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 C_{2} 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. |
Abstract 5-7 Abstract 7-10 directory 10-15 1. Introduction 15-31 1.1 steel bearing capacity of the main factors 15-18 1.1.1 geometric nonlinear 15-16 1.1.2 material nonlinearity 16 1.1.3 initial defects 16-17 1.1.4 bending and torsion buckling 17 1.1.5 shear deformation 17 1.1.6 node semi-rigid 17-18 1.1.7 warpage 18 1.1.8 local buckling 18 1.2 subject background and the purpose and significance 18-21 1.2.1 the existing steel structure design method and its shortcomings 18-19 1.2.2 steel analysis and design of the development trend 19-20 1.2.3 of this research the purpose and significance 20-21 1.3 Advanced Analytical theory of characteristics and Research 21-28 1.3.1 advanced analysis features 21-24 1.3.2 Advanced Analytical Theory of Research 24-27 1.3.3 Advanced Analytical theory inadequate 27-28 1.4 of this article the main content and innovation 28-31 1.4.1 of this article the main research 28-29 1.4.2 In this paper, innovation 29-31 2. space beam-column element, the second-order elastic analysis, 31-63 2.1 basic assumption 31-32 2.2 based on the finite deformation theory of continuum space description 32-36 2.2.1 movement and deformation description 32-33 2.2.2 strain description 33-34 2.2.3 Stress description 34-36 2.3 space thin-walled beam-column element incremental principle of virtual displacement 36-45 2.3.1 Based on the updated Lagrangian configuration incremental virtual displacement principle 36-38 2.3.2 space thin-walled components of the strain-displacement description 38-42 2.3.3 space thin-walled beam-column element incremental virtual work equation 42-45 2.4 based on the interpolation function of the displacement field 45-50 2.4.1 consider the shear deformation of the lateral displacement and angle displacement function 46-49 2.4.2 consider the constrained torsion displacement interpolation function 49-50 2.5 space thin-walled beam-column element geometrically nonlinear stiffness equations 50-62 2.5.1 space thin-walled beam-column element geometrically nonlinear stiffness equations 50-55 2.5.2 space frame structure of the node equilibrium conditions 55-57 2.5.3 consider the stiffness matrix of the initial geometric imperfections 57-61 2.5.4 outside the moment effect 61-62 2.6 Summary 62-63 3. geometrically nonlinear analysis of a number of issues 63-91 3.1 unit coordinate transformation 63-76 3.1.1 three-dimensional rotation features 63-64 corner of the Euler formula 3.1.2 space large rotation 64-65 3.1.3 element coordinate transformation matrix 65-74 3.1.4 warping displacement pass 74-76 3.2 torque rotation features 76-79 3.3 Nonlinear equations 79-85 3.3.1 pure incremental method 80 3.3.2 incremental iterative method 80-81 3.3.3 Newton - Laffer Johnson method 81 3.3.4 Displacement Control Act 81 3.3.5 arc-length method 81-82 3.3.6 acting control law 82-83 3.3.7 generalized displacement control method 83-84 3.3.8 generalized displacement control method of the solution process 84-85 3.4 elastic structure of unbalanced force calculation 85-90 3.4.1 natural deformation 86-88 3.4.2 external stiffness method 88-90 3.5 Summary 90-91 4. space beam-column element of the second-order inelastic analysis 91-117 4.1 high steel frame analysis of the plastic zone model 92-98 4.1.1 plastic zone model based on the MP-Φ method 92-93 4.1.2 based on the finite element method, the plastic zone model 93-98 4.2 steel plastic zone analysis methods based on isotropic plastic damage 98-104 4.2.1 basic assumptions 98 strengthen the model of the structural steel Constitutive Equations 98-100 4.2.2 Zeigler mixed 4.2.3 isotropic damage evolution equation 100-101 4.2.4 consider the injury affect the three-dimensional thin-walled beam-column element nonlinear stiffness matrix 101-102 4.2.5 thin-walled beam-column element to consider the nonlinear stiffness matrix of injury 102-104 4.3 modified plastic hinge model of second-order inelastic analysis 104-116 4.3.1 basic assumptions 104 4.3.2 cross-section yield surface model of internal forces 104-107 4.3.3 residual stress caused by the stiffness degradation 107-108 the 4.3.4 beams The unit section elastoplastic parameters 108 4.3.5 plastic zone length and axial deformation influence coefficient 108-109 4.3.6-space beam-column element incremental stiffness equation of the second-order inelastic analysis 109-114 4.3.7 cross-section internal forces status beyond the handling of the yield surface 114 4.3.8 iteration convergence criteria 114-116 4.3.9 Structural Analysis of the failure criterion 116 4.4 Summary 116-117 5. beam - column semi-rigid node performance analysis and experimental study 117-141 5.1 semi-rigid connection characteristics and classification 117-123 5.1.1 nodes connected in the form 118-119 5.1.2 semi-rigid connection classification 119-122 5.1.3 semi-rigid connection features 122-123 5.2 semi-rigid connection mathematical model 123-127 5.2.1 linear model and linear model 124 5.2.2 polynomial model 124-125 5.2.3 B-spline model 125 5.2.4 Power function model 125-126 5.2.5 Exponential model 126-127 5.3 beam-column weak axis of semi-rigid connection test 127-139 5.3.1 trial design 127-128 5.3.2 steel timber and bolts of anti-slip test 128-130 5.3.3 test apparatus and measurement programs 130-131 5.3.4 loaded program 131 5.3.5 test phenomena and results 131-134 5.3.6 test results 134-139 5.3.7 test conclusions 139 5.4 Summary 139-141 node domain deformation nonlinear analysis of semi-rigid steel frame 141-159 6.1 consider the amendments connected semi-rigid plastic hinge unit 141-146 6.1.1 semi-rigid connection structure analysis method 141-143 6.1.2 beam-column element, semi-rigid connection stiffness matrix 143-146 6.2 node domain analysis model 146-152 6.2.1 Krawinkler model 147-148 6.2.2 Nakao model 148-149 6.2.3 Kato-Chen-Nakao model 149-151 6.2.4 Lui-Chen model 151-152 6.3 considering Shear Deformation element analysis 152-158 6.3.1 basic assumption 152-153 6.3.2 considering Shear Deformation node unit 153-154 6.3.3 consider Shear Deformation space beam element 154-156 6.3.4 considering Shear Deformation space column unit 156-157 6.3.5 consider Shear Deformation space second-order inelastic analysis 157-158 6.4 Summary 158-159 7 procedure and numerical example 159-175 7.1 object-oriented programming and design 160-162 7.1.1 object-oriented program analysis 160-162 7.1.2 object-oriented programming 162 7.2 numerical example 162-174 7.2.1 axial compression cantilever cylindrical 162-164 7.2.2 rectangular section beam lateral torsional buckling 164 7.2.3 Elbow framework 164-165 7.2.4 Williams double-rod system 165-166 7.2.5 hexagonal framework 166 7.2.6 hexagonal dome framework 166-167 7.2.7 dual shot at right angles to the plane cantilever framework 167 7.2.8 Vogel, six-story plane frame 167-169 7.2.9 eight-story space steel frame 169 7.2.10 single-layer single cross-frame 169-170 7.2.11 six-storey space steel frame 170-171 7.2.12 twenty layers of space steel frame 171 7.2.13 two layers of flat and semi-rigid framework 171-173 7.2.14 four-story space, semi-rigid frame 173-174 7.3 Summary 174-175 8 Conclusion 175-179 8.1 work and conclusions 175-177 8.2 Further research is needed 177-179 References 179-193 Appendix A. The tangent stiffness matrix 193-205 A.1 axial force pressure 193-201 A.2 axial force is tension when 201 A.3 axial force is very small 201-205 Appendix B. during the PhD thesis research in 205-207 thank 207 |