Advanced Analysis Method Study Of Space Steel Frames Based On Thin-walled Member Theory

The comprehensive structural analysis is the base for design of current buildings, so there are practical significance to establish a reasonable and reliable theoretical analysis model and process an accurate analysis. However, the effective length factor method is used to check the stability of individual member, it cannot accurately account for the interaction between structural system and its individual members, and it doesn't consider the inelastic redistribution of internal force and cannot predict the instability mode. Therefore, the advanced analysis method has become an important research trend at current stage. The advanced analysis is practically a kind of second-order elasto-plastic analysis method. It refers to any method that can capture the strength and stability of a structural system and its individual members in such a manner that individual member capacity checks are not required.To realize accurate structural analysis, based on traditional beam-column method and finite element method, a correct plastic hinge element stiffness equations of a 3-D beam-column for space steel frames are derived, nonlinear effects, such as second-order effect, material nonlinear, initial imperfections, shearing deformation, bowing effect dual-direction bending and torsion effect, warping deformation, and connection flexibility can be considered with the element formulation. A 3-D steel frame static analysis program is compiled using the object oriented program language C++, the general and accurate advanced analysis method for space steel frames is built up, the accuracy and effectiveness of the element are proved with some examples. The followings are the main contents in detail.Based on the theory of continuous medium mechanics, making use of updated Lagrangian formulation, in combination traditional beam-column method with finite element method, using virtual displacement principle and stability interpolation functions considering shearing deformation effect, second-order elastic stiffness equations of a 3-D beam-column for space steel frames are derived. In the analysis considering warping deformation, based on Kollbrunner-Hajdin modified constraint torsion theory, torsion-warping interpolation function was derived. And stiffness equations for the 3-D beam-column element are derived, nonlinear effects, such as initial imperfections, shearing deformation, warping deformation, dual-direction bending, torsion and axial deformation can be considered in element formulation.The finite space rotational properties and some update methods of beam-column element transformation matrix are discussed. And five types of moments generated by different mechanisms have been identified; all physical quantities and relations should be set up for the structure in the C₂ configuration in nonlinear analysis. The calculation methods of unbalanced force with natural deformation approach and external stiffness approach are introduced in detail, and the measures controlling iterative process in the incremental-iterative procedures are explained, the general stiffness parameters are used to get through snap-back points and trace the load-displacement curve of nonlinear structural analysis with appropriate controlling parameters.After introducing some plastic-zone models, inelastic stiffness matrix based on fiber element model is derived, the Von Mises yield criterion in conjunction with the Zeigler mixed hardening assumption which takes the Bauschinger effect, yield surface expansion into account and an association flow rule is incorporated into the material nonlinearity consideration, also the constitutive equations based on isotropic plastic accumulative damage are considered in the derivation. The refined plastic hinge model considering yielding surface equations, residual stress and spread of plasticity through cross section is presented. The current yielding surfaces of internal force in the second-order inelastic analysis are investigated and the Orbison yielding surface equation is modified. By introducing elasto-plastic hinge parameter of element cross section and influence factor of axial deformation, a correct plastic hinge model is put forward using plastic flow theory. The beam-column formulation not only traces the spread of yielding over the cross-section and along the whole element length, but accurately incorporates complicating effects such as residual stresses, initial imperfection.The behavior of the connection of steel beam-to-columns is nonlinear and the effect of connection flexibility on the structural behavior must be considered in the limit state analysis. After reviewing of the methods for researching the nonlinear capability of semi-rigid connections, the properties and the models considering connection flexibility with the correct plastic hinge beam-column element are introduced in detail. Moment-rotation relationship of semi-rigid beam-to-column minor axis connections was researched through experimental tests. A new type connection was proposed. The behabior of the connections was studied and contrasted with semi-rigid beam-to-column major axis connections. A tangent stiffness matrix of second order inelasticity analysis for multistory semi-rigid steel frames is derived. After reviewing of the panel zone models a new analysis model is proposed, the tangent stiffness matrixes of joint element and 3-D beam-column element in the integral coordinates are derived in a compact way. The dual-nonlinear incremental stiffness equation for steel frames with semi-rigid connections is established, which can also be used to consider the panel shear deformation.Finally based on the beam-column element stiffness equations of correct plastic hinge model, using the object oriented program language C++, a 3-D steel frame static analysis program is compiled. Inelastic strength limit state of space steel frames can be captured by proposed element. The static analytical results of proposed element are compared fairly well with those of typical calculation examples, test results and some representative steel frames' load-displacement curves, and only one proposed element for each member are needed to achieve acceptable accuracy. The proposed beam-column element has excellent efficiency since it does not do any numerical integration operation. A lot of computing time can therefore be saved in the analysis of large-scale structures by using proposed element, as compared to using numerically integrated element.