Steel Beam-Column Connections Designed for Robustness

STEEL BEAM-COLUMN CONNECTIONS

DESIGNED FOR ROBUSTNESS

Dissertation submitted as part requirement for the Degree of Master of Science in

Structural Engineering

By

Vishal Krishnan

Supervisor:

Dr Buick Davison

The University of Sheffield

Department of Civil and Structural Engineering

September 2009

Declaration

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DECLARATION

Vishal Krishnan, certifies that all the material contained within this document is his own

work except where it is clearly referenced to others.

(Signature)

Abstract

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ABSTRACT

Robustness of connections and structures has been a very keen area of research. Interest

in the subject was further advocated by the many disastrous events involving collapse of

buildings, which happened to occur. This dissertation investigates the behaviour of a

connection in the event of a dynamic event such as a progressive collapse. The study

compares a theoretical model of a connection, with a numerical model subjected to static

and dynamic loading.

A Finite Element Model of a flexible end-plate connection was used as the subject of

analysis. In order to perform the analysis the FEA package, ABAQUS was used. The 3D

model portrayed all surface interactions and properties of material non-linearity.

Presently the design codes make available certain provisions although not descriptive, to

determine the design tying resistance. The analysis consisted of determination of the

theoretical tying force of a flexible end-plate connection. A static analysis was

performed on the numerical model in order to validate the theoretical representation of

the connection model. An explicit dynamic solution was opted in order to analyse the

quasi-static process that was simulated in ABAQUS.

The analyses were performed by imposing various loads at different instances as tying

forces on the connection. It concluded that the tying resistance the numerical model

could provide under static loading was far greater than the value of design tying

resistance established by the present design rules. On proceeding to a dynamic analysis

at the same load instances it was found that the connection model underwent further

deformation than the static load case.

Thus it can be suggested from the analysis that although the present design provisions

cater for a static event the same cannot be considered as a satisfactory means of design

in the event of a progressive collapse.

Acknowledgement

Page | iv

ACKNOWLEDGEMENT

I am sincerely grateful to Dr Buick Davison for providing me this opportunity to work

on this dissertation. I am also thankful for his kind support and supervision during my

period of study.

Also, heartfelt gratitude towards Mr Ying Hu for his technical support which was most

helpful during the software analysis conducted for this dissertation.

Finally, I would like to thank my family and friends for their love and support.

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TABLE OF CONTENTS

Declaration .................................................................................................................... ii

Abstract ........................................................................................................................iii

Acknowledgement ........................................................................................................ iv

Table of Contents ........................................................................................................... v

Table of Figures ............................................................................................................. x

List of Tables .............................................................................................................. xiii

CHAPTER 1 .................................................................................................................. 1

1 Introduction ............................................................................................................ 1

1.1 Aims and objectives ......................................................................................... 2

1.1.1 Aims ......................................................................................................... 2

1.1.2 Objectives ................................................................................................. 2

1.2 Methodology ................................................................................................... 3

1.2.1 Review existing design methods ............................................................... 3

1.2.2 Capacity of design method ........................................................................ 3

1.2.3 Analysis .................................................................................................... 3

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1.2.4 Comparison of results ............................................................................... 4

1.3 Dissertation outline .......................................................................................... 4

1.3.1 Chapter 1 .................................................................................................. 4

1.3.2 Chapter 2 – Literature review .................................................................... 4

1.3.3 Chapter 3 – Description of the model ........................................................ 4

1.3.4 Chapter 4 – Analysis ................................................................................. 4

1.3.5 Chapter 5 – Results ................................................................................... 4

1.3.6 Chapter 6 – Conclusions and Recommendations ....................................... 5

CHAPTER 2 .................................................................................................................. 6

2 Literature Review ................................................................................................... 6

2.1 General terms .................................................................................................. 6

2.1.1 Robustness................................................................................................ 6

2.1.2 Progressive collapse.................................................................................. 7

2.1.3 Disproportionate collapse ......................................................................... 7

2.1.4 Tying ........................................................................................................ 8

2.1.5 Relevant events and findings................................................................... 10

2.1.6 Progressive collapse findings .................................................................. 13

2.2 Present advancement in research .................................................................... 14

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2.2.1 Robustness rules ..................................................................................... 15

2.3 Connections ................................................................................................... 16

2.3.1 Connection types .................................................................................... 17

2.3.2 Behaviour of connections and experimental investigations ...................... 20

2.4 Design approach to connections ..................................................................... 27

2.4.1 Indirect design ........................................................................................ 28

2.4.2 Direct design .......................................................................................... 28

2.4.3 Missing member strategy ........................................................................ 29

2.5 Scope of Eurocode (EN 1991-1-7) ................................................................. 29

CHAPTER 3 ................................................................................................................ 32

3 Numerical Model .................................................................................................. 32

3.1 Introduction ................................................................................................... 32

3.2 Components and Material properties .............................................................. 33

3.3 Design Features and considerations ................................................................ 35

3.4 Connection details ......................................................................................... 36

CHAPTER 4 ................................................................................................................ 37

4 Analysis ................................................................................................................ 37

4.1 Methodology of analysis ................................................................................ 37

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4.2 Design tying resistance .................................................................................. 38

4.2.1 Bolts in tension ....................................................................................... 40

4.2.2 End-plate in bending ............................................................................... 42

4.2.3 Supporting column flange in bending ...................................................... 46

4.2.4 Supporting column web in bending ......................................................... 46

4.2.5 Beam web in tension ............................................................................... 47

4.3 Static Analysis ............................................................................................... 48

4.4 Dynamic Analysis .......................................................................................... 49

CHAPTER 5 ................................................................................................................ 52

5 Results .................................................................................................................. 52

5.1 Theoretical Analysis ...................................................................................... 52

5.2 Static Analysis ............................................................................................... 52

5.2.1 Axial Displacement ................................................................................ 52

5.3 Dynamic Analysis .......................................................................................... 55

5.3.1 Axial Displacement ................................................................................ 55

CHAPTER 6 ................................................................................................................ 58

6 Conclusions And Recommendations ..................................................................... 58

6.1 Static Resistance ............................................................................................ 58

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6.2 Dynamic Resistance ....................................................................................... 60

6.3 Tying Resistance and connection geometry .................................................... 63

6.4 Recommendations.......................................................................................... 64

Bibliography ................................................................................................................ 65

APPENDIX A ............................................................................................................. 70

A.1 Static tying resistance (Calculation sheet) .......................................................... 70

A.1.1 Bolts in tension ....................................................................................... 72

A.1.2 End-plate in bending ............................................................................... 73

A.1.3 Supporting column web in bending ......................................................... 75

A.1.4 Beam web in tension ............................................................................... 76

Table of Figures

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TABLE OF FIGURES

Figure ‎2.1: Horizontal tying force ................................................................................. 9

Figure ‎2.2 Ronan Point – Partially Collapsed ............................................................... 11

Figure ‎2.3: Alfred P. Murrah Federal Building – Collapsed North Side ........................ 12

Figure ‎2.4: Robustness rules – concept ......................................................................... 16

Figure ‎2.5: Shear end-plate connection......................................................................... 17

Figure ‎2.6: Double angle connection ............................................................................ 18

Figure ‎2.7: Extended end-plate connection ................................................................... 19

Figure ‎2.8: Experimental setup ..................................................................................... 21

Figure ‎2.9: Failure modes of Owens and Moore‟s tests ................................................ 22

Figure ‎2.10: Apparatus used in experiment .................................................................. 23

Figure ‎2.11: Experimental setup ................................................................................... 24

Figure ‎2.12: Component based model for flexible end-plate ......................................... 25

Figure ‎2.13: Force-displacement curve for each component ......................................... 26

Figure ‎3.1: Flexible end-plate model (FE model) ......................................................... 33

Figure ‎3.2 Components of the flexible end-plate connection model .............................. 34

Table of Figures

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Figure ‎3.3: Flexible end-plate connection details .......................................................... 36

Figure ‎4.1: Parameters and notations of an end plate .................................................... 39

Figure ‎4.2: Equivalent T-stub (dimensions) .................................................................. 42

Figure ‎4.3: Parameters of an equivalent T-stub............................................................. 43

Figure ‎4.4: Endplate model as separate T-stubs ............................................................ 43

Figure ‎4.5: Weld dimensions ........................................................................................ 45

Figure ‎4.6: Structural integrity – end plate connecting to a column .............................. 46

Figure ‎4.7: Static load applied on the flexible end-plate connection model ................... 48

Figure ‎4.8: Static response at 250kN ............................................................................ 49

Figure ‎4.9: Dynamic loading ........................................................................................ 50

Figure ‎4.10: Load pattern ............................................................................................. 50

Figure ‎4.11: Dynamic response at 250kN (at t1=1ms) ................................................... 51


Figure ‎5.2: Static Response at 300kN ........................................................................... 54



Figure ‎5.5: Dynamic Response at 250kN ..................................................................... 55


Table of Figures

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Figure ‎6.1: Static Response at different load conditions ............................................... 58


Figure ‎6.3: Dynamic response at different load conditions ........................................... 60

Figure ‎6.4: Dynamic response at 450kN ....................................................................... 61

Figure ‎6.5: Static and dynamic response at 300kN ....................................................... 61

Figure ‎6.6: Static and dynamic response at 400kN ....................................................... 62

Figure ‎6.7: Static and Dynamic Response at 450kN ..................................................... 62

List of Tables

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LIST OF TABLES

Table ‎3.1: Material properties ...................................................................................... 34

Table ‎4.1: Design resistance for bolts and rivets subjected to tension or shear .............. 41

Table ‎4.2: Design resistance ......................................................................................... 44

CHAPTER 1

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CHAPTER 1

INTRODUCTION

In the past, there have been various events such as the Ronan Point collapse (London) on

16th

May 1968 and the collapse of the Alfred P. Murrah building (Oklahoma city, April

1995). Events such as these have known to have claimed many lives and injured several

others. This happened to result in a widespread awareness among many and invoked the

need for research and study in order to develop methods that can avoid disasters such as

these. The main objective is the safety of the people, who maybe the occupants of the

building or those around that can be affected by the collapse of the building.

A particular interest of research has been towards progressive collapse of structures,

which refer to global failure of the building that is caused by a local damage in the

structure. This chain reaction of failures leading to the Ronan point incident was of a

similar kind.

Introduction

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Such failures of connections and structures are possibly due to the customary method of

design and general norm to follow the known regulations without considering drastic

effects of such low probability. This along with the accountability of present rules and

adequacy of various considerations may be a key reason.

Connections on being made more robust pose another problem. Increasing strength may

lead to reduced ductility and hence possibility of brittle failure. Sufficient ductility is

necessary in order to ensure that fracture does not occur at any point of the connection

due to excessive deformation. It is then that the question arises whether a strong but

more brittle connection more robust than a weak ductile one?

Therefore in order to make connections more robust and less susceptible to failure due to

progressive collapse, there requires research in the subject.

1.1 Aims and objectives

1.1.1 Aims

Review the need for robust designs considering already available sources and

previous literature

Understand the theory of design and analyze the present rules provided for the

tying resistance of a connection

Value the need for robustness and its effect on ductility of connections

1.1.2 Objectives

Recognize the limitations of the current design methods

To perform a theoretical analysis using present rules of design, followed by static

and dynamic analysis

Introduction

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Examine the validity of the present design methods to model a connection in

terms of its tying force. Compare the results to the static and dynamic analysis

performed.

Analyse the results and the influence of connection geometry in affecting the

tying resistance.

1.2 Methodology

In order to attain the above aims and objectives the following methodology of research

and analysis were adopted.

1.2.1 Review existing design methods

This included an extensive research in regard to the present available methods of design

and existing proposed theories. Comparisons between conclusions drawn by various

articles and references were made. This is effectively an elaborate literature review on

the subject.

1.2.2 Capacity of design method

Using the present rules of design determination of the „Tying resistance‟ of a simple

end-plate connection was made.

1.2.3 Analysis

With the help of a numerical model (using ABAQUS) validity of the present theoretical

design model was established. The finite element model was used to perform a static and

dynamic analysis.

Introduction

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1.2.4 Comparison of results

The results of the static and the dynamic analysis were compared in order to establish

the validity of the present theoretical design model. This is further discussed in the light

of changing connection geometry in order to increase tying resistance of connections.

1.3 Dissertation outline

1.3.1 Chapter 1

This consists of a general introduction to the subject of the dissertation, aims and

objectives of the thesis and the methodology of research.

1.3.2 Chapter 2 – Literature review

This chapter consists of an elaborate literature review that discusses the need for

research in the area and the various events that led to it. It also progresses on to provide

an insight into previous research documentations.

1.3.3 Chapter 3 – Description of the model

The model that has been used to perform the analysis is shortly described. It illustrates

its features and the necessary assumptions that were made.

1.3.4 Chapter 4 – Analysis

The methodology of analysis and the procedure undertaken is explained. A detailed

explanation of the calculations and the analysis is done.

1.3.5 Chapter 5 – Results

The various outputs and results obtained from the FE analysis are shown. Graphs

denoting the static and dynamic responses are plotted and displayed.

Introduction

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1.3.6 Chapter 6 – Conclusions and Recommendations

The results are closely analysed and conclusions to the software analysis carried out are

made. A discussion in the light of changing connection geometry to increase tying

resistance is made. Recommendations on plausible further research are made.

CHAPTER 2

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CHAPTER 2

LITERATURE REVIEW

1.4 General terms

1.4.1 Robustness

The term robustness can be defined as,

“The ability of a structure to withstand events like fire, explosions, impact or the

consequences of human error, without being damaged to an extent disproportionate to

the original cause.” (BSEN 1990:2002)

It is also generally referred to as the insensitivity to local failure. Robustness is not only

associated with the structure itself but also considered an element of various indicators

such as risk, ductility, loads and resistances, occurrence probabilities of extraordinary

loads and exposure to the environment, structural monitoring and maintenance, and

general structural coherence (prEN 1991-1-7, 2003).

Literature Review

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It is the ability to survive a potentially damaging incident or exceptionally drastic event

without disproportionate loss of function (I Struct E, 2002). Thus in modern codes it

requires that the “consequences of damages to structures should not be disproportionate

to the cause of the damage”. Robustness is essentially covered by two Eurocodes, EN

1990: Eurocode: Basis of Structural Design and EN 1991-1-7 Eurocode 1: Part 1-7

Accidental Actions that speak about methods to achieve robustness and the various

actions to consider (Gulvanessian & Vrouwenvelder, 2006). Thus the term can be

summarized as the capacity of a structure to withstand load (that may be even unusual or

extraordinary in nature).

1.4.2 Progressive collapse

“It is a chain reaction of failures following damage to a relatively small portion of a

structure. The damage resulting from progressive collapse is disproportionate to the

damage that initiated the collapse” (BSEN 1990:2002)

“Progressive collapse denotes an extensive structural failure initiated by local

structural damage, or a chain reaction of failures following damage to a relatively small

portion of a structure. This can be also characterized by the loss of load-carrying

capacity of a relatively small portion of the structure due to an abnormal load which, in

turn, triggers a cascade of failures affecting a major portion of the structures.”

(Krauthammer, 2002)

One of the key reasons to develop interest in this area was the Ronan Point collapse in

London in 1968.

1.4.3 Disproportionate collapse

“A building which is susceptible to disproportionate collapse is one where the effects of

accidents and, in particular, situations where damage to small areas of structure or

Literature Review

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failure in single elements could lead to collapse of major parts of the structure”

(ANON, Structure, 2007).

Requirements in regulations were introduced after the collapse of Ronan Point in 1968.

The Building Regulations now require the design to be such that it avoids such disasters.

Progressive collapse as a phenomenon is not explicitly mentioned in the regulations.

But, a building that is vulnerable to progressive collapse will almost definitely result in a

disproportionate collapse. The collapse of Ronan Point was both progressive as well as

disproportionate.

It is stated according to requirement A3 of Approved document A of Building

Regulations that,

“The building shall be constructed so that in the event of an accident the building will

not suffer collapse to an extent disproportionate to the cause” (Way, 2004).

An approach is to ensure whole frame action by providing both horizontal and vertical

tying of the frame elements (Way, 2004)

1.4.4 Tying

Clause 2.4.5.2 of BS 5950 states that Tying of Buildings should be applied to buildings

of all kinds. It recommends the following

Columns are to be tied at approximate right angles, at each principle floor level.

All ties and end connections along the edges of the building and along each

column line should be able to resist a factored tensile load of at least 75kN

Horizontal ties (represented in Figure 2.1) are also to be provided at roof level.

But in cases where only imposed roof loads and wind loads are present and

where steelwork only supports cladding that weighs more than 0.7kN/m2 it may

not be necessary.

Literature Review

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The standard robustness measures state that connections should resist certain factored

tensile loads that are (Moore, 2002):

Internal ties: 0.5(1.4gk + 1.6qk)stL

Edge ties: 0.25(1.4gk + 1.6qk)stL

Where, gk – dead load per unit area

L – span

qk – imposed load per unit area

St – mean transverse spacing of the ties adjacent to that being checked.

It is to be noted that for both the ties the tensile capacity should not be less than 75kN.

Figure 0.1: Horizontal tying force (Gozzi & Uppfeldt, 2005)

There are two main objectives to horizontal tying. They are,

General ties, to provide catenary action when a support fails.

Column ties, to prevent columns becoming detached from the floor or roof they

are supporting.

Literature Review

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The general system is to use steel members as ties. It is necessary to use tie members

between frames, as it was traditionally done in order to obtain lateral restraint to the

columns. Generally they require being such that they restrain the column in two

directions. If not connected directly they should be as close to them as possible.

Currently the requirements relate to all buildings as opposed to the previous limit that

was to buildings of five or more storeys only. Usually the end connections of the

members provided are more than necessary, but tying checks are made as an alternative

to normal loads.

“Also, gross deformations under load are no problem when resisting accidental damage

so it should rarely be necessary to increase sizes of cleats, or other connection material

such as end plates, to cater for tying forces.” (AD063, SCI Advisory Desk, 2009)

It is stated that,

“The ties and their end connections should be of a standard of robustness commensurate

with the structure of which they form a part.” (AD 131, SCI Advisory Desk, 2009).

Recently there has been a lot of development that corresponds to structural integrity.

1.4.5 Relevant events and findings

A few events of extremely disastrous effects have resulted in the need to reconsider

certain norms of the past. These events generally referred to as progressive or

disproportionate collapses were responsible to trigger a major interest toward research

and study in order to avoid such collapses. Some of these prominent events are discussed

below.

1.4.5.1 Ronan Point, London 1968

Ronan Point was constructed in the West Ham region of East London. It was a 22-storey

block constructed using a technique known a Large Panel System building (LPS) that

Literature Review

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involved using precast wall and floor units. The prefabricated units were picked up by

crane, positioned and held together by bolts. In the event of a gas explosion that

happened to occur on the 18th floor, the connections between the wall and floor failed

that the wall units fell apart. Thus the rest could not support the slab and the falling slabs

contributed to the failure of the ones below as well. Thus it resulted in a progressive

collapse throughout until the ground floor instead of the failure being confined to just

the floor where the explosion had occurred (shown in Figure 2.2). Four people were

killed in the incident and seventeen injured.

Figure 0.2 Ronan Point – Partially Collapsed (Wikipedia)

The incident led to the phenomenon of progressive collapse to be taken on a serious note

among many. It called for serious investigation into the subject and study in order to

avoid further events as drastic as this (Campbell, 2001).

Literature Review

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1.4.5.2 Murrah Building, Oklahoma city 1995

Another incident of a similar category occurred on the 19th April 1995, due to the

explosion of a truck loaded with explosives, parked outside the Alfred P. Murrah federal

building in Oklahoma City. It resulted in the collapse of a large part of the nine-storey

building along with causing damages to buildings that were in the same complex, and

168 casualties (Tang, et al., 2006) It was estimated that the progressive collapse of the

building contributed to most of the damage that was seen (Prendergast, 1995). The

building collapsed with eight bays along the north face and two bays along the south

face. It suggested that the damage was made more severe as the result of the progressive

collapse rather than the explosion itself (I Struct E, 2002).

Figure 0.3: Alfred P. Murrah Federal Building – Collapsed North Side (Caruso, K.)

Other major events of international attention were the World Trade Centre towers

incident, New York, 2001 and the Manchester City Centre disaster in 1996.

Literature Review

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1.4.6 Progressive collapse findings

Following events such as the Ronan point incident and the Alfred P. Murrah building the

phenomenon was put in the spotlight, various research ideas have been proposed by

many. Usually, buildings should be safe by all means, and in case of any accident should

retain structural integrity. The intension being that the building should be such that it

may be prevented from posing a threat to the safety of people as a result of various

issues such as,

Loadings

Collapse or deformations

Stability of the buildings and other buildings in the vicinity

Environmental exposure or effects

Details of construction

Safety factors

For events such as gas explosions and attacks on civilian buildings, even though

provisions do exist, the importance given is far less due to assumed “low probability” of

its occurrence. It is evident from previously explained scenarios of disastrous events that

the collapse is initiated by the loss of structural integrity in a part of the structure mainly

due to the weakness of the connection between the members.

Therefore a new standard was introduced in the United Kingdom,

“Every building must be designed and constructed in such a way that in the event of

damage occurring to any part of the structure of the building the extent of any resultant

collapse will not be disproportionate to the original cause.” (ANON., 2007)

Literature Review

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1.5 Present advancement in research

A common conclusion to all the research and investigations that followed the various

drastic events were that in order to avoid such collapses, there should be provision for

construction of structures that are more robust in nature.

Post the twin tower incident it was stated that,

“It is insufficient merely to tie structural elements together. Tying alone does not

inherently provide a ductile structure or one with good energy absorption capability” (I

Struct E, 2002)

The National Institute of standards and Technology (NIST) in the year 2005 submitted a

report post the September 9/11 incident that summarized, as much as thirty

recommendations for actions in various areas of work among which included increasing

structural integrity and improving procedures and practises (Gustafon, et al., 2005).

Moreover, now it has also been suggested that robustness can be achieved by allowing

absorption of energy. The role of connections in the same is very significant. Failure of

connections jeopardizes the safety levels that we wish to maintain.

The mechanism of load transfer in damaged structures and the ability of connections to

sustain loads in extreme events remains a key research area. Building codes do not

provide sufficient guidance on achieving robustness even though they advice engineers

to ensure that collapse do not occur. Thus to enhance robustness in structures and

improve structural integrity the following are recommended (Davison & Tyas, 2005):

Applying prescriptive design and detailing rules that provide acceptable

robustness for the structure.

Designing key members to withstand accidental actions.

Accepting localized failure and ensuring that integrity of rest of the structure is

not comprised (the alternate load path method)

Literature Review

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Various other important principles are needed to develop this field of research

considering progressive and disproportionate collapse.

“Analytical tools to support performance-based engineering design of buildings for

extreme events, and in particular for combinations of events” (I Struct E, 2002)

To improve ductility based on parametric studies it is stated that,

“Connections performance under impact loads and during fire loads needs to be

analytically understood and quantified for improved design capabilities and

performance as critical components in structural frames” (FEMA/ASCE, 2002)

It is also required to develop tools and analysis methods to analyze members and

connections for engineers and designers (FEMA/ASCE, 2002).

1.5.1 Robustness rules

Generally robustness rules mean for the safety in the case of a collapse by requiring the

columns to be tied to the rest of the structure. This is to prevent the removal of columns

and to promote catenary action of beams in the case of an event such as the Ronan point

and others where the floor could not be supported by the members below that initiated a

progressive collapse. The concept of robustness rules is depicted in Figure 2.4, even

though the same is not recommended in the design procedures presently. Thus they are

more of a prescriptive nature than design recommendations that propose to create

structures that perform satisfactorily in the case of such drastic events, rather than well

defined systems of structural mechanics. In other words, it is acceptable that there may

be a permanent deformation of the members and connections, thus not necessarily

availing the structure to be still serviceable but preventing an initiated progressive

collapse to cause complete damage to a structure (Brown, et al., 2004).

Literature Review

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Figure 0.4: Robustness rules – concept (Brown, et al., 2004)

1.6 Connections

Beam-to-column connections are an integral part of a structure. They provide the

necessary strength by linking primary parts of the rest of the structure. It plays vital role

in the load transfer path of a structure. Thus it contributes largely to the stability and

integrity of the structure. Generally connections are designed in order to allow transfer

of joint forces to which they are subjected. Welded connectors, plates, beam elements

and other associated components are also designed with respect to the design loads

(Fisher & Iwankiw, 2002). Nowadays bolt type fasteners are preferred over rivet type

(which were quite sort after initially). This is majorly due to the increasing awareness

toward the benefits of bolted and welded connections in terms of fabrication and

erection. Thus research in the area was also encouraged (Kulak, et al. 1987)

There are various types of steel connections that are mainly classified into two major

categories. These are simple connections and moment connections. Simple connections

are those which are considered to behave as nominally pinned; this implies that they do

not create significant moments. On the contrary moment connections are those

considered to have full moment resistance or transfer of moments. They are further sub

categorized based on other design considerations which are discussed further. (Way,

2004 & Sarraj, 2007). Beam-to-column connections behave differently under different

conditions. Various other parameters also affect their behaviour extensively.

Literature Review

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Investigations into these characteristics under varying parametric conditions or

configurations have been conducted over the years.

1.6.1 Connection types

1.6.1.1 Simple connections

Even though they are assumed to have no moment transfer, experimental results have

shown some amount of end beam moments. But these rotational restraints ignored,

generate results that can be considered satisfactorily conservative. Adequate ductility

and sufficient rotational ductility is the main purpose of shear connections (Green, et al.,

1986)

1.6.1.1.1 Shear end-plate connection

Shear end-plate connections consist of a plate welded at the end of the supported beam

web that is bolted or welded to the supporting member (as shown in Figure 2.5 below).

In these types of connections the end plate is to be limited within the vertical length of

the beam. They are in general simple to design but due to the fact that the detailed length

is to be contained by the supports, fabrication is to be done with care (Green, et al.,

1986).

Figure 0.5: Shear end-plate connection (Green, et al., 1986)

Literature Review

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1.6.1.1.2 Double-angle connection

Double-angle connections also referred to as a cleat connection are fabricated with two

angles. Each angle is on either side of the beam web. The leg that is connected to the

supported beam web is called the web-framing leg and the leg connected to the

supporting column is known as the outstanding leg (Gong, 2007). They are also termed

in-plane and out-of-plane legs respectively (Green, et al., 1986). The connection type

maybe all bolted or all welded. Sometimes they are welded onto the beam and bolted

onto the column or vice versa (in which case they are called “knife angle connection”)

(Gong, 2007). Figure 2.6 below portrays a double angle connection (all bolted)

Figure 0.6: Double angle connection

1.6.1.2 Moment connections

Moment connections, as mentioned previously allow transfer of moments from the

flanges of the supported beam to the supporting column member. They are considered

to have no rotation between the beam and column. They are further sub categorized as

Fully Restrained and Partially Restrained. The former assumes that the angles between

the members remain constant whereas the latter considers there to be some rotation

although there is a transfer of moments (Green, et al., 1986).

Literature Review

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1.6.1.2.1 Extended end-plate connection

Extended end-plates are similar in appearance to shear end plates except for the fact that

the depth of the plate is longer than that of the beam. Another variation is that it is

welded to the web as well as the flange of the supported beam. This plate is then bolted

to the supporting member (Green, et al., 1986). They are also classified as one where the

end plate is extended to the tension side and where the end plate is extended to both the

tension and the compression side (Sarraj, 2007). Figure 2.7 depicts an extended end-

plate.

Figure 0.7: Extended end-plate connection

1.6.1.2.2 Flush end-plate connection

Flush end-plate connections are connections where the beam to be supported is welded

onto the plate before bringing to the site. The weld is applied along the web and the

flanges (Sarraj, 2007). This component is then bolted to the flange of the column.

1.6.1.2.3 T-Stub connections

T-stub connections have two T sections that connect the supported beam on each flange

side. They maybe bolted or welded.

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1.6.2 Behaviour of connections and experimental investigations

Experimental work on behaviour of connections under various conditions and subject to

various loads such as axial force, bending moment and shear force has been very popular

among researchers. The use of equivalent models and comparison of analytical results

with numeric results have been a successful methodology. Flexural behaviour and

stability of connections have also been an engaging area of study. A very keen interest in

research has been toward the tying forces that act on connections, which have been

emphasised as horizontal tying forces in the Eurocodes.

Owens and Moore (1992) conducted experiments on the static behaviour of connections

and their robustness. They considered various types such as web cleat, end-plate and fin-

plate connections. It was concluded that connections possess an innate quality of

robustness toward progressive collapse of structures. Tests showed that the forces the

connections could withstand were far more than the currently recommended resistance

of 75kN.

The arrangement basically was the form of an inverted Tee to which axial load was

applied and the behaviour was observed. The load was applied co-liner to the centroid of

the connection. A 2500kN Avery testing machine was used for the purpose. The beam-

to-column connection varied depending on the type. The column was supported onto the

apparatus as shown in Figure 2.10.

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Figure 0.8: Experimental setup (Owens & Moore, 1992)

From the experimental findings it was suggested that the question of connections failing

in the case of progressive collapse is not of very much concern, but then during the event

of dynamic loading it may pose a further threat as the forces that are produced are far

larger than in the occurrence of a static impact. Thus it is necessary to look into the

validity of the requirement 0.5(1.4gk + 1.6qk)stL as stated by BS5950: Part 1 (Garcia,

2005).

Owens and Moore‟s (1992) result suggested there were two main categories of failure

that the endplate connection was subjected to. They were:

Bearing failure of the endplate

Fracture close to the toe of the weld

The experiment showed that specimens that were single bolted, yield lines formed

around the bolts portraying the first mode of failure. This is shown in Figure 2.11(a)

below whereas Figure 2.11(b) depicts the second mode of failure where yield lines

formed along the toes of the welds which mainly occurred in all multibolt pair type of

connections (Owens & Moore, 1992).

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(a) (b)

Figure 0.9: Failure modes of Owens and Moore’s tests (Owens & Moore, 1992)

The tests showed that there were large amounts of energy absorption as the connections

underwent sufficient plastic deformation before failure. Such behaviour of connections

suggested that the connections would act as a hindrance and help arrest collapse of a

structure, although they vary through connections at different levels of strength and

ductility. This in turn depended on the many parametric variations in connections

(Garcia, 2005).

Pretlove and Ramsden (1991) studied the effects of dynamic loading and its association

to progressive collapse. Their studies proved that there are cases where a structure may

be safe under static loading but unsafe under dynamic loading. In the event of a fracture

there may result in two possibilities, the complete drastic failure of the structure or an

arrest of the collapse (Pretlove, et al., 1991). They also reviewed the effect of the

premature failure of one member, on the rest of the members and the sequential failure

of members that may lead to an eventual arrest of the collapse or on the contrary a full

collapse of the structure.

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The experimental setup consisted of a free central mass connected to a fixed outer ring

by 12 tensioned spokes as shown in Figure 2.12 below. The model was relatively simple,

easy and safe to use in the laboratory.

(a) (b)

Figure 0.10: Apparatus used in experiment (Pretlove, et al., 1991)

The experimental setup compared the margin for the initiation of progressive collapse in

the case of static loading and dynamic loading in the event of the failure of one wire. In

the case of failure of one wire (say wire 1) it was noted that the mass moved upward

thus distributing the tension to the other wires. The tension was dispersed such that it

was relieved on the top and increased below the mass. The failure of another element or

wire would cause the further collapse of the whole model. It was concluded that in the

case of a structural event if the initial static load is not bearable by the structure it may

result in the failure of the rest of the members by initiation. This suggests that even

though the static loading is taken into consideration during design transient overloading

may affect the structure which initially would have been thought to be safe (Pretlove, et

al., 1991). This supports the previous suggestions that it is necessary to consider the

criticality of a dynamic event although it satisfies the conditions to be fulfilled in

preparing for a static event.

Ying Hu et al. (2009) conducted a study that involved the use of a component based

model in order to simulate the behaviour of connections. The method proved to be

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simple and flexible in nature with a commendable level of accuracy. The concept was to

separate the different active components that the connection constituted of and represent

them as non-linear springs. The components were separated based on three main aspects,

tension, compression and shear which were referred to as the three major zones of

deformation. These zones consisted of a number of basic spring components which

contribute to the overall behaviour of the connection (Hu, et al., 2009)

A number of tests were also performed on end-plates in order to produce experimental

data on the behaviour of the connections. The experiment, (set up as shown in Figure

2.13) showed that most of the failure modes corresponded to Owens and Moore‟s (1992)

second mode of failure i.e. by fracture close to the toe of the weld.

Figure 0.11: Experimental setup (Hu, et al., 2009)

The component based model (shown in Figure 2.14) that was proposed included all the

active components of the end-plate. The experiment suggested that the failure

mechanism is largely controlled by the weakest component of the model. It was found

that most of the failures occurred close to the toe of the weld before the first row of

bolts. Most of the deformation was caused by the elongation of the bolt and bending of

the end-plate.

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Spyrou et al. (2004) conducted an experiment on t-stubs that concluded that one of the

common modes of failure was the complete yielding of the flange, with the development

of four plastic hinges. Most of the results here showed this type of failure.

Figure 0.12: Component based model for flexible end-plate (AL-Jabri, et al., 2005)

L Simões da Silva and Ana Girão Coelho (2001) performed research on beam-to-

column connections by examining a model for the ductility of connections. The

proposed model basically followed the ideology put forth by the component based

method, i.e. representation of a connection with an assembly of springs or components

in series and parallel. The model was able to provide satisfactory analytical results that

were in tally with the numerical solutions, in-spite of the complexity that may be

generally encountered in such connections. The various components that are represented

are individually characterised by a bi-linear force-displacement curve as shown in Figure

2.15. Already existing experimental results of a flush end-plate beam-to-column

connection tested at the University of Innsbruck were taken to perform comparisons.

The non-linear analysis that was carried helped understand the response and the yield

points of individual components. The yielding happened to be in the order as column

flange first, then the end-plate and eventually the bolts. The analytical and numerical

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results showed an error of 2.04 % that was accepted and considered negligible (da Silva

& Coelho, 2001).

Figure 0.13: Force-displacement curve for each component (da Silva & Coelho, 2001)

Another aspect of modelling was developed by Ying Hu et al. (2008) that use cohesive

elements in order to understand the resistance and ductility of connections. It is a very

suitable method in order to perform studies on the tying resistance. The numerical model

was created with intricate features of contact surfaces or interactions. Since the

procedure involved an explicit dynamic procedure to analyse the particular quasi-static

simulations, it was an imperative measure to consider the shortest time period such that

the inertial forces still remain insignificant. Load-Rotation relationships were compared

based on the results from the finite element modelling and the experimental results at

hand. This proved to be quite in agreement to each other even though variety could not

be represented in a numerical model. Moreover, the model was able to make a judgment

as to the failure of the steel connections due to the rupture of the endplate (Hu Y. et al.,

2008).

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1.7 Design approach to connections

It is necessary that the connections perform efficiently under severe cases. This relates

directly to the robustness of the structure. Although not a primary requirement of

structural analysis, sufficient ductility is necessary in order to ensure that fracture does

not occur in any point of the connection due to excessive deformation.

Thus to avoid such collapses and failures the Steel Construction Institute states that,

“in structural steel connections where possible, frame connections should provide full

continuity, but all connections, whether fully rigid or nominally pinned, should exhibit

ductility when overloaded” (Yandzio & Gough, 2009).

There are certain recommendations that relate to the type of connection used. They are

(Yandzio & Gough, 2009):

Welded connections: to mainly avoid brittle failure that result from high strains

an appropriate welding technique is required.

Bolted connections: this arrangement would generally have a capacity greater

than the plastic moment of the attached beams; therefore the latter should be an

upper bound value.

Fixed-ended connections: since the maximum moment and the maximum shear

act at the same point, it is often suggested to ensure that local or lateral buckling

is prevented.

Other precautions to be taken care of are,

Make sure that the steel connections can withstand dynamic loads.

It is able to withstand any load reversals imposed upon them.

It is able to withstand a level of distortion without being susceptible to fracture.

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Thus nominally pinned connections need to be designed being able to carry reversal of

loading and imposed distortion (Bertagnoli, 2003). Such precautions and

recommendations allow the connections to be robust and thus prevent collapses by

retaining the structural integrity in cases of drastic events.

There are two approaches of design that have been suggested in order to reduce the risk

of collapse in buildings.

1.7.1 Indirect design

Indirect design approach allows developing “resistance to progressive collapse

by specifying a minimum level of strength, continuity, and ductility”

(Krauthammer, 2002). The method provides specified minimums for strength

and continuity, i.e. tie forces etc. thus developing a specific capacity of the

members. This supports the plausibility of an alternative load path in case of

failure of a particular part or member.

1.7.2 Direct design

Direct design approach considers resistance to be achieved by the structure‟s

ability to absorb damages that it may be subjected to. This method has been

further classified into the following (Krauthammer, 2002):

i. Specific local resistance method

This method provides the generally required strength to withstand

accidental loads, but a specific collapse initiating event is identified that a

resistance can be provided locally in reference to a specific limit state. It

is also known as “key element design” as the loss of an element or

structural member in such situations cannot be tolerated by the structure.

This is in the case where it is not checked for disproportionate collapse. It

is to be checked that whether the elimination of a member or element

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may lead to disproportionate collapse. If the case may be so then the

element is to be designed as a key element (BS 5950-1:2000).

ii. Alternate path method

This method relies mainly on continuity and ductility of the structure. It is

based on the ability of the structure to redistribute forces such that “an

alternate path” is taken in case of local failure. This avoids the need of

identifying the initiating collapse event as that of the formerly discussed

method. Thus it focuses on the damage after it has occurred irrespective

of what the cause may be.

1.7.3 Missing member strategy

This is a strategy criterion was first adopted by codes in the United Kingdom. The

method involves the use of calculations that consider a particular member to be missing,

performing a damage state analysis and then examining the ability of the structure to

withstand the load under gravity in spite of loss of a member. (Bertagnoli, 2003). This

strategy is not applied in the thought of reproducing a particular event or abnormal load

condition but just as a “load initiator” and helps bring redundancy to the structure

(ANON, Progressive collapse analysis and design guidelines for a new federal office

buildings and major modernization projects, 2003)

1.8 Scope of Eurocode (EN 1991-1-7)

The Eurocode can be referred to as set of technical rules on the basis of which structures

are designed in Europe. The standard prEN1991 Eurocode 1: Actions on structures (Part

1-7 Accidental actions) “provides rules for safeguarding buildings and other civil

engineering works against accidental actions. For buildings, EN 1991-1-7 also provides

strategies to limit the consequences of localized failure caused by an unspecified

accidental event.”

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It thus provides recommendations in order to avoid or reduce the accidental actions and

to designing the structure to withstand such an event, but it is not necessarily a clear

guidance in an event of a gas explosion (such as the Ronan Point incident), warfare,

terrorist attacks or a seismic event. These events are generally assumed to be of a low

probability.

But there are certain areas that promote the adoption of robustness strategies (given in

Annex A) to ensure that collapse does not occur due to localized failure, and that in the

event of such a failure, the collapse should not be disproportionate to the cause of the

localized failure.

The subjects that are in fact dealt with are:

Impact

Explosions (internal)

The following are the types of design situations that the standard identifies under

accidental design situations (prEN 1991-1-7, 2003),

1. Indentified causes

a. Accidental actions

Strategies –

Preventing or reducing the action

Design the structure to sustain the action

2. Unidentified causes

a. Localized failure

Strategies –

Enhanced redundancy

Key element designed to sustain notional

accidental action.

The EN 1991-1-7 adopts regulations to avoid disproportionate collapse. It states that,

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“designing the building such that neither the whole building nor a significant part

of it will collapse if localized damage were sustained, is an acceptable strategy for

ensuring that the structure is sufficiently robust to survive a reasonable range of

undefined accidental actions.”

CHAPTER 3

CHAPTER 3

NUMERICAL MODEL

1.9 Introduction

In order to perform the analysis an already existing three dimensional numerical model

of a flexible end plate was used. The model was created using the finite element

package, ABAQUS. It is an assembly created through various components that include

end-plate, beam, bolts, welds and column. The model shown below in Figure 3.1 is able

to simulate the various surface interactions and show connection behaviour and

response.

Numerical Model

Page | 33

Figure 0.1: Flexible end-plate model (FE model)

1.10 Components and Material properties

The different components of the model (shown in Figure 3.2) and their specifications are

as given below:

1. Beam - 305x165x40UB

2. Column - 254x254x89UC

3. Endplate - 200x150x10

4. Bolts - M20 Grade 8.8

Numerical Model

Page | 34

Figure 0.2 Components of the flexible end-plate connection model

The beam and the end-plate sections are of steel S275 and the column section are of

S355. The material properties of the components have been tabulated in Table 3.1

Table 0.1: Material properties

Component Material Yield Stress

(N/mm2)

Ultimate

Stress

(N/mm2)

Density

(Kg/mm3)

Young's

Modulus

(kN/mm2)

Poisson's

ratio

Beam S275 275 450 7.85E+12 205 0.3

Column S355 355 550 7.85E+12 205 0.3

End-plate S275 275 450 7.85E+12 205 0.3

Bolt 8.8 640 800 7.85E+12 205 0.3

Numerical Model

Page | 35

1.11 Design Features and considerations

The finite element model and its components were basically of element type that is an

„eight-node continuum hexahedral brick element‟. This type of element has the ability of

demonstrating deformation of large proportions. It also displays non-linearity, both in

material and geometric characteristics. Another aspect of the element type used,

„C3D8R‟ is that it is conservative in nature in determining the behaviour of the

connection. A dense mesh was opted for the model in order to control the hourglass

modes (Hu, et al., 2008). Hourglass modes generally occur due to the lack of lateral

confinement that arises during the creation of the mesh.

The different contact areas were defined using the surface-to-surface interaction

(conditions of friction) between elements. These areas include areas between bolts, end-

plates and column flanges. It follows the process of assigning the different surfaces as

master and slave, where the master surface is generally a component of stronger material

or one with finer mesh (Hu, et al., 2008).

The solution that is applied to the numerical model is described as an explicit dynamic

procedure. This is relatively a preferred solution for quasi-static process such as this.

This is because of the benefits of an explicit dynamic solution over an implicit solution

in the case of a very long process such as a quasi-static process which may require

feasibly smaller time steps as opposed to the real time scale. Thus using an explicit

dynamic solution provides an accelerated event (Hu, et al., 2008).

Numerical Model

Page | 36

1.12 Connection details

The geometrical details of the numerical model of the flexible end-plate connection is

shown in Figure 3.3

Figure 0.3: Flexible end-plate connection details

CHAPTER 4

Page | 37

CHAPTER 4

ANALYSIS

1.13 Methodology of analysis

The analysis performed basically consisted of three parts. They are described shortly

below:

Theoretical Analysis (Calculation of design tying resistance)

The present design considerations were taken into account in order to perform a

theoretical calculation to determine the tying resistance and create a design

model based on the provided provisions of the Eurocode EN1993-1-8

Static Analysis

A static analysis was performed with predefined values of loading. The range of

loading was selected based on the calculated design tying resistance. This was

Analysis

Page | 38

done in order to validate the calculated design value and its coherence to the

analytical values.

Dynamic Analysis

The connection was then subjected to dynamic loading. This was compared to

the results of the static loading, thus examining the safety of a statically designed

model under dynamic loading.

1.14 Design tying resistance

Based on EN1993-1-8, NCCI provides rules to determine the tying resistance of a partial

depth end-plate connection. The design model that has been considered refers to the case

of accidental limit state. As for tying resistance, EN1993-1-8 does not give any guidance

per se but since the failure modes are associated with the deformations and strains

produced, it is recommended that the ultimate tensile strengths (fu) be used (ANON.,

2009).

The tying resistance and the mode of failure is that particular value of the resistance and

mode that corresponds to the lowest resistance of all the modes of failure. The individual

resistances of the various modes of failure are denoted as given below,

Bolts in tension - NRd,u,1

End-plate in bending - NRd,u,2

Supporting member in tension - NRd,u,3

Beam web in tension - NRd,u,4

Analysis

Page | 39

Figure 0.1: Parameters and notations of an end plate (ANON, 2009)

The notations and values of the parameters shown in Figure 4.1 (corresponding to the

model) are given below:

Depth of straight portion of the column web - dc

Diameter of hole - do

Width across the points of bolts head or nut - dw

Longitudinal edge distance (end-plate) - e1

Transverse edge distance (column flange) - e2

Ultimate tensile strength of bolt - e2,c

Ultimate tensile strength of supported beam - fu,b

Ultimate tensile strength of column - fu,b1

Ultimate tensile strength of end-plate - fu,c

Distance between bolt line and toe of the weld,

(Connecting the end-plate to beam) - fu,p

Height of end-plate - hp

Analysis

Page | 40

Distance between bolt line and toe of the weld,

(Connecting the end-plate to beam) - mp

Total number of bolts - n

Number of horizontal rows of bolts - n1

Number of vertical lines of bolts - n2

Longitudinal bolt pitch - p1

Distance between cross centres of bolts - p3

Column flange thickness - tf,c

End plate thickness - tp

Thickness of supported beam web - tw,b1

Thickness of column web - tw,c

Partial factor for tying resistance - γM,u

1.14.1 Bolts in tension

The tying resistance is given by,

(Equation 4.1)

The following Table 4.1 denotes the various modes of failure and respective design

resistances for fasteners.

uRdtuRd nFN ,,1,,

Analysis

Page | 41

Table 0.1: Design resistance for bolts and rivets subjected to tension or shear (prEN 1991-1-8: 2003)

Failure mode Bolts Rivets

Shear resistance per shear

plane

where the shear plane passes

through the threaded portion of

the bolt (A is the tensile stress

area of the bolt As)

- for classes 4.6,5.6 and 8.8:

αv=0.5

where the shear plane passes

through the unthreaded portion

of the bolt (A is the gross cross

section of the bolt): αv=0.6

Bearing resistance

where αb is the smallest of αd; fub/fu or 1.0;

in the direction of load transfer:

for end bolts: αd=(e1/3d0); for inner bolts αd=(p1/3d0)-1/4

perpendicular to the direction of load transfer

for edge bolts: k1 is the smallest of (2.8 e2/d0-1.7) or 2.5

for inner bolts: k1 is the smallest of (1.4 p2/d0-1.7) or 2.5

Tension resistance

where k2 = 0.63 for countersunk

bolt,

otherwise k2 = 0.9

Punching shear resistance Bp,Rd=0.6πdmtpfu/γM2 No check needed

Combined shear and

tension

2

,

M

ubvRdt

AfF

2

0

,

6.0

M

ur

Rdt

AfF

2

1,

M

ubRdt

dtfakF

Mu

subRdt

AfkF

2,

0.14.1 ,

,

,

,

Rdt

Edt

Rdv

Edv

F

F

F

F

2

0,

6.0

M

urRdt

AfF

Analysis

Page | 42

For the particular failure mode of bolts, the tension resistance is given as,

(Equation 4.2)

Where, k2 = 0.9 (for bolts other than countersunk bolts), and

As is the tensile stress are of the bolt

1.14.2 End-plate in bending

In the case of bolted connections, it may be assumed that for various parts such as the

end-plate in bending, the connection may be designed as an equivalent T-stub model.

Figure 0.2: Equivalent T-stub (dimensions) (prEN 1991-1-8: 2003)

Various considerations are taken into account while representing the connection as a T-

stub model in tension, in order to find the design resistance of the component. The mode

of failure and the design resistance of the component along with the associated bolts in

tension should be considered to be those of a T-stub connection. This is applicable for

both,

Individual bolt-rows required to resist tension

Mu

subRdt

AfkF

2

,

Analysis

Page | 43

Group of bolt-rows required to resist tension

Figure 0.3: Parameters of an equivalent T-stub (prEN 1991-1-8: 2003)

The group of bolt-rows on either side is considered as an individual T-stub. Thus the

design resistance is calculated for each individual equivalent T-stub. The dimension emin

can be obtained from Figure 4.3. The effective length is given as leff that is calculated

using the provisions for each bolt row. The variables m and mx can be obtained from

Figure 4.4

Figure 0.4: Endplate model as separate T-stubs

Analysis

Page | 44

Table 0.2: Design resistance at different modes of failure

Thus,

(Equation 4.3)

Hence, from the table 4.1, the different modes and design tension resistances are,

(Mode 1) (Equation 4.4)

And,

(Mode 2) (Equation 4.5)

The modes of failure, Mode 1 represent complete yielding of the flange and Mode 2 bolt

failure with yielding of the flange.

)2,,

;1,,

min(2,, epuRd

FepuRd

FuRd

N

ppwpp

Rdplwp

RdTnmenm

MenF

2

28 ,1,

,1,

pp

RdtpRdpl

RdTnm

FnMF

,,2,

,2,

2

Analysis

Page | 45

Where,

(Equation 4.6)

(Equation 4.7)

(Equation 4.8)

(dw is the width across the points of the bolt head)

For weld design (ANON, 2009) ,

The specification in the case of shear will be sufficient for the requirements of tying

resistance. Full strength double fillets are provided, and the welds are considered as side

fillet weld. The size of the weld throat „a‟ (shown in figure 4.2) conforms to the

conditions that follow:

Figure 0.5: Weld dimensions

a ≥ 0.38 tw,b1 (S235 beam) (Equation 4.8)



)25.1;;min( ,22 pcp meen

2

28.02( 1,3 atpm

bw

p

4

ww

de

Analysis

Page | 46

The plastic moment resistance is given as,

(Equation 4.11)

Thus from the previous section,

(Equation 4.12)

1.14.3 Supporting column flange in bending

In this case the column flange is thicker than the end –plate, therefore this check is not

considered to be a requirement.

1.14.4 Supporting column web in bending

The tying resistance for this component is given as

(Equation 4.13)

Figure 0.6: Structural integrity – end plate connecting to a column (SCI, 2006)

uM

pupp

uRdpluRdpl

fthMM

,

,

2

,,2,,,1,4

1

uRdtuRduRdt nFNF ,,1,,,,

))1()1(5.1()1(

85.0

1

5.0

11

1

,,

3,,

uRdpl

uRd

mN

Analysis

Page | 47

This check is done usually in compliance with the structural integrity requirements. It is

to validate the tying capacity in the case of an axial compression in the column. The

basic requirement being that the „tie force‟ be less than the tying capacity of the column,

where the tying capacity is given by Equation 4.13 shown above (SCI, 2006)

The moment capacity is given as

(Equation 4.14)

And,

(Equation 4.14)

(Equation 4.15)

(Equation 4.16)

The factor 1.5 in Equation 4.13 is in order to incorporate an allowance for the axial

compression in the column.

1.14.5 Beam web in tension

The resistance is given as

(Equation 4.17)

Thus the tying resistance is determined as the least value of resistance provided among

these components.

uM

cwcu

uRdpl

tfm

,

2

,,

,,4

1

cd

p31

cd

dn

p 01

11

12

)1(

c

o

d

d1

uM

bupbw

uRd

fhtN

,

1,1,

4,,

Analysis

Page | 48

1.15 Static Analysis

In order to compare to the theoretical design model and the design tying resistance a

static analysis on the numerical FEA model was performed. As the same model was

used for both the analyses the static load was imposed as a linear curve, which depicted

a dynamic force applied in a static condition. This was in the intention of saving time in

applying changes to the already available model although it increased analysis time. For

the analysis four predefined loads were assumed to which the connections were

subjected. The loads were applied at 250kN, 350kN, 400kN and 450kN. The loads were

applied uniformly at the beam end of the connection as depicted in Figure 4.2.

Figure 0.7: Static load applied on the flexible end-plate connection model

The setup up considered for the numerical analysis resembles Owens and Moore‟s

(1991) experimental setup where the load was applied co-linear to the connection. In this

analysis the load has been input in the form of load/surface area.

Analysis

Page | 49

For each load case that is applied, the static response was obtained and was compared to

the theoretical model. The response at 300kN is shown below in Figure 4.3.

Figure 0.8: Static response at 250kN

1.16 Dynamic Analysis

The same predefined loads were applied at different rates in order to perform a dynamic

analysis and observe the response of the model. An explicit dynamic solution was

applied to the quasi-static loading. The load pattern that was chosen was that of one that

is generally produced in the case of an accidental impact, as of a vehicular impact onto

an external column.

Analysis

Page | 50

Figure 0.9: Dynamic loading

The load is applied (as shown above in Figure 4.3) monotonically or linearly for a

particular duration and then a constantly at a peak value for the rest of the time duration

of the analysis. The load pattern is shown in Figure 4.5.

Figure 0.10: Load pattern

Analysis

Page | 51

The load is applied at different instances of time, i.e. the peak load is achieved at

different instances of time. In this analysis in order to compare different responses the

corresponding peak times (t1) at different instances are chosen at 1,10,100,1000

milliseconds. The time duration for the analysis varied from three to four days and it

seemingly increased with slower rates of loading. The dynamic response at 300kN load

at 1000 milliseconds is shown below in Figure 4.6.

Figure 0.11: Dynamic response at 250kN (at t1=1ms)

CHAPTER 5

CHAPTER 5

RESULTS

1.17 Theoretical Analysis

The design of the theoretical model concluded that the numerical model created has a

tying resistance of 270kN (Appendix A). Thus using the rules provided by the Eurocode

the connection would effectively be able to with stand such a force.

1.18 Static Analysis

Following the static analyses the subsequent results were obtained

1.18.1 Axial Displacement

The displacement measured at each static load condition was recorded (from ABAQUS)

and is shown in the stress vs. displacement graphs below. The displacement was

recorded at the centroid of the connection.

Results

Page | 53


From Figure 5.1 it can be noticed that at the particular load condition of 250kN which is

smaller than the design static resistance that was found, the connection obviously

provides adequate resistance as expected. Moreover it is far larger than the

recommendations provided by the code that suggests it should be able to possess a tying

resistance of at least 75kN. Below are the responses at 300kN, 400kN and 450kN

respectively.

0

50

100

150

200

250

-0.5 0 0.5 1 1.5 2

Stre

ss (N

/mm

2)

Displacement (mm)

0

50

100

150

200

250

-0.5 0 0.5 1 1.5 2 2.5 3 3.5

Stre

ss (N

/mm

2)

Displacement (mm)

Results

Page | 54

Figure 0.2: Static Response at 300kN



From the above Figures 5.2, 5.3 and 5.4, it can be seen that the response or the

displacements to the various load cases that have been considered is quite reasonable. At

0

50

100

150

200

250

-1 0 1 2 3 4 5 6 7 8

Stes

s (

N/m

m2 )

Displacement (mm)

0

50

100

150

200

250

300

-2 0 2 4 6 8 10

Stre

ss (N

/mm

2 )

Displacement (mm)

Results

Page | 55

a load of 450kN the connection undergoes a maximum axial displacement to a value of

9.5 mm.

1.19 Dynamic Analysis

In order to validate the safety of a static design in the case of a dynamic event, the model

of end-plate connection was subjected to dynamic loading. The results of these tests at

various instances are shown below.

1.19.1 Axial Displacement

The following graphs depict the stress vs. displacement of the various load cases and

instances. Due to errors in the analysis results, certain load instances are not shown here.

Figure 0.5: Dynamic Response at 250kN

The above Figure 5.5 shows that on applying a tying force of 250kN dynamically there

seems to be a displacement up to 3.8 mm at the fastest rate of loading. The following

figures portray the response of the connection at further cases of loading.

0

50

100

150

200

250

0 1 2 3 4 5

Stre

ss (N

/mm

2 )

Displacement (mm)

1ms

10 ms

Results

Page | 56



-50

0

50

100

150

200

250

-1 0 1 2 3 4 5

Stre

ss (N

/mm

2 )

Displacement (mm)

1000 ms

0

50

100

150

200

250

300

-5 0 5 10 15

Stre

ss (N

/mm

2)

Displacement (mm)

10 ms

1000 ms

Results

Page | 57


As it can be seen from the above graphs in Figures 5.6, 5.7 and 5.8 as the rates of

loading is increased there is evident increase in displacement of the connection..

0

50

100

150

200

250

300

350

0 5 10 15 20 25

Stre

ss (N

/mm

2)

Displacement (mm)

1 ms

10 ms

100 ms

CHAPTER 6

Page | 58

CHAPTER 6

CONCLUSIONS AND

RECOMMENDATIONS

1.20 Static Resistance

Figure 0.1: Static Response at different load conditions

0

50

100

150

200

250

300

-2 0 2 4 6 8 10

Stre

ss (N

/mm

2 )

Displacement (mm)

450 kN

400 kN

300 kN

250 kN

Conclusions And Recommendations

Page | 59

On studying Figure 6.1 above it can be seen that various values of displacement at the

different loads may be acceptable considering the load applied. The provisions given

presently suggest a minimum tying resistance of 75kN. The theoretical analysis by

NCCI that follows the rules provided by the Eurocode assumes that the connection be

designed for a tying resistance of 270kN.

From figure 6.2 (ABAQUS screenshot), it can be observed the connection does not seem

to undergo a failure as portrayed through the experiments of Owens and Moore (1991)

even at a load of 450kN. The value is 60 % higher than the tying resistance that the

connection is expected to resist.


Thus it shows that the theoretical design model that the Eurocode provides is quite

adequate as the connection is able to withstand far higher loads or provide a much higher

resistance.


Page | 60

1.21 Dynamic Resistance

The figure 6.3 below shows the summary of the results depicted above

Figure 0.3: Dynamic response at different load conditions

For each load case it can be noted that the displacements are quite larger than as seen

before at any instance of load rates applied. The displacement in the case of the highest

load case values up to 19 mm that is very high in comparison to the static case. The

figure 6.4 below shows the dynamic response at a loading of 450kN in 1 millisecond.

-50

0

50

100

150

200

250

300

350

-5 0 5 10 15 20 25

Stre

ss (N

/mm

2 )

Displacement (mm)

450 kN

400 kN

300 kN

250 kN


Page | 61

Figure 0.4: Dynamic response at 450kN

The following graphs illustrate the comparison between the applied dynamic and static

load cases. Two instances viz. at 300 kN and 400 kN are shown below,

Figure 0.5: Static and dynamic response at 300kN

-50

0

50

100

150

200

250

-1 0 1 2 3 4 5

Stre

ss (N

/mm

2 )

Displacement (mm)

Static load (300 kN)

Dynamic load (300 kN)


Page | 62

Figure 0.6: Static and dynamic response at 400kN

In both the cases of loading it can be seen that (Figure 6.5 and 6.6), in the event of a

dynamic load (a scenario of a vehicular impact in this case) there is considerably larger

displacement. The Figure 6.7(a) showing the static impact and Figure 6.7(b) showing the

dynamic response, corroborates the fact that the tying resistance provided in the case of

a dynamic event is smaller than the resistance provided in a static condition of loading.

(a) (b)

Figure 0.7: Static and Dynamic Response at 450kN

0

50

100

150

200

250

300

-2 0 2 4 6 8

Stre

ss (N

/mm

2 )

Displacement (mm)

Static load (400 kN)

Dynamic load (400 kN)


Page | 63

Thus it can be concluded that even though the static load analysis results seem to

comply with the design values that were calculated theoretically, the dynamic case are

not in consistency with the expectations. In addition, a dynamic event is complicated in

terms of the varying results obtained at different rates of loading under the same load

case. Thus it implies that although the static design considerations that are made are

reliable in the event of a static failure of the connection, this cannot be considered a safe

design methodology in the event of a dynamic impact.

1.22 Tying Resistance and connection geometry

The robustness of a connection is crucially determined by the tying resistance of the

connection. In this dissertation it has been concluded that the static design procedure is

not a preferably safe design consideration to be applied in the case of a dynamic event.

Therefore it is necessary to increase the tying resistance of the connection in order to

render the connection robust in the occurrence of a dynamic event. It can be seen from

the design calculations in 4.2 (Calculations in Appendix A) that the tying resistance of

the connection depends invariably on the parameters of the connection viz. end-plate

thickness, number of bolts, throat weld, end-plate length etc. In order to increase the

tying resistance of the connection it is thus a favourable direction of research to change

connection geometry in order to increase the tying resistance of the connection.

But on increasing the robustness of connections there may be reduction in its

characteristic ductility as in the case of a dynamic event the deformation is largely

different from a static event. The failure may be brittle in nature at higher loads in the

case of a dynamic impact. Thus it might be sensible to change the geometry of the

connection in order to analyse the varying resistances the connection to provide.


Page | 64

1.23 Recommendations

There should probably be a wider time span in order to get accustomed to the software;

therefore maybe getting acquainted with the software a little earlier would be perhaps a

good solution as modelling more than one connection and simulating it is task that

would require a little more time. In regard to further research, there could be substantial

scope in a parametric study of connections.

<Bibliography

Page | 65

BIBLIOGRAPHY

AD 131, SCI Advisory Desk. (2009). Structural Integrity - Tying.

AD063, SCI Advisory Desk. (2009). Accidental Damage - tying. The Steel Construction

Institute.

AL-Jabri, K., Burgess, I., & Plank, R. (2005). Spring-stiffness model for flexible end-

plate bare-steel joints in fire. Journal of Constructional Steel Research , 61, p. 1672-

1691.

ANON. (2009). NCCI: Shear resistance of a simple end plate connection SN014a-EN-

EU. Access Steel.

ANON. (2009). NCCI: Tying resistance of a simple end plate connection SN015a-EN-

EU. Access Steel.

ANON. (2003). Progressive collapse analysis and design guidelines for a new federal

office buildings and major modernization projects. General Services Administration.

ANON. (2007). Structure.

Bertagnoli, L. (2003). Robustness of Steel Structures. Universita' Degli Studi Di Trento.

Brown, D., King, C., Rackam, J., & Way, A. (2004). Design of multi-storey braced

frames. Berkshire: The Steel Construction Institute.

BS 5950-1:2000. Structural use of steelwork in building - Part 1: Code of practice for

design - Rolled and welded sections. London: Bristish Standard Institution.

BSEN 1990:2002. Eurocode 0: Basis of Design. London: British Standards Institution.

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Campbell, P. (2001). Learning from construction failures (Applied forensic

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Davison, J. B., & Tyas, A. (2005). Robustness of Steel Connections. New York:

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Fisher, J., & Iwankiw, N. (2002). Appendix B: Structural steel and steel connection. In

World Trade Centre Building Performance Study: Data Collection, Preliminary

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Garcia, M. (2005). Structural integrity of connections. Sheffield: The University of

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Green, P., Sputo, T., & Veltri, P. (1986). Connections Teaching Toolkit - A Teaching

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Gulvanessian, H., & Vrouwenvelder, T. (2006). Robustness and the Eurocodes.

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Gustafon, K., Duncan, C. T., & Schafly, T. (2005). Structural Integrity - What does this

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Page | 69

APPENDIX A

Page | 70

APPENDIX A

A.1 Static tying resistance (Calculation sheet)

Calculation Reference

The tying resistance and the mode of failure is that

particular value of the resistance and mode that

corresponds to the lowest resistance of all the modes of

failure.

NCCI

SN015a-

EN-EU

The individual resistances of the various modes of failure

are denoted as given below

Bolts in tension

- NRd,u,1

End plate in bending

- NRd,u,2

Supporting member in

bending - NRd,u,3

Beam web in tension - NRd,u,4

Figure A-1: Parameters and notations of an end plate

The notations and values of the parameters shown in Figure A-1 as it

APPENDIX A

Page | 71

corresponds to the model are given below:

Depth of straight portion of

the column web

- dc 200.3 mm

Diameter of hole

- do 22 mm

Width across the points of bolt

head or nut

- dw 32.95 mm

Longitudinal edge distance

(end plate)

- e1 40 mm

Transverse edge distance (end

plate)

- e2 30 mm

Transverse edge distance

(column flange)

- e2,c 83.15 mm

Ultimate tensile strength of

bolt

- fu,b 800 N/mm2


supported beam

- fu,b1 450 N/mm2


column

- fu,c 550 N/mm2


end plate

- fu,p 450 N/mm2

Height of end plate

- hp 200 mm

Distance between bolt line and toe of

the weld (connecting the endplate to

beam)

- mp 42 mm

Total number of bolts

- n 8

Number of horizontal rows of

bolts

- n1 3

Number of vertical lines of

- n2 2

APPENDIX A

Page | 72

bolts

Longitudinal bolt pitch

- p1 60 mm

Distance between cross

centres of bolts

- p3 90 mm

Column flange thickness

- tf,c 17.3 mm

End plate thickness

- tp 10 mm

Thickness of supported beam

web

- tw,b1 6 mm

Thickness of column web

- tw,c 10.3 mm

Partial factor for tying

resistance

- γM,u 1.1

A.1.1 Bolts in tension


The resistance is given by

where, n is the number of bolts

Table 3.4

EN 1993-

1-8

where, k2 0.9

As, is the tensile stress area of the bolt =

245 mm2

uRdtuRd nFN ,,1,,

Mu

subRdt

AfkF

2,

APPENDIX A

Page | 73

Thus,

= 160.36 kN

Therefore the total shear is given as,

= 1282.91 kN

A.1.2 End-plate in bending


The resistance for this mode of failure

is,

For mode 1 and mode 2 respectively,

Table 6.2

EN 1993-

1-8

where,

36.16081,, uRdN

10001.1

2458009.0,

RdtF

)2,,

;1,,

min(2,, epuRd

FepuRd

FuRd

N

)25.1;;min( ,22 pcp meen

ppwpp

Rdplwp

RdTnmenm

MenF

2

28 ,1,

,1,

pp

RdtpRdpl

RdTnm

FnMF

,,2,

,2,

2

APPENDIX A

Page | 74

Now,

e2 = 30 mm

e2,c = 83.15 mm

For steel grade, 275

Throat thickness a > 0.39tw,b1

NCCI

0.39x6 = 2.34 mm

SN014a-

EN-EU

Thus,

a = 4 mm

So,

= 37.47 mm

and, 1.25mp = 46.84 mm

Therefore,

np = 30 mm

= 8.24 mm

= 2045.45 kN

2

28.02( 1,3 atpm

bw

p

4

ww

de

4

95.32we

10001.1

4508200

4

1 2

uM

pupp

uRdpluRdpl

fthMM

,

,

2

,,2,,,1,4

1

2

)248.02690( pm

APPENDIX A

Page | 75

Now,

= 1282.91 kN

From

section ,

1.1 Bolts

in tension Therefore,

For mode 1:

= 270.12 kN

For mode 2:

= 631.03 kN

The resistance is thus the minimum of FT,1,Rd and

FT,2,Rd

i.e. Nrd,u,2 = 270.12 kN

A.1.3 Supporting column web in bending


where,

= 13.26

uRdtuRduRdt nFNF ,,1,,,,

3047.3724.83047.372

45.204524.82308,1,

RdTF

3045.37

91.12823045.20452,2,

RdTF

))1()1(5.1()1(

85.0

1

5.0

11

1

,,

3,,

uRdpl

uRd

mN

uM

cwcu

uRdpl

tfm

,

2

,,

,,4

1

10001.1

3.10550

4

1 2

APPENDIX A

Page | 76

= 0.45

= 0.434

= 0.11

So,

= 286.01 kN

A.1.4 Beam web in tension


= 490.91 kN

Therefore the overall tying resistance is taken as the value that is

least of the various modes of failures,

NRd,u = 270 kN

cd

p3

1

cd

dn

pn 0

1

11

1

2)1(

3.200

90

3.200

222

360)13(

3.200

221

))11.01()45.01(5.1434.0()45.01(

26.138 5.05.0

3,,

uRdN

uM

bupbw

uRd

fhtN

,

1,1,

4,,

10001.1

4502006

Page | 77

Steel Beam-Column Connections Designed for Robustness

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