SKILLS Project. October 2013

Transcription

1 SKILLS Project October 2013

2 MOMENT CONNECTIONS PART 1

3 LEARNING OUTCOMES Design process for moment-resisting bolted connections Joint moment resistance Joint stiffness Details design (welds, bolts, stiffeners, end-plate) Best practice guidelines for moment connections 3

4 LIST OF CONTENTS Introduction Calculation of moment resistance Calculation of shear resistance Weld design Stiffeners Calculation of joint rotational stiffness Best practice guidelines Conclusion 4

5 INTRODUCTION

6 INTRODUCTION Types of moment connections in single-storey buildings 6 1. Eaves 2. Eaves haunch 3. Apex 4. Apex haunch 5. Intermediate joint

7 INTRODUCTION Typical eaves connection 1. Haunch 2. Compression stiffener 3. End-plate 7

8 INTRODUCTION Typical apex connection Alternative apex connection 1. Haunch fabricated from the same section 2. Stiffening plate 8

9 INTRODUCTION General design approach according to EN Joint is modelled as an assembly of basic components Basic components are localized in different zones of a joint Shear zone Tension zone Compression zone 9

10 CALCULATION OF MOMENT RESISTANCE

11 CALCULATION OF MOMENT RESISTANCE - GENERAL Design steps Calculate the design compression resistance in the compression zone F c,rd Calculate the design shear resistance of the column web panel (shear zone) V wp,rd Determine the potential resistance of the bolt rows in the tension zone F t,rd(r) Calculate the effective design tension resistance of each bolt row F tr,rd Calculate the design moment resistance of the joint M j,rd 11

12 CALCULATION OF MOMENT RESISTANCE GENERAL The effective design tension resistance for each individual bolt row may be limited by: The design resistance of a group of bolts The stiffness of the column flange or end-plate, which may preclude a plastic distribution of tension forces The shear resistance of the column web panel The resistance in the compression zone 12

13 CALCULATION OF MOMENT RESISTANCE TENSION ZONE The potential design tension resistance for each bolt row F min( F, F, F, ) EN (6) t, Rd(r) t,fc,rd t,wc,rd t,ep,rd Ft,wb, Rd Component Symbol EN clause number Column flange in bending F t,fc,rd and Tables: 6.2, 6.4, 6.5 Column web in transverse tension F t,wc,rd End-plate in bending F t,ep,rd and Tables: 6.2, 6.6 Rafter beam web in tension F t,wb,rd

14 CALCULATION OF MOMENT RESISTANCE TENSION ZONE Start from the furthest bolt row from the centre of compression (r = 1) r = 1 r = 2 r = 3 r = 4 Ignore the resistance of any bolt rows closer to the centre of compression h 1 h 2 h 3 h 4 Verify subsequent rows both in isolation and as a part of a group in combination with rows above When the sum of the resistances of tensile bolt rows is higher than the resistance of any compressive or shear component, the other bolt rows are not considered in the calculation 14 Centre of compression

15 CALCULATION OF MOMENT RESISTANCE TENSION ZONE Groups of bolt rows related to the joint basic components representing parts of a column and a rafter beam with an end-plate Group Group Group Group Group

16 CALCULATION OF MOMENT RESISTANCE TENSION ZONE Determination of the potential tension resistance of: end-plate in bending Ft,ep,Rd column flange in bending Ft,fc,Rd EN Real yield line patterns are converted into an equivalent T-stub Each possible yield line pattern is described by a length of equivalent T-stub eff The shortest equivalent T-stub is taken (min eff ) Effective length of equivalent T-stub is necessary to calculate the resistance of the T-stub 16

17 CALCULATION OF MOMENT RESISTANCE TENSION ZONE Failure modes of an equivalent T-stub EN Table 6.2 Mode 1 Mode 2 Mode 3 The flange of the T-stub is the critical feature, and yields in double curvature bending The flange of the T-stub yields and the bolts fail at the same load 17 The bolts are critical component and the resistance is the tension resistance of the bolts

18 CALCULATION OF MOMENT RESISTANCE TENSION ZONE Effective length of equivalent T-stub Circular patterns l eff,cp Non-circular patterns l eff,nc Bolt-row considered individually Bolt-row considered as part of a group of bolt-rows Mode 1: l eff,1 = l eff,nc but l eff,1 l eff,cp Σl eff,1 = Σl eff,nc but Σl eff,1 Σl eff,cp Mode 2: l eff,2 = l eff,nc Σl eff,2 = Σl eff,nc 18

19 CALCULATION OF MOMENT RESISTANCE TENSION ZONE Dimensions of equivalent T-stub flange EN Figure

20 CALCULATION OF MOMENT RESISTANCE TENSION ZONE Determination of the effective length of equivalent T-stub of an unstiffened column flange in bending Ft,fc,Rd EN Table 6.4 Bolt-row location Bolt-row considered individually Bolt-row considered as part of a group of bolt-rows Circular patterns l eff,cp Non-circular patterns l eff,nc Circular patterns l eff,cp Non-circular patterns l eff,nc Inner bolt-row 2πm 4m+1,25e 2p p End bolt-row The smaller of: 2πm, πm+2e 1 The smaller of: 4m+1,25e, 2m+0,625e+e 1 The smaller of: πm+p, 2e 1 +p The smaller of: 2m+0,625e+0,5p, e 1 +0,5p 20

21 CALCULATION OF MOMENT RESISTANCE TENSION ZONE Determination of the parameters e 1, p and w: for an unstiffened column flange for a stiffened column flange for an extended end-plate EN Table 3.3 t t min( t Maximum Structures made from steels conforming to: Minimum EN (except EN ) EN Steel exposed Steel not exposed Steel used unprotected to the weather or other corrosive influences e 1 1,2d 0 4t + 40mm max(8t; 125mm) p 2,2d 0 min(14t; 200mm) min(14t; 200mm) min(14t min ; 175mm) 21 w 2,4d 0 min(14t; 200mm) min(14t; 200mm) min(14t min ; 175mm) min p, t fc )

22 CALCULATION OF MOMENT RESISTANCE TENSION ZONE Determination of the effective length of equivalent T-stub of a stiffened column flange in bending Ft,fc,Rd EN Table 6.5 Bolt-row location Bolt-row considered individually Bolt-row considered as part of a group of bolt-rows Circular patterns l eff,cp Non-circular patterns l eff,nc Circular patterns l eff,cp Non-circular patterns l eff,nc Bolt-row adjacent to a stiffener 2πm αm πm+p 0,5p+αm -(2m+0,625e) Other inner bolt-row 2πm 4m+1,25e 2p p Other end bolt-row The smaller of: 2πm, πm+2e 1 The smaller of: 4m+1,25e, 2m+0,625e+e 1 The smaller of: πm+p, 2e 1 +p The smaller of: 2m+0,625e+0,5p, e 1 +0,5p End bolt-row adjacent to a stiffener The smaller of: 2πm, πm+2e 1 e 1 +αm -(2m+0,625e) Not relevant Not relevant 22

23 CALCULATION OF MOMENT RESISTANCE TENSION ZONE Values of α for stiffened column flanges and end-plates EN Figure m m e 2 m m e 2 23

24 CALCULATION OF MOMENT RESISTANCE TENSION ZONE Determination of the effective length of equivalent T-stub of an end-plate in bending Ft,ep,Rd EN Table 6.6 Bolt-row location Bolt-row considered individually Bolt-row considered as part of a group of bolt-rows Circular patterns l eff,cp Non-circular patterns l eff,nc Circular patterns l eff,cp Non-circular patterns l eff,nc Bolt-row outside tension flange of beam Smallest of: 2πm x, πm x +w, πm x +2e Smallest of: 4m x +1,25e x, e+2m x +0,625e x, 0,5b p, 0,5w+2m x +0,625e x - - First bolt-row below tension flange of beam 2πm αm πm+p 0,5p+αm- (2m+0,625e) Other inner bolt-row 2πm 4m+1,25e 2p p Other end bolt-row 2πm 4m+1,25e πm+p 2m+0,625e+0,5p 24

25 CALCULATION OF MOMENT RESISTANCE TENSION ZONE Modelling an extended end-plate as separate T-stubs EN Figure 6.10 For the end-plate extension, use e x and m x in place of e and m when determining the design resistance of the equivalent T-stub flange. 25

26 CALCULATION OF MOMENT RESISTANCE TENSION ZONE Calculation of the resistance of the T-stub in the different modes Mode 1 Mode 2 Mode 3 F T,2,Rd F T,1,Rd 2M 4 M m pl,2, pl,1, Rd n Rd Ft, Rd m n F T,3, F Rd t, Rd 26 EN Table 6.2 M 0 l 2 pl,1, Rd,25 eff,1t f fy / M 0 l 2 pl,2, Rd,25 eff,2 tf fy / n e 25m min 1, t f thickness of an equivalent T-stub flange (t f = t fc or t f = t p ) F t,rd design tension resistance of bolt 0,9 fubas F EN Table 3.4 t,rd M2 ΣF t,rd the total of F t,rd for all bolts in the T-stub M2 1,25 - partial safety factor for bolts 1,00 - partial safety factor for resistance of cross-sections M0 M0 M0

27 CALCULATION OF MOMENT RESISTANCE TENSION ZONE Determination of the potential tension resistance of: end-plate in bending F t,ep, Rd min( F T,1,Rd F T,1,Rd, F T,2,Rd, F T,3,Rd design resistances of the T-stub of the different modes of failure, representing the end-plate in bending, F T,2,Rd, F T,3, Rd ) column flange in bending Ft, fc,rd min( FT,1,Rd, FT,2,Rd, F T,3, Rd F T,1,Rd, F T,2,Rd, F T,3,Rd design resistances of the T-stub of the different modes of failure, representing the column flange in bending ) 27

28 CALCULATION OF MOMENT RESISTANCE TENSION ZONE Design resistance of a column web in transverse tension F t,wc,rd beff, t,wctwc fy,wc Ft,wc,Rd EN where: M0 ω is a reduction factor to allow for the interaction with shear in the column web panel (EN Table 6.3), replacing the value of b eff,c,wc by b eff,t,wc. b eff,t,wc is an effective width of the column web in tension; for bolted connection it is equal to the effective length of equivalent T-stub representing the column flange t wc M0 1,00 is the thickness of the column web - partial safety factor for resistance of cross-sections Note: Stiffeners or supplementary web plates may be used to increase the design resistance of a column web. 28

29 CALCULATION OF MOMENT RESISTANCE TENSION ZONE Determination of the reduction factor ω for the interaction with shear in the column web panel EN Table 6.3 Transformation parameter β Reduction factor ω 1 0 β 0,5 ω = 1 0,5 < β < 1 ω = ω 1 + 2(1 β)(1 - ω 1 ) β = 1 ω = ω 1 1 < β < 2 ω = ω 1 + (β 1)(ω 2 - ω 1 ) 11,3( b β = 2 ω = ω 2 eff,c,wc A vc is the shear area of the column β is the transformation parameter 1 t wc / A vc b eff,c,wc is the effective width of column 29 web in compression ) ,2( b 1 eff,c,wc EN EN (7) t wc / A vc ) 2 EN (1)

30 CALCULATION OF MOMENT RESISTANCE TENSION ZONE Determination of the transformation parameter β For single-sided joint configuration: 1 EN (9) or Table 5.4 Determination of the shear area of the column A vc For rolled I or H sections, load parallel to web: Avc Ac 2bfctfc tfc( t 2r wc c) hwctwc For welded I or H and box sections, load parallel to web: A h t vc wc wc For welded I or H and box sections, load parallel to flanges: A vc A c h wc η may be conservatively taken equal 1,0 h wc is the clear depth of the column web t wc 30 EN

31 CALCULATION OF MOMENT RESISTANCE TENSION ZONE Design resistance of a beam web in tension Ft,wb,Rd where: b eff,t,wb is an effective width of the beam web in tension; it is equal to the effective length of equivalent T-stub representing the end-plate in bending for an individual bolt-row or bolt-group t wb b t f eff, t,wb wb y,wb Ft,wb,Rd EN M0 is the thickness of the beam web M0 1,00 - partial safety factor for resistance of cross-sections 31

32 CALCULATION OF MOMENT RESISTANCE COMPRESSION ZONE The design resistance in the compression zone may be limited by F min( F, F, ) EN c, Rd c,wc,rd c,fb,rd Fc,hb, Rd Component Symbol EN clause number Column web in transverse compression F c,wc,rd Beam flange and web in compression F c,fb,rd Haunched beam in compression F c,hb,rd / The compressive resistance of the haunched beam should be considered as explained in EN Table 6.1 (component 20) 32

33 CALCULATION OF MOMENT RESISTANCE COMPRESSION ZONE Design resistance of a column web in transverse compression F c,wc,rd where: ω F k b t f k wc eff,c,wc wc y,wc wc eff,c,wc wc y,wc c,wc,rd EN M0 M1 is a reduction factor to allow for the interaction with shear in the column web panel (EN Table 6.3) k wc is a reduction factor (EN (2)) ρ is a reduction factor for plate buckling (EN (1)) b eff,c,wc is an effective width of the column web in compression M1 1, 00 - partial safety factor for resistance of members 1,00 M0 - partial safety factor for resistance of cross-sections b Note: Stiffeners or supplementary web plates may be used to increase the design resistance of a column web. 33 t f

34 CALCULATION OF MOMENT RESISTANCE COMPRESSION ZONE Effective width of the column web in compression b eff,c,wc EN For bolted end-plate connection: b eff,c, wc tfb 2ap 5( tfc s) 2 s p where: s p t p c 2t p for a rolled I or H section column: s r c for a welded I or H section column: s 2ac 34

35 CALCULATION OF MOMENT RESISTANCE COMPRESSION ZONE Reduction factor for plate buckling ρ p if p 0,72 1,0 or if is the plate slenderness: EN (1) p 0,2 p 0,72 2 p beff,c,wcdwc fy,wc p 0, Et wc for a rolled I or H section column: d wc h c 2( tfc rc ) for a welded I or H section column: d wc h c 2( tfc 2ac ) h c t fc r c a c is the height of the column cross-section is the column flange thickness is the root radius of an I or H section is the column flange to the column web weld thickness 35

36 CALCULATION OF MOMENT RESISTANCE COMPRESSION ZONE Reduction factor k wc EN (2) com, Ed 0,7 fy,wc kwc 1 or com, Ed 0,7 fy,wc kwc 1, 7 f com, Ed y,wc σ com,ed is the maximum longitudinal compression stress due to axial force and bending moment in the column web (adjacent to the root radius for a rolled section or the toe of the weld for a welded section) Generally the reduction factor k wc is 1,0 and no reduction is necessary. It can therefore be omitted in preliminary calculations when the longitudinal stress is unknown and checked later. 36

37 CALCULATION OF MOMENT RESISTANCE COMPRESSION ZONE Design resistance of a beam (rafter) flange in compression Fc,fb,Rd Mc,Rd F where: c,fb,rd EN ( h t ) fb M c,rd is the design moment resistance of beam cross-section, reduced if necessary to allow for shear (EN ); for haunched beam, such as a rafter, M c,rd may be calculated neglecting the intermediate flange h t fb is the depth of the section; for haunched beam, it is the depth of the fabricated section is the flange thickness of the connected beam; for haunched beam, it is the thickness of the haunch flange If the height of the beam (including the haunch) exceeds 600 mm the contribution of the beam web to the design compression resistance should be limited to 20%. Hence, if the resistance of the flange is t fb b fb f y,fb then: 37 F c,fb,rd t fb b fb f 0,8 y,fb

38 CALCULATION OF MOMENT RESISTANCE COMPRESSION ZONE Design resistance of a haunched beam (rafter) in compression Fc,hb,Rd EN (3) F c,wb,rd F c,hb,rd F c,wb,rd tan ( ) F c,hb,rd F c,hb,rd F c,wb,rd k wb b eff,c,wb M1 t wb f y,wb where: F c,wb,rd is the design resistance of the beam web to transverse compression (according to EN ) 38

39 CALCULATION OF MOMENT RESISTANCE COMPRESSION ZONE Effective width of the beam web in compression b eff,c,wb b eff,c, wb tfb 5( t sin fb r b ) r b b eff,c,wb t fb ( ) t fb /sin t fb F c,wb,rd Other parameters in the expression of F c,wb,rd : ω, k wb, ρ should be calculated similarly to the parameters of F c,wc,rd replacing particular values connected with the column by the proper values connected with the beam. 39

40 CALCULATION OF MOMENT RESISTANCE SHEAR ZONE Design resistance of a column web panel in shear V wp,rd 0,9 f y,wc vc Vwp,Rd EN M0 Expression given above is valid provided that the column web slenderness satisfies the condition: d / t w 69 where: A vc is the shear area of the column (EN (3)) d is the depth of the column web 235 f M0 1,00 - partial safety factor for resistance of cross-sections Note: Stiffeners or supplementary web plates may be used to increase the design resistance of a column web. A 40 y,wc

41 CALCULATION OF MOMENT RESISTANCE - ASSEMBLY F t1,rd = min(f t,rd(1), F c, Rd, V wp,rd /β) F t2,rd = min(f t,rd(2), F c,rd - F t1,rd,v wp,rd / β - F t1,rd ) F t3,rd = min(f t,rd(3),f t,rd(2+3) - F t2,rd,f c,rd - F t1,rd - F t2,rd,v wp,rd / β - F t1,rd - F t2,rd ) F t1,rd F t2,rd F t3,rd where: β is a transformation parameter; for one-sided connection β = 1,0 EN (7) or Table 5.4 h 1 h 2 h 3 Each value of F ti,rd should be > 0. In other case, when F ti,rd 0, the bolt row i is not active and its resistance should be omitted. 41

42 CALCULATION OF MOMENT RESISTANCE Plastic distribution of forces in bolt rows Plastic distribution of forces in bolt rows is permitted if the resistance of the bolt rows F tr,rd is no grater than 1,9 F t,rd where: EN (9) F t,rd design tension resistance of bolt EN Table 3.4 If F tr,rd > 1,9 F t,rd the limit is applied. The effect of this limitation is to apply a triangular distribution of bolt row forces. 42

43 CALCULATION OF MOMENT RESISTANCE Reduction of the design tension resistance of the bolt-rows F tr,rd F tx,rd h x h r EN (9) where: F tx,rd h x h r Triangular distribution of bolt row forces is the design tension resistance of the furthest row from the centre of compression that has a design tension resistance greater than 1,9F t,rd is the lever arm from the centre of compression to the row with resistance F tx,rd is the lever arm from the centre of compression to the row under consideration 43

44 CALCULATION OF MOMENT RESISTANCE - ASSEMBLY The design moment resistance of the joint M j,rd r F tr,rd h r EN (1) F t1,rd F t2,rd F t3,rd h 1 h 2 h 3 M j, Rd Ft1,Rdh1 Ft2,Rdh2 Ft3,Rdh3 44

45 CALCULATION OF SHEAR RESISTANCE

46 CALCULATION OF SHEAR RESISTANCE The bolts at the bottom of the connection are allocated to carry the vertical shear The bolts must be verified in shear and bearing V Ed n s min( F v,rd, F b, Rd EN (2) ) n s V Ed where: n s is the number of bolts carrying the vertical shear (usually there are bolts in the lowest rows) F v,rd is the shear resistance of the bolt F b,rd is a bearing resistance of the bolt (two types of bearing resistance have to be considered: of the end-plate and of the column flange) 46

47 CALCULATION OF SHEAR RESISTANCE Design shear resistance for an individual bolt F V,Rd F v,rd v f ub M2 A EN Table 3.4 where the shear passes through the threaded portion of the bolt: - A is the tensile stress area of the bolt A s - for classes 4.6, 5.6 and 8.8 => α v = 0,6 - for classes 4.8, 5.8, 6.8 and 10.9 => α v = 0,5 where the shear passes through the unthreaded portion of the bolt: - A is the gross cross section of the bolt - α v = 0,6 47

48 CALCULATION OF SHEAR RESISTANCE Design bearing resistance for an individual bolt F b,rd k1 b fudt F EN Table 3.4 where: b,rd M2 α b is the smallest of α d, f ub /f u or 1,0 f u is the ultimate tensile strength of the material of either: the end-plate or the column flange f ub is the ultimate tensile strength for the bolt t = t p when the bearing resistance of the end-plate is considered or t = t fc when the bearing resistance of the column flange is considered d is the bolt diameter M2 1,25 - partial safety factor for bolts 48

49 CALCULATION OF SHEAR RESISTANCE Determination of α d In the direction of load transfer: for end bolts: e1 d 3d 0 for inner bolts: EN Table 3.4 p d d d 0 e 1 p 1 is the hole diameter for a bolt is the end distance from the centre of a bolt hole to the adjacent end of any part, measured in the direction of load transfer is the spacing between centres of bolts in a line in the direction of load transfer 49

50 CALCULATION OF SHEAR RESISTANCE Determination of k 1 EN Table 3.4 Perpendicular to the direction of load transfer: for edge bolts: for inner bolts: e2 p2 k1 min( 2,8 1,7; 1,4 1,7; d d 0 0 2,5) p2 k1 min( 1,4 1,7; d 0 2,5) d 0 e 2 p 2 is the hole diameter for a bolt is the edge distance from the centre of a bolt hole to the adjacent edge of any part, measured at right angles to the direction of load transfer is the spacing measured perpendicular to the load transfer direction between adjacent lines of bolts 50

51 WELD DESIGN

52 WELD DESIGN Requirements to weld design The design moment resistance of the joint is always limited by the design resistance of its other basic components, and not by the design resistance of the welds; EN (4) Full-strength welds are required to components in tension; If the joint experiences a reversed bending moment (or seismic load), the weld in the compression zone will be required to carry some tension force; Lamellar tearing shall be avoided (guidance on lamellar tearing is given in EN ). 52

53 WELD DESIGN Nominal weld (but verified for tension when moment is reversed) 2. Continuous fillet weld 3. Full strength weld 53

54 WELD DESIGN Tension flange welds The welds between the tension flange and the end plate must be full strength. Common practice is to design the welds to the tension flange for a force which is the lesser of: - The tension resistance of the flange, which is equal to b f t f f y - The total tension force in the top three bolt rows for an extended end plate or the total tension force in the top two bolt rows for a flush end plate. 54

55 WELD DESIGN Compression flange welds Where the compression flange has a sawn end, a bearing fit can be assumed between the flange and end plate and nominal fillet welds will suffice (recommended throat thickness: a = 4 6 mm for t fb 12 mm or a = 6 8 mm for t fb > 12 mm ). If a bearing fit cannot be assumed, then the weld must be designed to carry the full compression force. In case of uplift forces and seismic forces, the welds should be verified for adequacy under this combination of actions. 55

56 WELD DESIGN Web welds - Tension zone Full strength welds are recommended. The full strength welds to the web tension zone should extend below the bottom bolt row resisting tension by a distance of 1,73g/2, where g is the gauge (cross-centres) of the bolts. This allows an effective distribution at 60 from the bolt row to the end plate. Tension zone Shear zone 56

57 WELD DESIGN Web welds - Shear zone The resistance of the beam web welds for vertical shear forces: Psw 2a fvw,d Lws where: a is the fillet weld throat thickness f vw,d L ws f u is the design strength of fillet welds fu / 3 f vw.d w is the vertical length of the shear zone welds (the remainder of the web not identified as the tension zone) is the nominal ultimate tensile strength of the weaker part joined β w is the appropriate correlation factor taken from Table 4.1. M2 57 EN (3)

58 WELD DESIGN Correlation factor β w for fillet welds EN Table

59 STIFFENERS

60 STIFFENERS Types of stiffeners Compression stiffener 2. Column flange stiffener 3. Cap plate 4. Shear stiffener 5. Supplementary web plate 6. End plate stiffener 7. Backing plate

61 STIFFENERS Stiffener type Effect Comments Compression stiffener Increases the rigidity and the resistance to compression Generally required in portal frame connections Flange stiffener in the tension zone Increases the bending resistance of the column flange Diagonal shear stiffener Improves the column web panel resistance and also strengthens the tension flange A common solution connections on the minor axis may be more complicated Supplementary web plate Increases the rigidity and the resistance of the web to shear and compression Minor axis connections are simplified. Detail involves much welding 61

62 STIFFENERS Stiffener type Effect Comments End plate stiffener Increases the bending resistance of the end plate Should not be used a thicker end plate should be chosen. Cap plate Increases the bending resistance of the flange, and the compression resistance (in reversed moment situations) Usually provided in the column, aligned with the top flange of the rafter. Flange backing plate Increases the bending resistance of the column flange Only effective to increase mode 1 behaviour. 62

63 CALCULATION OF JOINT ROTATIONAL STIFFNESS

64 CALCULATION OF JOINT ROTATIONAL STIFFNESS - GENERAL 1 Limit for S j EN Figure 6.1 Design moment rotation characteristic for a joint

65 CALCULATION OF JOINT ROTATIONAL STIFFNESS - GENERAL Classification boundaries depend on: EN The initial rotational stiffness S j,ini ; The second moment of area of the beam I b and of the column I c ; The span of the beam L b and the storey height of the column L c ; Factor k b that depends on the stiffness of the frame. where: k b = 8 for frames where the bracing system reduces the horizontal displacement by at least 80% k b = 25 for frames, provided that in every storey K b /K c 0,1 65 K b EI L b b K c EI L c c

66 CALCULATION OF JOINT ROTATIONAL STIFFNESS - GENERAL Classification of the joint by stiffness: Zone 1: rigid, if Zone 2: semi - rigid S k j, ini beib /Lb 0,5EI L b / Lb Sj,ini kbeib / b Zone 3: nominally pinned, if S 0 EI j, ini,5 b / Lb EN Figure

67 CALCULATION OF JOINT ROTATIONAL STIFFNESS - INITIAL STIFFNESS Initial rotational stiffness S Ez i 2 j, ini 1 k i EN (4) where: E z k i is the modulus of elasticity is the lever arm EN is a stiffness coefficient for basic joint component i 67

68 CALCULATION OF JOINT ROTATIONAL STIFFNESS - BASIC COMPONENTS Stiffness of basic components Stiffness coefficient EN Table 6.10 Joint component k 1 k 2 k 3 k 4 k 5 k 10 Column web panel in shear Column web panel in compression Column web in tension Column flange in bending End-plate in bending Bolts in tension The individual stiffness coefficients are determined in: 68 EN Table 6.11

69 CALCULATION OF JOINT ROTATIONAL STIFFNESS - BASIC COMPONENTS Unstiffened column web panel in shear EN ,38Avc k1 z Stiffened column web panel in shear (stiffened by shear stiffener) k 1 z β is the lever arm is the transformation parameter (in case of single-sided connections β = 1) EN (7) 69

70 CALCULATION OF JOINT ROTATIONAL STIFFNESS - BASIC COMPONENTS Unstiffened column web in compression EN k 2 0,7b eff,c,wc d c t wc Stiffened column web in compression (stiffened by horizontal stiffeners) b eff,c,wc is the effective width t wc d c k 2 is the thickness of the column web is the clear depth of the column web 70 EN

71 CALCULATION OF JOINT ROTATIONAL STIFFNESS - BASIC COMPONENTS Unstiffened or stiffened column web in tension EN ,7beff, t,wctwc k3 dc b eff,t,wc is the effective width of the column web in tension (for a single bolt-row); It is taken as equal to the smallest of the effective lengths l eff (individually or as a part of group of bolts) given for this bolt-row in: EN Table 6.4 for an unstiffened column flange EN Table 6.5 for a stiffened column flange t wc d c is the thickness of the column web is the clear depth of the column web 71

72 CALCULATION OF JOINT ROTATIONAL STIFFNESS - BASIC COMPONENTS Column flange in bending (for a single bolt-row in tension) EN k 4 0,9l m eff 3 t 3 fc l eff is the smallest of the effective lengths l eff (individually or as a part of group of bolts) given for this bolt-row in: EN Table 6.4 for an unstiffened column flange EN Table 6.5 for a stiffened column flange t fc is the thickness of the column flange m is defined in EN Figure

73 CALCULATION OF JOINT ROTATIONAL STIFFNESS - BASIC COMPONENTS End-plate in bending (for a single bolt-row in tension) EN k 5 0,9l m eff 3 t 3 p l eff t p is the smallest of the effective lengths l eff (individually or as a part of group of bolts) given for this bolt-row in EN Table 6.6 is the thickness of the end-plate m is defined in EN Figures 6.10 and

74 CALCULATION OF JOINT ROTATIONAL STIFFNESS - BASIC COMPONENTS Bolts in tension (for a single bolt-row in tension) EN k 10 1,6A L b s A s L b is the tensile stress area of the bolt EN Table 3.4 is the bolt elongation length, taken as equal to the grip length (total thickness of material and washers), plus half the sum of the height of the bolt head and the height of the nut 74

75 CALCULATION OF JOINT ROTATIONAL STIFFNESS GENERAL METHOD Spring model for multi bolt-rows end-plate joints EN

76 CALCULATION OF JOINT ROTATIONAL STIFFNESS GENERAL METHOD Initial rotational stiffness S j, ini k 1 Ez k 2 2 k eq EN k eq h r k eff,r z eq is the equivalent stiffness coefficient is the distance between bolt-row r and the centre of compression is the effective stiffness coefficient for bolt-row r taking into account the stiffness coefficients k i for the basic components is the equivalent lever arm z eq r r k k eff,r eff,r h h k 2 r r eq r k k z eff,r eq h eff, r 1 r i 1 k i, r 76

77 CALCULATION OF JOINT ROTATIONAL STIFFNESS GENERAL METHOD EN (4) In the case of an eaves joint with an end-plate connection, k eq should be based upon (and replace) the stiffness coefficients k i for: The column web in tension (k 3 ) The column flange in bending (k 4 ) The end-plate in bending (k 5 ) The bolts in tension (k 10 ) 77

78 CALCULATION OF JOINT ROTATIONAL STIFFNESS GENERAL METHOD EN (4) In the case of an apex joint with bolted end-plates, k eq should be based upon (and replace) the stiffness coefficients k i for: The end-plate in bending (k 5 ) The bolts in tension (k 10 ) 78

79 BEST PRACTICE GUIDELINES

80 BEST PRACTICE GUIDELINES - EAVES HAUNCH Additional triangular cutting, welded below the rafter beam at the connection to the column; The length of the cutting around 10% of the span (up to 15% of the span in the most efficient elastic designs); It is generally cut from the same section as the rafter, or deeper and heavier section, or fabricated from plate; Fabrication of haunch cuttings: 80

81 BEST PRACTICE GUIDELINES - END PLATE Generally fabricated from S275 or S235 steel; For class 8.8 bolts and steel S275, the end plate thickness should be approximately equal to the bolt diameter; It should be wider than the rafter section, to allow a weld all around the flanges and extend above and below the haunched section, to allow fillet welds; In the compression zone, it should extend bellow the fillet weld (for a distance t p ), to maximise the stiff bearing length when verifying the column in compression: t p 81 t p

82 BEST PRACTICE GUIDELINES - STIFFENERS A compression stiffener is usually provided, other stiffeners should be avoided if possible; Column flange stiffeners are used to increase the resistance of the connection; Increased resistance can also be achieved by: providing more bolt rows, increasing the depth of the haunch, increasing the weight of the column section, extending the end plate above the top of the rafter. 82

83 BEST PRACTICE GUIDELINES EXTENDED END-PLATE JOINT Example of an extended end plate connection: Extended column may require skew cut 2. End plate stiffener not preferred 83

84 BEST PRACTICE GUIDELINES - BOLTS Generally M20 or M24, class 8.8 or 10.9; Fully threaded (the same bolts may be used throughout a building); They are generally set out at cross-centres (gauge) of 90 or 100 mm; Vertical pitch is generally 70 to 90 mm; Preloaded bolts are not required in portal frame connections, but in the case of cyclic loads (fatigue), better to use preloaded bolts. The use of preloaded bolts is obligatory in the case of dissipative seismic design (DCM/DCH) according to Eurocode 8. 84

85 BEST PRACTICE GUIDELINES - WELDS Tension flange to end-plate weld Web to end-plate weld where: a f a w β w f y f u is the weld throat thickness of the tension flange is the weld throat thickness of the web is the correlation factor is the yield strength of rafter section is the nominal ultimate strength of the weaker part joined 1,0 M 1, 25 M a a w f t t fb wb f f y M0 y M0 w fu 2 w fu 2 EN Table 4.1 M2 M2

86 CONCLUSION

87 CONCLUSION Moment-resisting bolted end-plate connections in single storey steel framed buildings are discussed. The design method for a bolted eaves moment connection is presented. For apex (and intermediate) connections may be applied the same procedure as for eaves connections excepting the column basic components as well as that the tension zone is in the bottom and the compression zone in the top of the joint. Best practice guidelines on appropriate detailing of moment connections are offered. 87

88 REFERENCES

89 REFERENCES EN Eurocode 3 Design of steel structures Part 1-1: General rules and rules for buildings EN Eurocode 3 Design of steel structures Part 1-8: Design of joints ArcelorMittal Design Manuals for Steel Buildings in Europe Access Steel, NCCI Design of portal frame eaves connections SN041a-EN-EU The Steel Construction Institute and The British Constructional Steelwork Association Ltd. Joints in Steel Construction Moment Connections, P207/95 89

90 SKILLS training modules have been developed by a consortium of organisations whose logos appear at the bottom of this slide. The material is under a creative commons license The project was funded with support from the European Commission. This module reflects only the views of the authors, and the Commission cannot be held responsible for any use which may be made of the information contained therein.