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Bracing steel frames with calcium silicate element walls

Ng'Andu, B.M.

DOI:10.6100/IR607328

Published: 01/01/2006

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Citation for published version (APA):Ng'Andu, B. M. (2006). Bracing steel frames with calcium silicate element walls Eindhoven: TechnischeUniversiteit Eindhoven DOI: 10.6100/IR607328

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Bracing Steel Frames with Calcium Silicate Element Walls

Bright Mweene Ng’andu

CIP-DATA TECHNISCHE UNIVERSITEIT EINDHOVEN Ng’andu, Bright Mweene Bracing Steel Frames with Calcium Silicate Element Walls/ by Bright Mweene Ng’andu, Technische Universiteit Eindhoven, 2006. ISBN 90-6814-599-1 Subject headings: lateral stability/ infilled frames/ calcium silicate elements/ thin-layer mortar/interface elements/stiffness/design rules. Bouwstenen 104 Printed by the University Press Facilities, Eindhoven University of Technology, the Netherlands Copyright © 2006 Bright Mweene Ng’andu All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form by any means without prior written consent of the author.

Bracing Steel Frames with Calcium Silicate Element Walls

Proefschrift

ter verkrijging van de graad van doctor aan de Technische Universiteit Eindhoven, op gezag van de Rector Magnificus prof.dr.ir. C.J. van Duijn, voor een commissie aangewezen door

het College voor Promoties in het openbaar te verdedigen op donderdag 9 maart 2006 om 16.00 uur

door

Bright Mweene Ng’andu

geboren te Mazabuka, Zambia

Dit proefschrift is goedgekeurd door de promotor: prof.ir-arch. D.R.W. Martens Copromotor: dr.ir. A.T. Vermeltfoort

Constitution of the Doctoral Committee:

Prof. ir. J. Westra, Chair, and Dean of the Faculty of Architecture, Building and Planning, Eindhoven University of Technology, The Netherlands

Prof. ir-arch. D.R.W. Martens Eindhoven University of Technology, The Netherlands

Dr. ir. A.T. Vermeltfoort Eindhoven University of Technology, The Netherlands

Prof. Dr. D. I. McLean Washington State University, United States of America

Dr. P.L. Lapperre, Eindhoven University of Technology, The Netherlands

Prof. Dr. ir. J. G. Rots Delft University of Technology, The Netherlands

Prof. ir. H.H. Snijder Eindhoven University of Technology, The Netherlands

Prof. Dr. ir. G.P.A.G. van Zijl Stellenbosch University, Republic of South Africa

Preface

This dissertation is a culmination of over four years of research in the field of infilled frames with the particular application of calcium silicate elements as infill walls. The research was conducted at the Eindhoven University of Technology (TU/e) and was funded by the Technology Foundation STW, applied science division of NWO and the technology programme of the Ministry of Economic Affairs in the Netherlands.

The subject of calcium silicate elements as infill walls was proposed to me by Prof. Ir.-Arch. Dirk Martens and Dr Ir. Ad Vermeltfoort. The Calcium Silicate Industry enthusiastically supported the initiative and indicated that the steel frames were of immediate interest. We soon wrote a project proposal and made an application for funding to the STW. The STW honoured the scientific basis of the research and its potential application by agreeing to fund the research. As part of the monitoring system by the STW, a Users Committee composed of professionals from two universities and several industrial organizations was composed to meet every half year and review the progress and ‘potential use’ of the results of the research. The members of the Users Committee and the organizations they represented included: Prof. ir. H.H. Snijder of TU/e and the organization of ‘Steel Construction’, Prof. ir. F. van Herwijnen of TU/e and ABT Consulting Engineers, ir. H. Verkleij of Calduran Kalkzandsteen, ir. M.H.M Coppens of the Association of Calcium Silicate Manufacturers VNK, ir. G. Koers of the Royal Association of Clay Brick Manufacturers in the Netherlands, Dr ir. R. van der Pluijm of Wienerberger Bricks, Prof. Dr ir. J.G. Rots of Delft University of Technology, Dipl.-Phys. C.N.M Jansz and Dr ir. C. Meuleman of the STW and the researchers - Prof. ir-arch. D.R.W. Martens, Dr ir. A.T. Vermeltfoort and Mr B.M. Ng’andu, B.Eng., MSc.

My contact with the Department of Structural Design at TU/e was a spin-off from a previous intergovernmental cooperation project which involved the TU/e in the Netherlands and the University of Zambia (UNZA). Having studied Civil Engineering at UNZA and Structural Engineering at Strathclyde University in Glasgow, Scotland,

I saw my technical profession as a lever to improve real lives of real people, especially in my country. It was this view that inspired my curiosity in the interface between technology and economic development. And that is what latched me on to coordinate a joint exercise to draft a curriculum for ‘Non-technical courses for engineering students’ at the University of Zambia at which I was, then, lecturing. Together, with Dr. Paul Lapperre from the Technology Management faculty of TU/e, I co-edited a compendium on ‘Engineering, Management and Society.’ In the meantime, I was looking for opportunities to undertake further studies either in a wholly technical subject or an engineering and development combination subject. The TU/e offered both disciplines, but it was the former which presented the first definite opportunity.

The process of obtaining the results and deriving conclusions was of high interest to me. Being able to formulate the research questions, drawing up methods and plans of investigations and executing them are skills that I wanted to exercise. And I have had ample opportunity to do that. I believe that these methods and principles are applicable in my country just like anywhere else in the world. The type of materials used, particularly, for infill walls is most prevalent, currently, in Western Europe. There is still plenty of room to explore the potential use of calcium silicate element construction in other regions of the world.

But here then it is, never mind if it is a research of four years upon a life of four decades!

Acknowlegements

I wish to acknowledge Professor ir-arch. Dirk Martens and Dr. ir. Ad Vermeltfoort who initiated the topic and supervised this research. All along the way, they raised insightful questions with respect to the results and the process of obtaining them. They made practical suggestions and showed a close interest in the work. Their contribution to this work was invaluable. I wish also to express my gratitude to Professor Dr. ir. Jan Rots for lending me his support in fine tuning the numerical simulations. In the same vein, I am grateful to Professor Dr. ir. Gideon van Zijl for providing me with many useful comments, which, I believe, improved the final version of the thesis. I am grateful to all the members of the doctoral committee for taking time, and in the case of Professor Dr. David McLean, travelling a very long distance, to take part in the examination process of this work.

The ambient support of the whole Structural Design and Construction Technology Group of the Eindhoven University of Technology is acknowledged. Particular appreciation is due to Eric Wijen, who controlled the testing and measuring processes, Theo van der Loo, Rien Canters and Gerard Nabuurs (from Xella) who assembled and built the specimens and Cor Naninck who carried out the auxiliary material tests. I also received a lot of back-up support from Johan van den Oever, Sip Overdijk and Martien Ceelen.

I am indebted to many other colleagues who provided technical support and social encouragement, especially my several, successive officemates – Guillermo Gonzalez, Steffen Zimmermann, Dagowin la Poutré, Ernst Klamer and Sander Zegers. They, all, by virtue of proximity, became living sounding boards of ideas. Gabi Bertram deserves special mention for being an interface between my university environment and the logistical settlement of my family: securing bikes, learning Sinterklaas songs, searching for schools for the children and, of course, rowing!

A word of acknowledgement is due to Mr. Jan van Cranenbroek, the former Head of the now dissolved Bureau of International Activities at the Eindhoven University of Technology. He was in a

very large measure responsible for my initial contact with the Structural Design and Construction Technology Group.

I owe a debt of gratitude to all members of the International Baptist Church (IBC) of Eindhoven over the last five years for supporting my family in ways too numerous to itemize. My family acknowledges the practical assistance we received from Jan and Marianne van der Mijl, Huub and Annie Beeren, Margaret Tinsley, Zizi Colak, Alexandra Perros, Art and Sharon Houweling, Dianne Hija, Eunice Kruiswijk, Petra Kantelberg, Henry Kantelberg, just to mention but a few. Similarly, I would like to express my deep appreciation for the all round support of Anthony and Ivy Ng’oma, Paulos and Annie Nyirenda, Priscilla Mwansa, Mercy Umukoro and Misheck and Charity Mwaba. These people and their families have been indeed friends suited to be close to my family at ‘such a time as this’.

The last, but by no means least, word of appreciation must be reserved for my cherished wife, Priscillar, our dear son Bomba and our precious daughters Malelo and Bona-Luwi. Although they will no doubt have many precious memories of our Dutch experiences, the last four years have not always been buoyant for them. They often have had to make do with a preoccupied husband and papa, with many a reminder of the high opportunity cost incurred in allowing me to embark on this journey. Thankfully they have pretty much weathered the challenge. If there was any credit due to this work, it would be as much theirs as mine. Bright M. Ng’andu Eindhoven, The Netherlands January, 2006

CONTENTS Preface i Acknowlegements iii Summary ix

1 Introduction 1 1.1 Infilled frames 1 1.2 Building with Calcium Silicate Elements (CASIELs) 2 1.3 Infilled frames with CASIEL walls 4 1.4 Objectives, Methodology and Scope 6 1.5 Outline of thesis 8

2 Behaviour and analysis of infilled frames - State of the art 9 2.1 Background 9 2.2 Experimental evidence 11 2.3 Modelling of infilled frames 17

2.3.1 Global models 17 2.3.2 Fundamental models 27

2.4 Summary of literature review 31 2.5 Problem statement 32

3 Experimental design and procedure 35 3.1 Overview 35 3.2 Objectives of experiments 36 3.3 Testing apparatus 36

3.3.1 Reaction frame 37 3.3.2 Load introduction 40

3.4 Description of specimens 41 3.4.1 General description 41 3.4.2 Member sizes 41 3.4.3 Preparation of specimens 43 3.4.4 Specimen distinctives 44

3.5 Measurements 48 3.6 Load control and Test procedure 49 3.7 Summary 50

4 Evaluation of experimental results 53 4.1 Zero correction and rigid body movements 53 4.2 Overview of load deformation responses 56 4.3 Principal stress distributions 59 4.4 Influence of frame stiffness 65

vi Contents

4.5 Influence of gaps 68 4.6 Effect of corner bearing wedges 69 4.7 Conclusions 71

5 Finite Element Model 73 5.1 Modelling in general 73

5.1.1 The finite element method 74 5.1.2 Incremental-iterative solution procedure 76

5.2 Objective of the model 78 5.3 Development of infilled frame model 79 5.4 Physical and material modelling 80

5.4.1 Modelling beams and columns 80 5.4.2 Modelling bolted connections 82 5.4.3 Modelling of CASIELs and joints 84 5.4.4 Modelling frame-to-wall interfaces 89

5.5 Assembly and evaluation of model 91 5.5.1 Analyses of bare frames 92 5.5.2 Preliminary model of infilled frame 95 5.5.3 Influence of normal and shear stiffnesses

of frame-to-wall contact 100 5.5.4 Influence of normal and shear stiffnesses

of the joints 101 5.5.5 Influence of play in the bolted connections 102 5.5.6 The final model 104

5.6 Model validation 105 5.6.1 Comparison of numerical and

experimental global behaviour 105 5.6.2 Comparison between numerical and

experimental stress distributions 107 5.7 Deduction from numerical model 109

6 Parametric studies 111 6.1 General 111 6.2 Geometric Parameters 112

6.2.1 Overview of numerical results for geometric parameters 114

6.2.2 Influence of aspect ratio 116 6.2.3 Influence of frame member sizes 117 6.2.4 Influence of rigidity of connections 118 6.2.5 Influence of wall thickness 119

Contents vii

6.2.6 Influence of relative wall-to-frame stiffness ratio 120 6.2.7 Effective width of equivalent diagonal strut 122

6.3 Interface parameters 123 6.3.1 Influence of frame-to-wall gaps 123 6.3.2 The influence of top gaps on frames with

corner bearing wedges 124 6.4 Material parameters 126 6.5 Summary of parametric studies 127

7 Towards design guidelines 129 7.1 Preamble 129 7.2 Basic load-deflection curve 130 7.3 Resistance to diagonal tension cracking 131 7.4 Resistance to shear – sliding 133 7.5 Resistance to crushing 135 7.6 Horizontal deflections 136 7.7 Comparison of simplified equations with

numerical results 137 7.8 Conclusion 139

8 Conclusions and Recommendations 141 8.1 Conclusions 141 8.2 Design recommendations 144 8.3 Future research recommendations 145

Bibliography 151 Appendix A: Extracts from drawings of Test Set-up

and Frames 161 Appendix B: Basic principles of Sensors and Data

Acquisition System 165 Appendix C: Auxiliary tests 167 Appendix D: DIANA Elements used in FE model 173 Appendix E: Outline of design guideline and

explanatory notes 175 Notation 181 Samenvatting 185

Summary

This research aims at providing a scientific basis for development of design guidelines for steel frames infilled with calcium silicate element (CASIEL) walls, thus, providing stability to building frameworks. Although CASIEL infill walls are already commonly found in building structures, the structural role they play is frequently ignored. This research postulates that this role must be designed for rather than simply ignored or assumed.

Accounting for the contribution of infill walls in resisting loads leads to more efficient use of materials. This is because the rigidity and reserve strength provided by the infill walls allow for relatively lighter steel frames with simple connections. Evaluating the stiffness and strength of the infills also leads to reduced risks of damage to the infill walls, the bounding frames and the finishes. This in turn can lead to significant reductions in maintenance and rehabilitation costs.

A series of ten large-scale tests has been conducted and a finite element model to simulate these experiments has been assembled. The finite element model has been used to carry out parametric studies. Simplified equations for prediction of cracking loads and deflections have been proposed and evaluated in the light of numerical results.

The experimental set-up involved a rigid twin-triangular reaction frame as a platform for the support and loading of the specimens. Monotonic deformation controlled loads were applied at the top of one column until the specimens suffered several cracks. The parameters included in the experimental investigation were frame-to-wall contact, bounding frame stiffness and a novel bearing wedge construction detail.

The finite element model predicts the separation of frame-to-wall interfaces, the primary stiffness of the infilled frames, and the onset of cracking in the infill wall. The model utilises elements and material libraries provided with the commercial software, DIANA. Linear elastic behaviour with a brittle tension limit is assumed for the CASIELs. Non-linear elastic behaviour is prescribed for frame-to-wall contact and thin-layer mortar joints. Material properties used in the model were obtained either from auxiliary tests conducted along side

x Summary

the large-scale infilled frame tests or estimations based on information from literature. The model was validated by a comparing numerical with experimentally determined stiffnesses, cracking loads and stress distributions.

Load-deformation curves show a three stage trajectory prior to cracking. In general, there was an initial stiff stage followed by a much less stiff stage during which frame wall separation occurred and another stiff range leading to, in the majority of cases, diagonal tension cracking in the infill walls. Shear sliding along the top most bed joint was observed in some specimens. Increasing the stiffness of the bounding frames increased the stiffness of the infilled frames and moderately increased the cracking loads. An initial top gap resulted in reduced infilled frame stiffness during the transition phase, although it did not significantly reduce the cracking load. By using bearing wedges in the top corners, the influence of the top gap was practically eliminated. This technique may be significant in developing a construction technique for industrial application of infilled frames. The experimental global responses and the strain distributions on the walls were used as a basis for calibration of the finite element model.

It has been concluded that composite infilled frame action is optimum in infilled frames with aspect ratios in the range of 0.8 to 1. In relatively squat infilled frames, the wall dominates the behaviour while the frame’s contribution diminishes. On the other hand, for relatively slender infilled frames, bending deflections increasingly overshadow the composite action of the bounding frame and infill walls.

It has been proposed that the stiffness of an infilled frame may be approximated by a standard analysis of a frame braced with an equivalent diagonal strut. The equivalent diagonal strut is assumed to be pinned to the intersection of the centrelines of the beams and columns. The thickness and material properties of the equivalent strut are assumed to be the same as those of the CASIEL infill wall. For slenderness ratios less than 1, the effective width of the diagonal strut may be estimated as one-eighth of its length. The diagonal cracking resistance and shear sliding resistance in the joints are predicted on the basis of average stresses over horizontal or diagonal sections in the infill wall. The crushing resistance loads are nominally estimated by

Summary xi

using the cross-sectional area of the equivalent diagonal struts and the experimentally determined crushing strength. These simplified expressions are indicative of how design guidelines might be formulated.

Finally, a list of recommendations for continuation of the research, towards development of design guidelines, is provided. The importance of the research topic is underscored by worldwide efforts to improve design codes, in general, and in seismic engineering applications in particular.

xii Summary

Chapter 1

1Introduction

Abstract This introductory chapter highlights the primary relevance of this work, namely, lateral stability of building structures. It defines the terms ‘infilled frame’ and ‘calcium silicate element (CASIEL)’. The methods and results obtained are indicated, and the outlay of this thesis is given.

1.1 Infilled frames

Every statement on the purpose of structural design must include at least the four concepts: safety, function, economy and aesthetics. With respect to safety, most people learn very early in life that things have a tendency to fall, and that can hurt! As such everyone instinctively feels the need for safety from collapse due to gravity loads. The need for safety from damage due to lateral actions is less obviously recognised. However, as every structural engineer knows, it is vital that a structure be safeguarded, that is, braced, against the effect of lateral actions. Lateral actions on structures arise from wind, foundation movements, vibrations, differential moisture or temperature movements, earthquakes and blasts. These actions may result in excessive deflections, deformations or tilting of a structure. Consequently, a building may suffer damages to finishes (plaster, paint, window panes, doors, claddings, ceilings, electrical fittings, plumbing fittings etc.), cracks in walls, or worse still, structural damage leading to a catastrophic collapse.

In order to provide building structures with resistance to lateral actions, engineers traditionally incorporate diagonal steel cross braces

2 Introduction

in sections of roofs or walls. Another common way of bracing is through the use of concrete shear walls placed around stairways, lift shafts and service cores. Additionally, as has been recognized for a long time, infilled frames are a (potential) form of bracing.

Infilled frames are beams and columns confining walls. An example of infilled frames is shown in Figure 1.1. The beams and columns, which are part of the supporting frames, are usually made out of steel or reinforced concrete. The walls, hereinafter referred to as ‘infill walls’, commonly occur as space dividers or as cladding to the external envelope of buildings. As such, infill walls are usually ‘designed’ according to criteria such as fire resistance and sound proofing, rather than according to structural properties. Traditionally, these infill walls are built as brick (masonry) walls. With rising labour costs, diminishing craft skilled labour and mechanisation of production, new methods of erecting walls, especially tending towards prefabrication, are evolving. One such evolution is the use of calcium silicate elements.

1.2 Building with Calcium Silicate Elements (CASIELs)

In the last two to three decades, a new way of building walls, namely with calcium silicate elements in thin–layer mortar, has evolved (Berkers 1995). Calcium silicate elements are large building ‘stones’, produced by mixing sand, lime and water, moulding and curing under conditions of pressurized steam (Figure 1.2). The term ‘element’ is used to distinguish them or their size from traditional units and blocks. The dimensions of elements are 900 to 1000 mm long, 520 to 650 mm high and 100 to 300 mm thick, and they weigh approximately 100 - 360 kg per piece. As such, they are in the range of 10 – 36 times heavier than ordinary blocks, weighing, say, 10 kg.

Unlike traditional masonry in which a bricklayer must painstakingly place unit by unit, erecting CASIEL walls involves the use of a small crane. An element is gripped through purpose-inbuilt holes, hoisted and hand guided into position. Its edge, which has a groove is placed on the ‘tongue’ edge of the adjacent or preceding element (see Figure 1.3). Dimensional tolerances and adhesion at the

Building with Calcium Silicate Elements (CASIELs) 3

joints are achieved through special thin-layer ‘mortar’. The typical joint thickness is 2 to 3 mm.

Figure 1.1: Infilled frames - beams and columns confining walls

pressingmachine

reactorreaction

calcium silicate elementautoclave

sand

dosing

water

mixing

limewater

curing moulding

height: 520 - 600 mmlength: 900 - 1000 mmthickness: 100 - 300 mmcompressive strength:

15 - 45 N/mm2

mixing

Figure 1.2 : Production process and dimensions of Calcium Silicate Elements

4 Introduction

Figure 1.3 : Building walls with CASIELs

Building with calcium silicate elements has tremendously enhanced the speed of erecting walls while reducing labour costs and the physical stress of the bricklayers on site. Finishing costs are also significantly reduced, due to the smoothness of the surface of calcium silicate elements. Other factors cited in favour of calcium silicate elements include excellent structural performance of the material, environmental friendliness (the material can be crushed and used as earth fill or reused to produce other calcium silicate products after the structure’s life span), better quality products due to production of elements in factory controlled conditions and possibilities of construction during cold/rainy weather conditions.

1.3 Infilled frames with CASIEL walls

Depending upon the construction details, CASIEL walls may or may not have contact with the bounding frames. When construction details allow contact between frame members and walls, there results composite action between the frame and infill wall. This composite action entails that walls participate in carrying lateral and, conceivably, vertical loads. Consequently there is a structural interaction in which walls tremendously increase the stiffness and strength of the frames while frames provide some ductility to the otherwise brittle walls.

However, designers generally still ignore the structural contribution/influence of infill walls. The reluctance of engineers to include the influence of infill walls in design calculations is largely due

Infilled frames with CASIEL walls 5

to uncertainty concerning the complex behaviour of infilled frames. There is uncertainty also because of fear that partitions may be removed at a certain point during the life of a building. It must be argued, however, that ignoring the structural contribution/influence of infill walls simply due to uncertainty is not all together satisfactory because of at least two reasons.

Firstly, ignoring the structural influence of infill walls may lead to inefficient and uneconomical over-designs. That is to say that available stiffness and strength goes unused while larger frame member sizes and more rigid connections than necessary are employed. In today’s highly competitive business environment, limiting side sway of building frames using readily available infill walls can lead to significant cost savings.

Secondly, and probably more importantly, ignoring the structural influence of infill walls may lead to unanticipated damage of the infill walls or the structural frames. Due to their extra rigidity, infill walls may attract more stresses to certain parts of the structure. From the resulting frame-infill interaction, for instance, shear failure of bed joints in the wall can lead to brittle shear failure of columns. Infill walls also can also over-strengthen the upper storeys of a structure and induce a soft first storey, which is undesirable from the earthquake resistance point of view. In a word, ignoring the structural contribution of infill walls does not always lead to conservative designs.

The motivation of this research, therefore, was the need to evaluate the role played by an increasingly popular construction practice and material on the structural behaviour of building frameworks. It is postulated that:

the use of calcium silicate element walls to stiffen frames could lead to structurally more efficient and economic building construction. However, design of these infilled frames is hampered by the lack

of design guidelines. Clarifying the behaviour of these frames, taking into consideration construction details, which produce different frame-to-wall interface conditions, is a prerequisite to the development of the much desired design guidelines.

6 Introduction

1.4 Objectives, Methodology and Scope

Although much research has been done on infilled frames in the past, there has not yet been any research involving infill walls constructed from CASIELs. Most full-scale experiments have been on frames infilled with clay or concrete brick masonry. Scale model tests using micro-concrete have also been done.

While similarities may be expected between the behaviour of CASIEL walls and traditional brick masonry infills, significant differences might also occur. The major difference in the two types of walls is that the former has much fewer and much thinner joints than the latter. Depending upon the scale at which the wall is regarded, either of the wall types may be seen as more homogenous than the other. From a global point of view, a masonry wall, with small bricks, may be seen as a ‘homogenous’ composite while a CASIEL wall is an articulation of large blocks with discontinuities at the thin-layer joints. On the other hand, at a local level, CASIELs may be taken as homogeneous (and isotropic) while brick walls appear as a heterogeneous articulation of bricks and mortar through discrete interfaces.

A second peculiarity of CASIEL walls has to do with the construction process. By virtue of the size of the elements and the handling equipment, some working space, as illustrated in Figure 1.4, is required to fit in the last CASIEL row below the roof beam. The result is that initial gaps are left between the frame and the wall. This difficulty in achieving a snug contact between the wall and the frame results in boundary incompatibilities, which, coupled with shrinkage, deserve special attention in the modelling and design of the structure. If the walls must participate in carrying the load, construction techniques and details must be developed to ensure predictable transfer of stresses across the frame-to-wall interface. Conversely, if it is assumed that infill walls do not participate in carrying loads, details which match this assumption must be realised.

This research was aimed at developing design guidelines for steel frames infilled with CASIEL panels and subjected to external in-plane loads. In this regard, the objectives set were to experimentally

Objectives, Methodology and Scope 7

establish the general behaviour, develop a numerical model, calibrate it and perform parametric studies.

Single-storey, single-bay infilled frames without openings in the infills were treated. Although it was borne in mind that the combination of CASIEL infills with reinforced, particularly precast, concrete frames is of obvious interest, the current investigation was limited to steel frames. Monotonic in-plane loading has been used in the investigation. Other types of loading such as cyclic and out-of- plane loading were not treated. It is acknowledged that these other forms of loading are important issues which need to be investigated in follow-up research programmes.

working space

gap

Figure 1.4 : Infilling frames with CASIELs, leaving boundary gaps

In the large-scale infilled frame tests carried out in this research, the response of infilled frames to in-plane lateral monotonic loads was observed. In these tests, the variables were: sizes of frame members, gaps between the frame and infill wall and the use of ‘corner bearing wedges’. A numerical model using DIANA was created. DIANA is a finite element modelling program developed by the Netherlands Organization for Applied Research. Standard elements available in the software were used. The model was used to conduct parametric studies. On the basis of experimental and numerical studies, simplified equations for approximating the deflections and failure loads of this type of infilled frames are recommended.

8 Introduction

1.5 Outline of thesis

This thesis is divided into eight chapters. In the current, introductory chapter, the relevance of the subject has been anchored in the area of lateral stability of building structures. A case for possible use of CASIEL infill walls as braces has been postulated. The scope and limitations of the investigation have been indicated.

In the next chapter, the general behaviour of infilled frames, as found in the literature, is described. The evolution of analysis of infilled frames is delineated. Herein, the key factors that affect the behaviour of infilled frames are discussed.

Chapter 3 is a detailed description of the physical experiments that were conducted. Results from these experiments are evaluated in Chapter 4. Details of the developed numerical model are given in Chapter 5. Parametric studies are described and discussed in Chapter 6. In the penultimate chapter, simplified equations for prediction of the stiffnesses and failure loads of the infilled frames are proposed and evaluated.

Finally, the summary, main conclusions and recommendations from the research are given in Chapter 8.

Chapter 2

2Behaviour and analysis of infilled frames - State of the art

Abstract This chapter provides an overview of findings from experimental and analytical research in infilled frames during the last half century. The focus is kept on steel infilled frames although results of tests on reinforced concrete infilled frames are reflected on when they are deemed relevant. Experimental investigations have been conducted by several researchers using a wide range of testing scales, numbers of specimens, infill materials, experimental set-ups and parameter studies. Several damage patterns have been observed. Experimental research has been complimented by analytical attempts to model infilled frame behaviour. Global and fundamental models have been formulated. The infilled frame structure is however still difficult to model, partly, due to a host of non-linear phenomena associated with infills and with frame-to-infill contact areas. There are no universally accepted design guidelines for infilled frames. There is also no experimental or analytical data regarding the use of CASIELs in infilled frames. This research, therefore, represents a new application for a relatively young but significantly prevalent method of wall construction.

2.1 Background

Considerable interest in infilled frames as a research topic has persisted for more than half a century. In the early development of research in infilled frames it was military interest in harnessing the resistance of brickwork infills to blast loadings that inspired

10 Behaviour and analysis of infilled frames – State of the art

exploratory tests. References to these tests in the early 1950s have been made by Benjamin & Williams (1958), Mainstone & Weeks (1970) and Pereira Ricardo (2005). The work of Wood (1958) on stability of tall building structures, emphasizing the importance of restraining side sway in multi-storey frames, enhanced the interest in the stiffening effects of cladding in buildings. Wood pointed out that the benefits of the then new plastic design methods of steel frameworks were compromised by ‘simultaneous reduction in elastic stability’. It was suggested that including spine or end walls to eliminate side sway, and then using the then modern frame design methods which involved no-sway, could obtain economical design solutions. This approach begged for ‘more information’ on the effects of composite action between frames and walls.

The pioneering work of Polyakov (1956), Holmes (1961), Stafford-Smith (1962) and others led to recognition of the fact that infill walls provide strength and stiffness to frameworks while the bounding frames can provide the composite structure with some ductility. Subsequent research was aimed at identifying many issues of interest that affect the degree of this composite action between frames and infills. As well expressed by Stafford-Smith (1966), ‘the stiffness and strength of an infilled frame are different from the simple sum of the two component structures. The structural interaction between the two components of the structure produces a composite structure with a more or less unique behaviour. This behaviour is complicated because the frame and the infill panel mutually affect their respective contribution to carrying loads. The frame, while directly bearing a portion of the load, primarily serves to distribute the applied load onto the wall. The way in which this distribution occurs affects the stiffness response of the composite structure. Meanwhile, the contribution of the frame to the overall stiffness depends upon its deformed shape, which in turn is determined by the reaction from the wall. At the same time, the behaviour of the infill, that is its stiffness, failure mode and strength are affected by the stress state in the infill. This stress state is a function of the distribution of the load from the bounding frame. Inherently, therefore, the infilled frame structure is indeterminate.’ Experimental evidence for these conclusions is given in more detail in Section 2.2.

Background 11

From experimental observations, Kadir (1974) reinforced the observations of Stafford-Smith (1966) that the degree of composite action between frames and infill walls depends upon the relative stiffness of the bounding frames to walls. The role of frame-to-wall interface conditions leading to non-linear stress distributions was highlighted by Liauw & Lee (1973). The influence of frame-to-wall interface gaps was investigated by Riddington (1984). The behaviour of infilled frames with openings in the infill panels was investigated by, among others, Dawe & McBride (1985) and Dawe & Yong (1985).

In recent years, advances in earthquake engineering have brought to the fore, once again the need to assess the role played by infills in resisting lateral loads. Restoration and upgrading of existing building structures often demands an evaluation of the strength of infill walls. Moghaddam (2004), El-Dakhakhni (2004) and Saatcgoulu (2004), have explored the use of new materials, in particular, fibre reinforced polymers (FRP) in techniques for the rehabilitation of damaged masonry infills while El-Dakhakhni et al. (2005) have investigated the use of FRP as a form of reinforcement in hazard mitigation.

In the sections that follow, experimental evidence and analytical models found in literature are described in more detail.

2.2 Experimental evidence

There is a fair, though heterogeneous, volume of experimental data from tests on steel and reinforced concrete frames infilled with various types of infill panels. Comprehensive overviews of experimental results have been compiled by Moghaddam & Dowling (1987), Calvi (1996) and Drysdale (1994).

There are several issues found in the literature that relate to the behaviour of infilled frames, such as, stiffness of bounding frames, stiffness of walls, damage patterns, influence of openings, repair techniques, size effects and types of loading. In view of the number of issues of interest, the number of tests per research programme tends to be rather small. As such, part of the difficulty in trying to normalise the experimental results found in the literature is the variety of specimen sizes, materials and loading regimes.


The results of two early extensive small scale testing programs on infilled frames conducted by Stafford-Smith (1966) and Kadir & Hendry (1975) are instructive. Stafford-Smith tested forty-two square infilled frames. The steel frames were made out of rectangular mild steel sections rigidly connected by welding. The infills were made out of 152.4 mm by 152.4 mm by 19.1 mm thick mortar panels. Thirty-two of the frames were diagonally loaded (Figure 2.1a) while the rest, just as in the case of Kadir & Hendry, were laterally loaded (Figure 2.1b). Kadir and Hendry carried out forty-three tests on mild steel frames infilled with one-third model bricks in high bond strength mortar. Their specimens were 400 mm high by lengths ranging from 800 to 1400 mm.

(a)

load

infillwall

infillwall

infillwall

frameload

(b)

Figure 2.1 : Scheme of testing arrangements for (a) diagonally loaded (b) laterally loaded specimens

The main findings from the two testing programs were similar and as follows:

(i) Infill walls increased the stiffness of frames by factors ranging

from ten times to several hundredfold. (ii) The sequence of damage was: separation of the frame from the

walls at relatively low loads, diagonal shear cracking, proliferation

Experimental evidence 13

of cracks in the case of brickwork infills, spalling and crushing of the infill walls. Crushing indicated attainment of maximum resistance. Stiffer bare frames produced stiffer infilled frames. The increase in stiffness was however not directly proportional to the increase in bare frame stiffness. In Stafford-Smith’s tests, stiffer frames also led to higher cracking and crushing loads. In Kadir & Hendry’s tests, stiffer frames led to higher crushing loads, but not so much higher cracking loads.

(iii) For the more flexible frames, crushing occurred at the loaded corners. For stiffer frames however, crushing was more randomly distributed and remote from the loaded corners.

(iv) Increasing the strength of the bounding frames did increase the stiffness and ultimate strength much more than it did the cracking loads.

(v) Lack of fit, i.e., initial gaps between the frame and infill panel reduced the stiffness and cracking strength but not the ultimate load.

(vi) Kadir & Hendry reported that pinned frame connections led to a reduction of stiffness and ultimate load.

An extensive full-scale testing programme on steel infilled

frames was directed by Dawe and reported in Dawe & McBride (1985) Dawe & Yong (1985), Amos (1985), Richardson (1986) and Dawe & Seah (1989). In this programme, twenty-eight large scale steel frames infilled with concrete block masonry were tested. The steel frames were 3600 mm long and 2800 mm high and the infill panels consisted of 200 by 200 by 400 mm concrete block walls. As is common in most infilled frame testing arrangements, the frames were subjected to a concentrated monotonically increasing load at an upper corner of the frame (Figure 2.2). Variations in the infilled frames tested included rigid frame connections, articulated frames, panel-to-column ties, panel openings, bond beams, and gaping between the panel and roof beam.


infillwall

frameload

structural floor

Figure 2.2 : Common testing scheme for infilled frames

In general, failure modes and cracking patterns were similar to those of small-scale specimens described earlier. It was observed that in some infilled frames, cracking of bed joints between the upper layers of blocks occurred prior to diagonal cracking. Joint reinforcement led to a more random distribution of cracks while bond beams led to a cracking pattern that resembled sub frames within the infill. Joint reinforcement, panel to column ties and bond beams all increased the stiffness of infilled frames but did not, however, change the ultimate load.

With a similar test arrangement, and similar results, Dhanasekar (1985) carried out tests on three steel frames with brick infill walls. His specimens were 1555 mm long and 1060 mm high. Flanagan (1992) and Mosalam et al. (1997) carried out tests on three and five frames, respectively, on semi-rigidly connected frames with hollow tile clay brick walls and model concrete block walls respectively. The infilled frames were subjected to quasi-static cyclic loading. In addition to observations similar to those of others before, it was observed that strong blocks led to mortar cracking while weak blocks led to corner crushing as an early sign of damage. Mosalam et al. measured and observed the phenomenon of dilatancy of bed joints, whereby joints opened further in their thickness direction as the shear sliding progressed. Cracked specimens in which dilatancy was observed ended up with a tight fit against the bounding frames after cracking. The influence of openings in the infills was also investigated. It was observed that the reduction in load resistance of an infilled frame is


not directly proportional to the reduction in cross sectional area due to openings. The influence of openings rather varied depending on both size and position. Infilled frames with symmetrical window openings, for instance, yielded nearly the same resistance as those without openings while infilled frames with door openings had about 20% reduction in shear resistance. Infills with openings tended to start cracking at the corners of the openings. It was further observed that infilled frames with openings, although having a lower shear resistance, exhibited more ductile behaviour than those with solid infills.

More recently, large scale infilled frame tests have been conducted by Moghaddam (2004), El Dakhakini (2004), El-Dakhakhni et al. (2005). Moghaddam tested five rigidly connected steel frames with 1800 mm long and 940 mm high solid and perforated brick walls, subjected to cyclic loading. He investigated repair techniques on damaged infill walls by using concrete blocks in the corners and covering the panels with micro-concrete or chicken mesh reinforcement. Results showed that concrete corners and micro-concrete cover restored the stiffness and strength of damaged infill walls. El Dakhakini (2004) tested five steel frames, with hollow concrete block infill walls. The specimens were 3600 mm long and 3000 mm high. They were subjected to quasi-cyclic loading. He investigated a repair technique in which fibre reinforced polymer (FRP) was applied on the surfaces of the solid infills and infills with openings. It was shown that FRP enhances the shear resistance and ductility of infilled frames. A new damage characteristic that was observed was the delamination of the FRP from the wall. Plastic deformations of the steel near the frame connections were also observed at excessive levels of horizontal deflection.

Failure modes

From the experimental evidence drawn so far, and corroborated by results of tests on reinforced concrete infilled frames, a variety of (combinations of) failure modes, as shown in Figure 2.3 has been observed.


(f) out of plane

(e) failure of frame members

(d) corner crushing(c) diagonal tension

(a) shear slip (b) proliferationof cracks

Figure 2.3 : Failure modes of infilled frames

In all tests frame-to-wall separation at relatively low horizontal loads has been observed. Locking of the infill panel with the loaded corners of the frame makes the wall act like a compression strut. The evolution of a particular failure mode depends upon the geometric and material characteristics of the frame and the infill panel. The panel may crack by horizontal sliding along the bed joints (Figure 2.3a). Such a crack may be inclined by stepping over some courses of brickwork. If the shear strength of the mortar joints is particularly low, this can further lead to a multiplicity of sliding cracks (Figure 2.3b). If the joints of the infill wall are strong enough, the diagonal strut may eventually crack due to development of tension in the orthogonal diagonal direction (Figure 2.3c). This can further lead to crushing at the points of stress concentration (Figure 2.3d). Results of reinforced concrete infilled frame tests carried out by Mehrabi et al.


(1996) have shown that highly reinforced infill panels with weak frame members could result in failure of frame members (Figure 2.3e). Columns or beams may fail by formation of plastic hinges near their connections or at points of excessive shear stresses arising from sliding failure in the joints of the infill panel. Another important failure mode is out of plane failure of infill panels (Figure 2.3f). Out of plane resistance of infill panels has been experimentally investigated by Dawe & Seah (1989), Abrams et al. (1993) and Flanagan & Bennett (1999). In these tests, the effects of height-to-thickness ratio, combined in-plane and out-of-plane loading and the effect of prior damage due to in-plane loading were investigated. The results of all the tests indicated that an infill panel that is not isolated by gaps from the frame can develop enough out-of-plane resistance so as not to require any ties or anchors to the frame.

2.3 Modelling of infilled frames

Experiments have demonstrated that infill walls have a significant influence on the stiffness and strength of frames. Models to predict the behaviour of infilled frames have been formulated with moderate success. These models may be divided into two broad categories: global models (macro-level) or fundamental models (micro-level and meso-level).

2.3.1 Global models

Global models aim at reproducing or predicting the overall stiffness and failure loads of infilled frames. In this section, global models are discussed under the sub-headings: elastic and plastic methods. Elastic theory methods

The most developed elastic approach is the diagonal strut representation. A mention, however, is first made of an approximate analytical method proposed by Liauw (1972) for analysing infilled frames with or without openings in the infill walls.


Liauw’s method was based on the fact that the infill increases the stiffness and strength of the frame members by magnitudes which depend upon the dimensions and properties of the infill wall. Hence the actual frame was transformed into an equivalent rectangular frame with section properties of the columns and beams derived from ‘composite T-sections’. The equivalent frame was then analysed using standards structural analysis procedures. This method was found to yield good agreement with experimental stiffnesses for infilled frames with openings more than 50% of the full infill wall area. When the openings were less than 50%, the theoretical method underestimated the stiffness by as much as 40%. No comparison of collapse loads is available. There is no evidence that this equivalent frame method has been adopted by others. This may be due to the assumption made, that the infill wall and the members are formed as a monolithic structure, which is very rare in practice. Having observed the early separation of infill panels from frames except at regions near the loaded corners, Polyakov (1956) became the pioneer of the equivalent diagonal strut analogy. In this analogy, illustrated in Figure 2.4, an infill panel is replaced by a compression strut of uniform cross section, pin-connected to the frame at the compression corners. Standard frame analysis procedures can then be applied to the ‘braced’ frame. Width of equivalent strut, w

The key task in the equivalent diagonal strut model is how to determine the geometric and physical properties of the strut so that the behaviour of the strut is indeed equivalent to that of an infill wall. Several formulae have been suggested for the effective width of the equivalent strut. These range from simple fractions of the diagonal length of the infill panel to more complex expressions that define the effective width as a function of relative stiffness of the wall to the surrounding frame.

Holmes (1961) proposed the ‘one third rule’ for analysing steel frames with brickwork and concrete infills. According to this rule, the width of the equivalent strut is one third of the diagonal length of an infill panel. The cross-sectional area of the equivalent strut is thus

Modelling of infilled frames 19

taken as (ld t)/3 where ld and t are the diagonal length and thickness of the infill panel respectively.

equivalentstrut

w

direction ofloading

Figure 2.4 : Idealization of an infill panel as equivalent diagonal strut

Stafford-Smith (1962) used the beam on elastic foundation theory to express the contact length between the column and wall. In this case the infill wall is equivalent to the foundation and the column is the interacting member. If the column is considered as a beam on an elastic foundation which remains in contact with the foundation over a length αh when subjected to a concentrated load, P, (Figure 2.5) it can be shown that:

xP xyt k e

2 cosλ

λ λ= ⋅ (2.1)

where: kE I

4λ⎛ ⎞

= ⎜ ⎟⎝ ⎠

in which k is the foundation modulus

t is the constant width of the column in contact with the foundation, and EI is the flexural rigidity of the column.


P

infill wall

y

xah

column

Figure 2.5: Beam on elastic foundation analogy for contact length between column and infill

The contact length, αh, is defined when λx = π/2, and is given by:

2hh

παλ

= (2.2)

where:

244i

hf c

E t sinE I h

θλ⎛ ⎞

= ⎜ ⎟⎜ ⎟⎝ ⎠

(2.3)

in which: Ei is the modulus of elasticity of the infill, t is the thickness of the infill, Ef is the modulus of elasticity of the frame material, Ic is the second moment of area of the column, θ is tan-1 (h/l), h and l are the height and the length of the infill, respectively. By similar considerations for a beam on an elastic foundation

loaded with a moment, the contact length αl between the beam and the foundation can be expressed as:

παλ

=ll

(2.4)


where:

il

f b

E t sinE I l

244

θλ⎛ ⎞

= ⎜ ⎟⎜ ⎟⎝ ⎠

(2.5)

and Ib is the second moment of area of the beam.

The parameters λh and λl are sometimes multiplied by the length and height, respectively, to conveniently express them in dimensionless terms λhh and λll. The smaller the value of λh or λl, the longer the contact length and the larger the influence of the column or beam. In this way Stafford-Smith (1966) explained his experimental observations in which there were disproportionate increases in overall stiffness for relatively small increases in frame stiffness. Stafford-Smith proposed that the effective width of the equivalent diagonal strut should be expressed as a function of λh or λl. By assuming attainment of plastic failure in the infill panel at the loaded corners, the compressive diagonal failure loads could be expressed as functions of the contact lengths. However, when compared with experimental results, it was found that, in general, the theory tended to overestimate the stiffness and failure loads.

By assuming a triangular distribution of stress over the infill-to-frame contact (Figure 2.6) and using Stafford-Smith and Carter (1969)’s approach, Hendry (1990) proposed that the effective width be taken as:

l hw 2 212 α α= + (2.6)

l h

221 1

2 2π

λ λ⎛ ⎞⎛ ⎞

= +⎜ ⎟⎜ ⎟⎝ ⎠ ⎝ ⎠

(2.7)


infill ofthickness t

ah

h

Figure 2.6 : Triangular distribution of stresses along contact length

Other researchers have proposed refinements or alternative definitions of the effective width, w, of the equivalent diagonal strut. Based on experimental and analytical data Mainstone (1971) and Liauw & Kwan (1984) proposed expressions (2.8) and (2.9) respectively. Paulay and Priestly (1992) advocated a conservative value of one quarter of the diagonal length and FEMA 306 (1998) recommended a modification of Mainstone’s formula and proposed equation (2.10).

0.30.16 ( )h dw λ h l−= (2.8) 0.95

h

h cosθwλ h

= (2.9)

0.40.175 ( )h dw λ h l−= (2.10) where: ld is the diagonal length of the infill

These expressions for w yield unequal values of the effective

width of the equivalent diagonal strut. A fuller description and comparison of them is given in Chrisaffulli et al. (2000). Shing & Mehrabi (2002) have also pointed out that several researchers have reported a wide difference in the overestimations or underestimations of effective widths from these expressions compared to their experiments. There is therefore no definitive conclusion concerning the matter. The common agreement, however, is that the results


indicate that the width of the equivalent strut decreases when the parameter λh increases.

The major limitation of the equivalent diagonal strut analogy lies in its inability to give the stress distribution in the panel or indeed in the frame. In a bid to overcome this disadvantage, several researchers have proposed modifications to the single strut idealisation. Klinger and Bertero (1975) used two struts across the two diagonals (Figure 2.7a) to try and capture the degradation of stiffness when there is a reversal of loads. Thiruvengadam (1985) proposed the use of several short diagonal struts over the area of the infill (Figure 2.7c). In this way, openings could be conveniently incorporated by removing appropriate struts across the openings. This approach was also used by Srmakezis and Vratsanou (1986). Chrysostomou (1991) and Chrysostomou et al. (1992) proposed to model the infill by using three struts in either diagonal direction (Figure 2.7b). El Dakhakhini et al. (2003) have adopted the limit analysis approach of Saneinejad & Hobbs (1995) to define properties of struts in a three-diagonal strut model in order to assess the stresses in the bounding frame. In order to simulate the horizontal shear sliding in the joints, Leuchars & Scrivener (1976) suggested the model illustrated in (Figure 2.7d). There is however no available information on any evaluation of Leuchars & Scrivener’s model with experimental data.

(a) double equivalent strut accordingto Kilinger & Bertero (1976)

(c) several struts around openingaccording to Thiruvengadam (1985)

(b) six strut model accordingto Chrysostumuo (1991)

(d) proposed strut model includinghorizontal shear sliding byLeuchars & Scrivener (1976)

Figure 2.7 : Modified diagonal strut models


Plasticity theory models

Theories of plasticity have also been used to predict collapse loads of infilled frames.

Wood (1978) proposed determination of the collapse loads of infill panels using simple rigid-plastic analysis. He assumed that plastic hinges developed at the corners of a bounding frame and that the infill panel was in a state of pure shear strain (Figure 2.8). By assuming the infill to be rigid-plastic and obeying a square yield criterion, the collapse load of the panel was then given as:

4 1 '' 2p

c cM

F l th σ= + (2.11)

where: Mp is the plastic moment of the frame connection, σc is the crushing strength of the infill, t is the thickness of the infill panel, l’ is the length of the infill panel, and h’ is the height of the infill panel.

FFh’/l’

l’

uniform distributionof

shear strain

square yield criterion

compression

tension

s2

Mp

sc

s1sc

h’

Fh’/l’

F

Figure 2.8 : Collapse mode and failure criterion assumed by Wood (1978)

Similar expressions were developed for infilled frames in which plastic hinges developed at positions other than the bounding frame corners. May et al. (1982, 1985) used Wood’s approach to outline a design procedure which incorporated infill walls with openings and


bounding frames with pinned connections. Empirically obtained penalty factors were applied to collapse loads for solid panels as predicted by Wood’s expressions. A comparison of collapse loads derived from this approach with experimental ultimate loads showed that the theoretical loads were higher. The discrepancy was mainly attributed to the assumption of rigid plastic behaviour for the infill panel and the assumption of full interaction at the frame-infill boundary. Liauw and Kwan (1982, 1983) reduced the resulting collapse load by neglecting the shear forces at the frame-infill boundary.

Plasticity based methods used by Wood (1978), Liauw and Kwan (1982, 1983) and May (1981) assumed failure by collapse mechanisms due to development of plastic hinges in the frames. Saneinejad & Hobbs (1995) observed however that attainment of peak loads in infilled frames preceded the formation of collapse mechanisms. Saneinejad & Hobbs proposed a strut model that is based on attainment of plasticity in the infill at the loaded corners. From their experimental and finite element analyses they concluded that frame-infill interaction is associated with shear forces that may be evaluated closely using equations (2.12).

2 andh h l lF µα C F µ C= = (2.12) where: Fh and Fl are shear forces at the column–to-wall and beam–

to-wall contacts, respectively, Ch and Cl are normal forces at the column–to-wall and beam–to-wall contacts, respectively, µ is the coefficient of friction between the steel frame and the concrete infill panel, and

α is the panel aspect ratio defined as hl 1α = ≤

From these contact forces equilibrium considerations of a

concrete infill panel yielded equation (2.13) for the collapse load, H.


( )

(1 ) 2 pj jc c c b b

M MH σ t α α h τ tα l

h+= − + + (2.13)

where: αc is the ratio of the column contact length to the height of the column, αb is the ratio of the beam contact length to the span of the beam, σc and σb are the normal contact stresses on the face of the column and beam, respectively, τb is the uniform shear contact stress on the face of the beam, h and l are the column height and the beam span, respectively, Mpj is the minimum of the beam’s, column’s and the frame connection’s plastic moment, and, Mj is the frame connection’s plastic moment.

They further showed that the contact lengths can be approximated by:

2( )0.4pj c pc

cc

M β Mα h h

σ t+

= ≤ (2.14)

2( )

0.4pj b pbb

b

M β Mα l h

σ t+

= ≤ (2.15)

where: Mpc and Mpb are the column and beam plastic capacities, respectively, βc and βb are the ratios of the maximum elastic field moment developed within the height of the column to Mpc and that developed within the span of the beam to Mpb, respectively, and t is the thickness of the infill.

For simplicity, Saneinejad & Hobbs (1995) assumed that σc , σb,

βc and βb attain their upper bound values due to full plastification of the infill at the loaded corners. By using the Tresca hexagonal yield criterion, described in Chen (1982), and assuming rectangular stress


blocks at the frame-to-wall contacts, they derived equations (2.16) and (2.17) for the upper bound values of σc and σb.

'

2 41 3c

cofσµ α

=+

(2.16)

'

21 3c

bofσ

µ=

+ (2.17)

where f’c is the compressive strength of the plane concrete panel. They also demonstrated using finite element analyses that the limiting value of βc and βb is 0.2.

Collapse loads determined by the method of Saneinejad & Hobbs (1995) were shown to be consistently closer to experimental values than the earlier method.

2.3.2 Fundamental models

The advantages of the macro models presented above are in their computational simplicity and the use of structural mechanical properties obtained from relatively simple tests on material specimens of sufficiently large size. The limitation of these models is in their inability to simulate local behaviour. It is because of this limitation that fundamental models, principally represented by finite element models, have had an increasingly important role. In these models constitutive relationships are formulated to define the behaviour of finite parts of the frame members, infill panels and frame-to-wall contact zones. These models are intended to provide much more detailed information than is possible with global models. Local effects such as cracking, crushing and contact interaction can be modelled. This is of particular advantage, given the anisotropic nature of infill walls and discontinuities at their contact areas with bounding frames.

As pointed out by Dawe et al. (2001) an ideal finite element technique for infilled frames must take the following into consideration: • infill panel: non-linear behaviour of the infill resulting from

cracking due to shear and tension, and possible crushing of the infill material under the action of biaxial compressive stress;


• surrounding frame members: non-linear behaviour of peripheral frame members and the formation of plastic hinges due to critical combinations of axial loads, shear and moments in a frame member;

• frame-to-infill interaction: phenomena that occur include the effects of lack of fit, gaps between frame and infill, interface bond and friction, and separation and re-contact at the frame-to-infill interface.

Modelling infill panels Confinement of an infill panel, especially near the loaded corners subjects the infill material to multi-axial stress. Page (1981) has experimentally shown that the behaviour of brickwork under biaxial loading depends upon, among other factors, the ratio of the orthogonal stresses and the orientation of joints with respect to the load. This makes modelling masonry infill panels more complicated.

Based on the level of detail, fundamental models may be described under two modelling strategies, namely, the smeared (meso-level) and discrete (micro-level) modelling strategies.

In the smeared approach, the wall is treated as homogeneous with average properties of the units acting together with the mortar joints. Usually, the material model is elasto-plastic, based on the von Mises yield criterion combined with a Rankine type tension cut-off. Since the first effort to model infilled frames with finite elements by Mallick & Serven (1967), it is common to use rectangular plane stress elements with two nodal degrees of freedom to represent the infill walls. Provision may be allowed for the anisotropicity of masonry. Dhanaseker & Page (1986) used an orthotropic model to simulate the behaviour of brick infills. Liauw & Lo (1988) & Schmidt (1989) used smeared crack models to simulate micro-concrete and brick infills respectively.

The second strategy is a more detailed approach in which units and mortar joints are modelled discretely. Continuum elements are used for units while mortar joints are represented by interface elements. In an even more detailed approach, the mortar layer may be modelled by continuum elements joined to the unit continuum


elements with the mortar-unit adhesion areas being represented by interface elements. In most cases, units are modelled as elastic continua while non-linear behaviour under tension, shear and compression is simulated in the interface elements. Experimental research (Vermeltfoort & Pluijm, 1991) into the behaviour of small specimens of masonry materials and assemblages has demonstrated that they generally behave as quasi-brittle materials. This means that once they have attained their maximum stress, they undergo softening. The normal stress is usually defined by linear elasticity until the strength is attained. At that point the material behaviour may be modelled as brittle, softening or plastic. In shear, the coulomb friction theory is commonly accepted to represent interface behaviour. This theory asserts that ‘relative sliding between two bodies in contact along plane surfaces will occur when the net shear force parallel to the plane reaches a critical value proportional to the net normal force pressing the bodies together. The constant of proportionality is called the coefficient of friction’. It has also been observed as reported in Zijl et al. (2001) that dilatancy can play a significant role in shear compression of masonry. Dilatancy is the phenomenon by which there is an increase of volume upon inelastic shear deformation. In masonry, the physical effect is normal uplift during shear sliding, thereby widening the shear sliding cracks. If this dilatancy is constrained by the boundary conditions of the masonry, such as the bounding frame in infilled frames, there is a build-up of compression in the wall. Plasticity–based continuous interface models have been developed to model tension, and shear compression behaviour of mortar joints (Lourenço & Rots, 1997; Rots, 1997). Modelling Surrounding Frame Members Frame members can be represented either with beam elements or with a more refined discretization using continuum elements. Among others, Dhanaseker & Page (1986), and Liauw & Lo (1988) used linear and non-linear beam elements to model the behaviour of steel frame members. Seah (1998) used linear beam elements connected to non-linear hinge elements at the ends of the beams to model the non-linear


behaviour of frame members. Schmidt (1989) & Mehrabi (1994) used continuum elements to model concrete frame members. Modelling frame-to-infill interaction The interaction between the bounding frame and the infill can be modelled with interface elements in a similar manner to joints. These interface elements may take the form of springs, lines or surfaces on either of two interacting parts of the structure. Algorithms used in computation should be sensitive to interface conditions so as to transfer normal and shear forces only when there is contact between the frame and infill. Similarly, the interface element should fulfil the impenetrability condition when the surfaces are in contact.

Many researchers have grappled with the difficulties of modelling the separation and re-contact that takes place at the frame-to-wall interface. When spring interfaces such as in Seah (1998), also reported in Dawe, Seah & Liu (2001), are used, interface conditions in the normal direction have been represented by appropriate spring stiffnesses taking into account mortar that may be between; thus, high stiffnesses in compression and zero stiffnesses in tension. In the tangential direction, Seah assigned a force equal to the product of the normal force and the coefficient of friction. Asteris (2002) adopted a common gap/contact analysis procedure by initially linking the finite element meshes for the frame and infill only at two points at the loaded corners. Once an analysis has been run, infill mesh nodes are checked to evaluate whether they overlap with the frame mesh nodes. The nodes that overlap are linked to the frame nodes; otherwise the normal forces at the links are checked for tension. Nodes under tension are unlinked and the procedure is repeated. A solution is found when there are no overlaps and no tension. To the author’s knowledge, no detailed comparison of results with experimental data was made.

Limitations of fundamental models From the variety of fundamental material models presented above, it may be said that powerful tools are available to model the different


phenomena associated with the behaviour of masonry and interfaces under biaxial state. It must be mentioned however that there is still much room for matching developments in experimental tests to obtain relevant input data for models. Data to use when modelling masonry joints and frame-to-wall interfaces is generally scanty. There is, for instance, little data on the coefficients of friction between different types of brickwork and steel.

A second caveat that needs to be raised has to do with solution procedures within the finite element method. Frame-to-wall separation and cracking of infills lead to sudden changes in stress distribution and sudden drops in load resistance. In numerical terms, this implies introduction of very small or zero stiffness terms in the global stiffness matrix. This makes the inversion of the matrix less accurate and introduces large differences between successive iterations in the solution process. This leads to problems with convergence of the solution (Galanti et al. 2000). Various techniques, such as displacement control, arc length control and line search have been developed to overcome these convergence problems (Crisfield, 1984, 1992; DIANA, 2002). Tracing the non-linear post cracking load deflection response may still, however, be problematic. As indicated by Rots & Invernizzi (2004) more research needs to be directed into the area of solution techniques for structures that exhibit non-linear behaviour such as infilled frames.

2.4 Summary of literature review

Past and present research in infilled frames has been motivated by interest in using brickwork infills in resisting blast loads, providing stability of tall buildings, in rehabilitation of masonry structures and advances in seismic engineering.

In this chapter experimental research and modelling strategies used in the study of infilled frames have been reviewed. From the experimental investigations, the following observations have been progressively made.

(i) The stiffness and strength of the frames are significantly

enhanced by the infills.


(ii) Infills essentially act as a form of bracing. (iii) Diagonal tensile cracking, shear sliding in the joints and crushing

of the infill have all been observed as modes of damage. Formation of plastic hinges in reinforced concrete frames with reinforced infills has also been observed.

(iv) The stiffness and failure mode of infilled frames depend upon the frame-to-wall stiffness ratio, frame-to-wall interface conditions and material characteristics of the constituent parts of the infilled frame. Other factors that affect the behaviour of infilled frames include openings in the infill panels, type of loading, number of bays and number of storeys. Several global and fundamental models have been used to

further understand and predict the behaviour of infilled frames. The level of success of these models is difficult to ascertain because the experimental data on which the models are calibrated has often been derived from rather limited numbers of large scale tests. Consequently, most of the current design codes all over the world do not contain design guidelines for this type of structure.

2.5 Problem statement

The research problem in the current investigation is two fold. Firstly, there are no studies in the literature dealing with the use of calcium silicate element infills. Yet, because of the already prevalent existence of CASIEL walls as partition and cladding walls in building frameworks, research of their behaviour as infill walls is required. Although, in general, some similarities with other types of masonry infill walls may be expected, there are also differences. The large sizes of calcium silicate elements, the thin-layer mortar joints and the method of construction are all different from traditional brickwork.

Secondly, as pointed out in Chapter 1, the common practice of ignoring the influence of infills in structural design may be inaccurate and uneconomic or worse still may pose unacceptable risks to the structure, finishes and fittings. There is need to develop practical design guidelines for these infilled frames.

Problem statement 33

There is a wide range of issues that need to be studied in order to develop the desired guidelines. The first step needed is a description of the basic behaviour in terms of stiffness, strength and damage patterns for CASIEL-infilled steel frames. In this research, this is achieved by performing experiments and corroborated by a numerical model. The simplest form of infilled frames is used in the investigation, namely, a single-bay single-storey configuration with solid infills. The parameters of interest are those related to sizing of frames and walls and frame-wall contact conditions vis-à-vis construction procedures to realise composite action between the two parts of the structure.

The second step is an assessment of some parameters that influence the behaviour of these types of infilled frames. This is done using the numerical model.

In the third place, an indication of how design guidelines might be derived is given. Simplified equations to predict behaviour have been proposed and evaluated using the numerical analyses.

The experiments, numerical work and prediction equations are reported in the succeeding chapters.

Chapter 3

3Experimental design and procedure

Abstract This chapter describes the experimental set-up, measurements and procedures used in the investigation into the structural response of steel frames infilled with walls made out of calcium silicate elements (CASIELs) in thin- layer mortar. A reaction frame composed of twin triangular frames was used. Differences in the specimens were in terms of weak and strong frames, closed or open gaps below the roof beam and presence or absence of top corner bearing wedges. A measurement scheme using LVDTs and rosettes interfaced with a computerized data acquisition unit was used. Displacement-controlled in-plane monotonic horizontal loading was applied at roof beam level. Auxiliary tests were performed to monitor characteristics of wall materials.

3.1 Overview

Understanding the real behaviour of a structure, ultimately, comes from observations on the real structure. This understanding from a real structure, however, is not per se easily derived. Apart from the fact that, generally, the need to know the behaviour of a structure is in order to predict it, it is difficult to ascertain the boundary conditions that apply at any particular time during the service or failure of the structure. In laboratory observations, otherwise called physical experiments, it is relatively easier to control these boundary conditions and study the influence of different parameters on the behaviour. Even then, limitations due to costs and handling requirements of large scale specimens often dictate the use of scaled down specimens. This

36 Experimental design and procedure

presents the dilemma of hardly straight forward scaling up of conclusions drawn from laboratory experiments to real life behaviour.

In this research programme, large-scale laboratory tests of single-storey single-bay infilled frames were performed. In the following sections, considerations made in the design of these experiments are explained. These considerations refer to the design of the test apparatus, design and preparation of specimens, the types of specimens, measurements and the experimental procedure. Characteristics of wall materials were also obtained through auxiliary tests. Descriptions of these auxiliary tests are given in Appendix C.

3.2 Objectives of experiments

The first objective of the experiments conducted in this research programme was to observe and measure the response of steel-CASIEL infilled frames to in-plane monotonic loading. The second objective was to observe and measure the influence of chosen parameters on the response. The ‘response’ here refers to overall stiffness of infilled frames, stress/strain distributions in the structure, maximum loads and damage patterns on the structure. Observations and measurements would be used as a basis for calibration of a numerical model, which in turn would be used for parametric studies.

As pointed out in Chapter 2 several parameters are known to influence the structural response of infilled frames. In this programme, basic factors of immediate interest to designers and contractors were chosen. These are factors that relate to how to size structural members, how to detail interfaces and how to build the structure. These parameters are more specifically described in Section 3.4.4.

3.3 Testing apparatus

A testing apparatus was required for the purpose of providing a platform for the specimen and applying in-plane loading. The basic requirements of such an apparatus have to do with the way the apparatus interacts with its own support, normally the structural floor,

Testing apparatus 37

and the way it interacts with the specimen at the specimen supports and point of load introduction.

Several testing arrangements for achieving the above purpose are found in the literature. Typically this involves a rigid frame anchored to a ground beam or structural floor. A jack is placed between the rigid frame and the specimen. The reaction force from the specimen is transmitted to the ground support through the rigid frame.

3.3.1 Reaction frame

A unique reaction frame was used in the current testing programme. The key characteristics of the reaction frame are: the provision for large scale specimens, the non-reliance on a structural floor and necessarily, the sufficient rigidity.

A schematic concept of the reaction frame is shown in Figure 3.1. The reaction frame is composed of twin triangular frames, one on either side of the specimen, and connected through rigid steel members at its vertices. The members of the twin triangular reaction frames were made out of European HE 300 B profiles. The links between the twin rigid frames provide support points for the specimen and the loading jack.

At Support A, (Figure 3.1) this connection is by means of a heavy steel block. The steel block is bolted to the stiffened flanges of the triangular frames. The specimen rests on this block of steel so that the specimen is restrained from horizontal and vertical outward displacement. At Support B, a stiff steel I-beam is bolted to the triangular frames. Two types of Support B were used during the investigation. In the first type, shown in Figure 3.3a and used for the first four tests, denoted as Test 1 to 4, a slender steel plate was bolted to the reaction frame at the bottom and the specimen above. In the second type, shown in Figure 3.3b and used in the last six tests, denoted as Test 5 to 10, four steel rods were used to tie the reaction frame to the specimen. Both types of support were intended to provide high vertical restraint and as low horizontal restraint as possible. In this way, for evaluation of the behaviour of the structure, the supports A and B would be modelled as a pin and a roller support, respectively


At the top vertex of the reaction frame, another stiff steel plate spans across the two triangular frames. It is on this steel plate that the 2 MN jack is supported. Figure 3.2 depicts the test arrangement with a specimen mounted (slotted in).

Once a force is applied to the specimen, the jack pushes against the steel plate and the reaction force is transferred to the reaction frame. The insert in Figure 3.1 shows the forces acting on the infilled frame. The slanting members of the reaction frame share the tension while the vertical members bear the compression. A simple elastic analysis showed that with an ultimate jack force of 2 MN, strains in the reaction frames will be, insignificantly, in the order of 0.1 mm/m, representing stresses in the order of 5% of yield strength. Thus, for the level of loads attained in this testing programme, the reaction frame is sufficiently rigid and therefore able to absorb or release energy from the specimen without undergoing significant deformations.

Drawings with details of the test set-up can be found in Appendix A.

3700 mm10

40mm

3800

mm

SupportA

Support B

Pro

pfo

rJa

ck

F

F

F2specimen

Figure 3.1 : Schematic view of reaction frame and specimen

Testing apparatus 39

loadingjack

specimen

reactionfram

e

reaction framere

acti

on

fram

e

Figure 3.2 : Test arrangement with mounted specimen

specimen

(b) Type 2, for Tests 5 to 10

reaction frame

M20 steel rods connectspecimen to reactionframe

(a) Type 1, for Tests 1 to 4

A

A

A71

0

A - A

A - A

specimen

20 mm thick plate connects specimen to reaction frame

reaction frame

specimenA

specimen

688

Figure 3.3 : Connection of the windward columns to Support B


3.3.2 Load introduction

Boundary conditions in general and the manner of load application in particular have an influence on experimental results. Of particular importance are the concentration of the applied load, possible eccentricity while applying the load and effects of friction between the loading surface and the specimen. For instance, highly concentrated applied loads lead to high local stresses and possible premature failure. Eccentric loading results in bending moments in the specimen and may also lead to relatively lower failure loads. Friction between loading plates and specimen surfaces produces confining stresses which produce a tri-axial stress state in the specimen. This may lead to relatively higher failure loads. This effect is, however, not so significant for large specimens, such as the infilled frames under consideration here. As such no special interfaces were applied between the specimen and the loading plate.

As mentioned earlier, the monotonic load was applied by a hydraulic jack mounted at roof level of the specimen. The jack piston was 210 mm in diameter. At the end of the jack piston a 220 mm deep by 300 mm wide by 80 mm thick loading plate was fixed. The purpose of this loading plate was to uniformly spread out the applied load over an area covering approximately the specimen column width and depth. With a thickness of 80 mm, the loading plate was stiff enough to ensure negligible bending of the loading plate, thus achieving uniform displacement over the loading area. Further, the loading plate was fixed to the jack piston in such a way that it could tilt about the axis of the ram by gliding over a spherical seating, allowing it to press parallel onto the specimen surface. Once the loading surface was pressing parallel on the specimen surface, friction between the spherical seat and the loading plate would maintain its inclination. A description of this type of spherical seat and loading plate according to the requirements of ASTM E447-84 (1984) is given by Drysdale et al. (1999).

Description of specimens 41

3.4 Description of specimens

In this section, the choices made regarding characteristics of the specimens are described in terms of the member sizes, connections, infill wall thickness and interface details between the infill panels and the frame.

3.4.1 General description

The scale and construction of specimens were, as much as possible, made similar to real structure proportions and site practices. Each infilled frame was nominally 3000 mm by 3000 mm in overall dimensions between the centre lines of the bounding frame members. The dimensions of the infilled frame were chosen to represent a full-scale frame of at least the minimum practical size. Steel I-sections, with semi-rigid bolted connections were used for the bounding frame. The infill wall was constructed from 897 mm x 594 mm x 150 mm CASIELs in thin-layer mortar (Calsifix). Thin-layer mortar was also used between the infill wall and the bottom beam. All other gaps between the infill wall and the frame were packed with general purpose mortar, except where an open gap, as a parameter, was desired.

3.4.2 Member sizes

Member sizes for steel profiles, connections and wall thickness, were chosen on the basis of suitable frame-to-wall stiffness ratios, representation of common sizes used in building sites, compatibility with the test set-up and comparison with other test programs. Accordingly, sizing of the frames was done as follows: • CASIELs are produced in thicknesses ranging from 100 mm to

300 mm. A thickness of 150 mm, which is commonly used for load bearing walls, was used for all the tests.

• The basic interest in infilled frames is composite interaction between the frame and the wall. A too rigid wall eliminates, theoretically, the influence of the frame, and vice versa. Kadir’s


(1974) work was used as a basis for estimation. Kadir carried out some elastic analyses to establish a relationship between the total lateral load carried by an infilled frame and the load carried by the infill wall. The results, for square panels, are extracted and shown in Figure 3.4. In this graph λhh is a dimensionless factor that expresses the relative stiffness of the infill wall to the stiffness of the bounding frame as defined in Chapter 2 of this thesis.

100

90

80

70

60

30

50

1 2 3 4 5 6 7 8 9 10

40

lh h

Y=

Pw

all

Pto

tal

/

(%)

Figure 3.4 : Proportion of load carried by the wall as a function of λhh

• The graph shows that for low values of λhh, the contribution of the wall rapidly dwindles to approximately 35% of the total load. On the other hand for high values of λhh, say above 7, the wall practically carries the entire load. Stated differently, for a constant wall rigidity, and at high values of λhh, changing the frame stiffness does not make much of a difference to the total load since all the load is carried by the wall. For low values of λhh, changing the frame stiffness leads to appreciable differences in the total load carried by the infilled frame since the influence of the frame becomes more significant. On this basis, the frame


sizes in this research were designed such that λhh was between 3 and 5.

• Using infill walls should reduce the necessity of complicated moment connections in the frame. This, in practice reduces the cost of fabricating frames. It should however be born in mind that the stability of frames with simple connections should be guaranteed during construction. Semi-rigid connections were made by bolting beam end plates to the column flanges. Rotational stiffnesses of the frame connections were estimated using the following simplified formula devised by Steenhuis et al. (1994) and based on Eurocode 3 Annex J (revised):

,t f ci

x

Eh tC

k

2= (3.1)

where: E is Young’s modulus of elasticity, ht is equal to the beam depth, tf,c is the thickness of the column flange and kx is a factor dependent on the layout of the connection .

• It was considered desirable to use steel profiles that are commonly used in medium height storey building structures. Profiles used for the weak frames in this investigation are commonly used while profiles for the strong frames are heavier than those commonly used.

3.4.3 Preparation of specimens

Preparation of a specimen involved assembling and testing the stiffness of a the bare frame, building the wall, filling the interface gaps with mortar, plastering and curing in the laboratory for approximately four weeks. At the time of building the wall small specimens for auxiliary testing of wall materials were also prepared.

In the construction of walls, it was desirable to construct the walls in much the same way as is done in current site practices. For that purpose, a workman from the Dutch Calcium Silicate Industry was hired to erect the wall.


The bare frame was erected and tested for stiffness by loading it up to 20 kN for weak frames and 60 kN for strong frames. The bare frame was then placed vertical on the laboratory floor, and supported, out of plane, by an auxiliary frame. Thin-layer mortar was applied on top of the bottom beam. Starting with one bottom corner, CASIELs were hoisted, with a crane, into position and laid up until the other corner. Each subsequent layer of CASIELs was laid in a similar manner.

After a few days, where applicable, the gaps between the wall and frame were filled as completely as possible using a pointing tool to pack mortar.

Thin coats of gypsum plaster and white paint were applied to one side of the wall. This was meant to make any cracks more easily visible during the test.

Apart from general laboratory conditions, with temperatures of 15 to 20°C and relative humidity of 30 to 35%, no other treatment was applied.

3.4.4 Specimen distinctives

Five different types of specimens, in duplicate, were used. Table 3.1 and Figure 3.5 show the main characteristics of the specimens, thus, the strength of the bounding frames, interface conditions between the upper beams and walls and upper corner details. Specimen Types 1 and 2 were weak frames while Specimen Types 3, 4 and 5 were strong frames. Specimen Types 2 and 5 had gaps between the upper beams and the infill walls while Specimen Types 3, 4 and 5 had no gaps. Specimen Types 4 and 5 had corner bearing wedges.


Table 3.1 : Types of infilled frame specimens

Specimen Type

TEST No

Beam Section

Column Section

Wall Thickness

(mm)

Gap Below Roof Beam

(mm)

Bearing Wedge

1 1 & 2 HE200B HE180B 150 Nil Nil 2 3 & 4 HE200B HE180B 150 12 Nil 3 5 & 6 HE280M HE280M 150 Nil Nil 4 7 & 8 HE280M HE280M 150 Nil Present 5 9 & 10 HE280M HE280M 150 12 Present

Specimen Type 1 Specimen Type 2

Specimen Type 3 Specimen Type 4 Specimen Type 5

Figure 3.5 : Specimen Types

Strong or weak frames

The stiffness of the frame is a practical design parameter for a designer, and in theory an important factor in the level of composite action between the two parts of the structure.

In order to investigate the influence of this factor, Specimen Type 1 with ‘weak’ frames was contrasted with Specimen Type 3 with ‘strong’ frames (see drawings in Appendix A for details).


Weak frames were constructed from HE 200B sections (Ix = 5696 x 104 mm4) for beams and HE 180B sections (Ix = 3831 x 104 mm4) for columns. For each connection, a 15 mm thick plate welded to the beam was bolted with four M20 bolts to the column flange.

The strong frames were constructed from HE 240M (Ix = 24290 x 104 mm4) steel sections all round. Beam end plates of 30 mm thickness were bolted to stiffened column flanges. Back plates of 15 mm thickness were welded to the column flange.

Tests of the stiffness of the bare frames showed that the strong frames, at an average of 9.2 kN/mm were 3 times stiffer than the weak frames, at an average of 3.1 kN/mm.

Gaps

When fitting in an infill wall in an erected frame, there always remain tolerance gaps between the edges of the wall and the surrounding frame. Another cause of gaps may be shrinkage of the infill wall. In Chapter 2 reference has been made to past research into the influence of these gaps on infilled frame behaviour.

In these experiments, infilled frames with or without gaps between the top of the infill wall and the roof beam were compared. For Specimen Type 1, the 12 mm gap between the wall and the roof beam was packed with general purpose mortar while, for Specimen Type 2, the gap was left open. Bearing wedge technique

Observations of other researchers, which were corroborated with results from the current research, indicated that the presence of interface gaps reduces the stiffness of infilled frames during the early stages of loading. This is because of a delay in interlocking of the wall and frame, causing large deflections at this stage. Closing interface gaps by packing mortar, as was done in this research, is a slow process and does not guarantee consistent filling of the gap.

In order to eliminate the negative influence of the gap and at the same time remove the necessity of filling in the top gap with mortar, a novel construction technique was investigated. The basic idea of the


first wedge

second wedge

Step 2

void

Step 1

Step 3

Figure 3.6 : Pushing CASIELs sideways against steel using wedges

technique was to improve the contact between the frame and the wall at the frame corners. This was investigated by the use of Specimen Type 4 and Specimen Type 5. The steel frames for Specimen Types 4 and 5 were the same as those used in Specimen Type 3. However, in Specimen Types 4 and 5, triangular ‘bearing wedges’ were fixed (bolted) to the beam and column flanges at the top corners of the frames. The triangular bearing wedges were made from 20 mm thick webs welded to 20 mm thick flanges. The surfaces of the flanges were the bearing surfaces through which the load would be transmitted into the infill wall.


In order to place the CASIELs against these bearing wedges, the steps illustrated in Figure 3.6 were followed. Firstly, the top layer of CASIELs was laid, leaving a void in the middle. Next, one wedged piece, cut out of a CASIEL, was inserted into the void. Finally, by pushing the second wedged piece of a CASIEL downwards, CASIELs in that row were pushed sideways against the corner bearing wedges. The difference between Specimen Type 4 and Specimen Type 5 was that the top gap was packed with mortar in the former and left open in the latter.

3.5 Measurements

Measurements were made to evaluate the overall load deflection response of each specimen as well as local deformations on the wall. Linear Variable Displacement Transducers (LVDTs) and strain gauges in the form of rosettes were used to measure deformations and displacements. Basic principles of these sensors can be found in Appendix B. By virtue of the large number of measurements, it was convenient to use a computer logging data acquisition system (described in Appendix B) which was interfaced with the sensors. The arrangement of LVDTs and rosettes on the specimen is shown in Figure 3.7. During each test, measurements from all sensors were recorded every five seconds.

The position of the specimen in relation to the ground was measured by LVDTs (indicated by numbers 4, 5, 6, 7, 8, 9, 70, 71) at the four corners of the specimen. These LVDTs were fixed to a separate measuring frame.

In order to decipher the strain distribution in the wall, rosettes were placed on a 500 mm x 500 mm grid on the wall. The grid was arranged with a bias to cover the area along the compression diagonal since most of the deformations were expected to take place there.

Gaps and slip at the frame-wall interface as well as across and along joints were measured by LVDTs at specified points.

The applied force and displacement of the loading jack were also measured by inbuilt strain gauges in the load cell.

Measurements 49

.

Forc

e an

d Ja

ck

disp

lace

men

t

Rosette

LVDT for global position

LVDT over joint or interface

7 8

7170

6

5

94

Figure 3.7 : Measurement scheme

3.6 Load control and Test procedure

A deformation controlled load was applied using the 2 MN hydraulic jack mounted at roof beam level. A Schenck controlling unit regulated the flow of hydraulic oil depending upon the relative position of the actuator in the jack cylinder to the prescribed position. More details on the load controlling mechanism can be found in van Mier (1984).

The loading rate was determined on the basis of (a) the desire for a single test to last, practically, 30 to 60 minutes, (b) the loading rate to be comparable with those used in similar tests by other researchers and (c) the loading to be effectively static. A preliminary test had indicated that within an overall load point deflection of 10 mm, a specimen would suffer major cracking. Over a (diagonal) length of 4200 mm, this deflection would translate into an average strain in the order of 2400 µm/m. Investigations into the effect of strain rate on static and dynamic failure loads on concrete by Bischoff (1988) indicated that loading resulting in strain rates in the range 10-6 s-1 to 10-5 s-1 can practically be considered as static. Thus, in the current research, a loading rate of 1 mm/min was chosen. At this rate each test could be conducted in approximately 30 minutes, yielding a strain rate of 1.3 x 10-6 s-1, which can be considered static.


The procedure of each test involved a preliminary preload (and unloading), followed by the actual test (Figure 3.8). The preload and unloading was done in order to close up initial contact tolerances between the specimen and the support rig. It also provided a chance to verify that the measuring system was working properly.

The actual test was performed by displacing the jack head at 1 mm/min until the test was stopped, following major cracking. Figure 3.8 shows a typical graph of displacement of the jack head over time. The jack was first, by manual steering of the control system, steered towards the specimen. Once the loading plate came into contact with the specimen, the control system was fed with an automatic steady displacement rate. At a load of 20 kN for weak frames and 80 kN for strong frames, the specimen was unloaded. The load was then applied at 1 mm/min until the end of the test.

0 1000 2000 3000

time (s)

ho

rizo

nta

ldis

pla

cem

ent

(mm

)

0

10

30

20

40

50

unloading

unloading

load

ing

displacement

loading

Figure 3.8 : Example of loading procedure

3.7 Summary

In this chapter, a comprehensive description of the experimental technique and procedure has been given. Section 3.3 describes a unique rigid reaction frame that does not rely on a reaction with the floor, but, by axial forces in its members, supports the loading jack

Summary 51

and specimen. In Section 3.4, considerations made in the design of large-scale steel frames with semi-rigid connections are given. The rationale for the chosen parameters, thus, gaps, frame member sizes and a novel bearing wedge construction technique is given. The measuring scheme and the test procedure are outlined in Section 3.5 and 3.6 respectively. Concurrently with the infilled frame tests, auxiliary tests on small CASIEL prisms, mortar prisms and mortar joints were conducted. The aims of these auxiliary tests were to monitor the consistency of the wall materials and to determine values for parameters to be used in the numerical model. A compilation of the results can be found in Appendix C.

In the next chapter, the results of the infilled frame tests are evaluated and discussed.

Chapter 4

4Evaluation of experimental results

Abstract This chapter presents an evaluation of results of the experimental investigation into the structural response of steel frames infilled with walls made out of calcium silicate elements (CASIELs) in thin-layer mortar. Load-deformation curves show a two or three stage trajectory prior to cracking. In general, there was an initial stiff stage followed by a much less stiff stage during which frame-wall separation occurred and another stiff range leading to, in the majority of cases, diagonal tension cracking in the infill walls. Shear-sliding along the top most bed joint was observed in some specimens. Stress and strain distributions on the walls were plotted. Increasing the stiffness of bounding frames increased the stiffness of infilled frames and moderately increased the cracking loads. An initial top gap resulted in reduced infilled frame stiffness during the transition phase, although it did not significantly reduce the cracking load. By using bearing wedges in the top corners, the influence of the gap was significantly reduced. This may be significant in developing a construction technique for industrial application of infilled frames. The global responses, together with the strain distributions derived from rosette measurements on the walls provided data for calibration of the finite element model of the following chapter.

4.1 Zero correction and rigid body movements

Before delving into the results of the infilled frame tests, a brief note concerning the processing of measured data is given below.

In Section 3.5, it was pointed out that all measuring sensors were interfaced with a computerised data acquisition system. The raw

54 Evaluation of experimental results

output from the data acquisition system, being electrical quantities, is converted into displacements and forces by the use of appropriate calibration factors. Processing of this data then involved a zero correction and subtraction of rigid body movements.

Zero correction

As is typical in laboratory tests of similar types, the loading plate needs to gradually press and transfer the force on to the specimen. During this process, the loading plate itself glides over its spherical seat until it presses parallel to the surface of the specimen. Meanwhile, in the test set-up, tolerance gaps in the connections need to close up. These effects imply that although force measurements are made during this process, the force is not yet, properly, applied to the specimen. As such, in the load displacement diagrams, an initial slack curve is normally observed. Applying a preload and unloading largely eliminates this effect. However, in general, for purposes of calculating the initial stiffness, this slack in the curve needs to be ‘zero’ corrected. The way this was done in this research is illustrated in Figure 4.1. Firstly a linear regression was performed on data points on the more or less linear part of the load deflection curve after the initial slack. The linear curve was projected on to the abscissa. Secondly the original graph was translated so that the corrected curve passes through the origin. The translation was done by subtracting the abscissa intercept value from all displacement measurements.

0

5

10

15

0 0.5 1.0displacement ( mm )

forc

e(k

N)

original graph

translation

projection

zero correctedgraph

Figure 4.1 : Example of zero correction

Zero correction and rigid body movements 55

Rigid body movements

Ideally, the supports to the infilled frame specimens were required to provide an equivalent of a roller support at the windward side and a pinned support at the leeward side. However, in reality there were movements in the supports due to sliding of the specimen over the supports, small deformations in the supports and movements in the support connections. (See Figure 3.3 for support connection details). These movements and deformations resulted in rigid body translations and rotations of the specimen. In other words, the measured deflection at the point of load application, for instance, was not purely due to deformation of the specimen. As illustrated in Figure 4.2, the measured deflection, denoted as ∑, included translation, T, and rotation, R, of the whole specimen as a rigid body. In order to determine the net deflection, D, of each specimen, displacements due to translation and rotation, measured by LVDTs at the specimen corners, are deducted from the total displacement measured at the point of load application.

.

initialposition, I

rotation, R

deformation, D

translation, T

D = IΣ - T - R -measuredposition, Σ

Figure 4.2 : Translation, rotation and deformation of a specimen

In Figure 4.3 a comparison is made between the horizontal deflection measured at the point of load application and the horizontal deflection deduced from deformation measurements over


the compression diagonal. These measurements are taken from Test 5. It is clear that there is a significant difference between horizontal measurements recorded at the point of load application and derived from the diagonal deformation. When the rigid body movements are accounted for, the two methods of obtaining the horizontal deflection yield plots which are very close. The two ways of determining the horizontal deflection provided counter checks on the validity of the measurements. In the discussions that follow the deflections determined from the measured diagonal deformations are used.

0

100

200

300

400

0 5 10 15horizontal deflection (mm)

deflection of loadapplication point

displacement of loadapplication point lessrigid body movements

horizontal component ofdiagonal deflection

ho

rizo

nta

lfo

rce

(kN

)

Figure 4.3 : Comparison between deflections measured at the point of load application and along the compression diagonal

4.2 Overview of load deformation responses

A load deflection graph, shown in Figure 4.4, from the results of Test 5, is hereby used to typify the behaviour of the infilled frames tested. The stiffening effect of the wall on the bare frame is self evident. The bare frame used in Test 5 had a stiffness of 9.8 kN/mm. (This was measured only up to a deflection of 5 mm; it is extrapolated up to 20 mm in Figure 4.4). A deflection of 7.6 mm, that is, at the onset of the cracking phase, corresponds with a load of 409 kN for the infilled frame. The secant stiffness of the infilled frame at that point is 54 kN/mm. That represents a 5.5 times increase in the stiffness on account of the infill wall. Similar comparisons between stiffnesses of the other bare frames and secant stiffnesses of corresponding infilled frames at the onset of the cracking phase are presented in Table 4.1. These results show that addition of infill panels increased the stiffness

Overview of load deformation responses 57

of frames between threefold to tenfold. The least increase was in the cases of Test 3 and Test 4 which were weak frames with gaps between the roof beams and the walls. The stiffnesses for these frames are particularly low due to the influence of the frame-to-wall gaps.

0

200

400

600

800

100

i. initial phaseii. frame-wall separation phase

bare frame

iii. d

iago

nal

stru

tphas

e

iv. cracking phase

v. residual phase

20 30 40 50 60 70horizontal deflection ( mm )

ho

rizo

nta

lfo

rce

(kN

)

Figure 4.4 : Typical load deflection behaviour, from Test 5

Table 4.1: Comparison between bare frame and infilled frame stiffnesses

Stiffness (kN/mm) Specimen

Type Test Bare frame infilled frame*

factor increase in stiffness

1 2.9 25 8.6 1 2 3.5 22 6.3 3 3.3 12 3.6 2 4 3.4 16 4.7 5 9.8 54 5.5 3 6 8.5 65 7.7 7 10.7 61 5.7 4 8 12.1 100 8.3 9 17.7 139 7.9 5 10 11.9 114 9.6

* secant stiffness of infilled frame at onset of cracking


Figure 4.4 further shows that the response of the infilled frames can be categorized in five stages, namely, an initial phase, a frame-wall separation phase, a diagonal strut phase, a cracking phase and a residual strength phase. During the initial phase the bounding frame and the infill wall act as one composite ‘shear element’. The infilled frame is, at this stage, very stiff. At the end of this initial stage, typically within the first 0.3 mm of load point horizontal deflection, the wall separates from the bounding frame, with the gap propagating from the tension corners. The wall adjusts in position within the bounding frame. In general the gap between the wall and the frame members extended more than three quarters of the length or height of the infill panels.

This ‘frame-wall separation’ phase was accompanied by a temporal drop in the stiffness, and in some cases, in the load carried by the frame. The frame-wall separation phase was succeeded by a structural configuration in which the wall, being locked with the frame at the loaded corners, acted as a diagonal strut in the frame, thus, the ‘diagonal strut phase’. In this phase, the load deflection response was typically a linear curve, although its slope was less than that of the initial phase. Diagonal strutting led to a cracking phase. A big crack more or less parallel to the compression diagonal suddenly appeared, accompanied with an explosive bang, and as much as a 30% drop in load. The diagonal crack cut through the CASIELs and the joints. In some cases, a shear crack occurred along the uppermost bed joint prior to the diagonal crack. Such a shear crack led to a drop in the load although the stiffness of the infilled frame was almost immediately recovered. With increased deflection, more diagonal cracks appeared. Figure 4.5 shows examples of cracked specimens. A residual phase follows in which the infilled frame bears increasing loads, albeit at a much reduced stiffness. Crushing at the loaded corners and some junctions between header and bed joints occur as the load becomes more or less constant. At this point the test was stopped.

Principal stress distributions 59

Figure 4.5 : Cracking patterns, photographs from Test 1 and Test 5

4.3 Principal stress distributions

In order to configure the geometry of the diagonal strut formed by the wall, it is desirable to evaluate the distribution of strains and stresses in the wall. In these tests strains were measured by rosettes arranged in a 500 mm x 500 mm grid. Principal strains can be derived through an analysis of a two dimensional stress state. Using the principal strains, the stresses can be estimated for known values of the elastic modulus, E, and Poisson’s ratio, υ. Furthermore, the principal strains and stresses so derived can be used to compare with those of the numerical model. Determination of principal stresses

In a two-dimensional stress state in which direct and shear strains in two mutually perpendicular directions are known, the strains in any other plane can be determined from the following equations:

x y x y xy1 1 1( ) ( ) cos 2 sin 22 2 2ε ε ε ε ε θ γ θ= + + − + (4.1)

x y xy1 1 1( ) sin 2 cos 22 2 2γ ε ε θ γ θ= − − + (4.2)


where: ε and γ are the direct and shear strains in the inclined plane, εx and εy are direct strains in two mutually perpendicular directions, γxy is the shear strain along those planes, and, θ is the angle between the inclined plane and the known x-plane

If εx and εy are principal strains, say denoted by ε1 and ε2, they

occur on planes at which shear strains are zero. Substituting γxy = 0 and εx = ε1 and εy = ε2 in the equations (4.1) and (4.2) above gives:

1 2 1 21 1( ) ( ) cos 22 2ε ε ε ε ε θ= + + − (4.3)

That is to say, provided the principal strains are known, the

strains at any other plane inclined at angle θ to the principal x-plane may be determined. In practice, the principal strains are unknown. However, if the direct strains in three different directions are measured, equation (4.3) yields three linear equations with three unknowns, ε1, ε2 and θ. Thus

a 1 2 1 21 1( ) ( ) cos 22 2ε ε ε ε ε θ= + + − (4.4)

b 1 2 1 21 1( ) ( ) cos 2( )2 2ε ε ε ε ε θ α= + + − + (4.5)

c1 1

1 2 1 22 2( ) ( ) cos 2( )ε ε ε ε ε θ α β= + + − + + (4.6)

where: α is the angle of inclination of εb from εa and β is the angle of inclination of εc from εb.

If the rosettes are arranged such that α = β = 45°, (Figure 4.6)

the above expressions can be reduced to the quadratic equation:

a a c b a c2 2

21( ) (2 ) 04ε ε ε ε ε ε ε ε ε⎡ ⎤− + + − − − =

⎣ ⎦ (4.7)

whose roots are the values of the principal strains, ε1 and ε2. The direction of the principal planes can be determined by:

b a c

c a

2tan2 ε ε εθε ε− −

=−

(4.8)


The corresponding principal stresses can be deduced using the relations:

Eε1 = σ1 – υσ2 and Eε2 = σ2 – υσ1. The principal stresses are then given by:

a ca b c b

E E 2 21,2 ( ) ( )

1 2 2 (1 )ε εσ ε ε ε ε

ν ν+

= ± − + −− −

(4.9)

εc

εbεa

Figure 4.6 : 45° Rosette

The values and directions of principal stresses at different locations and at different loading stages were calculated. Values of E and Poisson’s ratio were obtained from auxiliary tests of the CASIEL materials described in Vermeltfoort & Ng’andu (2005). These values were determined as 6000 N/mm2 and 0.2 respectively. As an example from Test 5, in Figure 4.7, principal stresses at various measuring points are depicted as Mohr’s circles. Each Mohr’s circle is drawn with its centre coinciding with the measuring point. At each point, the arrow and its length indicate the direction and magnitude of the major (compressive) principal stress. The magnitude of tensile principal stresses is indicated by the unshaded areas of the circles. Otherwise the shaded area denotes compression. The plots are for loads 50 kN, 200 kN, 300 kN and 400 kN respectively. This specimen cracked at 409 kN. Below each diagram, a scale of the stress diagrams is indicated. The pattern of principal stress distribution shows the following:


(d) at 400 kN(c) at 300 kN

(b) at 200 kN(a) at 50 kN=2 N/mm2

=2 N/mm2

= 4 N/mm2

= 2 N/mm2

Figure 4.7 : Principal stress distribution, from Test 5

(i) Along the compression diagonal and in the central region of the infill panel the direction of major (compressive) principal stresses is generally parallel to the compression diagonal. Off the compression diagonal close to the columns, major principal stresses may be even, perpendicular to the compression diagonal.

(ii) There is a concentration of compressive principal stresses in the proximity of the loaded corners. In Figure 4.7 this is apparent from the lengths of the arrows representing major principal stresses and from the sizes of the Mohr’s circles. This is further visualized in Figure 4.8 in which the major principal stresses are plotted along the compression diagonal. (It should be born in


mind that these major stresses are not necessarily in the same direction). The highest compressive principal stress recorded was 6.36 N/mm2 at the measuring point near the loaded corner. Since the crushing strength of the CASIELs was higher than this, (in the order of 15 N/mm2), crushing, at this stage was not observed.

measuring point

(a) major principal stresses (b) minor principal stresses

-4-6

-2

-1

1

-2

22

00

at 300 kNat 400 kN

at 200 kN

at 50 kN

stres

s (N/m

m)2

stres

s (N/m

m)2

Figure 4.8 : Principal stresses along compression diagonal

(iii) Tensile principal stresses are higher in the central region of the wall. In Figure 4.7 this can be visualized from the size of the unshaded areas in the Mohr’s circles. This is further graphically shown in Figure 4.8b in which minor principal stresses are plotted against the measuring points along the compression diagonal. The tensile stress recorded at centre of the infill panel was 0.83 N/mm2. However, as shown in the Mohr’s circles of Figure 4.7d, the highest tensile stress recorded was off the centre of the panel, and was in fact 1.31 N/mm2. This was because the specimen was not exactly symmetrically supported.

(iv) The regions near the loaded corners are in biaxial compression while the central regions of the wall are subjected to


compression and tension. Tensile stresses led to diagonal tensile cracking.

(v) With respect to the distribution of stresses across the compression diagonal (i.e. along the tension diagonal), Figure 4.9a profiles the major and minor principal stresses. Both compressive and tensile principal stresses are pronounced at the centre of the infill panel and diminish along the tension diagonal.

measuring point

(a) principal stresses (b) triangular or gauss curvestress distribution profile

0

-2.0

1.0

-1.0

at 300 kNat 400 kN

at 200 kN

at 50 kN

minor principal

stress (N/m

m)2

major principal

stress (N/m

m)2

stress

Figure 4.9 : Principal stresses across compression diagonal

From the foregoing discussion on stress distributions in the infill panels, and with regard to the configuration of the diagonal strut formed by the infill wall, it is evident that the compression band is narrow near the loaded corners and wide (bulging) at the centre. For visualization, the shape of the diagonal strut can be portrayed as shown in Figure 4.9b. In Figure 4.9a a linear distribution of stresses between the measuring points is assumed. More measurement points would be required to show the actual profile of stress distributions. However, if a triangular distribution over the whole length of the


tension diagonal is assumed, the diagonal compressive force Fd, can be estimated from equation (4.10).

d max dF l t12σ= (4.10)

where: σmax is the compressive stress at the centre of the infill wall, ld is the diagonal length of the infill wall, and, t is the thickness of the infill wall.

For Test 5, as an example, the compressive stress at the centre of the panel, just before cracking was 1.89 N/mm2. With a diagonal length of 4200 mm and wall thickness of 150 mm, the diagonal force determined with equation (4.10) is 595 kN. The horizontal component of this force is 420 kN, which compares well with the measured 400 kN. Considering, though, the fact that the direct resistance of the frame is ignored in this approximation, it can be said that a triangular stress distribution curve across the compression diagonal overestimated the diagonal force. It is reasonable to suggest that the distribution of stress across the diagonal is more or less in the shape of a gauss curve, Figure 4.9b. It is expected that the characteristics of the gauss curve are a function of the contact lengths at the frame- infill interface and the geometry of the infill wall.

4.4 Influence of frame stiffness

One of the parameters of interest is the change in strength and stiffness of an infilled frame that is associated with an increase in the sizes of the frame members. By increasing the sizes of the bounding frame members, the stiffness of an infilled frame is increased, firstly, by the simple additional stiffness of the frame and secondly, by a change in the contact area at the frame-wall interface, leading to more composite action.

In section 3.4.4, the differences in frame sizes between Specimen Type 1, being a weak frame and Specimen Type 3, the strong frame was given. The weak frames were constructed from European HE 200B and HE 180B profiles for beams and columns respectively. On average the experimental stiffness of the bare frames


was 3.1 kN/mm. The strong frames on the other hand were constructed from HE 240M profiles and the stiffness of the bare frames were, on average 9.2 kN/mm.

Figure 4.10 shows load deflection responses for four tests. Frames for Test 1 and Test 2 were of the weak frame type while those for Test 5 and Test 6 were of the strong type. The responses of the two frame types are compared below.

Increasing the frame stiffness increased the stiffness of the infilled frames. For purposes of comparison, the slope of each load deflection graph in the more or less linear diagonal strutting phase, herein after referred to as the primary stiffness, was calculated. The primary stiffnesses as well as the values of the load at which the first major cracks appeared are shown in Table 4.2. With a threefold increase in the frame stiffness, the primary stiffness of the infilled frames increased by a factor of 1.5.

0

100

200

300

400

0 4 62 8 10

horizontal deflection ( mm )

Test 6

bare strong frame

bare weak frame

Test 2Tes

t 5

Test1h

ori

zon

talf

orc

e(k

N)

Figure 4.10 : Influence of the stiffness of the bounding frame

Influence of frame stiffness 67

Table 4.2 : Stiffnesses and cracking loads for Specimen Types 1 & 3 Specimen

Type Test Primary

Stiffness

Average Primary Stiffness

Shear Slip

Load

Diagonal cracking

load

Average diagonal

cracking load (kN/mm) (kN/mm) (kN) (kN) (kN)

1 42 not observed 293 1

2 39 41

235 275 284

5 54 not observed 409

3 6 63

59 not observed 390

400

Figure 4.10 and Table 4.2 further show that increasing the frame

stiffness also increased the load at which the first major (diagonal) cracking occurred. Increasing the frame ratio from 3.1 kN/mm to 9.2 kN/mm resulted in an increase in the (average) major cracking load from 284 to 405 kN, i.e., a difference of 121 kN. Although this increase is expected by virtue of the higher load resisted by the stiffer bare frame, the increase is not, per se directly proportional to the increase of the bare frame stiffness. For instance, at a deflection of 7 mm, which is the deflection at about which the stronger frame specimens cracked, the difference in loads resisted by the weak bare frame, of stiffness 3.1 kN/mm, and bare strong frame of stiffness 9.2 kN/mm would be 42.7 kN. As stated earlier, in Figure 4.10 the corresponding difference in the load resisted by the infilled frames is in the order of 121 kN.

This disproportionate increase in the strength of the infilled frame confirms the assertion of many researchers that the structural behaviour of an infilled frame is not just an ‘arithmetic’ summation of the stiffnesses of the two parts of the structure. It is rather a unique behaviour of the composite structure. It can also be seen from Figure 4.10 that the specimens with the stronger frames had shorter and smoother transition phases while those with weaker frames had longer, if jagged, transition curves. This can be attributed to a firmer confinement of the infill panel, in the case of stronger frames, thereby


reducing the rate of energy changes in the structure during the process of frame-wall separation.

It is further noted that for Test 2, a shear crack appeared along the top most bed joint, at a load of 235 kN, prior to the appearance of the diagonal crack. Presumably, the shear crack occurred due to a poor filling of the mortar joints in this specimen. Once the crack along the bed joint below the topmost CASIEL layer occurred, the infilled frame more or less instantly recovered its stiffness.

4.5 Influence of gaps

The influence of initial gaps between the upper beams and the infill panels is plainly evident in Figure 4.11. In the four tests depicted, the bounding frames were nominally identical. Specimens for Test 3 and Test 4, however, had 12 mm initial gaps between the upper beams and the infill panels. Due to the gaps, there was a large deflection range in which the infilled frames were essentially as flexible as the bare frames. During this range the walls glided within the boundary frame until they could establish a locking position with the bounding frames in the region of the loaded corners. Once in that position, the walls acted as bracing struts in a similar way to infilled frames without initial gaps.

0 10

horizontal deflection (mm)

5 15 20

ho

rizo

nta

lfo

rce

(kN

)

0

100

200

300

Test 3

Test

1

Test

2

Test4

Test 1 and Test 2: no gapTest 3 and Test 4: gap

Figure 4.11 : Influence of gaps between upper beam and infill wall

Influence of gaps 69

Table 4.3 : Stiffnesses and cracking loads for Specimen Types 1 & 2 Specimen

Type Test Primary

Stiffness


Shear Slip

Load

Diagonal cracking

load

Average diagonal.

cracking load

(kN/mm) (kN/mm) (kN) (kN) (kN) 1 42 nil 293 1 2 39 41 235 275 284

3 29 nil 270 2 4 36 33 285 285 278

It can be seen in Table 4.3 that the average stiffness of Type 2 specimens, which is 33 kN/mm, was 20% less than 41 kN/mm for Type 1 specimens. The difference is attributed to the fact that initial frame-to-wall gaps led to shorter frame-to-wall contact lengths compared to specimens without gaps.

4.6 Effect of corner bearing wedges

The effect of using corner bearing wedges on infilled frames with gaps between the upper beams and the infill panels can be seen in Figure 4.12 and in Table 4.4.

0 2 4 6 8horizontal deflection (mm)

10

ho

rizo

nta

lfo

rce

(kN

)

0

100

300

200

400

Test 7

Test 9

Test 10

Test 8 all specimens are with cornerbearing wedges

Test 7 and Test 8: no gap

Test 9 and Test 10: with gap

Figure 4.12 : Influence of gaps on behaviour of infilled frames with corner bearing wedges


Table 4.4 : Stiffnesses and cracking loads for Specimen Types 4 and 5 Specimen

Type Test Primary

Stiffness


Shear Slip Load

Diagonal cracking

load

Average diagonal.

cracking load (kN/mm) (kN/mm) (kN) (kN) (kN)

7 50 340 365 4 8 63

57 nil 430

398

9 74 350 370 5 10 75

75 290 360

365

It will be observed in the first place that in the initial phase Type

5 specimens, Test 9 and Test 10, resisted higher loads before the transition phase than Type 4 specimens, Test 7 and Test 8. It was observed that in Test 9 and Test 10, separation of the wall from the frame properly occurred at a higher load of approximately 130 kN as compared to approximately 70 kN for Test 7 and Test 8. Secondly, infilled frames with a corner bearing wedge and a gap were stiffer than infilled frames without an initial gap. A clear cause for this increase in the separation load and in primary stiffness could not be identified. A study of the strength characteristics of the mortar and CASIELs used did not reveal variations that could explain the difference. It is suspected that in assembling the bare frames, there was a difference in the tightness of the bolt connections which yielded stiffer behaviour in the last two tests. Indeed the bare frame stiffness of Test 10, at 17 kN/mm was significantly higher than the three other similar bare frames whose stiffnesses were in the order of 12 kN/mm (see Table 4.1).

It is clear however that the very flexible transition phase associated with frame-to-wall gaps, as observed in Test 3 and Test 4, was eliminated in Test 9 and Test 10. It is, here, assumed that without corner bearing wedges, the influence of initial gaps in weak frames and strong frames is similar. It was further observed that infilled frames with corner bearing wedges and initial gaps had a similar major cracking mode (diagonal tension) and cracking load compared to infilled frames with corner bearing wedges, without initial gaps.

The final observation is that Test 7 and Test 8, although of the same specimen type, had significant differences in stiffness and

Effect of corner bearing wedges 71

diagonal cracking loads. The difference underlines the statistical nature of masonry due to the variations in material properties and workmanship.

4.7 Conclusions

Ten large-scale steel frames infilled with CASIEL walls were subjected to in-plane monotonic horizontal loads at roof beam level. The variables investigated were the frame stiffness, the presence or absence of an initial gap below the upper beam, and the influence of top corner bearing wedges.

Stress distributions derived from rosette measurements on the panel showed that each wall essentially acted as a bulging diagonal strut. Load-deformation curves show an initially high stiffness which transits into a less stiff linear primary stiffness. The deflection range in which the transition took place was longer for infilled frames with a top gap. During this transition, the wall separated from the frame at the two tension corners and adjusted within the frame until it was firmly locked up at the compression corner. In all specimens, major cracking occurred by sudden formation of diagonal cracks cutting through the CASIELs and also following the joints. Shear cracking along the topmost bed joint was observed in some specimens, although when this happened, the frames almost instantly recovered their stiffness. Increasing the stiffness of the frames led to an increase in both the infilled frame stiffness and the diagonal tension cracking load. An initial top gap resulted in a long transition phase and a reduced primary stiffness although it did not significantly reduce the cracking load.

Results from this investigation strongly indicate that a relatively simple construction technique using CASIEL wedges to push the other CASIELs outwards effectively establishes good contact at the frame-wall interface. A good contact near the loaded corners eliminates the negative influence of a construction gap between the roof beam and the infill wall and consequently eliminates the necessity of packing the gap with mortar. This can lead to improved structural efficiency as well as time/cost effectiveness. Further investigation into


the possibility of making the corner bearing wedges out of materials other than steel, possibly CASIELs themselves, is required.

Due to the limited number of tests conducted for each parameter, the conclusions drawn from these results need to be corroborated with more tests and/or numerical analyses. In the following chapter, a numerical model developed for simulation of the tests and for use in parametric studies is described.

Chapter 5

5Finite Element Model

Abstract A finite element model has been developed to simulate the experiments described in the previous two chapters. In this chapter, choices made with respect to the physical and material representation of the different parts of the infilled frames are presented. A model of a bare frame is first assembled. This is followed by a preliminary model of an infilled frame model with frame-to-wall contact limited to the loaded corners. It is found that the model is generally stiffer than the experiments. A sensitivity analysis is performed to assess the influences of the normal and tangential stiffnesses in the frame-to-wall interfaces and the joints. It is suggested that, in addition to non-linear CASIEL behaviour, movements in the bolted connections of the frames account for the differences in stiffness between the experimental specimens and the numerical results. The model is finalised with frame-to-wall contact all around the wall. Provisions are made in the model to incorporate corner bearing wedges and frame-to-wall interface gaps. Validation of the model is accomplished by comparing experimental with numerical global behaviour. A good agreement between experimental and numerical load-deflection responses is found. Validation is further established by a comparison between experimental and numerical stress distributions in the walls. The final model will be used in the parametric studies presented in Chapter 6.

5.1 Modelling in general

The conclusiveness of observations from the experiments described in the previous chapter is tempered by the relatively limited number of tests. Full scale-tests, such as conducted in this program are costly.

74 Finite Element Model

During the preparation and mounting of specimens, constancy of factors other than the one under investigation is not, per se, guaranteed. Relatively, it is easier, in analytical or numerical models than physical tests, to study the influence of one variable while maintaining all other aspects of the model constant. A model can be a convenient tool to corroborate experimental results, predict behaviour, clarify details, and study the influence of chosen parameters. Provided that the model is a fair representation of the physical experiments the use of the model for parametric studies can be a cost and time effective research strategy.

However, in order to represent, fairly, the highly complex real behaviour of an infilled frame structure, some simplifications have to be made. Material behaviour has to be simulated, the means of support and the way that the parts fit together need to be modelled and the loading needs to be defined. The model may be in the form of a simple analytical model or a more detailed finite element model.

In Chapter 4, it was shown that the composite resistance of the bounding frame and infill wall to loading is complicated, not in the least, by a compression strut whose geometrical profile varies with the level of loading. This complexity is compounded by phenomena that take place at frame-to-wall interfaces and at mortar joints, not to mention post cracking behaviour. Simple analytical models are useful but inadequate to capture these phenomena. These complexities in addition to the ‘natural’ periodic pattern of masonry infill walls make finite element modelling an attractive approach to study the influence of individual parameters on the behaviour.

5.1.1 The finite element method

The finite element method for analysis of engineering problems is well documented (Zienkiewicz & Taylor 1989, 1991; Weaver & Johnston 1983; Bathè 1996). Only a brief treatment of its principles is laid down here.

Engineering structures are assemblies of several structural members of different sizes and material behaviours and, not uncommonly, loaded at different locations with various loads. In the finite element method, a structure is broken into several finite parts,

Modelling in general 75

thus finite elements, and knitted together at element nodes. Relationships between nodal forces and nodal displacements are formulated into the form of a set of simultaneous equations (5.1).

{ } { }eF K u⎡ ⎤= ⎣ ⎦ (5.1)

where: {F} is a set of nodal forces, [Ke] is a element stiffness matrix, and {u} is a set of nodal displacements (or degrees of freedom).

Entries in the element stiffness matrix are functions of the shapes of the finite elements and the stress-strain relationships of the materials used. The position of a particular node can be related to the positions of all other nodes in the structure. Displacements of nodes take place along their degrees of freedom. As such, nodal displacements can be expressed as functions of the degrees of freedom as in equations (5.2) and (5.3).

{ } [ ]{ }u X α= (5.2)

{ } [ ] { }X u1α −= (5.3) where: { }α is a set of coefficients, and

[X] is a matrix of degrees of freedom. By differentiating equation (5.2) with respect to the degrees of

freedom, the element strains can also be written as functions of the degrees of freedom. Thus:

{ } [ ]{ }u u XX X

ε α∂ ∂⎡ ⎤= = ⎢ ⎥∂ ∂⎣ ⎦ (5.4)

By substituting equation (5.3) into equation (5.4) and letting

[ ] [ ] [ ]X X Bx1−∂⎡ ⎤ =∂⎣ ⎦ , the strains can also be expressed in terms of

{u}, thus: { } [ ]{ }B uε = (5.5)


It is known that the strain in an element is related to the stress by a material law. The element stresses therefore may be expressed as functions of the strains by operation of a set of material laws, say, denoted as D. In a one dimensional linear elastic stress relationship, for instance, the material law is a constant of proportionality, the modulus of elasticity. The set of nodal stresses is therefore:

{ } [ ]{ } [ ] [ ] { }D D uBσ ε= = (5.6) The nodal forces are functions of element stresses as well as the

shape of the elements. It can be written that: { } [ ]{ }σ=F E (5.7)

and by integration of equation (5.6) it can be shown that

{ } TE B dV⎡ ⎤= ∫⎣ ⎦ (5.8)

where ∫dV is an integration over the area of the element.

The element stresses are determined with reference to points in the elements, known as gauss points. In order to find the forces at the element nodes, these element stresses must be integrated over the element. The integration takes into consideration the area or shape of the element and the distance of the nodes from the integration points. The element stiffness matrix is therefore:

[ ][ ]e TK B D B dV∫⎡ ⎤ ⎡ ⎤=⎣ ⎦ ⎣ ⎦ (5.9)

Once the stiffness matrix is known, the nodal forces are

computed by solving the set of simultaneous equations (5.1). The use of matrix notation combined with modern day phenomenal computer processing capabilities makes it possible to quickly solve many simultaneous equations.

5.1.2 Incremental-iterative solution procedure

When linear elastic element behaviour is assumed the solution of equation (5.1) is straight forward. In a non-linear force-deformation relationship, the stiffness is not constant; it varies depending upon

Modelling in general 77

factors such as the stress level, deformation level, loading history and time. The calculation of the force-deformation response for the structure then involves small load increments, with the stiffness of the elements being evaluated after each increment. It is normally assumed that over a small load increment, the element stiffnesses remain constant. This solution process is illustrated in Figure 5.1(a). For each load increment, a new stiffness is used. The difference between the actual load deformation curve and the computed one is the error. It is clear that the smaller the size of the load step, the smaller the error.

Finding the correct stiffness for each load step is an iterative procedure which can consume a lot of computer time. Different iteration techniques have been established to accelerate this process. A basic method is the Newton-Raphson method, which is illustrated in Figure 5.1(b). First, the tangent stiffness at Point A is established. Using this tangent stiffness, an estimate of the displacement, corresponding to Point B at a load Fi is determined. By using, for instance, the principle of virtual work, the work done by the internal forces is compared to the work due to external (applied) forces. In computation, the work done by external forces and the work done by internal forces are deemed equal when the difference between them is less than a predefined tolerance. If this is the case, the solution is said to have converged. If the solution has not converged, a new tangent stiffness at B is set up in order to establish point C. The process is repeated until there is convergence, at Point D. A load increment is made and the iteration process executed to find the displacement corresponding to the load (F+∆Fi+1).

displacement

(a) non-linear solution (b) Newton-Raphson Method

displacement

forc

e

forc

e

error

DFi

Fi

F Fi i+D +1Dui

A

BC

D

Figure 5.1 : Incremental and iterative process


However, in structures like infilled frames that exhibit sudden changes in load resistance and stiffness due to separation and cracking, the iteration may often diverge from rather than converge to the result being sought. Several variations of this procedure, such as, the arc-length method and the ‘line-search’, have been developed to attempt to overcome the problem of divergence in the solution procedure. Descriptions of such techniques can be found in, for instance, the DIANA manual (2002).

Hereinafter the application of finite elements is dealt with as it specifically relates to this research.

5.2 Objective of the model

In order to corroborate and shed more light on the experimental observations which are presented in Chapter 4, a numerical model was developed. The model is a compliment rather than a substitute of the experiments. Although an effort was made to, fairly, represent the complex real behaviour of the structure, no more sophistication than necessary was incorporated.

Experimental observations indicated that separation of the wall from the frame at the tension corners takes place at a very early stage in the loading process. This separation, typically, extended well over 75% of the length and height of the infill panel. Once this separation has occurred, the less stiff load–deflection response of the infilled frame is practically linear until the sudden appearance of a major diagonal crack. The diagonal crack both followed the joints and cut through the CASIELs. In some cases, shear sliding of the top most bed joint occurred. In those cases, this resulted in a temporal drop of the load resisted by the infilled frame. The load level and stiffness were however quickly recovered, due to the confinement that the frame provided to the wall. A proliferation of diagonal cracks reduced the stiffness of the infilled frame, notwithstanding the further increase in the resisted load. Finally, crushing of the CASIELs at sites of load concentration marked the end of any practical benefit of the structure.

The phenomena that need to be captured in the finite element model are, thus, separation of the wall from the frame, the behaviour of CASIELs under biaxial compressive and/or tensile stresses,

Objective of the model 79

behaviour of thin-layer mortar joints and the behaviour of the bounding frame.

Frame-to-wall separation and cracking led to sudden changes in the distribution of stresses in the wall. For instance, when cracks occurred, some gaps that had appeared earlier due to separation or cracking closed again. This re-contact with its concomitant non-linear transfer of stresses compounds the difficulty of modelling infilled frame behaviour. In the numerical simulations described herein, the objective was to simulate the behaviour up to the onset of diagonal cracking. A satisfactory model up to that point is useful, and probably, sufficient for the purposes of non-cracking design requirements and for a study of the influence of key parameters. Naturally, advancing these simulations beyond the cracking stage is a desirable future development of this research.

5.3 Development of infilled frame model

A structural analysis commercial package, DIANA, developed by TNO DIANA bv, in the Netherlands, was utilised. All elements and material models were taken from libraries provided in the software.

The development of the model may be described under three areas of discussion. The first deals with a description of the ‘physical’ representation and material behaviour of the different parts of the structure. To this extent, the elements used are presented and the assumed load deformation responses of the materials and interfaces between parts of the structure are described. The second area deals with the assembly of the model. A preliminary model is assembled and evaluated in the light of experimental data. On the basis of the results of the preliminary model, the model is completed. Thirdly and finally, the model is validated. The validation is done by comparing overall numerical load-deflection curves with experimental ones. The validation is further consolidated with a comparison of calculated stress distributions with experimental stress distributions.


5.4 Physical and material modelling

In this section, the element types and various material behaviour models adopted in this research are described. The descriptions are given according to the different physical aspects of an infilled frame, namely, beams and columns, frame connections, CASIELs, joints, and frame-wall contacts.

5.4.1 Modelling beams and columns

The most common way of representing the columns and beams in frame analysis is by using standard beam (line) elements passing through the centrelines of the members. Seah (1998) used such elements, ascribing linear elastic behaviour to the beam elements and providing for non-linear flexural behaviour through non-linear hinges at the ends of the beam elements. Dhanasekar & Page (1986) and Liauw & Lo (1988), among others, have used a similar approach in modelling infilled frames.

When this approach is used, however, as echoed by Crisafulli et al. (2000), there is the problem of shifting the centreline of the frame members to the edge of the wall. Conversely, this could entail ‘blowing up’ the wall so that its boundary coincides with the centrelines of the frame members. King and Pandey (1978) developed a rigid arm element to use in between the centreline and edge of the column. A further problem is related to the connection of beam elements to interface elements. Beam elements, typically, have three degrees of freedom at the nodes while interface elements typically have two degrees of freedom at each node. These problems, of maintaining the centreline and connecting the frame member to interface elements, can be solved by using rectangular plane stress elements for the frame members. In this case, a cross sectional area giving a stiffness equivalent to that of the I-section must be used.

Another work-around, which was adopted in this research, was to represent column and beam flanges as truss elements, with two nodal degrees of freedom while webs are represented by plane stress elements. A scheme of this representation is shown in Figure 5.2.

Physical and material modelling 81

truss elements

truss elements

plane stress elements

Figure 5.2 : Representation of columns and beams

Truss elements are bars which can be used when the dimensions perpendicular to the bar axis are small in relation to the bar's length. Although the width of the flange is not really small in relation to the length of the elements, the thickness of the flange, which is in the plane of the two dimensional model, is relatively small. The deformation of a regular truss element can only be the axial elongation, there is neither bending nor shear deformation. Since the local flexure of the flanges was considered not to be of significance to the global behaviour of the structure, the inability of the truss elements to sustain moments was of little consequence to the analysis. The topology of a truss element, as used in this model, is drawn in Figure 5.3. Axial displacements, ux correspond to axial stresses, σx. In the transverse direction, the element has no initial stiffness. The displacement uy is linked with the surrounding elements.

u(1) y

u(2)y u(3)y

u(1)x

s(1)x

s(2)x

s(3)x

u(2)xu(3)

x

1

2 3

Figure 5.3 : 3-node truss element

Plane stress elements with 8 nodes, as shown in Figure 5.4, with two translational degrees of freedom at each node are used to represent webs. Three stress components, σxx, σyy, and τxy at each integration point are related to strain components εxx, εyy, and εxy.


uy

ux

syy

tyx

txy

sxx

1

2 3

84

7 65

Figure 5.4 : 8-node plane stress element

Under the level of applied loads and deformations in this research program, it was assumed sufficient to model steel as a linear elastic material.

5.4.2 Modelling bolted connections

The function of bolts in the connections is to provide both rotational stiffness and shear resistance. Rotational stiffness is realised by development of tension in the bolts in the tension zone of the connection, and thereby providing the connection with a lever arm and capacity to resist moments. Preliminary analyses indicated that movements of the bolts in the holes, due to fabrication tolerances can have significant effects on the global behaviour of the infilled frame. In order to capture both the axial deformations and possible play in the connections, the bolts were modelled using pairs of translational springs, as illustrated in Figure 5.5. The horizontal springs represent axial stresses and deformations. The vertical springs represent the sum of tolerance movements, shear deformation in the bolts and friction in case of contact between the beam end plate and column flange. The topology of a 2-node translational spring is also shown in Figure 5.5. At each node there is one degree of freedom, ux, and a corresponding axial force, Fx.


beam

column u(1)x

F(1)x

u(2)x

F(2)x

1 2

Figure 5.5 : Translational springs for bolt connections

The horizontal springs were assigned either a stiffness determined according to equation (5.10) in tension or a very high ‘dummy’ stiffness in compression. Equation (5.10) includes two bolts. The high stiffness value in compression represents the impenetrable bearing between the beam end plate and the column flange.

boltsteelbolt

bolt

E dk

l

2

2

π= (5.10)

where: Esteel is the modulus of elasticity of the steel, dbolt is the diameter of the bolt, and, lbolt is the distance between the midpoints of the bolt head and the nut (Figure 5.6).

columnflange

beamendplate

lbolt

Figure 5.6 : Bolt length used in equations (5.10) and (5.11)

The stiffness of the each vertical spring, kplay, was, initially, assumed equal to the shear stiffness of two bolts. The value of kplay, was thus estimated using equation (5.11).


bolt steelplay bolt

A Gk l42⎛ ⎞= ⎜ ⎟

⎝ ⎠ (5.11)

where: Gsteel is the shear modulus of steel defined as steelsteel

E( )2 1 υ+ ,

υbolt is the Poisson ratio of steel, and, Ābolt is the shear area defined as 1.1 times the cross section area of one bolt.

5.4.3 Modelling of CASIELs and joints

In modelling masonry walls a choice has to be made between a smeared approach that treats the masonry as a homogenised continuum and a detailed model approach in which units and mortar joints are treated discretely. For large walls, the high level of detail and large volume of elements associated with detailed models normally tip the balance in favour of a smeared approach. Detailed modelling, such as developed by Ali & Page (1988), has been shown to be useful for evaluation of small laboratory specimens.

In the experiments of this research, cracking patterns on CASIEL infill walls indicated that joints played a key role, at least, in initiation of cracking. Given the relatively small number of joints in CASIEL walls, it was considered that a detailed approach would not lead to too large a volume of elements. By using a detailed approach the influence of the masonry joints in the overall behaviour of the panel would be studied in a direct way. In this approach, the CASIELs are modelled as continuum elements while the joints are modelled by interface elements. Similarly to the webs in the columns and beams described earlier, 8-node plane stress elements were used for the CASIELs.

Deformation controlled tests on small calcium silicate specimens have been performed by Vermeltfoort & Pluijm v.d. (1991). Results of these tests demonstrate that calcium silicate specimens loaded in compression, tension or shear exhibit quasi-brittle behaviour (Figure 5.7). The stress-deformation curve is linear nearly up to the strength of the material. There is some non-linearity prior to the maximum load. After cracking, the force hyperbolically decreases. That is to say


that the material undergoes softening, yielding a stress-deformation curve in between pure brittle fracture and pure plasticity. The rate of loss of resistance is commonly defined by the fracture energy, the area under the stress-strain curve.

elongation u

stre

ssσ

ft

Figure 5.7 : Stress-deformation response of CASIEL under tension

From the infilled frame experiments performed in this research, the predominant mode of cracking in the CASIELs was diagonal tension cracking. Therefore, in modelling calcium silicate elements, the compression and shear behaviour were treated as linear elastic while a limiting criterion was used for tension. Post cracking behaviour of the infilled frames was not numerically studied.

For material behaviour modelling purposes, the stress-deformation behaviour of CASIEL before fracture may be approximated as linear. Post-peak behaviour may be characterized as brittle, linear softening or non-linear softening. In tension, for instance, these are graphically portrayed in Figure 5.8. In the analyses conducted in this research, brittle material behaviour was used. Representation of joints Mortar joints in masonry can be modelled at a micro or meso-level. At the micro level, depicted in Figure 5.9(a), the mortar is represented by continuum elements while unit-to-mortar adhesion areas are represented by interface elements. This generates an immense volume


in the number of elements for the model, which in turn increases the calculation cost. This is not to mention the difficulties involved in experimentally determining the material behaviour of these adhesion areas. At the meso-level approach, shown in Figure 5.9(b), the whole joint, which includes mortar and adhesion areas is represented by an interface element. Owing to the very thin layer of mortar compared to very large CASIELs, a meso level approach is preferred in this research. Interface elements with the physical thickness of 3 mm were used.

elongation u

(a) brittle

elongation u

(b) linear tensionsoftening

elongation u

(c) non-linear tensionsoftening

stre

ssσ

stre

ssσ

stre

ssσ

ft ft ft

Figure 5.8 : Material behaviour models for CASIEL under tension

interface elementinterface element

interface elementcontinuum element

unit unit

unit unit

continuum element

continuum element

(a) (b)

continuum element

continuum element

Figure 5.9 : Modelling of joints (a) micro-level (b) meso-level

Interface elements serve to transfer normal and/or shear forces across discontinuities in the model. Three approaches are generally used to model interface behaviour, namely, by the use of springs,


surface or line interfaces and contact elements. The common thing in the approach is an assessment of the relative position of the two interacting parts and the use of a stiffness that corresponds to their relative positions.

Figure 5.10(a) is a schematic illustration of the concept of springs to model interfaces. Two nodes are connected by two springs. The springs are assigned stiffnesses according to the assumed material properties (conditions) of the joints. A better representation of interface behaviour is the use of line interface elements, in the case of two dimensional models, or surface interface elements, for three dimensional models. This is schematically shown in Figure 5.10(b).

continuum element

continuum element

(a) (b)

s

t

continuum element

continuum element

Figure 5.10 : Joint interfaces (a) spring concept (b) line interface

In this research, 3-pair node line interface elements, matching with the 3-node sides of the plane stress elements used for the CASIELs, were employed. The topology of such an interface element is shown in Figure 5.11. The general constitutive behaviour of the joints is described by equation (5.12).

uyty

uxtx

1

4

2

5

3

6

Figure 5.11 : Topology of line interface element


t Ku= (5.12) where: t represents stress components and

u represents displacement components. The stiffness matrix, K is assumed as in equation (5.13).

,

,

n joint

t joint

kK

k

0

0⎡ ⎤

= ⎢ ⎥⎢ ⎥⎣ ⎦

(5.13)

with kn, joint and kt, joint being the normal and shear stiffnesses of the joint respectively. Prior to cracking, the values of normal stiffness kn,joint and tangential stiffness kt,joint were determined from equations (5.14) and (5.15) respectively.

,joint

n jointjoint

Ek

h= (5.14)

,joint

t jointjoint

Gk

h= (5.15)

where: Ejoint and Gjoint are the modulus of elasticity and shear modulus, respectively, of the mortar joint (mortar and adhesion area), and, hjoint is the thickness of the mortar packed interface.

According to Pluijm v.d. (1992), equation (5.16) can more or less be used to estimate the shear modulus of a joint (mortar and adhesion areas between mortar and units).

jointjoint

joint

EG =

2(1+ )υ (5.16)

where υjoint is Poisson’s ratio for the mortar in the interface. Non-linear behaviour of the joints was described by a combined

tension, friction and crushing material model developed by Lourenço & Rots (1997), and enhanced by van Zijl v. (2000). In this model a breach of a multi-surface plasticity, comprising of a coulomb friction model combined with a tension cut-off and an elliptical compression cap (Figure 5.12) leads to softening. Although post cracking behaviour


was not numerically studied this model was considered a convenient tool to detect the onset of cracking.

direct stress s

ten

sio

nsu

rfac

e

coulombfrictionsurface sh

ear

stre

sst

com

pre

ssio

nsu

rfac

e

Figure 5.12 : Multi-surface plasticity model

In the absence of direct tensile test results, values of tensile strength were estimated on the basis of 4-point bending tests performed on 900 mm long by 200 mm deep and 150 mm wide CASIEL samples (Vermeltfoort & Ng’andu, 2005). Molnar (2004) carried out some numerical simulations to study the relationship between tensile strengths and bending strengths obtained from three-point bending tests. The results indicated tensile strengths in the range of 60% to 75% of bending strengths. In the current work, the tensile strengths of the CASIELs and thin-layer mortar joints were estimated at 70% of the bending strength.

5.4.4 Modelling frame-to-wall interfaces

Various modelling techniques have been used by researchers to simulate the phenomena that occur at the frame-to-wall contact. The purpose of the interface is to transfer stresses between the frame and the wall when these are in contact. An important aspect of the contact is a no-penetration criterion which should ensure that under compression, material bodies of the model do not cross over each other.

Early attempts by Mallick & Severn (1967) as well as recent models, such as by Dawe et al. (2001), used spring elements to represent the stress-deformation relationships in shear and normal


directions at the frame–to-wall interface, as illustrated in Figure 5.13(a). Contact is assumed to exist when there is compression in the spring. If there is tension exceeding a preset tensile strength, contact ceases to exist and the stiffness of the spring is reduced to zero. The no interpenetration criterion is usually fulfilled by assigning a very high stiffness to the normal spring in compression. Line interfaces, illustrated in Figure 5.13(b), work with the same principles as spring interfaces.

infill panelfram

e

infill panelfram

e

(a) (b)

Figure 5.13 : Frame-to-wall contact models (a) spring and (b) line concepts

Contact elements are an extension of line or surface elements. They attempt to address the necessary boundary criterion of impenetrability by use of contact elements with contacter nodes on one part of the structure and target nodes on the other. Contact is assumed when a target node penetrates a predefined contacter area. Depending upon the distance between the contacter and target nodes a gap, slip or no-slip condition is prescribed.

In this research, both line and contact elements were explored. Contact elements are complex and calculation-expensive elements. Many convergence difficulties in the solution process were encountered when using contact elements. In the model assembled to simulate experiments herein, line interface elements were chosen. Three-pair node elements matching with the type of continuum elements used to model the infilled panel were used.

Similarly to the case of the joint interfaces described in section 5.4.3, constitutive behaviour of the frame-to-wall interfaces is expressed by the equations (5.12) to (5.16), with modulus of elasticity,


shear modulus and Poisson ratio referring to the frame-to-wall mortar interface, accordingly.

From a calculation point of view, the easiest material model for frame-to-wall interfaces is the use of a non-linear elasticity model provided in DIANA (2002). In the non-linear elasticity model, the stiffness of the interface is defined by linear segments in the stress-displacement curve. Separate, independent force-displacement curves are used in the normal and shear directions. The main advantage of this material model is its simplicity. Its main disadvantage is that it decouples behaviour in the normal and tangential directions. It is not easy to ensure that as soon as there is no contact, the normal and tangential spring stiffnesses simultaneously drop to zero. As such, it is possible to have a situation whereby the maximum tensile stress has been reached, meaning that a gap exists, and yet shear is still transferred along the interface. This, in principle, leads to an overestimation of the shear stiffness of an infilled frame. However, in situations where the specified shear strength of the interface is very small, the error introduced is negligible. Comparisons between results of analyses where a coulomb friction model combined with tension cut-off was used on the frame-to-wall interfaces and others using non-linear elastic models showed that the results were practically similar. An additional incentive for using this material model was the fact that with a near zero stiffness for a displacement range equal to the width of the gap, it is also relatively easy to study the influence of an initial frame-to-wall gap. The non–linear elastic behaviour model was therefore used in most of the analyses.

5.5 Assembly and evaluation of model

In the previous section, the element types and various material behaviour models adopted in this research have been described. In this section the assembly and evaluation of the model is described through the following logical steps:

(i) analyses of bare frames, (ii) analyses of a preliminary infilled frame model with frame-wall

contact limited to loaded corners,


(iii) study of the influence of normal and shear stiffnesses of the frame-to-wall interfaces,

(iv) study of the influence of normal and shear stiffnesses of joints (v) study of the influence of play in the bolted connections, (vi) completion of model.

5.5.1 Analyses of bare frames

Each of the bare frames that were used in the experiments was tested for in-plane lateral stiffness prior to the incorporation of the infill wall. Modelling the bare frames was the basic step to ascertain that the finite element model captured the real behaviour of the steel frames. This was particularly of interest because the rotational stiffness of the semi-rigid bolted connections is not easy to predict.

.

pairs of 2-nodespring elements

(bolts)

detail X

full model

3 node beamelements (flanges)

8 node planestress elements(webs)

detail X

Figure 5.14 : Finite element model of a bare frame

A scheme of the detailed bare frame model is shown in Figure 5.14. The windward support is modelled as a roller while, in conformity with the experiments, limited lengths of the column-end on the leeward side are restrained from outward displacement. The geometric properties of the finite element model for the bare frame are given in Table 5.1. Linear elastic behaviour, with a modulus of elasticity of 205000 N/mm2 is assumed for steel. By using a bolt diameter of 24 mm and length of 60 mm, in equations (5.10) and

Assembly and evaluation of model 93

(5.11) the values of kt,bolt and kplay were determined as 3.09 x 106

N/mm and 5.23 x 106 N/mm, respectively.

Table 5.1 : Geometrical properties in finite element models of bare frames

Beam Column Web

Web

Frame type

Flange cross

sectional area

thickness depth

Flange cross

sectional area

thickness depth

Bolt diameter*

(mm2) (mm) (mm) (mm2) (mm) (mm) (mm) Weak Frame 1800 9.0 191.0 1530 8.5 171.5 24.0

Strong Frame 8640 18.0 238.0 8640 18.0 238.0 24.0

* In the model, the cross sectional area of one bolt is doubled to represent the two bolts at each elevation

For purposes of comparison, a standard elastic frame analysis

was also performed. In this simple analysis, moments of inertia of the beams and columns were calculated from the section profiles. Connections were represented by rotational springs. Rotational stiffnesses of the springs were calculated using a preliminary approximation formula proposed by Steenhuis et al. (1994), quoted in equation (3.1). A scheme of the simple model is shown in Figure 5.15 while the geometric and material properties are given in Table 5.2. Sizes of the steel profiles have been given earlier, in Table 3.1.

load

Figure 5.15 : Simple model of a bare frame


Table 5.2 : Geometric and physical properties in simple model of bare frame

Frame Moment of inertia; beam

Moment of Inertia; column

Modulus of elasticity

Rotational stiffness; connection

(x 10 mm4) (x 10 mm4) (N/mm2) (Nmm/radian) Weak Frame* 5696 3831 205000 1.1 x 1010

Strong Frame* 24290 24290 205000 4.3 x 1010

* Refer to Table 3.1 for steel section profiles.

Stiffnesses of bare frames

The calculated and experimental stiffnesses of the bare frames are tabulated in Table 5.3. It can be seen that the finite element computation yields values of stiffness closer to experimental values than the simple frame analysis. Presumably, the wider error in case of a simple frame analysis is in the estimation of the rotational stiffness of the connections. Table 5.3 : Calculated and experimental stiffnesses of bare frames

Frame Type

Test Measured Stiffness

Average measured stiffness

Simple model stiffness

FE model stiffness

(kN/mm) (kN/mm) (kN/mm) (kN/mm) 1 2.9 2 3.5 3 3.3

Weak Frame

4 3.4

3.3 2.4 3.0

5 9.8 Strong Frame 6 8.5

9.2 11.1 10.0

Figure 5.16 displays tensile principal stresses in a deformed

shape of the weak frame. This was at a deflection of the point of load application of 10 mm. A deflection of 10 mm in a span of 3000 mm


would be considered a limiting deflection in most serviceability design requirements. It is noteworthy that at this deflection, the maximum principal stresses are in the order of 50 N/mm2. Thus, the steel would still be in the elastic range.

tensile principal stress(N/mm )2

5042.935.728.621.414.37.140

Figure 5.16 : Deformed shape of bare frame and tensile principal stresses, at a deflection of 10 mm

5.5.2 Preliminary model of infilled frame

Experimental observations showed that the prominent configuration of an infilled frame prior to diagonal cracking is a wall in contact with the bounding frame only in the vicinity of the loaded corners. As a preliminary step, the model illustrated in Figure 5.17 was assembled to simulate an infilled frame in which frame-wall separation has already occurred. The wall is connected to the frame through interface elements, limited to the vicinity of the loaded corners. For easy connection of the elements at these corners the column-to-wall contact was initially 200 mm while the beam–to-wall contact was 450 mm. The geometry and physical properties of the frame are kept the same as those of the bare frame described in Section 5.5.1. Material properties are given in Table 5.4 and Figure 5.18. The properties of steel are taken from the literature. The properties of the CASIELs and joints are based on auxiliary compression, shear and 4-point bending tests that were carried out concurrently with the infilled frame tests.


Normal and shear stiffnesses for the interfaces were calculated using equations (5.14) to (5.16), with estimated values of elastic moduli.

detail X

detail X

3-node beamele

ments

(flanges

and bolts)

8-no

depl

ane

stres

s elem

ents

(web

s and

wall)

3-pair node interface

elements (joints and

frame-wall interface)

Figure 5.17 : Preliminary finite element model with frame-to-wall contact limited to loaded corners

The load-deflection responses of the infilled frames corresponding to Specimen Type 1 (with weak frame) and Specimen Type 3 (with strong frame) calculated from the finite element models are shown in Figure 5.19. For comparison, the corresponding experimental graphs from Test 2 and Test 6 of the experiments are also shown. The primary stiffnesses of the infilled frames are also indicated. The primary stiffness is defined as the slope of the nearly linear part of the curve after frame-to-wall separation has occurred. The three stages, I, II, and III, of the behaviour of experimental specimens prior to cracking in the infill are also indicated.


Table 5.4 : Material properties

Part Property Symbol Value Unit Source

Modulus of Elasticity Esteel 205000 N/mm2 Literature Frame

Poisson’s ratio υsteel 0.3 - Literature

Modulus of Elasticity Ecasiel 6000 N/mm2 Measured

Poisson’s ratio υcasiel 0.2 - Measured/ estimated CASIELs

Tensile strength ft,casiel 0.93 N/mm2 4pt bending tests

Modulus of Elasticity Ejoint 2600 N/mm2 Estimated

Normal stiffness kn,joint 867 N/mm3 Equation(5.14)

Shear Stiffness kt,joint 361 N/mm3 Equation(5.15)

Tensile strength ft,joint 0.56 N/mm2 4pt bending tests

Cohesion cjoint 0.53 N/mm2 Measured

Joints

Coefficient of friction µjoint 0.68 - Measured

Stiffness in compression kc,bolt 1x109 N/mm (dummy)

Stiffness in tension kt,bolt 3.1x106 N/mm Equation(5.10) Bolts

Stiffness of vertical spring kplay 5.2x106 N/mm Equation

(5.11)

Modulus of Elasticity Eint 1000 N/mm2 Estimated

Normal stiffness kn,int 50.0 N/mm3 Equation(5.14)

Frame-wall

interface Shear Stiffness kt,int 20.8 N/mm3 Equation

(5.15)


A comparison of the numerical and experimental results shows that: (i) the initial stage, I, is absent from the numerical graphs. This is

indeed expected since the numerical model represents an infilled frame in which frame-wall separation has already occurred.

(ii) in stage II, the experimental and numerical graphs have similar gradients. In the experiments, it was during this stage that frame-wall separation took place. This separation did not occur at a single instance. Since the numerical model simulates infilled frames in which separation has already occurred, the numerical and experimental curves, though similar, are not directly comparable.

(iii) a comparison can be made between the numerical stiffness and the experimental primary stiffness of the infilled frames in stage III, since in both the experimental and numerical situations, frame-to-wall contact is limited to the vicinity of the loaded corners. Figure 5.19 shows that the numerical stiffnesses are approximately 1.6 times higher than the experimental primary stiffnesses. Possible sources of the discrepancy are (a) non-linear material behaviour of the CASIELs, (b) deformations in the frame-to-wall mortar interface, (c) lower normal and/or shear stiffnesses in the joints, due to, for instance, imperfect filling of joints, and, (d) movements of the bolts within the frame connections.

(iv) numerically calculated cracking loads are more or less similar with experimental cracking loads.

(v) contour levels of the major principal stresses on the infill wall corresponding to Specimen Type 1, prior to cracking, are shown in Figure 5.20. The distribution of principal stresses, showing compression increasing from the centre of the panel towards the loaded corners and tension reducing from the centre of the panel towards the unloaded corners, is similar to experimental results (see Section 4.3.2).


= 1x10

(N/mm )kn,int

-9

3

= 1x10

(N/mm )kn,int

-9

3

= 867 (N/mm )kn,int3

= 50 (N/mm )kn,int3

= 361(N/mm )

kt,int3

= 20.8(N/mm )

kt,int3

= 1x10(N/mm )

kn,int9

3

= 1x10(N/mm )

kn,int9

3

stre

ssst

ress

stre

ssst

ress

displacementdisplacement


-0.015 mm

-1 mm

0.56(N/mm )2

0.15(N/mm )2

- 0.56(N/mm )2

- 0.15(N/mm )2

normal direction

normal direction

tangential direction

tangential direction

bottom frame-wall interface

side and top frame-wall interfaces

Figure 5.18 : Nonlinear elastic behaviour of frame-to-wall interfaces

0 10horizontal deflection (mm)

42 6 8

ho

rizo

nta

lfo

rce

(kN

)

0

100

200

300

400


stage I

stage I

stage IIstage II

stage IIIstage III

Specimen Type 1 Specimen Type 3

42 6 8

ho

rizo

nta

lfo

rce

(kN

)

0

100

200

300

Exp

erim

ent (

Test

2)

=39

kN/m

m

K pr

Exp

erim

ent (

Test

)6

=63

kN/m

m

Kpr

Mod

el=

67kN

/mm

Kpr M

odel

=10

2kN

/mm

Kpr

Figure 5.19 : Load-deflection diagrams from preliminary model and experiments for Specimen Types 1 and 3


.238E-6-1.43-2.86-4.29-5.71-7.14-8.57-10

majorprincipalstress

(N/mm )2

minorprincipalstress

(N/mm )2

1.51.291.07.857.643.429.2140

Figure 5.20 : Major and minor principal stresses just prior to cracking – Specimen Type 1

A sensitivity analysis of the influence of the normal and shear stiffnesses of the frame-to-wall interfaces, normal and shear stiffnesses of the joints and the influence of movements of bolts in the frame connections was the objective of the subsequent investigations presented in sections 5.5.3, 5.5.4, 5.5.5 below. As will be seen under the validation of the model in section 5.6.2, non-linear material behaviour of the CASIELs, though evident, does not totally account for the difference between the numerical and experimental stiffness.

5.5.3 Influence of normal and shear stiffnesses of frame-to-wall contact

The influence of the normal and shear stiffnesses of the frame-to-wall interface was investigated by running several analyses of the preliminary model using a range of interface stiffness values. In these analyses, all other parameters were kept as given in Table 5.4 and Figure 5.18. Primary stiffnesses obtained from these analyses are plotted against the interface stiffness values in Figure 5.21. The graphs show that, for realistic values, the frame-to-wall normal interface stiffness kn,int, has an insignificant influence on the primary stiffness of the infilled frame, whose calculated value was practically constant at 102 kN/mm. At low values of kt,int, relative increases of kt,int, lead to


rapid gains in infilled frame stiffness. At high values of kt,int, however, this gain in the primary stiffness of the infilled frame diminishes. It is noted however that, even at a low kt,int, value of 5 kN/mm3, which according to equation (5.15) corresponds to a very low interface elastic modulus of 240 N/mm2, the infilled frame stiffness is 90 kN/mm. This stiffness is still much higher than the average experimental equivalent of 59 kN/mm. It is therefore concluded that frame-to-wall stiffness values do not account for the too high calculated infilled frame stiffness.

0 50

frame-to-wall interface stiffness (N/mm )3

25 75 100

infi

lled

fram

ep

rim

ary

stif

fnes

s(k

N/m

m)

80

90

100

110

kn,int

kt,int

Figure 5.21 : Influence of frame-to-wall interface stiffnesses

5.5.4 Influence of normal and shear stiffnesses of the joints

The values of normal and shear stiffness used in the analyses so far assume that there is a complete filling of joints. If, as is often observed in practice, the workmanship does not guarantee the complete filling of the joints, the actual values of joint normal and shear stiffnesses may be much less. The influence of the former is hereby qualitatively evaluated. The influence of the latter was checked by analysing the model with a range of values of joint shear stiffness.

The influence of the normal stiffness of the joint interfaces can be evaluated by considering the resultant stiffness of a CASIEL wall prism of, say, 600 mm height (the height of one CASIEL), and including one joint of 2 mm thickness. Assuming linear elasticity of the joint and CASIEL, the deflection of the prism can be written as:


wall casiel jointE E Ex 600 = x 598 + x 2

σ σ σ (5.17)

where: σ is the direct stress in the wall, Ewall is the effective elastic modulus of the wall, Ecasiel is the elastic modulus of CASIEL, Ejoint is the elastic modulus of the joint,

thus:

( x )casiel

wall casieljoint

EE E

E

600= 598 21+ 598

(5.18)

From equation (5.18) it can be shown that for values of Ejoint between 10% and 100% of Ecasiel, the effective stiffness of the wall would be between 0.97Ecasiel and 1.0Ecasiel. It should be therefore expected that the normal stiffness of the mortar joints does not have a large influence on the stiffness of the wall.

The resulting infilled frame stiffnesses from analyses with several values of joint shear stiffness are given in Table 5.5. The table shows that reducing the shear stiffness of the joint, within a practical range, does not have a significant influence on the infilled frame stiffness and therefore cannot account for the overestimation in the stiffness of the infilled frame.

Table 5.5 : Influence of joint shear stiffness kt,joint on infilled frame primary stiffness, Kpr

kt,joint (kN/mm3) 2000 800 600 400 365 300 200 100 50 Kpr (kN/mm) 102 102 102 102 102 102 101 101 99

5.5.5 Influence of play in the bolted connections

Other than non-linear behaviour of the CASIELs, there remains one source of flexibility in the experiments to be checked, namely, the effect of movements in the holes of the connection bolts. Although it would be expected that any play in the bolted connections would take place at the beginning of the loading process, observations from


measurements of rigid body movements during the experiments showed that some friction movements occurred later in the loading process. The sensitivity of the model to play in the bolted connections was checked by running several analyses with a range of values of kplay. As an example the resulting stiffnesses for the infilled frame of Specimen Type 3 are shown in Table 5.6.

These results show that at lower values of kplay the model is fairly sensitive while at high values, kplay plays a less sensitive role. A kplay value of 500 kN/mm yields an infilled frame stiffness of the same order of magnitude as the physical experiment. By using the same value of kplay in the model of Specimen Type 1, an infilled frame stiffness of 39 kN/mm was calculated, which compares well with the average primary stiffness, 41 kN/mm obtained from Tests 1 and 2.

Table 5.6 : Influence of play in the bolted connections, kplay

kplay (kN/mm) 5000 700 600 500 400 300 Kpr (kN/mm) 102 97 97 65 40 28

Considering the fact that in each hole for an M24 bolt there is a

tolerance of 2 mm, some amount of play in the holes is not improbable. Although movements in the bolted connections were not, experimentally measured, the kplay value of 500 kN/mm is effectively used to calibrate the model and reconcile it with the experiments. In assuming a reduced value of the stiffness, kplay, of vertical springs in the connections, it is borne in mind that the effect of any movements in the bolted connection has been smeared over the loading process. In Section 5.6.2, it will be shown that by using this value of kplay numerical results agree with experimental results for all infilled frames tested. The validity of the model will be further strengthened by a comparison of the numerical with experimentally determined principal stresses on various parts of the wall.

In order to complete the model, frame-to-wall interface elements are incorporated all round the infill wall.


5.5.6 The final model

So far, the frame-to-wall contact has been limited to the vicinity of the loaded corners. In this approach the length of contact between the frame and the wall has been predetermined. In theory it is considered that the contact length which has an influence on the behaviour of an infilled frame depends upon the frame stiffness to wall stiffness ratio. It would therefore be desirable to model the initial frame-wall contact conditions and simulate, rather than predetermine, this contact length. In the complete model(s) of the infilled frame, frame-to-wall interface elements are incorporated all around the infill wall. Provisions were also made to incorporate initial frame-to-wall gaps as well as corner bearing wedges. An overview of the final model(s) is shown in Figure 5.22.

detail X

full model

bolted connections

detail X - modified for frameswith corner bearing wedges

3-node beam elements

(flanges and bolts)

8-no

depl

ane

stre

ssel

emen

ts

(web

san

dw

all)

3-pair node interface

elements (joints and

frame-wall interface)

detail X

beam

colu

mn

3-node truss elements

(flanges and bolts)

8-no

depl

ane

stre

ssel

emen

ts

(web

san

dw

all)

3-pair node interfaceelement (joints andframe-wall interface)

6-node triangular

plane stress elements

(wedge weband

wall)

Figure 5.22 : Final model and modifications for corner bearing wedges


In order to incorporate bearing wedges in the model, the web was represented with 6-node plane stress triangular elements while the flange was represented my matching 3-node truss elements. A part of the CASIEL wall bordering the wedge flange is also modelled using triangular plane stress elements (Figure 5.22).

Gaps were incorporated by the use of an appropriate non-linear elasticity material model for the upper beam-wall interface. This material model is illustrated in Figure 5.23. In the normal direction the interface has a near zero stiffness in tension. In compression, the stiffness remains small until a deformation equal to the size of the gap is reached. At that point the stiffness changes to a very high value. In shear, the interface has near zero stiffness.

.

=1x

10(N

/m

m)

k n,i

nt

9

3st

ress

stre

ss

normal direction tangential direction


= 1x10

(N/mm )kn,int

-9

3 = 1x10 (N/mm )kt, int

-9 312 mm gap

Figure 5.23 : Non-linear elasticity for gap interface

5.6 Model validation

5.6.1 Comparison of numerical and experimental global behaviour

A comparison of the numerical and experimental results for all specimen types is shown in Figure 5.24. It can be seen that there is an agreement of results in terms of the stiffnesses and cracking loads.


0

0

2

2

4

4

6

6

8

8



10

10

ho

rizo

nta

lfo

rce

(kN

)h

ori

zon

talfo

rce

(kN

)

0

0

100

100

300

300

200

200

400

400

numerical, SpecimenType 4numerical, SpecimenType 5Test 7

Test 8


5 15 20

ho

rizo

nta

lfo

rce

(kN

)

0

100

200

300

numerical,Specimen Type 1

numerical,Specimen Type 2

Test 1 Test 3

Test 2 Test 4

Test 5

numerical, SpecimenType 3

Test 6

Figure 5.24 : Comparison of calculated and experimental global behaviour for all specimen types

Model validation 107

Prior to frame-wall separation, the numerical stiffnesses are lower than the experimental values. This difference is due to the simplification made in the material model used for the frame-to-wall interface. Whereas in the experiment a small amount of tension is sustained at the frame-to-wall contact prior to separation of the wall from the frame, a nearly no tension condition was assumed in the non-linear elasticity model. After frame-wall separation, the numerical primary stiffnesses tend to be higher than the experimental values. It is assumed that imperfections in the physical experiments arising from weak spots in the wall or joints, imperfectly filled joints or frame-to wall interfaces and non-linearity of actual CASIEL behaviour could account for the difference.

5.6.2 Comparison between numerical and experimental stress distributions

As explained in Chapter 3, rosette measurements of strains at select sites on the wall were recorded throughout the infilled frame tests. These measurements were used to determine the principal stresses. In addition to a validation of the model by the criteria of overall stiffness and cracking loads, calculated and experimentally determined principal stresses were compared. This comparison is illustrated in Figure 5.25 where the numerically and experimentally determined principal stresses along the compression diagonal in Test 5 are compared. In Figure 5.25(b), (c), (d), (e) and (f) principal stresses at the measuring points, shown in Figure 5.25(a), are plotted against the deflection of the infilled frames at the point of load application.

At all measuring points, there is a good congruency between the calculated and experimentally determined major and minor principal stresses. Graphs from numerical values are expectedly more linear than from experimental results due to the choice of linear elastic behaviour for the CASIEL material behaviour. In reality there will be some differences in the elastic properties of the CASIELs over the area of the infill wall. Also, the model assumes perfect filling of the joints, which in practice is not the case. Other causes of non-linear experimental plots can be the presence of micro cracks, inconsistent workmanship and non-linearity of joint behaviour.


-4

-2

0

-6

major p. stress - modelmajor p. stress - experiment

minor p. stress - model

minor p. stress - experiment

pri

nci

pal

stre

ss(N

/m

m)2

-1

-2

0

1

pri

nci

pal

stre

ss(N

/m

m)2

-4

-2

0

0

00

0 0


(b) at P1

(f) at P15(e) at P13

(d) at P8(c) at P3

(a) measuring points

horizontal deflection

pri

nci

pal

stre

ss(N

/m

m)2

-1

-2

0



P1P3

P8

P13

P15

pri

nci

pal

stre

ss(N

/m

m)2

-1

-2

0

1

1

11

1 1

0

2

22

2 2

3

33

3 3

4

44

4 4

5

55

5 5



Pri

nci

pal

Str

ess

(N/

mm

)2

Figure 5.25 : Comparison between numerical and experimental major principal stresses (Test 5)

Model validation 109

The largest compressive stresses are at measuring points P1 and P15, with values of 3.9 N/mm2 and 5 N/mm2, respectively. At these points, even the minor principal stresses are compressive. Towards the centre of the infill wall, compressive stresses decline, while tensile principal stresses appreciate. The maximum tensile stress of 0.8 N/mm2 is at Measuring Point P8.

5.7 Deduction from numerical model

A finite element model has been assembled that simulates infilled frame tests that were conducted in this research. The model predicts the separation of frame-to-wall interfaces, primary stiffness of the infilled frames, and the onset of cracking in the infill wall. The model utilises 8-node plane stress elements for CASIELs, 3-pair-node interface elements of thin-layer joints and frame-to-wall contact. Webs of the steel profiles are modelled with 8-node plane stress elements while flanges are modelled with 3-node truss elements. Connection bolts are modelled with horizontal and vertical spring interface elements. Support conditions matching the test set-up were used. Linear elastic behaviour with a brittle tension limit is assumed for the CASIELs. Non-linear behaviour is prescribed for frame-to-wall contact and thin layer joints. Since the strains in the bounding frames tested were relatively small, linear elastic behaviour was assumed for steel.

Provision for some play in the bolts was made, in order to reconcile the calculated and experimental stiffnesses. A comparison of numerically calculated and experimentally determined stiffnesses and cracking loads of all specimen types shows a good agreement. A comparison between numerically calculated and experimental stress distributions on the infill walls further confirms the validity of the model.

In Chapter 6 the model will be used to investigate the influence of geometric, material and interface parameters.

Chapter 6

6Parametric studies

Abstract This chapter presents results of parametric studies obtained using the DIANA finite element model developed for analysis of CASIEL-infilled steel frames. The model predicts the stiffness of CASIEL-infilled steel frames and the onset of major cracking in the infill walls. The parameters investigated are those that pertain to choices that ordinarily need to be made in the design process, thus, aspect ratio of an infilled frame, frame member sizes, rigidity of connections, thickness of the wall, frame-to-wall interface gaps, corner bearing wedges and the modulus of elasticity of the CASIELs. It has been found that the influences of different parameters on the stiffness of infilled frames vary in magnitude depending upon the aspect ratio. In general, square infilled frames show the highest sensitivity to most parameters. With relatively squat infilled frames, the wall dominates the behaviour while the frame’s role diminishes. On the other hand, for relatively slender infilled frames, bending deflections increasingly overshadow composite action of the bounding frame and infill walls.

6.1 General

In the previous chapter, a finite element model developed for simulating the experiments described in Chapters 3 and 4 has been presented. As stated in Section 5.1, the finite element model was developed in order to supplement the generally limited experimental data obtained from large scale infilled frame tests. It was also pointed out that maintaining uniform material characteristics while studying one variable in a large scale testing program involving masonry is

112 Parametric studies

nearly impossible. In this chapter, the finite element model that was developed will be used to investigate the influence of several parameters. The parameters investigated are those that relate to choices that ordinarily need to be made in the design process, such as geometric sizes, material properties and frame-to-wall interface details. In Table 6.1 a list of parameters that may be of interest is shown. Only the highlighted ones are included in the parametric studies conducted in this work. The geometric parameters investigated are: the overall dimensions of infilled frames, thus, aspect ratio; the profiles of frame members; the wall thickness and the rigidity of frame connections. Under material properties is considered the elasticity modulus of CASIELs. The influence of frame-to-wall interface stiffnesses was covered in Chapter 5 during the development of the model. In this chapter frame-to-wall interface conditions refer to the presence of interface gaps and corner bearing wedges.

Table 6.1: Parameters of interest

Geometric Material properties Frame-to-wall interface conditions

Aspect ratio Modulus of Elasticity

of CASIELs Initials gaps

Size of frame members

Strength of CASIELs Corner bearing wedges

Thickness of wall Bond in joints Bond Rigidity of frame

connection Shear stiffness of

joints Cohesion

Openings in the wall Normal stiffness of joints

Shear stiffness

Cohesion of joints Normal stiffness

Yield strength of steel

6.2 Geometric Parameters

In Table 6.2 a summary of the geometric characteristics of the twenty four types of infilled frames analysed is given. Four geometric

Geometric Parameters 113

parameters, namely, aspect ratio, frame member sizes, frame connection stiffness and thickness of wall, are included in the study.

The aspect ratio is defined as h/l where h is the height of the infilled frame and l is its length. Three aspect ratios, 0.5, 1.0 and 1.5 were used in the analyses. The corresponding infilled frames, shown in Figure 6.1, are 3.0 m high by 6.0 m wide, 3.0 m high by 3.0 m wide, and 4.5 m high by 3.0 m wide respectively.

Table 6.2: Parametric characteristics of infilled frames analysed

Analyses Aspect Ratio Profile* Connection Wall thickness (mm)

1 to 3 0.5, 1.0, 1.5 Weak Pinned 150

4 to 6 0.5, 1.0, 1.5 Weak Rigid 150

7 to 9 0.5, 1.0, 1.5 Strong Pinned 150

10 to 12 0.5, 1.0, 1.5 Strong Rigid 150

13 to 24 As in Frames 1 to 12 100 * Strong = HE240M all round, Weak = HE200B Beams + HE180B Columns

h/l = 0.5

h/l = 1.0

- joint thicknessesare exaggerated

- dimensions in mm

= 1.5h/l

6000

3000

3000

3000

4500

3000

Figure 6.1 : Infilled frames with different aspect ratios


The size of frame members is designated either weak or strong. ‘Weak’ and ‘Strong’ frames refer to profiles that are identical to the weak frames and strong frames of the experimental program given in Section 3.4.4.

The rotational stiffness of frame connections is indicated either as pinned or as rigid. It will be recalled that connection bolts were represented by translational springs (see Figure 5.5) in the model. Rigid connections are modelled by using a very high stiffness of 1 x 109 N/mm for all the springs. Pinned connections are achieved by assigning a very low tensile stiffness of, say 10 N/mm, and maintaining the high stiffness in compression, for the horizontal springs. By so doing, the bolts in tension freely deform while the bolts in compression provide a pivot upon which the connection rotates.

The fourth geometric parameter studied is the thickness of the wall. The thickness is either 100 mm or 150 mm. Analyses 13 to 24 in Table 6.2 were derived by duplicating the first series of 12 analyses albeit with a wall thickness of 100 mm.

In conformity with the materials used in the experiments and the validation of the DIANA model, the properties of the materials used in the analyses are as shown in Table 5.4. In these 24 analyses, however, a high value of stiffness of 1 x 109 N/mm is used for vertical springs in the connections as well. This in effect means that it is assumed that there is no play in the frame connections.

6.2.1 Overview of numerical results for geometric parameters

In Figure 6.2 a contour map for major principal stresses in the wall at a racking load of 200 kN for the case of a strong square frame with fully rigid connections is shown. The figure, which typifies all frames analysed, shows that frame-to-wall separation at the tension corners occurs while diagonal strutting remains the basic mode of load transmission by the wall. Up to the onset of cracking, analyses of all the infilled frames yielded load deflection curves of the form shown in Figure 6.3. Points ‘a’ and ‘b’ on the curve correspond to frame-wall separation and tensile failure of the joints respectively.


The primary stiffness and cracking load of each type of infilled frame are given in Table 6.3. The primary stiffness of each infilled frame is hereby defined as the slope of the line between ‘a’ and ‘b’.

Figure 6.2 : Typical contour plot of major principal stresses

200

300

100

400

500

600

100

2 3 4 5horizontal deflection (mm)

a

b

ho

rizo

nta

llo

ad(k

N)

Figure 6.3 : Typical numerical load deflection diagram

Table 6.3 : Primary stiffnesses and cracking loads

Primary Stiffness (kN/mm) Cracking load (kN) Wall

thickness (mm)

Aspect Ratio

rigid pinned rigid pinned Strong frames

0.5 115 108 612 587 1.0 97 88 448 393 1.5 52 46 275 225

Weak frames 0.5 85 84 498 453 1.0 64 62 357 349

150

1.5 31 28 234 209 Strong frames

0.5 88 85 454 428 1.0 75 69 311 281 1.5 32 31 183 153

Weak frames 0.5 63 62 333 328 1.0 46 43 244 233

100

1.5 22 21 171 146 Note: Strong = HE240M all round, Weak = HE200B Beams + HE180B Columns


6.2.2 Influence of aspect ratio

It is evident from Table 6.3 that decreasing the aspect ratio of an infilled frame increases its primary stiffness and the load at which cracking in the wall starts. Considering, for instance, strong frames with rigid connections and 150 mm thick walls, infilled frames with aspect ratios of 1.5, 1.0 and 0.5 yielded primary stiffnesses of 52, 97 and 115 kN/mm respectively. The corresponding cracking loads were 371, 448 and 612 kN, respectively. The trend is similar for all sets of infilled frames in which the variable is the aspect ratio. The loss of stiffness with increasing aspect ratio is expected given the increased role of bending deflections in the relatively slender infilled frames.

In order to get further insight into the influence of the aspect ratio, elastic analyses of bare frames and plain walls, i.e., without bounding frames were performed. The same material properties and support conditions as in the analyses of the infilled frames were utilised. In Figure 6.4 the load-deflection responses of the bare frames and the plain walls are compared with those of the infilled frames. Once again the strong frames with rigid connections and 150 mm thick walls are used as an example.

These graphs show, first of all, that the mere confinement of a wall by a bounding frame produces a structure with a stiffness that is higher than the arithmetic sum of the bare frame and the wall. However, it will be observed that by changing the aspect ratio, the stiffnesses of the bare frame and plain wall are also altered. Reducing the aspect ratio from 1.0 to 0.5, for instance, doubles the stiffness of the plain wall. At the same time, the stiffness of the bare frame slightly reduces from 20 kN/mm to 17 kN/mm. This produces an overall increase by a factor of 1.2 in stiffness of the infilled frame, from 97 kN/mm to 115 kN/mm. In contrast, reducing the aspect ratio from 1.5 to 1.0 increases the stiffnesses of the bare frame and the plain wall by factors of 2.8 and 3.3 respectively. This produces a 1.9 factor increase in the stiffness of the infilled frame, from 52 kN/mm to 97 kN/mm. The trend is proportionally similar for all other similar frames in which the aspect ratio of the frame is the variable. Therefore, since changing the aspect ratio of an infilled frame


simultaneously alters other parameters, the other parameters must be investigated within distinguished aspect ratios.


horizontal deflection (mm)(b) = 1.0h/l

(a) = 1.5h/l

(c) = 0.5h/l


200

200

200

300

300

300

100

100

100400

400

500

600

2

2

2

0

0

0

0

0

0

4

4

4

6

6

8

8

ho

rizo

nta

llo

ad(k

N)

ho

rizo

nta

llo

ad(k

N)

ho

rizo

nta

llo

ad(k

N)

bare frameplain wallinfilled frame

Figure 6.4 : Bare frame, plain wall and infilled frame behaviour

6.2.3 Influence of frame member sizes

The results given in Table 6.3 show that increasing the profile sizes of the bounding frame members increases both the stiffnesses and cracking loads for all aspect ratios and frame connection types. A comparison of the relative increase in the stiffness and cracking load of each frame when the sizes of profiles are changed is shown in Table 6.4. By changing the profile sizes, the slender infilled frame relatively gained the most (67%) while the squat frame gained the least (35%) in stiffness. The square frame gained 52% in stiffness. This can be explained by the fact that for squat frames, the wall dominates the behaviour of the composite structure, such that changes in the bounding frame member sizes have relatively less influence. For slender infilled frames, on the other hand, the contribution of the bounding frame to the stiffness is more influential. A relatively small increase in the bounding frame stiffness yields a more pronounced


effect on the stiffness of the composite structure. The ratios of cracking loads of infilled frames with strong frames to those of infilled frames with weak frames are also shown in Table 6.4. Relatively squat and square infilled frames gained about 25% in cracking load when the frame sizes were increased while relatively slender infilled frames gained by 12%. The reason for the difference is that in addition to a wider distribution of the load onto the wall, the bounding frames in squatter frames are stiffer and therefore carry more loads than in the slenderer frames.

Table 6.4 : Ratios of stiffnesses and cracking loads of infilled frames with strong frames to those of infilled frames with weak frames

Aspect ratio Ratio of stiffnesses Ratio of cracking loads

0.5 1.35 1.23 1.0 1.52 1.25 1.5 1.67 1.12

Note: Strong = HE240M all round, Weak = HE200B Beams + HE180B Columns

6.2.4 Influence of rigidity of connections

The influence of the rigidity of frame connections is shown in Table 6.5 in which ratios of stiffnesses and cracking loads of infilled frames with rigid connections to those of infilled frames with pinned connections are tabulated. This table shows that changing connection details only marginally changed the infilled frame stiffnesses. For all the frames analysed the increase in infilled frame stiffness when pinned connections were replaced with rigid connections was less than 10%. Infilled frames of aspect ratios 0.5 and 1.0 hardly gained in cracking loads while infilled frames with aspect ratios of 1.5 gained as much as 22%. It must however be pointed out that the cracking loads for slender infilled frames are much lower than the squatter ones. When the connection rigidity is changed, the resulting cracking load reflects a relatively higher appreciation for the slender infilled frames than the squatter ones.


Table 6.5 : Ratios of stiffness and cracking loads of infilled frames with rigid connections to those of infilled frames with pinned connections

Wall thickness

(mm)

Aspect Ratio Ratio of stiffnesses Ratio of cracking

loads

Strong frames 0.5 1.06 1.04 1.0 1.10 1.14 1.5 1.09 1.22

Weak frames 0.5 1.01 1.10 1.0 1.03 1.02

150

1.5 1.10 1.12 Strong frames

0.5 1.04 1.06 1.0 1.03 1.11 1.5 1.03 1.20

Weak frames 0.5 1.01 1.02 1.0 1.07 1.05

100

1.5 1.05 1.17

6.2.5 Influence of wall thickness

Table 6.6 shows ratios of stiffness and cracking loads of infilled frames with 150 mm thick infill walls to those of infilled frames with 100 mm thick infill walls. These results indicate that there is a near linear relationship between the wall thickness and the infilled frame stiffness, as well as between the wall thickness and cracking loads. In all infilled frame types analysed increasing the wall thickness by 1.5 times led to average infilled frame stiffness and cracking load increases of 1.4.


Table 6.6 : Ratios of stiffness and cracking loads of infilled frames with 150 mm thick infills to those of infilled frames with 100 mm thick infills

Connections type

Aspect Ratio Ratio of stiffnesses Ratio of cracking

loads Strong frames

0.5 1.3 1.4 1.0 1.3 1.4

Pinned

1.5 1.5 1.5 Strong frames

0.5 1.3 1.4 1.0 1.3 1.4

Rigid

1.5 1.6 1.5 Weak frames

0.5 1.4 1.4 1.0 1.4 1.5

Pinned

1.5 1.5 1.4 Weak frames

0.5 1.4 1.5 1.0 1.4 1.5

Rigid

1.5 1.4 1.4

6.2.6 Influence of relative wall-to-frame stiffness ratio

The foregoing discussion on the influence of several geometrical factors highlights the interrelatedness of the factors. A change in one aspect of the geometry leads to changes in other factors of the geometry. The numerical results further show that changes in one geometric attribute of the bounding frame or wall has relatively different degrees of effects on infilled frames of different aspect ratios. It is therefore convenient and more objective to study the influence of a parameter, such as was proposed by Stafford-Smith and Carter (1969) that combines aspects of geometry into a relative wall-to-frame stiffness ratio. The relative wall-to-frame stiffness ratios λhh and λll have been defined in Chapter 2.


lhh ll l

40 40

60 60

100 100

20 20

80 80

120 120

2 20 00 0

4 46 68 810 10

infi

lled

fram

est

iffn

ess

(kN

/m

m)

infi

lled

fram

est

iffn

ess

(kN

/m

m)

h/l = 1.5h/l = 1.0h/l = 0.5

h/l = 1.5h/l = 1.0h/l = 0.5

Figure 6.5 : Infilled frame stiffness as a function of λhh and λl l

In Figure 6.5 the numerically calculated stiffnesses of infilled frames with rigid connections are plotted against wall-to-frame stiffness ratios λhh and λll. The graphs show that relatively slender infilled frames (h/l = 1.5) are the least sensitive to variations in wall-to-frame stiffness ratios. This is due to the fact that bending deflections of the bounding frame and wall dominate the behaviour rather than composite infilled frame behaviour. Square infilled frames exhibit the highest sensitivity to changes in wall-to-frame stiffness ratios. Infilled frames with an aspect ratio of 0.5 are slightly less responsive to changes in wall-to-frame stiffness ratio than square infilled frames. This is because for very squat infilled frames the wall dominates the behaviour. The contact length between the top beam and the infill wall relative to the length of the wall is small. As such the confining effect of the top beam on the whole wall is less significant. In addition as the infilled frame becomes squatter, shear deformation plays an increasingly important role. This tends to reduce the gains in stiffness that are otherwise accrue on account of increasing the member sizes of bounding frames or their connection rigidity. These results indicate that a too stiff bounding frame or too stiff wall reduces the composite infilled frame effect.


6.2.7 Effective width of equivalent diagonal strut

The results of the experiments and finite element analyses in this research support the observation that infill walls essentially provide diagonal bracing to bounding frames. As such, the wall can be replaced with an equivalent diagonal strut. In order to evaluate the effective widths of the equivalent diagonal strut for the walls in the infilled frames analysed, it is hereby assumed that the equivalent diagonal strut is pinned to the intersection of the beams and columns at the loaded corners; the modulus of elasticity and the thickness of the strut are the same as those of the wall; and the frame connections are rigid. As stated in Chapter 2, several theoretical and empirical formulae for the effective width have been proposed by various researchers. In Table 6.7 effective widths derived from the finite element analyses of rigidly connected infilled frames with 150 mm thick walls are compared with effective widths calculated from some of these expressions. The finite element (FE) effective widths have been determined by replacing the infill wall with a strut that results in the same infilled frame stiffness as the tangent stiffness, at cracking point, from the corresponding finite element analysis. All the effective widths are given in terms of the diagonal length. The table also gives the factor of the effective width calculated by each method with respect to the corresponding FE effective width.

From this table it can be seen that methods of approximating the effective widths of infilled frames, found in the literature, can give results with fairly large differences. Calculations based on Hendry’s (1990) method, with relative stiffness parameters according to Stafford-Smith, overestimate the effective widths of the equivalent struts by a 40 to 71%. It is noteworthy that the S304.1-04 of the Canadian Standards Association (2004) uses this approach to determine the width of diagonal strut and divides it by 2 to obtain the ‘effective diagonal strut width’. The FEMA 306 (1998) method, which is based on Mainstone’s empirical expressions, generally underestimates the effective widths. The simple method proposed by Angel et al. (1994) gives the closest, though conservative, estimates of the effective widths of the equivalent diagonal struts.

Interface parameters 123

Table 6.7 : Comparison of effective widths from different expressions, relative to the diagonal length, ld

Frame size

Aspect ratio Effective width/diagonal length

FE

Hendry

l h2 21 1

2 2( ) ( )πλ λ+

FEMA h dh l0.40.175( )λ −

Angel et al. dl0.125

w/ld w/ld Factor of FE

w/ld Factor of FE

w/ld Factor of FE

1.5 0.15 0.21 1.40 0.08 0.53 0.125 0.83 1.0 0.17 0.26 1.53 0.09 0.53 0.125 0.74 Weak 0.5 0.13 0.20 1.54 0.09 0.69 0.125 0.96 1.5 0.21 0.31 1.48 0.10 0.48 0.125 0.60 1.0 0.26 0.38 1.46 0.11 0.42 0.125 0.48 Strong 0.5 0.17 0.29 1.71 0.11 0.65 0.125 0.75

6.3 Interface parameters

6.3.1 Influence of frame-to-wall gaps

Gaps between a frame and an infill panel do arise because of the difficulty of achieving a tight fit between the frame and the panel during construction. In addition shrinkage of the CASIEL panels can also cause frame-to-wall interface gaps. Furthermore, if it is desired that a top beam should not transfer loads into the wall below, a gap between the top beam and wall might be intentionally detailed. The study of the influence of these gaps on the behaviour of infilled frames is therefore an important consideration.

With the FE model, analyses were performed on infilled frames with strong frames, rigid frame connections, 150 mm thick walls of aspect ratios 0.5, 1.0 and 1.5. Interfaces with 12 mm gaps between the top beam and wall were used in accordance with Figure 5.23. Other material properties were kept the same as given in Table 5.4. The resulting load deflection curves are shown in Figure 6.6. The influence of a gap below the roof beam is similar for all aspect ratios. Initially each infilled frame is very stiff as the wall and frame act as one shear element. The wall, then, begins to rotate within the frame. In this


process the infilled frame is relatively flexible. In the last stage, the infill panel is able to develop a compressive strut and the infilled frame behaves in a manner similar to one without a gap. In the case of the infilled frame with an aspect ratio of 1.5, the compressive strut could not be developed, even at excessive deflections.

200

300

100

2

2

0

0

0

4

4

6

6

8

8


(b) = 1.0h/l

(c) = 0.5h/l

(a) = 1.5h/l



ho

rizo

nta

lfo

rce

(kN

)

ho

rizo

nta

lfo

rce

(kN

)

0

0

100

100

200

200

300

300

600

400

400

500

0 4 106 1282m

odel

-w

ithou

tga

p

model - with gap

ho

rizo

nta

lfo

rce

(kN

)

mod

el- w

ithou

t gap

mod

el- w

ithga

p

mod

el- w

ithga

pmodel - without gap

Figure 6.6 : Influence of gap below roof beam for different aspect ratios

6.3.2 The influence of top gaps on frames with corner bearing wedges

The influence of initial gaps between an infill panel and the bounding frame has been elucidated in the previous section. In Chapters 4 and 5, experimental and analytical results for square infilled frames showed that the influence of gaps can be practically eliminated by using corner bearing wedges. Further analyses on infilled frames with strong

Interface parameters 125

frames, rigid connections, corner bearing wedges, 150 mm thick walls and aspect ratios of 0.5, 1.0 and 1.5 were carried out. The results are shown in Figure 6.7. These load-deflection graphs show that with the presence of corner bearing wedges, a gap between the roof beam and the infill panel has practically no influence on the global behaviour. The elimination of the negative influence of the gap is due to the introduction of the load into the infill panel through the corner bearing wedge. This enables the formation of a compressive strut from an early stage in the loading process.

200

300

100

2

2

0

0

0

4

4

6

6

8

8

horizontal deflection (mm)(b) = 1.0h/l

(c) = 0.5h/l

(a) = 1.5h/l



ho

rizo

nta

lfo

rce

(kN

)

ho

rizo

nta

lfo

rce

(kN

)

0

0

100

100

200

200

300

300

600

400

400

500

0 4 6 82

mod

el- w

ithou

t gap

model - withgap

ho

rizo

nta

lfo

rce

(kN

)

mod

el- w

ithou

t gap

mod

el- w

ithga

p

mod

el- w

ithga

p

model - without gap

Figure 6.7 : Influence of gaps on infilled frames with corner bearing wedges


6.4 Material parameters

As indicated in the introductory section of this chapter, there is a variety of material characteristics that are of interest, such as, the elastic properties and the strengths of CASIELs and steel, the bond and friction characteristics of joints and interfaces. Apart from the elastic stiffness characteristics of the interfaces that were studied in the development of the model, and presented in Chapter 5, the only material parameter investigated herein was the modulus of elasticity of the CASIELs.

Experimental evidence shows that the modulus of elasticity of the CASIELs, Ecasiel, can vary over a range of values depending upon the manufacturing process and grade of the elements. In this section, the influence of Ecasiel is shown by results of analyses with a range of Ecasiel values. All the results are of infilled frames with strong frames, rigid connections, and 150 mm thick walls. For square infilled frames, the load-deflection responses are shown in Figure 6.8. Over an Ecasiel range of 4000 to 12000 N/mm2, it can be seen that increasing the modulus of elasticity of CASIEL increases the stiffness of an infilled frame. The cracking load however only increases marginally. In Figure 6.9 the influence of Ecasiel on the stiffness of infilled frames with different aspect ratios is graphically shown. Here it can be seen that the gain in infilled frame stiffness due to increasing values of Ecasiel gradually diminishes. A probable explanation for this is that with increasing the values of Ecasiel, shear deformations in the joints play an increasing role, leading to gradual degradation of the infilled frame stiffness. It is also evident that variations in Ecasiel have the greatest influence on infilled frames with low aspect ratios. This can be explained by the fact that for stiffer CASIELs in squatter infilled frames the thrust of the compression strut is more horizontally inclined while the precompression provided by confinement by the roof beam is much less. Consequently, the joints suffer larger shear deformations.

Material parameters 127


ho

rizo

nta

lFo

rce

(kN

)

0

100

200

300

400

0 3 4 51 2

Ecasiel = 12000 N/mm2


Ecasiel 2= 8000 N/mm


Ecasiel 2= 4000 N/mm

Figure 6.8 : Influence of Ecasiel on infilled frames with h/l =1

0

modulus of elasticity ofCASIELs ( x 1000 N/mm )2

5 10

pri

mar

yst

iffn

ess

of

infi

lled

fram

e(k

N/m

m)

0

100

200

h/l = 0.5

h/l = 1.0

h/l = 1.5

Figure 6.9 : Influence of Ecasiel on infilled frames of different aspect ratios

6.5 Summary of parametric studies

The DIANA model that was described in the previous chapter has been used to study the influence of several parameters. These parameters included the geometric aspects of the infilled frames, the bounding frame members and the wall. The influence of a frame-to-wall gap below the top beam has also been investigated. Mitigation of the influence of the gap by employing corner bearing wedges has been demonstrated. Lastly, the influence of variations in the modulus of elasticity of the CASIELs has been studied.


It has been found that the influences of different parameters on the stiffness of infilled frames vary in magnitude depending upon the aspect ratio. In general, most geometrical parameters have the highest relative influence on the stiffness of square infilled frames. With relatively squat infilled frames, the wall dominates the behaviour while the bounding frame’s role diminishes. On the other hand, for relatively slender infilled frames, bending deflections increasingly overshadow composite action of the bounding frame and infill walls.

Tensile cracking of the wall joints was the dominant cause of cracking. All parameters investigated had only modest influences on the cracking loads. The reason for this is that cracking starts in the central regions of the infill walls where the confining effect of the loaded corners is remote. It would be expected, however, that confinement would have more influence on crushing failure.

Sizes of frame members have a greater influence on the stiffness of slenderer infilled frames than on squatter ones. Increasing the sizes of frame members however led to higher increases in cracking strengths of infilled frames with low aspect ratios. Increasing the rigidity of the frame connections produced only a marginal increase in the stiffness and cracking load of the infilled frames. Stiffer CASIELs in squatter infilled frames led to infilled frame stiffness degradation on account of larger horizontal forces, less pre-compression and therefore larger shear deformations.

A comparison of effective widths of an equivalent diagonal strut derived from finite element analyses in this study with those of other researchers showed that the simple method proposed by Angel et al. (1994) gives the closest, though conservative, estimates of the effective widths of the equivalent diagonal strut.

In the following chapter cracking loads and deflections from the numerical results are compared with calculated results from simplified equations. These simplified equations form a basis of design guidelines for predicting the behaviour of CASIEL-infilled steel frames.

Chapter 7

7Towards design guidelines

Abstract This chapter indicates how the stiffness and strength of CASIEL-infilled steel frames subjected to in-plane lateral loading can be predicted by using simplified equations. These predictions are compared with the numerical results presented in the previous chapter. It is shown that for infilled frames with aspect ratios equal to or less than 1, these simplified equations yield acceptable, though conservative, predictions of cracking loads and stiffnesses. The simplified equations are recommended as a basis of a formulation of design guidelines.

7.1 Preamble

Analysis methods such as the finite element method presented in Chapters 5 and 6 are powerful tools for detailed investigations of the structural behaviour of infilled frames. The application of such methods in ‘daily’ design practice, however, is impractical due to the level of sophiscation and the expertise required. For practical design procedures, simpler design tools are required.

It is generally acknowledged by experimental researchers in infilled frames that results of stiffness and strength typically have a wide scatter. The scatter is often attributed to the statistical nature of masonry materials as well as workmanship. Compounded by the inherent indeterminate nature of the phenomena that take place at frame-to-wall interfaces, the observation of Benjamin and Williams (1958) is still valid, namely, that exact analysis is superfluous. As such, it is considered prudent that, provided the fundamental behaviour is

130 Towards design guidelines

reproduced, design guidelines should be based on approximate rather than exact predictions. In this chapter some simplified equations for the prediction of stiffness and strength of steel-CASIEL infilled frames are proposed. The cracking loads and deflections predicted using these equations are compared with the results of the finite element analyses from Chapter 6.

It is envisaged that these simplified expressions will be the basis of formulation of design guidelines. The step towards design guidelines requires more discussion on the design philosophy, such as the ultimate and serviceability limit states and the partial safety factors that are appropriate for this type of structure. An outline of such a design guideline has been provided in Appendix E.

7.2 Basic load-deflection curve

It has been shown that the behaviour of CASIEL-infilled steel frames prior to major cracking in the infills can be fairly represented by a tri-linear load deflection curve, ‘oabc’, as shown Figure 7.1. Experimental results also showed that the curve from ‘c’ to ‘d’ represents the post-cracking phase leading to crushing of the infill at ‘d’. The structure then softens until total collapse of the bounding frame. This curve assumes that cracking and crushing precede the formation of a failure mechanism for the bounding frame. In a design procedure the capacity of the bounding frame not to fail prior to failure of the infill wall would need to be guaranteed.

The basic idea behind the formulation of simplified expressions is to be able to predict the Point ‘c’ and the Point ‘d’ in Figure 7.1. Point ‘c’ marks the onset of major cracking in the infill by either diagonal tension or shear sliding. This would represent an important serviceability limit state for an infilled frame. The lateral resistance at crushing of the infill, i.e. at Point ‘d’, is important for considerations of appropriate safety margins, and factors, between the cracking load and ultimate load. It is assumed that the curve ‘oabc’ can be approximated by ‘oc’. This is so because separation of the wall and frame occurs at low loads. This means that in case of a reversal of loads, the initial stiff behaviour would be absent.

Basic load –deflection curve 131

lateral deflection

a

o

b

Δ Δs or t

Δs = deflection at shear sliding

= deflection at diagonaltension cracking

Δt

Fc

Fs Ft

Fs = shear sliding load

Fc = crushing load

Ft = diagonal tension cracking load

c

d

gap

Kin

fra

Kinfra = predicted infilledframe stiffness

late

ralre

sist

ance

or

Figure 7.1 : Basic load-deflection behaviour for infilled frames

7.3 Resistance to diagonal tension cracking

In addition to the material strengths of the CASIELs and thin-layer mortar, diagonal tensile cracking results from a critical combination of biaxial stress and orientation of joints. Ideally, a failure envelope such as proposed by Dhanaseker et al. (1987) should be used to predict failure. A simpler method has been proposed by Saneinejad & Hobbs (1995). This approach is comparable to the ASTM E519 (1988) diagonal tension test in which the tensile strength is determined from a diagonally loaded square masonry prism. Experimental and numerical results have shown that tensile cracking starts at the centre of the infill panel. Assuming that the centre of the infill is sufficiently distant from the loaded corners, where the external loads are applied, it can be said that the cracking load is not affected by the way in which the load is distributed at the loaded corners. In that case Saint - Venant’s principle (Timoshenko & Goodier, 1982) can be applied to the cracking strength of the infill. Using this principle, Chen (1982) showed that the diagonal load, Fd,cube, causing diagonal tensile failure of a cube of edge length hc is given as:


c td cubeF t h f, 2≅ (7.1) where ft is the effective direct tensile strength of the infill

Equation (7.1) may be written in terms of a characteristic band

width, wc, which is normal to the compression diagonal. It can be

seen from Figure 7.2 that for a cube, cc

wh2

= . Substituting this into

equation (7.1) yields:

, c td cubeF t w f≅ 2 (7.2)

45°

Fd,cube

Fd,cube

R

hc

2

c

c

w

h

�

compression diagonalθ

Ft

h’

l’

w’

h’=

2co

sθ

Figure 7.2 : Diagonal cracking load of a cube and band width of a rectangular panel

Thus, the diagonal compressive load corresponding to a unit characteristic band width is:

d cube tF t f=, per unit charactersitic band width 2 (7.3) Therefore, in a generalized rectangular panel with a characteristic

band width, w’ = 2h’ cos θ , ( Figure 7.2), the diagonal compressive force, Fd, causing tensile cracking is:

d tF t h f2 2 ' cosθ= (7.4)

Resistance to diagonal tension cracking 133

The horizontal component of this force is then:

t tF t h f 22 2 ' cos θ= (7.5) Assuming simple frame connections are used, the lateral

resistance of the bounding frame can be neglected. The horizontal force at the onset of diagonal cracking may then be estimated by equation (7.5). If the connections of the frame can resist moments however, it is expected that this approximation will err on the conservative side.

7.4 Resistance to shear – sliding

The shear stress and the normal stress at any particular point in the infill wall depend upon the location of the point along both the length and height of the infill wall. As was observed from the experiments, (see Figure 4.9) the distribution of principal stresses across the compression diagonal in the wall is in the form of Gauss curves, with the peak stresses coinciding with the compression diagonal. On horizontal sections of the wall, the principal stresses are in the form of the curves shown in Figure 7.3. Since both the shear and normal stresses are induced by the same diagonal force, the distribution of both the shear stresses and the normal stresses along a bed joint will be in a similar form (Figure 7.3).

stre

ssst

ress

stre

ss

applied load

shear stress curve

assumed shearresistance curve

Figure 7.3: Shear distribution along a horizontal section


As can be seen in Figure 7.3, the shapes of the curves vary with the height of the section being considered in the infill wall. Although it has been observed that the most vulnerable bed joint is the top most one, the height of this joint from the bottom of the infill panel is determined by the overall geometry of the wall and the beams.

The relationship between the shear distribution and shear resistance of a horizontal section is difficult to reduce to a simple expression. This is because the point of highest shear stress, for instance, is also the point at which the shear resistance is highest due to a high normal compression. The points at which shear stress is lower, on the other hand, also have lower shear resistance because at those points there is less normal compression. The point of high shear stress does not, therefore, necessarily represent the location with the critical combination of normal and shear stresses at which shear sliding will initiate. For simplicity, a linear distribution of the shear resistance along the horizontal section is hereby assumed, as shown in Figure 7.3. This assumption does not take into account the variations of shear resistance with the height of the horizontal section under consideration. As will be shown in section 7.7, this leads to rather conservative estimates of shear-sliding resistance. However, the method is adopted here, bearing in mind the highly undesirable nature of shear-sliding failure. Further investigation into models of shear-sliding resistance is recommended.

Assuming that the horizontal component of the diagonal force is carried by the shear stresses along a bed joint of the wall, the shear-sliding resistance, Fs of a bed joint is given by:

s avF l t'τ= (7.6) where: τav is the average shear resistance over the bed joint

l’ is the length of the infill wall t is the thickness of the infill wall

The onset of sliding can be predicted by using a Coulomb’s

friction formulation. Thus, at any point along the bed joint, the shear strength, τmax, is given by:

Resistance to diagonal tension cracking 135

max oτ τ µσ= + (7.7) where: τo is the cohesion of the bed joint

µ is the coefficient of friction of the bed joint σ is the pre-compression normal to the bed joint

If, as is common in design practice, frames are designed to carry

all the gravity loads, the only compression normal to a bed joint is due to the vertical component of the diagonal force. The normal stress can be written as:

maxσ τ θ= tan (7.8) Substituting equation (7.8) into equation (7.7) yields:

omax 1 tan

ττµ θ

=−

(7.9)

Given the simplified triangular distribution of the shear stress

along the horizontal section, the average shear stress is: o

av maxττ τ

µ θ= =

−0.51

2 1 tan (7.10)

By substituting equation (7.10) into equation (7.6), the resistance

of the infilled frame to sliding shear can be calculated as: τµ θ

=−

0.5 '1 tan

os

l tF (7.11)

7.5 Resistance to crushing

In the infilled frames tested in this research, crushing of infill panels occurred at horizontal loads approximately twice as high as the cracking loads. This was at relatively large lateral deflections and after extensive diagonal cracking had occurred.

The horizontal force required to cause crushing can be calculated from equation (7.12) as suggested by Stafford-Smith and Carter (1969).


c cF wt f cosθ= (7.12) where fc is the mean cube compressive strength of the CASIEL wall.

It must be pointed out that this check is nominal because at the

point of crushing, the infill wall will have suffered extensive cracking and the validity of representation of the infill panel with a single equivalent strut will have ceased.

7.6 Horizontal deflections

The segment ‘ab’ in Figure 7.1 represents the transition phase during which the wall adjusts within the frame until it locks up with the frame at the compression corners. In an ideal tight fit construction the points ‘a’ and ‘b’ coincide. In the presence of frame-to-wall gaps, ‘ab’ will be a more drawn out curve. In that situation, the stiffness of the infilled frame from ‘o’ to ‘b’ can be conservatively equated with that of the bare frame for a horizontal deflection equal to the sum of the gap thicknesses. However, it must be recommended that frame-to-wall gaps must be avoided. When these gaps cannot be avoided, a bearing wedge construction method can be used to eliminate the sway arising from the influence of the gaps.

The primary stiffness of an infilled frame can be calculated using the equivalent diagonal strut approach. The infill wall is replaced by a single equivalent strut whose ends are assumed to be hinged at the intersection of the centrelines of the beams and columns. It has been shown in the parametric studies of Chapter 6 that the rigidity of the connections does not play a very significant role in determining the stiffness. Stafford-Smith (1962) also observed that assuming non-rigid connections results in ‘valid’ results even for rigidly connected frames, provided that the frames are not extremely stiff as compared to the infill wall. Since, indeed, one of the aims of using infill bracing is to remove the necessity of rigid connections, it is recommended herein that the CASIEL-infilled steel frames be designed using simple truss analysis in which only axial forces act on the members. In that case, the lateral stiffness of the frame, Kinfra, with an equivalent strut can be calculated using standard methods of structural analysis. By using

Horizontal deflections 137

the principle of virtual work, for instance, the Kinfra, can be calculated from equation (7.13).

The cross sectional area of the diagonal strut can be determined as the product of the effective width, w, and the thickness of the wall, t. In Chapter 6 effective widths obtained using various methods were compared with those derived from the finite element analyses in this work. It was found that the effective width can be conservatively estimated as one eighth of the diagonal length.

infram mm m

Kk LA E

21

∑

= (7.13)

where: the subscript m represents a member of the truss km is the force in a member per unit horizontal load at the top of the column. Lm is the length of a member, Am is the cross section area of a member, and Em is the modulus of elasticity of the respective member

7.7 Comparison of simplified equations with numerical results

The cracking loads and crushing loads for infilled frames with ‘pinned’ connections and 150 mm thick walls have been calculated using the proposed equations (7.5), (7.11) and (7.12). Deflections corresponding to diagonal cracking and shear sliding loads have also been calculated using the stiffnesses determined from equation (7.13). Just as in the finite element analyses, the tensile strength of the infill walls was taken as 0.56 N/mm2 while the cohesion and coefficient of friction were taken as 0.53 N/mm2 and 0.68 respectively. The crushing strength of the wall was assumed equal to the mean strength of the CASIELs, thus 15 N/mm2. In Table 7.1 the predicted loads and deflections are compared with the finite element results from Table 6.3. Crushing loads were not computed in the finite element results, and are therefore not tabulated. Similarly, either diagonal tension cracking or shear sliding, and not both, is tabulated for finite element analyses since these were carried out only up to the onset of major cracking.


The results show that the proposed expressions yield fair, though conservative predictions of the cracking loads and deflections for square and squat infilled frames. Calculations of the diagonal tensile cracking and shear sliding loads show that in squat frames, shear sliding precedes diagonal tensile cracking while the converse holds for square frames.

For slender infilled frames, predictions of the shear sliding loads yielded negative values, indicating that with this aspect ratio and friction characteristics it is not possible to obtain shear sliding. This is due to the fact that at this aspect ratio, the greater component of the diagonal load effectively applies pre-compression to the wall. On the other hand, the predicted tensile cracking loads are higher than those from the finite element analyses. This is due to the fact that in the finite element analyses, tensile cracking in the joints was due to global bending of the infilled frames while the proposed expression simply assumes diagonal tensile cracking. Table 7.1 : Comparison of cracking loads and deflections

h/l Method*

Ft (kN)

∆t (mm)

Fs (kN)

∆s (mm)

Fc (kN)

FE - - 453 5.4 - 0.5

PR 532 6.6 341 4.2 1124

FE 349 5.6 - - - 1.0

PR 332 6.8 343 7.0 562

FE 209 7.46 - - -

weak

1.5 PR 314 10.8 - - 562

FE - - 587 5.4 - 0.5

PR 532 6.2 341 4.0 1124

FE 393 4.5 - - N/A 1.0

PR 332 6.2 343 6.4 562

FE 225 4.9 - - -

strong

1.5 PR 314 9.7 - - 562

* FE= finite element analysis, PR = simplified prediction method

Conclusion 139

7.8 Conclusion

The aim of this chapter was to propose simplified expressions for prediction of cracking loads and deflections for non-integral CASIEL-infilled steel frames subjected to in-plane lateral loading. It has been proposed that the stiffness of an infilled frame may be determined by a standard analysis of a frame braced with an equivalent diagonal strut. The equivalent diagonal strut is assumed to be pinned to the intersection of the centrelines of the beams and columns. The thickness and material properties of the equivalent strut are assumed to be the same as those of the CASIEL infill wall. The effective width of the diagonal strut is estimated as one-eighth of its length. The diagonal cracking resistance and shear sliding resistance in the joints are predicted on the basis of average stresses over horizontal or diagonal sections in the infill. The crushing resistance loads are nominally estimated by using the cross-sectional area of the equivalent diagonal struts.

Results obtained using these simplified equations have been compared with results from the finite element analyses. Frames with simple connections are recommended. For square and squatter infilled frames the simplified equations predict the stiffness and cracking resistance of infills with acceptable accuracy. Predicted cracking loads for slender frames, though, are unconservative. The flexural cracking of slender frames due to bending needs further investigation. With appropriate material and load partial safety factors, the simplified equations can be used as a basis of design guidelines.

Chapter 8

8Conclusions and Recommendations

Abstract This chapter summarizes the contents of this work in terms of the experimental and numerical methods employed and the main findings. Recommendations of a possible sequence in future continuation of this research are given.

8.1 Conclusions

In this research the behaviour of steel frames infilled with calcium silicate element panels and subjected to in-plane lateral loads has been described. The influence of several geometrical, material and interface parameters on this behaviour has been investigated. Simplified expressions for prediction of the stiffness and cracking resistance of these types of infilled frames have been proposed.

CASIEL infill walls are already commonly used as partitions and claddings on building structures. Accounting for their contribution in resisting loads leads to more efficient use of materials. This is because the rigidity and reserve strength provided by the infill walls allow for relatively lighter steel frames with simple connections. Evaluating the stiffness and strength of the infills also leads to reduced risks of damage to the infills, bounding frames and the finishes. This in turn can lead to significant reductions in maintenance and rehabilitation costs of buildings.

Although infilled frames as such have been studied by many researchers, this research represents the first effort to investigate the use of CASIEL infill walls. The peculiarities of CASIEL infill walls as

142 Conclusions and Recommendations

compared to traditional masonry infill walls is in the larger size of the CASIELs, fewer and thinner joints, and boundary incompatibilities arising due to the handling methods in construction. It was therefore considered necessary to carry out an experimental and numerical investigation in order to describe the structural behaviour of these types of infilled frames.

A series of ten large scale tests was conducted and a finite element model to simulate these experiments was assembled. The finite element model was used to carry out parametric studies. Simplified equations for prediction of cracking loads and deflections have been proposed and evaluated in the light of numerical results.

The experimental set-up involved a rigid twin-triangular reaction frame as a platform for the support and loading the specimens. Horizontal monotonic deformation controlled loads were applied at the top of one column until the specimens suffered several cracks. In some tests, the load was increased until crushing of the infill walls occurred. The specimens were essentially 3 m-square semi-rigidly connected steel frames infilled with 150 mm thick infill walls built out of CASIELs in thin-layer mortar. The parameters included in the experimental investigation were frame-to-wall gaps, bounding frame stiffness and a novel bearing wedge construction detail. With a computerised data acquisition system, deflections and deformations at several sites on each specimen were recorded.

Load deflection responses showed that infills increased the stiffness of frames by as much as ten times. Diagonal tension was the predominant mode of major cracking in the walls. The confinement provided by the bounding frame prevented disintegration of the infills thereby giving the infilled frames as much as 100% reserve of strength after the onset of major cracking in the infill walls. Load-deformation curves of the infilled frames showed an initially high stiffness which transits into a less stiff linear primary stiffness. The deflection range in which the transition took place was larger for infilled frames with a top gap. During this transition, the wall separated from the frame at the two tension corners and adjusted within the frame until it was firmly locked up at the compression corners. In all specimens, major cracking occurred by sudden formation of diagonal cracks cutting through the CASIELs and also following the joints. Shear cracking

Conclusions 143

along the bed joint below the top most CASIEL layer was observed in some specimens, although when this happened, the frames almost instantly recovered their stiffness. The use of stiffer bare frames led to an increase in both the infilled frame stiffness and the diagonal tension cracking load. An initial top gap resulted in a long transition phase and a reduced primary stiffness although it did not significantly reduce the cracking load. Stress distributions derived from rosette measurements on the panel showed that the wall regions near the loaded corners were in biaxial compression stress situations while the central regions experienced combined compression and tension. Incorporation of corner bearing wedges effectively eliminated the influence of construction gaps between the upper beams and the infill walls.

The finite element model predicts the separation at frame-to-wall interfaces, the primary stiffness of an infilled frame, and the onset of cracking in the infill wall. The model utilises 8-node plane stress elements for CASIELs, 3-pair-node interface elements for thin layer joints and frame-to-wall contact. Webs of the steel profiles were modelled with 8-node plane stress elements while flanges were modelled with 3-node truss elements. Connection bolts were modelled with horizontal and vertical spring interface elements. Linear elastic behaviour with a brittle tension limit was assumed for the CASIELs. Non-linear elastic behaviour was prescribed for frame-to-wall contact and thin-layer joints. Linear elastic behaviour was assumed for steel. Material properties used in this model were obtained either from auxiliary tests conducted along side the large scale infilled frame tests or estimations based on the available literature. Provision for some play in the bolted connections was a made to reconcile the calculated and experimental stiffnesses. The model was validated by a comparison of numerical and experimentally determined stiffnesses and cracking loads of all specimens as well as a comparison of numerical and experimental stress distributions on the infill walls.

The finite element model has been used to study the influence of several geometric, material and interface parameters. These parameters included the aspect ratio of the infilled frame, the size of the frame members, the rigidity of frame connections, the thickness of the infill wall, the elasticity modulus of the CASIELs, the presence of gaps

144 Conclusions and Recommendations

between the upper beams and the infill wall and the presence of corner bearing wedges.

It has been concluded that composite infilled frame action is optimum in infilled frames with aspect ratios less than or nearly equal to one. In relatively squat infilled frames, the wall dominates the behaviour while the frame’s contribution diminishes. On the other hand, for relatively slender infilled frames, bending deflections increasingly overshadow composite action of the bounding frame and infill walls. In general, most geometrical parameters have the highest relative influence on the stiffness of square infilled frames.

All parameters investigated had only modest influences on the cracking loads. Sizes of frame members have a greater influence on the stiffness of slenderer infilled frames than on squatter ones. Increasing the rigidity of the frame connections produced only a marginal increase on the stiffness and cracking load of the infilled frames. Stiffer CASIELs in squatter infilled frames led to infilled frame stiffness degradation on account of larger horizontal forces, less pre-compression and therefore larger joint shear deformations. A comparison of effective widths of equivalent diagonal struts derived from finite element analyses in this study with those derived from other methods from literature showed that a width of one eighth of the diagonal length is a good, though conservative, approximation.

8.2 Design recommendations

The experimental and numerical results support the assertion that the role played by infills in carrying loads must be designed rather than arbitrarily assumed. On the assumption that the loaded corners of the infill are remote enough from the centre of the wall where cracking starts, an expression for predicting the diagonal cracking load of the infill is proposed. The infill wall is then treated like a standard masonry specimen in a diagonally loaded splitting test. The shear sliding load in the joints is predicted on the basis of a parabolic distribution of shear stresses along horizontal joints. Deflections are predicted by modelling the wall as a single diagonal strut. The thickness and material properties of the equivalent strut are assumed to be the same as those of the infill wall. The effective width of the

Design recommendations 145

diagonal strut is conservatively estimated as one-eighth of its length. Crushing loads are nominally estimated by using the cross-sectional area of the equivalent diagonal strut and the cube compressive strength of the CASIELs. Because the rigidity of the connections does not have a large influence on the stiffness and cracking resistance of the infilled frames, flexible rather than rigid connections are recommended. This also simplifies the design procedure.

There are several important issues concerning the behaviour and application of CASIEL-infilled frames that need further clarification before complete design rules can be developed. All experimental and analytical tests carried out in this study, for instance, dealt with single storey, single bay panels. The results of this research still need to be set in the context of more realistic multi-bay and/or even multi-storey configurations. Furthermore, the infilled frames investigated in this work are considered to be of practical full-scale dimensions; namely, lengths between 3 m and 6 m as well as heights between 3 m and 4.5 m. The conclusions of this study may not be directly applicable to infilled frames with aspect ratios outside the range of 0.5 to 1.5. In particular, prediction of cracking loads for slender infilled frames needs further investigation.

8.3 Future research recommendations

Recommendations are hereby made from the point of view of the future continuation of this research. Some of the issues can be experimentally investigated without major changes to the existing set-up used in this work. Because of the high costs and practical difficulties involved in conducting large-scale tests, it is essential that experimental tests should be carried out hand-in-hand with numerical analyses. As encountered in this investigation, although modelling non-linear behaviour of CASIEL walls and frame-to-wall interfaces is by no means easy, numerical modelling significantly contributed to understanding and interpreting the experimental behaviour. It is recommended that the numerical analyses conducted in this investigation should be extended into the post cracking range. This would facilitate an assessment of the ultimate load and give a more realistic assessment of the margin between the cracking (service) loads

146

and the ultimate load. This in turn would assist in determining the appropriate safety factors in the design guidelines.

It is hereby recommended that this research should be continued, generally, in the following order.

(i) The influence of shear deformations or play in the frame connections. Further experimental tests are required to verify the influence of shear deformations or play in the connections. The semi-rigid connections that were used in the experiments in the current research were intended to reflect real practice connection details. This choice however complicated the modelling process. It is recommended that further tests with welded fully rigid connections should be carried out to corroborate the current results.

(ii) Cyclic loading Reversed and cyclic loading are of important practical interest because of the nature of lateral loads that building structures are subjected to. As an immediate continuation of this research, specimens similar to those used in this investigation could be subjected to loading and unloading cycles in the pre-cracked load range. This can be achieved without any modifications to the existing experimental set-up. Subsequently, with some modifications to the set-up, cyclic in-plane loading can be applied.

(iii) An extension to the bearing wedge construction technique As has been observed in this work and by other researchers, the presence of gaps in between frames and infills significantly compromises the stiffness benefits that are otherwise derived from the use of infill walls. For this reason, the S304.1-04 of the Canadian Standards Association (2004) states that ‘Infill shear walls shall have no openings, and no gaps between the masonry infill and the surrounding frame, unless the designer is able to

Future research recommendations 147

show through experimental testing or special investigations that the diagonal strut action can be formed’. Gaps must be filled by packing mortar into the spaces between the frame and the wall. During the preparation of specimens in the experiments in this work it was clear that this procedure did not guarantee proper, let alone, uniform filling of the gaps. Although other methods of filling the gaps have been considered, such as, injection of mortar fillers in the gaps, there still is no easy practical way of dealing with the gap problem. In using CASIEL infills, gaps are expected to arise as a result of the construction method or indeed due to shrinkage of the CASIELs. Gaps may also be deliberately introduced to prevent transfer of vertical loads between upper beams and infill panels. In the experiments and finite element model in this research, it has been shown that the use of a corner bearing wedge technique solves the problem of slackness due to gaps between the upper beams and infill walls. Improvement of the technique should be a subject of further research. An extension of this technique is hereby proposed in order to ensure good contact between the columns and the infills as well. The extension of the wedge construction technique is illustrated in Figure 8.1. As each row of CASIELs is laid, a gap is left in the middle. A pair of wedge shaped CASIELs are the last two pieces to be installed. The upper wedge is pressed down to apply enough pressure and move the CASIELs towards the columns. The rest of the tolerances around the wedges are filled with thin-layer mortar. Since construction with CASIELs is a semi prefabricated procedure in which CASIEL shapes are programmed and sawn in a factory, the production and use of bearing wedges does not require any additional fabrication overheads. It is believed that this technique has potential for future use in construction and should therefore be further explored.

148

Figure 8.1 : Construction method using wedges

(iv) The behaviour of CASIEL infills with openings Infills with openings exist because of windows and doors. Findings from the literature reported in Chapter 2 of this thesis indicate that depending on the size and location of openings, infill walls with openings can still contribute significantly to the stiffness, strength and energy dissipation of building structures. Experiments into the behaviour of CASIEL infills with openings can be performed with the existing test-set up.

(v) Behaviour of infilled frames in multi-bay multi-storey structures When the issues mentioned above have been clarified in single-bay single-storey infilled frames, it is then recommended that experimental and numerical research is extended to the behaviour of multi-bay and multi-storey infilled frames.

(vi) Other topics of interest Other topics of interest are the study of combinations of in-plane and out-of-plane loading, the use of reinforced concrete frames with CASIEL infills, the application of reinforcement, such as fibre reinforced polymers, to strengthen or repair infill panels and experimental tests with aspect ratios other than 1.

Future research recommendations 149

Finally, it can be expected that the subject of infilled frames will remain an important topic of research for a long time. This is because of the prevalence of infill walls in building structures and efforts that are being made in different parts of the world to have improved design codes for rehabilitation of masonry structures and earthquake engineering. In the meantime there is still no clear consensus on how to model and analyse infilled frames. Indeed the diagonal strut approach is mostly considered to be a practical design approach. This approach is recommended in this work. However, there are still variations on how to determine the properties of the diagonal strut or even as to whether multi-diagonal strut models should be used. With regard to CASIEL-infilled steel frames, it is believed that this research has contributed to understanding of their basic behaviour and provided a good platform for further research and development of design guidelines.

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Zijl, G.P.A.G. van, Rots, J.G. & Vermeltfoort, A.T. (2001), Modelling shear-compression in masonry, Proceedings of the 9th Canadian Masonry Symposium, Fredericton, Canada.

Appendix A: Extracts from drawings of Test Set-up and Frames

ELE

VA

TIO

N A

Tes

t Se

t-u

p

ELE

VA

TIO

N B

162 Appendix A: Extracts from drawings of Test Set-up and Frames

Tes

t Se

t-u

p (

Ele

vati

ons

and

Sec

tion

)

ELE

VA

TIO

N A

SECT

ION

A-A

SECT

ION

B -

BE

LEV

ATI

ON

B

Appendix A: Extracts from drawings of Test Set-up and Frames 163

C

Windward column support - Tests 1 to 4A

A

A - A

SECTION C-C

filler block 2

filler block 1

Frames for Tests 1 to 4

Colu

mn

HE

180

B

4 Nos. M24 grade 8.8 bolts

TYPICAL BEAM-COLUMN CONNECTION

2 Nos. 200 x 200 x 15 mm thk plate welded to beams

C

1 No. 180 x 180 x 15 mm thk plate welded to column flange

Beam HE 200 B

164 Appendix A: Extracts from drawings of Test Set-up and Frames

2 Nos. 200 x 200 x 15 mm thk plate welded to beams

Colu

mn

HE

180

B

A - A

Frames for Tests 7 to 10Windward column support - Tests 5 to 10

TYPICAL BEAM-COLUMN CONNECTION

Colu

mn

HE

240

M

20 mm thick web and 30 mm thick flange welded to beam flange

Frames for Tests 5 and 6

Beam HE 240 M

B - B

C - C

4 Nos. M24 grade 8.8 bolts

1 No. 180 x 180 x 15 mm thk plate welded to column flange

Beam HE 240 M

Appendix B: Basic principles of Sensors and Data Acquisition System

Linear Variable Digital Transducers (LVDTs)

LVDTS are a common and reliable type of sensor for measuring relative displacements between two points. The basic principle of an LVDT is that displacement of an armature in an electromagnetic field of a primary coil generates a certain voltage across the terminals of a secondary coil. Over a certain range of armature positions, the relationship between the armature position and the generated voltage in the secondary coil is linear. In this range, therefore, the displacement of the armature can be derived by converting the voltage (which can be amplified) using an appropriate calibration factor.

Strain gauges

A strain gauge is a very useful sensor in measuring local deformations. A strain gauge employs the principle that the electrical resistance of a piece of wire varies with its length. The gauge is bonded to the surface of the material whose deformation is to be measured. When the material undergoes some deformation, the gauge is strained and the current flowing through the piece of wire changes. The change in the measured current is converted, by means of an appropriate calibration factor, into a corresponding deformation. Strain gauges can also be inbuilt in a load cell. By bonding strain gauges to the surface of a loading structure the force that is applied through a load cell can be measured.

Data acquisition system

As explained in the principles of LVDTs and strain gauges, the measured quantity was an electrical signal. This signal was input into a Peekel Autolog 2005 data acquisition unit. The data acquisition unit had several interfaces for different types of sensors. Each interface had provision for 5 or 10 channels. (Thus, two interfaces with 10

166 Appendix B: Basic principles of Sensors and Data Acquisition System

analog channels each, 5 interfaces with 10 channels per interface for strain gauges and 3 interfaces with 5 channels). In the data acquisition unit each signal was conditioned – read, amplified, filtered, transformed from a.c. into d.c. - and digitized. The digital value was then transmitted to a computer logging system via a standard serial connection (RS232). In the computer the values were written to an ASCII-file. By using appropriate calibration factors the ASCII values are converted into displacements and forces. A scheme of the data acquisition facility is shown in Figure B.1.

input (sensorson specimen)

PeekelAutolog 2005

load cell

computer

conditioner

conditioner

conditioneroutput(ascii file)

Rs232

x-y recorderData acquisition unit

Jack displ.LVDT

actuatorLVDT

Schenkcontrolunit

y

x

LVDT/Strain gauge

LVDT/Strain gauge

Figure B.1 : Data acquisition system

Appendix C: Auxiliary tests

C1: CASIEL prisms – compression tests

All CASIELs for all infilled frame tests were delivered from the factory (Hardewijk Calcium Silicate Factory, Netherlands) in one batch. They were stored in the laboratory over a period of up to 15 months during which the tests were performed. CASIEL prisms measuring 100 mm x 100 mm x 150 mm sampled and cut according to European Standard EN 771-2 (2000) were also delivered and stored under the same conditions as the CASIELs for the walls. At the time of performing each infilled frame test, three CASIEL prisms were tested in compression. Average compressive strengths are given in Table C.1. Table C.1 : Average CASIEL compressive strengths (N/mm2)

Infilled frame Test 1 2 3 4 5 6 7 8 9 10

Compressive strength* 15.3 14.6 14.2 15.0 15.1 15.4 12.8 13.3 12.4 13.6

* Average of three tests; ** Average of 30 tests = 14.4 N/mm2, with a coefficient of variation of 14%

C2: Mortar prisms – compression and three point bending tests

At the time of constructing each wall, prism samples of the mortar used in the wall joints were cast. Similarly, prisms of the mortar used to fill interface gaps were cast. The compressive strength and bending strength (modulus of rupture) of the mortar were determined according to NEN 3835 (1991). For either mortar type, a three point bending test was performed on three 40 x 40 x 160 mm mortar prisms. The six pieces broken off from the bending tests were then tested in compression. According to NEN 3835, the compressive strength so determined is equivalent to that of standard 40 x 40 x 40

168 Appendix C: Auxiliary tests

mm cubes. Averaged values of compressive and bending strength are given in Table C.2. Table C.2 : Mean mortar Strengths

Infilled Frame Test

Mean Compressive strength* (N/mm2)

Mean 3 point bending strength* (N/mm2)

Thin Layer Mortar

Interface Mortar

Thin Layer Mortar

Interface Mortar

1 13.1 11.0 5.5 2.9 2 15.4 4.7 4.8 1.63 3 15.2 7.3 3.7 1.67 4 15.7 7.9 5.0 2.1 5 14.0 8.1 4.6 2.2 6 13.1 9.0 4.5 2.5 7 15.1 8.6 4.6 2.4 8 16.1 8.9 4.3 2.4 9 14.9 10.4 4.0 3.2 10 15.3 11.8 3.3 2.7

Average** 14.6 9.1 4.4 2.4 c.o.v. 10% 25% 16% 21%

* Mean of three tests; ** Average of 30 tests

C3: Thin layer Mortar joints – shear tests

Shear tests were performed to monitor the consistency of mortar joint characteristics. Specimens for these tests were prepared at the time of building the walls and were left to cure under the same laboratory conditions as the large walls.

Figure C3.1 shows a schematic diagram and a photograph of the shear test arrangement. The shear stress, τ, over the joint was calculated as:

Fbd2

τ = (C3.1)

where: F = the applied force, b = width of the specimen and d = the depth of the specimen.

Appendix C: Auxiliary tests 169

As observed by Hofmann et. al. (1990) and alluded to by other researchers ( Pluijm, 1999; Gottfredsen, 1997; Molnár, 2004) achieving a state of pure shear or constant normal and shear stresses in a joint is nearly impossible. In the current research, a simple shear test, according to EN 1052-3 (1996) was used. The immediate use of the results is for purposes of monitoring joint mortar properties. For purposes of using the shear results in numerical modelling of infilled frames, the non-uniform stress distribution over the joint in the shear tests needs to be born in mind.

62mm20mm

20 mm

142 mm

12 mm dia

12 mm dia

load cell

loading beam

teflon layers

15 mm dia steel rod

F

0.5F0.5F

Figure C3.1 : Shear test set-up


A typical shear displacement diagram is shown in Figure C3.2. It shows a nearly linear curve, achieving a maximum shear value and rapidly dropping to more or less constant residual ‘dry friction’ strength. Results of all the shear tests are plotted and summarized in Figure C3.3. The shear characteristics of the joint can be modelled by a linear best fit curve yielding a shear coefficient of 0.53, an angle of internal friction of 28o and a cohesion of 0.68 N/mm2.

shea

rfo

rce

maximum shearforce

jack displacement

residual shearforce

Figure C3.2 : Typical load-deformation curve from shear test

0.00 1.000.400.20 0.60 0.80

shea

rst

ress

,(N

/m

m)

t2

normal stress, (N/mm )s 2

0.00

0.40

0.80

1.20

maximum shear stress

residual shear stress

ts= 0.53 + 0.68

ts= 0.55

Figure C3.3 : Maximum and residual shear strength

Appendix C: Auxiliary tests 171

C4: Thin-layer mortar joints – 4 point bending tests

Figure C4.1 shows a dimensioned scheme and a photograph of the test arrangement for the 4-point bending tests performed. The bending strength, ftu, was determined as:

tuFLfbd

= 234

(C4.1)

where: F is the applied force, b is the width of the specimen, and, d is the depth of the specimen L is distance between supports.

Dimensions in mm,not to scale.

900

F/2F/2

150

150150 150150 150150 150

Figure C4.1 : 4-Point bending test set-up


Three samples were prepared and tested concurrently with each infilled frame. The average strengths are given in Table C3. Some results were discarded because examination of the joint surfaces revealed large areas that were not filled with mortar.

Table C3 : Mean 4-point bending strength (N/mm2) for thin-layer mortar joints

Test No 1 2 3 4 5 6 7 8 9 10 Bending strength* 0.81 0.76 0.91 0.76 0.76 0.90** 0.97 0.94 0.80** 0.71**

Average bending strength =0.74 N/mm2 with a coeff. of variation of 30% * mean of three tests; **results of 2 out of 3 tests discarded because joint surface revealed a large unfilled area

Appendix D: DIANA Elements used in FE model

CQ16M

CQ16M

CQ16M

CQ16M

CQ16M

CQ16M

CQ16M

CQ16M

CQ16M

CQ16M

CQ16M

CQ16M

CQ16M

CQ16M

CQ16M

CQ16M

CQ16M

CQ16M

CQ16M

LT4RU

LT4RU

LT4RU

LT4RU

CL12I

CL12I

CL12

IC

L12I

CL1

2I

CL12

I

CL1

2I

LT4R

U

LT4R

U

LT4R

ULT

4RU

LT4R

U

LT4R

U

LT4R

U

LT4RU

LT4RU LT4RU

LT4RU

LT4RU

LT4RU LT4RU

LT4RU

LT4R

ULT

4RU

LT4R

U

16C

QM

16C

QM

16CQ

M16

CQ

M

16CQ

M16

CQM

LT4R

U

LT4R

U

LT4R

ULT

4RU

LT4R

ULT

4RU

CL12

IC

L12I

CL1

2IC

L12I

CL1

2I

CL12I CL12I CL12I

CL12I

CL12I

CL12I

CL12I

CL12I

2xSP2TR

2xSP2TR 2xSP2TR

2xSP2TR

2xSP2TR

2xSP2TR 2xSP2TR

2xSP2TR

CL12I

CL12I

CL12I

CL12I CL12I

CL12I

CL12I

CL12I CL12I

CL12I

CL12I

CL12I

CL12I

CL12I CL12I CL12I CL12I CL12I

Appendix E: Outline of design guideline and explanatory notes

E1 Preamble

In Chapter 7 of this thesis, simplified expressions for prediction of the behaviour of CASIEL-infilled steel frames subjected to in-plane lateral loading were proposed. This is an indicative draft guideline for the design this type of infilled frames. Infill panels with openings are not covered. Similarly, seismic loading is outside the scope of this draft.

E2 General conditions

In order to reduce torsional forces on the structure an even distribution of infill panels over each floor plan of a building is preferable.

In order to provide alternative load paths for horizontal loads, a sufficient number of infilled frames should be provided at each storey. This is a provision for possible collapse of a single panel or the removal of some panels in future structural alterations.

The influence of adjacent infill frames in a multi-bay arrangement is generally to stiffen each other. Designing the infilled frames on the basis of single bay infilled frames is therefore, conservative.

It is assumed that the surrounding frames are designed to carry the gravity loads.

In line with the provisions of the Eurocode 6 for load bearing masonry, it is recommended that the out of plane slenderness ratio defined as the lesser of the vertical or horizontal dimension to the thickness of the infill wall should not exceed 27.

176 Outline of design guideline and explanatory notes

Frame-to-wall interface gaps should not be allowed unless a construction procedure, such as the use of corner bearing wedges is employed.

Simple frame connections are recommended. As such, the stability of these frames during construction must be guaranteed.

E3 Basic behaviour and design curve

The assumed design behaviour of an infilled frame is shown in Figure 7.1. The design curve assumes that cracking and crushing of the infill precede the failure of the bounding frame. The capacity of the bounding frame to resist reaction forces from the infill wall must be checked.

lateral deflectiono

Δ Δs or t

Δs = deflection at shear sliding

= deflection at diagonaltension cracking

Δt

Fc

Fs Ft

Fs = shear sliding load

Fc = crushing load

Ft = diagonal tension cracking load

Kin

fra

Kinfra = predicted infilledframe stiffness

late

ralre

sist

ance

or

Figure E.1 : Design load deflection curve for infilled frames

E4 Limit states

There are three serviceability limit criteria to be considered; (i) cracking by diagonal tension must be checked (ii) shear sliding of the

Outline of design guideline and explanatory notes 177

joints prior to diagonal cracking must be prevented (iii) deflection of the frame must not exceed the allowable inter-storey drift.

Crushing of the infill is considered to be an ultimate limit state.

Characteristic strengths of the infill wall must be determined by the use of ‘appropriate’ partial safety factors. In order to allow for a safety margin between the ultimate load and cracking resistance, an appropriate limiting ratio between these loads must be applied.

E5 Infilled frame stiffness

El-Dakhakhni et al. (2003) have used frame moment expressions from Saneinejad & Hobbs (1995) and recommended a three-strut model with which moments in the frame members may be calculated. Design examples by Saneinejad & Hobbs however show that given the level of reserve strength after cracking in the structure, the design procedures can be made simpler by using simple connections. It has been therefore concluded that a single diagonal strut is sufficient to reproduce the response of the frame, particularly when simple connections in the frames are used.

By replacing the wall with an equivalent strut, the primary stiffness of an infilled frame, Kinfra, can be calculated using standard methods of structural analysis. Hence:

infram mm m

Kk LA E

21

∑

= (E1.1)

where: the subscript m represents a member of the truss km is the force in a member per unit horizontal load at the top of the column. Lm is the length of a member, Am is the cross section area of a member, and Em is the modulus of elasticity of the respective member

The cross sectional area of the diagonal strut is calculated as the

product of the effective width, w, and the thickness of the wall, t. The

178 Outline of design guideline and explanatory notes

effective width can be approximated as one eighth of the diagonal length.

E6 The cracking resistance of infilled frames

E6.1 Diagonal tension cracking The design resistance of an infilled frame to diagonal tension

cracking is given by:

t t mdF t h f θ γ= 22 2 ' cos / (E1.2)

where: ft is the tensile strength determined from direct tensile tests and γm is an appropriate material partial safety factor.

E6.2 Shear sliding failure

The design resistance of an infilled frame to shear sliding is given by: kvo

sdm

f l tFµ θ γ

=−0.5 '

(1 tan ) (E1.3)

Values of the characteristic cohesion fkvo and µ should be

determined experimentally or in accordance to Eurocode 6. In lieu of actual material data, Paulay and Priestly (1992) cited an average value of cohesion of 3% of the mean compressive strength of masonry.

E6.3 Crushing

The design resistance of an infilled frame to crushing in the infill is given by:

c d k mdF l t f cosθ γ= 0.125 / (E 1.4)

where: fk is the characteristic compressive strength of the CASIEL wall determined according to the provisions of Eurocode 6 ld is the diagonal length of the infilled frame, and, t is the thickness of the infill wall

Outline of design guideline and explanatory notes 179

E7 Assessing the capacity of the bounding frame

Beams and columns, and their connections, should be designed to carry the combinations of axial and shear forces resulting from both their interaction with the wall and imposed gravity loads. The beam-column connections should be designed to carry axial loads and horizontal and vertical shear loads including the horizontal and vertical components, respectively, of the diagonal force in the equivalent strut.

The horizontal shear force on the column may be taken as equal to the applied racking load, F.

The vertical shear force, V, on the beam is given by: FhVl

= (E 1.5)

Notation Ābolt shear area of a bolt Am cross section area of a frame member Cb normal force at the column-to-wall contacts Ci rotational stiffness of frame connection Cl normal force at the beam-to-wall contacts Ecasiel modulus of elasticity of CASIEL Ef modulus of elasticity of frame material Ei modulus of elasticity of infill material Ejoint modulus of elasticity of thin-layer mortar joint Esteel modulus of elasticity of the steel Ewall effective modulus of elasticity of wall Fc compression crushing resistance of infilled frame Fcd design crushing resistance of infilled frame Fd diagonal compressive force on infilled frame Fd,cube diagonal compressive force causing tension cracking of

cube Fh shear force at column-wall contact Fl shear force at beam-to-wall contact Fs shear sliding resistance of infilled frame Fsd design shear sliding resistance of infilled frame Ft diagonal tension cracking resistance of infilled frame Ftd design diagonal tension cracking resistance of infilled

frame Gjoint shear modulus of thin-layer mortar joint Gsteel shear modulus of steel Kinfra secant stiffness of infilled frame at onset of cracking Kpr primary stiffness of infilled frame L distance between supports Lm length of frame member Mj frame-connection’s plastic moment

182 Notation

Mpb plastic capacity of beam Mpc plastic capacity of column Mpj minimum of the beam’s, column’s and the frame-

connection’s plastic moment b width of rectangular section d depth of rectangular section dbolt diameter of bolt f’c characteristic cube compressive strength fc mean cube compressive strength fk characteristic compressive strength CASIEL wall fkvo characteristic cohesion ft mean tensile strength h column height, between centrelines of beams h’ height of infill panel hc edge length of cube hint thickness of frame-wall interface ht depth of I-section of beam Ib second moment of area of beam Ic second moment of area of column k foundation modulus kbolt stiffness of horizontal spring in bolted connection km force in a member per unit horizontal load at the top of

the column kn,int normal stiffness of frame-wall interface kn,joint normal stiffness of joint interface kplay stiffness of shear spring in bolted connection kt,joint shear stiffness of joint interface kt,int shear stiffness of frame-wall interface kx factor dependent on the layout of the connection l beam length, between centrelines of columns l’ length of infill wall lbolt distance between the midpoints of the bolt-head and the

nut

Notation 183

ld diagonal length of infilled frame t thickness of infill wall tf,c thickness of column flange u displacement w effective width of equivalent diagonal strut w’ characteristic band width of rectangular panel wc characteristic band width of cube α ratio of height to length of infill panel αb ratio of the beam contact length to the span of the beam αc ratio of the column contact length to the height of the

column αl contact length between beam and elastic foundation βb ratio of the maximum elastic field moment developed

within the span of the beam to the plastic capacity of the beam

βc ratio of the maximum elastic field moment developed within the height of the column to the plastic capacity of the column

γ shear strain in inclined plane γm material partial safety factor γxy shear strain in x-y plane ∆s deflection at onset of shear sliding ∆t deflection at onset of diagonal tension cracking ε direct strain in inclined plane εx direct strain in x-direction εy direct strain in y- direction θ tan-1 (h/l) λh relative column-wall stiffness ratio λl relative beam-wall stiffness ratio µ coefficient of friction σb normal contact stress on the face of beam σc normal contact stress on the face of the column τav average shear stress

184 Notation

τb uniform shear contact stress on the face of the beam τo cohesion υjoint Poisson’s ratio of joint interface υsteel Poisson’s ratio of steel

Samenvatting (Summary, in Dutch)

Dit onderzoek richt zich op de wetenschappelijke onderbouwing voor de ontwikkeling van ontwerpregels voor de laterale stabiliteit van stalen raamwerken met stabiliserende invulwanden van gelijmde kalkzandsteen elementen (CASIEL). Hoewel CASIEL invulwanden reeds veelvuldig in gebouwen worden toegepast, wordt de constructieve bijdrage ervan meestal genegeerd. In dit onderzoek wordt er voor gepleit om bij het ontwerp van de invulwanden en het raamwerk wel degelijk rekening te houden met de composietwerking van raamwerk en invulwand.

Het in rekening brengen van de constructieve bijdrage van invulwanden leidt tot efficiënter materiaal gebruik aangezien de stijfheid en de reservesterkte die worden geleverd door de invulwanden, relatief lichtere stalen raamwerken met eenvoudige verbindingen mogelijk maken. Het beschouwen van de stijfheid en sterkte van de invulling vermindert tevens het risico van schade aan de invulling, het raamwerk en de afwerking. Dit kan op zijn beurt leiden tot een significante reductie van de onderhouds- en saneringskosten van dergelijke gebouwen.

Tien proefstukken op ware grootte werden getest en een eindige elementen model werd ontwikkeld om deze experimenten te simuleren. Met het eindige elementen model werden parametrische studies uitgevoerd. Vereenvoudigde formules om de scheurbelasting en vervormingen te voorspellen werden opgesteld en vergeleken met de resultaten van de numerieke berekeningen.

De proefopstelling bestond uit twee naast elkaar staande, gekoppelde, identieke, stijve driehoekige raamwerken voor de ondersteuning van de proefstukken en voor het aanbrengen van de belasting. Aan de bovenhoek van het proefstuk werd de belasting monotoon toenemend vervormingsgestuurd aangebracht totdat er diverse scheuren ontstonden in het proefstuk. In het experimenteel onderzoek werden de volgende parameters gevarieerd: openingen

186 Samenvatting

tussen de bovenbalk en de invulwand, de stijfheid van het raamwerk en het gebruik van innovatieve wigvormig hoekstukken.

Het eindige elementen model voorspelt het loskomen van de invulwand en het raamwerk ter plaatse van het contactvlak, de primaire stijfheid van de invulwanden en het begin van scheurvorming in de invulwand. In het model zijn de elementen en materiaalbibliotheken gebruikt die in het commerciële software pakket DIANA beschikbaar zijn. Voor de CASIELs is uitgegaan van bros lineair elastisch gedrag met een gelimiteerde treksterkte. Niet-lineair elastisch gedrag is aangenomen voor de contactlaag tussen raamwerk en invulwand en voor de dunne lijmmortel voegen. De in het model gebruikte materiaaleigenschappen werden verkregen uit aanvullende proeven die parallel met de proeven op ware grootte werden uitgevoerd of met schattingen gebaseerd op informatie uit de literatuur. Het model werd gevalideerd door vergelijking van de numeriek en experimenteel bepaalde stijfheden, scheurbelastingen en spanningsverdelingen in de invulwanden.

In de last-verplaatsing-grafieken zijn drie stadia te herkennen voordat scheuren optreden. In het algemeen was er een initieel stijf stadium gevolgd door een veel minder stijf overgangsgebied waarin separatie tussen raamwerk en invulwand optrad en een derde minder stijf stadium totdat, in de meeste gevallen, diagonale trekscheuren in de invulwanden ontstonden. Bij enkele proeven werd afschuiving van de bovenste laag elementen waargenomen.

Bij stijvere raamwerken werd een relatief hogere stijfheid van het wand-raamwerk-samenstel vastgesteld terwijl een nauwelijks hogere scheurbelasting werd gemeten.

Bij een open voeg aan de bovenkant van de wand was de stijfheid in het overgangsgebied kleiner, doch de scheurlast was niet significant lager. Door het gebruik van de wigvormige hoekstukken boven in het raamwerk kon de invloed van de open voeg nagenoeg worden geëlimineerd. Deze vaststelling is essentieel voor de ontwikkeling van een industriële constructietechniek voor invulwanden. De meetresultaten van het globale vervormingsgedrag en rekverdeling werden gebruikt om het eindige elementen model te kalibreren.

Samenvatting 187

Uit het onderzoek kon worden afgeleid dat de samenwerking tussen raamwerk en invulwand optimaal is voor een slankheidsverhouding variërend tussen ongeveer 0,8 en 1,0. Bij relatief gedrongen invulwanden overheerst het constructief gedrag van de wand en is de bijdrage van het raamwerk beperkt. Voor slanke invulwanden daarentegen krijgt de buigvervorming van het raamwerk de bovenhand op de composietwerking van het samenstel raamwerk-invulwand.

In dit onderzoek wordt voorgesteld om de stijfheid van een ingevuld raamwerk te benaderen met een standaard raamwerkberekening waarbij de invulwand wordt geschematiseerd door een equivalente diagonale drukschoor. Deze drukschoor mag hierbij scharnierend worden verbonden aan het snijpunt van de systeemlijnen van de balken en de kolommen. Voor de dikte en de materiaal eigenschappen van de equivalente drukschoor worden de karakteristieken van de CASIEL invulwand aangenomen. Voor invulwanden met slankheidsverhoudingen kleiner dan 1.0 mag de effectieve breedte van de diagonale drukschoor worden geschat op een achtste van haar lengte. De diagonale scheurweerstand en de afschuifweerstand in de voeg kunnen worden bepaald op basis van de gemiddelde spanningen die respectievelijk optreden in de horizontale of verticale doorsneden in de wand. De bezwijkbelasting van de drukdiagonaal kan dan worden berekend als het product van de oppervlakte van de doorsnede van de equivalente diagonale schoor en de experimenteel bepaalde druksterkte. Deze vereenvoudigde uitdrukkingen geven aan hoe ontwerpregels geformuleerd zouden kunnen worden.

Het onderzoek wordt afgesloten met aanbevelingen voor vervolgonderzoek gericht op de verdere ontwikkeling van ontwerprichtlijnen. Het belang van het onderzoeksonderwerp wordt benadrukt door de wereldwijde aandacht die wordt besteed aan de verbetering van algemeen geldende ontwerprichtlijnen en normen en in het bijzonder van rekenregels voor toepassingen in aardbevingsgevoelige gebieden.

List of publications

Ng’andu, B.M. & Vermeltfoort, A.T. (2005), Experimenteel onderzoek naar de schoorwerking van kalkzandsteen invulwanden, Cement 2005, Jrg. 57, no. 5, pp. 71-74.

Ng’andu, B.M., Vermeltfoort, A.T. & Martens, D.R.W. (2005), The use of bearing wedges to eliminate the influence of initial gaps in steel frames infilled with CASIEL walls, Proceedings of 1st Canadian Conference on Effective Design of Structures, Hamilton, Ontario, Canada.

Ng’andu, B.M., Vermeltfoort, A.T. & Martens, D.R.W. (2005), Experimental investigation into the response of steel frames infilled with calcium silicate element walls to in-plane lateral loads, Proceedings of Canadian Masonry Symposium, Banff, Alberta, Canada.

Vermeltfoort, A.T. & Ng’andu, B.M. (2005), The response of calcium silicate element wallettes to 2d compression loading, Proceedings of Canadian Masonry Symposium, Banff, Alberta, Canada.

Ng’andu, B.M., Vermeltfoort, A.T. & Martens, D.R.W. (2004), The response of steel frames infilled with CASIEL walls to in-plane monotonic loads, Proceedings of the 13th International Brick and Block Masonry Conference, Amsterdam, The Netherlands, pp. 219-228.

Ng’andu, B.M., Vermeltfoort, A.T. & Martens, D.R.W. (2004), The behaviour of steel frames with calcium silicate element walls, Proceedings of the 5th International PhD Symposium, Delft, The Netherlands, pp. 1253-1260.

Ng’andu, B.M. & Vermeltfoort, A.T. (2003), Stabiliteit van raamwerken met kalkzandsteen invulwanden (in Dutch). Cement, nr.2. pp. 78-81.

Martens, D.R.W., Ng’andu, B.M. & Vermeltfoort, A.T. (2002), Twee-dimensionaal belast metselwerk onderzocht (in Dutch), Cement, nr.7. pp. 78-81.

Ng’andu, B.M., Vermeltfoort, A.T. & Martens, D.R.W. (2002), Biaxial Compression of Masonry, explorative research into the behaviour of a two jack test rig, Proceedings of the 6th International British Masonry Conference, London, U.K. pp. 365-370.

Curriculum vitae Bright Mweene Ng’andu was born in Mazabuka and raised on the Mabwetuba (white stones) foothills near Chikankata, Zambia. He attended Mabwetuba Primary School from 1972 to 1978 and Canisius Secondary School from 1979 to 1983. He studied at the University of Zambia (UNZA), from 1984 to 1989 and obtained a Bachelor’s Degree (with Merit), in Civil Engineering. He then worked as a Civil/Structural Engineer for John Burrow and Partners Consulting Engineers Ltd. in Lusaka, from 1989 to 1992. His main responsibilities were structural design and detailing of steel and reinforced concrete structures, and site supervision. In September 1991 he was awarded a scholarship by the British Council and commenced postgraduate studies at the University of Strathclyde in Glasgow, Scotland. In October 1993, he graduated with a Master of Science degree in Structural Engineering. During the same year he attended training at Sheffield University in the United Kingdom on ‘Developing Your Skills as a Lecturer.’ He then returned to Zambia and took up an appointment as Lecturer in the School of Engineering at UNZA. He taught structural engineering subjects, supervised project students and provided consultancy on several projects from industry. During the same period and under the auspices a Netherlands-Zambian international cooperation project, he worked with lecturers from the Department of Technology Management at the Eindhoven University of Technology (TU/e), on a redesign of the curriculum for non-technical courses for engineering students at the UNZA. He was co-editor of a course compendium on ‘Engineering and Society; Economic aspects of Development.’ During the period from February to September 2001, he visited the Department of Structural Design, in the Faculty of Building and Architecture at the TU/e and conducted experimental research into the behaviour of brickwork under biaxial compression. In October, 2001, at the same institution, he started his doctoral research in steel infilled frames using calcium silicate element walls. The research was sponsored by the Technology Foundation STW, applied science division of NWO and the technology programme of the Ministry of Economic Affairs in the Netherlands. During this period, he has presented the research results at several international conferences. From June to July, 2005, he was a visiting researcher at the Centre of Effective Design of Structures at McMaster University, Hamilton, Canada. The most important findings of the doctoral research are reported in this thesis.

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