Calculation Method For Stiffness Of Double Composite Beam Considering Concrete Damage

When the top concrete slab of the continuous composite beam is cracked under the negative bending,the concrete of the crack section has no effect on the bearing capacity.However,due to the bonding effect between the steel and the concrete,the concrete between the cracks can still withstand the tensile force,resulting in a tension stiffening effect.The current specification does not consider the influence of the tension stiffening effect when calculating the stiffness of the negative bending moment zone of the continuous composite beam.It directly ignores the tensile concrete in the negative moment zone and calculates the stiffness according to the converted section of the steel beam and the steel bar,so that the deflection calculated according to this method is not accurate.The static test of double composite beam is taken as the background of this dissertation.Based on the lumped flexibility model,the calculation method of effective stiffness and static deflection of double composite beams with damaged concrete is studied.Firstly,this dissertation summarizes the static deflection 、 slip and the development regularity of cracks of the double composite beam model test.Using ANSYS finite element analysis software,the solid element finite element model of the test beam was established and the finite element analysis results agree well with the experimental results.On the above basis,the effect of force ratio R and the height ratio of steel beam to concrete slab r on the effective stiffness of double composite beams after cracking is studied.Studies have shown that using the current specification to calculate the deflection of a composite beam will underestimate its bending stiffness,making the calculation results too conservative,which is not conducive to the practical application of the project.This situation is more serious when the force ratio and the height ratio of steel beam to concrete slab are smaller.Based on the lumped flexibility model,a massless equivalent spring is introduced to describe the local stiffness loss caused by the cracking of the concrete slab on the double composite beam.The stress intensity factor KΙ of the double composite beam under bending is obtained by the singular element finite element method,and the relationship between KΙ and crack depth ratio a/h is fitted.On the above basis,this dissertation applies the theory of fracture mechanics and Castigliano’s theorem to obtain the local additional flexibility c of the crack section of the double composite beam.The Dirac function is used to derive the general solution of the effective stiffness and deflection of the equal stiffness and variable stiffness cracked beams.On the above basis,combined with the local additional flexibility c obtained in the previous dissertation,the calculation method for effective stiffness and deflection of the double composite beams with concrete damage are proposed.After comparison and verification,the result calculated by this method is in good agreement with the simulation result of the solid element and the experimental result,which greatly improves the calculation accuracy compared with the calculation method specified in the current specification.