an analytical and computational investigation on end-plate thickness and bolt tension of a bolted...

AN ANALYTICAL AND COMPUTATIONAL INVESTIGATION

ON END-PLATE THICKNESS AND BOLT TENSION

OF A BOLTED EXTENDED END-PLATE MOMENT CONNECTION

by

Raasheduddin Ahmed

Submitted to the

DEPARTMENT OF CIVIL ENGINEERING,

BANGLADESH UNIVERSITY OF ENGINEERING AND TECHNOLOGY,

DHAKA

In partial fulfillment of the requirements for the degree of

BACHELOR OF SCIENCE IN CIVIL ENGINEERING, 2007

ii

DECLARATION

Declared that, except where specific references are made to other investigators, the

work embodied in this thesis is the result of investigation carried out by the author

under the supervision of Dr. Khan Mahmud Amanat, Professor, Department of Civil

Engineering, BUET, Dhaka.

Neither the thesis nor any part thereof is submitted or is being concurrently

submitted in candidature for any degree at any other institution.

________________________________

Author

iv

ABSTRACT

A finite element analysis was conducted, and a theoretical analytical formulation

was proposed to study bolted extended end-plate moment connections subjected

to static loading. A problem subjected to various parametric conditions,

representing typical end-plate moment connection configurations, was presented.

In the analytical formulation yield line theory was used to predict end-plate yielding,

and a method was developed to predict the bolt tensile forces, to aid in the design

of the extended end-plate moment connection. Large deflection and nonlinearity of

materials was considered in the finite element analysis. The end-plate thicknesses

and the bolt tensile forces obtained with the analytical predictions were compared

to the finite element model results, and good correlation was obtained between the

two approaches. Finally, the validity of using the proposed analytical formulation as

a guideline was discussed.

iii

ACKNOWLEDGEMENTS

I would like to express my wholehearted gratitude to the Almighty for each and

every achievement of my life.

I have the pleasure to state that, this study was supervised by Dr. Khan Mahmud

Amanat, Professor, Department of Civil Engineering, Bangladesh University of

Engineering and Technology (BUET), Dhaka. I am greatly indebted to him for all his

adept guidance, affectionate assistance, and enthusiastic encouragement

throughout the progress of this thesis. It would have been impossible to carry out

this study without his dynamic direction and critical judgment of the progress.

I would like to thank my friends for their assistance, motivation, appraisal and

support throughout the completion of this study. Finally, I would like to thank my

parents and my sister, for their undying love, encouragement and support at all

stages of my life. The achievement of this goal would have been impossible without

their blessings.

v

TABLE OF CONTENTS

Declaration Acknowledgements Abstract Table of Contents List of Figures List of Tables Chapter 1. Introduction

1.1 General 1.2 Objective of the Present Study 1.3 Methodology of the Study 1.4 Organisation of the Study

Chapter 2. Literature Review

2.1 Introduction 2.2 Previous Works 2.3 Remarks

Chapter 3. Methodology for Finite Element Analysis 3.1 Introduction 3.2 Finite Element Packages 3.3 Types of Analysis on Structures 3.4 Finite Element Modeling of the Problem

3.4.1 Modeling of the Beam Flange, Beam Web, End-Plate and Load Plate 3.4.2 Modeling of the Bolts and Contact Surface 3.4.3 Nonlinear Stress-Strain Materials

3.5 Parametric Study of the Problem 3.6 Meshing

3.6.1 Meshing of the Beam Flange and Beam Web 3.6.2 Meshing of the End-Plate 3.6.3 Meshing of the Load Plate 3.6.4 Properties of the Bolts 3.6.5 Properties of the Contact Element

3.7 Boundary Conditions 3.7.1 Restraint 3.7.2 Load

3.8 Solution Method 3.8.1 Arc-Length Method 3.8.2 Convergence of the Solution 3.8.3 Typical Deflected Shapes and Typical Stress Contours

ii iii iv v

vii viii

1 1 1 1 2

3 3 7

13

14 14 14 15 16

18 20 22 23 24 24 25 25 25 26 27 27 28 30 30 31 32

vi

Chapter 4. Proposed Analytical Formulation and Discussion of Results 4.1 Introduction 4.2 Proposed Analytical Formulation

4.2.1 Description of Problem and Objective of Formulation 4.2.2 Development of Analytical Formulation of End-Plate Thickness 4.2.3 Determination of Bolt Tensile Force

4.3 Description and Discussion of Results 4.3.1 Effect on End-plate Thickness 4.3.2 Effect on Bolt Tension

Chapter 5. Conclusion 5.1 General 5.2 Findings 5.3 Guideline for End-Plate Thickness and Bolt Tension 5.4 Scope for Future Investigation

References Appendix A - ANSYS Script used in the Present Analysis Appendix B - Data Tables of the Parametric Study

36 36 36 36 37 41 42 42 43

50 50 50 51 51

52 56 67

vii

LIST OF FIGURES

Figure 2.1 Figure 2.2 Figure 2.3 Figure 2.4 Figure 2.5 Figure 3.1 Figure 3.2 Figure 3.3 Figure 3.4 Figure 3.5 Figure 3.6 Figure 3.7 Figure 3.8 Figure 3.9 Figure 3.10 Figure 3.11 Figure 3.12 Figure 3.13 Figure 3.14 Figure 3.15 Figure 3.16 Figure 3.17 Figure 3.18 Figure 3.19 Figure 3.20 Figure 3.21 Figure 3.22 Figure 4.1 Figure 4.2 Figure 4.3 Figure 4.4 Figure 4.5

Extended end-plate beam-to-beam moment connection, Desh Bandhu Sugar Mills, Ghorashaal, Bangladesh A typical extended end-plate beam-to-column moment connection A typical all-bolted flange-plated moment splice Column base plate connection, Desh Bandhu Sugar Mills, Ghorashaal, Bangladesh End-plate connection used in gable frame, Desh Bandhu Sugar Mills, Ghorashaal, Bangladesh General sketch of a structure with an end-plate type beam splice General 3-D Sketch of the problem Typical 3-D Mesh of the finite element problem SHELL181 - 4-Node Finite Strain Shell COMBIN39 Nonlinear Spring The finite element mesh has more intense meshing near the end-plate Mesh of the end-plate Force-Deflection Behavior of the bolts Force-Deflection behavior of the contact springs Mesh showing COMBIN39 link elements used as contact elements Point of application of load End-plate with section of the beam Stress distribution for plastic moment Arc-Length Approach with Full Newton-Raphson Method Typical Force-Deflection curves for various end-plate thicknesses Typical deflected shape of problem Typical close-up deflected shape of the joint Typical fibre stress of beam Typical vertical fibre stress of end-plate Typical horizontal fibre stress of end-plate Typical vertical fibre stress of end-plate Typical axial force diagram of bolts 2-D sketch of the model Deflected shape of the problem due to deformation at the end of the beam-portion Formation of yield lines in the end-plate Free body diagram of the portion of the end-plate between the top bolt centerline and the top portion of the top flange of the beam Free body of the problem without the extended portions of the end-plate

4

4 5

6

6

16 17 17 18 21

24 25 26 27

27 28 28 29 30 31 32 32 33 33 34 34 35 36

37 37

38

38

viii

Figure 4.6 Figure 4.7 Figure 4.8 Figure 4.9 Figure 4.10 Figure 4.11 Figure 4.12 Figure 4.13 Figure 4.14 Figure 4.15 Figure 4.16 Figure 4.17 Figure 4.18 Figure 4.19 Figure 4.20

Free body of the portion of the end-plate without the extended portions Stress distribution on the end-plate due to Mp Stress distribution on the beam section due to complete yielding Change of end-plate thickness with beam height Change of end-plate thickness with flange width Change of end-plate thickness with flange thickness Change of end-plate thickness with web thickness Effect of change of beam height on bolt force Effect of change of flange width on bolt force Effect of change of flange thickness on bolt force Effect of change of web thickness on bolt force Effect of beam height on summation of bolt forces Effect of flange thickness on summation of bolt forces Effect of web thickness on summation of bolt forces Effect of flange width on summation of bolt forces

39 40 41 44 44 45 45 46 46 47 47 48 48 49 49

LIST OF TABLES

Table 3.1 Table 3.2 Table 3.3 Table B1 Table B2 Table B3 Table B4

SHELL181 Input Summary COMBIN39 Input Summary Various Parameters Effect of change in beam height on end-plate thickness and bolt forces Effect of change in flange width on end-plate thickness and bolt forces Effect of change in flange thickness on end-plate thickness and bolt forces Effect of change in web thickness on end-plate thickness and bolt forces

19 21 23

67

67

68

68

CHAPTER 1

INTRODUCTION

1.1 GENERAL

Bolted end-plate type moment connections are used extensively in steel structures.

However, despite the wide application of this connection and the great amount of

research in this field, it appears that no specific guidelines are available to assist

designers in choosing the appropriate end-plate thickness and in determining the

corresponding bolt tensile forces. The selection of the appropriate end-plate

thickness and bolt tension is of utmost importance to ensure the safety and

economy of the connection, and hence the steel structure. The present study aims

to provide the design engineer some definite guidelines on this matter.

1.2 OBJECTIVE OF THE PRESENT STUDY

The objective of the present study is to investigate a bolted extended end-plate

moment connection under loading, and to develop a decisive guideline to

determine the appropriate end-plate thickness and bolt tension for the bolted

extended end-plate moment connection.

1.3 METHODOLOGY OF THE STUDY

For the purpose of carrying out the investigation, a typical problem under various

parametric conditions, and the effect of the various parameters on end-plate

thickness and bolt tension, would be studied.

The problem would be approached from two sides. A theoretical analytical

formulation would be developed; and a finite element analysis of the problem

would be carried out. The analytical formulation would be based on the

fundamental theories of structure. The finite element analysis would use shell

element for the modeling of beam and end-plate. Nonlinear spring would be used

Introduction 2

to model the bolts and contact surface. The connection would then be subjected to

moment greater than the ultimate moment in order to ensure yielding of the steel.

Next, the two approaches would be compared with one another, and the

applicability of the suggested analytical approach established.

1.4 ORGANIZATION OF THE STUDY

The study is organized so as to best describe and discuss the problem and the

resulting findings. Chapter 1 introduces the problem and presents an overall idea of

the present study. Chapter 2 introduces the end-plate moment connection and

reviews the available literature that is required to understand the background

theories of end-plate moment connections. Chapter 3 presents the finite element

methodology used in the present study. The chapter describes the modeling,

meshing, boundary conditions, load conditions and solution methods used in the

finite element analysis. Chapter 4 presents the proposed analytical formulation;

discusses the results of the finite element analysis; and compares the finite element

analysis with the proposed analytical formulation. Chapter 5, the concluding

chapter, summarizes the entire work and makes some recommendations for future

research.

CHAPTER 2

LITERATURE REVIEW

2.1 INTRODUCTION

Bolted end-plate type connections have been used to a great extent in all steel

structures, e.g. buildings, bridges, water tanks, transmission towers, etc. They have

the advantages of requiring less supervision and a shorter assembly time than

welded joints. They also have a geometry that is easy to comprehend and can

accommodate minor discrepancies in the dimensions of beams and columns. Also,

bolted joints can be disassembled, if necessary, and are not permanent like welded

joints. Furthermore, as a result of poor performance of flange-welded moment

connections in comparison to the performance of bolted and riveted moment

connections in the 1994 Northridge earthquake and the 1995 Kobe earthquake,

end-plate moment connections are under serious consideration as an alternative to

welding in seismic regions.

The extended end-plate connection is used for beam-to-column connections, as

well as for beam-to-beam connections. It consists of a plate with bolt holes drilled

or punched, and shop welded to a beam section. In case of beam-to-beam

connections, the connection is completed in the field when the beam end is bolted

to another beam end. The extended end-plate connection is termed extended

because the plate extends above or below the flange that will be in tension under

load. In the case of extended end-plates used for seismic design, the end-plate is

extended above and below both beam flanges.

In Figure 2.1 an extended end-plate beam-to-beam moment connection used in

Desh Bandhu Sugar Mills, Ghorashaal, Bangladesh is shown. Figure 2.2 shows a

typical extended end-plate beam-to-column moment connection. The moment

connections transfer the moment carried by the flanges of the supported beam to

Literature Review 4

the supporting member. Moment connections are assumed to have little or no

relative rotation between the supporting member and the supported members.

Figure 2.1 Extended end-plate beam-to-beam moment connection, Desh Bandhu Sugar Mills, Ghorashaal, Bangladesh

Figure 2.2 A typical extended end-plate beam-to-column moment connection

Literature Review 5

A Fully Restrained (FR) connection assumes the measured angles between

intersecting members are maintained (i.e. no relative rotation) and there is full

transfer of the moments. Partially Restrained (PR) connections assume that there

will be some relative rotational movement that occurs between intersecting

members, though there will still be transfer of the moments.

Infinite rigidity can never be realistically attained; therefore, even fully restrained

moment connections do possess some minimal amount of rotational flexibility,

which is usually neglected. FR connections are idealized as having full fixity between

members. In this thesis, the connections are assumed to be fully restrained.

End-plate beam-to-beam moment connections have some inherent advantages

over flange-plated beam-to-beam connections. A typical all-bolted flange-plated

moment splice is shown in Figure 2.3. Specifications require the bolt holes to be

somewhat larger than the bolt diameters. This may cause minor slipping at the joint

leading to permanent deformations, which may still be adequate from the strength

point of view but may be inadequate from the serviceability and aesthetic point of

view. Such slipping at the joints does not occur in case of end-plate moment

connections.

Figure 2.3 A typical all-bolted flange-plated moment splice

Literature Review 6

Further examples of end-plate type connections are shown in Figure 2.4 and Figure

2.5. Figure 2.4 shows a column base plate connection which is essentially the same

as an end-plate connection.

Figure 2.4 Column base plate connection, Desh Bandhu Sugar Mills, Ghorashaal, Bangladesh

In Figure 2.5 the application of the end-plate moment connection in a gable frame is

shown.

Figure 2.5 End-plate connection used in gable frame, Desh Bandhu Sugar Mills, Ghorashaal, Bangladesh

Literature Review 7

This thesis is concerned with extended end-plate beam-to-beam connections. The

study aims to determine adequate end-plate thicknesses and corresponding bolt

forces with respect to changes in certain beam parameters such as beam height,

flange width, flange thickness and web thickness.

2.2 PREVIOUS WORKS

The first application of the end-plate moment connection was in the early 1960s. It

was established that end-plate moment connections offer several advantages over

tee-stub-moment connections (Disque, 1962).

An early study by Johnson et al. (1960) concluded that end-plate connections with

high strength bolts can develop the full plastic capacity of the connected members.

The formation of a plastic hinge in the beam provides inelastic rotation capacity

within the member instead of within the connection.

Douty and McGuire (1963, 1965) investigated the increase in bolt tension caused by

prying effects in the end-plate and compared theoretical and experimental results.

For the thinner end-plates, significant increases in bolt tension were reported.

Mann (1968) conducted six beam-to-column end-plate connection tests and

developed equations to predict the strength of the end-plate. Surtees and Mann

(1970) refined the work of Mann (1968) and developed an alternate equation for

determining the end-plate thickness, suggested the use of a 33 percent increase of

the direct bolt tension force to account for prying forces, and concluded that the

bolt pretension had little effect on the connection stiffness.

Krishnamurthy and Graddy (1976) conducted one of the earliest studies to

investigate the behavior of bolted end-plate moment connections using finite

element analysis.

Packer and Morris (1977) developed design equations for determining the end-plate

thickness and the column flange strength. Yield line analysis, considering straight

Literature Review 8

and curved yield lines, was used to predict the end-plate and column flange

strengths. Good agreement with experimental results was achieved.

Krishnamurthy (1978) used finite element analysis to develop empirical

relationships for determining the end-plate thickness. The relationships resulted in

much thinner end-plates than previously obtained. It also resulted in much smaller

prying forces than predicted by previous studies. As a result, Krishnamurthy

neglected prying forces and determined the bolt forces directly from the flange

force.

Mann and Morris (1979) considered the results of several research programs and

proposed a design procedure for the extended end-plate connection. The

procedure considered both strength and stiffness criteria. Yield line analysis was

used to determine the strength of the end-plate and column flange. Prying forces

were considered in the design of the bolts.

Tarpy and Cardinal (1981) used finite element analysis to develop equations for the

design of unstiffened beam-to-column flange end-plate connections. The adequacy

of the analytical model was shown through comparisons with experimental results.

Bahia et al. (1981) investigated the strength of tee-stubs and beam-to-column

extended end-plate connections. The end-plate and column flange strengths were

determined using yield line theory. The bolt forces including prying action were

shown to depend on the areas of contact between the end-plate and column.

Kennedy et al. (1981) introduced a method for predicting bolt forces with prying

action in end-plate connections. The prediction equations were obtained by

assuming an end-plate to be analogous to a split-tee connection. Kennedy et al.

assume that a tee-stub or a flange plate goes through three stages of behavior as

the load applied to the plate increases. The first stage of behavior, at lower loads, is

thick plate behavior. At this stage, no plastic hinges have formed in the plate and

prying forces are assumed to be zero. The second stage of plate behavior occurs as

two plastic hinges form at the intersections of the plate centerline and each web

Literature Review 9

face. The yielding of the plate marks the thick plate limit and indicates the onset of

intermediate plate behavior. The prying force in this stage is between zero and

maximum bolt prying force. The final stage of plate behavior, thin plate behavior, is

marked by the formation of a second set of hinges at the bolt line. The prying force

after thin plate behavior is initiated is equal to the maximum prying force. Kennedy

et al. present equations which set thick and thin plate limits as a function of

geometric properties of the plate, yield stress values of the plate, and applied flange

force. Finally, bolt prying forces are calculated according to the type of plate

behavior determined.

Srouji et al. (1983a, 1983b) developed design methods for different end-plate

moment connection configurations. The end-plate thickness was determined using

yield line analysis. The bolt force predictions include the effects of prying, and were

based on the tee-stub analogy design method developed by Kennedy et al. (1981)

with a few modifications. Finite element analysis was used to establish stiffness

criteria. The analytical procedure was verified with experimental testing and good

correlation was observed. It was concluded that yield line analysis and the modified

Kennedy method accurately predict the end-plate strength and bolt forces.

Abolmaali et al. (1984) used finite element analysis to develop a design

methodology for the two bolt flush end-plate moment connection configuration.

Both 2-D and 3-D analyses were conducted to generate correlation coefficients.

Finite element 2-D analysis was used to generate regression equations for the

design of the connections. The results were adjusted by the correlation coefficients

to more closely match the experimental results.

Morrison et al. (1985) conducted an analytical study to develop a design method for

multiple row extended end-plates. The results were verified by full-scale testing.

The testing program involved the monotonic testing of six beam-to-beam

specimens, ranging from 30 in. to 62 in. in depth. The design methods derived and

verified by this testing include end-plate thickness requirements based on straight

yield-line analysis, as well as bolt force predictions. The method consists of finding a

Literature Review 10

thickness of the end plate based on strength. The thickness is then determined to

act as a thick, thin, or intermediate plate under a given load. The bolt forces,

including prying action, if present, are then determined using the modified Kennedy

method.

Aggarwal and Coates (1987) conducted fifteen experimental tests on four bolt

extended unstiffened end-plate moment connections. The specimens were tested

under static and dynamic loads. It was shown that the Australian and British

standards produced conservative end-plate and bolt strength predictions for the

test loading.

Morris (1988) reviewed the connection design philosophies adopted in the United

Kingdom and made practical recommendations and observations that are important

for designers. The importance of proper design and detailing of extended and flush

end-plate moment connections was emphasized.

Murray (1988) presented an overview of the past literature and design methods for

both flush and extended end-plate configurations, including column side limit

states. Design procedures, based on analytical and experimental research in the

United States, were presented.

Kukreti et al. (1990) used finite element modeling to conduct parametric studies to

predict the bolt forces and the end-plate stiffness of the eight bolt extended

stiffened end-plate moment connection. Regression analysis of the parametric

study data resulted in equations for predicting the end-plate strength, end-plate

stiffness, and bolt forces. The predictions were compared to experimental results

with reasonable correlation.

Murray (1990) presented design procedures for the four bolt unstiffened, four bolt

wide unstiffened and the eight bolt extended stiffened end-plate moment

connections. The end-plate design procedures were based on works of

Krishnamurthy (1978), Ghassemieh et al. (1983), and Murray and Kukreti (1988).


The column side procedures were based on works by Curtis and Murray (1989), and

Hendrick and Murray (1984).

Gebbeken et al. (1994) investigated the behavior of the four bolt unstiffened end-

plate connection using finite element analysis. The study emphasized modeling of

the non-linear material behavior and the contact between the end-plate and the

column flange or the adjacent end-plate. Comparisons between the finite element

analysis and experimental test results were made.

Borgsmiller (1995) presented a simplified method for the design of four flush and

five extended end-plate moment connection configurations. The bolt design

procedure was a simplified version of the modified Kennedy method to predict the

bolt strength including the effects of prying. The end-plate strength was determined

using yield line analysis. Fifty-two end-plate connection tests were analyzed and it

was concluded that the prying forces in the bolts become significant when ninety

percent of the end-plate strength is achieved. This established a threshold for the

point at which prying forces in the bolts can be neglected. If the applied load is less

man ninety percent of the plate strength, the end-plate is considered to be 'thick

and no prying forces are considered; when the applied load is greater than ninety

percent of the end plate strength, the end-plate is considered to be 'thin and the

prying forces are assumed to be at a maximum. This distinct threshold between

'thick and 'thin' plate behavior greatly simplified the bolt force determination

because only the case of no prying and maximum prying must be determined. Good

correlation with past test results was obtained using the simplified design

procedure.

Sherbourne and Bahaari (1997) developed a methodology based on three

dimensional finite element design, to analytically evaluate the moment rotation

relationships for moment end-plate connections. ANSYS 4.4 was the software

package used. The purpose for this research was to provide designers with a

method of determining stiffness for these connections. It was apparent at the time

that the ability of designers to produce a moment-rotation curve for moment end-


plate connections was limited. Because of advancements in computer technology,

Sherbourne and Bahaaris models included plate elements for the flange, webs, and

stiffeners of the column and beam, as well as taking into account the bolt shank,

nut, head of the bolt, and contact regions. However, bolt pre-stressing was not

included. It was determined that the behavior of a moment end-plate throughout

an entire loading history, up to and including failure, can be feasibly and accurately

modeled by three-dimensional finite element analysis. This is particularly useful

when one of the plates in contact, either the column flange or the end plate, is thin.

The analysis of such a plate is inaccurate when using two-dimensional models. An

additional advantage to the use of the three-dimensional model is the separation of

the column, bolt, plate, and beam stiffness contributions to the overall behavior of

the connection.

Troup et al. (1998) presented a paper describing finite element modeling of bolted

steel connections. ANSYS was used for this study, which included an extended

moment end-plate model as well as a tee-stub model. The model utilized a bilinear

stress-strain relationship for the bolts. Also, special contact elements were used

between the end-plate and the column flange for the extended end-plate model,

and between the tees for the tee model. By using the contact elements between

the contact surfaces of the models, the geometric non-linearities that are present

between the surfaces as separation occurs due to increased load can be realistically

modeled.

Both models were calibrated with experimental test data to show excellent

correlation between analytical and experimental stiffness. Bolt forces were also

analyzed. It was found that for the simple four-bolt arrangement about the tension

flange, the tee design prediction is accurate. However, for more complex bolt

patterns, the distribution of prying forces is not as clear. Troup, et al. (1998)

concluded the following:

1. Tee-stub analogy is a useful benchmark problem providing an indication

of the performance of analysis techniques.


2. Shell elements are more accurate for modeling beam and column

sections. Thick endplate design provides additional rotational stiffness and

moment capacity but may result in bolt fracture.

3. Thin end plates provide enough deformation capacity to allow semi-rigid

connection design, but may result in excessive deflection.

4. The moment capacity prediction of Eurocode 3 has been shown to be

reasonable, but conservative, for simple end-plate bolt configurations. The

code is inaccurate when analyzing more complicated bolt arrangements. If

these inaccuracies do not lead to bolt failure, they are acceptable.

Mays (2000) used finite element analysis to develop a design procedure for an

unstiffened column flange and for the sixteen bolt extended stiffened end-plate

moment connection. In addition, finite element models were developed and

comparisons with experimental results for the four bolt extended unstiffened, eight

bolt extended stiffened, and the four bolt wide unstiffened end-plate moment

connections were made. Good correlation with experimental results was obtained.

2.3 REMARKS

Although a great amount of research work has been done on the subject of end-

plate connections, regrettably all the research work is not readily useful and there is

only scantly available textbook reference. Furthermore, it appears that no definite

guidelines are available to assist the designer. Therefore, there is great scope for

study in pursuit of the development of a decisive guideline.

CHAPTER 3

METHODOLOGY FOR FINITE ELEMENT ANALYSIS

3.1 INTRODUCTION

Finite element calculations more and more replace analytical methods, especially if

problems have to be solved which are adjusted to specific tasks. Finite element

modeling can be used to accurately predict the behavior of end-plate moment

connections (Mays, 2000).

A finite element model has been developed to describe the behavior of the joint in

a beam-to-beam extended end-plate moment connection. Apart from an exact

geometry modeling, the description of the material behavior of all components is of

essence for the quality of the performed analysis. This applies to finite element

analytical models as well as to numerical methods. This enables the accurate

simulation of the elasto-plastic behavior of steel.

The actual work regarding the finite element modeling of the beam-to-beam

extended end-plate moment connection has been described in detail in this

chapter.

3.2 FINITE ELEMENT PACKAGES

A large number of finite element analysis computer packages are available now.

They vary in degree of complexity and versatility. The names of few such packages

are:

ANSYS 10.0 AMaze Catalog PROKON STARDYN

DIANA ROBOTICS FEMSKI ALGOR

MICROFEAP STRAND MARC LUSAS

STADD PRO ETABS NASTRAN SAMTECH

ABAQUS CADRE AxisVM SAP

Methodology for Finite Element Analysis 15

Of these packages ANSYS 10.0 has been chosen for its versatility and relative ease of

use. ANSYS is a general purpose finite element modeling package for numerically

solving a wide variety of structural as well as mechanical problems. These problems

include: static and dynamic structural analysis (both linear and non-linear), heat

transfer and fluid problems, as well as acoustic and electromagnetic problems.

ANSYS finite element analysis software enables engineers to perform the following

the tasks:

Build computer models or CAD models of structures, products, components and systems.

Apply operating loads and other design performance conditions. Study the physical responses, such as stress levels, temperature

distributions, or the impact of electromagnetic fields.

Optimize a design early in the development process to reduce production costs.

Do prototype testing in environments where it otherwise would be undesirable or impossible (for example, biomedical applications).

The ANSYS program has a comprehensive graphical user interface (GUI) that gives

users easy, interactive access to program functions, commands, and documentation

and reference material. An intuitive menu system helps users navigate through the

ANSYS program. Users can input data using a mouse, a keyboard, or a combination

of both.

3.3 TYPES OF ANALYSIS ON STRUCTURES

Structures can be analyzed for small deflection and elastic material properties

(linear analysis), small deflection and plastic material properties (material

nonlinearity), large deflection and elastic material properties (geometric

nonlinearity), and for simultaneous large deflection and plastic material properties.

By plastic material properties, we mean that the structure is deformed beyond yield

of the material, and the structure will not return to its initial shape when the


applied loads are removed. The amount of permanent deformation may be slight

and inconsequential, or substantial and disastrous.

By large deflection, we mean that the shape of the structure has changed enough

that the relationship between applied load and deflection is no longer a simple

straight-line relationship. This means that doubling the loading will not double the

deflection. The material properties, however, can still be elastic.

In the present study, in order to analyze the bolted extended end-plate moment

connection, large deflection and plastic material properties (material nonlinearity)

are used. Though it costs more time, it gives a more realistic result.

3.4 FINITE ELEMENT MODELING OF THE PROBLEM

A typical situation where end-plate type beam splice is used is shown in Figure 3.1.

It consists of two beams, joined in a beam-to-beam extended end-plate moment

connection, in order to cover a large span. For any load applied on the structure the

beam will sag, which will lead to the development of moments. The joint should be

adequate to transfer this moment.

Figure 3.1 General sketch of a structure with an end-plate type beam splice


Figure 3.2 General 3-D Sketch of the problem

For finite element analysis of the moment capacity, a part of the beam on one side

of the joint is modeled with appropriate load and boundary connections. A 3-D

sketch of the problem is shown in Figure 3.2. The finite element analysis is not of

the whole structure, but of the connection with a part of the beam.

The problem as shown in figure 3.2 consists of a total of 6 bolts. 3 bolts are above

the top flange, while 3 are below the bottom flange. The typical 3D mesh of the

problem is shown in figure 3.3.

Figure 3.3 Typical 3-D Mesh of the finite element problem

Separate elements have been used for the modeling of the beam flange, beam web,

end-plate, load plate, bolts and contact surface. SHELL181 has been used for the


beam flange, beam web, end-plate and load plate. COMBIN39 has been used for the

contact surface and the bolts. The modeling of the contact surface is essential to

simulate the behavior between the two end-plates in a beam-to-beam end-plate

type splice. A load plate has been used in order to avoid the local yielding of the

beam, at the point of the application of load.

3.4.1 MODELING OF THE BEAM FLANGE, BEAM WEB, END-PLATE AND LOAD PLATE

The behavior of the beam flange, beam web, end-plate and load plate is described

by SHELL181 element.

SHELL181 - 4-Node Finite Strain Shell

SHELL181 is suitable for analyzing thin to moderately-thick shell structures. It is a 4-

node element with six degrees of freedom at each node: translations in the x, y, and

z directions, and rotations about the x, y, and z-axes as shown in Figure 3.4.

Figure 3.4 SHELL181 - 4-Node Finite Strain Shell

SHELL181 is well-suited for linear, large rotation, and/or large strain nonlinear

applications. Change in shell thickness is accounted for in nonlinear analyses. In the

element domain, both full and reduced integration schemes are supported.

SHELL181 accounts for follower (load stiffness) effects of distributed pressures.

Input Data

The geometry, node locations, and the coordinate system for this element are

shown in Figure 3.4. The element is defined by four nodes: I, J, K, and L. The


element formulation is based on logarithmic strain and true stress measures. The

element kinematics allow for finite membrane strains (stretching). However, the

curvature changes within a time increment are assumed to be small. To define the

thickness and other information, either real constants or section definition can be

used.

A summary of the element input data is given in Table 3.1.

Table 3.1 SHELL181 Input Summary

Nodes I, J, K, L

Degrees of Freedom UX, UY, UZ, ROTX, ROTY, ROTZ

Real Constants TK(I), TK(J), TK(K), TK(L), THETA, ADMSUA

Surface Loads Pressures face 1 (I-J-K-L) (bottom, in +N

direction), face 2 (I-J-K-L) (top, in -N direction),

face 3 (J-I), face 4 (K-J), face 5 (L-K), face 6 (I-L)

Material Properties EX, EY, EZ, PRXY, PRYZ, PRXZ, or NUXY, NUYZ,

NUXZ, ALPX, ALPY, ALPZ, DENS, GXY, GYZ, GXZ

Special Features Plasticity, Hyperelasticity, Viscoelasticity,

Viscoplasticity, Creep, Stress stiffening, Large

deflection, Large strain, Initial stress import, Birth

and death,

Thickness Definition Using Real Constants

The thickness of the shell may be defined at each of its nodes. The thickness is

assumed to vary smoothly over the area of the element. If the element has a

constant thickness, only TK(I) needs to be input. If the thickness is not constant, all

four thicknesses must be input.


Material Properties

SHELL181 can be associated with linear elastic, elastoplastic, creep, or hyperelastic

material properties. Only isotropic, anisotropic, and orthotropic linear elastic

properties can be input for elasticity. The kinematic hardening plasticity models can

be invoked with BKIN (bilinear kinematic hardening). Invoking plasticity assumes

that the elastic properties are isotropic.

Assumptions and Restrictions

Zero area elements are not allowed (this occurs most often whenever the elements are not numbered properly).

Zero thickness elements or elements tapering down to a zero thickness at any corner are not allowed (but zero thickness layers are allowed).

In a nonlinear analysis, the solution is terminated if the thickness at any integration point that was defined with a nonzero thickness vanishes (within

a small numerical tolerance).

Using this element in triangular form is not recommended. No slippage is assumed between the element layers. Shear deflections are

included in the element.

Stress stiffening is always included in geometrically nonlinear analyses (NLGEOM,ON). It is ignored in geometrically linear analyses (NLGEOM,OFF)

when specified by SSTIF,ON. Prestress effects can be activated by the PSTRES

command.

3.4.2 MODELING OF THE BOLTS AND CONTACT SURFACE

The behavior of the bolts and the contact surface is described by COMBIN39 spring

element.

COMBIN39 Nonlinear Spring

COMBIN39 is a unidirectional element with nonlinear generalized force-deflection

capability that can be used in any analysis. The element has longitudinal or torsional

capability in 1-D, 2-D, or 3-D applications. The longitudinal option is a uniaxial


tension-compression element with up to three degrees of freedom at each node:

translations in the nodal x, y, and z directions. No bending or torsion is considered.

The element has large displacement capability for which there can be two or three

degrees of freedom at each node.

Figure 3.5 COMBIN39 Nonlinear Spring

The geometry, node locations, and the coordinate system for this element are

shown in Figure 3.5. The element is defined by two node points and a generalized

force-deflection curve. The points on this curve represent force (or moment) versus

relative translation (or rotation) for structural analyses. The force-deflection curve

should be input such that deflections are increasing from the third (compression) to

the first (tension) quadrants. The last input deflection must be positive. If the force-

deflection curve is exceeded, the last defined slope is maintained.

A summary of the element input is given in Table 3.2.

Table 3.2 COMBIN39 Input Summary

Nodes I, J

Degrees of Freedom UX, UY, UZ, ROTX, ROTY, ROTZ, PRES, or TEMP.

Real Constants D1, F1, D2, F2, D3, F3, D4, F4, ..., D20, F20

Material Properties DAMP

Special Features Nonlinear, Stress stiffening, Large displacement


Assumptions and Restrictions

For KEYOPT(4) = 0, the element has only one degree of freedom per node. This degree of freedom defined by KEYOPT(3), is specified in the nodal

coordinate system and is the same for both nodes. KEYOPT(3) also defines

the direction of the force.

The element assumes only a 1-D action. Nodes I and J may be anywhere in space.

The element is defined such that a positive displacement of node J relative to node I tends to put the element in tension.

For KEYOPT(4) 0, the element has two or three displacement degrees of freedom per node. Nodes I and J should not be coincident, since the line

joining the nodes defines the direction of the force.

The element is nonlinear and requires an iterative solution. Loading and unloading should occur gradually.

The nonlinear behavior of the element operates only in static and nonlinear transient dynamic analyses.

The real constants for this element can not be changed from their initial values.

3.4.3 NONLINEAR STRESS-STRAIN MATERIALS

The behavior of nonlinear stress-strain materials can be simulated accurately in

ANSYS. Bilinear kinematic hardening is one such option to describe such material

behaviors.

Bilinear Kinematic Hardening (BKIN)

This is a rate-independent plasticity option which requires a uniaxial stress-strain

curve to be input. Elastically isotropic (EX = EY = EZ) materials are also required.

Required values that are not included in the data table are assumed to be zero. If

the data table is not defined, the material is assumed to be linear. BKIN assumes the

total stress range is equal to twice the yield stress, so that the Bauschinger effect is

included. BKIN may be used for materials that obey von Mises yield criteria (which


includes most metals). The material behavior is described by a bilinear total stress-

total strain curve starting at the origin and with positive stress and strain values.

The initial slope of the curve is taken as the elastic modulus of the material. At the

specified yield stress (C1), the curve continues along the second slope defined by

the tangent modulus, C2 (having the same units as the elastic modulus). The

tangent modulus cannot be less than zero nor greater than the elastic modulus.

3.5 PARAMETRIC STUDY OF THE PROBLEM

The parameters used in the finite element problem are shown in Table 3.3.

Table 3.3 Various Parameters

Parameter Value(s)

Beam Height, hb 150mm to 600mm @ 75mm increment

Average Value 375mm

Flange Width, bf 150mm to 500mm @ 50mm increment

Average Value 300mm

Flange Thickness, tf 6.25mm to 31.25mm @ 3.125mm increment

Average Value 18.75mm

Web Thickness, tw 3.125mm to 25mm @ 3.125mm increment

Average Value 12.5mm

Length of beam portion 2000mm

Yield Stress of Steel 275 Mpa

Steel Modulus of Elasticity 207000 MPa

Poissons Ratio 0.25

Number of Bolts Total 6

3 above top flange, 3 below bottom flange

Bolt Diameter 25mm

Load Plate Thickness 75mm


The parametric study of the beam height, flange width, flange thickness and web

thickness is carried out. In the parametric study of a given variable, only the

dimension of the concerned variable is changed, while the other variables are kept

constant at their respective average values. For example, in the parametric study

of the beam height, the beam height is varied from 150mm to 600mm at an

increment of 75mm, while the flange width, flange thickness and web thickness are

kept at 300mm, 18.75mm and 12.5mm respectively. The objective of the

parametric study is to determine the thickness of the end-plate and the tensions in

the bolts for a particular dimension of beam.

3.6 MESHING

3.6.1 MESHING OF THE BEAM FLANGE AND BEAM WEB

Figure 3.6 The finite element mesh has more intense meshing near the end-plate

SHELL181 is used to model the entire beam. Separate real constants are used for

the beam flange and web in order to account for different thicknesses. Bilinear

kinematic hardening (BKIN) option is used in order to describe the behavior of the

bilinear isotropic steel.

The meshing is done in such a way that the aspect ratio of the element is

reasonable. It can be seen in Figure 3.6 that more intense meshing is done near the

end-plate. This is because the effect of bending is greater in that region.


3.6.2 MESHING OF THE END-PLATE

SHELL181 is used to model the end-plate. BKIN option is used in order to describe

the behavior of the bilinear isotropic steel.

The meshing is done in such a way to ensure that nodes exist at the desired

locations of the bolts, as shown in Figure 3.7.

Figure 3.7 Mesh of the end-plate

3.6.3 MESHING OF THE LOAD PLATE

The meshing of the load plate is identical to the meshing of the end-plate.

3.6.4 PROPERTIES OF THE BOLTS

COMBIN39 link elements are used to simulate the behavior of bolts. In the

concerned problem, these link elements in position of bolts were assigned bolt

properties. That is, these elements can resist compression as well as tension.


Figure 3.8 shows the force-deflection behavior of bolts. The values of both Kc and Kt

are equal here. Kc and Kt represent the stiffness of the bolt and are calculated as

follows:

LAEKK tc

==

where, E = Youngs modulus of elasticity

A = bolt cross-sectional area

L = length of bolt

Figure 3.8 Force-Deflection Behavior of the bolts

3.6.5 PROPERTIES OF THE CONTACT ELEMENT

Contact elements are used to describe the behavior of two end-plates in contact

with each other. The same COMBIN39 spring element is used for this purpose. The

nodes of the end-plate are extruded along the axis of the beam, in the opposite

direction of the beam, to generate the COMBIN39 contact elements. The stress-

strain relationship for the element is described so that it can resist compression but

is very weak in tension. The element develops compression normal to the plane of

the end-plate.

Figure 3.9 shows the force-deflection behavior of contact springs. The value of Kc is

large while that of Kt is very small. The value of Kc is taken as 100 times the bolt


stiffness, as calculated in the previous section. Kt is arbitrarily assigned a value of

0.0001.

Figure 3.9 Force-Deflection behavior of the contact springs

3.7 BOUNDARY CONDITIONS

3.7.1 RESTRAINT

The free ends of the COMBIN39 link elements, which simulate the contact surface,

are restrained in all directions. The other ends of the COMBIN39 link elements are

attached to the end-plate. Now, COMBIN39 does not have any bending capability.

Therefore, to protect against sliding, one node of the end-plate is restrained in the

vertical direction and two nodes are restrained in the horizontal direction. The

mesh of the structure with the COMBIN39 elements clearly visible is shown in

Figure 3.10.

Figure 3.10 Mesh showing COMBIN39 link elements used as contact elements


3.7.2 LOAD

A point load is applied at the load plate end of the beam. The point load is applied

at the intersection of the top flange of the beam with the web as shown in Figure

3.11.

Figure 3.11 Point of application of load

The magnitude of the load is such that it ensures that yielding of steel occurs. This is

of importance for determining the corresponding thickness of end-plate for a

particular dimension of beam. The load to be applied is determined as follows.

The end-plate with the section of the beam is shown in Figure 3.12.

Figure 3.12 End-plate with section of the beam


Where,

bf = flange width

bh = beam height

tf = flange thickness

tw = web thickness

c = distance of bolt centre-line from top of flange

The plastic moment capacity of the beam section is determined by considering the

stress distribution as in Figure 3.13.

Figure 3.13 Stress distribution for plastic moment

Let h be the centre to centre distance between the two flanges.

22 fh

tbh =

Thus, the plastic moment capacity is as follows:

2)42

(2)2

( += hfhthftbM ywyffp

Once the plastic moment capacity is known, the equivalent force, P, to create that

moment for a moment arm of the length of the beam portion, L, is

LM

P p=


3.8 SOLUTION METHOD

A number of solution tools are available for the solution of nonlinear structural

problems. For the present problem Arc-Length Method has been used.

3.8.1 ARC-LENGTH METHOD

The arc-length method is suitable for nonlinear static equilibrium solutions of

unstable problems. Applications of the arc-length method involve the tracing of a

complex path in the load-displacement response into the buckling/post buckling

regimes. The arc-length method uses the explicit spherical iterations to maintain

the orthogonality between the arc-length radius and orthogonal directions. It is

assumed that all load magnitudes are controlled by a single scalar parameter (i.e.,

the total load factor). As the displacement vectors and the scalar load factor are

treated as unknowns, the arc-length method itself is an automatic load step

method. For problems with sharp turns in the load-displacement curve or path

dependent materials, it is necessary to limit the arc-length radius using the initial

arc-length radius. During the solution, the arc-length method will vary the arc-

length radius at each arc-length substep according to the degree of nonlinearities

that is involved. The convergence of the arc-length method at a particular substep is

shown in Figure 3.14.

Figure 3.14 Arc-Length Approach with Full Newton-Raphson Method


3.8.2 CONVERGENCE OF THE SOLUTION

The objective of the finite element study is to determine the end-plate thickness for

a particular beam dimension. Ideally, the end-plate should be thick enough so that

the failure of the structure due to overloading is initiated by the yielding of the

beam; the end-plate should not yield. For thin end-plate thicknesses the failure of

the structure will be initiated by yielding of the end-plate. The required end-plate

thickness is that thickness for which the failure is just initiated by the yielding of the

beam. This thickness can be determined by a trial and error solution involving the

force-deflection relationship of the structure.

Figure 3.15 Typical Force-Deflection curves for various end-plate thicknesses

It can be seen from the force-deflection curves in Figure 3.15 that as the thickness

of the end-plate is increased gradually, the maximum load capacity of the structure

increases. However beyond a certain limit, the load capacity does not increase

anymore. It can be seen that for the present example, the maximum load capacity

does not increase beyond a thickness of 32mm. Thus, for this case the required end-

plate thickness is 32mm.


Once the end-plate thickness has been determined, the corresponding bolt tensions

can be determined.

3.8.3 TYPICAL DEFLECTED SHAPES AND TYPICAL STRESS CONTOURS

Figure 3.16 Typical deflected shape of problem

Figure 3.17 Typical close-up deflected shape of the joint


Figure 3.18 Typical fibre stress of beam

Figure 3.19 Typical vertical fibre stress of end-plate


Figure 3.20 Typical horizontal fibre stress of end-plate

Figure 3.21 Typical vertical fibre stress of end-plate


Figure 3.22 Typical axial force diagram of bolts

CHAPTER 4

PROPOSED ANALYTICAL FORMULATION AND

DISCUSSION OF RESULTS

4.1 INTRODUCTION

Detailed modeling and solution procedure of the extended end-plate moment

connection is described in Chapter 3. In this chapter, an analytical formulation of

the problem is proposed. This is followed by a description and discussion of the

results of the finite element analysis of the problem with supporting graphs.

4.2 PROPOSED ANALYTICAL FORMULATION

4.2.1 DESCRIPTION OF PROBLEM AND OBJECTIVE OF FORMULATION

The description of the problem was given in Article 3.4 of Chapter 3. A typical

situation where end-plate type beam splice is used was shown in Figure 3.1. A 3-D

sketch of the problem was shown in Figure 3.2.

A general 2-D sketch of the problem is shown in Figure 4.1. It consists of a bolted

extended end-plate moment connection along with the portion of a beam.

Figure 4.1 2-D sketch of the model.

Proposed Analytical Formulation and Discussion of Results 37

The objective of the analytical formulation is (1) to determine the thickness of the

end-plate, t, at which plastic hinges will just form in the end-plate; (2) to determine

the corresponding bolt forces.

4.2.2 DEVELOPMENT OF ANALYTICAL FORMULATION OF END-PLATE THICKNESS

Let us begin by first considering the deflected shape of the problem due to a

deformation at the end of the beam-portion as shown in Figure 4.2. In the

analytical formulation it is assumed that the bolts are strong enough to resist the

tensile forces they are subjected to. Only, the failure of the end-plate is considered.

Thus, for a large enough , plastic hinges will form in the end-plate. Formation of

plastic hinges implies the initiation of failure of the end-plate.

Figure 4.2 Deflected shape of the problem due to deformation at the end of the beam-portion.

It can be seen that plastic hinges form in the end-plate - at the top bolt line, just

above the top flange of the beam and just below the bottom flange of the beam.

The formation of plastic hinges and thus, yield lines are illustrated more clearly in

Figure 4.3.

Figure 4.3 Formation of yield lines in the end-plate.


Let us consider the free body diagram of the portion of the end-plate between the

top bolt centerline and the top portion of the top flange of the beam, as shown in

Figure 4.4. The height of this portion is c. Since, the top and bottom boundaries of

the segment coincides with two yield lines, the moments acting on both the top and

bottom is Mp. Thus, the force, F can easily be calculated as Mp/c.

Figure 4.4 Free body diagram of the portion of the end-plate between the top bolt centerline and

the top portion of the top flange of the beam.

Let us now consider the free body of the problem without the extended portions of

the end-plate above the top beam flange and below the bottom beam flange, as

shown in Figure 4.5. It can be seen that the deformation has been replaced by an

equivalent force P at the end. The two are related by the equation,

EIPL3

3

= (1)

Figure 4.5 Free body of the problem without the extended portions of the end-plate.


As plastic hinges form in the end-plate just above the top flange and just below the

bottom flange of the beam, the moments at these points are Mp. The force P at the

end produces a moment PL. Thus, the entire beam portion can be replaced with a

moment, Mbeam that acts on the end-plate, as shown in Figure 4.6.

Figure 4.6 Free body of the portion of the end-plate without the extended portions.

In order to determine the value of Mp, the summation of moments about A, is

taken.

)2(

)2(

02

020

+=

=+

=+

=+

=

cbMMp

McbMp

MMbc

MMMbF

M

h

beam

beamh

beamphp

beamph

A

Another approach in determining Mp involves considering the stress distribution on

the end-plate thickness due to the plastic moment. This is shown in Figure 4.7.

The plastic moment capacity, Mp can now be expressed in terms of the yield stress,

fy, the end-plate thickness, t and the width of the end-plate, b.

4

242

2btfM

bttfM

yp

yp

=

=

(2)

(3)


Figure 4.7 Stress distribution on the end-plate due to Mp

Combining equations (2) and (3), a general expression for the end-plate thickness is

determined,

)2(

4

4)2(

2

+=

=+

cbbf

Mt

btf

cbM

hy

beam

y

h

beam

The term Mbeam in equation (4) should be the plastic moment capacity of the beam

section. This ensures the maximum possible contribution of moment from the

beam. Thus, the beam will then transfer its maximum capacity to the end-plate.

Mbeam can be determined by considering the stress distribution on the beam section

for complete yielding, as shown in Figure 4.8.

{ }

+=

+

=

2

2)(

22

22

2)22

(

fh

ywfhyffbeam

fh

yfh

wfh

yffbeam

tbfttbftbM

tb

ftbttbftbM

(4)

(5)


Figure 4.8 Stress distribution on the beam section due to complete yielding

Combining equations (4) and (5), a generalized expression for the end-plate

thickness for a particular beam section and end-plate width can be determined.

{ }

)2(

2)(4

2

+

+

=

cbbf

tbfttbftb

th

y

fh

ywfhyff

Theoretically, an end-plate thickness greater than t, ensures that the end-plate is

thick enough to be safe from the development of any yield stress, i.e., the beam will

start yielding before the end-plate. A thickness less than t, means that the end-plate

will yield, before the yielding of the beam.

4.2.3 DETERMINATION OF BOLT TENSILE FORCE

In order to determine the bolt forces, let us consider the distribution of yield lines

as in Figure 4.3. The yield line distribution implies equal bolt forces in the top 3 bolts

and equal bolt forces in the bottom 3 bolts. Considering the force in a particular bolt

to be Fb, the moment applied on the beam section to be Mapplied, and the center to

center distance of the top and bottom bolt rows to be hbolt, the bolt tension can be

determined as follows,

bolt

appliedb h

MF =

31

(6)

(7)


The term hbolt can be determined from the geometry of the end-plate section,

cbh hbolt 2+= (8)

Mapplied can be determined as PappliedL for any point load, Papplied, applied at the end

of the beam portion with a moment arm of the length of the beam portion, L.

4.3 DESCRIPTION AND DISCUSSION OF RESULTS

The sample problem under investigation with the variable data was described in

Section 3.4 of Chapter 3. The results obtained from the finite element analysis and

the comparison of the results with the proposed analytical formulation is described

in the following articles.

4.3.1 EFFECT ON END-PLATE THICKNESS

The effects of the changes of different beam parameters on the thickness of end-

plate are shown in the curves in Figure 4.9 through Figure 4.12. The beam

parameters varied in the study are the beam height, the flange width, the flange

thickness and the web thickness.

The end-plate thickness has an increasing trend with the increases in beam height,

flange thickness and web thickness as can be seen in Figure 4.9, Figure 4.11 and

Figure 4.12. This is because increasing any one of the three parameters results in an

increased moment capacity of the beam. Thus, to counter the increase in moment,

a greater end-plate thickness is required.

The increase in flange width does not have any noticeable effect on the end-plate

thickness as can be seen in Figure 4.10. This is because, though the moment

capacity of the beam increases with the increase in flange width, the end-plate

width is also increasing by the same amount. Thus, no further increase in thickness

is necessary to take the additional moment.

The results from the finite element analysis (FEA) closely agree with the results of

the proposed analytical formulation. For most of the values of the different beam


parameters, the end-plate thickness from the finite element analysis is less than the

corresponding end-plate thickness obtained from the proposed analytical

formulation. Thus, the proposed analytical formulation gives conservative results

with respect to the finite element analysis.

4.3.2 EFFECT ON BOLT TENSION

The effects of the changes of different beam parameters on the bolt tensile force

are shown in the curves in Figure 4.13 through Figure 4.16. The same beam

parameters, i.e. the beam height, the flange width, the flange thickness and the

web thickness are varied in the study.

The bolt forces show an increasing trend with the increases in the different beam

parameters, which can be attributed to increases in moment capacity of the beam

section. However, while the proposed analytical formulation gives equal values to

middle and end bolt forces, the finite element study gives distinctly different values

for the same. The finite element study gives middle bolt forces about twice in

magnitude than the edge bolt forces. Thus, the proposed analytical formulation

gives conservative results for the edge bolts, but less than adequate values for the

middle bolts.

The effect of the different beam parameters on the summation of bolt forces are

shown in the curves in Figure 4.17 through Figure 4.20. The summation of bolt

forces from both the finite element analysis and the proposed analytical

formulation show the expected increasing trends. The proposed analytical

formulation gives higher values compared to the finite element analysis. Thus, the

proposed analytical formulation can be said to give conservative results for the

summation of bolt forces.


0

5

10

15

20

25

30

35

40

45

50

75 150 225 300 375 450 525 600 675

Beam Height, hb (mm)

End-

Plat

e Th

ickn

ess,

t (m

m)

Present Finite Element Analysis

Proposed Analytical Formulation

Figure 4.9 Change of end-plate thickness with beam height

0

5

10

15

20

25

30

35

40

45

50

0 50 100 150 200 250 300 350 400 450 500 550

Flange Width, bf (mm)

End-

Plat

e Th

ickn

ess,

t (m

m)



Figure 4.10 Change of end-plate thickness with flange width


0

10

20

30

40

50

60

3.125 6.25 9.375 12.5 15.625 18.75 21.875 25 28.125 31.25 34.375

Flange Thickness, tf (mm)

End-

Plat

e Th

ickn

ess,

t (m

m)



Figure 4.11 Change of end-plate thickness with flange thickness

0

5

10

15

20

25

30

35

40

45

50

3.125 6.25 9.375 12.5 15.625 18.75 21.875 25 28.125

Web Thickness, tw (mm)

End-

Plat

e Th

ickn

ess,

t (m

m)



Figure 4.12 Change of end-plate thickness with web thickness


Figure 4.13 Effect of change of beam height on bolt force

Figure 4.14 Effect of change of flange width on bolt force


Figure 4.15 Effect of change of flange thickness on bolt force

Figure 4.16 Effect of change of web thickness on bolt force


Figure 4.17 Effect of beam height on summation of bolt forces

Figure 4.18 Effect of flange thickness on summation of bolt forces


Figure 4.19 Effect of web thickness on summation of bolt forces

Figure 4.20 Effect of flange width on summation of bolt forces

CHAPTER 5

CONCLUSION

5.1 GENERAL

The thesis originated with the aim to develop a procedure for determining the

appropriate end-plate thickness, and the corresponding bolt tensile forces, for a

bolted extended end-plate moment connection. The study is expected to generate a

reasonable solution of the focused problem.

The study was approached from two sides:

A theoretical analytical formulation of the problem was developed. A finite element analysis of the problem under certain parametric conditions

was carried out.

After the completion of the analysis, curves were drawn in order to compare the

two approaches, and to ascertain precisely the effect of various parameters on end-

plate thickness and bolt tensile force.

5.2 FINDINGS

The following conclusions may be drawn from the study:

The beam height, flange thickness and web thickness are the parameters studied to have significant effect on the magnitude of the end-plate

thickness. The end-plate thickness tends to increase with the increase of

any of the mentioned parameters.

The flange width does not have any effect on the end-plate thickness. The beam height, flange thickness, web thickness and flange width are the

studied parameters to have a significant effect on the bolt tensile force. The

bolt tension tends to increase with the increase of any of the four

parameters.

Conclusion 51

The finite element study establishes middle bolt tension higher than the edge bolt tension.

The proposed analytical formulation generally gives acceptable results on the conservative side compared to the finite element analysis of the

problem. Therefore, the suggested formulation to determine end-plate

thickness and bolt tension may be used for design.

5.3 GUIDELINE FOR END-PLATE THICKNESS AND BOLT TENSION

In view of the acceptable but conservative nature of the proposed analytical

formulation, the proposed formulas for determining end-plate thickness and bolt

tension can be said to be satisfactory for application in design of steel structures.

5.4 SCOPE FOR FUTURE INVESTIGATION

The following recommendations for future research work may be suggested:

In the present study three bolts were considered in each of the two extended portions of the end-plate. The effect of two bolts and greater than

three bolts can be studied.

The present study considered bolts only in the extended portion of the end-plate. The effect of bolts on the inside portion of the end-plate can be

studied.

The effect of double rows of bolts can be investigated. The effect of stiffeners on the end-plate thickness and bolt tension can be

studied.

The shear capacity, and the torsional capacity of the connection can also be studied along with the moment capacity.

The end-plate connection can be investigated for different sections of beam, e.g. L section, C section, etc.

References 52

REFERENCES

Abolmaali, A., Kukreti, A.R. and Murray, T.M. (1984). "Finite Element Analysis of Two Tension Bolt Flush End-Plate Connections," Research Report No. FSEL/MBMA 84-01, Fears Structural Engineering Laboratory, School of Civil Engineering and Environmental Science, University of Oklahoma, Norman, Oklahoma.

Aggarwal, A.K. and Coates, R.C. (1987). "Strength Criteria for Bolted Beam-Column Connections," Journal of Constructional Steel Research, Elsevier Applied Science, 7(3), 213-227.

Bahia, C.S., Graham, J. and Martin, L.H. (1981). "Experiments on Rigid Beam to Column Connections Subject to Shear and Bending Forces," Proceedings of the International Conference: Joints in Structural Steelwork: The Design and Performance of Semi-Rigid and Rigid Joints in Steel and Composite Structures and Their Influence on Structural Behaviour, Teesside Polytechnic, Middlesbrough, Cleveland, England, April 6-9, 1981, 6.37-6.56.

Borgsmiller, J.T. (1995). Simplified Method For Design of Moment End-Plate Connections, Master of Science Thesis, Virginia Polytechnic Institute and State University, Blacksburg, Virginia.

Curtis, L.E. and Murray, T.M. (1989). "Column Flange Strength at Moment End-Plate Connections," Engineering Journal, AISC, 26(2), 41-50.

Disque, R.O. (1962). "End Plate Connections," Proceedings of the 1962 AISC National Engineering Conference, Columbus, OH, April 12-13, 1962, AISC, 30-37.

Douty, R.T. and McGuire, W. (1963). "Research on Bolted Moment Connections - A Progress Report," Proceedings of the 1963 AISC National Engineering Conference, Tulsa, OK, April 24-26, 1963, AISC, 48-55.

Douty, R.T. and McGuire, W. (1965). "High Strength Bolted Moment Connections," Journal of the Structural Division, ASCE, 91(2), 101-128.

Gebbeken, N., Rothert, H. and Binder, B. (1994). "On the Numerical Analysis of Endplate Connections, Journal of Constructional Steel Research, Elsevier Applied Science, 30(1), 177-196.

Ghassemieh, M., Kukreti, A.R. and Murray, T.M. (1983). "Inelastic Finite Element Analysis of Stiffened End-Plate Moment Connections," Research Report No. FSEL/MBMA 83-02, Fears Structural Engineering Laboratory, School of Civil Engineering and Environmental Science, University of Oklahoma, Norman, Oklahoma.

Green, P.S., Sputo, T. and Veltri, P. Connections Teaching Toolkit, A Teaching Guide for Structural Steel Connections, AISC.

References 53

Hendrick, A. and Murray, T.M. (1984). "Column Web Compression Strength at End-Plate Connections," Engineering Journal, AISC. 21(3), 161-169.

Johnson, L.G., Cannon, J.C. and Spooner, L.A. (1960). "High Tensile Preloaded Bolted Joints for Development of Full Plastic Moments," British Welding Journal, 7, 560-569.

Kennedy, N.A., Vinnakota, S. and Sherbourne, A.N. (1981). "The Split-Tee Analogy in Bolted Splices and Beam-Column Connections," Proceedings of the International Conference: Joints in Structural Steelwork: The Design and Performance of Semi-Rigid and Rigid Joints in Steel and Composite Structures and Their Influence on Structural Behaviour, Teesside Polytechnic, Middlesbrough, Cleveland, England, April 6-9, 1981, 2.138-2.157.

Krishnamurthy, N. (1978). "A Fresh Look at Bolted End-Plate Behavior and Design," Engineering Journal, AISC, 15(2), 39-49.

Krishnamurthy, N. and Graddy, D.E. (1976). "Correlation Between 2- and 3-Dimensional Finite Element Analysis of Steel Bolted End-Plate Connections," Computers & Structures, Pergamon, 6(4-5/6), 381-389.

Kukreti, A.R., Ghassemieh, M. and Murray, T.M. (1990). "Behavior and Design of Large-Capacity Moment End Plates," Journal of Structural Engineering, ASCE, 116(3), 809-828.

Mann, A.P. (1968). "Plastically Designed Endplate Connections," Ph.D. Thesis, University of Leeds, England, 1968.

Mann, A.P. and Morris, L.J. (1979). "Limit Design of Extended End-Plate Connections, Journal of the Structural Division, ASCE, 105(3), 511-526.

Mays, T.W., (2000). Application of the Finite Element Method to the Seismic Design and Analysis of Large Moment End-Plate Connections, Ph.D. Dissertation, Virginia Polytechnic Institute and State University, Blacksburg, Virginia.

Morris, L.J. (1988). "Design Rules for Connections in the United Kingdom," Journal of Constructional Steel Research, Elsevier Applied Science, 10, 375-413.

Morrison, S.J., Astaneh-Asl, A. and Murray, T.M. (1985). "Analytical and Experimental Investigation of the Extended Stiffened Moment End-Plate Connection with Four Bolts at the Beam Tension Flange," Research Report No. FSEL/MBMA 85-05, Fears Structural Engineering Laboratory, School of Civil Engineering and Environmental Science, University of Oklahoma, Norman, Oklahoma.

References 54

Murray, T.M. (1988). "Recent Developments for the Design of Moment End-Plate Connections," Steel Beam-to-Column Building Connections, W.F. Chen, ed., Elsevier Applied Science, New York, 133-162.

Murray, T.M., (1990). AISC Design Guide Series 4, Extended End-Plate Moment Connections, American Institute of Steel Construction, Chicago.

Murray, T.M. and Kukreti, A.R. (1988). "Design of 8-Bolt Stiffened Moment End Plates," Engineering Journal, AISC, Second Quarter, 1988, 45-52.

Packer, J.A. and Morris, L.J. (1977). "A Limit State Design Method for the Tension Region of Bolted Beam-Column Connections," The Structural Engineer, Institution of Structural Engineers, 55(10), 446-458.

Ryan, Jr., J.C. (1999). Evaluation of Extended End-Plate Moment Connections Under Seismic Loading, M.Sc. Thesis, Virginia Polytechnic Institute and State University, Blacksburg, Virginia, 1999.

Sherbourne, A.N. and Bahaari, M.R. (1997). Finite Element Predictions of End Plate Bolted Connection Behavior. I: Parametric Study, Journal of Structural Engineering, Vol. 123, No. 2, pp. 157-164.

Srouji, R., Kukreti, A.R. and Murray, T.M. (1983a). "Strength of Two Tension Bolt Flush End-Plate Connections," Research Report No. FSEL/MBMA 83-03, Fears Structural Engineering Laboratory, School of Civil Engineering and Environmental Science, University of Oklahoma, Norman, Oklahoma.

Srouji, R., Kukreti, A.R. and Murray, T.M. (1983b). "Yield-Line Analysis of End-Plate Connections with Bolt Force Predictions," Research Report No. FSEL/MBMA 83-05, Fears Structural Engineering Laboratory, School of Civil Engineering and Environmental Science, University of Oklahoma, Norman, Oklahoma.

Sumner, E.A. (2003). Unified Design of Extended End-Plate Moment Connections Subject to Cyclic Loading, Ph.D. Thesis, Virginia Polytechnic Institute and State University, Blacksburg, Virginia, 2003.

Surtees, J.O. and Mann, A.P. (1970). End Plate Connections in Plastically Designed Structures, Conference on Joints in Structures, University of Sheffield, Sheffield, England, July 8-10, 1970, Paper A5, A501-A520.

Tarpy, Jr., T.S. and Cardinal, J.W. (1981). "Behavior of Semi-Rigid Beam-to Column End Plate Connections," Proceedings of the International Conference: Joints in Structural Steelwork: The Design and Performance of Semi-Rigid and Rigid Joints in Steel and Composite Structures and Their Influence on Structural Behaviour, Teesside Polytechnic, Middlesbrough, Cleveland, England, April 6-9, 1981, 2.3-2.25.

References 55

Troup, S., Xiao, R.Y., and Moy, S.S.J. (1998). Numerical Modelling of Bolted Steel Connections, Journal of Constructional Steel Research, Vol. 46, No. 1-3, Paper No. 362.

ANSYS Script 56

APPENDIX A

ANSYS SCRIPT USED IN THE PRESENT ANALYSIS

finish

/clear

/title, End_Reaction = %EndR%

!units - N,mm

!_____________________________________________________________

!beam dimensions

bdepth=375

bwidth=300

llb=2000 !length of beam portion

thkend=40 !!!!!!!end plate thickness!!!!!!!!

thkw=12.5 !beam web thickness

thkf=18.75 !beam flange thickness

thkp=75 !load plate thickness

fys=275 !Yield stress of steel

EE=207000 !steel modulus of elasticity

!_____________________________________________________________

!Calculation of Minimum Deflection (Del) to Yield Steel

hh=bdepth-thkf

Ixx=((bwidth*(thkf**3)/12)+bwidth*thkf*((hh/2)**2))*2 +

(thkw*(hh**3)/12)

Mp=(bwidth*thkf*fys*hh/2)*2 + (thkw*hh/2*fys*hh/4)*2

Py=Mp/llb

Del=Py*(llb**3)/(3*EE*Ixx)

ANSYS Script 57

deltay=4.0*Del !applied end displacement

!_____________________________________________________________

a1=12.5 !dimensions

a2=12.5

a3=bwidth/4

a4=a3

b1=25

b2=25 !!!!"c"!!!!!

b3=bdepth/4

b4=b3

ll=llb/4

divz2=nint(ll/30) !more intense meshing nearer to endplate

divz1=nint(ll/20)

lf=25 !length of contact spring

por=0.25 !Poisson's ratio

!_____________________________________________________________

pi=3.141592654

bd=25.4 !bolt diameter

ba=pi*(bd**2)/4 !bolt x-section area

bk=EE*ba/lf !bolt tensile stiffnes

/prep7

!_____________________________________________________________

!define element type

et,1,shell181 !end-plate and beam !

et,2,combin39 !contact spring and bolt

keyopt,2,4,1 !3-D longitudinal combin39 element

!_____________________________________________________________

ANSYS Script 58

!define real constants

r,1,thkend !endplate

r,2,thkw !beam web

r,3,thkf !beam flange

r,6,thkp !load plate

r,4,-1,-bk*100,0,0,1,0.0001 !contact spring

r,5,-1,-bk,0,0,1,bk !bolt (linear Combin39 element)

!_____________________________________________________________

!define material properties

mp,ex,1,EE !I-beam and end-plate

mp,prxy,1,por

! bilinear isotropic steel

tb,bkin,1

tbdata,1,fys,ee*.0001

!_____________________________________________________________

!modeling start

blc4,0,0,a1/2,b1/2

blc4,a1/2,0,a1/2,b1/2

blc4,a1,0,a2/2,b1/2

blc4,a1+a2/2,0,a2/2,b1/2

blc4,a1+a2,0,a3/2,b1/2

blc4,a1+a2+a3/2,0,a3/2,b1/2

blc4,a1+a2+a3,0,a4/2,b1/2

blc4,a1+a2+a3+a4/2,0,a4/2,b1/2

asel,all

agen,2,all,,,,b1/2,,,,0

blc4,0,b1,a1/2,b2/2

ANSYS Script 59

blc4,a1/2,b1,a1/2,b2/2

blc4,a1,b1,a2/2,b2/2

blc4,a1+a2/2,b1,a2/2,b2/2

blc4,a1+a2,b1,a3/2,b2/2

blc4,a1+a2+a3/2,b1,a3/2,b2/2

blc4,a1+a2+a3,b1,a4/2,b2/2

blc4,a1+a2+a3+a4/2,b1,a4/2,b2/2

asel,s,loc,y,b1,b1+b2/2

agen,2,all,,,,b2/2,,,,0

blc4,0,b1+b2,a1/2,b3/2

blc4,0+a1/2,b1+b2,a1/2,b3/2

blc4,a1,b1+b2,a2/2,b3/2

blc4,a1+a2/2,b1+b2,a2/2,b3/2

blc4,a1+a2,b1+b2,a3/2,b3/2

blc4,a1+a2+a3/2,b1+b2,a3/2,b3/2

blc4,a1+a2+a3,b1+b2,a4/2,b3/2

blc4,a1+a2+a3+a4/2,b1+b2,a4/2,b3/2

asel,s,loc,y,b1+b2,b1+b2+b3/2

agen,2,all,,,,b3/2,,,,0

blc4,0,b1+b2+b3,a1/2,b4/2

blc4,a1,b1+b2+b3,a2/2,b4/2

blc4,a1+a2,b1+b2+b3,a3/2,b4/2

blc4,a1+a2+a3,b1+b2+b3,a4/2,b4/2

blc4,0+a1/2,b1+b2+b3,a1/2,b4/2

blc4,a1+a2/2,b1+b2+b3,a2/2,b4/2

blc4,a1+a2+a3/2,b1+b2+b3,a3/2,b4/2

blc4,a1+a2+a3+a4/2,b1+b2+b3,a4/2,b4/2

ANSYS Script 60

asel,s,loc,y,b1+b2+b3,b1+b2+b3+b4/2

agen,2,all,,,,b4/2,,,,0

asel,all

agen,,all,,,-(a1+a2+a3+a4),,,,,1

arsym,x,all,,,,,0

asel,all

agen,,all,,,,-(b1+b2+b3+b4),,,,1

arsym,y,all,,,,,0

nummrg,kp

k,,0,0,-lf

l,kp(0,0,0),kp(0,0,-lf)

lsel,s,loc,z,-lf/2,-lf/2

*get,extline,line,0,num,min

nummrg,kp

ksel,all

ksel,u,loc,z,-lf,-lf

ldrag,all,,,,,,extline

nummrg,kp

ksel,s,loc,y,b4+b3,b4+b3

ksel,a,loc,y,-(b4+b3),-(b4+b3)

ksel,a,loc,x,0,0

ksel,u,loc,z,-lf,-lf

ksel,u,loc,y,b4+b3+b2,b4+b3+b2

ksel,u,loc,y,b4+b3+b2+b1,b4+b3+b2+b1

ANSYS Script 61

ksel,u,loc,y,b4+b3+b2+b1/2,b4+b3+b2+b1/2

ksel,u,loc,y,b4+b3+b2/2,b4+b3+b2/2

ksel,u,loc,y,-(b4+b3+b2),-(b4+b3+b2)

ksel,u,loc,y,-(b4+b3+b2+b1),-(b4+b3+b2+b1)

ksel,u,loc,y,-(b4+b3+b2+b1/2),-(b4+b3+b2+b1/2)

ksel,u,loc,y,-(b4+b3+b2/2),-(b4+b3+b2/2)

ksel,u,loc,x,a4+a3+a2,a4+a3+a2

ksel,u,loc,x,a4+a3+a2+a1,a4+a3+a2+a1

ksel,u,loc,x,a4+a3+a2+a1/2,a4+a3+a2+a1/2

ksel,u,loc,x,a4+a3+a2/2,a4+a3+a2/2

ksel,u,loc,x,-(a4+a3+a2),-(a4+a3+a2)

ksel,u,loc,x,-(a4+a3+a2+a1),-(a4+a3+a2+a1)

ksel,u,loc,x,-(a4+a3+a2+a1/2),-(a4+a3+a2+a1/2)

ksel,u,loc,x,-(a4+a3+a2/2),-(a4+a3+a2/2)

kgen,2,all,,,,,ll,,,0

lsel,all

a,kp(a4+a3,b4+b3,0),kp(a4+a3,b4+b3,ll),kp(a4+a3/2,b4+b3,ll),kp

(a4+a3/2,b4+b3,0)

asel,s,loc,z,ll/2,ll/2

agen,2,all,,,-a3/2,,,,,0

a,kp(a4,b4+b3,0),kp(a4,b4+b3,ll),kp(a4/2,b4+b3,ll),kp(a4/2,b4+

b3,0)

a,kp(a4/2,b4+b3,0),kp(a4/2,b4+b3,ll),kp(0,b4+b3,ll),kp(0,b4+b3

,0)


arsym,x,all,,,,,0


agen,2,all,,,,-2*(b3+b4),,,,0

ANSYS Script 62

a,kp(0,0,0),kp(0,0,ll),kp(0,b4/2,ll),kp(0,b4/2,0)

a,kp(0,b4/2,0),kp(0,b4/2,ll),kp(0,b4,ll),kp(0,b4,0)

a,kp(0,b4,0),kp(0,b4,ll),kp(0,b4+b3/2,ll),kp(0,b4+b3/2,0)

a,kp(0,b4+b3/2,0),kp(0,b4+b3/2,ll),kp(0,b4+b3,ll),kp(0,b4+b3,0

)


asel,u,loc,y,b4+b3,b4+b3

asel,u,loc,y,-(b4+b3),-(b4+b3)

arsym,y,all,,,,,0


agen,4,all,,,,,ll,,,0

!______________________

asel,s,loc,z,0,0

agen,2,all,,,,,llb,,,0

!modelling finish

!_____________________________________

an analytical and computational investigation on end-plate thickness and bolt tension of a bolted...

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