Study On Reasonable Warping Displacement Pattern And Application In Shear Lag Effect Analysis Of Box Girder

With the rapid development of bridge construction in our country, the box-section getsthe extensive favor of bridge designers. As is implied by the name, the shape of box-sectionwith advantages which other shapes lack of is like a box. Because the large cantilever boardand wide box-girder have become the main trend, the shear lag effect will gain the greatconsideration without any doubt. Virous analysis methodologies of shear lag effect wereconducted in the previous research. Each of the methodologies needs specific applicationconditions and has its own advantages and disadvantages. Among those analysismethodologies, the energy variational method based on the principle of minimum potentialenergy is regarded as the most classic and effective one. However, the traditional energyvariational method still has some deficiencies and defects, for instance, it is hard to meet theself-equilibrium conditions of the axial force, the selected warping displacement function ofthe shear lag lacks of rigorous theoretical evidence, wings with different sizes have noreasonable corrections, the formula of longitudinal stress is too complex, etc. Concerning theabove deficiencies, this thesis tried to make the detailed theoretical support and corrections aswell as set up the Ansys numerical model to test and verify the theories proposed in the thesis.The specific work is summarized as follows:1.Generalized the types of the definitions of shear lag warping displacement function inthe previous studies, the author found that the main types are parabolic and cosine curve type.Assumptions, advantages and disadvantages were given to the above two types respectivelyand a new method used to define the shear lag warping displacement function from theperspective of the law of wings’ shear deformation controlling the shear lag effect wasproposed as well.2.Based on the bending theory of computation of thin-walled box girders, the thesisanalyzed the different laws of shear displacement of wings and designed the computationalformula of shear flow. Assuming that lateral displacement of wing plate could be neglectedsince it had minor effect, the thesis made great effort to prove that the parabola is the moreequitable warping displacement function of the shear lag. The thesis made the warping stressmet the self equilibrium conditions by adding the constant, corrected the strip widths ofdifferent cantilever plates and backplanes as well as the horizontal spindle-shaped distances.The new warping displacement function of the shear lag had been proposed at the same time.3.Regarded the additional deflection caused by the shear lag effect as the generalizeddisplacement shear lag, this thesis defined the generalized moment shear lag as thegeneralized force corresponding with the shear lag warping stress. Under such conditions, theexpression of longitudinal stress, taking the shear lag effect into consideration, could correspond to the calculation of the corresponding elementary beam theory and its physicalmeaning could be more obvious.4.Controlling differential equations were set up via the variational method and both theconcentrated load and distributed load of the simply supported box-girder’s and the cantileverbox-girder’s the expressions of the additional deflection caused by the shear lag effect wereworked out through boundary conditions. Then the longitudinal stress and the verticaldeflection of box-girders could be obtained through the combined application of theexpressions and elementary beam theory5.Based on the theoretical methodologies proposed in the thesis, the longitudinal stressesof different warping displacement functions were worked out by means of calculationalexamples of the simply supported beams and the cantilever beams respectively. The Ansysnumerical model was also set up to test whether analysis methodologies and formulae arereasonable or not.6.The calculation of the simply supported beams, made of the prestressed concrete,which has balanced concentrated load shows that in the actual bridge design, if leave the shearlag effect out of account, the influence of the vertical deflection could be neglected while thelongitudinal stress couldn’t because of the obvious differences.