Energy Solution Of Stiffness Equation Of Elastio-plastic Beam-column

In various national design codes, limit-states design methods have been widely used. This has resulted in more rational consideration of the effects of inelasticity and stability at maximum design load levels. However, limit-states design is used only in the design of simple structures and individual members. Our current design procedure is to analyze a structure elastically, then to select the members on the basis of their ultimate strength. The analysis and design are therefore incompatible. On the other hand, because of the lack of analysis model that can represent the nonlinear behaviors structures in limit states accurately and directly, one has to check members according to the typical specification formulas. This situation does not match the advancements of computer. A new method of structural design, called advanced analysis, is trying to supply this gap between the analysis and design of structures. The thought of this method is to develop an analytical model that sufficiently represents the behaviors of structures in limit-states. The structure therefore is designed as a whole system, omitting the specification checks of component elements separated from the structural system.In the beam-column second-order inelastic structural analysis, there are four kinds of elements that describe the characteristic of loads and deformations. They are cubic element, four-termed beam-column element, pointwise equilibrating polynomial element and stability function. When we use one element to represent one member, in the case of axial force is large, the precision of cubic element and PEP element is low. When the axial force is change from compression to tension, the use of stability function is inconvenient for the different formulas of stiffness. In the other hand, the four-termed element can overcome the disadvantage of stability function, but the four-termed element is acquired by displace method, not by finite element method. So it is necessary to find a beam-column element with high precision and convenient in use. In this thesis, MEP element is proposed by the imposition of compatibility conditions at the end nodes as well as the principle of minimum potential energy. Moreover, it is shown that the accuracy is considerably high and MEP element caters for practical application. Second-order elastic analysis is already suggested in some advanced codes and specification. MEP element model described explicitly is formulated by using the principle of minimum potential energy, and the secant stiffness and tangent stiffness of MEP element are educed. Furthermore, MEP element can be applied not only for beam-column with invarying cross-section, but also for beam-column with varying cross-section. In chapter three, the secant stiffness and tangent stiffness of beam-column with varying cross-section are educed.Various national design codes impose different values of initial imperfection for member-strength determination. Today, effective methods have not been found to consider all kinds of imperfectionsbecause of the randomicity of the magnitude and distributing of imperfection. An imperfect MEP element model described explicitly is formulated by using the principle of minimum potential energy, for simulating directly the effects of imperfection on structures and stiffness. The structural sensitivity analysis to imperfection is performed and the numerical results are compared with the analytical solution.The plastic-zone analysis is the most accurate method for second-order inelastic structural analyses. It can trace the progress of the plasticity along member length and cross section and process initial imperfection directly. However, the plastic-zone method is very complicated and overloaded with details and not caters for practical application. The plastic-hinge method is a qualified method to the structural analysis, but the classical plastic-hinge method can not allow for initial imperfection and trace the progress of the plasticity along member length and cross section. Therefore, the assumption...