Analysis Theory And Application Of Shear Lag Effectd For Concrete Box Girders

Concrete box beams are commonly used as mail girders for simply supported girder bridges, continuum girder bridges, continuous rigid frame bridges, rigid tied arch bridges and concrete cable-stayed bridges. In this paper, key problems of shear lag calculation for concrete box beam are systematically studied through theoretical analysis, numerical simulation and experimental results. The mail work and achievements are as follows.(1) Based on variational principle of potential energy, new analysis method for shear lag effect is presented for commonly single cell concrete box beam which flanges' depth varying along cross section. General solution formulae of longitudinal stresses and bending deflections for simply supported girders and cantilever girders are developed under concentrated force, uniform load and concentrated bending moment.(2) For vertical bending box beams, shear lag occurs because of shear deformations of wide flanges in planes of themselves. According to this mechanism of shear lag, new method for defining functions of shear-lag warping displacement is presented. For commonly single cell box beam, new shear-lag warping displacements are defined which only includes one unknown maximum angular rotation but satisfies shear deformation principle. The governing differential equations for shear lag of box girders are established based on variational principles. After shear lag analysis according to typical structures, it's shown that the results obtained using new warping displacement are in good agreement with model test results, finite element results and variational results with 3 maximum angular rotations. It's proved that the new method to define warping displacement of shear lag concerned on the shear deformations of flanges has the features of clear mechanism, fewer variables and higher precise.(3) When analysis shear lag of box girder by variation principle method and beam finite element method, the shear lag warping displacement of spanwise sheet is always supposed to be parabola. It will cause additional axial force when supposing the neutral axis through the sectional centroid. Based on the balance condition of whole section, the formula of additional axial force is presented for parabolical shear lag warping displacement, and the basic character of additional axial force is discussed. For measure the value of additional axial force, the parameter of ratio of additional axial stress (RAAS) is posed. The RAAS of simple supported, cantilever and continuous beam are analyzed under concentrated load and uniform load. It's shown for common concrete bridges RAAS are usual less than 5%, so additional axial force has little influence for precision of stresses, and the parabolical shear lag warping displacement has high analysis precision and needless to be revised with axial displacement. (4) Based on new shear lag method and new warping displacement functions, shear lag analysis method is developed for concrete box with varying flanges depth along cross section. For example concrete box girders, shear lag effect which calculated using this paper's theoretical formulae are good agreement with shell finite element method. By changing the depth of flanges, influence of varying depth on positive, negative shear lag and additional deformation caused by shear lag is investigated.(5) For prestressed concrete (PC) box girders, calculation method for shear lag effect caused by prestressed tendons is developed based on equivalent load method. Shear lag effect of PC continuum box girders with straight and arbitrary lineshape tendons is analyzed. It's drown for prestressed tendons which are mainly used to resist bending moment, shear lag effect will commonly increase the bending moment and stress. Prestressed tendons can always cause more significant shear lag effect in regions of near anchor end, angle changing and intermediate supports than smoothing curve regions. Finally, suggestions of prestressing design are presented according to distribution rules of shear lag for PC box girders.(6) Based on study of shear lag influence on deflection for box girders, two methods which are shear lag coefficient (SLC) and effective flange width (EFW) are presented to modify box girder's deflection. Researches for typical box girders show despite SLC method has more accuracy than EFW, EFW method can be used to calculation box girders'deflection when SLC is unknown.