Bracing steel frames with calcium silicate element walls
Citation for published version (APA):
Ng'Andu, B. M. (2006). Bracing steel frames with calcium silicate element walls. Technische Universiteit Eindhoven. https://doi.org/10.6100/IR607328
DOI:
10.6100/IR607328
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Bracing Steel Frames with
Calcium Silicate Element Walls
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:
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
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
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
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
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.
Chapter
1
1
Introduction
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
pressing machine
reactor reaction
calcium silicate element autoclave sand dosing water mixing lime water curing moulding height: 520 - 600 mm length: 900 - 1000 mm thickness: 100 - 300 mm compressive 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
2
Behaviour and analysis of infilled
frames - State of the art
AbstractThis 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.
12 Behaviour and analysis of infilled frames – State of the art
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 infill wall infill wall infill wall frame load (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.
14 Behaviour and analysis of infilled frames – State of the art infill wall frame load 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
Experimental evidence 15 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.
16 Behaviour and analysis of infilled frames – State of the art
(f) out of plane
(e) failure of frame members
(d) corner crushing (c) diagonal tension
(a) shear slip (b) proliferation
of 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.
Experimental evidence 17 (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.
18 Behaviour and analysis of infilled frames – State of the art
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.
equivalent strut
w direction of
loading
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:
x P x y t k e 2 cos λ λ λ = ⋅ (2.1) where: k E I 4 λ = ⎜⎛ ⎞⎟
⎝ ⎠ in which k is the foundation modulus
t is the constant width of the column in contact with the
foundation, and
20 Behaviour and analysis of infilled frames – State of the art P infill wall y x a h 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: 2 h h π α λ = (2.2) where: 2 4 4 i h f c E t sin E I h θ λ = ⎜⎛⎜ ⎞⎟⎟ ⎝ ⎠ (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:
π α λ = l l (2.4)
Modelling of infilled frames 21 where: i l f b E t sin E I l 2 4 4 θ λ = ⎜⎛⎜ ⎞⎟⎟ ⎝ ⎠ (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 h w 1 2 2 2 α α = + (2.6) l h 2 2 1 1 2 2 π λ λ ⎛ ⎞ ⎛ ⎞ = ⎜ ⎟ +⎜ ⎟ ⎝ ⎠ ⎝ ⎠ (2.7)
22 Behaviour and analysis of infilled frames – State of the art
infill of thicknesst
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). 0.3 0.16 ( h ) d w= λ h − l (2.8) 0.95 h h cosθ w λ h = (2.9) 0.4 0.175 ( h ) d w= 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
Modelling of infilled frames 23 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 according to Kilinger & Bertero (1976)
(c) several struts around opening according to Thiruvengadam (1985)
(b) six strut model according to Chrysostumuo (1991)
(d) proposed strut model including horizontal shear sliding by Leuchars & Scrivener (1976) Figure 2.7 : Modified diagonal strut models
24 Behaviour and analysis of infilled frames – State of the art 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 ' ' 2 p c c M F l t h 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.
F Fh’/l’
l’
uniform distribution of
shear strain
square yield criterion compression tension s2 Mp sc s1 sc 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
Modelling of infilled frames 25 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 and
h h l l
F = µ α 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 h l 1
α = ≤
From these contact forces equilibrium considerations of a concrete infill panel yielded equation (2.13) for the collapse load, H.
26 Behaviour and analysis of infilled frames – State of the art ( ) (1 ) 2 pj j c c c b b M M H σ t α α h τ t α 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( ) 0.4 pj c pc c c M β M α h h σ t + = ≤ (2.14) 2( ) 0.4 pj b pb b b M β M α 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
Modelling of infilled frames 27 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 4 1 3 c co f σ µ α = + (2.16) ' 2 1 3 c bo f σ 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;
28 Behaviour and analysis of infilled frames – State of the art
• 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-(meso-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
