Theory And Model Test Studies Of The Shear Lag In Thin Walled Box Girders Based On Energy Principle

Based on thin-walled bar theory and finite element method, an energy functional variation principle and a finite segment approach in structural analysis of the thin-walled box girders are presented. The analysis theory and computation method for thin-walled box girders in terms of bending, bending-torsion, compression-bending and shear lag effect are established. The dissertation emphasizes particularly on theory and model test studies of the shear lag in thin-walled box girders and consists of ten chapters. A summary on theories and method for shear lag of thin-walled box girders is presented in chapter one. From chapter two to chapter five the shear lag of straight box girder is studied. While the shear lag of horizontal curved box girder is studied from chapter six to chapter nine. And in chapter ten the shear lag of box girder subjected to simultaneous bending and axial forces is studied. Lastly, in this dissertation the conclusion is made as well as prospects of researches are presented. In this dissertation the main characteristic contribution is as follows:(1) A methodology for theory of elasticity under bending, bending-torsion, compression- bending and shear lag effect in thin-walled box girder is systematically established on the basis of the thin-walled bar theory and potential energy variation functional principle, thus consummating thin-walled structural theories.(2) The warping displacement functions with the shear lag effect for the thin-walled box girder are constructed. Furthermore, displacement parameters and space displacement fields of box girders are proposed. Then based on energy functional variation principle, the governing differential equations considering shear lag for theory of elasticity in box girders are established.(3) The closed-form solutions of the governing differential equations are derived from differential equation operation principle. Then, combining the boundary condition, the calculation formulations of the shear lag are obtained. Moreover, an analytical theory for shear lag effect upon the box girders, including the straight, the curve and compression-bending structures are established, thus enriching and developing theories of the shear lag.(4) The homogeneous solutions derived from the shear lag governing differential equations used as the displacement patterns of finite segment are put forward. The displacement field functions are formed. Based on the finite element technology, the stiffness matrix and load column matrixes of the segment element are derived by means ofthe displacement approach and energy functional variation principle. The semi-solution of the finite segment method (one-dimension) is proposed. The computation methods of the shear lag effect fitted for the complication structures such as box girder with varying section, horizontal curved box girder and box girder under combined bending and axial loading are established. The proposed approach can achieve higher calculation accuracy with extremely few discretization nodal unknowns, and conveniently bring into the program system for the conventional beam-bar elements as well as improve resolution efficiency, thus laying a foundation for the study of the shear lag of thin walled box girders.(5) As to thin-walled straight box girder, three different shear lag warp displacement functions considering the different displacements on top and bottom slabs as well as cantilever flanges are proposed in order to reflect change range for the shear lag effect of different flanges with different width. As for the established governing differential equations with consideration of shear lag and shear deformation effects, if the width of top, bottom slabs and that of cantilever flanges are equal, it is proved that the governing differential equations will be degenerated into one shear lag warp displacement function. The calculating formula obtained is completely the same with the precious theory. Therefore, the proposed theory possesses generality.(6) As to thin-walled curved box girders, the shear lag warp displacement functions in fundamental deformation of the flanges complements the theory of thin-walled curved bar, the energy functional variation principle considering shear lag in straight box girder is popularized to the curved box girder. The governing differential equations with consideration of bending, torsion and shear lag coupling are derived. It can be proved that as the curvature central angle becomes zero (or the radius of curvature becomes infinitely large), the differential equations of the straight box girder can be obtained. On the other hand, if the shear lag effect is neglected, the Vlasov's theoretical solutions is obtained. Therefore, this dissertation not only popularizes the theory of shear lag for straight girders but also develops Vlasov's curved girder theory.(7) To thin-walled straight box girder subjected to simultaneous bending and axial forces, the longitudinal displacement differential and axial displacement functions of webs are put up to reflect shear lag effect duo to axial force. According to the small deformation theory, the governing differential equations for shear lag under only axial loading (axial force action) as well as under combined bending axial load (beam-column action) are established respectively by adopting the principle of minimum potential energy. It can be proved from theory that as axial force equals to zero, the same results as the shear lageffect in general box girder under bending are obtained. The calculation formulas derived for compression-bending box girder has not only taken shear lag effect of flanges and webs but also taken beam-column action (P-A effect) into consideration so as to reflect the influences of axial force upon shear-lag under bending. The present methods have new contents as compared with those of the previous theory, which studied only the shear lag of box girder under bending load, therefore, making up to the previous limitation of the simple linearity superimpose of compression-bending structures.(8) The perspex models, a three-span continuous straight box girder bridge model with varying depth, a two-span horizontal curved box girder model bridge and two simple supported straight box girder model bridges are designed and made to meet the specific requirements of this research work. Three kinds of experimental studies on the shear lag effect on box girder model bridge are conducted to verify the accuracy and reliability of thepresent theories and computation module.(9) Based on theory research and model test, the dissertation has analyzed systematically shear lag effect on box girder and brought to light the objective law governing shear lag of box girder. The author is the first person to put forward girder-height ratio (h/H) and axial compressive ratio (N/Ncr) —two importantparameters affecting shear lag effect on box girder. Combining the structure type and size for box girder, the author has found that the factors such as width to span ratio, girder-height ratio, the central angle of curvature, axial pressure ratio, supporting condition, the section position, type of loading have a great effect on shear lag. Last but not least, some important conclusions have been made for shear lag effect on box girder. Based on those important parameters, calculation table for shear lag has been compiled for design reference, which enjoys practical value.