Static And Dynamic Performance Of Thin-Walled Beams With Shear Lag Effect

Shear lag issues were studied by some scholars long before, but they were limited in the aviation structures only. Since 1960s, some scholars started to pay attention to shear lag problem because it resulted in the damage of bridges. Over the past several decades, the research outcomes solved the part of engineering problems relating to shear lag effect. However, the existing research achievements still do not handle the shear lag issues completely and accurately. With the development of communication, new problems about shear lag effect appeared continuously. If these problems are not treated seriously and properly, the local cracking and instability of structures from shear lag effect will appear so that it can cause serious damage of structures. Hence, the analysis of shear lag effect is more and more important and critical in theoretical and practical significances. This dissertation makes some contributions in the shear lag effect on the thin-walled beams which are commonly used in the modern bridges. The main contents of this dissertation are as follows:(1) The static analysis of straight and curved rectangle box beamsOn the basis of the thin-walled bars theory and the thin-walled curved bars theory, the governing differential equations and the natural boundary conditions of straight or curved rectangle box girders are established using an energy variation principle and the closed-form solutions of generalized displacement functions are obtained. The established governing differential equation applies one or two different longitudinal displacement difference functions to accurately reflect the amplitude of change of shear lag in the thin-walled box girder's wing slabs according to the practical configuration of the beam. The variation in the shear lag effects on straight and curved rectangle box girders, caused by the changes of factors such as natural boundary conditions, types of loading, lengths of cantilever flanges and curvature radius R , is discussed systematically. Meanwhile, an analysis is made for the change of stress in the top and bottom flanges.(2) The analysis of the natural frequency and dynamic response of straight thin-walled box beamsAccording to the structural features of straight rectangle and trapezoid box girders, one, two or three warping displacement functions are applied to accurately reflect the amplitude of change of shear lag in the thin-walled box girder's wing slabs respectively. In consideration of the shear lag effect, the natural frequency relating to the changes of factors such as natural boundary conditions, span-width ratio, height of thin-walled box girders, and length of cantilever flanges, is obtained. Also based on the direct method, the equation of dynamic response about rectangle box girders is deduced. The solution of the equation can rightly reflect the dynamic behaviour of thin-walled structures, which it develops and enriches the shear lag theory.(3) The static analysis of curved trapezoidal box beamsThree different longitudinal displacement difference functions are employed to accurately reflect the amplitude of change of shear lag in the thin-walled curved box girders with various widths of wing slabs respectively. Then, the governing differential equations and natural boundary conditions are proposed both using the minimum potential principle and taking into account of the curving, torsion, warping torsion (including secondary warping shear effect), shear deformation and shear lag effects. Thus, this dissertation develops Vlasov's thin-walled curved bars theory and clearly reveals the mechanical performance of curved trapezoid box girders.A bridge model with continuous curved trapezoid box girder is designed and made in order to verify the proposed analytical techniques. Two loading cases, uniform and concentrated loads, are applied to study the shear lag effect on the top and bottom flanges of curved trapezoid box girder.(4) The analysis of static and dynamic characteristics of webs of thin-walled straight and curved box beamsIn consideration of shear lag effect on thin-walled box girder's webs, the total potential energy stored in the box girders is obtained according to the relationship of strain-displacement. Also, the total kinetic energy of the box girders can be obtained based on web's vibrating characteristics. Therefore, the web's governing differential equations and corresponding natural boundary conditions can be obtained for the static and dynamic analysis of webs about thin-walled straight and curved box girders using the minimum potential principle and Hamilton principle. The web's shear lag effect on straight and curved rectangle box girders is systematically discussed, involved in the factors such as span-width ratio, length of cantilever flanges, height of thin-walled box girder and thickness of webs. The research results provide a reference for the analysis of web's mechanical characteristics.(5) The analysis on static and dynamic characteristics of straight and curved thin-walled I-beams with wide flangesTwo different longitudinal displacement difference functions ( U 1 ( x ), U 2( x )) are proposed in establishing the governing differential equations and corresponding natural boundary conditions, in order to accurately reflect the amplitude of change of shear lag in the thin-walled straight and curved I-beams with various widths of wing slabs. Then the mechanical analysis is conducted for the static and dynamic characteristics about straight and curved thin-walled I-beams.(6) An approach of accurately selecting longitudinal shear lag warping displacement function of thin-walled box girdersBased on the basic principle of longitudinal warping displacement function setting, this study selects a series of warping displacement functions that conform to basic warping mode of the box girder, in order to obtain the natural frequency equations corresponding to these proposed functions. Then, for the special boundary types, the natural frequency of the beam is determined under these given warping displacement functions. Finally, according to the magnitude of the natural frequency, the precision of warping displacement functions can be judged, and the static calculation examples indicate that the selection of warping displacement functions be necessary.