile tempering effect of concrete,the bond stress-slip relationship between reinforcement and UHPC and the material nonlinear intrinsic relationship,a numerical calculation model for the crack width of high-strength reinforced UHPC beams was established based on the test results and implemented by programming in MATLAB language,and the accuracy and applicability of the numerical calculation model were verified based on the test results and the code calculation results.When the reinforcement ratio was increased from2.48% to 3.16% and 4.78%,the lower the reinforcement ratio,the larger the crack width under the same load,and the larger the reinforcement ratio,the slower the crack expansion rate;when the protective layer thickness was increased from 15 mm to 25 mm,35mm and 45 mm,the larger the protective layer thickness,the larger the crack width under the same load.When the protective layer thickness is taken as 45 mm,the maximum crack width exceeds the code limit value of 0.2mm,which does not meet the structural design durability requirements.