Analysis On Distortion Effect Of Box Girders Based On Principle Of Energy Variation

The ratio of distortion warping stress to bending stress generated by thin-walled box girders under eccentric load has gradually increased as the wall thickness becomes thinner and thinner.Therefore,analyzing the distortion effect of box girders has become a work that cannot be ignored in engineering design.There are many analytic methods for the distortion effect of thin-walled box girders.Finite element numerical solutions and model tests are generally used to verifing and proofreading analytic solutions.Scholars have carried out many researches on the distortion effect of box girders,but there are still some shortcomings.In this paper,some of the existing problems was studied in detailed and in-depth from the following aspects.（1）The change of the right angle at distortion center was selected as basic unknown.The process of calculating the distortion total potential energy by the energy variation method and establishing the governing differential equation was introduced in detail,and the initial parameter solutions to the equation were achieved.The consistency of calculation results between the method of this paper and other methonds was verified through a numerical example.The distortion effect analytic formulas of box girders with different boundary conditions were derived whose correctness was verified by comparisoning with the numerical solution of ANSYS.（2）Compared with the cantilever box girder without diaphragm at the free-end,setting diaphragm at the free-end lead to positive and negative maximum of warping normal stress appears at two ends,and the cross section where its sign changes vary from 1/4 to 1/8 from the fixed-end.The longitudinal distribution curve of transverse unit-width bending moment changes from monotonous increase to first increase and then decrease,and the cross section where its maximum value appears vary from the free-end to 1/4 from the free-end.With the increase of the height to width ratio（ψ）,the absolute value of warping normal stress at the fixed-end and mid-span decreases when the cantilever box girder without diaphragm at the free-end,and the absolute value of transverse unit-width bending moment increases at the free-end and decreases at the mid-span.But it have a opposite change law about the two when the cantilever box girder have diaphragm at the free-end.Under the same section size and load conditions,the stronger the end restraint,the smaller the transverse unit-width bending moment and the larger the warping normal stress.The transverse bending moment is less affected but the warping normal stress is greatly affected by the boundary condition.With the increase of the ψ,the transverse unit-width bending moment decreases and the warping normal stress increases whose longitudinal distribution curve vary from double-peak to single-peak.With the increase of the ψ,the stronger the end constraint,the larger the amplitude of the transverse unit-width bending moment,and the smaller the amplitude of the warping normal stress.For a flat-width box girder with a small height to width ratio,regardless of the end constraints,the change of the relative width of cantilever slab（α）has less influence on the distortion effect.（3）The longitudinal distribution of stress amplification factor（SAF）and parameter change laws considering the distortion effect were analyzed through a simply-supported box girder subjected to the lane load.The results show that SAF is symmetrically distributed along the span.The SAF of normal stress at the intersection of the web and top slabs(ε_σ1)reaches its minimum at the mid-span and maximum at 1/4 of the span.The SAF of normal stress at the intersection of the web and bottom slabs(ε_σ2)reaches its maximum at the mid-span and minimum at 1/4 of the span.And the SAF of shear stress（ε_τ）reaches its maximum at the mid-span and minimum at about 3/20 of the span.The ψ has the same influence on ε_σ1 and ε_σ2,while the α has a much greater influence on ε_σ2 than on ε_σ1.The ψ andα have a little effect on ε_τ who decrease as they increases.The ε_σ1 reaches its maximum of0.9647 and the ε_σ2 reaches its minimum of 1.0735 when ψ is equal to 0.8.The ε_σ1 reaches its minimum of 0.7452,the ε_σ2 reaches its maximum of 2.0197 and ε_τ reaches its maximum of 1.6173 when α is equal to zero.