Zeng Yuan - Core

342 Pages·2009·5.17 MB·English

by  Zeng Yuan

Advanced Analysis of Steel Frame
Structures Subjected to Lateral
Torsional Buckling Effects

By

Zeng Yuan

A THESIS SUBITTED TO THE SCHOOL OF CIVIL ENGINEERING
QUEENSLAND UNIVERSITY OF TECHNOLOGY IN PARTIAL FULFILMENT
OF REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

August 2004

Keywords

Lateral torsional buckling, Steel I-section, Rigid frame, Advanced analysis, Nonlinear
analysis, Steel frame design, Ultimate Capacity, Structural Stability, load-deflection
response, and Finite element analysis

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Abstract

The current design procedure for steel frame structures is a two-step process including
an elastic analysis to determine design actions and a separate member capacity check.
This design procedure is unable to trace the full range of load-deflection response and
hence the failure modes of the frame structures can not be accurately predicted. In
recent years, the development of advanced analysis methods has aimed at solving this
problem by combining the analysis and design tasks into one step. Application of the
new advanced analysis methods permits a comprehensive assessment of the actual
failure modes and ultimate strengths of structural steel systems in practical design
situations. One of the advanced analysis methods, the refined plastic hinge method,
has shown great potential to become a practical design tool. However, at present, it is
only suitable for a special class of steel frame structures that is not subject to lateral
torsional buckling effects. The refined plastic hinge analysis can directly account for
three types of frame failures, gradual formation of plastic hinges, column buckling
and local buckling. However, this precludes most of the steel frame structures whose
behaviour is governed by lateral torsional buckling. Therefore, the aim of this
research is to develop a practical advanced analysis method suitable for general steel
frame structures including the effects of lateral-torsional buckling.

Lateral torsional buckling is a complex three dimensional instability phenomenon.
Unlike the in-plane buckling of beam-columns, a closed form analytical solution is
not available for lateral torsional buckling. The member capacity equations used in
design specifications are derived mainly from testing of simply supported beams.
Further, there has been very limited research into the behaviour and design of steel
frame structures subject to lateral torsional buckling failures. Therefore in order to
incorporate lateral torsional buckling effects into an advanced analysis method, a
detailed study must be carried out including inelastic beam buckling failures.

This thesis contains a detailed description of research on extending the scope of
advanced analysis by developing methods that include the effects of lateral torsional
buckling in a nonlinear analysis formulation. It has two components. Firstly,
distributed plasticity models were developed using the state-of-the-art finite element
analysis programs for a range of simply supported beams and rigid frame structures to
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investigate and fully understand their lateral torsional buckling behavioural
characteristics. Nonlinear analyses were conducted to study the load-deflection
response of these structures under lateral torsional buckling influences. It was found
that the behaviour of simply supported beams and members in rigid frame structures
is significantly different. In real frame structures, the connection details are a decisive
factor in terms of ultimate frame capacities. Accounting for the connection rigidities
in a simplified advanced analysis method is very difficult, but is most critical.
Generally, the finite element analysis results of simply supported beams agree very
well with the predictions of the current Australian steel structures design code
AS4100, but the capacities of rigid frame structures can be significantly higher
compared with Australian code predictions.

The second part of the thesis concerns the development of a two dimensional refined
plastic hinge analysis which is capable of considering lateral torsional buckling
effects. The formulation of the new method is based on the observations from the
distributed plasticity analyses of both simply supported beams and rigid frame
structures. The lateral torsional buckling effects are taken into account implicitly
using a flexural stiffness reduction factor in the stiffness matrix formulation based on
the member capacities specified by AS4100. Due to the lack of suitable alternatives,
concepts of moment modification and effective length factors are still used for
determining the member capacities. The effects of connection rigidities and restraints
from adjacent members are handled by using appropriate effective length factors in
the analysis. Compared with the benchmark solutions for simply supported beams, the
new refined plastic hinge analysis is very accurate. For rigid frame structures, the new
method is generally more conservative than the finite element models. The accuracy
of the new method relies on the user’s judgement of beam segment restraints. Overall,
the design capacities in the new method are superior to those in the current design
procedure, especially for frame structures with less slender members.

The new refined plastic hinge analysis is now able to capture four types of failure
modes, plastic hinge formation, column buckling, local buckling and lateral torsional
buckling. With the inclusion of lateral torsional buckling mode as proposed in this
thesis, advanced analysis is one step closer to being used for general design practice.
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Publications

Yuan Z. and Mahendran M., (2002), “Development of an Advanced Analysis Method
for Steel Frame Structures Subjected to Lateral Torsional Buckling”, Proceeding of
3rd European Conference on Steel Structures, pp. 369, Coimbra, Portugal.

Yuan Z. and Mahendran M., (2001), “Behaviour of Steel Frame Structures subject to
Lateral torsional Buckling effects”, Proceeding of 9th Nordic’s steel construction
conference, pp. 168, Helsinki, Finland.

Yuan Z., Greg, D., and Mahendran M., (2001), “Steel Design Tools using Internet
Technologies”, Proceedings of Australian Structural Engineering Conference, pp.445,
Gold Coast, Australia.

Yuan, Z., Mahendran, M. and Avery, P., M (1999), “Steel Frame Design using
Advance Analysis”, Proceeding of the 16th Australasian Conference on the
Mechanics of Structures and Materials, pp. 295, Sydney, Australia.

Yuan, Z., Mahendran, M., (1999), "Finite Element Modelling of Steel I-beam
subjected to Lateral Torsional Buckling Effects under Uniform Moment", Proceeding
of 13th Compumod User's conference, pp.12.1, Melbourne, Australia.

Papers to be submitted to the ASCE Journal of Structural Engineering are in
preparation, they include:

Yuan, Z. and Mahendran, M., “Modelling of Idealized Simply Supported Beams
using Shell Finite Element”.

Yuan, Z. and Mahendran, M., “Analytical Benchmark Solutions for Steel Frame
Structures Subjected to Lateral Torsional Buckling Effects”.

Yuan, Z. and Mahendran, M., “Refined Plastic Hinge Analysis of Steel Frame
Structures Subjected to Lateral Torsional Buckling Effects”.
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Table of Contents

KEYWORDS............................................................................................................................I
ABSTRACT.............................................................................................................................II
PUBLICATIONS...................................................................................................................IV
TABLE OF CONTENTS.......................................................................................................V
LIST OF FIGURES...........................................................................................................VIII
LIST OF TABLES..............................................................................................................XVI
STATEMENT OF ORIGINAL AUTHORSHIP...........................................................XVII
ACKNOWLEDGMENTS...............................................................................................XVIII
NOTATION.........................................................................................................................XIX
CHAPTER 1. INTRODUCTION.....................................................................................1
1.1 GENERAL.........................................................................................................................1
1.2 OBJECTIVES......................................................................................................................4
1.3 RESEARCH METHODOLOGY.............................................................................................5
1.4 ORGANISATION OF THE THESIS........................................................................................6
CHAPTER 2. LITERATURE REVIEW.........................................................................9
2.1 COMMON PLASTIC FRAME ANALYSIS PRACTICE............................................................9
2.1.1 Calculation of Plastic Collapse Loads...................................................................10
2.1.2 First Order Elastic Plastic Analysis.......................................................................11
2.1.3 Second Order Elastic Plastic Analysis...................................................................11
2.2 ADVANCED ANALYSIS OF STEEL FRAME STRUCTURES................................................12
2.2.1 Plastic Zone Analysis.............................................................................................13
2.2.2 Plastic Hinge Analysis...........................................................................................14
2.2.3 Semi-rigid Frames..................................................................................................26
2.3 LATERAL TORSIONAL BUCKLING..................................................................................29
2.3.1 Methods of Stability Analysis.................................................................................30
2.3.2 Beams Subjected to Uniform Bending Moment......................................................31
2.3.3 Transverse Loads...................................................................................................36
2.3.4 Moment Gradient...................................................................................................37
2.3.5 Effects of Restraints................................................................................................38
2.3.6 Inelastic Beams......................................................................................................43
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2.4 DESIGN OF MEMBERS SUBJECTED TO LATERAL TORSIONAL BUCKLING EFFECTS.......45
2.4.1 Australian Standard - AS4100................................................................................46
2.4.2 AISC (American) Design Specification – LRFD....................................................48
2.4.3 European Standard - EC 3 (ENV1993) Part 1.10..................................................51
2.4.4 Comparison of Design Specifications....................................................................54
2.5 SUMMARY......................................................................................................................55
CHAPTER 3. DISTRIBUTED PLASTICITY ANALYSES OF SIMPLY
SUPPORTED BEAMS..........................................................................................................59
3.1 MODEL DESCRIPTION.....................................................................................................61
3.1.1 Elements.................................................................................................................61
3.1.2 Material Properties................................................................................................63
3.1.3 Load and Boundary Conditions.............................................................................63
3.1.4 Initial Geometric Imperfections.............................................................................74
3.1.5 Residual Stresses....................................................................................................77
3.2 ANALYSIS METHODS.....................................................................................................80
3.3 RESULTS AND DISCUSSIONS..........................................................................................82
3.3.1 Simply supported beams subjected to a uniform bending moment and an axial
compression force...........................................................................................................84
3.3.2 Simply supported beams subjected to transverse loads.......................................101
3.4 SUMMARY....................................................................................................................115
CHAPTER 4. DISTRIBUTED PLASTICITY ANALYSES OF FRAME
STRUCTURES .................................................................................................................119
4.1 STEEL FRAME MODEL DESCRIPTION...........................................................................121
4.1.1 Elements...............................................................................................................124
4.1.2 Material model and properties.............................................................................124
4.1.3 Loads and boundary conditions...........................................................................125
4.1.4 Frame base support boundary conditions............................................................125
4.1.5 Beam-column connection.....................................................................................128
4.1.6 The use of symmetry boundary conditions...........................................................130
4.1.7 Loading conditions...............................................................................................131
4.1.8 Initial geometric imperfections............................................................................131
4.1.9 Residual stresses..................................................................................................132
4.2 USE OF PATRAN COMMAND LANGUAGE (PCL)...........................................................133
4.3 METHODS OF ANALYSIS..............................................................................................136
4.4 DISTRIBUTED PLASTICITY ANALYSIS RESULTS AND DISCUSSION..............................137
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4.4.1 Single bay single storey non-sway portal frames (Series 1 and 2).......................138
4.4.2 Single bay single storey sway portal frames (Series 3 and 4)..............................158
4.4.3 The G shape frame (Series 5)...............................................................................170
4.4.4 Portal frames with an overhang member (Series 6).............................................184
4.4.5 Two bay single storey frames (Series 7)...............................................................190
4.4.6 Single bay two storey frame (Series 8).................................................................196
4.4.7 Single bay gable frames (Series 9).......................................................................202
4.5 SUMMARY....................................................................................................................207
CHAPTER 5. DEVELOPMENT OF A NEW ADVANCED ANALYSIS METHOD
FOR FRAME STRUCTURES SUBJECTED TO LATERAL TORSIONAL
BUCKLING EFFECTS.......................................................................................................211
5.1 REFINED PLASTIC HINGE METHOD...............................................................................213
5.1.1 Frame element force-displacement relationship..................................................214
5.1.2 Tangent modulus..................................................................................................217
5.1.3 Second-order effects and flexural stiffness reduction factor................................218
5.2 CHARACTERISTICS OF OUT-OF-PLANE BUCKLING........................................................220
5.3 CONSIDERATION OF LATERAL TORSIONAL BUCKLING IN REFINED PLASTIC HINGE
ANALYSIS...........................................................................................................................227
5.3.1 Stiffness reductions due to out-of-plane buckling................................................229
5.3.2 Numerical implementation in refined plastic hinge analysis...............................247
5.4 VERIFICATION OF THE NEW ADVANCED ANALYSIS METHOD.......................................251
5.4.1 Simply supported beams.......................................................................................252
5.4.2 Frame structures with rigid connections..............................................................264
5.5 GRAPHICAL USER INTERFACE.....................................................................................295
5.6 SUMMARY....................................................................................................................301
CHAPTER 6. CONCLUSIONS....................................................................................303
6.1 CONCLUSIONS..............................................................................................................303
6.2 FUTURE RESEARCH......................................................................................................310
REFERENCES.....................................................................................................................311

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List of Figures

Figure 1.1 Lateral Torsional Buckling of steel beams and frames.............................................2
Figure 1.2 Experimental and Numerical Analyses of Steel Frame Structures undertaken at
QUT..................................................................................................................................5
Figure 2.1 Elastic and Plastic Analyses (From White and Chen, 1993)....................................9
Figure 2.2 Example of Using Equivalent Notional Load (From EC3)....................................16
Figure 2.3 Spread of Plasticity (From Chen, 1997).................................................................19
Figure 2.4 Rotation of beam-column with end moments.........................................................20
Figure 2.5 Stability functions...................................................................................................22
Figure 2.6 Tangent modulus calculation using column curve.................................................23
Figure 2.7 Bi-linear Interaction Equations (From AISC 1999)...............................................25
Figure 2.8 Beam to column connection...................................................................................27
Figure 2.9 Shear Stress Distributions due to Uniform and Non-uniform Torsions.................32
Figure 2.10 Lateral Torsional Buckling of a Beam subjected to Uniform Moment................33
Figure 2.11 Moment Components in a Cross Section..............................................................34
Figure 2.12 Lateral Torsional Buckling of a Beam subjected to Midspan Point Load............36
Figure 2.13 Case 1, Fixed End Beam (Plan View)..................................................................41
Figure 2.14 Case 2, Warping Prevented Beam (Plan View)....................................................41
Figure 2.15 Case 3, Warping Permitted Fixed Beam (Plan View)..........................................41
Figure 2.16 Plan View of a Beam with Intermediate Lateral Restraint...................................42
Figure 2.17 Experimental Moment Capacities of Beams in Near Uniform Bending (From
Trahair, 1993)..................................................................................................................45
Figure 2.18 Schematic Plot of Beam Curve in LRFD.............................................................49
Figure 2.19 Comparison of Beam Curves (uniform bending moment case)...........................54
Figure 2.20 Comparison of Beam Curves (midspan point load case)......................................55
Figure 3.1 Loading Configurations of Simply Supported Beams............................................64
Figure 3.2 Idealised Simple Support Boundary Conditions of the Models.............................65
Figure 3.3 First Trial of Simple Support Boundary Conditions...............................................66
Figure 3.4 Second Trial of Simple Support Boundary Conditions..........................................66
Figure 3.5 Third Trial of Simple Support Boundary and Load Conditions.............................67
Figure 3.6 Fourth Trial of Simple Support Boundary and Load Conditions...........................68
Figure 3.7 Fifth Trial of Simple Support Boundary Conditions..............................................69
Figure 3.8 Final Version of Idealised Simple Support Conditions..........................................71
Figure 3.9 Warping Restrained Simple Support Boundary Conditions...................................73
Figure 3.10 Ultimate Capacities versus Initial Imperfections for a 6 m Beam........................75
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