Univerza v Ljubljani Fakulteta za gradbeništvo in geodezijo Primož Može, univ. dipl. inž. grad. Ductility and resistance of bolted connections in structures made of high strength steels DOCTORAL THESIS Duktilnost in nosilnost vijaČenih spojev v konstrukcijah, narejenih iz jekel visoke trdnosti DOKTORSKA DISERTACIJA Podiplomski študij gradbeništva Ljubljana, 2008 Univerza v Ljubljani Fakulteta za gradbeništvo in geodezijo PODIPLOMSKI ŠTUDIJ GRADBENIŠTVA KONSTRUKCIJSKA SMER DOKTORSKI ŠTUDIJ Kandidat: PRIMOŽ MOŽE, univ. dipl. inž. grad. DUCTILITY AND RESISTANCE OF BOLTED CONNECTIONS IN STRUCTURES MADE OF HIGH STRENGHT STEELS Doctoral thesis No.: 180 DUKTILNOST IN NOSILNOST VIJAČENIH SPOJEV V KONSTRUKCIJAH, NAREJENIH IZ JEKEL VISOKE TRDNOSTI Doktorska disertacija štev.: 180 Temo doktorske disertacije je odobril Senat Univerze v Ljubljani na 7. seji dne 27. junija 2006 in imenoval mentorja prof. dr. Darka Bega. Pisanje doktorske disertacije v angleškem jeziku je odobril Senat Univerze v Ljubljani na 7. seji dne 27. junija 2006. Ljubljana, 6. maj 2008 Univerza v Ljubljani Fakulteta za gradbeništvo in geodezijo Komisijo za oceno ustreznosti teme doktorske disertacije v sestavi prof. dr. Darko Beg izr. prof. dr. Jože Korelc prof. dr. Dan Dubina, Politehnica University of Timisoara, Romunija je imenoval Senat Fakultete za gradbeništvo in geodezijo na 9. redni seji dne 19. aprila 2006. Komisijo za oceno doktorske disertacije v sestavi prof. dr. Darko Beg izr. prof. dr. Jože Korelc prof. dr. Dan Dubina, Politehnica University of Timisoara, Romunija je imenoval Senat Fakultete za gradbeništvo in geodezijo na 16. redni seji dne 26. marca 2008. Komisijo za zagovor doktorske disertacije v sestavi prof. dr. Bojan Majes, dekan, predsednik prof. dr. Darko Beg izr. prof. dr. Jože Korelc prof.dr. Dan Dubina, Politehnica University of Timisoara, Romunija je imenoval Senat Fakultete za gradbeništvo in geodezijo na 17. redni seji dne 23. aprila 2008. Univerza v Ljubljani Fakulteta za gradbeništvo in geodezijo IZJAVA O AVTORSTVU Podpisani PRIMOŽ MOŽE, univ. dipl. inž. grad., izjavljam, da sem avtor doktorske disertacije z naslovom: “DUKTILNOST IN NOSILNOST VIJAČENIH SPOJEV V KONSTRUKCIJAH, NAREJENIH IZ JEKEL VISOKE TRDNOSTI”. STATEMENT OF AUTHORSHIP I, undersigned Primož Može, Univ. B.C.E., hereby declare that I am the author of the doctoral thesis titled: “DUCTILITY AND RESISTANCE OF BOLTED CONNECTIONS IN STRUCTURES MADE OF HIGH STRENGTH STEELS”. Ljubljana, 6.5.2008 (podpis/signature) Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. VII Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. ERRATA Page Line Error Correction Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. IX Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. BIBLIOGRAPHIC-DOCUMENTALISTIC INFORMATION UDC: 624.014.2:624.078(043.3) Author: Primož Može Supervisor: Prof Darko Beg Title: Ductility and resistance of bolted connections in structures made of high strength steels Notes: 156 p., 29 tab., 130 fig., 118 eq., 6 app. Keywords: high strength steel, ductility, bolted connections, net cross-section, tension splices Abstract Structural steel grades with yield strength higher than 420 MPa are considered as high strength steels. They undoubtedly have lower ductility than mild steels in terms of engineering measures of ductility, such as ultimate-to-yield strength ratio, uniform strain and elongation at fracture. A typical values for high strength steels are: ultimate-to-yield strength ratio fulfy = 1,05, uniform strain su = 0,05 and elongation after fracture sfr = 15%. The problem is that inelastic behaviour is hidden in numerous nominally elastic resistances checks of steel structures and therefore sufficient local ductility has to be assured. The focus is set on structural elements with holes subjected to tension and to tension splices with bolts in shear. Local ductility in terms of plastic deformations has to be sufficient in order to assure bolthole elongation, so the loading transfers through ali bolts. An extensive experimental research of plates with holes and tension splices made of steel grade S690 was conducted to determine maximum resistance and ductility. The reliability of the Eurocode design rules for net cross-section resistance to was statistically evaluated. The statistical analysis was substantiated by additional test results on net cross-section failure of high strength steel members available in literature. Moreover, the experiments were numerically simulated to look inside the stress state. The test results served as a guideline for the accuracy of numerical simulations. A comprehensive numerical parametrical study of tension splices and in addition, the numerical analyses of tests on tension splices found in literature were performed. The Eurocode design bearing resistance was critically assessed on the basis of the database of 266 connection results. In certain cases the Eurocode design bearing resistance formula gives inadequate results. Therefore, a new, simple design bearing resistance formula was proposed. Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. XI Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. BIBLIOGRAFSKO-DOKUMENTACIJSKA STRAN IN IZVLEČEK UDK: 624.014.2:624.078(043.3) Avtor: Primož Može Mentor: prof. dr. Darko Beg Naslov: Duktilnost in nosilnost vijačenih spojev v konstrukcijah narejenih, iz jekel visoke trdnosti Obseg in oprema: 156 str., 29 pregl., 130 sl., 118 en., 6 pril. Ključne besede: jekla visoke trdnosti, duktilnost, vijačeni spoji, oslabljen prerez, preklopni spoji Izvleček Jekla z napetostjo tečenja večjo od ali enako 420 MPa uvrščamo med jekla visoke trdnosti. V smislu inženirskih meril duktilnosti, imajo ta jekla nedvomno manjšo duktilnost kot običajna, mehka konstrukcijska jekla. Med inženirska merila duktilnosti, s tipičnimi vrednostmi za jekla visoke trdnosti, štejemo: razmerje med napetostjo tečenja in natezno trdnostjo/„#, = 1,05, deformacijo pri doseženi natezni trdnosti su = 0,05 in deformacijo po pretrgu sfr = 15%. Težava je v tem, da veliko nominalno elastičnih kontrol nosilnosti jeklenih konstrukcij v sebi skriva neelastično obnašanje in je zato potrebno zagotoviti zadostno duktilnost. V ospredje so postavljeni konstrukcijski elementi z luknjami, podvrženi natezni obremenitvi in natezni preklopni spoji z vijaki v strigu. Pri spojih je lokalna duktilnost v smislu plastičnih deformacij potrebna, da se obremenitev prenese med vse vijake. Narejena je bila obsežna eksperimentalna preiskava pločevin z luknjami in preklopnih spojev v nategu z namenom določitve največje nosilnosti in duktilnosti. Za izdelavo preizkušancev je bilo uporabljeno jeklo S690. Zanesljivost evrokodovih projektnih nosilnosti oslabljenih prerezov je bila ocenjena s statistično analizo. Ta je bila dodatno podkrepljena z rezultati preiskav na nateznih preklopnih spojih iz jekel visoke trdnosti iz literature. Preiskave preklopnih spojev so bile numerično simulirane, z namenom določiti in preiskati napetostno-deformacijsko stanje. Pri tem so rezultati testov služili kot smernica za oceno pravilnosti numeričnih simulacij. Z numeričnim orodjem je bila narejena obsežna parametrična študija nateznih preklopnih spojev. Prav tako so bili numerično simulirani testi nateznih preklopnih spojev iz literature. Evrokodova projektna nosilnost na bočni pritisk je bila kritično ocenjena na podlagi baze podatkov z 266 rezultati preklopnih spojev. V določenih primerih evrokodova projektna nosilnost na bočni pritisk podaja neustrezne rezultate. Zato je v disertaciji predlagana nova metoda za izračun projektne vrednosti bočnega pritiska na vijak, ki je enostavna za uporabo. Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. XIII Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. Zahvale Ministrstvo za visoko šolstvo, znanost in tehnologijo je financiralo moje usposabljanje v okviru programa mladih raziskovalcev. Iskreno se zahvaljujem podjetju Trimo d.d. iz Trebnjega, ki je podarilo material in poskrbelo za izdelavo preizkušancev. Zahvala gre v prvi vrsti mojemu mentorju prof. dr. Darku Begu, ki me je usmerjal pri znanstvenem delu in pri raznovrstnih strokovnih projektih, kjer sem se priučil mnogo inženirskih prijemov. Za jezikovni pregled angleškega dela teksta je zaslužna Romana Hudin. Sodelavci, prijatelji, skupaj smo poskrbeli za prijetno vzdušje na katedri in preživeli nekaj nepozabnih trenutkov. Svojci in prijatelji, vselej ste mi stali ob strani. Zaradi tebe, moja Petra, ki razumeš hrepenenje po znanju in odkrivanju neznanega, moja pot nikoli ni bila težka. Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. XV Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. Table of Contents 1 Introduction____________________________________________________________ 1 2 Methodology of experimental work__________________________________________9 2.1 General.........................................................................................................................9 2.2 Material characteristics.................................................................................................9 2.3 Descriptions of specimens, measuring devices and test set-up..................................11 2.3.1 Experimental phase one - specimen types H, HH, BI, B2........................................11 2.3.2 Experimental phase two - specimen type L...............................................................15 3 Methodology of numerical models_________________________________________ 19 3.1 General.......................................................................................................................19 3.2 Numerical model type Ml..........................................................................................19 3.3 Numerical model type M2..........................................................................................20 3.4 Numerical model type M3..........................................................................................21 3.5 Contact interactions....................................................................................................22 3.6 Finite elements and meshing......................................................................................23 3.7 Determination of material model...............................................................................25 4 Tension members with holes - net cross section failure_________________________29 4.1 Introduction................................................................................................................29 4.2 Test results..................................................................................................................30 4.3 Statistical evaluation of results...................................................................................36 4.3.1 Data for statistical evaluation of net cross-section resistance formula......................40 4.4 Results of statistical evaluation and discussion..........................................................41 4.5 Summary....................................................................................................................45 5 Tension splices with bolts in shear - failure in bearing__________________________47 5.1 Introduction................................................................................................................47 5.2 Design resistance of bearing type shear connections.................................................47 5.3 Definition of bearing resistance at bolt holes.............................................................48 5.4 Test results..................................................................................................................50 5.4.1 One- and two-bolt shear connections - specimens BI, B2........................................50 5.4.2 Bolted shear connections with 3 or 4 bolts positioned in the direction of load -specimens L................................................................................................................58 5.5 Numerical parametrical study of bolted shear connections........................................70 5.5.1 Width as the varying parameter..................................................................................71 5.5.2 Plate stiffness as the varying parameter.....................................................................72 5.5.3 Bolt diameter as the varving parameter......................................................................76 5.5.4 Number of bolts as the varying parameter.................................................................78 XVI Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. 5.6 Test results on bolted shear connection found in literature........................................78 5.7 Analysis of bearing resistances in relation to EN 1993-1-8.......................................83 5.7.1 General........................................................................................................................83 5.7.2 Single bolt connections...............................................................................................84 5.7.3 The connections with a single row of bolts positioned in the direction of load transfer........................................................................................................................89 5.7.4 The connections included in the numerical parametric study.....................................90 5.7.5 The connections with two lines of bolts in the direction of load transfer...................91 5.8 Development of new design resistance bearing formula............................................93 5.8.1 General........................................................................................................................93 5.8.2 Single bolt connections...............................................................................................93 5.8.3 The connections with a single row of bolts positioned in the direction of load transfer........................................................................................................................97 5.8.4 The connections included in the numerical parametric study...................................101 5.8.5 The connections with two lines of bolts in the direction of load transfer.................103 5.9 Comparison of new bearing resistance formula to Eurocode bearing resistance.....106 5.10 Summary...................................................................................................................112 6 Conclusions___________________________________________________________117 7 Povzetek_____________________________________________________________121 References_______________________________________________________________153 Appendix A Specimen types H, HH - Test results ______________________________157 Appendix B Specimen types BI, B2 - Test results______________________________167 Appendix C Specimen type L - Test results___________________________________175 Appendix D Results of parametric study______________________________________189 Appendix E Results of numerical FE analyses, replicating tests from literature________235 Appendix F Factors used in bearing resistance formulas _________________________ 251 Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. XVII Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. Table of Figures Fig. 1: Simple tension splice with bolts in double shear.........................................................................................5 Fig. 2: Stress-strain diagrams of standard tensile tests..........................................................................................10 Fig. 4: Specimen types H, HH - steel strips with holes subjected to tension........................................................12 Fig. 5: Specimen types BI - single bolt connection with bolt in double shear.....................................................13 Fig. 6: Specimen type B2 - two-bolt connection with bolts in double shear.........................................................13 Fig. 7: Specimen B2 under loading.......................................................................................................................13 Fig. 8: Testing machine with capacitv of 2500 kN................................................................................................16 Fig. 9: Specimen type L equipped with measuring devices...................................................................................16 Fig. 10: Symbols for measured distances of specimen type L...............................................................................17 Fig. 14: Pressure-overclosure relationship with possible negative pressure transmission (cohesion) and/or overclosure (SIMULIA, 2007)................................................................................................................22 Fig. 16: Load displacement curves for different meshes and finite elements........................................................25 Fig. 17: Comparison of numerical and experimental load-displacement curves...................................................27 Fig. 18: Numerical simulation of standard tensile test on specimen 291-1...........................................................27 Fig. 19: Reduced net cross-section........................................................................................................................30 Fig. 20: Specimen H10 under loading (elastic stage 4,3 kN, maximum resistance 678 kN, just first macro crack 600 kN, failure 207 kN).................................................................................................................32 Fig. 21: Load displacement curves for specimens H01 to H16 (steel grade S690)...............................................32 Fig. 22: Load displacement curves for specimens H - comparison of materials S690 and S235..........................33 Fig. 23: Failure of specimens of equal geometrv but different steel grade............................................................33 Fig. 24: Normalized resistance in relation to Ane/A (a) or displacement Du at maximum resistance (b) for steel grade S690 and S235.......................................................................................................................34 Fig. 25: Load displacement curves for specimens BI that failed in net cross-section...........................................35 Fig. 26: Load displacement curves for specimens B2 that failed in net cross-section...........................................35 Fig. 27: Load-disp. curves for specimens L18s, L20 that failed in net cross-section............................................35 Fig. 28: Net cross-section failure of specimen B122.............................................................................................35 Fig. 29: Net cross-section failure of specimen L20...............................................................................................35 Fig. 30: (re, rt) diagram - Model 1, data setO........................................................................................................44 Fig. 31: Sensitivitv diagram - Model 1.................................................................................................................44 Fig. 32: (re, rt) diagram - Model 2, data setO........................................................................................................45 Fig. 33: Sensitivitv diagram - Model 2.................................................................................................................45 Fig. 34: (re, rt) diagram - Model 3, data set 3........................................................................................................45 Fig. 35: (re, rt) diagram - Model 3, data set 5........................................................................................................45 Fig. 37: Failure modes for specimens BI..............................................................................................................52 Fig. 38: Comparison of experimental and numerical load-displacement curves...................................................52 Fig. 39: Force-displacement curves for two groups of specimens with the same width........................................53 Fig. 40: Results of numerical simulation of B109 at 5,365 mm of hole elongation in the middle surface............54 Fig. 41: Results of numerical simulation of Bili at 6,375 mm of hole elongation in the middle surface............56 Fig. 42: Magnitude of plastic strain at integration points at failure - a cut through Blll....................................56 XVIII Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. Fig. 43: Results of numerical simulation of B101 in the middle surface (a, b, c at 2,717 mm of displacement)...........................................................................................................................................57 Fig. 44: Force-displacement curves for different boundarv conditions.................................................................57 Fig. 45: Comparison of numerical and experimental resistances...........................................................................58 Fig. 46: Mises stress plotted over the actual specimens L20 and L21 (grid of lines), respectively.......................59 Fig. 47: Failure types of specimens L....................................................................................................................62 Fig. 48: Experimental and numerical load-displacement curves for specimen L14..............................................62 Fig. 49: Distribution of bearing forces and friction for specimen L14..................................................................62 Fig. 50: Distribution of bearing forces and friction for specimen L14 at global maximum..................................63 Fig. 51: Distribution of bearing forces and friction for specimen L14 at local maximum....................................63 Fig. 52: Contact pressure at surface nodes for specimen L14................................................................................63 Fig. 53: Frictional shear stress at surface nodes for specimen L14........................................................................63 Fig. 54: Stress state of specimen L14 in the middle surface..................................................................................63 Fig. 55: Stress state of specimen L03....................................................................................................................65 Fig. 56: Experimental and numerical load-displacement curves for specimen L03..............................................65 Fig. 57: Distribution of bearing forces and friction for specimen L03..................................................................65 Fig. 58: Distribution of bearing forces and friction for specimen L03 at global maximum..................................66 Fig. 59: Distribution of bearing forces and friction for specimen L03 at local maximum....................................66 Fig. 60: Stress state of specimen L18 in the middle surface at maximum force....................................................66 Fig. 61: Experimental and numerical load-displacement curves for specimen L18..............................................66 Fig. 62: Distribution of bearing forces and friction for specimen L18..................................................................66 Fig. 63: Distribution of bearing forces and friction for specimen L18 at global maximum..................................67 Fig. 64: Distribution of bearing forces and friction for specimen L18 at local maximum....................................67 Fig. 65: Experimental and numerical load-displacement curves for specimens L13 and L22, respectivelv..........67 Fig. 66: Experimental and numerical load-displacement curves for specimens L04, L04s...................................69 Fig. 67: Experimental and numerical load-displacement curves for specimens L06, L06s...................................69 Fig. 68: Distribution of bearing forces and friction for specimen L04..................................................................69 Fig. 69: Distribution of bearing forces and friction for specimen L06..................................................................69 Fig. 70: Distribution of bearing forces and friction for specimen L04s.................................................................69 Fig. 71: Distribution of bearing forces and friction for specimen L06s.................................................................69 Fig. 72: Distribution of bearing forces and friction for specimen L04s.................................................................70 Fig. 73: Distribution of bearing forces and friction for specimen L06s.................................................................70 Fig. 74: Distribution of bearing forces and friction for specimens L04, L04s at global maximum.......................70 Fig. 75: Distribution of bearing forces and friction for specimens L06, L06s at global maximum.......................70 Fig. 76: Distribution of bearing forces and friction for specimens L04, L04s at local maximum.........................70 Fig. 77: Distribution of bearing forces and friction for specimens L06, L06s at local maximum.........................70 Fig. 78: Distribution of bearing forces and friction for connections with basic geometrv L04.............................72 Fig. 79: Distribution of bearing forces and friction for connections with basic geometrv L14.............................72 Fig. 80: Mises stress at displacement 15,29 mm for L17_ls.................................................................................73 Fig. 81: Distribution of bearing forces and friction for connections with bolts in single shear and with equal plate bearing stiffness..............................................................................................................................74 Fig. 82: Distribution of bearing forces and friction for connections with bolts in double shear and with equal plate bearing stiffness.....................................................................................................................74 Fig. 83: Tension splice with bolts in double shear.................................................................................................75 Fig. 84: Different plate bearing stiffness................................................................................................................75 Fig. 85: The influence of thickness on the pattern of bearing forces.....................................................................75 Fig. 86: The influence of end distance on the pattern of bearing forces................................................................76 Fig. 87: Stress state of L06_2s_tlO-20_M27_b270...............................................................................................76 Fig. 88: Distribution of bearing forces and friction for connections with bolts M27............................................77 Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. XIX Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. Fig. 89: Distribution of bearing forces and friction for connections with bolts M27 and plate width b = 270 mm...........................................................................................................................................................77 Fig. 90: Distribution of bearing forces and friction for connections with 7 bolts..................................................78 Fig. 91: Comparison of numerical and experimental resistances..........................................................................82 Fig. 92: Comparison of numerical and experimental resistances (Kouhi, Kortesmaa, 1990)...............................82 Fig. 93: Connection KK E2 - Mises stress............................................................................................................82 Fig. 95: Displacement DEC at which bearing resistance acc. to EN 1993-1-8 was reached in relation to end distance a) or to bearing-to-maximum resistance ratio b); c) displacement at which maximum resistance was reached.............................................................................................................................86 Fig. 96: Normalized Eurocode bearing resistance and experimental results BI, B2 versus normalized end distance....................................................................................................................................................87 Fig. 97: Experimental results BI, B2 in relation to Eurocode bearing resistance function...................................87 Fig. 98: Experimental re vs. EC 3 bearing resistance Fb for single bolt connections............................................88 Fig. 99: Experimental re vs. minimum of bearing Fb and net cross-section Af, resistance for single bolt connections..............................................................................................................................................88 Fig. 100: Bearing forces on bolts for connections with one line of bolts positioned in the direction of loading.....................................................................................................................................................89 Fig. 101: Resistance of connections with one line of bolts positioned in the direction of loading........................90 Fig. 102: Bearing forces on bolts for connections included in the numerical parametrical study.........................91 Fig. 103: Resistance of connections included in the numerical parametrical study..............................................91 Fig. 104: Bearing forces on bolts for connections with rwo lines of bolts parallel to loading direction...............92 Fig. 105: Resistance of connections with rwo lines of bolts parallel to loading direction.....................................92 Fig. 106: Experimental results in relation to proposed bearing resistance function..............................................95 Fig. 107: Failure modes: a) net cross-section b) shear..........................................................................................95 Fig. 108: The effect of end (a) or edge (b) distance on product k-Jc2.....................................................................96 Fig. 109: Experimental re vs. new bearing resistance Fb for single bolt connections............................................96 Fig. 110: Factor k3 (left equation (87); right equation (88)) versus ei/pi ratio......................................................98 Fig. 111: Bearing forces on bolts for connections with one line of bolts positioned in the direction of loading.....................................................................................................................................................99 Fig. 112: Resistance of connections with one line of bolts positioned in the direction of loading......................101 Fig. 113: Bearing forces on bolts for connections included in the numerical parametrical study.......................102 Fig. 114: Resistance of connections included in the numerical parametrical study............................................103 Fig. 115: Resistance of connections included in the numerical parametrical study without geometries L11- L13, L21-L22........................................................................................................................................103 Fig. 116: Bearing force on bolt for the connections with rwo bolts positioned perpendicular to load transfer... 105 Fig. 117: Bearing forces on bolts for connections with rwo lines of bolts parallel to loading direction.............106 Fig. 118: Resistance of connections with two lines of bolts parallel to loading direction...................................106 Fig. 119: Comparison of results for the edge bolt...............................................................................................107 Fig. 120: Comparison of results for the inner bolt...............................................................................................108 Fig. 121: Comparison of results for the sum of bearing forces...........................................................................108 Fig. 122: Comparison of results for the minimum of sum of bearing forces, net cross-section resistance and bearing resistance..................................................................................................................................108 Fig. 123: Comparison of results for the minimum of sum of bearing forces, net cross-section resistance and bearing resistance - only results, where net cross-section or block tearing resistance is critical are Fig. 124: Comparison of results for the minimum of sum of bearing forces, net cross-section resistance and bearing resistance - only results, where net cross-section or block tearing resistance is critical are shown - friction also is considered on the ordinate...............................................................................109 Fig. 125: Diagrams in normalized format obtained for the edge bolt..................................................................110 Fig. 126: Diagrams in normalized format obtained for the inner bolt.................................................................110 XX Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. Fig. 127: Diagrams in normalized format obtained for the group of bolts .......................................................... 111 Fig. 128: Diagrams in normalized format obtained for the group of bolts, where additional Eurocode checks are considered ............................................................................................................................ 111 Fig. 129: Diagrams in normalized format obtained for the group of bolts, where additional Eurocode checks are considered and maximum resistance (including friction) as the “experimental” value ....... 111 Fig. 130: Bolt nomenclature ................................................................................................................................ 114 Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. XXI Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. List of Tables Table 1: Results of standard tensile test for plate I ................................................................................................ 10 Table 2: Results of standard tensile test for plate II .............................................................................................. 10 Table 3: Average material characteristics .............................................................................................................. 10 Table 4: Geometry of specimen types H, HH ........................................................................................................ 12 Table 5: Geometry of specimen types B1, B2 ....................................................................................................... 14 Table 6: Nominal dimensions of specimen type L ................................................................................................ 17 Table 7: Actual dimensions of specimen type L .................................................................................................... 17 Table 8: Comparison of the resistance and computational time for different meshes and finite elements ............ 24 Table 9: Material model applied in Abaqus for plate I .......................................................................................... 27 Table 10: Material model applied in Abaqus for plate II ...................................................................................... 27 Table 11: Test results of specimens that failed in net cross-section (specimens H, HH, B1, B2 and L) ............... 31 Table 12: Geometry and maximum force of specimens from literature ................................................................ 41 Table 13: Results of statistical analyses of design net cross-section resistance .................................................... 41 Table 14: Test results for specimens B1 and B2 ................................................................................................... 51 Table 15: Test results for specimens L .................................................................................................................. 58 Table 16: Results of numerical simulations for specimen type L .......................................................................... 60 Table 17: Maximum (experimental) resistance [kN] versus connection geometry ............................................... 61 Table 18: Geometry and results for the connections where width was the varying parameter .............................. 71 Table 19: Geometry and results for the connections where plate stiffness was the varying parameter ................. 73 Table 20: Geometry and results for the connections where bolt diameter was the varying parameter .................. 77 Table 21: Geometry and results for the connections where the number of bolts was the varying parameter ........ 78 Table 22: Geometry and results for connections found in literature ...................................................................... 80 Table 23: Material model for numerical simulations of Kim and Yura’s tests ...................................................... 81 Table 24: Material model for numerical simulations of Aalberg and Larsen’s tests for steel grade S1100 .......... 81 Table 25: Distribution of bearing forces on bolts for connections found in literature ........................................... 82 Table 26: Material models for numerical simulations in Abaqus for Kouhi and Kortesmaa connections ............ 83 Table 27: Bearing resistance of specimens B1 and B2 .......................................................................................... 85 Table 28: Reduction factors ß1 and ß2 ................................................................................................................... 97 Table 29: The calculation of the sum of bearing forces ...................................................................................... 100 Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. 1 Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. 1 Introduction Technological evolution began 2 million years ago when Homo habilis made the first tool from stone. From a simple spear, to steam engine and electronic microscope, tools have always been developed to survive and to serve mankind. What seemed impossible yesterday is commonly available today. Innovations are being introduced in ali fields of science, including the field of materials. Ali materials that have been used in structural civil engineering have one thing in common. They are available in almost infinitive quantities and they are reasonably easy for exploitation. The Earth’s crust is composed of about 5% of iron (Mil, 2008). Therefore, it was just a matter of tirne when man discovered steel. Steel - an old material under never ending development. In 2007 world’s crude steel production was 1344 millions of metric tons and it has doubled since 2000 (IISN, 2008). Many different types of steel have been developed, but only a fraction of them are used in structural civil engineering. Any new material has to fulfil two main conditions for its application in this branch: reliability and affordability. A fractured engine block may be replaced, but a fractured bolt may result in a collapse of an entire structural system (e.g. Kemper Arena in Kansas City, MO, USA in 1979 approx. 4000 m2 of roof collapsed due to bolt fatigue failure) and take human lives. Therefore structural engineers and scientists push, puli, tear... They depend on the knowledge of materials and their properties, in order to understand how different materials support and resist loads. Hopefully, this thesis will help to encourage designers to consider high strength structural steel as very a competitive material with several advantages and to apply it in their designs. In constructional practice across Europe structural high strength steels (HSS) are considered as steels with specified minimum yield strength (SMYS) equal to or higher than 420 MPa. In this work, mild steels are defined as steels with SMYS lower than 420 MPa. Weldable structural HSSs are delivered in the conditions: thermomechanically controlled rolled, normalised and quenched and tempered. They differ in their microstructure and accordingly in their mechanical properties. Herein quenched and tempered HSSs are considered. Such steels can reach a yield stress up to 1300 MPa (SAAB, 2005). For successful application of higher strength steels design and fabrication standards need to be accepted by the authorities responsible for safety and by industry. Eurocode 3, standard for the design of steel structures, is divided into several parts. Part EN 1993-1-1 (CEN, 2005a) includes steel grades up to S460. Additional rules for steel grades up to S700 are presented in EN 1993-1-12 (CEN, 2007) and were the lattermost addition to Eurocode 3. HSSs presented in this standard are covered in EN 10025-6 (CEN, 2004b) that maintains quality and defines steel grades for hot rolled flat product in the quenched and tempered condition. Important for fabrication was the 2 Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. presentation of ENV 1090-3 (CEN, 1997a) with supplementary rules for the execution of steel structures in HSS. Economic aspects are usually the deciding factors for the choice of the structural material, where the overall economy is of particular significance. Overall economy is based on material cost, production economy and maintenance costs during the design lifetime of the product. In general, the use of HSS is more attractive if strength is the governing factor. Accordingly, lower self weight of the final product is the primary advantage of HSS. Secondary benefits, on account of lower weight, are lower transportation and handling costs, both resulting in lower energy consumption, smaller weld metal volumes due to thinner steel plates and therefore increased production speed. The welding process can be automated due to smaller and simpler welds. In addition to ali foregoing, there is also lower energy consumption that has a favourable effect on the environment. Quenching hardens steel by introducing brittle martensite, which becomes ductile after tempering. Hence, there is always a tradeoff between ductility and brittleness. Ductility is a qualitative, subjective property of a material (Dowling, 1993). It is generally defined as the ability of a material to accommodate inelastic deformation without breaking. Ductile material tolerates the designer errors in stress calculation or the prediction of severe loads (Dieter, 1987). This definition is obsolete and refers to elastic design where maximum allowable stress should be less then yield stress. “Additional” strength is hidden in the difference between yield and ultimate tensile strength. There are several engineering measures of ductility obtained from the tension tests. The most commonly presented material ductility parameter is the ultimate-to-yield strength mtio fulfy. The yield strength^, is usually determined by offset yield strength Rp 0;2, which is stress corresponding to the intersection of the stress-strain curve and a line parallel to the elastic part of the curve offset by the strain of 0,002. The engineering fracture strain sfr is obtained from the length at fracture Lu of the gage section with original length U). Often sfr is expressed as percentage and is called percentage total elongation after fracture Ac. Because an appreciable fraction of the plastic deformation will be concentrated in the necked region of the test specimen, the value of Ac will depend on the original gage length U) over which the measurement was taken. Therefore, the gage length should always be given when reporting the percentage total elongation at fracture, or geometrically proportional tension test specimens should be machined according to appropriate standard. Another measure of ductility is percent reduction in area Z. It is obtained by comparing the cross-sectional area after fracture Su with the original gage area S0. Both quantities are obtained after failure by putting the specimen back together and taking the required measurements using marks placed a known distance apart prior to the tests. At=l00sfr=—------ (1) 2 = 100-2----- 1,10 to fu/fy > 1,05, elongation at failure is lowered from sfr > 15% to sfr > 10% while the requirement for ultimate strain remaines unchanged su > I5fy/E, where E is the Young’s modulus. The latter requirement is stri eter for higher steel grades (su> 1,68% - for S235, su > 4,93% - for S690, Su > 9,29% - for S1300). Very typical steel S690 has relative fraeture elongation sfr more than 14% (required by EN 10025-6), uniform strain su that corresponds to tensile strength/„ around 5% and ultimate-to-yield ratio around/„/^, = 1,05 (Beg, Hladnik, 1996. Fukumoto, 1996. Axhag, 1998. Kim, Yura, 1999. Langenberg et al., 2000. Aalberg, Larsen, 2001. Puthli, Fleischer, 2001. Sause, Fahnestock, 2001. Aalberg, Larsen, 2002. Clarin, Langerquist, 2005. Girao Coelho, Bijlaard, 2007. Aalberg, Larsen, March 1999). These material parameters were measured around the world on steels made by different producers. They doubtlessly prove that high strength steels have lower ductility than mild steels in terms of engineering measures of ductility. The strain hardening and the capability of large deformations have an essential role at the constitution of stress state in an element. However, aceording to literature HSSs have the ability of plastic resistance and enough rotation capacity to form plastic hinge (Axhag, 1998. Earls, 1999. Sause, Fahnestock, 2001. Chen, Tu, 2004. Girao Coelho et al., 2004b). Ductility is of great importance at connections to transfer the load between ali fasteners and to reduce stress concentrations. In čase the material does not have the ability of local plastic deformations, fraetures open due to stress peaks. Additionally, EN 1993-1-12 only allows the elastic global analysis for sections classified as Class 2 or higher. The standard disallows the use HSS for applications where capacity design is required. The use of HSS is favourable in members in tension where the strength governs. In čase of compressive loading, various buckling phenomena may occur (lateral buckling, local buckling and lateral torsional buckling). The buckling is mainly governed by elastic modulus E, which is the same for ali steel grades. Hence, the use of HSSs may seem umvise. However, weight savings can stili be obtained if slenderness is low X < 60-80 (Gresnigt, Steenhuis, 1997). Moreover, better buckling curve can be applied to HSS than to mild steels due to relatively lower residual stresses (Rasmussen, Hancock, 1995. Beg, Hladnik, 1996. Collin, Möller, 1998. Greco, Earls, 2003). An economic solution regarding the problem of local buckling are hybrid steel girders, where the flanges are made of higher steel grade than the web. A limitation that strength of the flanges should not exceed twice that of the web for serviceability reasons is suggested (Veljkovic, Johansson, 2004). It was also observed that significant improvements in rotational capacity can be achieved in hybrid girders (Greco, Earls, 2003). The deflections are important eriteria in serviceability limit state. The area moment of inertia and Young’s modulus, which are the parameters for the deflection funetion, are independent of steel grade, thus the stiffness needs relatively more attention for the struetures in HSS. 4 Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. When material weldability is discussed, it is essential that steel has a chemical composition that promotes the fusion of the base material and the filler metal, without the formation of cracks and other imperfection (Bjorhovde, 2004). In the last ten years the use of HSS has increased enormously, mainly due to contemporary welding methods (Günther, 2005). The costs of these steels are greatly reduced if preheating is omitted. With the correct choice of steel quality, welding consumables and welding process, the preheating is in many cases unnecessary (Gresnigt, Steenhuis, 1997). It can be necessary for thicker plates to avoid cold cracking. The scope of studies was also aimed at undermached welds, which can be successfully used in HSS structures (Johansson, 2004. Collin, Johansson, 2005). The fatigue resistance is mainly governed by stress range Acrand notch effect. The strength of steel has only a minor effect on the fatigue resistance. The use of HSS in fatigue loaded structures will result in higher stress ranges than in structures of mild steel. The important key to the fatigue resistance is the notch effect and micro cracks that usually form where large amount of energy is added (flarne cutting, welding, punching, drilling). Stress concentration leads to crack propagation, resulting in macro crack and finally in a brittle fracture. The solution at HSSs can be (Günther, 2005. Kuhlmann, Bergmann, 2005) new or modified detailing, shifting of details in less stressed sections, improved welding procedures, better workmanship and post-weld improvement methods (such as grinding, Tungsten Inert Gas dressing, needle or hammer peening...). The investigations showed positive fatigue behaviour for HSS in the high load cycle > 2*106, especially on special notch cases from mobile crane structures (Bucak, 2000), as well. A connection connects two or more members by means of structural elements such as welds, bolts, pins, rivets, cable sockets.... Each connection type has its own particular behaviour. This thesis will focus on tension splice connections with bolts in double shear (see Fig. 1). In the sequel these connections will be referred to as bolted shear connections. In a bolted shear connection the loading can be transmitted either by bolt bearing (bearing type connections) or by friction of the surfaces (slip resistance connections), where the friction is achieved by preloading of the bolts. Only bearing type connections are considered in this work. This connection type transfers loading from one steel plate to another by the contact between the bolt and the plates. The contact is characterized by high stresses that enforce transverse shear in the bolts and high local compression stress to the plate. Concentrations of stresses are therefore unavoidable. Another characteristic of bearing type connections is initial slip due to bolthole clearance. In general, contacts between bolts and plates are not established simultaneously. A single contact may be established sooner. In such čase the whole loading is transferred through this single contact. For that reason, the local ductility of the connection in terms of plastic deformations has to be sufficient in order to assure bolthole elongation, so that the remaining contacts will be established and the loading will be transferred through ali bolts. If local ductility was not sufficient, the stress concentration would cause rupture of the steel plate or shear fracture of the bolt. In either čase the maximum connection resistance Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. 5 Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. would be equal to the resistance of a single bolt connection. The problem is that the strength ratio in connections made of HSS is in favour of the steel plate. In the connections made of mild steel the bolt material is much stronger than the plate material. This situation can be referred to as “weak” plates and “strong” bolts, while in connections made of HSS the situation changes to “strong” plates and “weak” bolts. These “weak” bolts should be at least of material grade 8.8 or higher, which are considered as non-ductile. Therefore, assuring the ductility in bolts is not an option. In the this thesis it will be shown that local ductility of bolted shear connections is sufficient to distribute the loading between ali bolts evenly in four-bolt connection with the most unfavourable initial position of the bolts. But let us first summarize the work that has already been done in the field of joints made of HSS. The attention will be given to experimental testing of connections made of steel grades higher than S460. Fig. 1: Simple tension splice with bolts in double shear The characterization of the ductility of bolted end plate beam-to-column steel connections was done by Girao Coelho (Girao Coelho, 2004. Girao Coelho et al., 2004a. Girao Coelho et al., 2004b. Girao Coelho et al., 2006b. 2006a). The connections were made of steel grade S355 and S690. A methodology for the characterization of the rotational response of a joint based on the component method was implemented and calibrated against experimental results. The methodology was restricted to joints the behaviour of which was governed by the end plate modelled as equivalent T-stubs in tension. The results of this study along with the conclusions drawn from the analysis of individual T-stubs afforded some basis for the proposal of some criteria for the verification of sufficient rotation capacity. The proposal was made in terms of a non-dimensional parameter, the joint ductility index (Girao Coelho, 2004). The research on block shear tear-out failure in gusset-plate welded connections in structural hollow sections and steel S1300 showed that design rules for block tearing resistance according to Eurocode, as well as American standard are inadequate (Ling et al., 2007). A modification of the effective net area and failure stress definitions were proposed. Kouhi and Kortesma (1990) presented test results of multi-bolt shear connections. Steel grade with nominal yield strength of 640 MPa and nominal ultimate strength of 700 MPa was used in the test. Actual material strengths were given for 3, 4, 6 and 8 mm thick plates. Specimens were divided in four series regarding their failure. The investigation included connections with two bolts positioned in the direction of loading and a connection with four bolts in 2x2 6 Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. configuration. The main deformation and failure were performed in cover plates, except for test series H which failed in net cross-section. The test results were compared to bearing, net area and block tearing resistances according to various standards. The report on a comparative research of bolted connections in HHS and mild steel was prepared by Aalberg and Larsen (March 1999). The tests included tension splices with three bolts in double shear, block tear tests and tension tear-out test. Ali tension splices failed in net cross-section. The test resistance was compared to block tearing resistance according to Eurocode and AINSI standard. The conclusion was that the reduced ultimate-to-yield ratio fu/fy = 1,05 did not significantly affect the ductility. Kim and Yura (1999) investigated shear connections with one or two bolts placed parallel to the loading. Beside mild steel grade they used steel with yield strength oify = 483 N/mm2 and ultimate tensile strength of 545 MPa. The specimens were connected to rigid plate so that the bolts were in single shear. The failures were characterized as splitting and shear failures with large bolthole elongations. The experimental resistance was compared to bearing resistance according to American AISC standard and to Eurocode standard in which conservatism was found. Aalberg and Larsen (2001. 2002) duplicated Kim and Yura tests, using steel grades S690 and SI 100. The steel grade SI 100 is not considered in EN 1993-1-12. The value of ultimate tensile to yield ratio was equal to fulfy = 1,05 for both steel grades. The local ductility of connections was not decreased due to the \ow fulfy ratio. The test setup was similar to the tests in this thesis. The actual yield strength of steel SI 100 was 1330 MPa. The ultimate strain was reached at su = 0,03, while percentage total elongation after fracture was equal to^c = 10 %. With su = 0,03 ^ 15 fyIE = 15x1330/210000 = 0,095 this steel did not satisfy the ductility requirements set by EN 1993-1-12. Nonetheless, large hole elongations and ductile failures were observed. Puthli and Fleisher (2001) focused on shear connections made of steel grade S460 (fulfy = 1,23) with two bolts placed perpendicular to loading. They also experienced block tear failure. They compared experimental resistances to resistance according to EN 1993-1-8. The focus was set on minimum end and edge distances and the result was the suggestion to reduce minimum distances and to modify bearing resistance formula. More recent research was published by Rex and Easterling (2003). The research on the behaviour of a bolt bearing on a single plate was part of larger investigation of the behaviour of partially restrained steel and composite connections. The 6,5 mm thick plate of different high steel grades (ultimate strength from 665 to 752 MPa ) was tested against bearing resistance. Due to small plate thickness and large end distance ex several curling failures were observed. A research on single bolt shear connection was conducted on Delft University of Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. 7 Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. technology (de Freitas et al., 2005). Ductile behaviour of the connections and the conservatism of Eurocode bearing resistance formula were reported. The papers on the net cross-section resistance and ductility of members and connections made of HSS were presented in journals and conferences (Može, Beg, 2006. Može et al., 2006a. 2006b. Može, Beg, 2007. Može et al., 2007a. 2007b). The application of HSS in engineering structures is increasing. Lightweighting is particularly important in commercial vehicle and mobile crane construction, where dimensions, axle loads and total weight of the vehicle are restricted by legal regulations. The development of mobile cranes for loads of up to 800 tons was only made possible by the advent of high-strength steels (ThyssenKrupp Steel AG, 2006). The highest grades of HSS are applied to heavy lifting machinery. HSS can replace forged forks for trucks and carbon fibre in boat keels (SAAB, 2008). In several bridges and high buildings HSS (AG der Dillinger Hiittemverke, 2005. Günther, 2005) was the best solution for certain structural elements (Ilverich bridge, 0resund Viaduct, Ennëus Heerma, Car park of the Stuttgarter Trade Fair, Millau viaduct - France, Verrand viaduct - Italy, the roof of Sony Centre in Berlin - Germany, Mittadalen hybrid steel bridge girder - Sweden, Fort City Bridge - USA...). The purpose of this thesis is to determine the local ductility members in HSS and the relation of local ductility to the resistance. The local ductility was studied on members with tension with or without holes and on tension splices with bolts in shear (see Fig. 1). The methodology of experimental work is presented in Chapter Methodology of experimental work. The chapter gives detailed information on material testing, measuring techniques and actual, as well as nominal geometry of specimens. The methods used in numerical modelling are presented in the Chapter Methodology of numerical models. The numerical models, used to simulate the experiments, are presented and a description of main features on contact interactions, finite elements, meshing and on determination of material model is given. The test results of members with holes in tension with net cross-section failure are reported in Chapter Tension members with holes - net cross section failure. The (un)reliability of the design provisions for net cross-section resistance is assessed by a statistical analysis. Local ductility and resistance of tension splices with bolts in shear is the topic of Chapter Tension splices with bolts in shear - failure in bearing. The particular attention is given to the bearing resistance and to bearing failure. The stress state of tests results is described by means of numerical simulations. The bearing resistance is presented in view of the Eurocode standard together with other results on bolted shear connections in HSS gathered from literature. A new modified approach to bearing resistance is presented and a new design formula for bearing resistance per bolt is statistically evaluated. 8 Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. The summary with the main conclusions are given in Chapter Conclusions. The thesis is wrapped up with the list of references in Chapter References. The expanded summary in Slovenian language is given in the chapter titled Povzetek. The work is completed by several appendixes, where additional test results and results of numerical simulations are presented. Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. 9 Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. 2 Methodology of experimental work 2.1 General The experimental work was completed in two phases. The first phase was done from summer 2005 to winter 2006 (specimen types H, HH, BI, B2) and the second in spring 2007 (specimen type L). The material was ordered separately for each phase. The first phase of the investigation of local ductility of high strength steel was divided into two main sets. In the first set local ductility of high strength steel was studied on steel strips with holes subjected to tension. The second set of tests was dedicated to tension splices with bolts in double shear. The investigation included single bolt connections, two-bolt connections with bolts positioned perpendicular to loading. The second phase of the experimental work included tension splices with three or four bolts in double shear positioned parallel to loading. The connections were designed to impose failure in the high strength steel plate and not in the bolts. Special attention was devoted to the selection of measuring devices and techniques so that the results could be compared to numerical simulations. 2.2 Material characteristics For each of experimental phases a separate plate was delivered; plate I and plate II. The plates were made by Belgium producer Industeel (Industeel, 2008). The marketing name of the used steel is Supralsim® 690, which fulfils requirements of S690 QL according to EN 10025-6 (CEN, 2004b). The dimensions of the plates were b/l/t = 1500/6000/10 mm. The material characteristics were obtained by standard tensile tests according to EN 10002-1 (CEN, 2001). Proportional test pieces from each plate were extracted from the plates according to EN ISO 377 (CEN, 1997b); six pieces from plate I and three from plate II. The standard tensile tests were performed in longitudinal direction of rolling, using testing machine ZWICK Z 700 Y. The displacements were measured on a defined original gauge length L0 by sensor arm extensometers. The speed of the test was defined by the displacement of the extensometers. The measured material parameters for each plate are given in Table 1-2. The original geometry of test pieces 488.1-488.3 was not measured correctly. Therefore the average Rm andi?p0,2 were obtained only from specimens 488.4-6. Average material characteristics which are used for analyses are presented in Table 3. The engineering stress-strain curves are shown in Fig. 2. 10 Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. Table 1: Results of standard tensile test for plate I Sample name Thickness t [mm] Width b [mm] S0 [mm2] L0 [mm] Fm [kN] Rpi>,2 [MPa] Rm [MPa] Agt [%] [%] Z [%] 488.1 10 25 250 90 218,74 798 875 / 14,0 61,7 488.2 10 25 250 90 228,70 876 915 / 14,5 62,6 488.3 10 25 250 90 228,03 875 912 / 14,6 62,4 488.4 10,2 24,9 254 90,0 224,89 848 885 5,1 15,0 57,3 488.5 10,1 24,9 251,5 90,0 222,42 846 884 5,1 14,6 55,2 488.6 10,1 25,0 252,5 90,0 222,69 837 882 5,1 13,6 51,4 Sample name Speed 488.1 to Rp,02: 0,001 after Rp,02: 0,007 s-1 488.2 to Rp,02: 0,001 after Rp,02: 0,007 s-1 488.3 to Rp,02: 0,001 after Rp,02: 0,007 s-1 488.4 0,001 s"1 488.5 0,00025 s"1 488.6 to Rp,02: 0,001 after Rp,02: 0,007 s-1 Table 2: Results of standard tensile test for plate II Sample name Thickness t [mm] Width b [mm] S0 [mm2] L0 [mm] Fm [kN] Rp%2 [MPa] Rm [MPa] Agt [%] Ac [%] Z [%] 291.1 10,01 24,51 245,3 90,49 206,96 796 844 6,4 17,1 58,9 291.2 10,03 24,68 247,5 90,04 208,98 795 844 6,3 16,9 59,6 291.3 10,04 24,41 245,1 91,22 206,91 798 844 6,4 17,2 59,5 Sample name Speed 291.1 0,01 mm/s 291.2 0,03 mm/s 291.3 0,03 mm/s Table 3: Average material characteristics Plate Rp 02 = fy [MPa] /t ^ / [MPa] Agt [%] A" [%] Z [%] I 847 884 5,1 14,4 58,4 II 796 844 6,4 17,1 59,3 900 | i—*" ~"^ Si, 900 - 750 - 750 600 - ^t1 N 600 450 - 450 - 300 -150 - ----488.4 ----488.5 ----488.6 300 150 - ----291.1 ----291.2 ----291.3 3 6 9 12 15 18 0 - 0 Str ain [%] C 3 6 9 12 15 Strain [%] Fig. 2: Stress-strain diagrams of standard tensile tests Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. 11 Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. 2.3 Descriptions of specimens, measuring devices and test set-up 2.3.1 Experimental phase one - specimen types H, HH, BI, B2 The first phase of the experiments was done in University of Ljubljana, Faculty of Civil and Geodetic Engineering, Jamova 2, Ljubljana from July 2005 to Februarv 2006. Testing machine Instron with capacitv of 1000 kN was available for the tests (Fig. 3). The displacements were measured by inductive displacement transducers (IDT) with range ±25 mm (HBM WA50). Special extensometers were made to measure the displacements up to 5 mm. Ali measuring devices were connected to a universal measuring unit. Records of force and displacements were detected every 0,0Is and an average of ten records was recorded. Ali the tests were displacement controlled through the crosshead position. The experimental work was divided into two groups of specimens: steel strips with holes subjected to tension and shear connections. Fig. 3: Test rig (testing machine Instron) Specimens types H and HH were strips of plates equal in geometry and with different size and position of holes. The hole diameter was varied form 0 to 50% of specimen width. In certain cases the hole was made eccentrically. Letter H in the specimen name represents hole and is followed by consecutive number of the specimen. Similarly, letters HH stand for hinge hole. Ali specimens (17 of type H, 6 of type HH) were manufactured from plate I (steel S690 -Table 3), except H17-H20 which were made of steel grade S235 with nominal yield strength fy = 235 N/mm2. The actual material characteristics of steel S235 were not measured and the results were used merely for visual comparison of deformed state to evaluate ductility. The specimens were fabricated by flame cutting, in such way that the longitudinal direction 12 Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. corresponded to the loading direction. The speed of the tests was about 1,5 mm/min and is given in Appendix A. 2== H -*---- -*---- fracture -# IDT m HH loading fracture loading a) specimen type H b) specimen type HH Fig. 4: Specimen types H, HH - steel strips with holes subjected to tension Specimens H were directly attached to testing machine in such way that the rotation around strong axis of the specimen was prevented (Fig. 4a). The attachment of specimens HH allowed rotation around their strong axis (Fig. 4b). The actual and nominal geometry of specimens is presented in Table 4. At specimen type H, a relative displacement was measured between two points 280 mm apart, as shown in Fig. 4a. Displacements were measured by two inductive displacement transducers (IDTs) which were mounted on each side of the specimen. At specimen type HH, displacements were measured only from the relative displacement of the testing machine grips. The rotation of specimens did not allow installation of the IDTs. Table 4: Geometry of specimen types H, HH Specimen name Eccen-tricity Nominal dimensions [mm, mm2] Actual dimensions [mm, mm2] b t d0 e2,min-d0/2 e2,max-rf(/2 ^net b t d0 e2,min-d0/2 e2,max-rf(/2 ^net H01 No 100 10 0 50 50 1000 101,3 10,15 0 1013 H02 No 100 10 0 50 50 1000 101,5 10 0 50,0 50,0 1015 H03 No 100 10 5 47,5 47,5 950 101,9 10 5 47,7 48,8 969 H04 No 100 10 10 45 45 900 100,9 10 10 45,0 45,4 909 HO 5 No 100 10 10 45 45 900 101,3 10 10 45,4 45,8 913 H06 No 100 10 13 43,5 43,5 870 101,7 10 13 44,3 44,4 887 H07 No 100 10 18 41 41 820 101,3 10 18 41,7 42,0 833 HO 8 No 100 10 22 39 39 780 101,7 10 22 39,6 39,7 797 H09 No 100 10 22 39 39 780 102,4 10 22 39,6 40,9 804 H10 No 100 10 26 37 37 740 101,6 10 26 37,0 38,6 756 Hll No 100 10 30 35 35 700 101,6 10 30 35,1 36,4 716 H11A No 100 10 30 35 35 700 99,9 10 30 34,8 35,1 699 H12 No 100 10 30 35 35 700 101,3 10 30 34,5 36,4 713 H13 Yes 100 10 30 28 42 700 101,4 10 30 29,4 42,0 714 H14 Yes 100 10 30 21 49 700 101,6 10 30 22,4 49,1 716 H15 No 100 10 40 30 30 600 101,8 10 40 29,2 32,5 618 H16 No 100 10 50 25 25 500 101,6 10 50 25,5 26,1 516 H17* No 100 10 0 50 50 1000 101,3 10 0 1013 H18* No 100 10 10 45 45 900 101,1 10 10 45,3 45,8 911 H19* No 100 10 22 39 39 780 101,2 10 22 39,4 39,8 792 H20* No 100 10 50 25 25 500 100,8 10 50 24,9 25,9 508 HH01 Yes 80,0 10 24 28 28 560 78,4 10 24 26,4 27,3 544 HH02 Yes 80,0 10 24 22 34 560 79,0 10 24 19,9 35,1 550 HH03 Yes 80,0 10 24 16 40 560 78,5 10 24 14,1 40,4 545 HH04 Yes 80,0 10 18 31 31 620 77,9 10 18 22,7 32,1 599 HH05 Yes 80,0 10 18 25 37 620 78,5 10 18 22,1 38,4 605 HH06 Yes 80,0 10 18 19 43 620 78,5 10 18 17,2 43,3 605 steel S235 280 Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. 13 Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. Blxx do Q §2^ iT T 2 120 ,,Qly Blxx iExtensometer w IDT, -0- 100 Fig. 5: Specimen types BI - single bolt connection with bolt in double shear B2xx ^ jQ. (jo B2xx i k^ p Extensometer IDT L J i, 80 ^ Fig. 6: Specimen type B2 - two-bolt connection with bolts in double shear Fig. 7: Specimen B2 under loading The second group of specimens were bolted shear connections with one bolt (25 connections) or two bolts (13 connections) positioned perpendicular to loading direction. The specimens were designated as types BI (BI stands for one bolt) and B2 (B2 stands for two bolts). The connection was assembled of a specimen, one or two bolts and two cover plates which were welded together to form forks. The forks were locally strengthened in bolt bearing area with another 10 mm thick plate to prevent hole elongation. Ali the specimens and forks were made of steel S690 - plate I with the actual material characteristics presented in Table 3. The Bi b & 14 Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. test series included 25 single bolt shear connections (Fig. 5). Bolts M27 were used in drilled standard size holes d0 = 30 mm (with some exceptions - see Table 5). Some of the holes were positioned eccentrically to loading axis. The B2 test series included 13 two-bolt shear connections, with bolts positioned perpendicular to loading direction (Fig. 6). Bolts M22 in standard size holes d0 = 24 mm were used. Bolts were designed to withstand resistance of the steel plate, thus grades 10.9 and 12.9 were selected to avoid bolt shear or bending. Relative displacement between the specimen and the fork was measured by IDTs. An extensometer was also mounted between the fork and the bolt to control the deformation of forks and the bending of the bolt (Fig. 7). Bolts were snug tightened to ensure that the load was transferred primarily by bearing and not by friction. Bolt shear failure and bearing failure of the plate were prevented by proper design. Geometry of specimens was selected so that for each of the selected edge distance e2 the end distance e\ was varied. Distance between bolts was also varied for B2 specimens. Actual and nominal geometry of ali specimens is shown in Table 5. The speed of the test is presented in Appendix A. Table 5: Geometry of specimen types BI, B2 Specimen name Bolt Nominal dimensions [mm, mm2] Actual dimensions [mm, mm2] b [mm2] t [mm2] d« [mm2] ^2,min do/2 ^l,min do/2 P2-do ^net [mm2] b [mm2] t [mm2] do [mm2] ^2,min d«/2 ^l.min d«/2 P2-do ^net [mm2] B101 M27 60,0 10 30 1,00 3,00 300 61,0 10 30 0,95 3,01 310 B102 M27 72,0 10 30 1,20 1,20 420 73,2 10 30 1,20 1,21 432 B103 M27 72,0 10 30 1,20 1,50 420 71,2 10 30 1,15 1,50 412 B104 M27 72,0 10 30 1,20 2,00 420 71,7 10 30 1,19 2,01 417 B105 M27 72,0 10 30 1,20 3,00 420 72,0 10 30 1,16 2,98 420 B106 M27 81,0 10 30 1,35 2,50 510 81,0 10 30 1,33 2,52 510 B107 M27 81,0 10 30 1,35 3,00 510 80,5 10 30 1,32 3,02 505 B108* M27 81,0 10 30 1,18 3,35 410 81,1 10 30 1,17 3,34 402 B109 M27 90,0 10 30 1,50 1,00 600 90,0 10 30 1,47 1,00 600 B110 M27 90,0 10 30 1,50 1,20 600 92,0 10 30 1,53 1,21 620 Bili M27 90,0 10 30 1,50 1,50 600 90,0 10 30 1,48 1,51 600 B112 M27 90,0 10 30 1,50 2,00 600 90,0 10 30 1,47 2,01 600 B113 M27 90,0 10 30 1,50 2,50 600 90,3 10 30 1,46 2,49 603 B114 M27 90,0 10 30 1,50 3,00 600 90,0 10 30 1,46 3,00 600 B115* M27 90,0 10 30 1,33 3,00 500 90,3 10 30 1,30 3,00 480 B116 M27 90,0 10 30 1,50 1,50 600 87,4 10 30 1,42 1,50 574 B117 M27 90,0 10 30 1,50 1,50 600 89,2 10 30 1,48 1,50 592 B118 M27 120,0 10 30 2,00 1,50 900 118,0 10 30 1,90 1,53 880 B119 M27 120,0 10 30 2,00 2,00 900 118,2 10 30 1,93 2,06 882 B120 M27 120,0 10 30 2,00 2,50 900 119,4 10 30 1,96 2,56 894 B121 M27 120,0 10 30 2,00 3,00 900 122,1 10 30 2,02 3,06 921 B122 M27 120,0 10 30 2,00 3,50 900 118,8 10 30 1,95 3,54 888 B123 M22 80,0 10 24 1,67 4,17 560 78,7 10 24 1,61 4,22 547 B124* M22 80,0 10 24 1,42 4,17 440 79,1 10,2 24 1,44 4,21 459 B125* M22 80,0 10 24 1,17 4,17 320 79,1 10,15 24 1,18 4,21 333 B201 M22 96,0 10 24 1,00 3,00 2,00 480 97,2 10,15 24 0,96 2,97 2,03 499 B202 M22 115,2 10 24 1,20 1,20 2,40 672 115,9 10,15 24 1,20 1,20 2,36 689 B203 M22 115,2 10 24 1,20 2,00 2,40 672 115,9 10,15 24 1,20 2,01 2,37 689 B204 M22 115,2 10 24 1,20 3,00 2,40 672 116,0 10,15 24 1,20 2,99 2,36 690 B205 M22 122,4 10 24 1,20 3,00 2,70 744 124,1 10,15 24 1,21 2,96 2,70 772 B206 M22 129,6 10 24 1,50 1,50 2,40 816 130,3 10,15 24 1,50 1,50 2,38 835 B207 M22 136,8 10 24 1,50 3,00 2,70 888 137,0 10,15 24 1,48 3,03 2,70 903 B208 M22 144,0 10 24 1,50 1,00 3,00 960 144,0 10,15 24 1,49 1,03 3,00 974 B209 M22 144,0 10 24 1,50 1,20 3,00 960 144,1 10,15 24 1,50 1,21 3,00 975 B210 M22 144,0 10 24 1,50 1,50 3,00 960 144,0 10,15 24 1,50 1,53 2,98 975 B211 M22 144,0 10 24 1,50 2,00 3,00 960 143,7 10,15 24 1,44 2,05 3,00 971 B212 M22 144,0 10 24 1,50 3,00 3,00 960 144,4 10,15 24 1,47 3,04 3,01 978 B213 M22 122,4 10 24 1,35 2,00 2,40 744 121,0 10,15 24 1,33 2,01 2,39 741 * eccentric hole Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. 15 Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. 2.3.2 Experimental phase two - specimen type L The second phase of the experimental work was completed in May 2007 at the Slovenian National Building and Engineering Institute, Dimičeva 12, Ljubljana. Digitally controlled, hydraulic, multi-purpose testing machine Zwick with capacity of 2500 kN was used for the tests (Fig. 8). Phase two included bolted shear connections with three or four bolts positioned in the loading direction. A total of 26 specimens type L (L for long connection) were tested. The specimen was fastened between two cover plates with three or four bolts M20 12.9 to form tension splice with bolts in double shear. The diameters of bolt holes were d0 = 22 mm. The bearing area of the cover plates was stiffened by additional plate so that bolt bearing was transferred on 20 mm thick plate as show in Fig. 9. In this way the deformations were enforced only in the specimen while the cover plates deformed only elastically. The cover plates were welded together to from forks. Together with the bolts, they were not the subject of the investigation, thus they were designed accordingly. The forks and specimens were fabricated form plate II (steel grade 690 - Table 3). The functional fabrication tolerances were simulated at specimens coded by s (see Table 7), where the first or the last hole was shifted by 2 mm. In this way, only one bolt was carrying the bearing load for the first 2 mm of hole elongation and after that the remaining bolts were activated. The geometry of the specimens was designed to cover different types of failures. The range of pitches p\ and end distances e\ were selected from minimum allowed distances by EN 1993-1-8 (CEN, 2005b) to the most common ones. The edge distance e2 was constant for ali specimens and was equal to 4,5J0. The actual and nominal geometries of specimen type L are listed in Tables 6-7. The tests were carried out at a prescribed displacement rate 1,5 mm/min. The records of force and displacements were recorded every 0,0Is. A relative displacement between the specimen and the cover plates was measured by two inductive displacement transducers (IDT) and alternatively by sensor arm extensometers (SAE). The positions of measuring instruments are illustrated in Fig. 9. The SAEs were also used to control test speed. Ali measuring devices were connected to an external universal recording unit. The original gauge length of SAE was 40 mm. The reference point on the specimen for displacement measurement is illustrated in Fig. 10 and the value of distance g from the end of the specimen to the point is given in Table 7. The IDTs were fixed to the forks by a magnetic holder. The difference in displacement of SAE and IDT was in the elastic deformation of forks. The bolts were snug tightened to ensure that the load was transferred primarily by bearing and not by friction. The tests were carried out until fracture of plate in bearing or the bolt (except at L18 and L20s where the test was stopped significantly before failure). 16 Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. Fig. 8: Testing machine with capacity of 2500 kN Fig. 9: Specimen type L equipped with measuring devices Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. 17 Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. Table 6: Nominal dimensions of specimen tvpe L Specimen e1/d0 name p1/d0 e2/d0 d0 [mm] b [mm] t [mm] d No. of [mm] bolts L01 1,5 2,0 4,5 22 198 10 20 3 L02 2,0 2,0 4,5 22 198 10 20 3 L03 3,0 2,0 4,5 22 198 10 20 3 L04 1,5 2,0 4,5 22 198 10 20 4 L04s 1,5 2,0 4,5 22 198 10 20 4 L05 2,0 2,0 4,5 22 198 10 20 4 L06 3,0 2,0 4,5 22 198 10 20 4 L06s 3,0 2,0 4,5 22 198 10 20 4 L07 1,5 2,5 4,5 22 198 10 20 3 L08 1,5 2,5 4,5 22 198 10 20 4 L09 2,5 2,5 4,5 22 198 10 20 4 L10 3,0 2,5 4,5 22 198 10 20 4 Lil 2,0 3,0 4,5 22 198 10 20 3 L12 2,5 3,0 4,5 22 198 10 20 3 L13 3,0 3,0 4,5 22 198 10 20 3 L14 1,23 3,0 4,5 22 198 10 20 4 L15 1,5 3,0 4,5 22 198 10 20 4 L16 2,0 3,0 4,5 22 198 10 20 4 L17 2,5 3,0 4,5 22 198 10 20 4 L18 3,0 3,0 4,5 22 198 10 20 4 L18s 3,0 3,0 4,5 22 198 10 20 4 L19 5,0 3,0 4,5 22 198 10 20 4 L20 2,0 3,50 4,5 22 198 10 20 4 L20s 2,0 3,50 4,5 22 198 10 20 4 L21 2,0 3,50 4,5 22 198 10 20 3 L22 2,0 3,77 4,5 22 198 10 20 3 s – hole shifted for 2 mm (L04s, L06s, L18s – bolt B1 activates first, L20s – bolt B3 activates first) j5 g * • 4 L> .o Fig. 10: Symbols for measured distances of specimen type L Table 7: Actual dimensions of specimen tvpe L Specimen name Connected to forks a1 [mm] a2 [mm] a3 [mm] a4 [mm] b1 [mm] b2 [mm] b3 [mm] b4 [mm] d1 [mm] d2 [mm] d3 [mm] d4 [mm] t [mm] g [mm] L01 L02 L03 L04 L04s L05 L06 L06s L07 L08 L09 L10 Lil L12 L13 L14 L15 L16 L17 L18 L18s L19 L20 L20s L21 L22 LF1 LF1 LF1 LF1 LF1B LF1B LF1B LF1B LF2B LF2A LF2A LF2A LF3E LF3E LF3B LF3B LF3B LF3B LF3B LF3C LF3C LF3C LF4 LF4 LF4 LF5 22,2 33,7 55,3 22,8 23,0 33,6 55,9 55,0 22,0 21,8 43,9 55,1 32,8 44,1 55,2 16,3 22,0 32,7 43,9 55,1 55,0 99,2 33,0 33,0 33,5 33,3 22,1 21,6 22,1 21,5 19,4 21,6 21,5 19,4 32,7 33,6 32,7 32,7 44,2 44,0 43,7 43,5 43,6 43,7 43,5 43,5 41,2 43,9 54,6 54,8 55,4 60,9 21,6 22,1 21,8 21,9 21,8 22,0 21,3 22,2 32,7 33,0 32,9 33,3 44,0 43,7 44,0 43,5 44,2 44,0 44,2 44,1 44,3 43,6 54,5 55,0 55,1 60,9 21,5 21,7 22,0 21,8 21,8 33,0 32,8 32,9 43,8 43,8 43,7 43,8 43,5 46,0 43,9 55,0 56,9 88,3 88,3 88,7 88,4 88,8 88,9 88,3 88,2 88,5 88,9 88,6 88,0 88,5 88,0 88,0 88,3 88,7 88,4 88,2 87,7 88,3 88,1 88,5 88,3 88,4 88,3 87,2 87,6 87,5 87,9 87,6 87,9 87,3 87,6 87,5 87,0 87,4 88,1 87,7 88,0 88,3 87,9 87,4 87,6 88,1 88,6 88,0 88,0 87,8 87,7 87,8 87,8 88,7 88,3 88,5 88,4 88,8 88,8 88,4 88,0 88,7 88,3 87,9 88,4 NM 88,3 87,7 88,3 88,7 88,2 88,4 88,1 88,3 88,0 88,6 88,3 88,5 88,5 88,3 87,6 87,5 87,6 87,5 87,8 87,6 88,0 87,3 87,0 88,2 88,7 NM 88,7 88,2 87,7 87,1 88,1 87,9 87,9 87,9 88,0 87,7 87,7 87,6 87,6 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 22,0 10,15 10,20 10,20 10,15 10,15 10,15 10,20 10,15 10,15 10,15 10,20 10,15 10,15 10,20 10,15 10,15 10,15 10,15 10,15 10,15 10,00 10,10 10,10 10,10 10,10 10,10 195,0 206,0 228,0 239,0 239,0 250,0 272,0 272,0 206,0 261,0 283,0 294,0 250,0 261,0 272,0 299,0 305,0 316,0 327,0 338,0 338,0 384,0 360,0 362,0 283,0 301,0 NM not measured Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. 19 Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. 3 Methodology of numerical models 3.1 General This section deals with methodology and techniques used in numerical simulations. Each of the described numerical models was used for parametric studies of tension splices. The models differ mainly in complexity. The parameters in the study were geometry, material parameters, number of bolts and shear planeš. They are described and presented in the following sections. The finite element environment ABAQUS v6.5 to v6.7 (SIMULIA, 2007) was used to simulate shear connections. Three conceptually different numerical model types were built to describe the connections. The models were named Ml, M2 and M3, where Ml was the simplest model type and M3 the most complex one. Ali models were three-dimensional. Deformable bodies were meshed by solid continuum finite elements. The geometry of a model was defined by parts, positioned relative to one another in an assembly. Ali models consisted of at least two parts: bolt(s) (either rigid or deformable) and steel plate(s). Different interactions were prescribed between parts. The full Newton solution method with nonlinear effect of large deformations and displacement was used to trace nonlinear load-displacement curve. 3.2 Numerical model type Ml This numerical model was used to simulate connections with bolts in double shear where bolts stay in their initial position and where cover plates do not restrain deformation of the plate in thickness direction. The simplification of the numerical model, described in the sequel, greatly reduces the computational tirne. The numerical model Ml was assembled of two separate parts. The bolt was presented by a 3D discrete rigid cylinder, while the steel plate with boltholes was modelled as a 3D deformable solid body. Bolt head, nut and washers were not modelled. The individual parts are presented in Fig. lla-b, assembled and meshed connection is shown in Fig. lic. An elastic-plastic material was defined for steel plate. A “hard” contact property was defined between the outer surface of the bolt and the bolthole surface. The reference point was applied to the bolt to govern the motion of the entire rigid body. A rigid body constraint was created between the leading face of the plate and a separate reference point to simplify the definition of boundary conditions. In this way boundary conditions and the outputs of results were prescribed only to the reference points. A displacement was prescribed to the plate’s reference point, while ali other degrees of freedom of the reference points were prevented. 20 Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. a) rigid bolt – meshed b) deformable plate – meshed c) single bolt shear connection Fig. 11: Numerical model type Ml 3.3 Numerical model type M2 The numerical model M2 was an upgrade of model Ml. It was used to simulate shear connections with bolts in double shear, where cover plates restrain the deformation of the inner plate, while bolts remain in their initial position. Therefore bolt was modelled as 3D solid deformable body (Fig. 12a). Washers were not considered in the numerical model. In addition, cover plates (Fig. 12c) were presented as a separate part in a model. The purpose of cover plates was to obstruct the deformation of inner plate and to introduce friction betvveen the plates. Bolt bearing was not introduced to the cover plates; therefore they did not have any boltholes. An elastic-plastic material was defined for inner steel plate, while elastic material was prescribed to the bolts and cover plates. A “hard” contact property was introduced betvveen the follovving surface pairs: bolt shanks-boltholes in the inner plate, bolt head (nut)-cover plate. A “hard” contact property with penalty definition of friction was prescribed betvveen inner and cover plate. Contact control vvith stabilization vvas prescribed to the contact bolt head (nut)-cover plate to overcome chattering betvveen contact surfaces at the start of the analysis. Similarly as in model type Ml, rigid body constraints vvere prescribed to the leading faces of the plates and outside surfaces of the bolt head (nut). Thus, ali boundary conditions vvere defined on the reference points. Bolt displacements in the plane of the connection vvere restrained. Ali three rotations vvere also restrained. The displacement of the bolts and cover plates perpendicular to connection vvas unrestrained. In this way the bolts could freely deform because of the tensile force, introduced to them by transverse deformation of the inner plate. A displacement vvas prescribed to the inner plate’s reference point. The friction vvas defined only by the coefficient of friction. The friction coefficient betvveen steel-to-steel contact surfaces may vary from 0,05 to 0,8 (Beardmore, 2008). The value of friction coefficient used in numerical simulations vvas obtained through an iterative process. The value of friction vvas determined for one connection, so that numerical resistance matched the experimental one. The same friction coefficient vvas then applied to the vvhole series of connections. The friction coefficient influenced only the value of the resistance and had no Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. 21 Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. impact on the stiffness of load displacement curve. The vales of the coefficient are given in the sequel, when describing the simulations for a specific connection series. a) deformable c) shear connection b) deformable inner plate c) deformable cover plate elastic bolt Fig. 12: Numerical model type M2 3.4 Numerical model type M3 This model type was the most realistic one. It was similar to model type M2, except that the cover plates have boltholes (Fig. 13c) and a contact was defined between the bolt shank and bolthole in the cover plate. Therefore, the loading was transmirted from the inner plate through the bolt(s) to the cover plate(s). A part of loading was also transmitted by means of friction vvhen the inner plate deformed in thickness and introduced pressure to the cover plate. Boundarv conditions vvere defined at the reference points that vvere included in rigid body constraints as in model type M2. a) deformable c) shear connection b) deformable inner plate c) deformable cover plate elastic bolt Fig. 13: Numerical model type M3 22 Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. 3.5 Contact interactions A “hard” surface-to-surface contact interaction in normal direction was always defined between bolt shank and bolthole on the plate. The contact pressure is in Abaqus defined between two surfaces at a point p, as a function of the “overclosure” h of the surfaces (the interpenetration of the surfaces). For “hard” contact it applies: p = 0 for h < 0 - the contact is opened - and: h = 0 for p > 0 - the contact is closed (see Fig. 14). The contact constraint is enforced with a Lagrange multiplier representing the contact pressure in a mixed formulation. Fig. 14: Pressure-overclosure relationship with possible negative pressure transmission (cohesion) and/or overclosure (SIMULIA, 2007) In models M2, M3 a default, penalty friction formulation of tangential contact was used. The friction was defined by coefficient of friction /u and by slip tolerance Ff. The basic concept of the Coulomb friction model is to relate the maximum allowable frictional (shear) stress across an interface to the contact pressure between the contacting bodies. In the basic form of the Coulomb friction model, two contacting surfaces can carry shear stresses up to a certain magnitude across their interface before they start sliding relative to one another; this state is known as sticking. A critical shear stress, at which sliding of the surfaces starts, is defined as a fraction of the contact pressure between the surfaces. The stick/slip calculations determine when a point passes from sticking to slipping or from slipping to sticking. The fraction of contact pressure is known as the coefficient of friction /u. In Abaqus there are two ways to define the basic Coulomb friction model. In the default model the friction coefficient is defined as a function of the equivalent slip rate and contact pressure. The stiffness method used for friction in Abaqus/Standard is a penalty method that permits some relative motion of the surfaces (an “elastic slip”) when they should be sticking. While the surfaces are sticking, the magnitude of sliding is limited to this elastic slip. Abaqus will continually adjust the magnitude of the penalty constraint to enforce this condition. The default value of allowable elastic slip y used by Abaqus/Standard generally works very well, providing a conservative balance between efficiency and accuracy. Abaqus/Standard calculates y as a small fraction of the “characteristic contact surface length li/\ and scans ali of the facets of ali the slave surfaces when calculating li . The allowable elastic slip is given as yi = F f li, where Ff = 0,005 is the default value of slip tolerance. Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. 23 Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. 3.6 Finite elements and meshing Linear eight-noded reduced-integration brick finite elements C3D8R with hourglass control were used to mesh the numerical models. Additionally, 6-node linear triangular prisms C3D6 were used only to complete the mesh. Reduced integration reduces running tirne, especially in three dimensions. Hourglassing can be a problem with first-order, reduced-integration elements in stress-displacement analyses. Since the elements have only one integration point, it is possible for them to distort in such a way that the strains calculated at the integration point are ali zero, which, in turn, leads to uncontrolled distortion of the mesh. First-order, reduced-integration elements in Abaqus include hourglass control, but they should be used with reasonably fine meshes. Hourglassing can also be minimized by distributing point loads and boundary conditions over a number of adjacent nodes. The option to C3D8R elements were 20-node, quadratic, brick elements with reduced integration C3D20R, but due to almost 10 times longer computational tirne at the same mesh size they were not selected for simulations. C3D20R behaved “softer” in post-critical region especially where necking occurred (approximately 5% difference). The difference in maximum resistance was less than 2%. The finite element mesh was generated automatically on the basis of approximate element size for a specified celi. Cells were constructed from each part in the model. The largest finite element edge size was equal to plate thickness, if the thickness was smaller than 10 mm. At plate thickness equal to or larger than 10 mm, the edge size was 7,5 mm. There were at least two elements in thickness direction, and at 20 mm thick plates there were four elements in thickness. The mesh was generally denser in the zone of boltholes. The zone width of denser mesh was three times diameter of bolthole and there were four elements in the thickness direction. The cover plates in model type M2 were meshed very coarse. The size of finite element edge was equal to plate thickness. On one hand denser mesh gives more accurate results and on the other hand coarser mesh is more effective at contact convergence. Thus, an optimal mesh density was chosen and confirmed by mesh convergence study. The mesh convergence study is shown on the connection BI 16 modelled with model type Ml. Five different meshes are illustrated in Fig. 15, where meshl is the coarsest with average FE edge size equal to 10 mm. Fig. 16 presents load-displacement curves for the described mesh types and different FE type. Beside the described FE types C3D8R and C3D20R, the element type C3D8I with incompatible modes was included in the study, as well. This element experienced convergence problems. Hence, it was not applied in further analyses. As can be seen in Fig. 16, the FE type C3D20R gives lower resistance in post-critical region. The difference at maximum resistance is in comparison to FE type C3D4R negligible (see also Table 8). The element type C3D20R becomes very expensive when denser mesh is used (Table 8). In some cases of model type M3 and FE type C3D4R the computational tirne increased to 23 hours (connection L12_tl0-20_M27_b270)), thus the use of element type 24 Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. C3D20R would be too expensive. Therefore, the combination of mesh types mesh4 and mesh5 and FE type C3D8R was used for comprehensive numerical study of tension splices. Table 8: Comparison of the resistance and computational time for different meshes and finite elements Mesh Finite Pmax Error P(u=24 mm) Error Wallclock Time tvpe element tvpe [%] [%] time [s] ratio meshl C3D4R 406 18,6 406 47,8 40 1,00 mesh2 C3D4R 356 4,1 303 10,3 84 2,10 mesh3 C3D4R 356 3,9 309 12,5 141 3,53 mesh3 C3D8I 353 3,0 N/A NA 236 5,90 mesh3 C3D20R 344 0,5 281 2,3 936 23,40 mesh4 C3D4R 348 1,7 296 7,7 888 22,20 mesh4 C3D20R 342 0,0 275 0,0 7109 177,73 mesh5 C3D4R 356 4,0 308 12,0 337 8,43 a) mesh1 – average FE edge size 10 b) mesh2 – average FE edge size 5 c) mesh3 – average FE edge size 5 mm, 1 element in z direction mm, 1 element in z direction mm, 2 element in z direction d) mesh4 - average FE edge size 3 e) mesh5 - average FE edge size 5 mm, 3 element in z direction mm, 4 element in z direction Fig. 15: Mesh types Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. 25 Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. 410 j 246 164 0 r^ —— —\_^--+-—¦ i i —-=:^^—««»-.' 1/ ^§^ ------meshl_C3D4R ------mesh2_C3D4R ------mesh3_C3D4R — mesh4_C3D4R — mesh5_C3D4R 410 ^46 164 0 0 4 20 8 12 16 Displacement [mm] a) different mesh type, same FE type 410 24 0 4 20 8 12 16 Displacement [mm] b) same mesh type, different FE type 24 328 ' 746 164 82 1 1 "¦----», 1 1 1 1 1 1 1 1 1 1 1 1 ------mesh4_C3D4R ------mesh4_C3D20R ------mesh5_C3D4R i i 8 12 16 Displacement [mm] c) effectiveness of FE type C320R Fig. 16: Load displacement curves for different meshes and finite elements 3.7 Determination of material model The procedure for the determination of material characteristics is standardized. On the basis of standard tensile test a number of parameters are measured. The output of this test is an engineering stress-strain diagram. The engineering stress (force per unit undeformed area) in the metal is known as the nominal stress, with the conjugate nominal strain (length change ?L per unit undeformed length L0). Metal deforming plastically under tensile load may experience highly localized extension and thinning, called necking, as the material fails. Thus, necking is the reason that nominal strain is not uniform through gauge length. In Abaqus elastic and plastic behaviours are entered separately. As far as elastic part is concerned the input is trivial. Elastic modulus E and Poisson’s ratio ? are sufficient parameters for stress-displacement analysis. In the case of our simulations the choice of parameters was always equal to: E = 210 GPa and ? = 0.3. The plastic behaviour is defined by true stress and plastic part of true strain. This definition is reasonable because nominal stress-strain plots are not necessarily equal for tension and compression. A mathematical model describing the plastic behaviour of metals should be able to account for differences in the compressive and tensile behaviour independent of the structure's geometry or the nature of the applied loads. Strains in compression and tension are the same only if considered in the limit as ?L›dL›0; i.e 328 328 82 82 0 ¦ 4 26 Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. ds = — (3) L L L L (4) where L is the current length, L0 is the original length, and s is the true strain or logarithmic strain. The stress measure that is the conjugate to the true strain is called the true stress and is defined as: F 100) is available, the characteristic and design values may be obtained from: rk =bgrt(Xm)Qxp(-kcoQ-0,5Q2) = bgrt(Xm)-Rk (41) rd = bgrt (Xm)exp(-kd jQ-0,5Q2) = bgrt (Xm)-Rd . (42) Material partial factor yu covering also uncertainty in the resistance model and geometric derivations is determined in two steps directly from characteristic, design and nominal resistances. The initial estimate for partial factor yu is defined as ratio between characteristic and design value. r exp(-kxartQrt-knasQs-0,5Q 2 ) R Ym = — =----------------------------------------- = —- (43) rd zxy(-kdxartQrt -kdnasQs -0,5Q2 ) Rd The design resistance function contains basic variables defined as nominal values Xn. The nominal value of the material strength may be adopted as characteristic value and the nominal values for the geometrical variables may be adopted as mean values. Thus, on the basis of actual material strengths, characteristic material strengths need to be obtained. This can only be done, if additional prior knowledge is available. The deviation of the nominal material strengths of selected steel grade from actual strengths may be too large and consequently the choice of partial factor would be incorrect. To justify this step, an upper bound (conservative assumption) for coefficient of variation V/, which is known from a significant number of previous tests, should be taken. Therefore, the characteristic value for material strength is determined by using prior knowledge. Characteristic value of material strength is equal to: rk = exp (-2,0Vr - 0,5V2) rem, (44) where Vr is maximum variation coefficient obtained from previous tests and rem is the mean value of at least three tests. This procedure is limited by: \r -r \<0Ar , (45) ee em ? em where ree is the extreme measured value. The variation coefficient for yield and tensile strengths given by equations (25), (26) were taken from literature. The Backgroud documentation to EC 3 (Snijder et al., 1988a) gives coefficient for/M independent of steel grade. Although there are also some tests with HSS, the coefficients probably apply to mild steels. The same coefficients were used in our čase. Characteristic values^ and/„fc calculated according to equation (44), give: fyn = fyk = ^p(-2 • 0,07 - 0,5 • 0,072) fyact = 0,867 • fyact, (46) 40 Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. Ratio kc between the nominal resistance r„ and the characteristic resistance rk is written as follows: k = — . (47) The corrected partial factor for the use with the nominal resistance is finally obtained from: ^ =&c;km =—— = — . (48) rk rd rd 4.3.1 Data for statistical evaluation of net cross-section resistance formula To statistically evaluate the net cross-section resistance checks, our test results and results found in literature were used. Specimens that failed in net cross-section are evident from Table 11. Only those tests on bolted connections made of HSS found in literature with net cross-section failure mode were used in the evaluation. A series of 6 bolted shear connections that failed in net cross-section was tested in Finland (Kouhi, Kortesmaa, 1990). The connections with 4 bolts positioned rectangularly were made of steel grade equivalent to S620. Bolted connections with 3 bolts positioned parallel to loading were investigated by Aalberg and Larsen (March 1999). Two high steel grades (S460, S690) were used and 18 connections failed in net cross-section. Puthli and Fleisher (2001) tested bolted connections with two bolts positioned perpendicular to loading. Steel grade S460 was used and 4 connections failed in net cross-sections. The net cross-section, actual material parameters and maximum force of the results from literature are presented in Table 12. The specimens are denoted by authors’ surname initial and specimen name used in the literature (e.g. PF 10 -Puthli, Fleischer speč. no. 10 as denoted in Puthli, Fleischer, 2001). Experimental resistances are expressed by vector re. In Fig. 30 test results rei are plotted versus the theoretical resistance rft-3. The scatter of data is small, except for the eccentric specimens where load is transferred through bolts. Sensitivity diagram in Fig. 31 suggest that the data set could be independent of bolt number and that hole eccentricity of specimens H and HH does not effect the resistance. To exclude the effect of eccentricity, six data sets are formed. Data sets are formed as follows: • data set 0: ali results • data set 1: only specimens with concentric holes • data set 2: ali specimens, except BI with eccentric holes (specimens H, HH with eccentric holes are included) • data set 3: ali specimens with eccentric holes (H, HH, B1 eccentric) • data set 4: only specimens B1 with eccentric holes • data set 5: only specimens BI (single bolt shear connections) Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. 41 Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. Table 12: Geometrv and maximum force of specimens from literature Specimen name Actual^4„a Nominalni Actual/^ [mmz] [mmz] [MPa] Actual/„ [MPa] [kN] KK H1 700,0 707,2 622 733 529,0 KK H2 936,0 915,2 622 733 679,0 KK H3 1121,0 1913,6 622 733 795,0 KK H4 851,0 832,0 622 733 652,0 KK H5 1058,0 1040,0 622 733 795,0 KK H6 1200,0 1164,8 622 733 890,0 PF 10 840,0 840,0 524 645 568,0 PF 11 997,5 997,5 524 645 630,0 PF 15 997,5 997,5 524 645 660,0 PF 16 1155,0 1155 524 645 762,0 AL 460-1 882,5 880 472 556 507,8 AL 460-2 876,4 880 472 556 506,4 AL 460-3 878,1 880 472 556 506,8 AL 460-4 845,7 840 472 556 487,8 AL 460-5 837,3 840 472 556 487,8 AL 460-6 834,8 840 472 556 492,9 AL 460-7 773,8 780 472 556 443,4 AL 460-8 776,1 780 472 556 442,4 AL 460-9 775,5 780 472 556 443,4 AL 700-1 888,8 880 820 873 768,6 AL 700-2 888,8 880 820 873 758,3 AL 700-3 884,3 880 820 873 750,0 AL 700-4 839,2 840 820 873 729,0 AL 700-5 837,8 840 820 873 727,0 AL 700-6 838,8 840 820 873 729,5 AL 700-7 786,2 780 820 873 678,7 AL 700-8 780,0 780 820 873 672,4 AL 700-9 786,2 780 820 873 673,3 4.4 Results of statistical evaluation and discussion The results of statistical analysis are presented in Table 13. The difference in the value of partial factor ?M* for the data sets 1 and 2 is negligible. As mentioned above, the eccentricity of the hole at specimens H and HH did not affect the resistance. In Figs. 30, 32, 34-35 the diagrams of experimental resistances versus theoretical resistances are plotted. If the resistance function was exact and complete, all points (rti, rei) would lie on the bisector of 1st quadrant. In general the points (rti, rei) show some scatter due to incorrect resistance model, scatter in material properties and error in geometry. Table 13: Results of statistical analyses of design net cross-section resistance Model Data set No. tests k„ kd b Vg K Ym Ym* 1 Eq. (14) 0 80 1,73 3,44 1,002 0,068 0,110 1,182 1,237 1 70 1,73 3,44 1,007 0,027 0,091 1,138 1,143 2 76 1,73 3,44 1,007 0,027 0,090 1,137 1,142 1* 0 80 1,73 3,44 1,113 0,068 0,110 1,182 1,113 1 70 1,73 3,44 1,119 0,027 0,091 1,028 1,028 2 76 1,73 3,44 1,118 0,027 0,090 1,137 1,027 2 Eq. (15) 0 80 1,73 3,44 1,071 0,098 0,131 1,229 1,252 1 70 1,73 3,44 1,078 0,072 0,113 1,188 1,161 2 76 1,73 3,44 1,077 0,070 0,111 1,185 1,157 3 Eq. (16) 3 10 1,73 3,44 1,286 0,239 0,254 1,524 1,635 4 4 2,63 11,4 1,028 0,043 0,096 1,318 1,333 4a 4 1,73 3,44 1,028 0,043 0,096 1,151 1,144 5 8 2 5,07 1,020 0,031 0,092 1,156 1,151 4a – considered as large number of tests were preformed (in factors kn, kd) 42 Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. Resistance model 1, with correction factor b close to 1 and relatively small scatter, most appropriately describes the ultimate load of a net cross-section. According to Eurocode 3 partial factor yu2 (with recommended value yui = 1,25) should be assigned to this resistance model to form design resistance, since the resistance model is defined by fracture mechanism. For data set 1 it is clear that design resistance: Af Nt Rd = " (49) / M2 meets reliability requirements of EN 1990, since partial factor yu2 = 1,25 is greater than the value of yu = 1,143 (data set 1, Table 13). Moreover, design resistance (49) has also some extra safety for parameters which were not included in our analysis, like the effects of fabrication tolerances for hole position, that may be larger than assumed in VXl parameters. It was shown that additional partial factor should be approximately 1,1 (Sinur, Beg, 2008) to account for the characteristic value (as 5% quantile) of fabrication tolerance for hole position equal to ±2 mm. The resistance model 1 multiplied by 0,9 (further in the text referred to as resistance model 1*) and in combination with partial factor yui forms the design net cross-section resistance as defined in EN 1993-1-1 given by equation (8). This design resistance was determined on the basis of tests (Snijder et al., 1988a. 1988b) mainly for steel grade S235. 77 tests for steel grade S235 and only a few test results for other steel grades (3 tests for A43 and 3 for StE460) were processed in that research. The estimator for variation coefficient for scatter F 690 N/mm2 and Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. 43 Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. Tadd = J^ =-----= 1,06. (51) fun > 770 N/mm2. Considering the common ratio fu/fy = 1,05, which was for steel S690 and higher grades measured in several researches done around the world the nominal yield strength should not be lower than f to classify steel as S690: ,, /„„ 770 MPa / =^ns- =-----------= 733 MPa. (50) 1,05 1,05 Under the assumption/„/L, = 1,05, additional relative resistance or additional safety is present in the design resistance given by equation (10). This additional safety can be expressed as the ratio of yield strengths: J yn / J J f ~690 Nevertheless, additional safety yadd is smaller than the partial factor obtained in statistical analysis (/m = 1,161, see data set 1 in Table 13). This was more engineenng approach to prove that design net cross section resistance (10) is not safe enough, at least for steel grade S690. In the čase of unsymmetrical members the test results showed that eccentricity of the hole was very important for specimens where loading was transferred through the bolt. For plates in tension with eccentrically drilled holes (specimens H and HH - different boundary condition) the eccentricity of the hole had almost no effect on the resistance. This fact is confirmed in Figs. 30-33, where the resistance models 1 and 2 (data set 0) are suitable for ali specimens H and HH (including unsymmetrical ones). Models 1 and 2 give too optimistic values for unsymmetrically loaded specimens BI, where loading was transferred by means of the bolt. The small estimator for variation coefficient for scatter V s = 0,043 and correction factor b = 1,028 indicates that data set 4 meets resistance model 3, which is appropriate for unsymmetrically connected members. Since only 4 results were available in data set 4, k„ and * kd factors are very large and consequently partial factor yM = 1,333 is large (see data set 4 in Table 13). The resistance model 4 can also be used for symmetrically connected elements with single bolt. Therefore, data set 5 was created. Now, ali parameters are even more *.,.,—., favourable and the value of partial factor drops to yM = l,l5l (see data set 5 in Table 13). If data set 4 was treated as a larger set, the k„ and kd factors would be higher and a similar value of partial factor would be obtained (see data set 4a in Table 13). Thus, resistance model 3 could be formed with yy2 = 1,25 and the design net cross-section resistance of unsymmetrically connected members in tension with one bolt (12) could also be applied to high strength steels. Fig. 34 plots the theoretical resistances against the experimental resistance for ali specimens with eccentric holes (data set 3) calculated according to resistance model 3. Because this resistance model is inappropriate for specimens H and HH with eccentric hole, the scatter of points and the value of yM = 1,635 are large (data set 3 in Table 13). The resistance of net cross-section of members with eccentric holes in tension may be verified according to equation (8) for concentric holes or conservatively also by equation (12) for eccentric holes. 44 Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. Current ANSI/AISC 360-05, Specification for structural steel buildings (AISC, 2005), covers steel grades up to yield strength 690 N/mm2 with some limitations. The standard gives two distinct methods: Load and Resistance Factor Design (LRFD) and Allowable Strength Design (ASD). LRFD is in principle equal to design approach according to Eurocodes. Under the assumption that the definition of the characteristic and the design value is equal to Eurocode, safety factors can be directly compared. In AISC 360-05 the design tensile strength of tension members should be the lower value obtained according to the limit states of tensile yielding in the gross cross section and tensile rupture in the net section. The yielding in the gross cross section for HSSs is almost never or never decisive because of very \ow fulfy ratio. Hence, design tensile strength is Pn u = (pfuAnet (p = 0,75. (52) Equation (53) is consistent with resistance formula (8) and resistance model 1*: 0,94*/. 0,9 n,u t net Ju h M,AISC (t> 1,20. (53) ? M,AISC Partial factor ?M,AISC is larger than ?M* = 1,028 for data set 1 in Table 13. Then it follows that equation (53) is acceptable according to reliability criteria of EN 1990. Furthermore, the design resistance function according to AISC 360-05 gives slightly less conservative values than equation (8) in EN 1993-1-1, where the recommended partial factor is ?M2 = 1,25. 1500 1000 500 1.25 250 500 750 1000 1250 1500 Theoretical resistance [kN] 0.75 0.5 - Model 1 A BI - eccentric holes ¦ H - eccentric + HH - eccentric • BI eccentric ¦ L XPF 12 Number of bolts 1 0 ' Fig. 30: (re, rt) diagram – Model 1, data set 0 Fig. 31: Sensitivity diagram - Model 1 Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. 45 Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. 1500 • Model 2, Data set 0 ------re= b rt 1250 750 250 0 250 500 750 1000 1250 1500 Theoretical resistance [kN] Fig. 32: (re, rt) diagram – Model 2, data set 0 600 450 300 150 150 300 450 600 Theoretical resistance [kN] 1.25 0.75 0.5 ¦ H - eccentric + HH - eccentric • BI eccentric ¦ L XPF 0123 Number of bolts Fig. 33: Sensitivity diagram - Model 2 600 — 450 — 300 — 150 150 300 450 Theoretical resistance [kN] 600 Fig. 34: (re, rt) diagram – Model 3, data set 3 Fig. 35: (re, rt) diagram – Model 3, data set 5 4.5 Summary High strength steels, with a typical/„//^ ratio of 1,05, are considered to be less ductile than mild structural steel. Therefore it is believed that they are suitable only for elastic analysis. The problem is that inelastic behaviour is hidden in numerous nominally elastic resistance checks of steel structures and therefore sufficient local ductility has to be assured. In this chapter the net cross-section design resistance as it was defined in draft of EN 1993-1-12 was discussed. An extensive experimental research of plates with holes and bolted connections made of steel grade S690 (nominal yield strength fyn = 690 N/mm2) was conducted to determine maximum resistance and ductility of the net section area. It was confirmed that a low fu/fy ratio does not affect local ductility significantly. Ali net section failures were ductile and comparable to failures of mild steels. However, a \ow fulfy ratio does not allow yielding of gross cross-section and therefore net section check gains its importance. 1000 o o o o o 46 Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. The primary goal of this research work was the validation of design provisions for elements in tension by statistical analysis of experimental results. Local ductility and failure mechanisms of elements in tension were quantitatively and qualitatively assessed. Additionally, high strength steel net cross-section test resistances were gathered from literature to include different steel grades in the statistical evaluation. By statistical analysis of the test results according to Annex D of EN 1990 the following results were obtained: • Net cross-section design resistance for high strength steels: 0 9 A f Nt Rd =—^^- (54) ? M2 is with ?mi = 1,25 safe. Moreover, it was established that this design resistance is very conservative for high strength steel sections. The partial factor needed is only 1,03 (data set 1 in Table 13). This design resistance has some extra safety for cases of accidental eccentric hole position and is safe even without factor 0,9. • Additional rule for lower bound of net cross-section design resistance for high strength steels as was defined in the draft of EN 1993-1-12: Af NtRd = mt y (55) ? M0 (with ?m$ = 1,00) may not be safe enough. Based on our test results, the design resistance according to equation (55) was in the final draft of EN 1993-1-12 changed to equation (54). • It was established that the design net cross-section resistance of unsymmetrically connected member in tension with one bolt may also be used for high strength steel sections, although EN 1993-1-12 disallows its use: 2(e9-0,5 1.2 d0, edge distance e2 > 1.2 d0, pitch/7i > 2.2 d0 and pitch/?2 > 2.4 d0. Standard EN 1993-1-12 (CEN, 2007) gives no additions to any of these rules. Ratio fui/fu in factor ccb considers cases where bolts have lower strength than plates in order to control deformations. Additional rules apply for non-standard bolt holes. ab = min _, . J ub . i "d' r 51 V Ju J ad = —*- for end bolts 3d0 a, = —------ for inner bolts d 3d0 4 perpendicular to the direction of load transfer kx = min 2,8-f-l, 7;2,5 v "o J for edge bolts kx = min 1 4^—1 V d0 7; 2,5 J for inner bolts 50 Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. \ e2 / P2 e, - o o Pi e, Fig. 36: Definition of distances For a group of bolts the following statement is given in 3.7(1), EN 1993-1-8: “The design resistance of a group of fasteners may be taken as the sum of the design bearing resistances Fb,Rd of the individual fasteners provided that the design shear resistance FvM of each individual fastener is greater than or equal to the design bearing resistance FhM . Othenvise the design resistance of a group of fasteners should be taken as the number of fasteners multiplied by the smallest design resistance of any of the individual fasteners.” This paragraph was commented by Bijlaard (Bijlaard, 2006): “This statement is meant to persuade the designer to choose a balanced bolt pattern and to avoid having a relatively small end distance in combination with a relatively large pitch. A wrong design may lead to premature failure of the end bolts before the inner bolts reach their capacities. The capacity of the group of bolts will be overestimated in such cases.” In order to correctly predict a balanced bolt pattern and consequently the desired ductility and failure, the bearing resistance formula should accurately describe the phenomena and should also be supported by experimental results. ANS/AISC 360-05 (AISC, 2005) defines the available design bearing strength R„ at bolt holes as follows (resistance factor ^= 0,75): • When deformation at the bolt hole at service load is a design consideration Rn = 1,2Lctfu < 2,4dtfu. (65) • When deformation at the bolt hole at service load is not a design consideration Rn = \ 5Lctfu < 3,0dtfu. (66) In equations (65)-(66) parameter Lc is clear end distance in the direction of the force, between the edge of the hole and the edge of the adjacent hole or edge of the material (p} - d0/2 or e} -d0/2). For connections, the bearing resistance shall be taken as the sum of the bearing resistances of the individual bolts. Additional rules apply for long-slotted holes with the slot perpendicular to the direction of force. 5.4 Test results 5.4.1 One- and two-bolt shear connections - specimens BI, B2 Several failure modes were observed among 25 single bolt shear connections (specimens BI) and 13 two-bolt shear connections (specimens B2). Nominal and actual geometry of specimens is presented in Table 5, while the failure mode and maximum resistance are shown Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. 51 Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. in Table 14. In Table 14 failure mode, maximum force Fmax and displacement at maximum force Dufor specimens BI and B2 are displayed. The experiment was also numerically simulated to obtain the stress state and to develop an effective numerical model for later simulations. Specimens that failed in different ways (B101 - net cross-section failure, BI09 - plate shear failure, BI 11, BI 12 - splitting failure - see Fig. 37) were numerically simulated. Numerical model type Ml was applied for the simulation (see Chapter 3.2). Material model in terms of true stress - true plastic strain curve, applied in the simulation, is presented in Table 9 (see also Chapter 3.7). Additionally, numerical model M2 (see Chapter 3.3) was applied for the numerical simulation of BI 12. Friction coefficient /u = 0,25 was used in the model. The choice of friction coefficient is explained in Chapter 3.3. The comparison of numerically and experimentally obtained load-displacement curves is presented in Fig. 38. The agreement of both (experimental and numerical) curves is outstanding. Numerical model Ml gave very satisfactory results for the determination of maximum resistance, while stiffness was in good agreement with the test only for specimens where deformations in thickness direction were not too large. The disadvantage of model Ml was corrected by model M2. Table 14: Test results for specimens B1 and B2 Specimen Failure J max Du Specimen Failure J max Dv name mode" [kN] [mm] name mode" [kN] [mm] B101 3 262 2,4 B201 3 457 2,4 B102 1 273 5,1 B202 1 471 5,8 B103 1 342 6,1 B203 3 643 4,3 B104 1 360 3,5 B204 3 638 3,9 B105 3 355 3,5 B205 3 689 6,2 B106 3 445 5,8 B206 1 596 6,7 B107 3 440 5,6 B207 3 789 10,4 B108* 3 370 4,0 B208 1 398 3,9 B109 1 228 5,2 B209 1 491 4,9 B110 1 286 5,8 B210 1 603 5,6 Bili 1 363 6,4 B211 1,3 776 10,2 B112 1 483 8,9 B212 3 851 12,6 B113 3 516 8,5 B213 3 678 5,8 B114 3 510 9,1 B115* 3 435 6,2 B116 1 371 5,8 B117 1 362 6,6 B118 1 392 9,8 B119 1 530 12,0 B120 1 629 19,5 B121 1,3 763 24,8 B122 3 788 24,3 B123 3 483 15,9 B124* 3 400 10,0 B125* 3 322 5,6 * eccentric hole a 1 fracture in the specimen between hole and free edge per pendicu 2 fracture in the specimen between bolt holes 3 net cross-section failure 52 Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. b) splitting failure of specimen Bili c) mixed failure specimen B121 d) net cross-section failure of specimen B114 Fig. 37: Failure modes for specimens B1 500 400 300 200 100 splitting failure BI01 - Abbqus B109 - At*qus BI 11 - Ablaus B112 BI 12 - Abaqus M2 10 15 20 Displacement [mm] 25 30 0 0 5 Fig. 38: Comparison of experimental and numerical load-displacement curves Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. 53 Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. 800 700 -600 -500 - 400 - 300 -200 -100 - 0-........................................ 0 4 8 12 16 20 24 28 32 36 40 Displacement [mm] Fig. 39: Force-displacement curves for two groups of specimens with the same width Fig. 39 illustrates load displacement curves for two groups of specimens. The first group includes B109 to BI 14 and the second group includes BI 18 to B122. The widths of specimens in the first and second groups were 90 mm (e2 = l,5d0) and 120 mm (e2 = 2d0), respectively. End distance e\ was the varying parameter. B109 (see Fig. 39a) and B118 failed in shear. The displacements at failure were approximately equal to clear end distance (e\ -0,5d0). Splitting failure was observed at specimens BI 10, Bili (see Fig. 39b), BI 19 and B120 due to transverse tensile stress on a free edge perpendicular to load direction. Specimens BI 12, B121 (see Fig. 39c) almost reached net cross-section resistance. The necking appeared on the edge of the hole in the net cross-section, but splitting failure occurred sooner than the fracture in the net cross-section. These failures could also be characterized as mixed failures. Specimens BI 13, BI 14 (see Fig. 39d) and B122 failed in the net cross-section after hole elongation. The fractures were characterized as ductile failures (necking of net cross-section, reduction of thickness). The load displacement curves of ali the remaining specimens are shown in Appendix B as well as in photographs of deformed specimens. Shear failure of the plate due to bolt bearing occurred when the absolute and relative values of end distance e\ were small enough compared to the edge distance e2 (see Fig. 37a). This type of failure only occurred if the specimens were sufficiently wide for the net section not to yield. The fractures were instantaneous after excessive local plastic deformations of the specimen. The stress state of BI09 at maximum resistance is shown in Fig. 40. Maximum principal stresses (Fig. 40c) were not able to hold back the steel in front of the bolt due to high shear (Fig. 40d) that caused the fracture (bolt tearout). It followed the path of high shear in a straight line. These kinds of failures were very ductile where load displacement curves were characterized by a long yield plateau (exp. as curve B109 in Fig. 39). 54 Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. a) active yield flag at integration points b) minimal principal stress (compression - blue is the lowest stress) c) maximal principal stress (tension - red means the d) shear stress (-56 IMPa blue; 561 MPa red) highest stress) Fig. 40: Results of numerical simulation of B109 at 5,365 mm of hole elongation in the middle surface If end distance e\ was increased (at a constant edge distance e2), specimens failed as shown in Fig. 37b - splitting failure. Numerical simulation of specimen Bili revealed that stress redistribution resulted in yielding of the area shown in Fig. 41a. Maximal principal stresses shown in Fig. 41c formed an are of high tensile stresses that contained the bursting aetion. The free edge of the plate perpendicular to loading direetion was subjeeted to high tensile stress which caused neeking, followed by fraeture which progressed to the area with the highest shear stress (see Fig. 41d) in a curved pattern, as shown in Fig. 37b. Minimal principal stress - mostly in compression - (Fig. 41b) forced the specimen to deform in thickness direetion. These kinds of failures were characterized by higher resistance and larger displacement at maximum resistance than pure shear failures. The magnitude of plastic strain at integration points higher than 1 shown in Fig. 42 should be interpreted as rupture of the material. At even larger end distances e\ (narrow specimens) net eross-seetion failure prevailed (see Fig. 37d). The fraeture formed after neeking of the net area and after large bolthole elongation. The net eross-seetion resistance was also the maximum resistance possible for specimens of equal widths. The stress state of specimen B101 just after reaching the maximum resistance is illustrated in Fig. 43. Maximum principal stresses concentrated in the Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. 55 Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. net cross-section causing failure. It seems that load (ec)centricity is of vital importance at single bolt connections. Experimentally (Fig. 37d) as well as numerically (Fig. 43d) the necking and failure were observed only on one (the weakest) side of the specimen. At certain end distance e\ a mixed failure was observed, where splitting failure occurred simultaneously with net cross section failure (see Fig. 37c). Excessive plastic deformations of net section and plate in bearing were typical for this kind of failure. Ali types of failures were denoted by severe plastic deformations, especially in front of the bolt where steel literally flowed into the hole between the bolt and the bolthole in the adjacent plates. The specimens tended to deform in thickness direction. This caused pressure on adjacent plates and therefore introduced tension into the bolts. The bolts acted like a spring, which reduced the out of plane deformations. The effect of restraining in thickness deformations on stiffness of load-displacement curves was observed in the test and in numerical simulation. This deficiency of model Ml was effectively suppressed by model type M3 which gave excellent results for specimen BI 12. To study different boundary conditions three specimens of equal geometry with different tightening force were tested. Specimens Bili and BI 16 were snug tightened, but to BI 16 additional half a turn of the nut was given. At specimen BI 17 a gap between adjacent plates was left for specimen to freely deform in thickness. The load displacement curves (see Fig. 44) and failures of ali three specimens were very similar. Slightly larger maximum resistance of BI 16 went on account of friction between specimen and forks. Fracture in the tensile area opened later at unrestrained specimen BI 17 and therefore BI 17 developed higher resistance in the post-critical region. Therefore, the choice of numerical model Ml, M2 or M3 is dependent on boundary conditions. It has to be considered that model type Ml shortens the computational tirne by 4,5 times. 56 Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. a) active yield flag at integration points b) minimal principal stress (compression – blue means the lowest stress) c) maximal principal stress (tension – red means the highest stress) d) shear stress (-541MPa blue; 541 MPa red) Fig. 41: Results of numerical simulation of B111 at 6,375 mm of hole elongation in the middle surface Fig. 42: Magnitude of plastic strain at integration points at failure - a cut through Bili Larger geometry of single bolt connection in terms of end, edge distances results in large hole elongation at maximum resistance. The stiffness of load-displacement curves was equal to the point of yielding of the material (see Fig. 39). If the hole elongation was considered as a limit state, then the bearing resistance should be limited for connection with larger geometry (as e.g. B120-B122). The gradually decreasing stiffness of these geometries resulted in large hole elongations, long before maximum resistance was reached. On the other side, the stiffness of connections with smaller geometries decreased quickly. Thus, hole elongation at e.g. 0,8Pmax was much lower than at maximum resistance Pmax. Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. 57 Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. a) active yield flag at integration points c) maximal principal stress (tension – red means the highest stress) b) minimal principal stress (compression – blue means the lowest stress) d) Mises stresses at 17,33mm of displacement Fig. 43: Results of numerical simulation of B101 in the middle surface (a, b, c at 2,717 mm of displacement) 400 350 300 250 200 150 100 50 0 9 12 15 Displacement [mm] 18 21 24 Fig. 44: Force-displacement curves for different boundary conditions The failure modes of specimens B2 were similar to failure modes of specimens B1. Although, ratio 2e2/p2 was varied from 0,89 to 1,25, the pitch p2 had only a slight effect on the stress state. For these connections it is obvious that the bearing forces on both bolts are equal. Therefore, the results of specimens B2 can be directly compared to the results of specimens B1. 0 3 6 58 Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. 5.4.2 Bolted shear connections with 3 or 4 bolts positioned in the direction of load -specimens L In the second experimental phase 9 three-bolt and 17 four-bolt shear connections were tested. Ali tests were numerically simulated in order to observe stress-deformation state and to obtain the distribution of bearing forces between bolts. Model type M2 (see chapter 3.3) with nominal geometry was applied in numerical simulations. Material model (see chapter 3.7) was based on material characteristics obtained from standard tensile test for plate II - S690 (see Table 3) since specimens were fabricated from that plate. The true stress - true plastic strain values are presented in Table 10. Friction coefficient /u = 0,25 was used in the numerical simulations. The choice of friction coefficient is explained in Chapter 3.3. In Table 15 failure modes and maximum force Fmax for specimens L are displayed. Table 15: Test results for specimens L Specimen Failure Fmllx name mode" [kN] L01 1 778 L02 1 908 L03 2 1088 L04 1 1066 L04s 1 1057 L05 1 1185 L06 2 1386 L06s 2 1374 L07 1 945 L08 1 1294 L09 3 1521 L10 3 1522 Lil 1 1155 L12 1 1268 L13 4 1329 L14 1 1425 L15 1 1501 L16 3 1537 L17 3 1539 L18** 3 1537 L18s 3 1533 L19 3 1507 L20 3 1527 L20s** 3 1480** L21 1, 4 1271 L22 1, 4 1250 1 fracture in the specimen between hole and free edge perpendicular to the direction of load 2 fracture in the specimen between bolt holes 3 net cross-section failure 4 shear failure of the bolt test stopped before failure 1600 /% L2 Os a^ • m L13 i2 L22 •? /• 800 800 1000 1200 1400 Numerical max. resistance [kN] 1600 Fig. 45: Comparison of numerical and experimental resistances The numerical response curves agree with the experimental ones in resistance (Fig. 45), stiffness and in deformation state (Fig. 46) for ali kinds of failures. The only exceptions are the connections where bolt shear failure was observed (see Table 15 - L13, L21, L22) or where the test was stopped before reaching the maximum resistance (L20s). The numerical and experimental load displacement curves for ali specimens are presented in Appendix C. a Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. 59 Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. Fig. 46: Mises stress plotted over the actual specimens L20 and L21 (grid of lines), respectively The bolts are denoted as B1, B2, B3 and B4, where bolt B1 is the closest to specimen’s free edge (see Fig. 46). Similar notification is considered for holes. Hole H1 on the specimen is paired with bolt B1 and is considered as the first hole. Bearing forces per bolts, friction, maximum resistance Pmax and displacement at Pmax for two sets of maximums are shown in Table 16. Global maximums refer to maximum resistance and local maximums refer to the resistance, where the first among ali bolts reached its maximum resistance. The bolt that first reached the maximum resistance is printed in bold. Local and global maximums are also graphically presented in the sequel. 60 Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. Table 16: Results of numerical simulations for specimen type L Specimen U *max BI Global maximums B2 B3 B4 Friction EBi U *max BI Local maximums B2 B3 B4 Friction EBi [mm] [kN [kN] [kN] [kN] [kN] [kN] [kN] [mm] [kN [kN] [kN] [kN] [kN] [kN] [kN] L01 5,7 813 176 241 278 117 696 2,9 771 178 227 271 94 676 L02 5,9 912 214 261 284 152 760 3,8 891 220 256 282 133 758 L03 8,7 1115 289 276 287 263 852 5,1 1088 294 282 290 222 866 L04 4,7 1052 159 210 265 279 138 913 2,3 988 169 201 242 261 115 873 L04s 7,3 1023 161 198 256 277 130 893 2,6 543 231 51 90 110 61 482 L05 5,1 1169 198 234 272 284 181 988 2,3 1061 209 214 241 260 137 924 L06 7,2 1374 273 261 281 281 277 1097 3,7 1309 285 260 273 280 211 1098 L06s 9,4 1360 275 247 277 281 279 1081 3,3 1000 320 154 188 200 138 862 L07 6,8 937 182 265 323 167 770 3,2 893 192 262 301 138 755 L08 5,9 1265 176 235 304 320 230 1035 2,9 1190 185 242 285 292 186 1004 L09 11,0 1481 225 279 319 323 333 1148 3,5 1372 256 275 298 299 244 1129 L10 11,0 1520 282 301 327 282 327 1193 4,0 1433 293 285 304 291 259 1174 Lil 11,4 1172 207 308 364 293 879 3,2 1047 247 298 317 184 862 L12 12,2 1293 234 321 375 354 929 3,4 1127 279 306 322 211 907 L13 14,0 1390 263 338 380 408 982 4,2 1225 308 324 333 260 965 L14 15,3 1434 143 224 342 383 342 1092 3,7 1316 180 276 315 316 229 1087 L15 11,7 1458 183 243 344 349 339 1119 4,0 1365 206 279 319 316 246 1120 L16 10,4 1528 241 324 354 300 310 1219 4,1 1449 246 305 332 306 261 1189 L17 10,0 1519 277 313 338 273 318 1201 3,1 1395 275 289 299 293 239 1155 L18 8,6 1518 308 314 327 263 306 1211 3,1 1416 292 289 300 288 246 1170 L18s 10,0 1519 325 289 311 277 317 1202 3,7 1292 324 195 215 324 233 1058 L19 9,1 1518 324 312 323 258 301 1217 2,8 1388 286 283 294 290 235 1153 L20 10,4 1520 261 320 340 279 318 1200 3,4 1405 257 297 308 297 243 1158 L20s 12,0 1529 268 314 330 300 315 1212 4,2 1292 234 249 247 335 220 1066 L21 18,4 1357 203 336 459 350 998 4,3 1154 267 321 346 211 934 L22 18,0 1408 207 334 422 437 964 4,8 1212 274 330 345 255 948 Table 17 presents the dependency between connection geometry and maximum resistances. The nominal width of specimens in Table 17 is equal. The resistance of the connection was generally increasing if pitches p\, end distance e\ or the number of bolts were higher. The upper limit of the resistance was net cross-section resistance (approx. 1537 kN). If the distances were even larger or the number of bolts was lower, the resistance was lower due to bolt shear failure. The connection geometry also dictated the type of failure. If the end distance was small (e\ < 2d0) and smaller than the pitch/?i (ei < pi), a longitudinal crack was formed between hole HI and a free edge perpendicular to load direction (see Fig. 47a). The crack was initiated primarily by transverse tension, which formed at the edge trying to contain the bursting action, as the specimen tended to splay out. This kind of failure was defined as a splitting failure. In several cases (L04, L04s, L07, L08, L14, L15, L21) a splitting failure between the hole HI and the edge was simultaneously followed by another fracture between holes HI and H2. The secondary fracture was also of a splitting type. The first crack opened in a curved pattern starting from a point on the free edge with the highest tension and ending on the edge of the hole with the highest shear stress, similar with at single bolt connection described earlier. The second crack just initiated at the back edge of hole HI. The test was stopped before it could progress. At specimen L21 bolt shear failure was followed immediately after the fractures. Shear failure of plate was surprisingly not observed Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. 61 Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. even at the smallest end distance e1 = 27 mm combined with large pitch p1 = 66 mm (specimen L14). Table 17: Maximum (experimental) resistance [kN] versus connection geomet 3 bolt connections 4 bolt connections e1/d0 e1/d0 1,5 2 2,5 3 1,2 1,5 2 2,5 3 5 2 778 908 1088 2 1066 1185 1386 2 2 1057 1374 2,5 945 2,5 1294 1521 1522 3 1155 1268 1329 3 1425 1501 1537 1539 1537 1507 3 3 1533 3,5 1271 3,5 1527 3,5 3,5 1480 3,77 1250 3,77 Fig. 48 compares experimental and numerical load-displacement curves for specimen L14. The experimental curve was shifted due to initial position of the bolts in the experiment. The decrease in stiffness and the resistance were very accurately fitted by numerical model. Fig. 49 illustrates load-displacement curves of bearing forces on bolts. Its distribution became unequal at a small displacement (2,5 mm). The maximum resistance of bearing force on bolts BI and B2 was reached at 4,4 mm of displacement (local maximum). The linear patterns of bearing forces at global and local maximums are shown in Figs. 50-51, respectivelv. Although the contact surfaces were small (Fig. 52), friction significantlv influenced the connection resistance. Bolts restrained the deformation of specimen in thickness direction, while plate thickness increased due to high compression stress introduced by the bolts. The thickness of the plate increased only locally at the bolt. Therefore the frictional contact was formed only in the vicinity of the holes (Fig. 53). This can also be seen on the specimen surface as the shiny surface at holes (see Fig. 54a). In Fig. 54a the contours of Mises stress were plotted over the deformed specimen L14. The calculated deformation state accurately fits to the real one. Figs. 54b-d show that the load was distributed over the whole specimen. Net cross-section yielded and due to small end distance e\ the failure of net cross-section did not occur. The area of high compression stress (Fig. 54d) spread in width approximately 3d0. 62 Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. i::::::::::::::::-- ---------------------------------------------------- . i --------------------1-------------------------------------- -fih ~^ \i-l \vil \ih ^^-,- ~\mrHmrwh&m a) splitting failure of the material in front of hole H1; L15 b) shear failure between bolts; L06 c) net cross-section failure; L17 d) bolt shear failure; L22 1500 1200 900 600 300 Fig. 47: Failure types of specimens L 400 L14 Abaqus M2 L14 300 200 100 5 10 15 Displacement [mm] 20 5 10 Displacement [mm] 15 0 0 0 Fig. 48: Experimental and numerical load- Fig. 49: Distribution of bearing forces and friction displacement curves for specimen L14 for specimen L14 Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. 63 Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. 400 i 300 200 100 0 L14 400 300 200 100 0 L14 BI B2 B3 B4 Friction BI B2 B3 B4 Frict ion Fig. 50: Distribution of bearing forces and friction Fig. 51: Distribution of bearing forces and friction for specimen L14 at global maximum for specimen L14 at local maximum Fig. 52: Contact pressure at surface nodes for specimen L14 Fig. 53: Frictional shear stress at surface nodes for specimen L14 a) Mises stress plotted over actual specimen (grid of lines) L14 after failure b) yield flag at displacement 11,8 mm c) maximum principal stress at displacement 11,8 mm d) minimum principal stress at displacement 11,8 mm Fig. 54: Stress state of specimen L14 in the middle surface 64 Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. If the end distance e\ was large (e\ > 3d0) and the pitch/?i was small (p\ ~ 2d0), the capacity of the material between holes was exhausted (see Fig. 47b, Fig. 55a). Two fractures usually formed symmetrically to the bolt line. The direction of the fractures coincided with maximum shear stresses in the plate (Fig. 55e) and they usually opened between ali holes simultaneously. Transverse tension in the area between free edge and hole HI (Fig. 55c) caused necking of the material, while pitches p\ were too small for the development of transverse tension. High ductility (Fig. 56) and equal distribution of bearing forces (Figs. 57-59) characterized this failure mode. This second type of failure can be considered as a shear failure. The third type of failure was a typical net cross-section failure (Fig. 47c) with two types of tensile flow instabilities. The diffuse necking as the first unstable flow was followed by localized necking, where the neck was a narrow band about equal to the plate thickness inclined at an angle to the specimen axis, across the width of the specimen (Fig. 46, Fig. 60a,c). This kind of failure is distinctive for a sheet tensile specimen, where width is much greater than thickness. Failure was ductile due to bolthole elongations and necking. The experimental load-displacement curve (Fig. 61) was characterized by initial sliding and several plateaus before reaching its true stiffness. This was due to bolthole clearance and geometrical tolerances of the forks to which specimen L18 was attached. Distribution of bearing forces between bolts was balanced equally, although bearing force on bolts B4 decreased when net cross-section yielded (Figs. 62-64). The pattern of bearing forces is also noticeable from minimum principal stresses in Fig. 60d. Friction had significant impact on resistance (Fig. 62), as well. Its magnitude at maximum resistance was equal to bearing force of one bolt (see Fig. 63). The shear failure of the bolt was observed at specimens L13, L21, L22. In ali three cases the last bolt B3 failed. Shear deformation of the bolt (Fig. 47d) was small due to high steel grade of the bolts 12.9. In these cases the numerical load-displacement curves deviate from the experimental ones, because the bolts were modelled elastically (Fig. 65). Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. 65 Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. a) Mises stress plotted over actual specimen (grid of lines) L03 after failure b) yield flag at max. force c) maximum principal stress at max. force d) minimum principal stress at max. force 1500 1200 900 600 300 e) shear stress at max. force Fig. 55: Stress state of specimen L03 400 300 L03 -----^ L( )cal maxjmum BI po ction pi 0 5 10 15 Displacement [mm] 20 6 9 12 Displacement [mm] 15 18 0 0 0 3 Fig. 56: Experimental and numerical load-displacement curves for specimen L03 Fig. 57: Distribution of bearing forces and friction for specimen L03 66 Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. 400 300 200 100 0 - L03 BI 400 300 200 100 0 - B2 B3 Friction L03 BI B2 B3 Friction Fig. 58: Distribution of bearing forces and friction Fig. 59: Distribution of bearing forces and friction for specimen L03 at global maximum for specimen L03 at local maximum a) Mises stress plotted over actual specimen (grid of lines) L18 b) yield flag c) maximum principal stress d) minimum principal stress Fig. 60: Stress state of specimen L18 in the middle surface at maximum force 1500 1200 900 600 300 Glob al maximum Loca maximiim 400 300 200 100 5 10 15 Displacement [mm] 20 5 10 Displacement [mm] 15 0 0 0 Fig. 61: Experimental and numerical load- Fig. 62: Distribution of bearing forces and friction displacement curves for specimen L18 for specimen L18 Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. 67 Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. 400 -300 200 100 0 L18 400 300 200 100 0 L18 BI B2 B3 B4 Friction BI B2 B3 B4 Friction Fig. 63: Distribution of bearing forces and friction Fig. 64: Distribution of bearing forces and friction for specimen L18 at global maximum for specimen L18 at local maximum 1500 1200 900 600 300 1500 1200 900 600 300 5 10 15 Displacement [mm] 20 5 10 15 Displacement [mm] 20 Fig. 65: Experimental and numerical load-displacement curves for specimens L13 and L22, respectively It has been presented that distribution and magnitude of bearing forces depend mainly on the geometry, number of bolts and on the stiffness of the plates. The average ratio between local connection resistance and global maximum connection resistance is 0,9 (see Table 16). Nevertheless, the displacement at which local resistance was reached was up to four times lower than the displacement at maximum global resistance. This indicates a long yield plateau for certain geometries (see Fig. 48). There are two extreme distributions of bearing forces. On one hand there is unequal distribution of bearing forces, where bolt BI transfers the smallest load and the last bolt the highest load (Fig. 51). This force pattern is typical for specimens with end distances smaller than the pitches, where the fracture formed on the free edge. On the other hand, equal distribution of bearing forces was observed at specimens with pitch larger than end distance (Figs. 58, 63). This distribution led to failure of the material between bolt holes (Fig. 47b) or to the net cross section failure (Fig. 47c). If the failure occurred between boltholes, the distribution remained equal at local and global maximums (Figs. 58-59). At net cross-section failure the distribution of forces remained equal to the local maximum (Fig. 64) and after that the force on the last bolt (B4) decreased (Fig. 63). Thus, at the global resistance the load on the last bolt was the smallest, whereas the load on the remaining bolts remained more or less equally distributed. o o o o 68 Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. The stiffness of the connections with several bolts in the direction of loading was larger than the stiffness of single bolt connections. The displacements at maximum resistances for specimens L were from 5 to 18 mm (Table 16). These caused average hole elongations up to 6 mm. Therefore, the limitation of hole elongations is not necessary. Surprisingly, friction had significant impact on resistance and also on failure mode. Its magnitude at maximum resistance was equal to bearing force of one bolt (see Figs. 50, 58, 63). Although the bolts were only snug tightened, the friction developed due to high bearing pressure. The stress peaks were eliminated by yielding of the material. Therefore, the plate plastically deformed in thickness creating pressure on the cover plates. The deformation was restricted by bolts that acted as elastic springs. The contact area generating the friction was actually quite small (see Fig. 52), located in the bearing (stressed) edge of bolt holes. Due to large friction force, net cross-section failure could develop instead of some other failure mode. Moreover, this friction force is hard to estimate and should therefore be interpreted with caution. The effect of functional tolerances the distribution of bearing forces The functional fabrication tolerances had almost no effect on the connection resistance. As expected, the distribution of bearing forces between bolts was affected. Load displacement curves for connections with perfect (L04, L06) and shifted (L04s, L06s) geometry are plotted in Figs. 66-71. In both connections with shifted holes (L04s, L06s) the hole closest to the free edge was shifted by 2 mm (equal to bolthole clearance), thus bolt BI was activated before ali the remaining bolts. The connections behaved as single bolt shear connections for the first 2 mm of deformation (bolthole clearance). Figs. 72, 73 illustrate Mises stress just before bolts B2-B4 were activated. The red area indicates stress higher than yield stress. After that the remaining bolts were activated and the distribution of bearing forces tended to become equal to the connection with perfect geometry (see Figs. 66-67, 74-75). In the previous tests of single bolt shear connections it was shown that the maximum resistance of the connection was developed at a displacement much larger than 2 mm (Table 15, Fig. 39). Therefore, the significant decrease of bearing force on bolt BI (Figs. 70, 71) was merely load redistribution and not connection component failure. At L06 and L06s the bearing force reached local maximum on bolt BI at 285 and 320 kN (Fig. 77), respectively. Bearing forces on the remaining bolts were always lower than 285 kN (Figs. 75, 77). In čase of specimen L06s, the maximum bearing force on the bolt increased by 12% due to fabrication tolerances. This increased bearing force should be accounted for especially in čase of slotted holes with the slot parallel to the direction of the bearing force, othenvise bolt shear failure might be critical. Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. 69 Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. 1000 - 800 600 - 400 200 L04 L04 Abaqus M2 L04s L04s Abaqus M2 5 10 15 Displacement [mm] 20 1500 1200 900 600 300 <^^" a*4^ f i 1 i i i i i 5 10 15 Displacement [mm] 20 Fig. 66: Experimental and numerical load-displacement curves for specimens L04, L04s Fig. 67: Experimental and numerical load-displacement curves for specimens L06, L06s 300 200 100 L04 i Global "-"---- maxi|num —^i i i ~^— Lpcal raximum i HI B3 Friction ,B2 B4 400 Displ acement [m m] 12 300 200 100 L06 6 9 12 Displacement [mm] 15 Fig. 68: Distribution of bearing forces and friction Fig. 69: Distribution of bearing forces and friction for specimen L04 for specimen L06 300 200 100 L očal maximum t04s Friction Displacement [mm] 12 400 300 200 100 L06^ 6 9 12 Displacement [mm] 15 0 0 0 o o o o o Fig. 70: Distribution of bearing forces and friction for specimen L04s Fig. 71: Distribution of bearing forces and friction for specimen L06s 70 Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. Fig. 72: Distribution of bearing forces and friction for specimen L04s Fig. 73: Distribution of bearing forces and friction for specimen L06s 300 240 180 120 60 Global maiimums 279 277 265 256 159 161 D L04 D L04s 325 i 260 195 130 65 0 Global masimums191 ,al 273 275---- /sl /sl 261 247 281 277 277 279 D L06 B L06s BI B2 B3 B4 Friction BI B2 B3 B4 Friction Fig. 74: Distribution of bearing forces and friction for specimens L04, L04s at global maximum Local maiimums 231 242 300 -240 -180 -120 -60 -0 261 51 90 D L04 0 L04s 110 115 61 Fig. 75: Distribution of bearing forces and friction for specimens L06, L06s at global maximum 325 260 195 130 65 0 32( __ Local maiimums 260 273 280 188 154 _.,., D L06 S L06s 211 138 BI B2 B3 B4 Friction BI B2 B3 B4 Friction Fig. 76: Distribution of bearing forces and friction for specimens L04, L04s at local maximum Fig. 77: Distribution of bearing forces and friction for specimens L06, L06s at local maximum 5.5 Numerical parametrical study of bolted shear connections The comparison of test results and numerical simulations for specimens B1 and L showed that numerical simulations followed the experimental load-displacement curves with a desired accuracy (see Figs. 48, 56, 61, 66, 67). Furthermore, the comparison of the specimens after failure to the deformation state of the specimen as a result of numerical simulation revealed an excellent resemblance (see Figs. 46, 54, 55, 60). Hence, the numerical simulations of the connections present a reliable tool for the analyses of stress-strain state. A comprehensive numerical parametric study was done in order to obtain the influence of different parameters on bearing resistance. The results were used for the evaluation of bearing resistance (59) according to Eurocode standard and for the development of a new formula for _ ¦' 198 138 130 0 285 _¦¦ 169 Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. 71 Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. bearing resistance. Numerical model types M2 and M3 (see Chapters 3.3, 3.4) were used in the analyses. Material model was adopted from the second phase of experiment (see Table 10). Geometry and results of parametrical study are presented in Tables 18-21. Distribution of bearing forces on bolts are printed at their maximum sum max(E5z), neglecting the friction. Displacement U and resistances Pb of connections at max(E5z) are also presented in Tables 18-21. The maximum resistance Pmax of the connection was reached at displacement equal to or larger than displacement U. Detailed results of this parametrical study are presented in Appendix D. 5.5.1 Width as the varying parameter This group includes 19 numerical simulations. The geometry of the connections was based on specimen type L. The geometry of specimens L04, L06, L10, L14, L16 and L19 was taken as the basic geometry. The only variable was width b. The coding e.g. L04_bl00 stands for specimen geometry L04, where width b of the connection is equal to 100 mm. The philosophy was to obtain the resistance and distribution of bearing forces for very narrow (net cross-section failure is critical) and very wide (shear failure of the plate is critical) connections with small and large pitches p\ and end distance e\. The geometry of the series is presented in Table 18. Table 18: Geometrv and results for the connections where width was the varving parameter Specimen Model Basic b U P> BI B2 B3 B4 Friction maxEI name type geometry [mm] [mm] [kN] [kN] [kN] [kN] [kN] [kN] [kN] L04_bl00 M2 L04 100 4,1 680 135 145 158 177 65 615 L04M50 M2 L04 150 4,6 1054 162 213 266 277 136 919 L04M75 M2 L04 175 3,8 1048 164 214 262 276 132 916 L04_b242 M2 L04 242 4,7 1057 165 214 264 277 137 920 L06M50 M2 L06 150 6,1 1107 257 225 248 231 147 960 L06M75 M2 L06 175 6,8 1310 295 262 272 258 222 1088 L06_b242 M2 L06 242 5,0 1355 271 266 282 288 247 1107 L10_bl32 M2 L10 132 5,3 954 206 206 223 206 115 840 L10_b260 M2 L10 260 6,8 1601 263 299 330 336 373 1228 L14M54 M2 L14 154 6,5 1143 175 273 292 249 154 988 L14_b230 M2 L14 230 16,0 1422 158 227 345 399 281 1129 L14_b330 M2 L14 330 16,0 1489 167 260 350 393 287 1169 L16_bl60 M2 L16 160 6,1 1194 232 261 281 235 184 1010 L16_b242 M2 L16 242 7,2 1581 228 286 343 352 371 1210 L16_b286 M2 L16 286 7,5 1584 229 283 341 354 377 1207 L16_b330 M2 L16 330 7,4 1584 234 284 339 353 375 1210 L19M54 M2 L19 154 6,0 1142 243 240 259 235 164 977 L19_b330 M2 L19 330 30,0 2489 356 424 459 553 698 1791 L19 b440 M2 L19 440 30,0 2542 394 438 466 555 689 1853 These simulations revealed that the resistance of the connection becomes constant at a certain width of the plate, regardless of end distance and pitch (see Figs. 78-79). The work of bolt bearing exhausts the material between bolts of before the first bolt. Therefore the stress cannot activate the unstressed area of the connection. The net cross-section failure is distinctive for narrow plate width (e.g. L04_bl00, L19M54). The magnitude of friction for L19_b330 and L19_b440 is unrealistic (Fig. 79). In the actual connection the bolts would yield and therefore elongate, decreasing the friction force. Due to large bearing forces, the bolts would fail in shear. The point of these geometries was to show the magnitude of bearing force that arises if 72 Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. bolts remain elastic. Very stiff cover plates (if compared to the inner plate) result in the linearly increasing, unsymmetrical distribution of bearing forces. 300 i 240 180 120 60 0 Linear distribution of bearing forces p bL04_M00 DL04_bl50 D L04M75 ¦ L04_b242 ....... 700 525 350 175 0 Linear distribution of bearing forces Bl B2 B3 B4 Frict ion BI B2 B3 B4 Frict ion Fig. 78: Distribution of bearing forces and friction Fig. 79: Distribution of bearing forces and friction for connections with basic geometry L04 for connections with basic geometry L14 5.5.2 Plate stiffness as the varying parameter The cover plates in the experiment were designed to deform only elastically. The thickness and end distance of the cover plates affect the distribution of bearing forces. In total 43 connections with two configurations were analysed. The geometry of the connections was equal to the geometry of specimens L. The first group included bolted shear connections with bolts in single shear, where both connected plates are equal in geometry. The coding e.g. L08_ls stands for connection geometry L08 with bolts in single shear (Is). The second group of connections were the connections with bolt in double shear. The geometry of inner plate and cover plates was equal, except in thickness. The thickness of cover plate (10 mm) was equal to half of the thickness of inner plate (20 mm). The coding e.g. L03_2s_tlO-20 stands for connection geometry L03 with bolts in double shear (2s), where cover plates and inner plate were 10 mm and 20 mm thick, respectively. Numerical model type M3 (see chapter 3.4) was selected for the analyses. The connections with bolts in single shear were loaded eccentrically and therefore a moment was introduced which resulted in bolt rotation (see Fig. 80). The rotated bolts acted like a wedge, increasing the resistance of the connection. Therefore, the sum of bearing forces on bolts and friction is lower than Pb in Table 19. At a displacement around 15 mm most of the calculations did not converge due to bolt rotations and contact difficulties. Nevertheless, most of the the load-displacement curves reached their maximum (see Appendix D). Bolts in the initial and rotated position are shown in Fig. 80. The force on the first bolt was equal to the force on the last bolt (Figs. 81-82). The symmetrical distribution of bearing forces was also observed at the connections with bolts in double shear (Fig. 82). Therefore, stiffness of cover plates has significant influence on the distribution of load between bolts. Moreover, in the ultimate limit state the friction forces are relatively lower if plates have equal bearing stiffness. Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. 73 Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. Table 19: Geometrv and results for the connections where plate stiffness was the varving parameter Specimen Model Basic ti te u Pb BI B2 B3 B4 Friction maxSI name type geometry [mm] [mm] [mm] [kN] [kN] [kN] [kN] [kN] [kN] [kN] LOlls M3 L01 10 10 11,2 753 225 244 225 51 694 L02_ls M3 L02 10 10 14,0 858 252 263 261 56 777 L03_ls M3 L03 10 10 9,1 986 283 274 287 92 845 L04_ls M3 L04 10 10 8,7 964 207 229 230 208 78 874 L05_ls M3 L05 10 10 10,6 1089 238 246 248 238 95 970 L06_ls M3 L06 10 10 8,8 1258 275 264 265 272 124 1077 L07_ls M3 L07 10 10 12,2 836 236 277 244 60 758 L08_ls M3 L08 10 10 13,8 1109 222 267 268 231 85 988 L09_ls M3 L09 10 10 14,7 1362 286 299 304 283 117 1172 LlOls M3 L10 10 10 12,2 1391 297 300 300 291 124 1188 Lllls M3 Lil 10 10 14,6 1030 286 305 295 78 886 L12_ls M3 L12 10 10 13,7 1119 315 322 315 93 951 L13_ls M3 L13 10 10 13,9 1178 324 325 327 96 975 L14_ls M3 L14 10 10 13,0 1149 202 299 301 198 97 1001 L15_ls M3 L15 10 10 12,9 1234 238 295 298 240 111 1071 L16_ls M3 L16 10 10 15,1 1367 275 311 310 277 112 1173 L17_ls M3 L17 10 10 15,2 1439 296 319 320 290 115 1225 L18_ls M3 L18 10 10 14,5 1456 301 320 319 296 127 1235 L19_ls M3 L19 10 10 14,5 1442 302 316 315 293 115 1226 L20_ls M3 L20 10 10 14,6 1433 287 324 325 286 121 1221 L21_ls M3 L21 10 10 14,8 1085 297 322 306 83 925 L22_ls M3 L22 10 10 14,7 1113 302 324 312 86 938 L01_2s_tlO-20 M3 L01 20 10 8,4 1485 460 499 472 82 1432 L02_2s_tlO-20 M3 L02 20 10 12,7 1684 532 545 534 109 1612 L03_2s_tl0-20 M3 L03 20 10 13,9 2107 638 609 656 245 1903 L04_2s_tlO-20 M3 L04 20 10 8,5 1883 424 468 484 434 95 1810 L05_2s_tlO-20 M3 L05 20 10 9,1 2127 483 509 517 497 146 2006 L06_2s_tlO-20 M3 L06 20 10 13,7 2635 601 598 601 598 268 2398 L07_2s_tlO-20 M3 L07 20 10 13,4 1637 483 586 499 100 1568 L08_2s_tl0-20 M3 L08 20 10 13,9 2144 460 556 556 480 130 2051 L09_2s_tlO-20 M3 L09 20 10 12,6 2681 588 634 623 583 280 2429 L10_2s_tlO-20 M3 L10 20 10 14,7 2890 634 667 671 635 323 2607 Lll_2s_tlO-20 M3 Lil 20 10 13,8 2026 602 647 603 209 1852 L12_2s_tlO-20 M3 L12 20 10 13,8 2245 657 683 660 290 2001 L13_2s_tl0-20 M3 L13 20 10 13,7 2429 700 716 698 353 2114 L14_2s_tlO-20 M3 L14 20 10 13,7 2227 415 636 642 391 178 2084 L15_2s_tlO-20 M3 L15 20 10 14,7 2395 469 639 636 487 200 2231 L16_2s_tlO-20 M3 L16 20 10 14,1 2705 573 660 657 569 281 2458 L17_2s_tlO-20 M3 L17 20 10 14,7 2904 612 695 694 611 327 2612 L18_2s_tl0-20 M3 L18 20 10 14,6 2968 625 696 695 649 336 2665 L19_2s_tlO-20 M3 L19 20 10 14,2 2962 636 689 692 656 328 2673 L20_2s_tlO-20 M3 L20 20 10 14,6 2878 594 703 695 597 326 2589 L21 2s tlO-20 M3 L21 20 10 13,8 2151 630 683 635 251 1948 conneetion with bolts in single shear a cut through bolts - top view - initial and deformed state Fig. 80: Mises stress at displacement 15,29 mm for L17_1s 74 Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. 350 280 210 140 70 Symmetric distribution of bearing forces BI B2 B3 B4 Friction 700 560 420 280 140 0 Symmetric distribution of bearing forces A ¦ L14_2s_tlO-20 DL15_2s_tlO-20 ? L16 2s tlO-20 BI B2 B3 B4 Frict ion Fig. 81: Distribution of bearing forces and friction Fig. 82: Distribution of bearing forces and friction for connections with bolts in single shear and with for connections with bolts in double shear and with equal plate bearing stiffness equal plate bearing stiffness Definition of equal or different plate bearing stiffness It was shown that the pattern of bearing forces between bolts is also dependent on plate bearing stiffness. In this section a relative distinction between different and equal bearing stiffness of the connection plates is drawn. The results of the FE analyses presented in this section also prove the validity of numerical model M2. Further on, the FE analyses are presented for specimen L14 with different geometries of the cover plates. It is also defined when it may be considered that the cover plates have equal or different bearing stiffness than the specimen (inner plate). The bearing stiffness of plates is equal\i end distance e\ on ali plates (inner and cover plates -Fig. 83) is equal and if the thickness of inner plate is equal to the sum of plate thicknesses of outer plates (see Fig. 83). Othenvise, the bearing stiffness of plates is different. In the sequel, the term “the connections with different plate bearing stiffness” is used for the connections, where the difference in plate stiffness causes linear pattern of bearing forces as illustrated in Fig. 79. The difference is considered to be large enough, if the thickness of the inner plate is at least equal to (or smaller than) the thickness of the cover plate in the connections with two cover plates (see Fig. 84 - upper drawing). Similar applies to the connections with bolts in single shear. In čase that the sum of cover plate thicknesses is equal to the thickness of the inner plate, the difference is large enough to cause linear pattern of bearing forces, if the end distance ex of the cover or inner plate is at least three times larger than the end distance on the opposite plate (see Fig. 84 - middle drawing). The influence of plate thickness on the pattern of bearing forces is presented in Fig. 85. Additional numerical simulations on specimen L14 were performed, where the thickness of a single cover plate equalled to 5 and 10 mm, respectively. If the thickness of the cover plate was equal to 10 mm, the pattern of bearing forces was similar as if the cover plates were rigid. o Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. 75 Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. The influence of end distance on the pattern of bearing forces is presented in Fig. 86. Additional numerical simulations on specimen L14 were performed, where the thickness of a single cover plate equalled 5 mm. The end distance of the cover plate was larger than the end distance of the inner plate by factor 1,5 and 3 (see Fig. 84 - middle drawing), respectively. The linearly increasing pattern of bearing forces was observed, if the end distance of the cover plate was at least 3 times larger than the end distance of the inner plate. Plate 3 - cover plate Fig. 83: Tension splice with bolts in double shear (Žfa^fa)' .( ti> ti) ei y P1 y P1 y P1 y ei \K \k "-V /\\ /K ' j^>3e^ pi pi pi ey Bn | Bi |B2 [BI Distribution of bearing forces Fig. 84: Different plate bearing stiffness 420 -336 252 168 84 0 D L14, t(inner)=10mm, t(cover)=5mm ¦ L14, t(inner)=10mm, t(cover)=10mm ¦ L14, t(inner)=10mm, t(cover)=rigid B1 B2 B3 B4 Friction Fig. 85: The influence of thickness on the pattern of bearing forces 76 Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. 420 336 252 168 84 0 ¦ L14, t(inner)=10mm, t(cover)=rigid ¦ L14, t(inner)=10, t(cover)=5, el(cover) = l,5xel(inner) ¦ L14, el(cover) = , 3,0xel(inner) BI B2 B3 B4 Friction Fig. 86: The influence of end distance on the pattern of bearing forces 5.5.3 Bolt diameter as the varying parameter This series of numerical simulations includes two groups. The only difference to the second group of previous series (see Section 5.5.2) is bigger bolts. The bolthole clearance for bolts M27 is 3 mm. The first group of connections (coded e.g. L03_2s_tlO-20_M27) is based on the geometry of specimen type L, so that ratios e\ldk, p\l A Kim, Yura * L • Aalberg, Larsen - W700 * • Aalberg, Larsen - W1000 100 100 210 320 430 540 Numerical max. resistance [kN] 650 Fig. 91: Comparison of numerical and experimental resistances Table 25: Distribution of bearing forces on bolts for connections found in literature Specimen BI B2 *max Specimen BI B2 B3 B4 Friction max(EB)i P, *max name [kN] [kN] [kN] name [kN] [kN] [kN] [kN] [kN] [kN] [kN] [kN] KY BT0510 42 95 137 KK El 153 242 48 396 437 462 KY BT0520 36 124 160 KK E2 168 233 98 401 493 493 KY BT0530 39 143 182 KK E3 168 240 102 408 504 506 KY BT1510 86 100 186 KK E4 191 233 76 425 493 508 KY BT1520 77 136 214 KK E5 197 244 93 441 526 552 KY BT1530 91 158 249 KK E6 200 246 90 446 528 561 AL W700-5 68 143 211 KK F1 125 147 125 148 141 546 674 677 AL W700-6 60 195 255 KK F2 127 148 130 150 154 555 695 697 AL W700-7 71 215 285 KK F4 128 147 127 147 125 549 660 679 AL W700-8 133 150 282 KK F5 137 151 136 148 170 572 727 737 AL W700-9 135 190 325 KK Gl 120 144 116 147 86 527 599 624 AL W700-10 148 219 366 KK G2 115 127 115 128 74 486 549 563 AL W1000-5 110 242 352 KK G4 123 125 123 126 98 497 584 592 AL W1000-6 101 331 432 KK G5 115 146 113 146 81 521 590 617 AL W1000-7 125 334 458 KK HI 110 115 107 119 76 452 522 522 AL W1000-8 221 256 477 KK H2 129 147 128 141 120 546 658 660 AL W1000-9 220 338 559 KK H3 147 166 145 167 148 626 766 766 AL W1000-10 257 348 606 KK H4 118 142 120 139 107 519 621 621 KK H5 141 167 141 166 146 616 755 756 KK H6 153 181 153 183 176 671 837 837 900 _ • • • • 9>. • 400 V • Kouhi, Ko rtesmaa i------------------------------------------------------------- Fig. 93: Connection KK E2 – Mises stress 400 500 600 700 800 Numerical max. resistance [kN] 900 Fig. 92: Comparison of numerical and experimental resistances (Kouhi, Kortesmaa, 1990) Fig. 94: Connection KK G5 – Mises stress Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. 83 Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. Table 26: Material models for numerical simulations in Abaqus for Kouhi and Kortesmaa connections 3 mm thick plate 4 mm thick plate 6 mm thick plate 8 mm thick plate True yleld stress True plastic strain 623 725 750 810 0 0,085 0,13 1 660 760 790 860 0 0,085 0,13 1 604 712 730 790 0 0,085 0,13 1 622 735 771 830 0 0,085 0,13 1 5.7 Analysis of bearing resistances in relation to EN 1993-1-8 5.7.1 General Design bearing resistance per bolt (59) in EN 1993-1-8 was evaluated on the basis of 167 tests of plates in bearing (Snijder et al., 1988a. 1988b). There was only one test result available for more than one bolt. 137 tests results were for S235 and 30 results for higher steel grades with StE690 as the highest grade (equivalent to S690). The resistance model studied did not account for the reduction of resistance for edge distances between 1,2 d0Ao o 3?a c 3 A Specimens BI O Specimens B2 -----1------'-----'----- 1,25 A Specimens BI o Specimens B2 1,00 0,75 — *fc, 0,50 A 900 600 300 0 cP A o c *V A At A Specimens BI o Specimens B2 0 3 6 9 D [mm] 03 69 0 5 10 15 20 25 D EC [mm] U(Pmax) [mm] b) c) a) Fig. 95: Displacement DEC at which bearing resistance acc. to EN 1993-1-8 was reached in relation to end distance a) or to bearing-to-maximum resistance ratio b); c) displacement at which maximum resistance was reached A disagreement between the test results and the Eurocode formula is shown also in Fig. 97. The plot Fig. 97 presents the end-to-edge distance ratio e1/e2 versus normalized resistance. The graph suggests that a transition between increasing and constant part of the curve (bearing and net cross-section failures) is a function of e1/e2 ratio. Although the transition happens gradually, a transition line is constructed. The line separates net cross-section failures from other kinds of failures and lies between 1,4 – 1,5 e1/e2. In Eurocode’s bearing formula (69) this transition is for HSS not accounted correctly. Correct resistance model is vital for correct assumption of failure mode in a connection with more than one bolt. Furthermore, Eurocode underestimates bearing resistances for HSS for any kind of geometry. Moreover, it underestimates maximum bearing resistance per bolt (where net cross-section is critical) for large edge distances e2 ? 1,5 d0 and overestimates the resistance for smaller edge distances. Fortunately, a separate net cross-section resistance check is also required. o Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. 87 Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. X e2/d0=l,0 -e—BI - e2/d0=l,2 A—BI - e2/d0=l,35 -eBI - e2/d0=l,4 - 1,6 HBI - e2/d0=l,9 - 2,0 -¦—B2 - e2/d0=l,2 •B2 - e2/d0=l,5 0,7 3,2 2,7 2,2 1J - BI 10 1,2 Jks^"ws>i h""°'*5rBl02 BI®* B125* 1,5 2,5 3 Normalized end distance ei/do 3,5 Fig. 96: Normalized Eurocode bearing resistance and experimental results B1, B2 versus normalized end distance 3,2 2,2 1,7 1,2 X e2/d0 = 1,0 B1 - e2/d0 = 1,2 B1 - e2/d0=1,35 «------B1 - e2/d0=1,4 - 1,6 B1 - e2/d0=1,9 - 2,0 -+------B2 - e2/d0 = 1,2 •------B2 - e2/d0 = 1,5 EC - e1/d0=const EC - e2/d0=const Transition line 0,7 0,6 0,9 1,2 1,5 1,8 2,1 2,4 2,7 End to edge distance ratio ei/e2 3,0 3,3 3,6 3 1 2 4 Fig. 97: Experimental results B1, B2 in relation to Eurocode bearing resistance function 88 Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. Figs. 98-99 illustrate experimental result for single bolt connections. Several BI and Rex, Easterling results fall below the dotted diagonal line (danger side) in Fig. 98a. For these results the bearing resistance (69) according to EC 3 gives too optimistic results. As it has already been already established, the results BI failed in net cross-section, while the results Rex, Easterling failed in curling. Partial factor yM = 1,631 should be chosen for the design formula, if ali the results were considered. The results with curling failures were removed from the Fig. 98b. Consequently the scatter and the required partial factor lowered (Vs = * -» t 0,152; ym = 1,396). If a minimum of the net cross-section formula^ and bearing resistance formula had been considered on the x-axis, only the results with net area failures moved above the dotted diagonal. For several results the bearing resistance (69) is too safe and * therefore the scatter of points is enlarged. The partial factor equal to yM = 1,166 should be applied for the calculation of design values in Fig. 99b. 800 O 0 V* O o c>ZP V5 = 0,193 b = 1,105 Jfr^ pOO O BI + Aalberg, Larsen X Kim, Yura O Rex, Easterling 600 400 — a 5UU 600 - O O / o 400 - * O SV/* P V5 = 0,152 o b = 1,131 200 O BI jŠr + Aalberg, Larsen M^» X Kim, Yura o Rex, Easterling 0 i-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 200 400 600 Fb - EC 3 [kN] a) all results 800 200 F 400 600 EC 3 [kN] 800 b) curling failures excluded Fig. 98: Experimental re vs. EC 3 bearing resistance Fb for single bolt connections v5 = b = 0,178 1,167 600 400 s&y<>7 200 200 400 600 min(Fb , N u ) [kN] a) all results 800 v5 = b = 0,114 1,205 200 ~ + Aalberg, Larsen X Kim, Yura O Rex, Easterling 200 400 600 min(F6, Nu) [kN] b) curling failures excluded 800 Fig. 99: Experimental re vs. minimum of bearing Fb and net cross-section Nu resistance for single bolt connections 0 0 0 0 0 0 0 Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. 89 Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. 5.7.3 The connections with a single row of bolts positioned in the direction of load transfer Figs. 100-101 show the results for connections with one line of bolts positioned in the direction of loading. The experimental load-displacement curves were traced by numerical simulation in order to obtain the distribution of bearing forces between bolts. The accuracy of numerical results was additionally proved by comparison of experimentally and numerically deformed specimens in section 5.4.2. Bearing resistance formula (69) estimates the bearing force on the edge bolt (Fig. lOOa) too bravely, especially for three or four bolt connections. Considering the bearing force on the inner bolts (Fig. lOOb), the situation is the opposite. The bearing force was underestimated only for connections that failed in the net area that had large end and pitch distances. If the bearing resistances were summed according to equation (68) and compared to the maximum sum of numerically obtained bearing resistances (Fig. lOla), the scatter of points became smaller. The negative error at the estimation of bearing force on the edge bolt and positive error on the inner bolt were summed approximately to zero. Therefore the numerically obtained maximum resistance of the connection Pmax was compared to the minimum of the net cross-section Nu and bearing resistance formula. Maximum resistance Pmax besides bearing forces also accounts for friction forces. Some connections failed in bolt shear, thus numerical and not experimental Pmax was considered on ordinate in Fig. lOlb. Due to friction, ali points moved considerably above the dotted diagonal line - on the safe side. The net area check was critical only for the results marked in Fig. lOla. The choice of the partial factor to form design resistances should be equal to 2,472 for bearing resistance on the edge bolt (Fig. lOOa), 2,122 for the resistance on the inner bolt (Fig. lOOb), 1,689 for the resistance of group of bolts (Fig. lOla) and 1,133 for the resistance of group of bolts together with net area check (Fig. lOlb). 450 360 180 90 + Aalberg, Larsen X Kim, Yura X Kouhi, Kortesmaa ¦ L 450 T 180 270 360 b edge bolt - EC 3 [kN] a) bearing force on edge bolt 90 F 450 360 270 180 - 90-----X2^ + Aalberg, Larsen X Kim, Yura X Kouhi, Kortesmaa ¦ L 90 180 270 360 F b inne r bolt - EC 3 [kN] b) bearing force on inner bolt 450 Fig. 100: Bearing forces on bolts for connections with one line of bolts positioned in the direction of loading 0 0 0 0 90 Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. 1500 1200 900 600 300 0 + Aalberg, Larsen X Kim, Yura X Kouhi, Kortesmaa----- ¦ L # Net area check is 1600 V8 = 0,114 b = 1,239 V5 = 0,163 b = 0,969 1200 800 400 0 + Aalberg, Larsen X Kim, Yura X Kouhi, Kortesmaa ¦ L 0 300 600 900 1200 1500 Sum of bearing resistances - EC 3 [kN] a) sum of bearing resistances 0 400 800 1200 1600 min(?Fb , N u ) [kN] - EC 3 b) minimum of sum of bearing resistance and net area resistance Fig. 101: Resistance of connections with one line of bolts positioned in the direction of loading 5.7.4 The connections included in the numerical parametric study The results from numerical parametrical studv are gathered in Figs. 102-103. In Fig. 102a the Eurocode’s bearing resistance on the edge bolt was higher than numericallv obtained bearing force (danger side). On one hand, the resistance function (69) does not consider important parameters that influence the bearing force on the edge bolt. For this reason the points are grouped in vertical lines. On the other hand, the bearing force was constant but the function (69) gave higher resistance (horizontal line of points). Function (69) also does not consider the net cross-section failure as the maximum resistance of the connection for connections with equal net cross-sections. Similar storv goes for the bearing force on the inner bolt, except that in more cases function (69) gives the results that are on the safe side (Fig. 102b). The resistance of group of bolts was calculated according to equation (67) or (68), depending on the connection tvpe in terms of plate stiffness. The positive and negative errors were summed approximately to zero, thus most of the points in Fig. 103a lie near the dotted diagonal. There are several points that deviate from the diagonal. These points present the connections where net area fullv vielded. If minimum of the net area and sum of bearing resistances is taken as theoretical resistance on x-axis and friction is accounted for on >>-axis (Fig. 103b), then the scatter of points is small with Vs= 0,098 and ali point move close to the dotted diagonal. There are two results on very safe side. L19_b330 and L19_b440 are connections with 4 bolts, large pitch, end and edge distances, where stiff cover plates enforced large friction forces. The choice of the partial factor to form design resistances should be equal to 2,109 for bearing resistance on the edge bolt (Fig. 102a), 1,729 for the resistance on the inner bolt (Fig. 102b), 1,571 for the resistance of group of bolts (Fig. 103a) and 1,164 for the resistance of group of bolts together with net area check (Fig. 103b). The design values were calculated by equation (42) for large number of tests. Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. 91 Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. 1200 r V5 = 0,201 b = 0,813 900 300 1200 r 600 ---- % 900 600 --±e.^ ---- 300 300 600 900 Fb edge bolt - EC 3 [kN] a) bearing force on edge bolt 1200 300 600 900 1200 Fb inner bolt - EC 3 [kN] b) bearing force on inner bolt Fig. 102: Bearing forces on bolts for connections included in the numerical parametrical study 4000 V5 = 0,139 b = 0,918 3125 AAbaqus 2250 4000 r 3125 L19_2sjt10-20_M27 2250 1375 500 500 1375 2250 3125 4000 Sum of bearing resistances - EC 3 [kN] 1375--- 500 500 1375 2250 3125 4000 min(?Fb , N t ) [kN] - EC 3 b) minimum of sum of bearing resistance and net area resistance a) sum of bearing resistances Fig. 103: Resistance of connections included in the numerical parametrical study 5.7.5 The connections with two lines of bolts in the direction of load transfer The connections with two lines of bolts in the direction of bearing forces remain. The connections B2 and Puthli, Fleischer (2001) are with two bolts positioned perpendicular to loading, while Kouhi, Kortesmaa (1990) are connection with bolt configurations in a 2x2 pattern as described previously. In Fig. 104a the abscissa is defined by equation (69). The reduction due to p2 < 3db (eq. (64)) was considered. The bearing force on the ordinate applies to numerical results for Kouhi, Kortesmaa connections and to experimental results for B2 and Puthli, Fleischer connections, where half of the experimental resistance was considered. Eurocode formula gives much lower values for bearing force on the edge bolts than the experiment for Puthli, Fleisher connections, regardless of the failure mode (see Fig. 104a). The Eurocode bearing formula (63) is conservative due to resistance reduction for small edge distances and pitches p2. The bearing force on the edge bolt was overestimated by about 4 o o o o 92 Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. times in Eurodode for Kouhi, Kortesmaa connections that failed in net area. Similar conclusions are drawn for B2 connections. Eurocode formula also overestimated the bearing force on the inner bolt for any kind of failure (Fig. 104b). The sum of bearing resistances was calculated according to equation (68). In this case the points are scattered over whole diagram (Fig. 105a). If beside the sum of bearing resistances also net area and block tearing checks are considered on the abscissa and maximum experimental resistance is considered on the ordinate in Fig. 105b, all points are pushed above the dotted diagonal on the safe side. In the latter case (Fig. 105b) the partial factor for the determination of design values should be at least 2,708. This large partial factor is unrealistic. The group of results for which the conservativeness of the Eurocode formula is known should be eliminated from the evaluation. This would decrease the scatter of points and result in realistic partial factor. The problem is identifying the mentioned group of results. 350 - i i i A ¦ ¦ A 7 * V5 =0,686 > b = 1,420 50 m > i * ¦ B2 A Puthli, Fleischer X Kouhi, Kortesmaa 150 r l25 X Kouhi, Kortesmaa V5 =0,178 b = 0,654 100 50 75------------- v 50 200 350 500 Fb edge bolt - EC 3 [kN] a) bearing force on edge bolt 50 75 100 125 Fb inner bolt - EC 3 [kN] b) bearing force on inner bolt 150 Fig. 104: Bearing forces on bolts for connections with two lines of bolts parallel to loading direction 1000 uuu ^B2 A Puthli, Fleischer X Kouhi, Kortesmaa k \ Ž a ¦ 700 - ! ¦ ¦ ¦ / ¦ A 400 /&* X X X * X V5 =0,664 b = 1,259 100 750 ----BBJ* 500 250 ¦ B2 A Puthli, Fleischer X Kouhi, Kortesmaa 100 400 700 1000 Sum of bearing resistances - EC 3 [kN] a) sum of bearing resistances Fig. 105: Resistance of connections with two lines of bolts parallel to loading direction 0 250 500 750 1000 min(?Fb , N t , Veff ,1) [kN] - EC 3 b) minimum of sum of bearing resistance, net area and block tearing resistance o Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. 93 Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. 5.8 Development of new design resistance bearing formula 5.8.1 General The modern standards for structural design (like the group of Eurocode standards) introduce the limit state design method. The ultimate limit state typically represents the collapse of the structure due to loss of structural stiffness and strength, while serviceability limit state conventionally represents failure states for normal operations due to deterioration of routine functionality. Although Eurocode standard defines the bearing resistance by hole elongation (see Section 5.3), the design bearing resistance is an ultimate limit state check. Therefore it is proposed that the bearing resistance is defined by the maximum strength of plate caused by the bearing pressure. In view of the proposed definition, the sum of bearing resistances of the individual fasteners would be equal to the maximum resistance of a shear connection - like net section failure, block shear, rupture of one bolt... In general bearing resistance of the single bolt shear connection with infinite end and edge distances is limited by bolt shear failure. Nevertheless, hole elongation could be easily limited by a prescribed reduction factor. A new formula that would anticipate the bearing resistance of the plate in ultimate limit state is suggested in this section. The new formula is applicable only to high strength steel and is supported by the results of our tests, the results of other tests on similar bolted shear connection found in literature and by numerical simulations for additional connection configurations, totalling of 266 results. A design function will be determined by the procedure given in EN 1990, Annex D (CEN, 2004a), described and used on a practical čase in chapter 4.3. Identically as in Eurocode, the new bearing formula should be expressed by the mean bearing stress and various factors ki as geometry parameters. 5.8.2 Single bolt connections Let us first consider single bolt connections. Factors k\ and k2 are linear functions of end to edge distance ratio e\le2 and of absolute value of normalized edge distance e2/d0, respectively. In čase of unsymmetrically connected member the minimum edge distance e2,min is considered (Fig. 19). Written in mathematical language, it follows: Fbnew = klk2-d-t-fu (72) kx = min k e-- k V e2 J min (73) 1 3^-- 1 9 e 2 J k2 =k2ld + k22 =0,9 d----- (74) e[ = e1 (75) e2 = e2 or in čase of unsymmetrically connected member e2 = e2 mm (76) 94 Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. Coefficients kl} are determined by the following procedure. According to EN 1990, Annex D (CEN, 2004a) the estimator for the coefficient of variation of the error, term V5\§ calculated. Term F^is the measure for scatter of points in the re - rt diagram (scatter diagram), where re is a vector of test results (measured resistances) and rt is a vector of theoretical resistances calculated by a prescribed expression (e.g. (72)). Coefficients kl} are evaluated by minimizing Vs. The preferred solution is the one with correction coefficient b > 1 (b is the slope of regression line obtained by the least square method) and that the design resistance could be formed by partial factor yu2 = 1,25. In addition, the coefficients should also have some theoretical explanation. Considering ali these demands, coefficients kj were evaluated through nonlinear optimization by Microsoft Excel Solver. Function (72) is plotted in thin lines in Fig. 106. The slope and the position of the curves are defined by both coefficient h and k2, while ki defines the transition between shear and net cross-section failure which occurs at (see equation (73)): hI 1,3 1,46. (77) 2 11 1'-* The transition can also be simply theoretically derived. The main assumption is that shear resistance is equal to net cross-section resistance (Fig. 107). Such failure was observed at specimen B121 (Fig. 37c). It follows: (78) (79) F = F net shear (2e2-d0)tfu=2U 2) V3 e S 1 v d (80) e2 1,7... 1,46. 1,43. .e2 » d0 e2 = 1,35 d0 .— = \2 d0 (81) Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. 95 Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. 3,2 2,2 1,7 1,2 0,7 *H B122 B121 * unsymmetrical X e2/d0 = 1,0 ¦$—BI - e2/d0 = 1,2 BI - e2/d0=l,35 BI - e2/d0=l,4 - 1,6 BI - e2/d0=l,9 - 2,0 125* e j/^1,2 e/^2,5 e^/d0=2,0 6^=1,5 B201 X et/0^=3,0 0,6 0,9 1,2 1,5 1,8 2,1 2,4 2,7 3,0 3,3 3,6 End to edge distance ratio e1/e2 Fig. 106: Experimental results in relation to proposed bearing resistance function Fig. 107: Failure modes: a) net cross-section b) shear Theoretically, the transition between shear failure and net cross-section failure occurs when end-to-edge distance ratio is from 1,4 to 1,7. This agrees with experimental results in Fig. 97, where the transition line separates splitting failure from the net cross-section failure. There are two extreme possibilities that are also considered in the new formula. On one hand it gives an upper limit for plates with a constant width and increasing end distance ex (see Fig. 108a). In this čase the net cross-section becomes the critical failure. On the other hand it also limits the resistance of very wide plates with a constant end distance e\, where shear failure of the plate is the limiting resistance (see Fig. 108b). 96 Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. 6,2 5,1 4 2,9 1,8 0,7 3,4 2,9 2,4 1,9 1,4 0,9 e xld {) = 3 0,8 2,1 3,4 4,7 e/rf0 (a) 7,3 0,8 3,2 4,4 5,6 (b) Fig. 108: The effect of end (a) or edge (b) distance on product kji2 As can be seen in Fig. 106, function (72) matches with experimental results very well. The function becomes slightly conservative only for large e\le2 ratios with larger edge distance (for instance e2 > l,9d0). For such cases bolt shear is usually relevant. In Fig. 109 the new bearing resistance function is compared to experimentally determined bearing forces of single bolt shear connections, where besides our results also the results found in literature are included. There is a group of points in Fig. 109a that deviate from the dotted diagonal. These are the connections with thinner plate thickness that failed in curling (Rex, Easterling, 2003). The resistance of these connections was reduced due to the curling of the plates. Therefore an additional reduction factor should be prescribed in the formula (72). The results with curling failures were excluded in Fig. 109b. Now, the theoretical function (72) describes the experiment with satisfying accuracy. The scatter of point is outstandingly low V ? = 0,061, so the design bearing resistance for single bolt shear connections may be defined by ? M2 (?m = 1,165 < ? M2 = 1,25), having some extra safety for parameters which were not included in our analysis, like the effects of fabrication tolerances, that may be larger than assumed in (29) to (30), especially for small end and edge distances. 800 -r 600 400 200 O BI + Aalberg, Larsen X Kim, Yura o Rex, Easterling 800 T V? = 0,061 t> = 1,049 1,173 400 200 0 + Aalberg, Larsen X Kim, Yura o Rex, Easterling 200 600 800 0 200 400 600 F 400 F„,ne. ik a) ali results Fig. 109: Experimental re vs. new bearing resistance Fb for single bolt connections 800 b) curling failures excluded 6 2 */<*«, 0 o Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. 97 Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. 5.8.3 The connections with a single row of bolts positioned in the direction of load transfer Let us consider the connections with several bolts positioned in the direction of load transfer. Factor k\ that divides net area failures from other kinds of failures remains equal as in equation (73), while e'2 is defined by an effective width beff which is equal to connection width. Parameter e[ is expanded to include pitch^i and the number of bolts n. The analysis of experimental and numerical work revealed that the bearing force on the edge bolt decreased, if another bolt was put behind it. Hence, another factor k3 was introduced in the bearing formula to reduce the force on the edge bolt. Furthermore, the pattern of force distribution between bolts was dictated by plate bearing stiffness. Coefficient h also controls the bearing force pattern. The description of the choice of factor k3 is given in the sequel. In view of ali, the bearing resistance formula is rewritten: Fb,neW=klk2k3-d-t-fu k2 o V2 d ] n eff 2e e + (n-l)(Pl-d{)) (82) (83) (84) (85) c = eff (86) for edge bolt k3 = min k3 = min 2 e 1 1 +-; 1 v3 Pl 2 2 eJdo 3 (a K)2 for plates with equal bearing stiffness min -----jd0+-; 1 3 A2 2 j (87) for plates with different bearing stiffness (88) • for inner bolt or n = 1 k3=\ (89) In čase of unsymmetrically connected member, the effective width should be considered as: b eff 1 t (90) where fi are the same factors /?i and fh. as defined in section 3.10.3 of EN 1993-1-8 (CEN, 2005b). Table 28: Reduction factors Px and fl Pitch p1 < 2,5 d0 > 5,0 do 2 bolts 3 bolts or more 0,4 0,5 0,7 0,7 2 98 Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. Coefficient k3 in equations (87)-(88) controls the bearing force pattern. The relation of factor k3 to the e1/p1 ratio is illustrated in Fig. 110. It was shown that the difference between minimum and maximum value of bearing force is primarily dependent on ratio e1/p1. The coefficients in equation (87) were evaluated on the bases of results of parametric study. The difference between minimum and maximum value of bearing force is larger if the plate in a connection have different bearing stiffness. To achieve larger reduction on bearing force on the edge bolt in case of different plate bearing stiffness, the normalized pitch p1/d0 was raised to the second power. The negative effect of this reduction is that for equal ratios e1/p1, the reduction is larger at larger pitches p1 (see the right diagram in Fig. 110). The positive effect is that designers are forced to choose a balanced bolt pattern in order to avoid the reduction of bearing resistance. Moreover, in case of large pitches and insufficient number of bolts, the bolt shear failure is usually critical. 1 0,9 0,8 0,7 0,6 0,5 ej/p j= 0,7f 1 0,9 0,8 0,7 0,6 0,5 2,2(3,, Pj = 4,0d0 = 4,0dn 3,0d0 0,3 0,6 0,9 1,2 1,5 1, 0,3 0,6 0,9 1,2 1,5 1,8 ei/Pi Fig. 110: Factor k3 (left equation (87); right equation (88)) versus e^lp^ ratio Fig. 111 compares the bearing force on the edge and inner bolt calculated according to equation (82) and to the result of numerical simulation, presented in Sections 5.4.2 and 5.6. Numerical resistance on the inner bolt is the largest bearing force among all except the edge bolt. For the edge bolt, the points are scattered about the dotted diagonal (b = 1,057, Vd = 0,191 – Fig. 111a). The deviation of points above the dotted diagonal (safe side) is due to factor k3. For larger pitch distances equation (88) gives larger reduction than for smaller pitch p1 at the same e1/p1 ratio. Just the opposite is true for the points below the dotted diagonal. The situation is more favourable for the resistance on the inner bolt. In general all points are moved slightly to the safe side (Fig. 111b). The required partial factors are quite high (?M* = 1,697 for edge bolts; ?M* = 1,533 for inner bolts), but still low compared to Eurocode bearing resistance formula (see section 5.7.3). The quantile factors for 30 tests were used for its calculation. If lower values of quantile factors were used, the required partial factors would lower for about 0,1 (to 1,4). Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. 99 Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. 330 264 1 1 66 Vg = 0*191 b = lb057 v *= h697 /M + X Kim, Yura X Kouhi, Kortesmaa ¦ L 460 -r ------ 276 184 - Vs = 0,173 b = l,]l00 1^323 92------X^p --------+ Aalberg, Larsen X Kim, Yura X Kouhi, Kortesmaa ¦ L 66 132 198 264 330 F 92 184 276 368 460 b,new - edge bolt[kN] a) bearing force on edge bolt b,new inner bolt[kN] b) bearing force on inner bolt Fig. 111: Bearing forces on bolts for connections with one line of bolts positioned in the direction of loading The calculation of the sum of bearing forces on individual bolt Y.Fbt„ew was done under the assumption that the pattern of bearing forces depends on plate bearing stiffness. The pattern of bearing forces for the connections with different plate bearing stiffness is more or less increasing lineariv (see Figs. 50, 58, 63, 74, 75, 78, 79). Thus, the sum is given by: IX m-n C b,new + K b,new 2 (91) For the connections with equal plate bearing stiffness the pattern of bearing forces is svmmetrical (see Figs. 81-82, 88-90). A conservative approach is proposed for the summation of bearing forces. The svmmetrical pattern is simplified to the symmetrical linearly increasing pattern as shown by dotted lines in Fig. 90. Therefore, the sum of bearing forces on individual bolt LFb,new for the connections with equal plate bearing stiffness, with odd number of bolts positioned in the direction of load transfer in one line, is given by the following equation. Z^ b,new m (»+i)fa5 , j^inner b,new K b,new (92) For the connections with even number of bolts positioned in the direction of load transfer in one line the equation (91) applies. In equations (91)-(92) parameter m is the number of bolts in a single column positioned in the direction of load transfer. In cases when m > 1, the equations (91)-(92) assume constant distribution of bearing forces in the didection perendicular to bearing force. In the sequel, the equations will be evaluated only for m < 2. The application of equations (91)-(92) is presented in Table 29. Equations (91)-(92) are nothing less than the sum of arithmetic series. o o o o 100 Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. Table 29: The calculation of the sum of bearing forces Different plate bearing stiffness Equal plate bearing stiffness Distribution of bearing forces * F* n=n n=i n=2 n=l n=2i+l n=l n=n n=2i+l n=2i n=l Eauation (91) n - odd number (91) n - even number ______(92)______ In Fig. 112a the sum Y 3d0 and end distance ex > 2d0. For such large distances the maximum resistance developed at larger displacement or hole elongations. The problem was that the numerical calculations were stopped at displacements around 14 mm due to convergence difficulties; before the maximum resistance of the connection was not reached. The other thing was that high bearing forces led to curling of the plates. Thus, the resistance was not as high as it would be, if the plates were restrained. When analvzing of single bolt connections, it was established that the new bearing resistance formula does not account for curling. Moreover, for these geometries bolt shear is usuallv o o 102 Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. critical. This is also indicated by large friction forces that result in high tension stress in the bolt, which causes yielding of the bolt. The yielding causes plastic elongations, which consequently decrease the friction forces. Therefore the high friction for the mentioned geometries as a result of numerical simulations is not realistic. If these results were removed from the analysis, the scatter as well as the required partial factor to form design values would decrease (F^= 0,109, yM = 1,309 for edge bolt; F,? = 0,087, y^ = 1,175 for mner bolt). 1100 850 600 100 Vs = 0,120 b = 0,984 1,230 350 /t a Abaqus - linear distr. Fb l Abaqus - symmetric distr. Fb 100 350 F 600 850 edge bolt[kN] 1100 b,new a) bearing force on edge bolt 1100 850 «= 600 350 Vs = 0,122 b = 1,025 1,232 1734T----------- 100 l Abaqus - linear distr. Fb l Abaqus - symmetric distr. Fb 100 350 600 850 1100 b) bearing force on inner bolt Fig. 113: Bearing forces on bolts for connections included in the numerical parametrical study The sum of bearing resistances on individual bolt Y,Fbt„ew was calculated according to equations (91)-(92) and compared either to maximum sum of bearing forces max(ZBi) (see Fig. 114a) from numerical analyses or to connection resistance Pb at max(ZBi) which also includes friction (see Fig. 114b). In both cases the scatter of points is quite low. If geometries L11-L13, L21-L22 are removed from the analysis, the scatter becomes even lower and the design formula could be formed by partial factor yM2 in both cases. The connection maximum resistance could be estimated according to formulas (93), (95). Adequate design reliability would also be achieved by ym2- Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. 103 Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. 3500 2900 - 4000 3125 - 2250 -1375 t vs = b = 0,114 t,020 a i vs = b = = 0,lil5 1,1^3 1,222 *L A i M 1,325 A-a aaali ^ A- 2300 Ym .. A°5 A AA" A A^ A .^4 A 1700 - A A^A " A /T " 4a 1100 -____l y gjL a Abaqus a Abaqus - linear distr. Fb - symmetric distr. Ft v 2 %A* Abaqus - linear distr. Fb a Abaqus - symmetric distr. Fb 5C 0 1100 1700 2300 2900 3500 ^ b,new l J 500 1375 2250 3125 4000 a) sum of bearing resistances b) sum of bearing resistance compared to Pb 4000 r Fig. 114: Resistance of connections included in the numerical parametrical study 4000 Vs = 0,088 b = 1,°|52 1,189 3125 \ •= ir2!e9 2250 1375 500 a Abaqus - linear distr. Fb a Abaqus - symmetric distr. Fb 3125 2250 1375 500 500 1375 2250 3125 4000 500 1375 2250 3125 4000 ^ [kN] " [kN] a) sum of bearing resistances b) sum of bearing resistance compared to Pb Fig. 115: Resistance of connections included in the numerical parametrical study without geometries Lll- L13, L21-L22 5.8.5 The connections with two lines of bolts in the direction of load transfer The new bearing resistance formula can be expanded to its general form for nxm bolt connections, where n is the number of bolts in a single row positioned parallel to load transfer and m is the number of bolts in a single column positioned perpendicular to load transfer. The main assumption is that the elongation of ali bolt holes positioned in a column perpendicular to loading is equal. Therefore, the bearing forces on ali bolts are equal. Coefficients ki and k2 remain equal as for «xi bolt connections and are calculated according to equations (73) and (83), respectively. Accordingly, the number of bolts m positioned perpendicular to loading is included in parameter e'2 and in the effective width beff. Additionally, two factors k4, k5 are introduced in order to reduce resistance due to block tearing. Both factors are applied only to inner bolts in čase where m > 1. Coefficient k3 does not change (see equations (87)-(88)). The 104 Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. equations are rewritten in the most general form, but are valid only for m < 2, since no results for m > 2 were available: Fb new = klk2k3k4k5 ¦ dtfu (97) beff = 2e2+(m-l)(p2-d0) (98) b e'2 = — (99) 2m for edge bolt or when m = 1 k4=l (100) k5=l (101) for inner bolt k4=mm — +-*- + — ; 1 (102) v2 A 2 , k,=mm —^- + -; 1 (103) 2 e 2 The čase of block tearing, where bolt holes are put very close together and far away from the edge of the plate(e2 » p2), is considered directly in coefficient (103) and indirectly in (102). The mx\ bolt connection geometries that lead to block tearing failures result in hyperbolic decrease of ki factor and linear increase of k2 factor, thus the product k\k2 tends to stabilize, similarly as in Fig. 108b. The experimental results support the statement. Therefore, coefficients k4, k5 should not be applied to m* 1 bolt connections. In the čase of proposed approach, the new bearing resistance function (97) for mxn = 2* 1 bolt connections gives much better results than the Eurocode bearing resistance function (69). Again, the scatter of the results is for modified function very small (Vs= 0,089, b = 1,252 -Fig. 116). Our experimental results B2 and Puthli and Fleisher’s (2001) results show very good agreement with a proposed bearing function. It is important to stress that different types of failures are covered in presented experimental results. Besides shear, bearing and net cross-section failures in our experimental results, Puthli and Fleisher also experienced block tearing (Puthli and Fleischer defined block tearing failure as a mixed failure in their paper). The required partial factor for modified bearing resistance for two-bolt connection is yM = 1,044. Therefore, the design resistance can be formed with partial factor yy2- The mean correction factor b = 1,252 is large, probably due to friction forces. Numerical simulations were not performed for these series of test, thus friction could not be estimated. Previous results showed that friction forces were smaller if net area failure developed. In Fig. 116 the points that are the closest to the dotted diagonal present net area failures with the lowest friction forces. Higher friction developed at the connections with significant hole elongation which resulted in shear, splitting or bolt tearing failures. These points are positioned further from the dotted diagonal. Therefore it is reasonable to assume that friction increased the connection Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. 105 Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. resistance in čase of B2 and Puthli, Fleisher results. Moreover, the maximum connection resistance (93) could be established by factor kfnc equal to 1,1 (95). 450 350 250 150 Vs = 0,089 b = 1,252 v,,= 1,213 /M yM*= 1,044 A a Sr^ /aa A v A B2 A Puthli, Fleischer 150 250 350 450 b,new [kN] Fig. 116: Bearing force on bolt for the connections with two bolts positioned perpendicular to load transfer The last data set includes connections with bolts configured in a pattern 2x2. The numerical simulation for this data set was based on experiments performed by Kouhi and Kortesmaa (1990). The new bearing resistance formula (97) estimated the bearing force on the edge bolt satisfactory with mean bearing ratio b = 1,182. Reasonably low scatter of point (Vs= 0,119) allows partial factor y^ = 1,229 smaller than ymi even lf quantile factors for 20 tests were applied (see Fig. 117a). At first sight it seems that the estimation of the bearing force on the inner bolt was a missed approach. A detailed review discovered that the new formula gives good results for the connections that failed in net cross-section (coded as KK H; black crosses in Fig. 117b). The failures of test series coded as KK F and KK G were recognized as bearing and block tearing by authors of the report (Kouhi, Kortesmaa, 1990). The photographs in the report as well as our numerical simulations (see Fig. 94) evidently testify that the failures were primarily curling, which is a typical failure for thin plates. The thickness of the plates of KK F and KK H were only 3 mm. Coefficients k4 and k5 reduced the resistance of inner bolt, so only three results fell below the dotted diagonal, while one result was explicitly on the safe side. These four results increased the scatter {Vs= 0,130), thus the required partial factor is * Yu = 1,459. In Fig. 118a the sum ob bearing forces calculated according to the new function is compared to the sum of forces from the numerical simulation. The required partial factor * 1 • • 1 • yu = 1,316 is shghtly larger than yM2- Considenng that only one point hes considerably below the dotted diagonal and even for this point the error (ZBi-ZF6j„ew)/ZBi = -10% is low and that ali other point lie either on the safe side or close to the dotted diagonal, sufficient reliability could be achieved by recommended value of yy2 = 1,25. Beside that, several connections failed primarily in curling, which is not covered by the new bearing function. On top of ali, the friction forces in these connections were around 30% of bearing forces. If friction is also considered (Fig. 118b), the required partial factor drops to 1,036. The 106 Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. estimation of maximum connection resistance could be performed according to equations (93), (95). Large friction forces are the consequence of the large friction coefficient used in the numerical simulations (k = 0,37). vs = 0,119 x b = 1,182 X 70 - X Ym 1,28 r X 60 - Ym 1,229 w X * X X 50 -40 - > < > < KK G > < KK H 30 - 30 40 50 60 70 80 F\ - edge bolt [kN] a) bearing force on edge bolt b) bearing force on inner bolt Fig. 117: Bearing forces on bolts for connections with two lines of bolts parallel to loading direction 350 215 170 450 r ------ 305 260 394 338 282 226 170 0,117 _U3ij6 1,283 1,036 X KK F X KK G X KK H 170 215 260 I.Fbnew [kN] 305 350 170 226 282 335 394 450 ZF b,new [kN] a) sum of bearing resistances b) sum of bearing resistance compared to Pmax Fig. 118: Resistance of connections with two lines of bolts parallel to loading direction 5.9 Comparison of new bearing resistance formula to Eurocode bearing resistance Figs. 119-121 compare the bearing resistance according to EN 1993-1-8 to the bearing resistance formula developed in this chapter. The Eurocode formula is plotted on the abscissa and the new formula is plotted on the ordinate. In Fig. 119 the resistances on the edge bolt are compared. In ali cases of specimens L, the new formula gives lower values. In the cases of specimens B1 and B2 the new formula gives lower values if net cross-section failure was observed. Higher values of bearing resistances were obtained by new formula for Puthli, Fleisher connections, where edge distances and pitch p2 were small. The new formula also Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. 107 Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. gives lower values in most cases of the connections from the numerical parametric study. Similarly is true for the resistance on the inner bolt in Fig. 120 for these results. In several cases of specimens L, the new formula gives higher values. If the resistance of the whole connection is considered (Fig. 121), then the sum of bearing forces according to Eurocode gives higher values than the sum of bearing forces according to new formula, mainly in cases of net cross-section failure. In Fig. 122 the minimum of bearing resistance, net cross-section failure and block tearing resistance according to Eurocode is compared to the sum of bearing forces according to new formula as presented in this chapter. The scatter of points around dotted diagonal is much lower than in previous case in Fig. 121. Fig. 123 shows the same as Fig. 122, but only the results, where net cross-section or block tearing resistance is critical are shown. It is presented in this figure that new formula successfully accounts for net cross-section and block tearing resistance check. There are some results for specimen L for which the new formula gives lower results than Eurocode (safe side!). The reason for this is that the friction increased the resistance of the connection. If the friction forces were considered for the connections with more than two bolts by factor kfric = 1,1 (see Fig. 124), all point moved even closer to the dotted diagonal, but not above it. 525 AB2 + Aalberg, Larsen X Kim, Yura O Rex, Easterling O o - L X Kouhi, Kortesmaa A Puthli, Fleischer o o o 350 - °*L j 1 ¦ 1 ¦ ¦ 0 1150 - 920 690 - 460 A Abaqus 175 350 525 Fb [kN] - edge bolt, EC 700 230---------&LH^> ' 5A A A SA s *A'A ž ^g A A A 0 230 460 690 920 1150 Fb [kN] - edge bolt, EC 0 0 Fig. 119: Comparison of results for the edge bolt 108 Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. 410 - 328 246 — + Aalberg, Larsen X Kim, Yura ¦ L X Kouhi, Kortesmaa 164--------------------- 82------«• X& X X X «x noo ------------ 825 550 275 A Abaqus ~fr A A& && 82 164 246 328 410 F b [kN] - inner bolt, EC 275 550 825 Fb [kN] - inner bolt, EC 1100 1600 1200 O BI AB2 + Aalberg, Larsen X Kim, Yura O Rex, Easterling Fig. 120: Comparison of results for the inner bolt 4000 X Kouhi, Kortesmaa A Puthli, Fleischer 800 400------&&& A Abaqus 3200 — 2400 — 1600 800 -a ___________^a^aa -------------------A- A7? Aa &* bV* '*$ A A A*Ž A A-A- ^ 400 800 1200 2 i7,, [kN] - EC 1600 800 1600 2400 3200 4000 T,Fb [kN] - EC Fig. 121: Comparison of results for the sum of bearing forces 1600 1200 O BI AB2 + Aalberg, Larsen X Kim, Yura O Rex, Easterling - L X Kouhi, Kortesmaa A Puthli, Fleischer 4000 800 400-------a-a 3200------------------------------------- 2400 1600 800 - 0 400 800 1200 min(I.Fb, N „ Veffl) [kN] - EC 1600 0 800 1600 2400 3200 4000 min(E.r 6, N t, Veffl) [kN] - EC 0 0 0 o o o o o Fig. 122: Comparison of results for the minimum of sum of bearing forces, net cross-section resistance and bearing resistance Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. 109 Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. 1600 r 1200 800 400 O BI A B2 ¦ L A Puthli, Fleischer A A * V ^AA < 4000 X 3200 - 2400 l 1600 800 A Abaqus A \J± 1 h, $& 400 800 1200 min(ZFb, Nt, V^,) [kN] - EC 1600 800 1600 2400 3200 min(LFb, Nt, V\ffl) [kN] - EC 4000 Fig. 123: Comparison of results for the minimum of sum of bearing forces, net cross-section resistance and bearing resistance – only results, where net cross-section or block tearing resistance is critical are shown 1600 J 800 400 O BI AB2 ¦ L X Kouhi, Kortesmaa A Puthli, Fleischer A A *V 1?^ A Aba qus A 3200 - A A 2400 1600 1 g A A 800 4 a.Lk X 400 800 1200 1600 800 1600 2400 3200 4000 minClF,,, N„ Vm) [kN] - EC minCSi7,,, N„ Veml) [kN] - EC Fig. 124: Comparison of results for the minimum of sum of bearing forces, net cross-section resistance and bearing resistance - only results, where net cross-section or block tearing resistance is critical are shown - friction also is considered on the ordinate The comparison of resistances in normalized format obtained as ratios theoretical/ experimental values is shown in Figs. 125-129. In these figures the results for geometries L11-L13, L21-L22 and Rex, Easteriing results with curling failures are excluded. The reasons for the exclusion of the results for geometries L11-L13, L21-L22 were convergence difficulties of numerical simulations before reaching the maximum resistance of the connections. The Eurocode and new bearing resistance formula do not account for curling failures, therefore and Rex, Easteriing results with curling failures are excluded. The abscissas in Figs. 125-129 present the ratio between Eurocode bearing resistance formula and numerical (or experimental) resistance. The ordinates in these figures present the ratio between new bearing resistance formula and numerical (or experimental) resistance. The values lower than 1 are on the safe side. The thick black lines (horizontal and vertical) in the mentioned figures present unity, where theoretical and experimental results are equal. In these cases the dotted diagonal presents the equality of Eurocode and new bearing resistance formula. o o o o o o o 110 Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. In Fig. 125 the normalized resistance for the edge bolt is shown. Eurocode bearing resistance formula gives in certain cases very unrealistic results that are for more than three times on the unsafe side. There are also a lot of larger than 1,2 (danger side). The new formula much better estimates the values on the edge bolt. There are only a few results above the unity line, where one Kim, Yura result strikes the eye. Due to the rigid cover plates the distribution of bearing forces is very unequal. The new model does not account for such inequality. The new model gives the range of values between 0,7 and 1,1 for most of the results. Fig. 126 depicts the normalized resistances on the inner bolt. The Eurocode formula scatters the values from 0,48 to 2,05. The most results are scattered approximately between 0,6 to 1,2. This is another confirmation of inaccurate resistance model of Eurocode function. On the other hand the new formula scatters the results between 0,55 to 1,18. The majority of results are placed in range of 0,75 to 1,1. The range of the results is significantly reduced by the new bearing resistance formula. 1,5 1>2 o,9 0,6 i 0,6 1,8 / F BI B2 Aalberg, Larsen Kim, Yura Rex, Easterling L Kouhi, Kortesmaa Puthli, Fleischer 1,3 2,4 3,0 3,6 0,6 A aa aa ^ a j A A A A A A i in '4h AAA A A A A ------------- A i----------------------------------------------------------------------------------------------- A A Abaqus )---------------------------- 0,6 1,3 2,0 2,7 F / F - e dge bol t b,EC b,numerical 3,4 - edge bolt b,EC b,numerical Fig. 125: Diagrams in normalized format obtained for the edge bolt 1,2 0,8 0,4 0,4 + Aalberg, Larsen »C Kim, Yura ¦ L X Kouhi, Kortesmaa 0,8 F / F b,EC b,numerical 1,2 1,6 - inner bolt 1,2 T F^ 0,6 0,6 A^A f A* A ,4VrA a a 0,9 1,2 A Abaqus F / F b,EC b,numerical 1,5 1,8 2,1 inner bolt Fig. 126: Diagrams in normalized format obtained for the inner bolt Može, P. 2008. Ductility and resistance of bolted connections in structures made of high strength steels. 111 Doctoral thesis. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo. 1,2 0,9 0,6 O BI B2 + Aalberg, Larsen »C Kim, Yura O Rex, Easterling - L X Kouhi, Kortesmaa A Puthli, Fleischer 1,2 X * x>< 0,2 0,5 0,8 1,1 1,4 1,7 2,0 2,3 2,6 2* b,EC ^ b,numerical-experimental 0,7 + 0,7 1,2 1,7 2,2 ^ 6,LC ^ b,numerical-experimmtal Fig. 127: Diagrams in normalized format obtained for the group of bolts 1,2 1,0 0,6 AB2 XKim & 0,8 - A -K L a aL A A A A X -i k A Ax >f Yura O BI + Aalberg, Larsen o Rex, Easterling ¦ L X Kouhi, Kortesmaa A Putr li, Fleischer --------------cr X- y v* 0,20 0,40 0,60 0,80 1,00 1,20 v^* b,EC> t> eff^l* 2j b,numerical, experimmtal 1,1----- 1,0 0,9 0,8 4 0,7 A# JA A A*\ A A ^4^ A A< A a4 A .