BASE PLATE CONNECTIONS

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Transcription:

SKILLS Project

BASE PLATE CONNECTIONS

LEARNING OUTCOMES Design process for pinned and fixed column base joints Base-plate resistance Anchor bolt resistance Concrete resistance Weld resistance Application of the component method to pinned and fixed column base joint. 3

LIST OF CONTENTS Introduction Pinned column base joint Rigid column base joint Application Conclusion 4

INTRODUCTION

INTRODUCTION Typical pinned column base joint Column Grout Base plate Concrete foundation Anchor bolt 6

INTRODUCTION Typical fixed column base joint Column Base plate Anchor bolts Concrete foundation 7

INTRODUCTION Analysis of the joint according to EN 1993-1-8 Joint is modelled by a typical components : T-stub Two models for loadings : Resistance in compression : T-stub in compression with concrete, Resistance in tension : T-stub in tension (anchor bolts + base plate + column web). F T,Rd F T,Rd F T l eff 8

INTRODUCTION Recommended partial safety factors according to EN 1993-1-8 : g M0 =1 : column web in tension, bending of the base-plate g M2 =1,25 : Anchor bolts in tension/shear, weld resistance Recommended partial safety factors according to EN 1992-1-1 : g C =1,5 : Concrete in compression, bond anchorage resistance The national annexes may give indications 9

PINNED COLUMN BASE JOINT

PINNED COLUMN BASE JOINT - RESISTANCE IN COMPRESSION Evaluation of the resistance in compression of T-stubs in contact with concrete. EN 1993-1-8 6.2.5 Resistance in compression of the joint : association of resistances of T-stubs in compression. F c,rd Concrete resistance reached : fjd l eff f jd b eff Web T-stub : F c,bw,rd 11 Flange T-stubs : F c,fc,rd

PINNED COLUMN BASE JOINT - RESISTANCE IN COMPRESSION Foundation bearing strength f a b f jd bf j cd EN 1993-1-8 6.2.5 EN 1992-1-1 6.7 Where: a bf b j coefficient which accounts for diffusion of concentrated force within the foundation. may be taken as 2/3 (see Note) f cd Concrete design strength : fck f ck a cc = 1 g c = 1,5 fcd acc g c Compressive cylinder strength of concrete at 28 days 12

PINNED COLUMN BASE JOINT - RESISTANCE IN COMPRESSION Expression of a bf : a bf d e e f h b = min 1+ ; 1+2 ; 1+2 ; 3 max( hp, bp ) h p b p Note : b j = 2/3 if : e m e m 50 mm min0,2bp 0,2h p d f Axis x-x e h Strength of grout 0,2 f cd Axis y-y e b Else : f jd f cd bp Axis z-z 13 hp

PINNED COLUMN BASE JOINT - RESISTANCE IN COMPRESSION Resistance in compression of a T-stub : F f b l C,Rd jd eff eff EN 1993-1-8 (6.4) Where: l eff Effective length of the T-stub b eff Effective width of the T-stub such as : c Additional bearing width of the flange : f yp g M0 =1 c t p f jd yp 3f g M0 Yield strength of base plate l eff b t c eff 2 F c,rd t p b eff 14 c t c f jd

PINNED COLUMN BASE JOINT - RESISTANCE IN COMPRESSION Large and short projections : EN 1993-1-8 6.2.5 t = t fc t = t fc or t wc b eff b eff t p t p f jd f jd b c c c Flange T-stub : Flange T-stub : b t c bc beff t fc2c eff fc 15 c c a) Short projection b) Large projection Web T-stub : b t c eff wc 2

PINNED COLUMN BASE JOINT - RESISTANCE IN COMPRESSION Resistance in compression of a flange T-stub : Where: l min b ; b 2c eff p fc b min c; h h /2 t min c; h /2 t F c,fc,rd jd eff eff eff p c fc c fc f b l c b eff c b eff c c c t fc l eff b fc b p l eff b fc b p c c h c h p Large projection 16 h c h p Short projection

PINNED COLUMN BASE JOINT - RESISTANCE IN COMPRESSION Resistance in compression of the web T-stub : Where: l h 2t 2c 0 eff c fc b 2c t eff wc F c c f b l c,bw,rd jd eff eff c l eff t wc c c b eff t fc h c 17

PINNED COLUMN BASE JOINT - RESISTANCE IN COMPRESSION Resistance in compression of the joint : N 2F F C,Rd c,fc,rd c,bw,rd NC,Rd fjd hcpb cp lcp bcp twc 2c Where : h min h ; h 2c cp p c b min b ; b 2c cp p fc c c t fc c l h 2t 2c 0 cp c fc t wc b fc b p c h c h p 18

PINNED COLUMN BASE JOINT - RESISTANCE IN TENSION Joint modelled by a T-stub (anchor bolts, base plate) in tension Evaluation of the tensile resistance of the T-stub 6 possible failure modes : Base plate/anchor bolts (modes 1, 2, 1-2 and 3) Column web (mode 4) and weld F T,Rd F T,1,Rd F T,Rd F T,Rd l eff b) 19

Failure modes of base plate/anchor bolts F T,1,Rd PINNED COLUMN BASE JOINT - RESISTANCE IN TENSION Mode 1 : Yielding of the base plate Mode 2 : Failure of anchor bolts F T,1,Rd F T,1,Rd F T,2,Rd F T,2,Rd Prying effect Q Q Q Q No prying effect Mode 1-2 : Yielding of the base plate F T,1-2,Rd Mode 3 : Failure of anchor bolts F T,3,Rd F T,3,Rd F T,3,Rd F T,4,Rd F T,4,Rd 20

PINNED COLUMN BASE JOINT - RESISTANCE IN TENSION Mode 4 : Yielding of the column web in tension d F T,4,Rd The prying effect has an influence on the choice of failure modes. Failure modes 1 and 2 are not possible without prying force and are replaced by failure mode 1-2. 21

PINNED COLUMN BASE JOINT - RESISTANCE IN TENSION Prying effect and failure modes : EN 1993-1-8 Table 6.2 Prying effect Presence of prying effect Absence of prying effect F F T,1,Rd T,Rd F T,Rd F T,2,Rd Deformation Q Q Condition L b L * b L b > L * b Resistance of the T-stub F T,Rd FT,1,Rd ; FT,2,Rd min FT,3,Rd ; FT,4,Rd F T,Rd T,1-2,Rd; T,3,Rd min F F FT,4,Rd F F T,3,Rd F T,4,Rd F

PINNED COLUMN BASE JOINT - RESISTANCE IN TENSION Anchor bolt elongation length : L 8d e t t 0,5 k b m p wa EN 1993-1-8 Table 6.2 Where: t wa d Thickness of the washer Anchor bolt diameter base plate grout k t p e m Concrete 8d 23

PINNED COLUMN BASE JOINT - RESISTANCE IN TENSION Limit anchor bolt elongation length : Where: A s Tensile stress area of one anchor bolt l eff,1 Effective length : l =min l ; l eff,1 eff,cp eff,nc m p/2 t /2 0,8 2a wc w 8,8m A 3 * s b 3 leff,1tp L t wc a w p/2 m EN 1993-1-8 Table 6.2 Base plate t p 24

PINNED COLUMN BASE JOINT - RESISTANCE IN TENSION Effective lengths of the T-stub : Circular mechanism e m m e Non circular mechanism e m m e EN 1993-1-8 Table 6.6 p Yield line t wc l eff,cp 2 m eff,nc 4 1,25 l m e 25

PINNED COLUMN BASE JOINT - RESISTANCE IN TENSION Resistance of modes 1 and 1-2: EN 1993-1-8 Table 6.2 Failure mode Mode 1 Mode 1-2 F T,1,Rd T,1,Rd F T,1-2,Rd F T,2,Rd Yielding of the base plate m Q Q Resistance of the T-stub F T,1,Rd 4M pl,1,rd m F T,1-2,Rd 2M pl,1,rd m Where: t f M m l m l l l 2 p yp pl,1,rd pl,rd eff,1; pl,rd ; eff,1=min eff,cp; eff,nc 4g M0 F T,3,Rd 26 F T,3,Rd F T,4,Rd F T,4,Rd

PINNED COLUMN BASE JOINT - RESISTANCE IN TENSION Resistance of modes 2 and 3: EN 1993-1-8 Table 6.2 Failure mode Mode 2 Mode 3 F T,1,Rd Failure of anchor bolts F T,2,Rd F t,rd,anchor m e F t,rd,anchor F T,3,Rd F t,rd,anchor Q Q Resistance of the T-stub F T,2,Rd 2Mpl,2,Rd 2nF m n t,rd,anchor F T,3,Rd 2F t,rd,anchor F T,3,Rd Where: F t,rd,anchor M m l ; l = l ; n=min e; 1,25m pl,2,rd pl,rd eff,2 eff,2 eff,nc Resistance of one anchor bolt F T,4,Rd 27

PINNED COLUMN BASE JOINT - RESISTANCE IN TENSION Tensile resistance of anchor bolts : EN 1993-1-8 6.2.6.12 1. Base plate 2. Grout 3. Concrete foundation (a) Hook : bond resistance (b) Washer plate : No bond 28

PINNED COLUMN BASE JOINT - RESISTANCE IN TENSION Resistance of one anchor bolt, two failure modes: Tensile resistance of the anchor bolt section, Ft,Rd, Bond anchorage resistance, Ft,bond,Rd. Ft,Rd,anchor min F t,rd; Ft,bond,Rd Design tensile resistance of the anchor bolt section : Where: f ub g M2 = 1,25 F t,rd Tensile strength of the anchor bolt 0,9 f A g ub M2 s EN 1993-1-8 Table 3.4 EN 1993-1-8 Table 3.1 29

PINNED COLUMN BASE JOINT - RESISTANCE IN TENSION Bond anchorage resistance of a straight bolt : Where: d Nominal diameter of an anchor bolt f bd Design bond strength : If d < 32 mm : If d 32 mm : g c = 1,5 f bd bd F fyb 600 N/mm f t,bond,rd dl f 0,36 fck g C 0,36 fck 132 d g 100 2 C fyb : Yield strength of the anchor bolt. 30 b bd lb Ft,Bond,Rd

PINNED COLUMN BASE JOINT - RESISTANCE IN TENSION Bond resistance of a bolt with a hook : F t,bond,rd dlb f 0,7 bd EN 1993-1-8 6.2.6.12 (5) Ft,Bond,Rd Check that : fyb 300 N/mm 2 l b 5d 90 31

PINNED COLUMN BASE JOINT - RESISTANCE IN TENSION Resistance of mode 4: Failure mode Mode 4 F T,3,Rd F T,4,Rd Yielding of the column web in tension t wc Where: Resistance of the T-stub T,4,Rd t,wc,rd f y,wc Yield strength of the column web beff,t= leff,1 32 F F b t f eff,t wc y,wc g M0

PINNED COLUMN BASE JOINT - RESISTANCE IN TENSION Weld resistance : Where: a w b w f u l w,wb u Ft,w,Rd lw,eff,taw bg w M2 weld throat thickness of the web correlation factor nominal ultimate strength of the weaker joined part total effective length of the web welds l =2l l w,eff,t eff,1 w,wb Final resistance of the joint in tension : f / 3 N min F ; F N T,Rd T,Rd t,w,rd t,ed EN 1993-1-8 Table 4.1 33

PINNED COLUMN BASE JOINT - SHEAR RESISTANCE Three ways to transmit shear force to concrete block : Friction resistance between base plate and concrete (compression), Shear of anchor bolts (compression/tension), Use of shear nibs (important tension force). 34

PINNED COLUMN BASE JOINT - SHEAR RESISTANCE Design friction resistance : Ff,Rd Cf,dNc,Ed EN 1993-1-8 6.2.2 (6) Where: N c,ed C f,d Compression force Coefficient of friction For sand-cement mortar : Cf,d 0,2 Axial force N c,ed Shear force V Ed <0,2 N c,ed Friction 35 h p e h

PINNED COLUMN BASE JOINT - SHEAR RESISTANCE Shear resistance of an anchor bolt: Where: f yb vb,rd bc ub s M2 Yield strength of the anchor bolt F a g f A EN 1993-1-8 6.2.2 (7) a 0,44 0,0003 f and 235 N/mm f 640 N/mm 2 2 bc yb yb Fvb,Rd 36

PINNED COLUMN BASE JOINT - SHEAR RESISTANCE Shear resistance in presence of compression : Addition of friction resistance and shear resistance of anchor bolts : Where: n Number of anchor bolts Fv,Rd Ff,Rd nfvb,rd VEd Axial force N c,ed EN 1993-1-8 6.2.2 (8) Shear force V Ed Friction Shear of anchor bolts 37 e h

PINNED COLUMN BASE JOINT - SHEAR RESISTANCE Shear resistance in presence of tension : Where: F T,Rd V nf Ed vb,rd N 1,4F t,ed T,Rd 1 Tensile resistance of the T-stub in tension Axial force N t,ed Shear force V Ed Shear of anchor bolts 38 e h

PINNED COLUMN BASE JOINT - SHEAR RESISTANCE Shear resistance of welds (in compression) : Where: l w,eff a f vw,d fu / 3 bg w M2 Vw,Rd fvw,d alw,eff VEd total effective length of the welds in the direction of shear weld throat thickness in the direction of shear Check of the shear resistance of welds (in tension) : 2 2 N V t,ed Ed Fw,Ed fvw,d a l w,eff,t l w,eff 39

FIXED COLUMN BASE JOINT

FIXED COLUMN BASE JOINT- INTRODUCTION Calculation of the bending resistance and initial rotational stiffness in presence of axial force : M j,ed M j,rd N j,ed M j,ed M j,rd j,ed S j,ini j,ed Initial rotational stiffness : S j,ini M j,ed j,ed 41

FIXED COLUMN BASE JOINT- INTRODUCTION Application of the component method : N j,ed M j,ed M j,rd j,ed F T F c F T Mode 2 Mécanisme partiel et rupture des tiges T-stub in tension : T-stub in compression : F T,2,Rd =(2M pl, 2, Rd +nf t, Rd )/(m +n) F C Tronçon en T comprimé Aire de répartition m uniforme de pression entre la platine et son appui 42 e l eff b eff

FIXED COLUMN BASE JOINT- INTRODUCTION Lever arms : Tensile force positioned at the centre of anchor bolts, Compression force at the centre of the column flange. Bending moment : M z F z F j,ed C C T T Bending resistance : resistance reach on a T-stub. h c M j,ed t fc F F or F F C C,Rd T T,Rd z T z C F T F C 43

FIXED COLUMN BASE JOINT- BENDING RESISTANCE Bending resistance depend on eccentricity : e Dominant tensile force : Dominant compression force : 0 e z N T N M N z e j,ed j,ed C N 0 M N j,rd j,rd N j,rd N j,rd M j,rd M j,rd F T,Rd z T z T F T F C z C z C F C,Rd 2 T-stubs in tension 44 2 T-stubs in compression

FIXED COLUMN BASE JOINT- BENDING RESISTANCE Dominant bending moment : en zt or en zc Joint composed of a tensile part and a compressive part : Resistance reaches in one these parts, N j,rd N j,rd M j,rd M j,rd z T z C z T z C F T,Rd F C F T F C,Rd T-stub in tension critical 45 T-stub in compression critical

FIXED COLUMN BASE JOINT- BENDING RESISTANCE Resistance in compression of a flange T-stub : Where: l min b ; b 2c eff p fc F f b l C,Rd jd eff eff h hp h c c beff min c, tfc tfc min c, 2 2 c t p 3f f jd yp g M0 l eff c c EN 1993-1-8 (6.4) F C,Rd b eff t fc c l eff t wc b fc b p b eff c h c h p 46

FIXED COLUMN BASE JOINT- BENDING RESISTANCE Resistance of the tensile part of the joint (2 anchor bolts): Analysis of the resistance of an equivalent T-stub : F T,Rd EN 1993-1-8 Figure 6.10 Same calculation as for pinned column base joint: Different effective length, leff Replace m by mx, e by ex in resistance of T-stub 47

FIXED COLUMN BASE JOINT- BENDING RESISTANCE Effective lengths of the T-stub : Circular mechanism Non circular mechanism 2 m 4m x x 1,25ex leff,cp min mx w 2mx 0,625 ex w /2 l eff,nc min mx 2e 2 mx 0,625 ex e bp /2 EN 1993-1-8 Table 6.6 e w e x b p m x 48

FIXED COLUMN BASE JOINT- BENDING RESISTANCE Loading Lever arm z Bending resistance M j,rd for a given value of e N Dominant compression force Dominant tension force z = z C + z C z = z T + z T N j,ed < 0 and 0 e N +z C N j,ed < 0 and-z C e N 0 The smaller of and N j,ed > 0 and 0 e N +z T N j,ed > 0 and -z T e N 0 The smaller of z F C C,Rd / e 1 N z F C,Rd / e 1 FT,Rdz FT,Rdz and z / e 1 z / e 1 T N z T C N N z N j,ed 0 N j,ed 0 Dominant bending moment z = z T + z C M j,ed > 0 is clockwise, N j,ed > 0 is tension. and e N > +z T or e N < - z T e N The smaller of M N j,ed j,ed 49 M N j,rd j,rd and e N < - z C or e N > z C FC,Rdz FT,Rdz and z / e 1 z / e 1 T N C N Table 6.7

FIXED COLUMN BASE JOINT- INITIAL ROTATIONAL STIFFNESS The column base joint can be classified rigid : for frames where the bracing system reduces the horizontal displacement by at least 80% : EN 1993-1-8 (2) 5.2.2.5 - if 0,5 - if 0,5 3,93 and S 72 2 1 EI / L Otherwise : Where : 0 0 j,ini 0 c c - if 3,93 and S 48 EI / L 0 j,ini c c S j,ini 30EI Lc : storey height of the column, Ic : second moment of area of the column, L c c : slenderness of the column in which both ends are assumed to be pinned. 0 50

FIXED COLUMN BASE JOINT- INITIAL ROTATIONAL STIFFNESS Otherwise the column base joint is semi-rigid : Joint model by a rotational stiffener in the global analysis : Rotational stiffener S j S S if M 2 M /3 j j,ini j,ed j,rd Sj,ini S if 2 M /3 M M j j,rd j,ed j,rd S j (1,5 M / M ) ; 2,7 j,ed j,rd 51

FIXED COLUMN BASE JOINT- INITIAL ROTATIONAL STIFFNESS Model for the calculation of the initial rotational stiffness : Tensile and compressive parts modelled by axial stiffener. Initial rotational stiffness : S j,ini M j,ed j,ed N j,ed M j,ed N j,ed M j,ed F T j,ed j,ed F C 52 k T z T z C k C

FIXED COLUMN BASE JOINT- INITIAL ROTATIONAL STIFFNESS Stiffness of compressive part of the joint Where: l eff b eff C 13 Effective length of the T-stub, Effective width of the T-stub, E c Elastic modulus of concrete (see EN 1992-1-1), E Elastic modulus of steel. k E l b k 1,275E c eff eff EN 1993-1-8 Table 6.11 F C Flange c Concrete 53 Contact between flange and concrete

FIXED COLUMN BASE JOINT- INITIAL ROTATIONAL STIFFNESS Stiffness of the tensile part of the joint EN 1993-1-8 Table 6.11 Depends on the presence or absence of prying effect. Presence of prying effect : L b L * b Absence of prying effect : L b > L * b F T F T B B B B T T Q Q 54

FIXED COLUMN BASE JOINT- INITIAL ROTATIONAL STIFFNESS Stiffness of the tensile part in presence of prying effect : k T 1 1 1 k k 15 16 EN 1993-1-8 Table 6.11 k16 : stiffness coefficient of anchor bolts in tension : k 16 1,6 A L s b k15 : stiffness coefficient of base plate in bending under tension : k 3 0,85 lefftp 15 3 m 55

FIXED COLUMN BASE JOINT- INITIAL ROTATIONAL STIFFNESS Stiffness of the tensile part in absence of prying effect : k T 1 1 1 k k 15 16 EN 1993-1-8 Table 6.11 k16 : stiffness coefficient of anchor bolts in tension : k 16 2 A L s b k15 : stiffness coefficient of base plate in bending under tension : k 3 0,425 lefftp 15 3 m 56

FIXED COLUMN BASE JOINT- INITIAL ROTATIONAL STIFFNESS Rotational stiffness depend on the eccentricity : Dominant tensile force : Dominant compression force : 0 e z N T e z e N C N 0 M N j,ed j,ed N j,ed M j,ed N j,ed M j,ed F T,1 j,ed F T,2 F C,1 F C,2 j,ed k T z T z T k T k C z C z C k C 2 T-stubs in tension 57 2 T-stubs in compression

FIXED COLUMN BASE JOINT- BENDING RESISTANCE Dominant bending moment : en zt or en zc Joint composed of a tensile and compressive part : F T N j,ed M j,ed j,ed F C k T z T z C k C 58

FIXED COLUMN BASE JOINT- INITIAL ROTATIONAL STIFFNESS Loading Lever arm z Initial rotational stiffness S j,ini for a given value of e N Dominant compression force Dominant tension force z = z C + z C z = z T + z T N j,ed < 0 and 0 e N +z C N j,ed < 0 and-z C e N 0 S j,ini 2 E z k 2 N j,ed > 0 and 0 e N +z T N j,ed > 0 and -z T e N 0 S j,ini 2 E z k 2 C T N j,ed 0 N j,ed 0 Dominant bending moment z = z T + z C M j,ed > 0 is clockwise, N j,ed > 0 is tension. and e N > +z T or e N < - z T e N S j,ini M N E z 1 ek 1 1 1ak kc kt ak j,ed j,ed 59 2 and e N < - z C or e N > z C z k -z k = k + k e = e C C T T k N T C Table 6.12

APPLICATION

APPLICATION PRESENTATION OF THE EXAMPLE Detail of the joint and the concrete block Axial force : N Ed Column : IPE 450 in S235 Base plate 48022010 in S235 Shear force V z,ed Grout of 30 mm thickness Concrete class C25/30 d f =500mm l b =400mm Axis x-x Anchor bolts M24 class 4.6 e h Axis y-y e b 400 b p =220 Axis z-z h p =480 800 61

APPLICATION PRESENTATION OF THE EXAMPLE Detail of the joint 15 10 14,7 2 anchor bolts M24 Class 4.6 225 190 9,4 225 15 40 140 40 Flange weld : 6 mm e m 60,8 40 Web weld : 4 mm 62

APPLICATION PRESENTATION OF THE EXAMPLE Load Case 1 (compression) : N c,ed = 85 kn V z,ed = 35 kn 1-1 Check the resistance in compression 1-2 Check the shear resistance Load Case 2 (tension) : N T,Ed = 8,86 kn V z,ed = 17,5 kn 2-1 Check the resistance in tension 2-2 Check the shear resistance 63

APPLICATION 1-1 RESISTANCE IN COMPRESSION Concrete (C25/30) design strength : fck f cd acc g c 25 fcd 1 16,7 MPa 1,5 The value of b j is equal to 2/3, as : Coefficient a bf : e m 50 mm 30 mm min0,2 bp 0,2 hp a a bf bf d e e f h b = min 1+ ; 1+2 ; 1+2 ; 3 max( hp, bp ) h p b p 500 800 480 400 220 min 1 ; 1 ; 1, 3 1,67 480 480 220 64

APPLICATION 1-1 RESISTANCE IN COMPRESSION Foundation bearing strength : f a b jd bf j cd fjd 1,672/316,7 18,6 MPa Additional bearing width of the flange : c t p 3 f f jd yp g f M0 235 c 10 20,5 mm 318,61,0 65

APPLICATION 1-1 RESISTANCE IN COMPRESSION Geometrical parameter : cp p c h min h ; h 2c min 480;450 220,5 480 mm cp p fc b min b ; b 2c min 220;190 220,5 220 mm cp c fc Short projection l h 2t 2c 450 214,7 220,5 379,6 mm 0 Resistance in compression of the column base joint : N f h b l b t c C,Rd jd cp cp cp cp wc 2 18,6 480220 379,6 220 9,4 220,5 /1000 766,6 kn 66

APPLICATION 1-1 RESISTANCE IN COMPRESSION Check of the resistance in compression: N C,Rd 766,6 kn N 85 kn c,ed h c = 450 bc =15 20,5 bc =15 b fc =190 t fc = 14,7 c c t wc = 9,4 l eff = 220 c c= 20,5 h p = 480 c b eff 67

APPLICATION 1-2 SHEAR RESISTANCE (CASE 1) Friction resistance : F C N f,rd f,d c,ed Ff,Rd 0,285 17 kn Shear resistance of one anchor bolt : F F vb,rd a bc ub s Shear resistance of the joint F F nf g f M2 A (0,44 0,0003240) 400353 41,6 kn 1,2510 vb,rd 3 v,rd f,rd vb,rd Fv,Rd 17 241,6 100,2 kn 68

APPLICATION 1-2 SHEAR RESISTANCE (CASE 1) Shear resistance of welds : u Vw,Rd a lw,eff bg w M2 l V w,eff w,rd f / 3 2 450 214,7 221 757,2 mm 360 / 3 4757,2/1000 629,5 kn 0,81,25 Check of the shear resistance : z,rd v,rd w,rd z,ed V min F ; V 100,2 kn V =35kN 69

APPLICATION 2-1 RESISTANCE IN TENSION (CASE 2) Length m : m p/2 t /2 0,8 2a wc (140-9,4) m = -0,8 2 4 = 60,8 mm 2 Effective lengths and mechanisms : l l eff,cp eff,cp eff,nc eff,nc =2 m =2 (60,8)=381,9 mm l =4 m+1,25e l =4 60,8+1,25 40=293,1 mm Effective lengths of mode 1 and 2 : l min l ; l 293,1 mm l eff,1 eff,cp eff,nc eff,2 l eff,nc 293,1 mm w 40 140 40 e m 60,8 40 Web weld : 4 mm 70

APPLICATION 2-1 RESISTANCE IN TENSION (CASE 2) Presence of prying effect? Limit anchor bolt elongation length : Anchor bolt elongation length : L 8d e t t 0,5 k L b m p wa b 8,8m A 3 * s b 3 leff,1tp L 3 * 8,860,8 353 b 3 2382 mm L 293,110 824 30 10 5 0,522 248 mm L 2382 mm Prying effect develops and failure modes 1, 2, 3 and 4 will be considered. * b 71

APPLICATION 2-1 RESISTANCE IN TENSION (CASE 2) Bending resistance of the base plate (per unit length) : m m pl,rd 2 p t f 4 g yp M0 pl,rd 3 2 10 235 41,010 5,87kN.mm/mm Bending resistances of the base plate Mode 1 : Mode 2 : Mpl,1,Rd leff,1 mpl,rd 293,1 5,87 1722 kn.mm Mpl,2,Rd leff,2 mpl,rd 293,1 5,87 1722 kn.mm 72

APPLICATION 2-1 RESISTANCE IN TENSION (CASE 2) Resistance of one anchor bolt in tension Design tensile resistance of the anchor bolt section: 0,9 fub As Ft,Rd g Design bond strength : F M2 0,9353400 101,6 kn 1,2510 t,rd 3 f f bd bd 0,36 g C f ck 0,36 25 1,5 1,2 MPa 73

APPLICATION 2-1 RESISTANCE IN TENSION (CASE 2) F t,bond,rd Design bond anchorage resistance: dl f b bd Ft,bond,Rd 24 400 1,2/1000 36,2 kn Ft,Bond,Rd Design anchor bolt resistance : Ft,Rd,anchor min F t,rd ; Ft,bond,Rd 36,2 kn lb = 400 mm 74

APPLICATION 2-1 RESISTANCE IN TENSION (CASE 2) Resistance in tension of the T-stub : modes 1 and 2 Failure mode Mode 1 Mode 2 F T,1,Rd F T,1,Rd = 113,3 kn F T,2,Rd =62,9kN F T,2,Rd Form of the mode m F t,rd,anchor m e Q Q Q Q Resistance of the T-stub F F T,1,Rd T,1,Rd 4M pl,1,rd m 41722 113,3 kn 60,8 F F T,2,Rd T,2,Rd 2M 2nF pl,2,rd t,rd,anchor m n 21722 40236,2 62,9 kn 60,8 40 n = min ( e ; 1,25 m) = min (40 ; 1,25 60,8) = 40 mm F T,3,Rd F T,3,Rd F T,4,Rd F T,4,Rd 75

APPLICATION 2-1 RESISTANCE IN TENSION (CASE 2) Resistance in tension of the T-stub : modes 3 and 4 Failure mode Mode 3 Mode 4 F T,3,Rd F T,3,Rd =72,4 kn F T,4,Rd = 647,5 kn F T,4,Rd Form of the mode F t,rd,anchor F t,rd,anchor t wc Resistance of the T-stub F F T,3,Rd T,3,Rd 2F t,rd,anchor 236,2 72,4 kn F F T,4,Rd b t f eff,t wc g M0 y,wc 293,19,4 235 647,5 kn 110 T,4,Rd 3 b eff,t = l = 293,1 mm eff,1 76

APPLICATION 2-1 RESISTANCE IN TENSION (CASE 2) Resistance of the equivalent T-stub in tension: Weld resistance : F min F ; F ; F ; F 62,9 kn T,Rd T,1,Rd T,2,Rd T,3,Rd T,4,Rd F l a F t,w,rd w,eff,t w t,w,rd Check of the resistance of the joint in tension : fu / 3 bg 360/ 3 293,1 2 4 487 kn 0,81,251000 T,Rd T,Rd t,w,rd t,ed w N min F ; F 62,9 kn N 17 kn M2 77

APPLICATION 2-2 SHEAR RESISTANCE (CASE 2) Check of the shear resistance of bolts : V nf Ed vb,rd Nt,Ed 17,5 8,86 0,31 1 1,4 N 241,6 1,4 62,9 T,Rd Check of the shear resistance of weld : 2 2 N t,ed VEd f vw,d a 1? lw,eff,t lw,eff 2 2 8,86 17,5 360 / 3 4 0,033 1 2293,1 757,2 0,81,25 78

CONCLUSION

CONCLUSION Design methods, based on EC3 and EC2, are presented to check the resistance of pinned column base joint for different internal forces (compression/tension/shear). The bending resistance and initial rotation stiffness of rigid column base joint are determined considering T-stubs in tension and compression. These methods are based on the component method of EN 1993-1-8. The different components are: anchor bolts in tension and/or shear, bending of base plate, base plate in compression with concrete, welds. 80

REFERENCES

REFERENCES EN 1992-1-1 Eurocode 2 Design of concrete structures Part 1-1: General rules and rules for buildings EN 1993-1-1 Eurocode 3 Design of steel structures Part 1-1: General rules and rules for buildings EN 1993-1-8 Eurocode 3 Design of steel structures Part 1-8: Design of joints. 82

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