Tan Eng Hooi – Behaviour and Strength Study on Steel Semi Rigid Connection Using Lusas

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BEHAVIOUR AND STRENTH STUDY ON STEEL SEMI RIGIDCONNECTION USING LUSAS

TAN ENG HOOI

UNIVERSITI TEKNOLOGI MALAYSIA



UNIVERSITI TEKNOLOGI MALAYSIA

PSZ 19:16 (Pind. 1/97)

BORANG PENGESAHAN STATUS TESIS

JUDUL : BEHAVIOUR AND STRENGTH STUDY ON STEEL SEMI RIGID

CONNECTION USING LUSAS

SESI PENGAJIAN : 2005/2006

Saya : TAN ENG HOOI

(HURUF BESAR)

mengaku membenarkan tesis ini disimpan di Perpustakaan Universiti Teknologi Malaysia dengan

syarat-syarat kegunaan seperti berikut :1. Hakmilik tesis adalah dibawah nama penulis melainkan penulisan sebagai projek bersama dan

dibiayai oleh UTM, hakmiliknya adalah kepunyaan UTM.2. Naskah salinan di dalam bentuk kertas atau mikro hanya boleh dibuat dengan kebenaran bertulis

daripada penulis.3. Perpustakaan Universiti Teknologi Malaysia dibenarkan membuat salinan untuk tujuan pengajian

mereka.4. Tesis hanya boleh diterbitkan dengan kebenaran penulis. Bayaran royalti adalah mengikut kadar

yang dipersetujui kelak.5.*Saya membenarkan/tidak membenarkan Perpustakaan membuat salinan tesis ini sebagai bahan

pertukaran di antara institusi pengajian tinggi.6. **Sila tandakan ( )

SULIT (Mengandungi maklumat yang berdarjah keselamatan ataukepentinganMalaysia seperti yang termaktub di dalam AKTA RAHSIARASMI 1972)

TERHAD (Mengandungi maklumat TERHAD yang telah ditentukan oleh organisasi/ badan di mana penyelidikan dijalankan)

TIDAK TERHAD

Disahkan oleh

____________________________________ _______________________________

(TANDATANGAN PENULIS) (TANDATANGAN PENYELIA)

Alamat Tetap : 403, LORONG KILANG 4, PM DR. SARIFFUDDIN SAADKAW PERUSAHAAN TUPAI, 34000 TAIPNG, PERAK.

Tarikh : 30 APRIL 2006 Tarikh : 30 APRIL 2006

CATATAN : * Potong yang tidak berkenaan.** Jika Tesis ini SULIT atau TERHAD, sila lampirkan surat daripada pihak

berkuasa/organisasi berkenaan dengan menyatakan sekali tempoh tesis ini perludikelaskan sebagai SULIT atau TERHAD.

NAMA



I hereby declare that I have read this report and in my opinion

this report is sufficient in terms of scope and quality

for the award of the degree of Bachelor of Civil Engineering.

Signature : ....................................................

Name of Supervisor : PM DR. SARIFFUDDIN SAAD

Date : 30 APRIL 2006



BEHAVIOUR AND STRENGTH STUDY ON STEEL SEMI RIGIDCONNECTION USING LUSAS

By

TAN ENG HOOI

A report submitted in partial fulfillment of the requirements for the

award of the degree of Bachelor of Civil Engineering

Faculty of Civil Engineering

Universiti Teknologi Malaysia

2006



KAJIAN KELAKUAN DAN KEKUATAN

SAMBUNGAN SEPARUH TEGAR KULULI

DENGAN MENGGUNAKAN LUSAS

OlehTAN ENG HOOI

Laporan ini dikemukakan sebagai memenuhi syarat

penganugerahan Ijazah Sarjana Muda Kejuruteraan Awam

Fakulti Kejuruteraan Awam

Universiti Teknologi Malaysia

2006



ii

I declare that this thesis entitled “Behaviour and Strength Study on Steel Semi Rigid

Connection Using LUSAS” is the result of my own research except as cited in the

references. The thesis has not been accepted for any degree and is not concurrently

submitted in candidature of any other degree.

Signature : ....................................................

Name : TAN ENG HOOI

Date : 30 APRIL 2006



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Specially dedicated to my family, friends and coursemates…….



iv

ACKNOWLEDGEMENTS

First of all, I would like to thank my supervisor, PM Dr. Sariffuddin Saad for

his advice and guidance in this research study. Thank you very much for your

support and kindness.

I would also like to thank my academic advisor, PM Ir. Dr. Ramli Nazir forhis kindness and always willing to help me throughout my study life in UTM.

Next, I would also like to acknowledge my coursemates. They are so kind

and always willing to share their experience and knowledge with me.

Last but not least, to my family and my beloved friends for supporting and

encouraging me throughout my study.



v

ABSTRACT

Extended end plate connections are widely used in structural steelworks

because of the ease in fabrication and erection. Although it is easy to use, the

extended end plate connection is complex to be understood and analysed in their

behaviour because it is affected by a lot of parameters of connection component.

Laboratory tests had been carried out to analyse the connection, however they are

expensive and time consuming. With the development of the fields of numerical

analysis and computer technology, modeling by finite element method using

software becomes the alternative to the expensive laboratory test. Three dimensional

model of extended end plate connections has been developed and non-linear analysis

was being carried out using LUSAS, an finite element software is presented in this

study. The result of analysis was then compared with existing experimental data to

determine the accuracy of the analysis prediction. Comparisons between the result

from LUSAS analysis and laboratory tests shows satisfactory agreement. However,

modeling techniques need to be improved in future research to obtain more accurate

results.



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ABSTRAK

Sambungan hujung plat memanjang semakin banyak digunakan dalam

struktur keluli disebabkan kesenangan dalam pemasangan dan pembinaan.

Walaupun sambungan ini senang digunakan, pemahaman terhadap kelakuannya

adalah amat kompleks disebabkan terdapat banyak parameter komponen sambungan

yang akan mempengaruhi sifatnya. Di mana yang lalu, ujian makmal telah

dijalankan untuk menganalisis sambungun ini, tetapi ia memerlukan kos yang tinggi

dan masa yang lama. Dengan adanya pembangunan dalam bidang analisis dan

teknologi komputer, kerja-kerja permodelan dengan kaedah unsur terhingga

menggunakan program komputer telah menjadi satu alternatif kepada ujian makmal

yang mahal. Model tiga dimensi bagi sambungan plat hujung memanjang telah

dibina dan analisis tidak lelurus telah dijalankan menggunakan LUSAS. Keputusan

daripada LUSAS akan dibanding dengan data ujikaji makmal sedia ada untukmengetahui kejituan analisis. Perbandingan antara keputusan analisis LUSAS dan

ujikaji makmal menunjukkan persamaan yang memuaskan. Walau bagaimanapun,

teknik-teknik permodelan perlu dimajukan dalam penyelidikan masa depan supaya

keputusan yang lebih jitu dapat diperoleh.



vii

TABLE OF CONTENTS

CHAPTER TITLE PAGE

DECLARATION iiDEDICATION iii

ACKNOWLEDGEMENTS i vABSTRACT vABSTRAK viTABLE OF CONTENTS viiLIST OF TABLES xLIST OF FIGURES xiLIST OF SYMBOLS xiii LIST OF APPENDICES xiv

1 INTRODUCTION

1.1 Introduction 11.2 Problem Statement 2

1.3 Research Objective 2

1.4 Research Scope 3

1.5 Hypothesis 3

2 LITERATURE REVIEW

2.1 Finite Element 42.1.1 Introduction of Finite Element 4

2.1.2 History of Finite Element 4

2.1.3 Steps of the Finite Element Method 5

2.1.4 Nonlinear Finite Element Analysis 6

2.1.4.1 Geometry Nonlinearity 7

2.1.4.2 Boundary Nonlinearity 8

2.1.4.3 Materially Nonlinearity 8



viii

2.1.5 Advantages & Limitations of Finite

Element 9

2.2 LUSAS 10

2.2.1 Introduction of LUSAS 10

2.2.2 Data Processing 11

2.2.3 LUSAS Analysis Types 12

2.2.3.1 Linear Analysis 12

2.2.3.2 Non-linear Analysis 12

2.2.4 Element Library 13

2.2.5 Materials Library 16

2.2.6 Solution Procedure Library 17

2.2.7 Post-processing 17

2.2.8 Advantages of LUSAS 18

2.3 Connection 19

2.3.1 Types of Connection 19

2.3.2 Benefit of Semi Rigid Connection 20

2.3.3 M- φCurve 20

2.3.4 End Plate Connection 22

2.3.5 M- φCurve for End Plate Connection 24

2.4 Research Paper Study 26

2.4.1 “Finite Element Analysis of Structural

Steelwork Beam to Column Bolted

Connections” 25

2.4.2 “Finite Element Analysis of Unstiffened

Flush End-Plate Bolted Joints” 26

2.4.3 “Experimental Behavior of End-Plate

Beam to Column Joints Under Bending

and Axial Force” 28

2.4.4 “Pemodelan Sambungan Paksi Minor

Dengan Menggunakan Perisian Lusas” 28

2.4.5 “Performance of Extended End-Plate

Connection Connected to Column Flange” 29

2.5 Conclusion of Research Paper Study 30



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3 METHODOLOGY

3.1 General 31

3.2 Experimental Test 31

3.3 Experimental Procedure 32

3.4 Basic Concept in Using LUSAS 33

3.5 Finite Element Model 34

3.5.1 Generate Structure Model Component 34

3.5.2 Element Types 36

3.5.3 Material Properties 39

3.5.4 Boundary Condition 40

3.5.5 Loading 41

4 RESULT AND DISCUSSION

4.1 Prediction of Result 42

4.2 Experimental Result 43

4.2.1 Specimen EEP 1 43



4.3 Non Linear Analysis Results 48

4.3.1 Moment Rotation Curve 48

4.4 Comparison of Results between LUSAS and

Experiment 63

4.4.1 Comparison of Moment Rotation Curve 63

4.4.2 Comparison of Mode of Failure 65

5 CONCLUSION AND RECOMMENDATION 5.1 Conclusion 68

5.2 Recommendations 69

REFERENCES 71

APPENDICES 73-88



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LIST OF TABLES

TABLE NO. TITLE PAGE

2.1 Element groups in LUSAS 16

3.1 Test specimens with various parameters 32

3.2 Material properties of model 39

4.1 Experimental results of resistance moment and

mode of failure 43

4.2 Moments and rotations calculation for EEP1

(simplified bolt model) 51






(actual bolt model) 57





4.8 Comparison of resistance moment 63





xii

3.9 (i) HX8M (ii) QTS4 (iii) JNT4 (iv) BRS2 38

3.10 Model after meshing 38

3.11 Meshed bolt (simplified model) 38

3.12 Meshed bolt (actual model) 38

3.13 Contact spring stiffness, k c 40

3.14 Boundary condition 41

4.1 Predicted failure mode 42

4.2 Experimental moment rotation graph of EEP1 45



4.5 Position of node A where displacement is taken 49

4.6 Actual calculation of rotation 49

4.7 Approximate calculation of rotation 50

4.8 Moment vs rotation graph for EEP1












4.14 Full model of connection 644.15 Half model of connection 64

4.16 Mode of failure of connection 66

4.17 Mode of failure at bolt 66





xiv

LIST OF APPENDICES

APPENDIX. TITLE PAGE

A/1 Manual 73



CHAPTER 1

INTRODUCTION

1.1 Introduction

Steel structures typically consist of many components. The basic components

of a steel structure are tension members, compression members, bending members,

combined force members and connections. The connections provide contact regions

between the first four structural members, so that these members can work together

as a unit.

Connections of steel structural members are important. Inadequate

connection will cause failure of structures due to “weak link”. Most of steel

structures fail because of poor design and inadequate detailing of connection; failure

due to main structural members is rare.

In the past, expensive laboratory work and testing need to be done to

understand the behaviour of connections in steel structures. Many of researchersdepend mainly on the result from the experiments to derive equations for prediction

and design. Understanding the behaviour of connection is important, so that the

designer will have a clearer view on the topics such as the stability of columns and

frames and also the minimum cost of members and connections. Because of the

development in the fields of numerical analysis and computer technology, modeling

by finite element method using computer software become the alternative to the

expensive laboratory test.



2

The experimental method is costly because there are a lot of parameters

involved in analyzing the behaviour of connections. Different types of test need to

be carried out in order to develop empirical formulae for designing a specific

connection. So, the finite element modeling becomes a more economically method

to analyse the parameters. However, this does not mean the finite element modeling

will replace the laboratory test at all. The experimental test is needed to validate the

result of numerical analysis.

1.2 Problem Statement

Connection of steel beam to steel column using end plate is a common

application in construction nowadays. Conservative method is always being used in

designing this connection. Over design of connection may happened and this will

cause waste of material and increase of cost. Detail design for connection will take

much time which is not practical in construction industry. In case of that, design

using finite element software is preferable. However, it is important to check the

accuracy of the result from software analysis. Thus, proper research should becarried out in terms to determine the accuracy of the software result.

1.3 Research Objective

The objective of this research is to:-

(a) Determine the moment-rotation curve characteristic of the extended end plate

steel beam to column connection obtained from LUSAS analysis.

(b) Determine the accuracy of the analysis result from LUSAS [1] by comparing

them with the result obtain from full scale laboratory test.



3

1.4 Research Scope

The connection of steel beam to column will be modeled using finite element

software, LUSAS. The research is focused on the extended end plate connection.

The dimensions of the connection will be the same as the dimension used in the full

scale laboratory test. The analysis results were compared with the results obtained

from laboratory test.

1.5 Hypothesis

The results from the analysis of the connection model will show a smooth

moment rotation curve. This moment rotation curve will have the values close to the

result obtained from full scale laboratory test.



CHAPTER 2

LITERATURE REVIEW

2.1 Finite Element

2.1.1 Introduction of Finite Element

Finite element method is a numerical method to find out an approximate

solution for variables in a problem which is difficult to obtain analytically. The

calculation of potential design changes such as temperature, fluid velocities and

displacement are usually complicated. A numerical method that is able to solve

these engineering problems is the finite element method.

The concept of the finite element method is solving a continuum by a discrete

model. It is done by dividing the problem into small several elements. Each element

is in simple geometry and this is easier to be analyzed than the actual problem. Each

element is then applied with known physical laws. The equation which is formed by

each element is then combined to form a global equation. The global equation can

be used to solve the field variables such as displacement, temperature and so on.

2.1.2 History of Finite Element

In the ancient time, the mathematicians estimated the value of π by assuming

that the circle is a polygon of a finitely large number of sides. By this assumption,they can predict the accuracy of the value of π up to 40 digits. The framework



5

method was introduced by Hrenikoff in 1941 [2]. He assumed that the plan elastic

medium as a set of bars and beams. In 1943, R.Courant introduces the piecewise-

continuous functions [2]. He used a set of triangular elements to study the St Venant

torsion problem. He had been using the Ritz method of numerical analysis and

minimization of variational calculus to obtain approximate solutions to vibration

systems. The formal introduction of finite element was published in paper by

Argyris and Kelsey [3] and Turner, Clough, Martin, and Topp [3]. Clough became

the first person to use the term “finite element” in 1960 [3]. Since then, the finite

element application has been developed greatly.

In the early 70’s, the aeronautics, automotive, defense and nuclear industrieshad started using the finite element application. However, this is limited to

expensive mainframe computer. Zeinkiewicz & Cheung [2] are the important person

in developing the finite element technology at that period. Later, Hinton & Crisfield

[2] carried out the finite element into modeling and solution of nonlinear problems.

With the development of the CAE technology, engineering drawing can be

produced. Besides that, the analysis can be carried out and also the finite elementmodeling can be done. Nowadays, the finite element has become more and more

important. It is a vital tool that is used to solve various type of engineering

problems.

2.1.3 Steps of the Finite Element Method

There are seven steps involved in solving an engineering problem using the

finite element method:-

Step 1

Formulation of the governing equations and boundary conditions. This is to obtain

the suitable finite element solution algorithm.



6

Step 2

Divide the analysis region into suitable shape of elements. For example, rod element

is chosen for 1D problem, triangular and rectangular for 2D problem, tetrahedron and

rectangular prism for 3D problem.

Step 3

Select the appropriate interpolation functions. Normally a polynomial is chosen as

the interpolation function because it is easy to differentiate and integrate.

Step 4

Determine the element properties such as number of node point, degree of

interpolation function and other variables.

Step 5

Assemble all element properties to form a set of algebraic global equation.

Step 6

Solve the global equation. It is much easier to solve linear global equations than

nonlinear global equation. The Gauss elimination method can be used.

Step 7

Verify the accuracy of the solution. This can be known by increasing the number of

elements nodes and then check whether the solution converges to a certain value.

2.1.4 Nonlinear Finite Element Analysis

In a linear finite element analysis, all materials are assumed to have linear

elastic behaviour and deformations are small enough not to significantly affect the

overall behaviour of the structure. However, this analysis is limited to very few

situations in the real world, but with a few restrictions and assumptions, linear

analysis will be sufficient for the majority of engineering applications. However,



7

nonlinear finite element analysis is required in situations such as gross changes in

structural geometry, permanent deformations, structural cracks, buckling, stresses

greater than the yield stress and contact between component parts. The nonlinear

analysis generally can be divided into three types: geometry nonlinearity, boundary

nonlinearity and material nonlinearity.

2.1.4.1 Geometry Nonlinearity

Geometric nonlinearity occurs when there is significant change in the

structural configuration during loading. Common examples of geometricnonlinearity are plate structures which develop membrane behaviour, or the

geometric split of truss or shell structures. Figure 2.1 shows two simple structures

which have geometrically nonlinear behaviour. In Figure 2.1(i), the linear solution

would predict the simply supported bending moment and assumes zero axial force in

the simply supported beam. But, in reality as the beam deforms its length increases

and an axial force will be occurred. For the loaded strut in Figure 2.1(ii), the linear

analysis would fail to consider the progressive eccentricity of the vertical load on the bending moment diagram. These examples show the importance of nonlinear

geometry in structural analysis.

(i) (ii)

Figure 2.1 Examples of geometry nonlinearity behaviour [1]



8

2.1.4.2 Boundary Nonlinearity

In boundary nonlinearity, the modifications to the external restraints resulting

from deformation process such as lift-off, or smooth or frictional contact are taken

into account within an analysis. Figure 2.2 shows the structure and its supporting

surface which can resist being pushed together, but not being pulled apart. The

required contact condition may be imposed to connect between the structure and the

rigid support, and specifying a incorporating large, and zero local stiffness in

compression and tension respectively.

Figure 2.2 Example of nonlinear boundary condition [1]

2.1.4.3 Materially Nonlinearity

Materially nonlinear effects occur from a nonlinear constitutive model which

has disproportionate stresses and strains. Common examples of nonlinear material

behaviour are the plastic yielding of metals, the ductile fracture of granular

composites such as concrete or time-dependent behaviour such as creep.



9

2.1.5 Advantages & Limitations of Finite Element

The advantages of finite element method are:-

(a) It can be used to solve any engineering problem where the governing differential

equation can be written.

(b) It has proven successful in representing various types of complicated material

properties that are difficult to incorporate into other numerical methods. For

example, formulations in solid mechanics have been devised for anisotropic,

nonlinear, hysteretic, time-dependent, or temperature-dependent material behaviour.

(c) It accounts for non-homogeneity by assigning different properties to different

elements. It is even possible to vary the properties within an element according to a

pre-selected polynomial pattern.

(d) Flexible general-purpose computer programme can be constructed based on the

systematic generality of the finite element method. ASKA, STRUDL, SAP,

NASTRAN, and SAFE are the structural analysis packages which include a variety

of element configurations and can be applied to several categories of structural

problems, even in different field with little or no modification.

(e) An engineer may develop a concept of the finite element method at different

levels. The method can be interpreted in physical terms and also in mathematical

terms.

The limitations of the finite element method are:-

(a) It is a complex method. The differential equation may be difficult even for a

simple physical system.





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management system controls the communication of all LUSAS processors through a

common database.

2.2.2 Data Processing

The data input for LUSAS has been designed to be compact, easy to

understand and in a free-format data to reduce the error of input system. Besides that,

the free-format input allows the system to be driven by engineering command words

in the data stream. Figure 2.3 shows the data processing stages in LUSAS.

Figure 2.3 Data processing stages [4]

Error data can be found by the error analyst during each of the process. If

there is an error, error message will be showed up and the error node or element will

be pointed out. If there is a fatal data error, a restart point further along the data

stream will be located, and data processing is continued to check for further error.

PROBLEM

RESTART READ

ELEMENT TOPOLOGY

SOLUTION ORDER AUTOMATIC

NODE COORDINATES

GEOMETRIC PROPERTIES

MATERIAL PROPERTIES

CARTESEAN SETS

TRANSFORMED FREEDOMS CONSTRAINT E UATIONS

SUPPORT NODES

LOAD CASES

ELEMENT OUTPUT CONTROL

NONLINEAR CONTROL

PLOT FILE

RESTART WRITE

END



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2.2.3 LUSAS Analysis Types

2.2.3.1 Linear Analysis

In linear analysis, it is assumed that the overall structural response is linear,

and implies linearity of both the geometric and material response. This type of

analysis is only suitable for simple structure, for example, the structure without tall

frame and no large rotation.

2.2.3.2 Non-linear Analysis

Non-linear stress analysis is becoming increasingly important with designers

employing a wider variety of materials in different applications. This type of

analysis is useful in analysing the problem of tall and complex structure to ensure

that the additional of structure self weight do not cause a bad effect to the whole

structure.

Material non-linearity is used to analyse the structure which is subjected to

the conditions of elasto-plastic, ductile fracture, cracking, damage and creep

applications. In LUSAS, there are nonlinear material models for metals, plastics,

composites, rubber, foam, soils, rock and concrete. These material models may

account for temperature dependent effects if required. Both isotropic and anisotropic

nonlinear material models are available and material response may be dependent on

the history and direction of straining. The direction of anisotropy is fully userdefinable. To ensure a fast and efficient solution, the von Mises and Hill material

models use a consistent formulation in the evaluation of the stiffness matrix which

provides quadratic convergence characteristics. The speed of stress computation has

been optimised by using the latest backward Euler technique. In addition, material,

damage and creep model interfaces are provided, so user-defined material definitions

may be added as required.



13

Geometric nonlinearity needs to be accounted when the structure deforms

from the original geometry and position and direction of the loads significantly affect

the structural behaviour. Many LUSAS elements can accommodate large

deformations and large rotations and the latest co-rotational formulation ensures that

large strains can be accommodated when necessary.

2.2.4 Element Library

The main function of element library included in LUSAS is to help to reduce

user’s time in analysing process. The element library enables coarse meshes to beused in modeling and this will save the user’s time in data preparation and also

interpretation of result. Even with the coarse meshes, LUSAS can provide a good

result.

All elements in LUSAS are included with a shape function. This will reduce

the coding effort and also lead to high performance elements. Besides that, all

elements in LUSAS have to pass several tests before being accepted. These tests

include the patch test for convergence, the patch test for mechanisms, convergence

rate tests and comparisons of results with extensive experimental and theoretical

results.

The LUSAS Element Library contains more than 100 element types. The

elements are classified into groups according to their function. The groups are:

- Bars

- Beams

- 2D Continuum elements

- 3D Continuum elements

- Plates

- Shells

- Membranes

- Joints



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- Field elements

- Interface elements

Followings are some brief explanation of the element groups:

(a) Bar Elements

Bar elements are used to model plane and space truss structures, and

stiffening reinforcement. There is 2D and 3D bar elements in LUSAS which can

either be straight or curved. Bar elements model axial force only.

(b) Beam Elements

Beam elements are used to model plane and space frame structures. LUSAS

beam elements may be either straight or curved. Beam element can model axial

force, bending and torsion behaviour.

(c) 2D Continuum Elements

2D continuum elements are used to model solid structures that can be

assumed to be 2-dimensional. 2D continuum elements may be applied to plane

stress, plane strain and axis-symmetric solid problems.

(d) 3D Continuum Elements

3D continuum elements are used to model fully 3-dimensional structures.

(e) Plate ElementsPlate elements are used to model flat structures which deformation can be

assumed as flexural. Both thin and thick plate elements are included in LUSAS.

Triangular, quadrilateral and ribbed flexural plate elements are also available.



15

(f) Shell Elements

Shell elements are used to model 3-dimensional structures which behaviour is

depend on both flexural and membrane effects. Both flat and curved shell elements,

either triangular or quadrilateral, thin or thick elements are available in LUSAS.

(g) Membrane Elements

Membrane elements are used to model 2 and 3-dimensional structures which

behaviour is depend on in-plane membrane effects. LUSAS includes both axis-

symmetric and space (3-dimensional) membrane elements.

(h) Joint ElementsJoint elements are used to model joints between LUSAS elements. Joint

elements may also be used to model point masses, elastic-plastic hinges, or smooth

and frictional element contacts.

(i) Field Elements

Field elements are used to model quasi-harmonic equation problems such as

thermal conduction or potential distribution. LUSAS includes bar, plane, axis-

symmetric solid and 3-dimensional solid field elements.

(j) Interface Elements

These elements should be used at places of potential delamination between

2D continuum elements for modeling delamination and crack propagation.

Table 2.1 shows the element groups available in LUSAS.



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Table 2.1 Element groups in LUSAS [1]

2.2.5 Materials Library

The types of material included in LUSAS are:-

(a) Isotropic

(b) Orthotropic for plates/ shells/ continuum

(c) Anisotropic(d) Nonlinear friction/gap



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(e) Isotropic elastic-plastic hardening, with exact positioning on the yield surface

using automatic sub-increment size selection

(f) Concrete with cracking control

(g) Mohr-Coulumn for geomechanics problems

(h) User supplied material, dependant on history, stresses, strains, temperature,

time etc.

2.2.6 Solution Procedure Library

LUSAS is using the Frontal method as the main solution. The Frontalmethod is used mainly on the solution of the load deflection equations. This method

has been proven to be the most suitable for nowadays computer.

Others solution procedures that are available in LUSAS are:-

(a) Incremental loading

(b) Newton Raphson iterations

(c) Modified Newton Raphson iterations

(d) Conjugate Newton line research

(e) Total Lagrangian geometric nonlinearities

(f) Updated Lagrangian geometric nonlinearities

(g) Implicit finite difference time integration (Newmark-Beta)

(h) Transient field/heat (Crank-Nicholson)

(i) General linear and nonlinear constraint equations

(j) User supplied solution procedures

2.2.7 Post-processing

The data output and the post processing of LUSAS can be summarized as:-

(a) element results such as stresses and strain

(b) displacements, velocities, acceleration



18

(c) residual force at nodes

(d) Lagrange Multipliers

(e) Reactions

(f) User supplied interface

(g) Graphics output

2.2.8 Advantages of LUSAS

(a) With the element library of LUSAS, all types of engineering materials such as

metal, plastics, foams and rubber can be modeled to solve engineering problem.

(b) The graphical user interface (GUI) makes the modeling and the result processing

become easier.

(c) Rapid design changes can be made to the LUSAS model, automatic meshing is

available for certain types of problem, other than that, problem can be solved to a

user specified accuracy by LUSAS. User will get a better result in less time.

(d) LUSAS can be upgraded to the LUSAS plus easily where the LUSAS plus will

include an extended element set, additional material models, Fast Iterative Solver

Technology and access to advanced analysis capabilities.

(e) Model information can be exchanged with other CAD systems using the formatsuch as dxf.

(f) LUSAS includes comprehensive nonlinear analysis, impact and contact analysis,

thermal analysis, dynamic analysis and also fatigue analysis.



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2.3 Connection

2.3.1 Types of Connection

Refer to LRFD-A2.2 and ASD-A2.2 (Allowable Stress Design) [5], the

connections are categorized depending on their resistant to the rotation caused by the

applied load. With this criterion, the connections are divided into three main groups:

fully restraint, partial restraint and simple connection.

(a) Fully Restraint Connection

The example for this fully restraint connection is the rigid connection. Thereshould be no rotation at all at the joint theoretically when the load is applied. This

situation occurs when full continuity connection is being used between the

intersection members. The angle between the members is maintained when load is

applied. In design, any influence on the moment distribution and the structure

deformation may be neglected.

(b) Partial restraint ConnectionThe semi rigid connection is the example of the partial restraint connection.

The moment resistant of semi rigid connection is located between rigid connection

and simple connection. This means that the moment resistant of semi rigid

connection is neither zero as simple connection nor full continuity as the rigid

connection. These connections are designed to provide a predictable degree of

interaction between members based on the M- φcharacteristic of the joint.

(c) Simple Connection

It is assumed that the simple connection resists shear and normal force only.

No moment resistant at all for the simple connection and it is free to rotate when load

is applied. In some countries, the structures are design with simply supported basis

and then to provide connections which give semi rigid effect. This may be unsafe

due to insufficient of rotation capacity of connection.









23

connection strength. When the length of the plate is the same as the length between

the flanges of the beam, the plate is called flush end plate. The other type of end

plate is the header plate. Figure 2.7 shows the different types of end plate connection.

Extended end plate Flush end plate Header plate

Figure 2.7 Types of end plate connection [6]

Header plate connection is categorized as flexible connection while the

extended end plate connection and the flush end plate connection are categorized as

semi rigid connection. Since they are semi rigid, the extended end plate connection

and the flush end plate connection are subjected to axial force, shear force and

bending moment when the load is applied to the member as shown in Figure 2.8.

Figure 2.8 Forces in end plate connection [7]

A lot of parameter such as column flange and web thickness, end plate

thickness, beam depth, bolt size and grade affects the behaviour of the end plate

connection. So, these parameters should be taken into account when analysing the

end plate connection. This makes the analysing process becomes more complicated.

In recent years, Jenkins, Jenkins et al., Bose et al., Bahaari and Sherbourne, and



24

Sherbourne and Bahaari [2] have use the finite element method to analyse end plate

connection. Finite element method has been proven to be the suitable method in

analysing this type of connection.

2.3.5 M- Curve for End Plate Connection

Figure 2.9 M-φcurve for different end plate connection [5]

Figure 2.9 shows the comparison of M- φcurve between the three types of end

plate connection: extended end plate, flush end plate and header plate. The typical

M-φcurve is almost linear at the beginning and then yielding occurs before the strain

hardening process happened. This is because the initial elastic stiffness is affected

by the reduction of bolt preloading and the value of elastic stiffness after the

pretension of bolt has gone. The extended end plate will have greater initial stiffness

and moment capacity and can carried larger rotation. The rotational stiffness will beincreased with the increase of the thickness of plate and also by placing the bolts as

close as possible to the beam flange.

Extended end plate

Flush end plate

Header plate

M (kNm)

φ (rad)



25

2.4 Research paper study

2.4.1 “Finite Element Analysis of Structural Steelwork Beam to Column BoltedConnections” [7]

In this research work, the main objective was to compare the beam to column

bolted extended end plate connections analysis result between the finite element

analyse (FEA), the full scale test and the Green Book. The Green Book is a design

guide for moment resisting connection that is jointly published by the Steel

Construction Institute (SCI) and the British Constructional Steelwork Association

(BCSA) in 1995.

LUSAS FEA software was used for the finite element analysis. At the

beginning of the research a number of trial models were created. The final FEA

models use the five elements as shown in Figure 2.10. A series of five full scale tests

were completed using the self straining frame in the Heavy Structures Laboratory at

the University of Teesside. Figure 2.11 shows the typical model of the beam to

column connection. Figure 2.12 shows the LUSAS extended end plate model and

bolt enlarge FEA bolt arrangement.

Figure 2.10 Element used in LUSAS modeling

Figure 2.11 LUSAS connection modeling



26

Figure 2.12 LUSAS extended end plate and bolt enlarge FEA bolt arrangement

In both the FEA and the laboratory tests, it was consistently found that the

Green Book design theory underestimated the bolt forces in the top rows of the

connection and overestimated the forces in the lower rows. In spite of this the Green

Book theory with the increased connection capacities still had a reserve of

approximately 30%. Overall the finite element analysis of extended end plate

connections using LUSAS can be seen to provide advantages in terms of time and

expense over full scale testing and can produce a more complete picture of stress,

strain and force distributions.

2.4.2 “Finite Element Analysis of Unstiffened Flush End-Plate Bolted Joints” [8]

This paper reports part of the results of an investigation on the analysis of

unstiffened flush end plate steel bolted joint using finite element method. A

sophisticated three dimensional model of the joint was developed using LUSAS.

Several full scale test of flush end plate joint were also been carried out. The resultfrom LUSAS was compared with that from full scale and the accuracy of the LUSAS

analysis was determined.

Due to the symmetry of the joint configuration and the load transmitted about

both x- and z- axes, so only a quarter of the joint was modeled. The flush end plate

joint has been model as Figure 2.13 and Figure 2.14.



27

Figure 2.13 LUSAS modeling

Figure 2.14 Generation of bolt hole and bar element

Six full scale tests with different beam sizes, connection details, bolt sizes

and column sizes were carried out. These joint were based on the details from the

standard range relating to flush end plates.

From the comparison, it was found that there was a good agreement between

experimental and LUSAS analysis results. However, there was some discrepancy in

the elastic range and in the final elastic plastic range of the curve. The experimental

curve which not linear in the elastic range due the combination of bolt tightening

effect, imperfection in the test setup, and lack of fit. In the final elastic plastic stage,

the connection failure was due to postyield column web buckling but LUSAS is

incapable of handling postyield buckling.



28

2.4.3 “Experimental Behavior of End-Plate Beam to Column Joints Under

Bending and Axial Force” [9]

The objective of the paper was to present the results of an experimental

research project on end-plate beam-to-column bolted steel joints subjected to

bending and axial force which was carried out at the University of Coimbra. 15 tests

were conducted involving the flush end plate and extended end plate joints.

A series of eight experimental tests have been carried out on beam-to-column

steel connections with flush endplates. Besides that, a series of seven tests have also

been performed on extended endplate joints.

In all tests, the columns were simply-supported at both ends and consist of a

HEB240, the beams consist of an IPE240 and the endplate was 15 mm thick, all

manufactured from S275 steel. The bolts were M20, class 10.9.

The moment-rotation curves from the results of the 15 tests showed the

typical relationship between moment and rotation. The curves were almost linear at

the beginning and then the yielding occurs before the strain hardening process

happened. This is because the initial elastic stiffness is affected by the reduction of

bolt preloading and the value of elastic stiffness after the pretension of bolt had gone.

2.4.4 “Pemodelan Sambungan Paksi Minor Dengan Menggunakan PerisianLusas” [10]

The main objective of this thesis was to determine the accuracy of the

analysis result from LUSAS of the bolted steel beam-column flush end plate

connection at the minor axis by comparing with the experimental result.





30

experimental moment and stiffness showed good agreement with predicted values

calculated based on Eurocode 3 and BS 5950.

2.5 Conclusion of Literature Review

It can be concluded that many successful analyse of semi rigid connection

had been performed by previous researchers using finite element software, LUSAS.

However, some of the research works, for example, the analysis on connection of

universal beam to the web of universal column that was carried out by Tan Chin

Thiam [10] still can be improved by using nonlinear analysis instead of linearanalysis in order to obtain more accurate result. And for the analysis on connection

of universal beam to the flange of universal column that have been done by Jim

Butterworth [7], the results of analysis can be improved by using actual model of bolt

instead of simplified bolt model. To avoid repetition on previous researchers’ works

in the present study, it was decided to focus on the semi rigid connection of universal

beam to the flange of universal column using extended end plate using improved

LUSAS analysis method.



CHAPTER 3

METHODOLOGY

3.1 General

Finite element method is used in this research. LUSAS is chosen as the finite

element software to be used to analyse and determine the characteristic of M- φ curve

of steel beam column end plate connection. To meet the research objective which is

to find out the reliability of the LUSAS results, full scale experiment results that have

been obtained in a previous research are used as the reference, and compared with

the LUSAS analysis results.

To increase the accuracy of research, the LUSAS modeling process used the

connection dimensions as similar as possible to that of the full scale experiment

model. In this case, all the geometry and materials properties of experiment model

are applied into the LUSAS model. However, to obtain better and accurate results,

many models need to be generated before the most suitable element discretisation

can be found.

3.2 Experimental Test [11]

A total of nine experiments were carried out by Assoc. Prof. Dr. Mahmood

Md. Tahir, Assoc. Prof. Dr. Shahrin Mohamed, M.A.Hussin and A.A.Saim [11] at

University Teknologi Malaysia laboratory. These experiments focused on the





33

The experiment was set up by connecting a 3 m long column with a 1.5 m

long beam. The beams used were HB 300 x 300 x 83.5 and HB 450 x 200 x 74.9.

The columns used were HB 500 x 200 x 102 and HB 250 x 250 x 63.8. The top and

bottom part of column was restrained from any movement. A total of 8 bolts were

used in EEP1 and EEP3. For EEP6, a total of 6 bolts were used. All bolts were M20

Grade 8.8 and the steelwork used was S275.

Load was applied through an automatic operated hydraulic jack and

monitored with a pre-calibrated 100 tonne capacity load cell. The data logger system

was set up to read displacements from inclinometer in millimeters and load in

kiloNewton. Load with an increment of 5 kN was applied to the specimen untilfailure, when large deformation occurred or the load decreases significantly.

3.4 Basic Concept in Using LUSAS

There are two basic steps in using LUSAS:

(a) Generate the structure model.

(b) Assign the relevant attribute to the model.

In LUSAS, the geometry command is the part which is used to draw out the

structure model according to the real structure. There are four geometry feature

types in LUSAS which are points, lines, surfaces and volumes. Points define the

vertices of the finite element model; lines define the edges of the finite element

model and the combined lines define complex edges built from a series of continuous

lines; surfaces define external faces or internal construction surfaces of a model; and

volumes define simple solid components of a model. All geometry should be

ensured that they are in the same Cartesian axis system either global axis system or

local axis system.

The attribute command is the part where user can assign the properties to the

model. Assigned attributes are not lost when the geometry is edited, or the feature is



34

re-meshed at a different density. Attribute assignments are inherited when features

are copied and are retained when features are moved. The LUSAS attribute types are

mesh, geometric, material, support and loading. Mesh describes the element type

and discretisation on the geometry; geometric specifies any relevant geometrical

information that is not inherent in the feature geometry, for example section

properties or thickness; material defines the behaviour of the element material

including linear, plasticity, creep and damage effects; support specifies how the

structure is restrained and is applicable to structural, pore water and thermal

analyses; and loading specifies how the structure is loaded.

3.5 Finite Element Model

3.5.1 Generate Structure Model Component

A total of 6 models were generated. Three of them were generated using

simplified bolt model and the rest are built using actual bolt model. The simplified

bolt model was used based on the model made by Jim Butterworth [7]. In thismodel, the bolt head was assumed to have a shape of a cube and the bolt body was

modeled using line geometry. Based on this concept, the bolt hole was neglected

when generating the end plate (see Figure 3.2) and column flange. In actual bolt

model, the bolt is modeled exactly the same as that of the geometry of the actual bolt.

The bolt hole was provided in the end plate (see Figure 3.3) and in the column

flange.

Taking the advantage of the symmetry of the joint configuration and the load

applied at y axes, only half of the joint was modeled. This will effectively reduce the

computational effort, time and also the model file size. The geometry and properties

of the model were made as similar as possible to that of the actual experiment

specimen. The components of the extended end-plate connections were modeled as

follows:



35

(i) End-plate

The end-plate was modeled with volume geometry.

Figure 3.2 Plate (simplified model) Figure 3.3 Plate (actual model)

(ii) Beam

The beam was modeled with the length of 1200 mm from the centre of columnflange instead of using the actual length of 1500 mm. It is because the load was

applied at the distance of 1200mm from the center of column flange. Assumption

was made that the extra 300 mm beam length after the position of the applied load

had no any effect to the connection. The beam flanges were modeled with volume

geometry. The beam web is assumed as less critical component in this connection,

therefore it is modeled with surface geometry. Figure 3.4 shows the beam model.

Figure 3.4 Beam (simplified and actual model)

(iii) Column

The column was modeled with a length of 3000 mm. The column flange was

modeled using a volume geometry. Like beam web, the column web was modeled

using a surface geometry. Figure 3.5 shows the column when the bolt body was

generated using line element while Figure 3.6 shows the model of the column

containing the actual holes to accommodate the bolts.





37

efficiently. Elements types HX8M, QTS4, BRS2 and JNT4 were chosen to model

the various components of the extended end-plate joint.

Below are the explanations of the various types of elements:

(a) HX8M (3D Continuum Element)

HX8M elements are three dimensional solid hexahedral elements comprising

8 nodes each with 3 degrees of freedom (see Figure 3.9(i)). Although the HX8M

elements are linear with respect to geometry, they employ an assumed internal strain

field which gives them the ability to perform as well as 20 noded quadratic iso-

parametric elements. These elements were used to model the beam flanges, end plate

and connecting column flange of the connection.

(b) QTS4 (Thick Shell Element)

QTS4 elements are three dimensional flat face thick shell elements

comprising either 3 or 4 nodes each with 5 degrees of freedom (see Figure 3.9(ii)).

The element formulation takes account of membrane, shear and flexural

deformations. These elements were used to model the beam and column webs of the

connection.

3. JNT4 (Joint Element)

JNT4 is a 3D joint element which connects two nodes by three springs in the

local x, y and z-directions (see Figure 3.9(iii)). The element has four nodes, the third

and fourth nodes are used to define the local x-axis and local xy-plane. Active node

1 and 2 each has three degrees of freedom. These elements were employed to

generate the prying force at the interface of the end-plate and column flange. This

non-linear contact gap joint element was used to model the interface between the end

plate and the column flange of the connection.

4. BRS2 (Bar Element)

BRS2 is a two-noded, straight and curved iso-parametric bar element in 3D

which can accommodate varying cross sectional area (see Figure 3.9(iv)). Each node



38

has three degree of freedom. This element was used to model the bolts in the tension

and compression zone of the joint.

Figure 3.10 shows the completed model of the joint. Figure 3.11 and Figure3.12 show the simplified bolt model and the actual bolt model respectively.

(i) (ii)

(iii) (iv)

Figure 3.9 (i) HX8M (ii) QTS4 (iii) JNT4 (iv) BRS2 [1]

Figure 3.10 Model after meshing

Figure 3.11 Meshed bolt(simplified model) Figure 3.12 Meshed bolt(actual model)

HX8M

BRS2









CHAPTER 4

RESULT AND DISCUSSION

4.1 Prediction of Result

Referring to the literature review on several research papers, some prediction

can be made on the results which would be obtained from the analysis of the

connection between beam and column using an extended end plate. The predictions

are as follows:

(a) Beam – column connections generally have non-linear moment rotation curves.

(b) Initially they have a stiff initial response which is then followed by a second

phase of much reduced stiffness.

(c) The curves are almost linear at the beginning and then the yielding occurs before

the strain hardening process happened.

(d) The resistance moment decreases if less stiff of connected members and joint are

used like smaller size of beam, column and end plate.

(e) The predicted type of failure of connection is shown in Figure 4.1

Figure 4.1 Predicted failure mode



43

4.2 Experimental Result

Experimental results are obtained from the research paper of Mahmood Md.

Tahir, Shahrin b. Mohamed, M.A.Hussin, A.A.Saim [11]. 3 specimens are chosen

and their results are summarized in Table 4.2 and the moment rotation curves are

shown in Figure 4.1.

Table 4.1 Experimental results of resistance moment and mode of failure

Test No. Resistance Moment M R (kNm) Mode of Failure

EEP1 225Bending of end plateDeformation of column flangeDeformation or slip on bolt



4.2.1 Specimen EEP 1

The moment rotation curve of EEP1 is shown in Figure 4.2. The column

flange started to deform at the tension and compression zone when the applied load

reached 92.6 kN. The upper part of end plate started to bend at the load of 183.3 kN.

Significant deformation occurred at the column flange tension zone at the load of

202.6 kN. The experiment was stopped at the moment of 303.7 kNm when the

rotation reached 41.5 mrad and the failure of connection was seen clearly. Slight

bending occurred at the upper part of end plate, while the column flange deformed at

the tension and compression zone. Slip of the bolts occurred at the tension zone.



44


Moment rotation curve of EEP3 is shown in Figure 4.3. The tension zone of

the column flange deformed when the load reached 105.1 kN. The end plate started

to bend at the load of 156.3 kN. The compression zone of the column flange

deformed at the load of 195 kN. Significant deformation occurred when the applied

became 207.6 kN. The experiment was stopped at the load of 252.3 kN when the

rotation is 26.9 mrad. Deformation occurred at the tension and compression zone of

the column flange, bending of the end plate occurred at the upper part. Slip of the

bolts occurred at the tension zone.


Moment rotation curve of EEP6 is shown in Figure 4.4. When the applied

load reached 135.5 kN, the upper part of the end plate started to bend and

deformation occurred at the column flange in the tension zone. The experiment was

stopped at the load of 132.6 kN when the rotation became 41.2 mrad. Only the upper part of the end plate bent. Deformation occurred at the tension and compression zone

of the column flange. Slip of the bolts occurred at the tension zone.



45

F i g u r e

4 . 2

E x p e r i m e n t a l m o m e n t r o t a t i o n g r a p h o f

E E P 1



46

F i g u r e

4 . 3


E E P 3



47

F i g u r e

4 . 4


E E P 6





49

centroidal line of the beam and the centroidal line of the column, which is shown as

point B in Figure 4.5. The values of moments were taken at the node where the point

loads were applied which is shown as point C in Figure 4.5.

Figure 4.5 Position of node A where displacement was taken

From the values of loadings and displacements, the corresponding values of

moments and rotations were calculated. An example of the calculations to get the

moment and rotation at the first load increment for specimen EEP1 (simplified bolt

model) is shown below.

Moment

Loading = 5kN

Moment = Loading x 1.2 m

= 5 x 1.2

= 6 kNm

Figure 4.6 Actual calculation of rotation

AB

x 180 mm

Electronic Inclinometer

loading

C

x

y

φ

180 +x + A x - B x

Αy - B y



50

Figure 4.7 Approximate calculation of rotation

As shown in Figure 4.6, actual calculation of rotation needs a complex

equation of mathematic. So, an approximate calculation of rotation can be used in

calculating the value of rotation as shown in Figure 4.7.

Rotation

Horizontal displacement of beam, A x = 0.01526 mm

Horizontal displacement of column, B x = 0 mm

Distance column flange to normal line,x = 147 mm

Distance column flange to point A = 180 mm

Vertical displacement of beam, A y = 0.08728 mm

Vertical displacement of column, B y = 0 mmRotation, φ = tan-1 ( Αy - B y) / (180 +x + A x - B x)

= tan-1 (0.08728) / 327.01526

= 2.66877 x 10 -4

= 0.266877 mrad

The results of the analyses based on the specimens EEP1, EEP3 and EEP6

using simplified bolt model and also actual bolt model are shown in Table 4.2 to

Table 4.7 and the moment rotation graphs are shown in Figure 4.8 to Figure 4.13.

φ

180 +x + A x - B x

Αy - B y



51

Table 4.2 Moments and rotations calculation for EEP1 (simplified bolt model)

Loading(N)

Moment(kNm) dx (mm)

dx+180+147(mm) dy (mm)

Rotation(mrad)

0 0.000 0.00000 327.00000 0.00000 0.00000

5000 6.000 0.01526 327.01526 0.08728 0.26690

10000 12.000 0.03052 327.03052 0.17456 0.5337815000 18.000 0.04578 327.04578 0.26185 0.80066

20000 24.000 0.06016 327.06016 0.35082 1.07263

25000 30.000 0.07377 327.07377 0.44124 1.34906

30000 36.000 0.08735 327.08735 0.53246 1.62789

35000 42.000 0.09703 327.09703 0.63321 1.93585

40000 48.000 0.10489 327.10489 0.74220 2.26899

45000 54.000 0.11147 327.11147 0.86182 2.63463

50000 60.000 0.11854 327.11854 0.99136 3.03057

55000 66.000 0.12063 327.12063 1.16367 3.55728

60000 72.000 0.13266 327.13266 1.36663 4.17759

65000 78.000 0.15739 327.15739 1.58799 4.85387

69519 83.422 0.18387 327.18387 1.82848 5.58850

74362 89.235 0.21940 327.21940 2.12534 6.49505

79244 95.093 0.25072 327.25072 2.45017 7.48700

83735 100.482 0.27171 327.27171 2.80475 8.56989

88431 106.117 0.28722 327.28722 3.23001 9.86872

93102 111.722 0.29608 327.29608 3.73153 11.40058

98010 117.611 0.30812 327.30812 4.33149 13.23291

102675 123.210 0.31950 327.31950 5.00655 15.29443

107734 129.281 0.34658 327.34658 5.79574 17.70336

112741 135.289 0.39686 327.39686 6.61143 20.19118

117792 141.350 0.45748 327.45748 7.45649 22.76692

122928 147.514 0.52972 327.52972 8.30063 25.33771

127948 153.538 0.60767 327.60767 9.11851 27.82644

132902 159.482 0.69660 327.69660 9.95068 30.35621

137894 165.473 0.80043 327.80043 10.82157 33.00070

142791 171.349 0.91485 327.91485 11.71080 35.69775

147672 177.206 1.04545 328.04545 12.66421 38.58590







54

M o m e n

t v s

R o

t a t i o n E E P 3 ( s i m p

l i f i e d b o

l t m o

d e

l )

0 1 0

2 0

3 0

4 0

5 0

6 0

7 0

8 0

9 0

1 0 0

1 1 0

1 2 0

1 3 0

1 4 0

1 5 0

1 6 0

1 7 0

0

5

1 0

1 5

2 0

2 5

R o

t a t i o n

( m r a

d )

M o m e n t ( k N m )

F i g u r e

4 . 9

M o m e n t v s r o t a t i o n g r a p h

f o r E E P 3 ( s i m p l i f i e d

b o l t m o d e l )



55

Table 4.4 Moments and rotations calculation for EEP6 (simplified bolt model)

Loading(N)

Moment(kNm)

dx(mm)

dx+180+147(mm) dy (mm)

Rotation(mrad)

0 0.000 0.00000 302.00000 0.00000 0.00000

5000 6.000 0.02976 302.02976 0.15147 0.50151

10000 12.000 0.05953 302.05953 0.30294 1.0029315000 18.000 0.08873 302.08873 0.45554 1.50797

20000 24.000 0.11644 302.11644 0.61107 2.02263

25000 30.000 0.14380 302.14380 0.77154 2.55355

30000 36.000 0.17086 302.17086 0.95807 3.17062

35000 42.000 0.21478 302.21478 1.19735 3.96190

40000 48.000 0.28366 302.28366 1.49907 4.95911

45000 54.000 0.36590 302.36590 1.91536 6.33451

50000 60.000 0.47290 302.47290 2.39575 7.92039

55000 66.000 0.59822 302.59822 3.02918 10.01023

60000 72.000 0.75069 302.75069 3.87709 12.80552

65000 78.000 0.80216 302.80216 4.83755 15.97459

70000 84.000 0.89331 302.89331 6.06736 20.02867

75000 90.000 1.06026 303.06026 7.45625 24.59824

80000 96.000 1.49226 303.49226 9.38026 30.89791

86108 103.330 1.75675 303.75675 11.56592 38.05786

91108 109.329 2.00484 304.00484 13.35123 43.88961

95663 114.795 2.34041 304.34041 15.26421 50.11306

100333 120.400 2.84801 304.84801 17.73518 58.11163

105290 126.348 3.44263 305.44263 20.59228 67.31598

110633 132.760 4.07019 306.07019 23.50473 76.64479

116132 139.359 4.62855 306.62855 26.27437 85.47915

121268 145.522 5.08379 307.08379 28.71296 93.23098

126277 151.533 5.50256 307.50256 31.11466 100.84182

131372 157.646 5.89592 307.89592 33.58019 108.63409

136542 163.851 6.30844 308.30844 36.00350 116.25102

141640 169.968 6.71003 308.71003 38.35456 123.60798

146636 175.963 7.11246 309.11246 40.66321 130.79725

151629 181.955 7.53763 309.53763 43.01285 138.07419

156605 187.926 7.99310 309.99310 45.40972 145.45174



56

F i g u r e

4 . 1

0 M o m e n t v s r o t a t i o n g r a p h

f o r E E P 6 ( s i m p l i f i e

d b o l t m o d e l )

M o m e n

t v s

R o

t a t i o n

E E P 6 ( s i m p

l i f i e d b o

l t m o

d e

l )

0 1 0

2 0

3 0

4 0

5 0

6 0

7 0

8 0

9 0

1 0 0

1 1 0

1 2 0

1 3 0

0

5

1 0

1 5

2 0

2 5

3 0

3 5

4 0

4 5

5 0

5 5

6 0

6 5

R o

t a t i o n

( m r a

d )






58

M o m e n

t v s

R o

t a t i o n

E E P 1 ( a c

t u a

l b o

l t m o

d e

l )

0 1 0

2 0

3 0

4 0

5 0

6 0

7 0

8 0

9 0

1 0 0

1 1 0

1 2 0

1 3 0

1 4 0

1 5 0

1 6 0

1 7 0

1 8 0

1 9 0

0

5

1 0

1 5

2 0

2 5

3 0

3 5

4 0

4 5

R o

t a t i o n

( m r a

d )


F i g u r e

4 . 1

1 M o m e n t v s r o t a t

i o n g r a p h

f o r E E P 1 ( a c t u a l b o l t m o d e l )



59

Table 4.6 Moments and rotations calculation for EEP3 (actual bolt model)

Loading(N)

Moment(kNm)

dx(mm)

dx+180+147(mm) dy (mm)

Rotation(mrad)

0 0 0.00000 327.00000 0.00000 0.00000

5000 6 0.00841 327.00841 0.07660 0.23425

10000 12 0.01682 327.01682 0.15320 0.4684815000 18 0.02522 327.02522 0.22980 0.70270

20000 24 0.03363 327.03363 0.30640 0.93691

25000 30 0.04204 327.04204 0.38300 1.17111

30000 36 0.05045 327.05045 0.45960 1.40530

35000 42 0.05864 327.05864 0.53653 1.64048

40000 48 0.06588 327.06588 0.61496 1.88023

45000 54 0.07240 327.07240 0.69474 2.12411

50000 60 0.07709 327.07709 0.77743 2.37691

55000 66 0.08028 327.08028 0.86327 2.63932

60000 72 0.08240 327.08240 0.95532 2.92071

65000 78 0.08412 327.08412 1.05273 3.21853

70000 84 0.08484 327.08484 1.16100 3.54953

75000 90 0.08528 327.08528 1.28397 3.92548

80000 96 0.08331 327.08331 1.42628 4.36058

85000 102 0.07628 327.07628 1.60490 4.90676

90000 108 0.06083 327.06083 1.83082 5.59775

95000 114 0.04296 327.04296 2.11063 6.45359

100000 120 0.03826 327.03826 2.41896 7.39643

105000 126 0.04226 327.04226 2.76463 8.45324

110000 132 0.04606 327.04606 3.13096 9.57316

115000 138 0.05284 327.05284 3.51273 10.74015

120000 144 0.06708 327.06708 3.92821 12.00982

125000 150 0.08905 327.08905 4.37401 13.37173

130000 156 0.11608 327.11608 4.83832 14.78974

135000 162 0.13955 327.13955 5.34953 16.35099

140000 168 0.16246 327.16246 5.88938 17.99944

145000 174 0.18517 327.18517 6.45391 19.72299





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Table 4.7 Moments and rotations calculation for EEP6 (actual bolt model)

Loading(N)

Moment(kNm)

dx(mm)

dx+180+147(mm) dy (mm)

Rotation(mrad)

0 0 0.00000 302.00000 0.00000 0.00000

5000 6 0.03042 302.03042 0.12428 0.41149

10000 12 0.06084 302.06084 0.24856 0.8228915000 18 0.09126 302.09126 0.37284 1.23421

20000 24 0.12168 302.12168 0.49713 1.64545

25000 30 0.15182 302.15182 0.62203 2.05867

30000 36 0.18047 302.18047 0.75044 2.48342

35000 42 0.20858 302.20858 0.88597 2.93163

40000 48 0.23645 302.23645 1.03328 3.41876

45000 54 0.26936 302.26936 1.19938 3.96791

50000 60 0.31419 302.31419 1.39864 4.62640

55000 66 0.36728 302.36728 1.65366 5.46899

60000 72 0.41429 302.41429 2.00280 6.62261

65000 78 0.45048 302.45048 2.52621 8.35229

70000 84 0.50003 302.50003 3.12908 10.34369

75000 90 0.55276 302.55276 3.79999 12.55911

80000 96 0.61372 302.61372 4.58672 15.15585

85000 102 0.73565 302.73565 5.48308 18.10978

90000 108 0.88766 302.88766 6.47333 21.36879

95000 114 1.07794 303.07794 7.49655 24.72970

100000 120 1.32576 303.32576 8.63600 28.46336

104295 125 1.68186 303.68186 9.87406 32.50303



62

M o m e n

t v s

R o

t a t i o n

E E P 6 ( a c

t u a

l b o

l t m o

d e

l )

0 1 0

2 0

3 0

4 0

5 0

6 0

7 0

8 0

9 0

1 0 0

1 1 0

1 2 0

1 3 0

1 4 0

0

5

1 0

1 5

2 0

2 5

3 0

3 5

R o

t a t i o n

( m r a

d )


F i g u r e

4 . 1

3 M o m e n t v s r o t a

t i o n g r a p h

f o r E E P 6 ( a c t u a l b o l t m o d e l )



63

4.4 Comparison of Results between LUSAS and Experiment

The comparison of results is done to determine the accuracy of finite element

method in analysing the connection of beam to column using extended end plate.Due to limited data recorded in experiment, so the comparison of results is mainly

focus on the moment rotation curve and the mode of failure only.

4.4.1 Comparison of Moment Rotation Curve

The comparisons between moment rotation curves obtained from laboratory

test and those from LUSAS are summarized in Table 4.8.

Table 4.8 Comparison of Moment Rotation Curve

Specimen Resistance Moment (kNm) Difference(%)Experimental LUSAS simplified actual

simplified actual

EEP1 225 210 222 6.67 1.33EEP3 240 220 238 8.33 0.83EEP6 182 164 178 9.89 2.20

The moment rotation curves from testing and LUSAS are shown in Figure 4.8

to Figure 4.13. The value of resistance moment of Table 4.8 is determined by

estimating when a “knee” formed in each of the moment rotation curves. By using

this technique, the experimental and LUSAS values of M R can be obtained. The

value of M R obtained from each graph need to be multiplied by 2 because only half

model was generated due to symmetry of the connection configuration. Further

explanation of the calculation of M R is shown in Figure 4.14 and Figure 4.15.



64

Figure 4.14 Full model of connection

Figure 4.15 Half model of connection

In Figure 4.14, moment M R1 = P x L

= PL

In Figure 4.15, loading F = ½ x P (due to half model)

MR2 = F x L

= P/2 x L

= PL/2

= M R1/2

MR1 = 2 M R2

The results from the laboratory tests have recorded that the resistance

moment of the connection is in the range of 182-240 kNm while the results from the

analysis of LUSAS show that the resistance moment is ranged from 164 kNm to 220

kNm for the simplified bolt model and 178 kNm to 238 kNm for the actual bolt

model. Overall results indicate that the experimental values of resistance moment

are greater than LUSAS analysis values. For the simplified bolt model, the

differences are in the range from 6.67% to 9.89%. The values of resistance moments

Loading PL

MR1

Loading FL

MR2



65

obtained from actual bolt model are lower than experimental results with the

differences range between 0.83% and 2.20%. Based on the differences, it is proven

that the actual bolt model can provide more accurate results compared to the

simplified bolt model.

All moment rotation curves show that the connections behave linearly in the

first phase followed by non linear behaviour in the second phase and gradually losing

the stiffness with increasing in rotation. This is typical type of graph for a semi rigid

connection. In the second phase, yielding occurred before strain hardening process

happened.

Based on Table 3.1, specimen EEP1, EEP3 and EEP6 are made up using

different size of column, beam, thickness of end plate and numbers of bolts. From the

result of analysis, specimen EEP1 with a smaller thickness of end plate gives a

smaller value of resistance moment compared to specimen EEP3. This is a logical

phenomenon in which the end plate with a higher thickness has a stronger resistance

to the applied load. This causes the specimen EEP3 to posses a higher resistance

moment. For specimen EEP6, it is a connection between smaller size of column and beam. Only 6 bolts are used in this specimen compared to 8 bolts used in EEP1 and

EEP3. Beam and column with smaller sizes have less strength to sustain the moment

caused by applied load. Because of this reason, specimen EEP6 gives the smallest

value of resistance moment compared to others.

4.4.2 Comparison of Mode of Failure

From the comparison of failure mode obtained from experiment and LUSAS

analysis, it shows that both results give same mode of failure which the failure occurs

on the bending of end plate, bending of column flange and deformation or slip on

bolt as shown in Figure 4.16. The failure mode at tension zone is shown in Figure

4.17. These failures show that the behaviour of the connection is considered as

ductile and can be categorized as partial strength connection.



66

Figure 4.16 Mode of failure of connection

Figure 4.17 Mode of failure near the tension bolt





69

3. A total 6 model of connection were generated. Three of them were modeled

using simplified bolt model referring to the model work done by Jim

Butterworth [7] and the rest were modeled using actual bolt model according

to the actual geometry dimensions of the bolts. Based on the comparison

with the experimental results, the simplified bolt model give the differences

of results in the range from 6.67% to 9.89% and differences of results of the

actual bolt model are in the range of 0.83% and 2.20%. These comparisons

show that the more accurate results are obtained by using the actual bolt

model.

5.2 Recommendations

Some problems have been encountered during the modeling process. In order

to improve the modeling process and thus get a more accurate result, these problems

need to be overcome. The problems and some recommendations will be explained

below as a reference for future research.

(a) Inadequate data recorded in experiments causes comparison of experimental

results other than resistance moment cannot be made with the LUSAS

analysis results. It is recommended that laboratory tests are conducted in the

same time as that of the modeling process. Additional parameters should be

recorded during the experiment. One of the parameter that needs to be

recorded is strains in the bolt and column. Stress occurred in the bolt and

column can be calculated from recorded strain and compared with LUSASanalysis results. Mistake can be spotted from the comparisons and thus the

finite element model can be improved.

(b) Convergence test should be made in future analysis in order to obtain good

results using minimum elements. Convergence test can be done by

increasing or decreasing the total number of elements and then check whether

the solution converge to a certain equilibrium value.









73

APPENDIX A/1

MANUAL

In general, modeling can be divided into 9 steps, there are:1. Creating a new model.2. Feature geometry.3. Meshing.4. Assign geometry properties.5. Assign material properties.6. Assign boundary condition.7. Assign loading.8. Analysis.9. Results.

Specimen EEP1 will be used as example in explanation of the modeling process. 2modeled have been built using simplified bolt model and actual bolt model.

SIMPLIFIED BOLT MODEL

STEP 1 Creating a New Model

- Enter the file name as extended end plate (simplified bolt model).- Enter the title as Analysis of Extended End Plate.- Set the units as N mm t C s- Select the startup template Standard from those available in the drop down list.- Set the vertical axis as Y .- Click the OK button.

Note. It is useful to save the model regularly as the example progresses. This allowsa previously saved model to be re-loaded if a mistake is made that cannot be

correctedeasily by a new user.

STEP 2 Feature Geometry

The composite plate will be modeled as a half model and symmetry boundaryconditions will be used to reduce the size of the model.

1. Defined the bolt into four equal surfaces.





75

5. Sweep the surface of end plate and the shared surfaces of bolt and end plate toform end plate volume.

6. At this stage, the model of end plate together with bolts should be looked like below when the model points are not shown.



76

7. Form the volumes of beam flanges by using sweeping from the end plate surface.

This is to ensure the beam flanges are sharing the same surface with end plate.

8. Move the model +1000mm in Z direction. This is to prevent the sharing of pointwhile modeling the column.

9. Copy the surface of end plate and extend it to form column flange surface by usingsweeping.

X

Y

Z



77

10. Sweep the column flange surface to form column flange volume and copy toform column flange on the other side.

X

Y

11. Form the volume of nut by using sweeping from the surface of column flange.The model of nut together with column flange in x direction, should be as shown below

12. Sweep the suitable line of end plate to form the surface of beam web between the beam flanges.

13. Sweep the suitable line of column flange to form the surface of column web between the column flanges.











82

7. The whole model after meshing should be as shown below.

X

Y

Z

STEP 4 Assign Geometry Properties

1. Line geometric with the cross sectional area (A) of 245mm 2 is assigned to the four bolt body.

2. Surface geometric with the thickness of 6mm is assigned to the surface of columnweb.

3. Surface geometric with the thickness of 5.5mm is assigned to the surface of beamweb.

STEP 5 Assign Material Properties

The material properties are assigned as shown below.

1. Beam, column and end plate (Isotropic)Young’s modulus, E = 205 kN/mm 2 Poisson’s ration, v = 0.3Initial uniaxial yield stress = 305 N/mm 2 Hardening gradient, slope 1 = 0

plastic strain 1 = 0.02slope 2 = 10000

plastic strain 2 = 100

2. Bolt (Isotropic)

Young’s modulus, E = 205 kN/mm2

Poisson’s ration, v = 0.3





84

STEP 8 Analysis

Since this is a nonlinear problem the load incrementation strategy needs to be defined.- From the Treeview right click on Loadcase 1 and select the Properties option.- Define the analysis as a Nonlinear & Transient problem and click on the Set

button. The Nonlinear & Transient dialog will appear.- Select the Nonlinear option.- Set Incrementation to Automatic - Set the Starting load factor to 1- Set the Maximum change in load factor to 1- Set the Maximum total load factor as 40- Change the Incremental displacement norm to 100- Leave the Maximum number of time steps or increments as 0- Click the OK button to return to the loadcase properties.- Click the OK button to finish.

To avoid mechanisms in the element formulation when some of the Gaussintegration points fail, it is necessary to switch on fine integration for the elements.- Select the Solution tab and click on the Element Options button.- Select the option Fine integration for stiffness and mass and click OK to returnto the main model properties form and OK to return to the graphics display.

Save the model file.

A LUSAS data file name of extended end plate (simplified bolt model) will beautomatically entered in the File name field.- Ensure that the options Solve now and Load results are selected.- Click the Save button to solve the problem.

Note. In running this nonlinear analysis 5 load increments are evaluated. This maytake up to 1 hour on older personal computers but will be significantly faster onmodern machines. An indication of the time remaining can be attained by observingthe number of the increment being evaluated.

A LUSAS Datafile will be created from the model information. The LUSAS Solveruses this datafile to perform the analysis.

The LUSAS results file will be added to Treeview.In addition, 2 files will be created in the directory where the model file resides:- extended end plate (simplified bolt model).outThis output file contains details of model data, assigned attributes and selectedstatistics of the analysis.- extended end plate (simplified bolt model).mysThis is the LUSAS results file which is loaded automatically into the Treeview toallow results processing to take place.



85

STEP 9 Results

Loadcase results can be seen in the Treeview. If the analysis was run from withinLUSAS Modeller the results will be loaded on top of the current model and the loadcase results for the first load increment are set active by default.

If present, delete the Mesh, Geometry and Attributes layers from the Treeview.- In the graphics window, with no features selected, click the right-hand mouse

button and select the Deformed mesh option to add the deformed mesh layer to theTreeview.- Click Close to accept the default properties and display the influence surface of thecurrent loadcase.

Select the node where the load is applied, click Utilities on the menu bar, and clickon the Graph Wizard .- Select Time History , click the next button.- For x dataset, , select Displacement in the dropdown menu of Entity, and select RSLT for Component , then click the next button.- For y dataset, select Nodal and click next button, select Loading in the dropdownmenu of Entity, and select RSLT for Component , then click the next button, thenclick the finish button.- A graph will be shown and the value of displacement and loading are stated next tothe graph.- Displacement in different direction can be obtained by repeating the previous steps.

ACTUAL BOLT MODEL

STEP 1 Creating a New Model

- Enter the file name as extended end plate (actual bolt model).- Enter the title as Analysis of Extended End Plate.- Set the units as N mm t C s- Select the startup template Standard from those available in the drop down list.- Set the vertical axis as Y .

- Click the OK button. Note. It is useful to save the model regularly as the example progresses. This allowsa previously saved model to be re-loaded if a mistake is made that cannot becorrectedeasily by a new user.

STEP 2 Feature Geometry

1. Defined the bolt hole into four equal surfaces.



86

2. Define the bolt head into four equal surfaces.

3. Copy the bolt surfaces to form other bolt surfaces.

4. Extend the surface of bolts to form the surface of end plate by using sweeping.This is to ensure the end plate and bolts are sharing the same surfaces.

5. Sweep the surfaces of bolt head from the end plate’s surface to form bolt volumes.



87

6. The following steps are same with the feature geometry of simplified bolt modelfrom step 5 to step 15.

7. Sweep the bolt hole surface to the other side of bolt to form the bolt body.

STEP 3 Meshing

1. Mesh the bolt head and bolt body with volume mesh HX8M with automaticdivision. All bolt line then is meshed with line of division of 2 except bolt line in zdirection which is meshed with line with division of 1.

2. The meshing for other components is same as step 2 to step 7 of meshing ofsimplified bolt model.

STEP 4 Assign Geometry Properties

1. Surface geometric with the thickness of 6mm is assigned to the surface of columnweb.

2. Surface geometric with the thickness of 5.5mm is assigned to the surface of beamweb.

STEP 5 Assign Material Properties1. The material properties are assigned same as simplified bolt model.

STEP 6 Assign Boundary Condition

1. The boundary condition is assigned same as simplified bolt model except therestraint in Y direction below the end plate is not needed.



88

STEP 8 Analysis1. Follow the steps in simplified bolt model.

STEP 9 Results

1. Follow the steps in simplified bolt model.

Tan Eng Hooi – Behaviour and Strength Study on Steel Semi Rigid Connection Using Lusas

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