Guidelines and Rules for Detailing of Reinforcement in Concrete Structures A Compilation and Evaluation of Ambiguities in Eurocode 2 Master of Science Thesis in the Master’s Programme Structural Engineering and Building Technology ANNELI DAHLGREN LOUISE SVENSSON Department of Civil and Environmental Engineering Division of Structural Engineering Concrete Structures CHALMERS UNIVERSITY OF TECHNOLOGY Göteborg, Sweden 2013 Master’s Thesis 2013:142 a) h) d) g) f) e) c) b) MASTER’S THESIS 2013:142 Guidelines and Rules for Detailing of Reinforcement in Concrete Structures A Compilation and Evaluation of Ambiguities in Eurocode 2 Master of Science Thesis in the Master’s Programme Structural Engineering and Building Technology ANNELI DAHLGREN LOUISE SVENSSON Department of Civil and Environmental Engineering Division of Structural Engineering Concrete Structures CHALMERS UNIVERSITY OF TECHNOLOGY Göteborg, Sweden 2013 Guidelines and Rules for Detailing of Reinforcement in Concrete Structures A Compilation and Evaluation of Ambiguities in Eurocode 2 Master of Science Thesis in the Master’s Programme Structural Engineering and Building Technology ANNELI DAHLGREN LOUISE SVENSSON © ANNELI DAHLGREN & LOUISE SVENSSON, 2013 Examensarbete / Institutionen för bygg- och miljöteknik, Chalmers tekniska högskola 2013:142 Department of Civil and Environmental Engineering Division of Structural Engineering Concrete Structures Chalmers University of Technology SE-412 96 Göteborg Sweden Telephone: + 46 (0)31-772 1000 Cover: Different configurations of links used as shear or torsional reinforcement in concrete structures. Chalmers Reproservice Göteborg, Sweden 2013 I Guidelines and Rules for Detailing of Reinforcement in Concrete Structures A Compilation and Evaluation of Ambiguities in Eurocode 2 Master of Science Thesis in the Master’s Programme Structural Engineering and Building Technology ANNELI DAHLGREN LOUISE SVENSSON Department of Civil and Environmental Engineering Division of Structural Engineering Concrete Structures Chalmers University of Technology ABSTRACT A proper detailing of reinforcement in concrete structures is very important with regard to structural behaviour, safety and good performance. However, rules in codes for detailing and minimum reinforcement ratios are not always easy to understand and interpret, since there is very limited or no background information explaining the function and providing motivations. The aim of this project was to investigate and explain the background for the rules in the codes, especially Eurocode 2, and give guidelines for good detailing, based on previous research and experience. Rules and guidelines for detailing of reinforcement that might be difficult to interpret or understand were identified by an initial study of the European Standard. From this study the background to some of the ambiguities were examined more thoroughly in a detailed literature study. An investigation consisting of interviews and a qualitative survey was performed in order to evaluate how structural engineers interprets and applies the rules provided in Eurocode 2. This was performed also with the intention to illuminate ambiguities to be able to suggest improvements of the new standard. The literature study showed that there is very limited background information to Eurocode 2 and that it can be difficult to find answer, if something is perceived as unclear in the code. However, knowledge about the fundamental theory and required structural behaviour of reinforced concrete structures can be enough to understand many requirements, why this is provided in this report. The result from the investigation indicated that there are sections in Eurocode 2 that can be difficult to interpret. The standard needs to be improved or clarified in order to facilitate for the users and in order to know how to apply the rules on cases other than standard cases. Some of the identified problem areas in Eurocode 2 are for instance lapping of longitudinal reinforcement, concrete frame corners subjected to opening moment and limitations of crack widths for concrete members subjected to shear and torsion. In some cases, specific changes of Eurocode 2 have been suggested, while it in some cases is sufficient to add even stronger references between sections or include a short description of the motive for the intended rule, in order to improve the standard. A need for further research has also been identified in order to be able to improve certain parts of Eurocode 2. Key words: Eurocode 2, EN 1992-1-1, Reinforcement, Reinforced concrete, Detailing II Riktlinjer och regler för detaljutformning av armering i betongkonstruktioner En sammanställning och utvärdering av oklarheter i Eurokod 2 Examensarbete inom mastersprogrammet Structural Engineering and Building Technology ANNELI DAHLGREN LOUISE SVENSSON Institutionen för bygg- och miljöteknik Avdelningen för konstruktionsteknik Betongbyggnad Chalmers tekniska högskola SAMMANFATTNING God detaljutformning av armering i betongkonstruktioner är väldigt viktigt med hänsyn till säkerhet, funktion och verkningssätt. Trots detta är regler för detaljutformning och minimiarmering inte alltid så lätta att förstå och tolka eftersom det finns väldigt begränsad, om ens någon, bakgrundsinformation som förklarar funktionen och ger motiv för reglerna. Målet med projektet var att undersöka och förklara bakgrunden för reglerna i standarderna, särskilt Eurokod 2, och ge riktlinjer för god detaljutformning, baserad på tidigare forskning och erfarenhet Regler och riktlinjer för detaljutformning av armering som kan vara svåra att tolka eller förstå identifierades i en inledande studie av den europeiska standarden. Utifrån denna studie utforskades därefter bakgrunden till några av svårigheterna i en mer ingående litteraturstudie. En undersökning innefattande intervjuer och en kvalitativ enkätundersökning utfördes för att utreda hur konstruktörer tolkar och tillämpar regler som finns i Eurokod 2. Detta gjordes också med avsikten att ytterligare kunna belysa problemområden och komma med förslag till förbättringar av den nya standarden. Litteraturstudien visade på att det finns mycket begränsad bakgrundsinformation till Eurokod 2 och att det kan vara svårt att finna svar om något uppfattas som oklart i normen. Dock kan kunskap om grundläggande teori och erforderligt verkningssätt hos armerade betongkonstruktioner räcka för att förstå många av reglerna, varför detta ges i denna rapport. Resultatet från undersökningen indikerar att det finns avsnitt i Eurokod 2 som kan vara svåra att tolka. Standarden behöver förbättras eller förtydligas för att underlätta för dess användare och för att veta hur regler ska tillämpas i situationer som inte medför standardlösningar. Några exempel på identifierade problemområden i Eurokod 2 är omlottskarvning av längsgående armering, ramhörn utsatta för öppnande moment samt beräkning av sprickbredd för betongelement som belastas av både tvärkraft och vridning. Konkreta ändringar av Eurokod 2 har föreslagits medan det i andra fall räcker med tydligare hänvisningar mellan avsnitten eller en kort förklaring av motivet för den avsedda regeln. Ett behov av mer ingående forskning har också identifierats för att kunna förbättra vissa delar av Eurokod 2. Nyckelord: Eurokod 2, EN 1992-1-1, armering, armerad betong, detaljutformning CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2013:142 III Contents ABSTRACT I SAMMANFATTNING II CONTENTS III PREFACE IX ABBREVIATIONS AND TRANSLATIONS X NOTATIONS XI 1 INTRODUCTION 1 1.1 Background 1 1.2 Aim 1 1.3 Method 2 1.4 Limitations 3 1.5 Outline of the thesis 4 2 DEVELOPMENT OF STANDARDS FOR DESIGN OF CONCRETE STRUCTURES 5 2.1 Transition to the European Standards 5 2.1.1 Development of European Standards - Eurocodes 5 2.1.2 Development of Standards for design of concrete - Eurocode 2 6 2.1.3 Codes for design of concrete in Sweden 7 2.1.4 Additional information to the Swedish Standards 8 2.2 Consequences due to poor detailing 8 2.2.1 General 8 2.2.2 Alvik’s Bridge and Gröndal’s Bridge 9 2.2.3 Sleipner concrete off shore platform 10 2.3 Compilation of ambiguities in Eurocode 2 12 3 REINFORCED CONCRETE STRUCTURES 18 3.1 Material properties 18 3.2 Transfer of forces between the materials 21 3.2.1 Bond between reinforcing steel and concrete 21 3.2.2 Friction 26 3.2.3 Shear friction at joint interface with transverse reinforcement 28 3.2.4 Dowel action 29 3.3 General behaviour of reinforced concrete structures 31 3.3.1 Response 31 3.3.2 Modelling 32 3.4 Design based on different analysis approaches 37 3.4.1 General 37 3.4.2 Linear elastic analysis 39 CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2013:142 IV 3.4.3 Linear elastic analysis with limited redistribution 39 3.4.4 Plastic analysis 40 3.4.5 Non-linear analysis 40 3.5 Strut and tie method 41 4 DESIGN AND DETAILING FOR BENDING 45 4.1 Structural response and modelling 45 4.2 Minimum longitudinal reinforcement 48 4.2.1 Requirements in Eurocode 2 48 4.2.2 Explanation and derivation 49 4.2.3 Discussion 50 4.3 Maximum longitudinal reinforcement 52 4.3.1 Requirements in Eurocode 2 52 4.3.2 Explanation and derivation 53 4.3.3 Discussion 54 4.4 Reinforcement detailing for concrete frame corners 57 4.4.1 Requirements in Eurocode 2 57 4.4.2 Explanation and derivation 59 4.4.3 Discussion 65 5 DESIGN AND DETAILING FOR SHEAR 70 5.1 Structural response and modelling 70 5.2 Shear sliding failure 73 5.2.1 Requirements in Eurocode 2 73 5.2.2 Explanation and derivation 73 5.2.3 Discussion 75 5.3 Web shear compression failure 76 5.3.1 Requirements in Eurocode 2 76 5.3.2 Explanation and derivation 77 5.3.3 Discussion 79 5.4 Minimum shear reinforcement 81 5.4.1 Requirements in Eurocode 2 81 5.4.2 Explanation and derivation 82 5.4.3 Discussion 83 5.5 Additional tensile force due to inclined cracks 86 5.5.1 Requirements in Eurocode 2 86 5.5.2 Explanation and derivation 86 5.5.3 Discussion 88 5.6 Configurations of shear reinforcement 91 5.6.1 Requirements in EC2 91 5.6.2 Explanation and derivation 92 5.6.3 Discussion 93 5.7 Load close to supports 98 5.7.1 Requirements in Eurocode 2 98 CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2013:142 V 5.7.2 Explanation and derivation 99 5.7.3 Discussion 101 5.8 Suspension reinforcement 103 5.8.1 Requirements in Eurocode 2 103 5.8.2 Explanation and derivation 103 5.8.3 Discussion 105 6 DESIGN AND DETAILING FOR TORSION 110 6.1 Structural response and modelling 110 6.2 Longitudinal torsional reinforcement 112 6.2.1 Requirements in Eurocode 2 112 6.2.2 Explanation and derivation 113 6.2.3 Discussion 116 6.3 Transversal torsional reinforcement 117 6.3.1 Requirements in Eurocode 2 117 6.3.2 Explanation and derivation 119 6.3.3 Discussion 122 6.4 Combination of torsional moment and shear force 123 6.4.1 Requirements in Eurocode 2 123 6.4.2 Explanation and derivation 124 6.4.3 Discussion 126 6.5 Configuration of transversal torsional reinforcement 128 6.5.1 Requirements in Eurocode 2 128 6.5.2 Explanation and derivation 129 6.5.3 Discussion 129 7 SHEAR BETWEEN WEB AND FLANGES 133 7.1 Structural response and modelling 133 7.2 Longitudinal shear stress 136 7.2.1 Requirements in Eurocode 2 136 7.2.2 Explanation and derivation 136 7.2.3 Discussion 139 7.3 Transversal reinforcement 140 7.3.1 Requirements in Eurocode 2 140 7.3.2 Explanation and derivation 141 7.3.3 Discussion 142 8 SHEAR FRICTION AND DOWEL ACTION 144 8.1 Structural response and modelling 144 8.2 Shear at the interface between concrete cast at different times 146 8.2.1 Requirements in Eurocode 2 146 8.2.2 Explanation and derivation 149 8.2.3 Discussion 151 8.3 Maximum transversal reinforcement 151 CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2013:142 VI 8.3.1 Requirements in Eurocode 2 151 8.3.2 Explanation and derivation 152 8.3.3 Discussion 154 8.4 Shear capacity due to dowel action 154 8.4.1 Requirements for dowel action 154 8.4.2 Explanation and derivation 155 8.4.3 Discussion 158 9 BOND AND ANCHORAGE 159 9.1 Structural response and modelling 159 9.2 Curtailment of reinforcement with respect to inclined cracks 161 9.2.1 Requirements in Eurocode 2 161 9.2.2 Explanation and derivation 162 9.2.3 Discussion 164 9.3 Anchorage of bottom reinforcement at end supports 167 9.3.1 Requirements in Eurocode 2 167 9.3.2 Explanation and derivation 168 9.3.3 Discussion 171 9.4 Lapping of longitudinal reinforcement 174 9.4.1 Requirements in Eurocode 2 174 9.4.2 Explanation and derivation 175 9.4.3 Discussion 178 9.5 Concrete cover and distance between bars 181 9.5.1 Requirements in Eurocode 2 181 9.5.2 Explanation and derivation 183 9.5.3 Discussion 183 9.6 Permissible mandrel diameters for bent bars 185 9.6.1 Requirements in Eurocode 2 185 9.6.2 Explanation and derivation 186 9.6.3 Discussion 187 10 CRACK CONTROL 190 10.1 Structural response and modelling 190 10.2 Minimum reinforcement requirements for crack control 193 10.2.1 Requirements in Eurocode 2 193 10.2.2 Explanation and derivation 195 10.2.3 Discussion 197 10.3 Limitation of crack widths for shear and torsion 201 10.3.1 Requirements in Eurocode 2 201 10.3.2 Explanation and derivation 201 10.3.3 Discussion 203 11 INVESTIGATION 207 11.1 Introduction 207 CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2013:142 VII 11.2 Interviews 207 11.2.1 Overview 207 11.2.2 Interviewed persons 208 11.2.3 Result from interview with Ebbe Rosell 209 11.2.4 Result from interview with Mikael Hallgren 215 11.2.5 Result from interview with Bo Westerberg 223 11.2.6 Result from interview with Johan Söderberg 227 11.2.7 Result from interview with David Eriksson 234 11.3 Survey 236 11.3.1 Procedure 236 11.3.2 Result from survey 238 12 EVALUATION AND ANALYSIS 267 12.1 General remarks 267 12.2 Bending 267 12.2.1 Minimum longitudinal reinforcement 267 12.2.2 Maximum longitudinal reinforcement 268 12.2.3 Reinforcement detailing of concrete frame corners 268 12.3 Shear 269 12.3.1 Minimum shear reinforcement 269 12.3.2 Configuration of shear reinforcement 270 12.3.3 Load close to supports 271 12.3.4 Suspension reinforcement 272 12.4 Torsion 272 12.4.1 Longitudinal torsional reinforcement 272 12.4.2 Transversal torsional reinforcement 273 12.4.3 Combination of torsional moment and shear force 274 12.5 Shear between web and flanges 275 12.6 Shear at the interface between concrete cast at different times 275 12.7 Bond and anchorage 276 12.7.1 Anchorage of bottom reinforcement at end support 276 12.7.2 Lapping of longitudinal reinforcement 276 12.7.3 Concrete cover and distance between bars 278 12.8 Crack control 280 12.8.1 Minimum reinforcement requirements for crack control 280 12.8.2 Crack reinforcement for relatively high cross-sections 281 12.8.3 Limitation of crack widths for shear and torsion 282 12.9 Cooperation between structural engineers and contractors 283 12.10 Influence from professional background on the choice of detail solution 284 13 SUMMARY OF RESULTS 285 13.1 Introduction 285 13.2 Recommended improvements of Eurocode 2 286 13.3 Needed improvements of Eurocode 2 288 CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2013:142 VIII 13.4 Derived and explained expressions 290 13.5 Clarified items 291 13.6 Conclusions from survey and interviews 292 14 CONCLUSIONS 293 14.1 Concluding remarks 293 14.2 Further investigation 294 15 REFERENCES 295 APPENDIX A COMPILATION OF AMBIGUITIES TREATED IN THE REPORT A-1 APPENDIX B COMPILATION OF AMBIGUITIES NOT TREATED IN THE REPORT B-1 APPENDIX C REINFORCEMENT AMOUNT FOR DIFFERENT DUCTILITY REQUIREMENTS C-1 APPENDIX D CONCRETE FRAME CORNERS D-1 APPENDIX E ACTION EFFECT DEPENDENT ON ANCHORAGE DEGREE OF TRANSVERSAL BAR E-1 APPENDIX F ULTIMATE SHEAR CAPACITY DUE TO DOWEL ACTION F-1 APPENDIX G CALCULATION OF TOTAL LONGITUDINAL TENSILE FORCE WITH REGARD TO INCLINED CRACKS G-1 APPENDIX H PERMISSIBLE MANDREL DIAMETER OF BENT BARS H-1 APPENDIX I WEIGHT OF DIFFERENT BAR DIAMETERS AND LENGTHS I-1 APPENDIX J SURVEY QUESTIONS J-1 APPENDIX K RESULT FROM SURVEY K-1 CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2013:142 IX Preface In this project a literature study has been conducted searching for the background to ambiguities encountered in the new European standard, Eurocode 2. The literature study was followed by an investigation consisting of interviews and a quantitative survey, where the ambiguities were further evaluated and discussed. The work has mostly been performed by the authors together. However, when the background to the rules and guidelines in Eurocode 2 were investigated more thoroughly a division of the subjects was made. Continuous discussions and exchange of knowledge between the authors have been made in order to ensure that both authors understand the content of the report. The project has been carried out during 2013, from February to December at Reinertsen Sverige AB in cooperation with the Department of Civil and Environmental engineering, Division of Structural Engineering, Concrete Structures at Chalmers University of Technology. Supervisors have been PhD Morgan Johansson from Reinertsen Sweden AB and Prof. Björn Engström at the Division of Structural Engineering at Chalmers University of Technology, who also was the examiner of the master’s thesis. We would like to thank both of them for their friendly approach, persistent and tireless manner and the desire to always answer our questions. The discussions between the supervisors themselves have been extremely educational and inspiring to take part of. The peoples chosen for the interviews were Ebbe Rosell at Trafikverket, Mikael Hallgren at Tyréns and Bo Westerberg at Bo Westerberg konsult AB. These are all highly regarded structural engineers with long and extensive experience from design of concrete structures. We would like to thank all of them for their fast and yet comprehensive answers and for adding important aspects to the discussions. Their participation and informative answers provided perspectives to the rules and guidelines in Eurocode 2 that otherwise would not have caught the attention of the authors. During the master’s thesis project we also had the opportunity to come and visit Johan Söderberg, foreman at PEAB, at his working place, the construction site at Perstorp industry in Stenungsund. He provided us with valuable information from a contractor’s point of view. We would like to thank him and his colleague David Eriksson for answering our questions and providing an additional dimension to our project. We also send our greatest appreciation to the persons that participated in the survey. We got the impression that those who answered took the questions seriously and did their best to bring out their opinion. The comments obtained from the survey have been extremely valuable in the evaluation of the results. Engineers from the following companies were involved in the survey and earn special attention; Chalmers, COWI, ELU, Inhouse Tech, Reinertsen, Skanska, Structor, Sweco, Trafikverket, Vattenfall and WSP. Finally, we thank our opponents Anna Sandberg and Joanna Klorek for their thoughtful and improving comments. Göteborg, December 2013 Anneli Dahlgren & Louise Svensson CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2013:142 X Abbreviations and translations Abbreviations ACI American Concrete Institute BABS Byggnadsstyrelsens anvisningar till byggnadsstadgan (Byggnadsstyrelsen’s Instructions to the Building Law) BBK Boverkets Handbok om Betongkonstruktioner (Boverket’s Handbook on Concrete Structures) BBR Boverkets Byggregler (Boverket’s Building Regulations) BFS Boverkets Författningssamling (Boverket’s Statutes) BKR Boverkets Konstruktionsregler (Boverket’s Regulations for Structural Design) BSI British Standards Institute CEN Comité Européen de Normalisation European Committee for Standardisation CEB Comité Euro-International du Betón (Euro-International Concrete Committee) EC2 Eurocode 2 EC Eurocode EC European Commission ECC European Economic Community ECP European Concrete Platform EN European Standards ENV European Prestandards EK Eurokod (Eurocode) EKS Europeiska konstruktionsstandarder (European Standards for Structural Design) EU European Union fib Féderation Internationale du Betón (International Federation for Structural Concrete) FIP Fédération Internationale de la Précontrainte (International Federation for Prestressing) JRC Joint Research Centre MC Model Code NA National Annex NDP Nationally Determined Parameters CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2013:142 XI NR Nybyggnadsregler (Building Regulations) PBL Plan- och bygglagen (The Planning and Building Act) SBN Svensk Byggnorm (Swedish Building Code) SIS Swedish Standards Institute TK Teknisk Komitte (Technical Committee) VVFS Vägverkets Föreskrifter (Vägverket’s Regulations) Translations Boverket Swedish National Board of Housing, Building and Planning Byggnadsstyrelsen Swedish National Board of Building Planverket Swedish national Board of Planning Statens Betongkomitté Swedish National Concrete Committee Svenska betongföreningen Swedish Concrete Association Svensk Byggtjänst Swedish Building Service Trafikverket Swedish Transport Administration Vägverket Swedish Road Administration Notations Roman upper case letters A area Ac cross-sectional area of concrete Act area of concrete within the part of the section which is calculated to be in tension just before formation of the first crack Aef effective concrete area Aeff effective flange area Aeff,i effective area of flange i Af part of the compressive zone or the area of the bending reinforcement within the width beff,1 Ak area enclosed by the centre-lines of the connecting walls, including inner hollow areas As cross-sectional area of steel bar or dowel Asf cross-sectional area of transversal reinforcement in flange CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2013:142 XII Asi area of one reinforcing bar Asi cross-sectional area of one leg of reinforcement Asi,l cross-sectional area of one longitudinal torsional bar Asl area of longitudinal torsional reinforcement Asl,tot total area of longitudinal torsional reinforcement in bottom horizontal wall As,max maximum area of bending reinforcement As,min minimum area of bending reinforcement Asw cross-sectional area of one shear reinforcement unit Asw,i cross-sectional area of one torsional link Asw,max, i maximum amount of transversal torsional reinforcement As provided provided reinforcement amount (ACI) As required required reinforcement amount (ACI) E modulus of elasticity Ec modulus of elasticity of concrete Es modulus of elasticity of reinforcing steel F force Fbt is the tensile force from ultimate loads in a bar, or group of bars in contact, at start of a bend Fc force in concrete compressive strut Fc,i force in concrete in part i (flange or web) Fcd design value of compressive force Fct force taken by the concrete in tension prior to cracking Fcw compressive force due to inclined cracks Fcw,i compressive force due to inclined cracks in one wall, i, of a cross-section FE tensile force that needs to be anchored at a support section Ftd design value of tensile force Fs force in reinforcing steel Fsl tensile force that needs to be resisted by longitudinal torsional reinforcement Fsl,i tensile force that needs to be resisted by longitudinal torsional reinforcement in one wall i Fsw force that can be taken by shear reinforcement Fsw,n force that can be taken by one shear reinforcement unit Ft force in transverse bar Fu,dow ultimate dowel capacity Fv shear force acting on a dowel Fv,el elastic shear capacity of a dowel CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2013:142 XIII FvR shear capacity of dowel Ieq second moment of area of equivalent concrete cross-section in state I or II M bending moment Mcr cracking moment ME applied bending moment MEd design value of the applied bending moment MEd,max maximum design value of the applied bending moment Mmax maximum bending moment MR moment resistance MRd design moment resistance Mu ultimate moment, moment at failure My yield moment N axial force Na longitudinal component due to inclined compressive stress field Nb longitudinal component due to inclination of the shear reinforcement Ncr axial cracking force NEd normal force that should be added or subtracted from the tensile force P point load Sbd force growth T torsional moment TEd design torsional moment TRd,max design value of maximum torsional moment that needs to be sustained by a wall i of the cross-section V shear force Vc contribution to shear capacity from concrete VEd design value of the applied shear force Vi shear force i in one wall of a hollow box section VRd,max design value of maximum shear force that can be sustained by the member VRd,s design value of shear force that can be sustained by the yielding shear reinforcement Vs contribution to shear capacity from reinforcement VT torsional shear force VV vertical shear force (VEd) Q distributed load CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2013:142 XIV Roman lower case letters a distance between bars a width of compressive strut ab for a given bar (or group of bars in contact) is half of the centre-to-centre distance between bars (or groups of bars) perpendicular to the plane of the bend. For a bar or group of bars adjacent to the face of the member, ab should be taken as the cover plus ϕ/2 al distance for shifting the moment curve sideways av distance between load and support b width of cross-section b width of support bi width of the interface bef effective width of the support beff effective width bt mean width of the part of cross-section in tension bw web width c cohesion factor, factor which depends on the roughness of the joint interface c concrete cover ce coefficient that considers the eccentricity cmin minimum concrete cover cmin,b minimum cover due to bond requirement cmin,dur minimum cover due to environmental conditions cnom nominal concrete cover c0 coefficient that considers the bearing strength of concrete d effective depth of cross-section dg maximum aggregate size e eccentricity fbd bond strength fc compressive cylinder strength of concrete at 28 days fcc design concrete compressive strength fcd design value of concrete compressive strength fck characteristic compressive cylinder strength of concrete at 28 days fct tensile strength of concrete fctd design axial tensile strength of concrete fctk characteristic axial tensile strength of concrete fctd concrete design strength in tension CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2013:142 XV fct,eff mean value of the tensile strength of the concrete at the time when the cracks may first be expected to occur. This is equal to fctm or fctm(t). fcth = 1.5fctk. High value of the tensile strength of concrete fctm mean value of axial tensile strength of concrete fu ultimate tensile strength of reinforcing steel fv =0.35fct fy yield tensile strength of reinforcing steel fyd design yield tensile strength of reinforcing steel fyk characteristic yield tensile strength of reinforcing steel fym mean value of the yield strength of the reinforcement fywd design yield strength of shear reinforcement h height of cross-section hcr depth of tensile zone immediately prior to cracking hef height of effective concrete area hf thickness of the flange at the junctions between web and flange k coefficient factor la minimum grouting length for a dowel lbd design anchorage length lb,max maximum anchorage length lb,rqd required anchorage length lt transmission length lt,max maximum transmission length l0 lap length l0,min minimum lap length n number of shear reinforcement units n number of links that crosses each crack nleg number of shear reinforcement legs in one of the shear reinforcement units that crosses the crack in one section r bending radius of reinforcing bar s shear slip, shear displacement s spacing of bars sb,max maximum spacing between bent up bars sel elastic shear slip sf spacing of transversal reinforcement in flange sl maximum spacing of torsional links sl,max maximum spacing between shear reinforcement CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2013:142 XVI smax maximum shear slip sr,max maximum crack distance sr,max,x maximum crack distance in the x-direction sr,max,y maximum crack distance in the y-direction st,max maximum distance between legs of a series of shear legs tef,i thickness of a wall i in a hollow box section u height of the node uk is the perimeter of the area Ak vEd longitudinal shear stress at the junction between one side of a flange and the web vEdi design value of shear stress at joint interface vRdi design value of the shear resistance at joint interface 1/v curvature w joint separation, crack width wmax maximum joint separation x depth of compression zone xu depth of neutral axis at the ultimate limit state x0 distance to maximum bending moment z inner lever arm z distance from gravity centre zi side length of wall i between the intersection points with the adjacent walls zs level of reinforcing steel in relation to gravity centre q shear flow qc concrete reaction wk crack width wm mean crack width Greek letters α angle of inclination α ratio between Es and Ec α coefficient factor β coefficient factor β ratio β angle γc partial factor for concrete CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2013:142 XVII γn partial factor considering the safety class γs partial factor for reinforcing steel Δcdev factor that allow for some deviation of concrete cover in design Δcdur,add reduction of minimum cover for use of additional protection Δcdur,st reduction of minimum cover for use of stainless steel Δcdur,γ additive safety element ΔFc change of normal force in the joint intersection over the length Δx ΔFd change of normal force in the flange over the length Δx ΔFtd additional tensile force Δx length under consideration in shear between web and flanges Δσc compressive force at joint intersection due to pullout resistance Δσs tensile force in transverse bar in joint intersection due to pullout resistance ε strain εc concrete strain εcc compressive concrete strain εcm mean concrete strain εct tensile concrete strain εcu ultimate concrete strain in concrete εcu2 ultimate compressive strain in concrete, parabolic stress-strain relation εcu3 ultimate compressive strain in concrete, bi-linear stress-strain relation εc2 compressive concrete strain at the peak of fc, parabolic stress-strain relation εc3 compressive concrete strain at the peak of fc, bi-linear stress-strain relation εs steel strain εsm mean steel strain εsx steel strain in x-direction εsy steel strain in y-direction εsy yield strain of reinforcing steel εud strain limit of reinforcing steel εuk characteristic strain of reinforcing steel at maximum load η1 coefficient related to the quality of the bond condition and the position of the bar during concreting η2 coefficient related to diameter of the reinforcing bar θ angle between compression strut and the longitudinal axis θf angle between compression strut and the longitudinal axis in the flange θI angle of the tensile principal stress, σI CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2013:142 XVIII μ friction coefficient, factor which depends on the roughness of the joint interface v strength reduction factor ν1 strength reduction factor vEdi shear stress at a joint interface vRdi shear resistance at a joint interface ρ reinforcement ratio ρmax maximum reinforcement ratio ρw shear reinforcement ratio ρw,min minimum shear reinforcement ratio ρx reinforcement ratio in x-direction ρy reinforcement ratio in y-direction ρρ,ef effective reinforcement ratio σ stress σc concrete stress σcc compressive strength in concrete σcc,max design compressive strength in concrete σct tensile strength in concrete σcw,i compressive stress in one wall, i, due to inclined strut σcw,t stress acting in the compressive strut σn stress per unit area caused by the minimum external force across the interface that can act simultaneously with the shear force σn normal stress σr radial compressive stress σs steel stress σsd design steel stress σsx steel stress in x-direction σsy steel stress in y-direction σx concrete stress in x-direction σy concrete stress in y-direction σq transversal component related to bond stress σI tensile principal stress σII compressive principal stress τb bond stress τc shear stress in concrete τmax maximum shear stress CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2013:142 XIX τt,i torsional shear stress in wall i τxy shear stress ϕ frictional angle ϕ diameter of the reinforcing bar or the dowel ϕm mandrel diameter ϕm,min minimum mandrel diameter ϕs maximum bar diameter ϕ * s maximum bar diameter given in Table EC2 7.2N ωs mechanical reinforcement amount ωs’ mechanical reinforcement amount with regard to the factor v CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2013:142 XX CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2013:142 1 1 Introduction 1.1 Background In the beginning of 2011 the European Standard Eurocode became mandatory for design of supporting structures in Sweden, SIS (2013a). Eurocode 2, SIS (2008), is the current standard in Sweden concerning concrete structures and replaced the previous Swedish handbook BBK 04, Boverket (2004). According to the Swedish standards institute, SIS (2013b), the goal of the establishment of a unified standard is to facilitate the cooperation between structural engineers from different countries all over Europe. A common technical language will increase the opportunity of exchange of knowledge as well as services between countries. Eurocode 2 provides rules and guidelines in short sentences and equations complemented with informative figures in order to facilitate for the users of the code. However, there is very limited or no background information explaining the mechanical response and providing motivations for the different expressions. It is essential that the detailing of reinforcement in concrete structures is performed in such a way that the intended response of the structure with regard to safety and good performance is fulfilled. It is also important that the fundamental theory and required structural behaviour of reinforced concrete structures are known in order to reduce the risk for incorrect interpretations that can lead to a great diversity and even unacceptable solutions. Therefore an investigation where the background to Eurocode 2 is determined is of great interest within the building industry to provide sufficient information of how to implement the rules and guidelines in a correct manner. It is also interesting to investigate and evaluate how structural engineers interprets and applies Eurocode 2 in order to illuminate ambiguities and to be able to identify need for improvements of the new standard. This master’s thesis has been carried out in collaboration with engineers in Reinertsen Sverige AB who have identified ambiguities concerning requirements and rules for configuration of reinforcement in concrete structures. A compilation where problems concerning the design and detailing of reinforcement in concrete structures are identified, investigated, exemplified and discussed was therefore desired by the company. 1.2 Aim The purpose of this master’s thesis was to, from a compilation of ambiguities identified in Eurocode 2 concerning reinforcement requirements and configurations in concrete structures, determine and explain the background for the rules and guidelines based on previous research and experience. This should be performed in order to facilitate the use of Eurocode 2, but also to identify lack of information. As a part of the project an investigation, by means of interviews and a qualitative survey, should also be carried out to evaluate the usage of Eurocode 2 in order to be able to identify the need for and recommend further development of the standard. CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2013:142 2 1.3 Method Starting from Eurocode 2 Part 1-1, SIS (2008), different ambiguities concerning reinforcement requirements and configurations in concrete structures were identified. Comparisons to the old Swedish standards were made to detect any notable changes in the new standard. Further, thoughts and reflections were reconciled during interviews and meetings with people who have experience within the industry. Identification of ambiguities in Eurocode 2 has partly been based on already performed studies within the area. However, the studies that were found were at a lower academic level of knowledge and emphasis has therefore been on interviews with experienced structural engineers and discussions with supervisors. In order to make the extensive amount of compiled ambiguities more manageable a categorisation based primarily on mechanisms to resist certain load effects was made. From that categorisation a number of ambiguities were chosen to be illuminated and investigated even further. A more detailed literature study was executed where the background to the highlighted areas was looked into further. This was performed to clarify and explain where expressions and requirements descend from. Main references have been European model codes such as fib Model Code 2010, fib (2012), CEB-FIP Model Code 1990, CEB-FIP (1991), and Model Code for Concrete Structures, CEB-FIP (1978), that laid the base to Eurocode, as well as Svenska betongföreningens handbok till Eurokod 2, Betongföreningen (2010) and Commentary and Worked Examples to Eurocode 2 published by the European Concrete Platform, ECP (2008). To get further information and increase the understanding codes and related publications from other countries like USA and Great Britain were also used. In contrast to Eurocode 2 and the European model codes the concrete code from the American Concrete Institute, ACI (2007), include many references to publications and articles. However, this has only been used to some extent due to time constraints. When the information in the literature mentioned above was insufficient, a literature search among articles and publications at the library at Chalmers University of Technology was executed. Illustrative and educational examples of reinforcement solutions within the area were derived from a combination of interviews and meetings as well as information from literature. No practical experiments or numerical modelling using FE-programs have been executed within this project. This was not performed because of the reliability of that there already existed such investigations. To determine how actors in the industry interpret Eurocode 2 a survey was conducted including multiple choice questions consisting of possible detail solutions of reinforcement configurations. The motivation of the survey was to stress problem areas where it is believed that Eurocode 2 might be interpreted differently. Structural engineers with experience of detailing and design of reinforcement in concrete structures were chosen to participate in the survey. Multiple choice questions were used for the convenience of those who answered the questions but also to make it easy to compare the results. CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2013:142 3 For additional and more detailed information interviews were performed with experienced structural engineers in order to capture the overall way of thinking and to get the opinion of the persons who have participated in the development and implementation of Eurocode 2 in Sweden. Questions from the survey laid the base for the discussions at these interviews. In addition to structural engineers production managers from the construction company PEAB were interviewed in order to examine whether the different practices between the actors are compatible and to find reinforcement detailing solutions that are practically applicable at the construction site. The methodology chosen for this project have resulted in interpretation of answers form the survey, interviews and technical handbooks. It should be emphasised that texts and answers can be interpreted differently depending on who is reading it and in what context it is read. In the worst situation this can result in an interpretation that the creator of the text or answer did not intend. The authors have therefore throughout the report tried to reproduce the content from texts and interviews as concrete and correct as possible. Interpretations that have been made have also been clarified. In order to make sure that the progress was going in the right direction and that the aim of the master’s thesis was reached, continuous reconciliation with the supervisors, Morgan Johansson, Reinertsen Sverige AB and Björn Engström, Chalmers University of Technology, was carried out throughout the project. 1.4 Limitations This project was only related to the general rules and requirements of reinforcement in concrete structures found in Eurocode 2, Part 1-1. Some of the questions encountered where chosen to be processed more deeply while some were only brought to the surface. Furthermore, plain-, prestressed- and prefabricated concrete structures should be left out in order to reduce the number of issues into a manageable amount. The report should primarily concentrate on design and detailing of reinforcement in beams and slabs and less focus should be on columns and walls since many of the rules applicable for beams and slabs also apply for walls and columns. Dowel action is something that is not treated in Eurocode 2, but was included in the previous Swedish handbook, BBK 04, Boverket (2004). It is important to take this effect into account when designing connections, why this was chosen to be included in this master’s thesis. The survey, which was performed in the investigating part of the project, should be limited to about 20 structural engineers in order to get a glimpse of how they practice the standard. The need for a larger number of participants was not considered to be as important as the quality of the answers obtained, why a smaller number, but more experienced structural engineers, were selected for the survey. Due to time constraints focus have been on the theoretical parts of Eurocode 2 and only a small part of the project has been devoted to examining the constructability and practical aspect of the reinforcement configurations recommended in Eurocode 2. CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2013:142 4 1.5 Outline of the thesis The first part, Chapter 2, gives background knowledge about the development of codes for design of concrete structures in Europe and in Sweden. It includes a short overview of what have influenced the codes and the reason why a transition to a common European standard for design of concrete structures was agreed upon. This chapter also provides some examples of consequences due to poor detailing as well as a compilation of ambiguities found in Eurocode 2 in order to provide motivation for increased knowledge and further development of the European Standard. In Chapter 3 the basic theory behind design and detailing of reinforced concrete structures is presented. Material properties of both reinforcing steel and concrete are explained as well as the composite behaviour of reinforced concrete structures. In order to understand how concrete and reinforcement interact with each other at a global level, models describing the overall structural response and different analyse approaches used in design are also described. Chapter 4-10 are the result of the literature study performed in this project, and are referred to as the main chapters. Each chapter represent different mechanisms to resist certain load effects, in which different ambiguities identified in Eurocode 2 are presented, explained and discussed in each subchapter. Each main chapter begins with a short description of the required structural response and way of modelling it in order to facilitate the understanding of the requirements presented, explained and discussed in the following subchapters. The investigating part of the project has been compiled in Chapter 11. This chapter contains presentations of the procedures and the results obtained from the interviews and the survey. The result from each question also contains a short discussion. In Chapter 12 the result from Chapter 11 is compared to, evaluated and analysed together with some of the results from the literature study presented in Chapter 4-10. A summary of the results obtained and the conclusions drawn in Chapter 12 is presented in Chapter 13, where references to relevant chapters in this report as well as to treated equations or paragraphs in Eurocode 2 are provided. Finally, more general conclusions and suggestions for further investigations are presented in Chapter 14. It should also be clarified that abbreviations and Swedish words that are used in the report are compiled and can be found with English translation in the beginning of this report. Throughout the report references are made to sections, paragraphs and equations in Eurocode 2. To clarify that a reference is referring to an item in Eurocode 2 the notation “EC2” has been added to the reference number. CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2013:142 5 2 Development of standards for design of concrete structures 2.1 Transition to the European Standards 2.1.1 Development of European Standards - Eurocodes In 1957 an international agreement named the Treaty of Rome was made between the following European countries: Belgium, France, the Federal Republic of Germany, Italy, Luxemburg and the Netherlands, Treaty of Rome (2013). The treaty established a common market and custom union named the European Economic Community, ECC, which was going to be an important part of the European Union, EU, created in 1993. As a result of the agreement in Rome the European Commission, EC, who is the executive part of the European Union, introduced the work of Eurocodes in 1975, JRC (2013). This was an action program in the field of construction meant to result in a harmonization of technical rules among the member states, EC (2003). In 1989 the European Commission approved the mandate to the European Committee for Standardisation, CEN, to prepare the Eurocodes, SIS (2013b). By that, the Swedish Standards Institute, SIS, got involved in the development of standardised rules for structural design by being a part of CEN. The publication of the first European Standards, EN, i.e. Eurocodes, started in the beginning of the 21 st century. These standards were based on the released pre- standards, ENV, that were published between 1992 and 1998, EC (2003). During 2006 a period began where both Eurocodes and other standards were used simultaneously for design of load-bearing structures, JRC (2013). At the start of 2011 it became mandatory in European countries including Sweden. Eurocode have ten main parts, depending on type of structure, see Table 2.1, which in turn are divided into several parts, SIS (2008). All these parts are regularly revised and updated versions are intended to be released about every five years, Johansson (2013). Table 2.1 Subdivisions of Eurocode. EN 1990 Eurocode 0: Basis of Structural Design EN 1991 Eurocode 1: Actions on structures EN 1992 Eurocode 2: Design of concrete structures EN 1993 Eurocode 3: Design of steel structures EN 1994 Eurocode 4: Design of composite steel and concrete structures EN 1995 Eurocode 5: Design of timber structures EN 1996 Eurocode 6: Design of masonry structures EN 1997 Eurocode 7: Geotechnical design EN 1998 Eurocode 8: Design of structures for earthquake resistance EN 1999 Eurocode 9: Design of aluminium structures CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2013:142 6 In Sweden SIS has distributed the responsibility of the Eurocodes on a number of technical committees. In order to meet the need for information about the Eurocodes in Sweden a homepage, www.eurokoder.se, and a helpdesk function, eurokoder@sis.se, have been established, SIS (2013c). 2.1.2 Development of Standards for design of concrete - Eurocode 2 Eurocode 2 is the collective name of the European Standards on design of concrete structures, SS-EN 1992, and the code is divided in eight parts presented in Table 2.2, SIS (2013d). Table 2.2 Subdivision of Eurocode 2. SS-EN 1992 Design of concrete structures SS-EN 1992-1-1 General rules and rules for buildings SS-EN 1992-1-2 General rules - Structural fire design SS-EN 1992-1-3 General rules - Precast element and structures SS-EN 1992-1-4 General rules - Lightweight aggregate concrete SS-EN 1992-1-5 General rules - Structures with unbonded and external prestressing tendons SS-EN 1992-1-6 General rules - Plain concrete structures SS-EN 1992-2 Concrete bridges - Design and detailing rules SS-EN 1992-3 Liquid retaining and containment structures Eurocode 2 part 1-1 containing general rules and rules for buildings is in the scope of this master’s project and is in the following recalled simply by Eurocode 2 or EC2. Eurocode 2 has to a large extent been developed from CEB-FIP Model Code, CEB- FIP (1978) , which was published in 1978 after a longstanding collaboration between the Euro-International Concrete Committee (CEB) and the International Federation for Prestressing (FIP) to produce international recommendations within the area of concrete structures, fib (2013). Since 1978 two more editions of Model Code have been published: CEB-FIP Model Code 1990 published in 1991, CEB-FIP (1991), and fib Model Code 2010 published in 2012, fib (2012). The latest were published by the International Federation for Structural Concrete (fib) which is a fusion between CEB and FIP that took place in 1998. At fib’s webpage the following purpose of Model Code 2010 is stated: “The objectives of MC2010 are to serve as a basis for future codes for concrete structures, and present new developments with regard to concrete structures, structural materials and new ideas in order to achieve optimum behaviour”. As a complement to Eurocode 2 the European Concrete Platform, ECP, a non-profit association aiming to promote concrete as the material of choice, has published Commentary to Eurocode 2, ECP (2008a) and Worked Examples for Eurocode 2, ECP (2008b). The reason for the development of these publications was to facilitate the transition to the new set of codes that by many were considered to be too general in character and therefore difficult to work with. CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2013:142 7 Another handbook that can provide additional information to the rules and guidelines in Eurocode 2 is Designer’s guide to EN 1992-2, Hendy and Smith (2010). This is published by Thomas Telford Publishing in collaboration with Eurocodes Expert, Eurocodes Expert (2013). The book refers mainly to design of concrete bridges in Eurocode 2, Part 2. However, it also covers the general rules and guidelines in Eurocode 2, Part 1, since Part 2 often refers to the general rules. It should be noted that this book refers to the British version of Eurocode 2. 2.1.3 Codes for design of concrete in Sweden In Sweden it is Boverket that is responsible for issuing building regulations for housing. Boverket is the successor of Byggnadsstyrelsen and Planverket. The predecessor to Eurocode in Sweden was Boverkets konstruktionsregler, BKR, which became effective in 1994, Boverket (2013). BKR, Boverket (1994), was in turn the successor of a number of building regulations that are presented in Table 2.3. Table 2.3 Building codes in Sweden from 1947 until today, Boverket (2013). Standard Published /Entry BABS Byggnadsstyrelsens anvisningar till byggnadsstadgan, BABS Byggnadsstyrelsen’s Instructions to the Building Charter 1946/1947 1950/1950 1960/1960 SBN Svensk byggnorm, SBN Swedish Building Code 1967/1968 1975/1976 1980/1982 PBL a) Plan- och bygglagen, PBL The Planning and Building Act 1987/1987 (2010/2011) NR Boverkets nybyggnadsregler, NR Boverket’s Rules for New Construction 1988/1989 1990/1991 1991/1992 1993/1993 BBR a) Boverkets byggregler, BBR Boverket’s Building Rules 1993/1994 BKR Boverkets konstruktionsregler, BKR Boverket’s Designing Rules 1993/1994 EKS a) Europeiska konstruktionsstandarder, Eurokoder, EK European Standards, Eurocodes, EC 2010/2011 a) Still valid The previous Swedish code for design of concrete structures was Boverkets handbok om betongkonstruktioner, BBK 04, Boverket (2004), and is thus the predecessor to Eurocode 2. BBK 04 was published by Boverket in 2004 as a supporting text to the application of regulations and general advice to the law on technical requirements for CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2013:142 8 structures in BKR, Boverket (1993). BBK 04 has in turn two predecessors, BBK 94, Boverket (1994), and BBK 79, Boverket (1979). It can be added that Model Code 78 has influenced the content in BBK 79. The new European Standard is developed to fit the requirements of its members. However, it has not been possible to fully satisfy the demands of all the countries and a number of nationally determined parameters, NDP, have therefore been introduced to the Eurocodes. These national parameters are in Sweden published by Boverket in BFS 2011:10 – EKS8, Boverket (2011) and by Trafikverket in VVFS 2004:43, Vägverket (2004), SIS (2013b). All relevant national parameters are also complied and attached to each Eurocode in a National Annex, NA, SIS (2008). It should be emphasised that the new European Standard and the previous Swedish code BKR and handbook BBK 04 treat combinations of loads and application of partial safety factors somewhat differently, resulting in that it is not possible to combine the rules and guidelines provided in the different codes. Examples of the differences can be found in Hammar (2011). 2.1.4 Additional information to the Swedish Standards In addition to the codes for design of concrete structures used in Sweden a number of different types of publications have been written. The text that lay the basis for BBK 79 was written by Statens Betongkommitté and contains provisions for design of concrete structures with comments (1975). It can be noted that this text is a draft and it was not allowed to be published or referred to. Another helpful book is Betonghandbok – Konstruktion edited by Svensk Byggtjänst in 1990, Svensk byggtjänst (1990). The book is a compliance of demands, design requirements, calculation methods, diagrams and examples on the basis of building codes in NR 89, Boverket (1989), and BBK 79, Boverket (1979), Svensk Byggtjänst (2013). Svenska betongföreningen has published a handbook to Eurocode 2, Betongföreningen (2010), which explains, comments and exemplifies rules and guidelines in order to facilitate the use of Eurocode 2 in Sweden. 2.2 Consequences due to poor detailing 2.2.1 General Poor detailing is something that needs to be avoided and is often coupled with lack of sufficient consideration in design in combination with poor workmanship at the construction site. This combination can lead to an insufficient performance, damages and catastrophic failure. Insufficient design can depend on that the designer has performed detailing of similar structures before and due to experience performs it in the same way, only with small modifications, in the next project. This may result in that important checks might not be performed and a safe structure is not ensured. If the designer does not know how to interpret the requirements, the development of the code is insignificant. This is why there is a need for further explaining of the background to expressions and paragraphs in Eurocode 2. In Sections 2.2.2 and 2.2.3 two different types of failure due to poor detailing will be briefly described. CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2013:142 9 2.2.2 Alvik’s Bridge and Gröndal’s Bridge The two tramway bridges in Stockholm were finished between the year of 1998 and 1999 and opened for traffic the same year and cost 2 million SEK to build, see Figure 2.1a, Aftonbladet (2002a). They are designed with a beam consisting of a hollow box section and are prestressed in the top and bottom of the cross-section, see Figure 2.1b, Ny Teknik (2002). In order to make the structure consistent and resistant against shear forces and torsional moment the vertical walls are reinforced with vertical shear reinforcement. Alviks Bridge Alviks bridge b) a) Alvik’s Bridge Gröndal’s Bridge Figure 2.1 Alvik’s Bridge and Gröndal’s Bridge in Stockholm, a) map showing the locations, b) photo of Gröndal’s Bridge taken from below and from the side. Inclined cracks in the webs of the bridge girder were observed already at the first inspection, Aftonbladet (2002b). However, the cracks of the two bridges became, after three years of use, too large. This is a problem in the service state with regard to corrosion of the reinforcement. Consulted experts are still not sure if it was any danger with regard to resistance in the ultimate limit state. The reason for insufficient crack control depended on insufficient amount of transverse reinforcement. It should be mentioned that no one got injured due to the cracks. According to Håkan Sundqvist, professor in bridge building at KTH, the shear reinforcement should have been three times as large as the amount that was provided, Ny Teknik (2002a). The designer's that were responsible for the detailing of the bridges state that the current code in Sweden regarding bridges has been followed. The designers argue that the code might be wrong since external consultant companies have controlled the calculations and no errors could be found, Aftonbladet (2002c). However, when comparing to the, then upcoming, European standard Eurocode and German and American codes the requirements in the Swedish code were significantly lower. The difference can depend on that larger effect of prestressing was accounted for differently in the Swedish code, which led to lower need of shear reinforcement. However, the problem was also that it in the Swedish code was no clear instructions for control of crack widths in the service state and in combination with the fact that cracks can occur due to other effects than because of external loads, Engström (2013). A master’s thesis performed at Chalmers University of Technology in 2003 implied CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2013:142 10 that the cracks at the two bridges occurred because of restraint stresses caused by temperature changes, Borbolla and Mazzola (2003). After the cracks were detected and the bridges were closed, the girders were at first preliminary reinforced in order to get traffic moving as quick as possible, Ny Teknik (2002), and in 2002 the final reinforcement of the bridge was performed. When Vägverket, current Trafikverket, performed calculations later on, they realised that a limitation of the utilised steel stress in the ultimate limit state of 250 MPa would probably be sufficient in order to keep any inclined shear cracks sufficiently small in the service state. This was only a fast and temporary requirement that Vägverket recommended. However, it was removed later on and replaced by the rules in Eurocode. This problem is mainly related to the rules for checking crack widths of inclined cracks in webs and minimum reinforcement for crack control in the service state. 2.2.3 Sleipner concrete off shore platform The offshore platform named Sleipner included a large cellular concrete structure below the three towers, see Figure 2.2, Whittle (2013). During the construction the platform was lowered down in the water in order to interfitting the deck. After this the plan was to raise the platform again and tow it to its final position in the oil field. One of the tri-cells failed just before the deck mating took place. Thereafter the structure started to take in water which resulted in sinking and a total collapse at the sea bottom occurred. Alviks bridge b) a) Figure 2.2 The offshore platform Sleipner a) during construction, b) plan section of cell structure. Figure a) is taken from and figure b) is based on Whittle (2013). The tri-cells were from the beginning designed in order to resist the water pressure, see Figure 2.3b. However, the cylindrically shaped walls were changed to having more sharp edges, see Figure 2.3a. In this case the natural arch action could not be utilised. The modification was made because the formwork became simpler to construct. CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2013:142 11 Alviks Bridge Alviks bridge Gröndals Bridge b) a) Alviks Bridge Gröndals Bridge Water pressure High tensile stresses Figure 2.3 Detail of tri-cells with a) sharp edges and b) cylindrical edges. The figure is based on Whittle (2013). The design of the cell structure was carried out by an analysis using finite element models. However, the quadratical elements used in the analysis did not capture the entire response of the structure and the elements at the edges of the tri-cells became distorted from the ideal square shape. It has been realised after the collapse that the analysis provided values of the shear stresses on the unsafe side. T-headed bars were used in the critical shear sections, see Figure 2.4. In order to get a sufficient design and capture the whole stress field the bars should extend across the full width of the cross-section. However, they were difficult to anchor through the outer layer of reinforcement why the bars were shortened. Alviks Bridge Alviks bridge Gröndals Bridge a) Alviks Bridge Gröndals Bridge Water pressure Initial cracking Compression zone T-headed bar as required T-headed bar as placed Figure 2.4 Section through the tri-cells where failure occurred. The figure is based on Whittle (2013). During the submerging of the structure a crack developed at a corner of the cell where the propagation accelerated due to the water pressure. The crack eventually spread to the other end at the compression zone and resulted in a brittle failure. In linear elastic analysis high tensile stresses were observed in the region where the inclined cell walls meet. However, it was not fully understood how the corresponding tensile force must be resisted in cracked reinforced concrete. The failure at the corner of the cell could have been prevented and so also the collapse of the whole structure by elongating the transverse reinforcement along the full width CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2013:142 12 of the cross-section. This mistake in detailing can be assumed to be the main reason why the structure failed. Another way to prevent failure could have been to ensure that sufficient arch action can take place by changing the shape of the tri-cells to intersected cylinders. The element mesh used in the finite element program was too coarse in order to get accurate result and was needed to be made finer. At the time the designer was involved in three other more complicated platforms. This, in combination with that it was a type of structure that was well established, resulted in that few checks of the design and detailing were performed. The rebuilding of the platform was made with cylindrical shaped tri-cells and T-headed bars that were extended to the outer reinforcement. This problem is mainly related to transformation of calculation results of structural analysis to proper reinforcement detailing that fulfils equilibrium in cracked reinforced concrete in the ultimate state. 2.3 Compilation of ambiguities in Eurocode 2 The European standard, Eurocode 2, summarises information and knowledge concerning design of structural members in concrete and becomes like a tool for the daily work of structural engineers. The code tries to facilitate the design process by presenting the rules and guidelines in and recalling some of the basic theories in a brief way. This can cause problem since the information in the standard is not written in an educational manner and a lot of background information is missing explaining motivations and reasons for the requirements. Therefore it can in several paragraphs be difficult to interpret the different rules and requirements. This risk concerning incorrect interpretations of the standard can lead to insufficiently designed or detailed structures that will not fulfil the demands in the ultimate limit state and serviceability limit state. This is why a careful investigation of the different rules and requirements in the standard was performed in this project in order to highlight problem areas that will be further discussed in this report, see Chapter 4-10. In these chapters the requirements in the code are further explained and clarified. This will hopefully facilitate the interpretation and increase the probability in reaching acceptable design and detailing solutions. Table 2.4 to Table 2.10 give an overview of different paragraphs and expressions in Eurocode 2 that are treated in this report and each table correspond to one chapter in the report. These tables are based on a larger compilation of ambiguities concerning reinforcement in concrete structures identified in Eurocode 2. This compilation can be found in Appendix A and B. In Appendix A the ambiguities and questions that laid the base for Chapter 4-10 in this report are presented and in Appendix B additional questions found in Eurocode 2 during the initial literature study are stated. It should be noted that all questions presented in Appendix A have not been fully answered in this report, but most of them have been explained or discussed in some way. CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2013:142 13 Table 2.4 Paragraphs and expressions in Eurocode 2 treated in Chapter 4, Bending. Paragraph in EC2 Expressions, figures and tables Subject Section in report 9.2.1.1 (1) (9.1)N Minimum reinforcement 4.2 9.2.1.1 (3) Maximum reinforcement 4.3 5.6.2 (2) Ductility requirements 4.3 5.6.3 (2) Ductility requirements 4.3 J.2.2 (4), J.2.3 (1), (2) Fig. J.2, Fig. J.3, J.4 Concrete frame corners 4.4 CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2013:142 14 Table 2.5 Paragraphs and expressions in Eurocode 2 treated in Chapter 5, Shear. Paragraph in EC2 Expressions, figures and tables Subject Section in report 6.2.3 (3), (4) (6.8), (6.13) Needed shear reinforcement 5.2 6.2.3 (3), (4) (6.9), (6.14), (6.12), (6.15) Maximum shear reinforcement 5.3 9.2.2 (5) (9.4), (9.5N) Minimum shear reinforcement 5.4 9.2.2 (6), (7), (8) (9.6N), (9.7N), (9.8N) Spacing of shear reinforcement, beams 5.4 9.3.2 (4), (5) (9.9), (9.10) Spacing of shear reinforcement, slabs 5.4 6.2.1 (4), (5) Minimum shear reinforcement 5.4 6.2.3 (2), (7) (6.18), (6.7N) Additional tensile reinforcement due to shear cracks, θ 5.5 9.2.2 (1) Additional tensile reinforcement due to shear cracks, α 5.5 9.2.2 (2), (4) Fig. 9.5 Detailing of shear reinforcement, beams 5.6 9.3.2 (2), (3) Detailing of shear reinforcement, slabs 5.6 6.2.3 (8) (6.19), Fig. 6.6 Load close to supports 5.7 6.2.2 (6) Load close to supports 5.7 6.2.1 (8) Load close to supports 5.7 9.2.5 (1), (2) Fig. 9.7 Indirect support Suspension reinforcement 5.8 6.2.1 (9) Suspension reinforcement 5.8 9.2.1.4 Fig. 9.3 Indirect support 5.8 CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2013:142 15 Table 2.6 Paragraphs and expressions in Eurocode 2 treated in Chapter 6, Torsion. Paragraph in EC2 Expressions, figures and tables Subject Section in report 6.3.2 (1) (3) (6.28), Fig. 6.11 Longitudinal torsion reinforcement 6.2 9.2.3 (4) Longitudinal torsion reinforcement 6.2 6.3.2 (1), (4) (6.26), (6.27), (6.29), (6.30) Transversal torsion reinforcement 6.3 9.2.3 (1), (2), (3) Fig. 9.6 Detailing of torsion reinforcement 6.3 9.2.2 (3) Detailing of torsion reinforcement 6.3 6.3.2 (2), (4) (6.29) Combination of shear and torsion 6.4 Table 2.7 Paragraphs and expressions in Eurocode 2 treated in Chapter 7, Shear between web and flanges. Paragraph in EC2 Expressions, figures and tables Subject Section in report 6.2.4 (3), (6) (6.20), Fig. 6.7 Shear between web and flanges, longitudinal shear stress 7.2 6.2.4 (4), (5) (6.21), (6.22) Shear between web and flanges, transversal reinforcement 7.3 Table 2.8 Paragraphs and expressions in Eurocode 2 treated in Chapter 8, Shear friction and dowel action. Paragraph in EC2 Expressions, figures and tables Subject Section in report 6.2.5 (1), (3), (4) (6.23), (6.24), (6.25), Fig. 6.10 Shear at the interface between concrete cast at different times 8.2, 8.3 - Dowel action 8.4 CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2013:142 16 Table 2.9 Paragraphs and expressions in Eurocode 2 treated in Chapter 9, Bond and anchorage. Paragraph in EC2 Expressions, figures and tables Subject Section in report 6.2.3 (7) Curtailment of reinforcement 9.2 6.2.2 (5) Curtailment of reinforcement 9.2 9.2.1.1 (4) Curtailment of reinforcement, beams 9.2 9.2.1.3 (1), (2) (9.2), Fig. 9.2 Curtailment of reinforcement, slabs 9.2 8.4.3 (2) (8.3) Basic anchorage length 9.3 8.4.4 (1) (8.4) Anchorage length 9.3 8.4.2 (2) (8.2) Design ultimate bond stress 9.3 9.2.1.4 (1), (2), (3) (9.3), Fig 9.3 Anchorage of bottom reinforcement at supports, beams 9.3 9.3.1.2 (1) Anchorage of bottom reinforcement at supports, slabs 9.3 6.5.4 (7) Fig. 6.27 Anchorage of reinforcement in compression-tension nodes 9.3 8.7.2 (2), (3), (4) Fig. 8.7 Lapping of reinforcement 9.4 8.7.3 (1) (8.10), Tab. 8.3 Lap length 9.4 8.7.4.1 Transversal bars in the lap zone 9.4 4.4.1.2 (1), (2), (3) (4.2), Tab. 4.2 Concrete cover 9.5 4.4.1.1 (2) Concrete cover 9.5 4.4.1.3 (1) Concrete cover 9.5 8.2 (1), (2), (3) Clear distance between bars 9.5 8.3 (3) (8.1) Mandrel diameter 9.6 CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2013:142 17 Table 2.10 Paragraphs and expressions in Eurocode 2 treated in Chapter 10, Crack control. Paragraph in EC2 Expressions, figures and tables Subject Section in report 7.3.2 (1), (2) (7.1) Minimum reinforcement for crack control 10.2 7.3.3 (2) Tab. 7.2N, 7.3N, (7.6N), (7.7N) Simplified method for crack control 10.2 7.3.1 (2) Crack control for shear and torsion 10.3 7.3.4 (1), (2), (3) (7.8), (7.9), (7.10), (7.11), (7.14), (7.15) Calculation of crack width 10.3 CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2013:142 18 3 Reinforced concrete structures 3.1 Material properties Concrete has been used as a structural material for thousands of years. Floorings made of concrete discovered in southern Israel have been dated to as early as 7000 B.C., Domone (2010). It is also well known that the old Greek and Roman societies used concrete to build large structures, such as Pantheon in Rome Figure 3.1 that dates back to about 125 A.D, Fazio et al. (2008). Figure 3.1 Pantheon in Rome. Figure is taken from Fazio et al. (2008). Pantheon is a good example of that the Romans knew the properties of concrete and how to work with such a material. The building is made out of arches and vaults, not to mention the gigantic dome; –structures that transfer forces mainly in compression. In Figure 3.2 a schematic stress-strain relation of concrete is presented, showing that concrete is much stronger in compression than in tension, something that the Romans obviously knew. σc εc fct fcc compression tension Figure 3.2 Schematic stress-strain relation of concrete. Due to its small strength in tension concrete is a material with important limitations. During the 19 th century the first reinforced concrete structures were introduced, Building Construction (2013), gaining from the advantageous properties of steel in tension, see Figure 3.3. Ordinary reinforcing steel has a tensile strength at yielding, fy, of about 500 MPa which can be compared to the tensile strength of concrete which is about 1.6-5.0 MPa dependent on concrete class, SIS (2008). CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2013:142 19 σs εs fy tension fu εsu Figure 3.3 Schematic stress-strain relation of reinforcing steel in tension. In design it is however convenient to use simplified stress strain relations for steel and concrete. Since it is favourable to let the concrete take compressive forces, while the reinforcement should act in tension the simplified relations for concrete in compression and steel in tension are of interest, see Figure 3.4 and Figure 3.5. These figures show both characteristic stress strain relations, denoted with the letter k, and the relations used in design situations, denoted with the letter d. σc εc fck fcd εc2 εcu2 σc εc fck fcd εc3 εcu3 a) b) Figure 3.4 Material models for compressed concrete, a) simplified parabolic- rectangular curve. b) simplified bi-linear curve. The figures and notations are based on SIS (2008). CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2013:142 20 σs εs fyk fyd εud εuk a) b) σs εs fyk fyd εud εuk kfyk kfyd kfyk Figure 3.5 Material models for reinforcing steel in tension, a) simplified bi-linear curve with inclined top branch, b) simplified bi-linear curve with horizontal top branch. The figures and notations are based on SIS (2008). It is a common misunderstanding that reinforcement is used in concrete to avoid cracking. This is however not the case, if not talking about prestressed concrete that is out of the scope of this project. For uncracked concrete the reinforcement has very limited influence and the concrete will crack when its tensile capacity is reached. This can be illustrated by a moment-curvature relation, see Figure 3.6, where the concrete cracks at Mcr. M 1/r Mcr Uncracked Cracked Uncracked Cracked Figure 3.6 Response of reinforced concrete cross-sections before and after cracking. The reinforcement will nevertheless contribute to the distribution of cracks and hence to the limitation of crack widths after cracking of concrete. This is illustrated in Figure 3.7. Figure 3.7 Response of plain and reinforced concrete. CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2013:142 21 Reinforcement will not only contribute to the tensile capacity of reinforced concrete structures, but it will also contribute to the ductility since it enables redistribution of forces in a structure, which is a desirable property. In Eurocode 2 the ductility class of reinforcing steel is defined by characteristic values of the ratio of tensile strength to the yield stress, k = (fu / fy)k and as the strain, εuk, at maximum tensile force, Betongföreningen (2010a). Different types of reinforcing steel hold different ductility properties and are therefore divided into three classes in Eurocode 2: A, B and C. Type B steel, e.g. B500B, is the most commonly used reinforcing steel in Sweden except for seismic design where the more ductile type of steel, class C, is used, Johansson (2013). It should be noted that the ductility of the reinforcement is not the same as the ductility of the structure. The behaviour of the structure is affected also by other properties as the bond between steel and concrete and the amount of reinforcement in relation to concrete, Betongföreningen (2010a). It should be noted that Eurocode 2 Part 1-1 is valid for normal strength steel within a yield strength range, fyk, from 400 MPa to 600 MPa and applies to ribbed and weldable reinforcement. Hence, no recommendations are given of how to proceed for plain bars, which is a problem in analysis of old concrete structures containing this type of reinforcement. The previous Swedish handbook BBK 04, Boverket (2004), did provide rules that applied for plain bars as well and can give some guidance of how to handle this problem. This is one example of how the technical development over the years results in uncertainties in how to use the codes in a correct manner. Over time there have been large changes in material properties of both concrete and reinforcing steel, Whittle (2013). The development of strength properties of both materials has increased significantly during the 20 th century. For concrete this is much thanks to the use of admixtures that have become common since the 1980s. Although this trend is a good thing, making the materials stronger, there is also a backside. Expressions and rules of thumbs used in Eurocode 2 can have been developed a long time ago and might be based on empirical results. It is therefore important to know and understand the background to, and under what conditions, the expressions were developed, in order to know if they are applicable to material properties of today. However, it can be assumed that the expressions provided in the codes are valid for the specified steel and concrete classes. Examples of this will be shown in this report, for instance in Section 4.2 concerning minimum reinforcement requirements in beams. 3.2 Transfer of forces between the materials 3.2.1 Bond between reinforcing steel and concrete Understanding about how forces are transferred between the materials, steel and surrounding concrete, is necessary when performing structural design. Transmission of forces between the materials depends on the roughness of the bar, i.e. if it is a plain or a deformed bar. The reinforcement normally used in Sweden is heat treated ribbed bar (K500B), hot-rolled ribbed bar (Ks600S) and cold-worked indented bar (Ps500), Engström (2011a). When a reinforced concrete member is loaded, the transmission of forces is due to bond stresses, τb, which are acting along the bar’s mantle surface within the transmission length, see Figure 3.8. CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2013:142 22 Ft τb transmission length, lt Figure 3.8 Bond stress acting along the bar’s mantle within the transmission length. The figure is based on Engström (2011a). The bond stress is largest closest to the loaded end of the bar and decreases successively along the bar. It should be noted that the bond stress is related to a certain deformation, slip, between the surface of the steel and the surrounding concrete. For moderate loads in the service state the slip increases in relation to bond stress, see Figure 3.9. N F c μN F N b) a) τb(x) slip slip lt τb(x) lt σs(x) τb(x) σs(x) τb(x) Fs1 Fs2 slip a) b) Figure 3.9 Inclined cracks occur out from the ribs from the reinforcing bar subjected to tension due to transfer of forces between the materials. The figure is based on Engström (2011a). Figure 3.9a illustrates how the bond stress varies for a bar subjected to a small tensile force. In this case the bond stress is only generated along a part of the embedded reinforcing bar. Hence, the transmission length, lt, is smaller than the available bar length. The bar will slip with different values along the transmission length. This depends on the fact that the tensile force decreases along this length, which results in horizontal equilibrium. Hence, the steel strain will also decrease successively along the bar. The maximum slip occurs at the loaded end, while it in the other end of the transmission length will not slide at all. Figure 3.9b illustrates how the bond stress and the transmission length both have increased when a large tensile force is acting on the bar, which also results in a large steel stress. In the case shown in Figure 3.9b the bond stress is acting along the whole length of the bar, i.e. the transmission length is equal to the available anchorage CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2013:142 23 length. This means that the whole bar is sliding, however, with different magnitudes in different sections. As can be seen in Figure 3.9b the bond stress will not be zero at the end of the bar since the whole bar is sliding. However, this is not the case for the steel stress which needs to be zero at the end of the bar. It can be noted that for moderate loading a large slip will generate large bond stress. When the tensile force in a section of the bar is small the bond stresses in this section depend on adhesion. However, when the force becomes larger, the bond stresses depend on the shear key effect that is obtained due to the roughness of the surface. It should be noted that in the ultimate state splitting cracks may occur around the bar resulting in that the bond stresses are evened out and the distribution becomes more uniform along the anchorage length. When a bar is pulled by a tensile force, shear stresses between the steel and the surrounding concrete give rise to inclined principal compressive stresses and principal tensile stresses in the regions of the concrete closest to the bar. Cracking will occur, with an angle out from the ribs of the bar, if the concrete tensile strength is reached, see Figure 3.10a. τb τb∙tan α α N a) b) Figure 3.10 Reinforcing bar subjected to tension, a) inclined cracks occur out from the ribs from the reinforcing bar, b) inclined compressive forces due to shear key effect between the surfaces of the reinforcing bar and the surrounding concrete. The figure is based on Engström (2011a). At this stage it is in general the inclined compressive forces that are anchoring the bar into the concrete, see Figure 3.10b. The longitudinal component of the compressive stress can be described as the bond stress, τb. The transversal component can be calculated as τb tanα, where α is the angle between the bar and the inclined compressive force. Figure 3.11 shows how the compressive force is spread in all directions out from the bar, creating compressed conical shells. These shells only exist between the cracks and start from the ribs of the bar. The compressed conical shell needs to be equalised by tensile forces due to equilibrium. This is achieved by tensile stresses in the concrete in form of tangential stresses formed as a ring at the bottom of the cone. CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2013:142 24 α F μN F α Figure 3.11 Compressive forces that are spread in all direction in a compressed conical shell that is hold together by tensile stresses in the concrete at the outer edge. The figure is based on Engström (2011a) who has borrowed it from Tepfers (1973). If the concrete cover is small in relation to the bar dimension, splitting cracks may occur, see Figure 3.12. These cracks can be described by looking at the bar as a tube. The tube has a large inner pressure, which results in radial compressive stresses to the surrounding concrete that needs to be equalised by tensile stresses in the tangential direction, see Figure 3.12. The tensile stresses cause splitting cracks when the concrete tensile strength is reached. At this stage the effect of the circle in Figure 3.11 is lost. tensile circle F μN F new equilibrium condition spalling crack the circle bursts Figure 3.12 Radial compressive stresses are balanced by tension stresses in the tangential direction. If the tensile strength of the concrete is reached splitting cracks through the concrete cover will occur. The figure is based on Engström (2011a). To counteract a decrease of stiffness in the concrete section when splitting cracks occur transverse reinforcement can be provided within the concrete cover and perpendicular to the anchored bar. If the concrete cover is sufficient, the concrete can equalise the radial component of the inclined compressive force and thereby prevent the splitting cracks. Then it is instead the longitudinal component of the compressive force, see Figure 3.10b, which becomes critical for the failure. The concrete between the ribs of the bar will be crushed and sheared off. When the bar starts to slide significantly, frictional forces develop due to the compressive stresses that are still acting at the mantle surface. It can be explained as the bar will be prevented to slide because of the ribs that are embedded in the concrete. Three different types of anchorage failure can be distinguished:  pullout failure in concrete without splitting cracks, see Figure 3.13a  pullout failure in concrete with splitting cracks  splitting failure, see Figure 3.13b CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2013:142 25 If the concrete cover is sufficient pullout failure will occur without splitting cracking, see Figure 3.13a. In order to get pullout failure without splitting cracks it is recommended to use a concrete cover of 3ϕ, where ϕ is the diameter of the anchored bar and a large distance between adjacent bars. This type of failure will give an upper limit for the anchorage capacity. If the concrete cover or distance between adjacent bars is insufficient, then splitting cracks will occur through the concrete cover or between the bars. However, if transversal reinforcement is provided the final failure will be pullout failure with splitting cracks, but with a lower anchorage capacity than what is btained when splitting cracks are avoided, since the concrete cover is weakened by cracks in this case. The capacity is affected by the amount of transversal reinforcement. If the concrete cover is small and no, or an insufficient amount, of transversal reinforcement is provided, splitting cracks might lead to spalling of the concrete so that the reinforcing bar is detached, see Figure 3.13b. This type of splitting failure will have a sudden and brittle nature. The expected failure when designing beams and slabs with regard to anchorage is pull-out failure with splitting cracks or splitting failure. In order to prevent very brittle failure of the member a certain amount of transversal reinforcement is helpful. In Chapter 9 more about bond and anchorage of reinforcement in concrete is explained. b) a) Figure 3.13 Different types of anchorage failure, a) pullout failure without splitting cracks in the case of large concrete cover, b) splitting failure when the concrete cover is small. The figure is based on Engström (2011a). CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2013:142 26 3.2.2 Friction The frictional force can in a simple way be defined as the friction coefficient times the normal force, FvR = μN, and describes the shear resistance when two elements are sliding along an interface. The frictional force acts in the opposite direction to the force, F, that causes the movement, see Figure 3.14a. It develops from the roughness of the surfaces that are sliding against each other. Friction expresses the resistance of movement and cohesion expresses the molecular forces and interlocking effects holding an element together. Note that cohesion also exists when no normal force is acting on the body, see Figure 3.14b. N load effect, F resistance, FvR = μN C μN FvR N b) a) Figure 3.14 Frictional resistance, a) model of the frictional force, b) the relation between the normal force and friction force. Here the cohesion, C, gives a start value for the shear force. The cohesion, C, gives a start value for the shear force and can be calculated according to Equation (3.1). This can be compared to the cohesion coefficient, c, in Figure 3.15c where it gives a start value for the shear stress, τ. The cohesion factor, c, is part of a general model and can express various effects which results in that the cohesion between concrete elements is difficult to describe. cctct AfcFcC  (3.1) Fct tensile force taken by the concrete c cohesion coefficient fct tensile strength of concrete Ac area of the concrete nR c   (3.2) σn normal stress μ friction coefficient where  tan (3.3) ϕ frictional angle CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2013:142 27 σn a) s w τ τ σn c) c τ σn b) τ τ wmax s Figure 3.15 Model for shear resistance along an interface, a) shear slip, s, develops which results in a lateral joint separation, w, and b) eventually in wmax, c) relationship between the normal stress and the shear stress. The cohesion also depends on the scale, Engström (2013). When the scale is normal it can be understood as a glue-effect between the interfaces, see Figure 3.16a. However, when the scale is smaller and a microscope is used, see Figure 3.16b, it is the sharp edges of the roughness at the interface that hooks into each other, called interlocking effects. When slip occurs along the interface, contact regions at the irregular joint face, are successively teared off contributing to the shear resistance. This will prevent the shear sliding to develop and that adds to the cohesion factor. Due to this the cohesion can be regained even after cracking has occurred. Small scale – very rough surface a) Small scale – rough surface Large scale – smooth surface b) Figure 3.16 Different levels of the scale describe the cohesion in different ways, a) glue-effect holds the joint interface together, b) interlocking effects. When a joint, consisting of concrete surfaces, is subjected to a shear force along a joint a shear sliding, s, develops, fib (2008). The frictional resistance that is obtained can be compared to shear transfer in cracks due to aggregate interlock effects and can be determined by Equation (3.2), see Figure 3.15c. The aggregate interlock effect can be described by wedging of the joint interface surface. When the roughness of the joint faces is more distinct, the influence of aggregate interlock will be more significant, i.e. the shear damage of the joint faces will contribute to the shear resistance. The roughness of the joint interface will generate a joint separation, w, when it is subjected to a shear displacement, s, see Figure 3.15a, fib (2008). The maximum shear slip, wmax, is determined by adding the largest tip of the irregularities of each adjoining member’s surface, see Figure 3.15b. The shear slip, and hence the joint separation, is decreased if a transverse compression force is acting on the joint interface. This compression force can be an externally imposed load or the pullout resistance of reinforcing bars crossing the interface. CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2013:142 28 3.2.3 Shear friction at joint interface with transverse reinforcement One of the basic mechanisms for shear transfer is frictional resistance in joint interfaces, fib (2008). It should be noted that this mainly refers to connection in precast members. The frictional resistance is further on referred to as shear friction. When the joint contains transverse reinforcement and is subjected to shear sliding, s, internal compressive forces are generated acting on the concrete, due to the pullout resistance of the transverse reinforcing bar, see Figure 3.17. When the shear slip develops along the joint it will separate because of the roughness of the concrete. This separation causes tensile stresses in the transverse bars and the tensile forces needs to be equalised by a compressive force of the same magnitude acting across the joint. This self-generated compressive force will clamp the adjacent concrete elements together; see Figure 3.17b and Figure 3.17c. Nc Nc Fv Fv μNc s w Δσc σs σs a) b) c) Fv Fv s Figure 3.17 Shear transfer at joint, a) external compression across the joint, b) and c) compression is generated by the pullout resistance of transverse bars across the joint. The figure is based on fib (2008). The shear transfer at a joint interface can be visualised schematically as shown in Figure 3.18, fib (2008). Here the saw-tooth geometry expresses the roughness of the joint interfaces and the inclination of each tooth is equal to the frictional angle, ϕ. This is actually a good illustration of how the shear force is transferred. The most pronounced irregularities of the joint face will be loaded first. The shear force creates high concentrated stresses at these spots that eventually will result in local crushing of the irregularities and shear-off of tips and sharp edges. When this has occurred the roughness will be more even and symmetric as shown in Figure 3.18. w s Δσs Δσs As Δσc Δσc = ρΔσs τR = μΔσc Figure 3.18 Schematic model of how the shear force is transferred by friction due to the pullout resistance of the transversal bars across the joint interface. The figure is based on fib (2008). If the joint is designed with properly placed transverse reinforcement, the pullout resistance of the bars will increase the shear capacity, since the reinforcement generates a compressive force at the joint interface making friction possible, CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2013:142 29 fib (2008). When the bars yield maximum shear resistance is reached. The conditions for this model are:  rough surfaces that gives a separation, w, when shear displacement, s, occurs  sufficient bond resistance between the steel and the concrete that will give large local steel strains for small shear displacement. Here a smaller bar diameter gives better result. If these two conditions are not fulfilled a different behaviour will develop in form of dowel action, which will give a lower shear capacity, see Section 3.2.4 and Chapter 8. 3.2.4 Dowel action A basic mechanism of shear resistance in concrete joint is dowel action of a partly embedded steel bar, fib (2008). As for shear friction at joint interface with transverse reinforcement this refers mainly to connection in precast members. The dowel action of transverse steel bars, pins and bolts resists the load by shear displacement, s, between the joint interfaces. When the dowel is loaded in shear it is supported by the concrete on the opposite side of the dowel where the load is acting. If comparing dowel action and shear friction the steel bar in the former case will fail in bending and the latter in tension. Thus, for the same steel bar and joint, the steel bar is more effectively used in shear friction than in dowel action. The shear resistance in shear friction is greater than the shear resistance in dowel action. Which type is decisive depends on the pull-out resistance of the bar and the roughness of the joint. You don´t need to take dowel action into account when designing a joint, if it is rough and the bars are well anchored. The shear force capacity of the connection is influenced by many factors, for instance the size of the dowel, the strength of the steel and concrete or the concrete cover of the dowel pin, fib (2008). The following failure modes can be distinguished  concrete splitting failure  steel shear failure  steel flexural failure (combined steel/concrete failure) Splitting cracks in the concrete is one of the failures that can occur in dowel connections between concrete elements, fib (2008). When the dowel is loaded in shear, high concentrated compressive forces will be applied to the area surrounding the dowel. When these forces are spread substantial tensile stresses develop in the concrete. Splitting cracks are likely to occur even for small shear forces, if the dimensions of the concrete elements are small or if the concrete cover of the dowel is inadequate. This can limit the shear resistance of the connection by causing a premature brittle failure. It is of importance that the c