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Advanced Analysis Method Study of Space Steel Frames Based on Thin-walled Member Theory

Author: WangLianKun
Tutor: HaoJiPing
School: Xi'an University of Architecture and Technology
Course: Structural Engineering
Keywords: pace steel frame advanced analysis stability function thin-walled member shearing deformation correct plastic hinge model semi-rigid connection panel zone
CLC: TU391
Type: PhD thesis
Year: 2008
Downloads: 318
Quote: 6
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Executive Summary


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.

Full-text Catalog


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

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