The Analysis Of Tube Structures Under Bending And Torsion Moments By Precise Integration Method

Due to good lateral force-resistance performance, tube structure is used widely in high-rise buildings. So it is significant to research tube structure's mechanical property under lateral force. Specific studies are as follows:(1) According to the continuous principle, frame-tube structure is made equal to equivalent solid thin-walled tube which is enclosed with orthotropic plates and corner column, so its continuous mechanical model is founded.(2) Hamilton duality solution system of tube structure under bending and torsion moment is deduced basing on elementary-beam theory and thin-walled structure's restrained-torsion theory; Elementary-beam theory is modified by assuming that the warping displacement (along axial direction) of flange and web frame are distributed along quadratic and cubic curve, and Hamilton duality solution system of tube structure considering shear-lag effect under bending moment is deduced; Abandoning the presumption about warping displacement in elementary-beam theory and thin-walled structure's restrained-torsion theory, Hamilton duality solution system is deduced basing on interpolating function.(3) Precise integration method is applied to solve solution system above which is implemented by program upon MATLAB language. The lateral displacement and warping stress can be gained, and the result is compared with those from other methods which turns out to be good agreement. It proves that the method in this thesis is reasonable and feasible. By comparing the results of Hamilton duality solution system above, it shows that the shear-lag effect can't be ignored in tube structure. Detail analysis about shear-lag effect and several factors which may influence the effect are made. The load type, variable-section or uniform-section, the ratio of height to width and the ratio of hole on the shear-lag effect are studied.(4) The thesis presents interpolating precise integration method first which extends its field of application to two-dimension problems. It affords a new idea and path to resolve similar problems.A new method to analyze the tube structure is offered in this paper. Both symmetric and asymmetric section, uniform and non-uniform section tube structure under usual types of load and twist moment can all be solved. The research findings of this paper can guide the design in engineering.