| For analyze the influence of shear deformation and shear lag effect to the concretesimply supported box girder deflection, reference our country high speed railway32m boxgirder, select equal section beam as the research object, take the combination of analytical andfinite element numerical method to calculate. With classic Euler Bernoulli beam theory, theTimoshenko beam theory and shear lag theory based on energy variation principle as thefoundation, carried on the thorough discussion to the the influence mechanism of sheardeformation and shear lag effect to box girder deflection theoretically. According to the threekinds of circumstances, bending deformation, considering shear deformation, consideringshear deformation and shear lag effect, calculated the theoretical value of box girderdeflection that under the action of the weight, uniformly distributed load and concentratedload. Adopt beam4, beam189and solsh190unit in ANSYS to establish the model, obtainedthe numerical solution of box girder deflection under different load. Based on the finiteelement numerical solution, contrast the effect size of shear deformation and shear lag effecton box girder deflection. Analyzed the influence law of deflection caused by sheardeformation as the change of depth-span ratio, obtained the depth-span ratio threshold valueof box girder considering the influences of shear deformation, by keep the cross sectiongeometry parameters the same and changed the size of the box girder span. According to thedefinition of shear correction factor on the basis of Timoshenko beam theory, through thefinite element numerical solution to make reverse deduction, get the shear correction factor ofthe same cross section of box girder. The conclusion is as follows:(1) For this paper’s example, under the weight of box girder, the bending deformationdeflection calculated by analytical solution and numerical solution is the same, it is8.1666mm. After considering the shear deformation influence, the analytical solution deflection is9.0187mm, numerical solution deflection is9.0936mm, error is0.82%, because web areavalue is uncertain in the analytical solution when calculating the shear correction factor. Thenumerical solution deflection is9.8492mm both considering shear deformation and the shearlag effect.(2) Relative to bending deformation deflection, under the action of gravity, the deflectionincreases rate is20.60%both considering shear deformation and the shear lag effect, whichthe shear deformation deflection of increase is at a rate of11.35%, the shear lag effect ofdeflection increases is9.25%. The influence of shear lag effect on the deflection slightlysmaller than the influence of shear deformation.(3) According to this paper calculation, when the depth-span ratio is less than1/16, thepercentage of the additional deflection caused by shear deformation is less than5%to bending deformation, which is negligible in engineering. When the depth-span ratio is equalto1/5, the additional deflection produced by shear deformation is more than50%of thebending deformation deflection therefore, the solid section consider the influence of sheardeformation depth-span ratio1/5threshold is not suitable for box girder, the depth-span ratiothreshold of the box girder section this article uses is1/16.(4) For the box girder cross section this article researched, its shear correction factor canbe the reference value of0.2326. The calculation of web height of roof to floor surface withweb convergence center distance is safe.(5)Box girder is analyzed with mechanics assume that its constraints are imposed on theneutral axis, but in practical engineering the girder is constraints by support. The mid-spandeflection increases the value of0.4288mm at the neutral axis web when the constraint on thesupport, about5.25%of the bending deformation deflection. So the actual deflection shouldbe considering plus additional deflection due to the difference of actual constraint location, onthe basis of shear deformation, the shear lag effect. |
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