A CONNECTION ELEMENT FOR MODELLING END-PLATE CONNECTIONS IN FIRE

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1 A CONNECTION ELEMENT OR MODELLING END-PLATE CONNECTIONS IN IRE Dr Zhaohui Huang Department of Civil & Structural Engineering, University of Sheffield 22 September 29

2 1. INTRODUCTION

3 Three approaches for modelling the behaviour of connections in fire To represent the moment rotation characteristics of a connection by mathematical expression in the form of curve-fitting equations. To use component-based (also nown as springstiffness) models for predicting the connection s behaviour. To model the connection as assembly of 3D finite shell, bric and contact elements using general commercial software, such as ABAQUS or ANSYS.

4 2. DEVELOPMENT O THE BOLTED END-PLATE CONNECTION ELEMENT

5 Two-noded connection element configuration Central line of column Node of connection element (beam side) Reference plane Slab element Offset l Node of connection element (column side) z Connection element Beam element w θ z v u θ y y θ x x Local coordinates

6 Stiffness matrix of connection element (2) ) ( ) ( ) ( ) (,2,2, ,1,1, ,2,2,2,2,2,2,1,1,1,1,1, z y x z y x z y x z y x z y x z y x w v u w v u M M M M M M θ θ θ θ θ θ l l l l l l l l l l l l (1) K u

7 Stiffness matrix of connection element In this model only the in plane (x-z plane) behaviour of the connection is considered. It is reasonable to assume that the stiffness coefficients of 22, 44, 66 in Eq. (2) have infinite magnitude (assumed to be 1 9 N / mm )

8 Modelled two-dimensional steel frame in fire The columns were fire protected and beams were uniformly heated with load of 25 N/m 35x35x97UC 9 m 9 m 9 m Symmetry line 4m Connection 533x21x92UB A B 4m ire The connection was represented as an axial pinned or rigid spring with different stiffnesses for modelling pinned or rigid connection

9 Predicted deflections at Position A for the connections using axial pinned spring with different stiffnesses Deflection (mm) N/mm 12 N/mm 4 N/mm 14 N/mm 7 N/mm Beam temperature ( o C)

10 Predicted deflections at Position B for the connections using axial pinned spring with different stiffnesses Deflection (mm) N/mm 12 N/mm 4 N/mm 14 N/mm 7 N/mm Beam temperature ( o C)

11 Predicted deflections at Position A for the connections using axial rigid spring with different stiffnesses Deflection (mm) N/mm 12 N/mm 4 N/mm 14 N/mm 7 N/mm Beam temperature ( o C)

12 Predicted deflections at Position B for the connections using axial rigid spring with different stiffnesses 35 Deflection (mm) N/mm 12 N/mm 4 N/mm 14 N/mm 7 N/mm Beam temperature ( o C)

13 Determination of axial and vertical stiffness coefficients, 11, 33 A very simplified approach was used for the current model to determine : 11, 33 Before the connection failure, N / mm When the connection fails due to tension, bending or. vertical shear, 11 When the connection failed by compression, N / mm Before the connection failure due to vertical shear, N / mm After the connection fails by vertical shear, 33

14 The detail of bolted end-plate connection between steel column and beam ep w ec ep w ec r 1, r 2, r 3, r 4, z Tension bolts e x p(1) p(2) p(3) p 2 r 1, r 2, r 3, r 4, r 5, z d 1 Tension bolts e x p(1) p(2) p(3) p(4) p 2 4 i 1 ri, Shear bolts p 3 (1) d 3 5 ri, i 1 Shear bolts p 3 (1) d 3 (a) lush end plate (b) Extended end plate

15 Rotational stiffness of a beam-to-column connection, S j µ E z E Young s module i 2 1 i (3) stiffness coefficient for basic connection i component i z lever arm μ stiffness ratio, S / j, ini S j S j

16 S j, ini The initial rotational stiffness of the connection is given by Eq. (3) with µ 1 S j, ini 2 E z 1 i i (4)

17 Column web panel in shear ( 1 ) or unstiffened single-side or double-sided connection in which the beam depths are similar: 1.38 β A z VC (5) β transformation parameter A VC shear area of the column

18 Column web in compression ( 2 ) 2.7b eff, c, wc d c, c t wc (6) d c, c t wc clear depth of the column web thicness of the column web b eff c, wc, effective width of the column web in compression

19 Column web in tension ( 3 ) 3.7b eff, t, wc d c, c t wc (7) b eff, t, wc effective width of the column web in tension and equal to the effective length, l eff,c l eff,c is calculated based on bolt-row considered individually for this bolt-row for an unstiffened column flange

20 End-plate in bending ( 5 ) 5.9l eff, p 3 p m t 3 p (8) t p thicness of end-plate l eff, p effective lengths for an end-plate p m a parameter related to geometry of the connection

21 Bolts in tension (for a single bolt-row, 1 ) L b A s (9) A tensile stress area of the bolt s L b the bolt elongation length

22 Equivalent stiffness coefficient, eq eq r z eff eq, r h r (1) h distance between bolt-row r and the centre r of compression, effective stiffness coefficient of bolt-row r eff r eff, r i 1 1 i, r 1 3, r + 1 4, r , r + 1 1, r (11)

23 equivalent lever arm z eq (12), 2, r r r eff r r r eff eq h h z Rotational stiffness for one bolt-row in tension, S j (13) E z E z S i i j µ µ

24 Rotational stiffness for two or more bolt-rows in tension, S j S j µ E z i 2 1 i µ 1 1 E z eq (14) E average Young s module for the connection and changes with temperature E E cw + E cf + E 5 bw + E bf + E p (15)

25 Tri-linear moment-rotation characteristic used for the connection element M j, M j B C φ Id 2M 3S j, j, ini 2 3 M j, A Unloading φ Xd 2 M S j, j, ini O φ Id S j, ini S η, j ini φ Xd φ Cd φ φcd 5φ Xd

26 or line OA ( φ φ Id ): M j 55 φ S j, ini φ (16) or line AB ( φ < φ ): j Id φ Xd 2 3 ( φ ) M (17) M φ + 55 Id j, 55 M j 3, ( φ φ ) Xd or line BC ( φ < φ ): j Id Xd φ Cd ( φ ) M (18) M φ + 55 Xd j, S j, ini

27 Resistance of bolt rows in the tension zone, tr, tr min ( t, fc, ; t, wc, ; t, ep, ; t, wb,, ) (19) t fc,, the column flange in bending t wc,, the column web in tension t ep,, the end-plate in bending t wb,, the beam web in tension

28 Using equivalent T-stub in tension model There are three failure modes: Mode 1: complete flange yielding Mode 2: bolt failure with flange yielding Mode 3: bolt failure

29 Column flange in bending, or failure Mode 1 (without bacing plates): t, fc, M pl,1,, r, c.25l eff, c γ t M 2 fc f y, c (2) T,1,, fc M 4 pl,1,, r, c m c (21) t fc f y, c thicness of the column flange yield strength of column

30 or failure Mode 2: M pl,2,, r, c.25l eff, c γ t M 2 fc f y, c (22) T,2,, fc 2M pl,2,, r, c + n p, c m + n c p, c t, (23) mc n p, c and are parameters related to geometry of the connection

31 or failure Mode 3: T, 3,, fc t, (24) t, t, resistance of individual bolt 2 γ f.9 2 f s ub M 2 A s (25) ub ultimate tensile strength of the bolt, A tensile area of the bolt, ( ; ; ) (26) min T,1,, fc T,2,, fc T,3,, t, fc, fc

32 Column web in transverse tension, t, wc, ω b eff, t, wc γ t M wc f y, c (27) t, wc, ω reduction factor to allow for the interaction with shear in the column web panel ω b 1 eff, c, wc A vc t wc 2 (28)

33 End plate in bending, or failure Mode 1 (without bacing plates): t, ep, M pl,1,, r, b.25l eff, p γ t M 2 p f y, p (29) T,1,, ep 4 M pl,1,, r, b m p1 (3) f y, p yield strength of end-plate

34 or failure Mode 2: M pl,2,, r, b.25l eff, p γ t M 2 p f y, p (31) T,2,, ep 2M pl,2,, r, b + n p, ep m + n p1 p, ep t, (32) m n p, ep p1 and are parameters related to geometry of the connection

35 or failure Mode 3: T, 3,, ep t, (33) The resistance of the end plate in bending is ( ; ; ) (34) min T,1,, ep T,2,, ep T,3,, t, ep, ep

36 Beam web in tension, t, wb, t, wb, b eff, t, wb γ t wb M f y, b (35) b eff, t, wb twb f y, b effective width of the beam web in tension and equal to l eff, p thicness of the beam web yield strength of beam

37 Compression Resistance, c, ( ) ; (36) min c, wc, c, fb, c, c wc,, column web in transverse compression c fb,, beam flange and web in compression

38 Resistance of column web in transverse compression, or an unstiffened column web: c, wc, ω wcbeff, c, wctwc f y, c ω wcρ beff, c, wctwc f y, c,, min ; c wc γ M γ M1 (37) wc reduction factor ρ reduction factor for plate bucling

39 Resistance of Beam flange and web in compression, c, fb, c, fb, M c, ( h t ) b fb (38) h b depth of the connected beam M c, t fb moment resistance of the beam cross-section flange thicness of the connected beam

40 If the height of the beam including the haunch exceeds 6 mm the contribution of the beam web to the compression resistance should be limited to 2%: c, fb,max b b t fb f y, b.8γ M (39) b b width of the beam section c, fb, c, fb,max (4)

41 The first condition that the effective tension resistance has to satisfy is: orce distribution in bolt rows c, Ed c, N, Ed r 1 c tr, (41) (42) N total number of bolt rows in tension

42 c, Ed > c, If the force distribution in bolt rows should be adopted to mae sure that: N c, Ed r 1 tr, c, (43)

43 Moment resistance, M j, M h j, r tr, r (44) tr, effective design tension resistance of bolt-row r h distance from bolt-row r to the centre r of compression r the bolt-row number

44 V Resistance for individual bolt subjected to vertical shear forces, ( ; ; ) (45) min v, b, cf, b, ep, b, b, v, shear resistance of one bolt b, cf, b, ep, bolts in bearing on column flange bolts in bearing on end plate

45 v, α V f γ u, bolt M 2 A s (46) f u, bolt ultimate tensile strength of bolt or classes 4.6, 5.6 and 8.8 bolts: α V.6 or classes 4.8, 5.8, 6.8 and 1.9 bolts: α V.5

46 b, cf, 1, c α b, c γ f u, c M 2 d t fc (47) b, ep, 1, p α b, p γ f M 2 u, p d t p (48) d f u, b f u, p nominal bolt diameter ultimate tensile strength of column ultimate tensile strength of end-plate

47 Resistance of the connection with the axial force in the connected beam N j, Ed M M j, Ed j, + N N j, Ed j, 1. (49) M j, N j, moment resistance of the connection, no axial force axial resistance of the connection, no applied moment

48 The moment resistance of the connection which consider the influence of axial force: M N j, Ed 1. M j, N j, ' j, (5) The axial resistance of the connection which consider the influence of applied moment: N M j, Ed 1. N j, M j, ' j, (51)

49 or tension resistance: N, r 1 N j tr, (52) or compression resistance: N j, c, (53)

50 Connection behaviours at elevated temperatures The model presented above can be extended into elevated temperatures by relating all material properties, such as yield strength; ultimate tensile strength and Young s module to the temperature. It is assumed that the material degradation of bolt at elevated temperatures is the same for the structural steel. The model specified in Eurocode 3 Part 1.2 is adopted in this research.

51 3. VALIDATIONS

52 Bolted end-plate connection tested at ambient temperature The detail of ambient temperature test (Leston-Jones 1997)

53 Comparison of predicted and measured momentrotation curves (Leston-Jones 1997) 4 3 Moment (Nm) 2 Test (Leston-Jones) Prediction (current model) Prediction, bolt rows 1 individually (Bloc et al) Prediction, bolt rows as a group (Bloc et al) Rotation (Millirads)

54 The detail of tests at elevated temperatures (Leston-Jones 1997) The load levels applied to Test 1, Test 2, Test 3 and Test 4 were 5 Nm, 1 Nm, 15 Nm and 2 Nm, respectively

55 Comparison of predicted and measured connection rotations for Test 1 and Test 3 (Leston-Jones 1997) Beam bottom flange temperature ( C) Test 1 (tested, Leston-Jones) Test 1 (predicted, Bloc et al) Test 1 (predicted, current model) Test 3 (tested, Leston-Jones) Test 3 (predicted, Bloc et al) Test 3 (predicted, current model) Connection rotation (Millirads)

56 Comparison of predicted and measured connection rotations for Test 2 and Test 4 (Leston-Jones 1997) Beam bottom flange temperature ( C) Test 2 (tested, Leston-Jones) Test 2 (predicted, Bloc et al) Test 2 (predicted, current model) 2 Test 4 (tested, Leston-Jones) Test 4 (predicted, Bloc et al) Test 4 (predicted, current model) Connection rotation (Millirads)

57 Influence of beam axial forces on the connection behaviour for Test 1 (Leston-Jones 1997) Beam bottom flange temperature ( C) Tested results (Leston-Jones) Predictions (axial force ) Predictions (axial force 2.9 N) Predictions (axial force 41.9 N) Connection rotation (Millirads)

58 The detail of Group 1 (B1) connection fire tests (Al-Jabri et al 25) our tests B11, B12, B13, B14 were conducted at load levels corresponding to connection moments of 4.4 Nm, 8.2 Nm, Nm and 17.1 Nm, respectively

59 Comparison of predicted and measured connection rotations for Group 1: B11, B13 (Al-Jabri et al 25) 8 Beam bottom flange temperature ( C) B11 (tested) B11 (predicted) B13 (tested) B13 (predicted) Connection rotation (Millirads)

60 Comparison of predicted and measured connection rotations for Group 1: B12, B14 (Al-Jabri et al 25) 8 Beam bottom flange temperature ( C) B12 (tested) B12 (predicted) B14 (tested) B14 (predicted) Connection rotation (Millirads)

61 The detail of Group 2 (B2) connection fire tests (Al-Jabri et al 25) our tests denoted as B21, B22, B23, B24 were carried out using the load levels of 27.4 Nm, 54.8 Nm, 82.1 Nm and 11 Nm, respectively

62 Comparison of predicted and measured connection rotations for Group 2: B21, B23 (Al-Jabri et al 25) 8 Beam bottom flange temperature ( C) B21 (tested) B21 (predicted) B23 (tested) B23 (predicted) Connection rotation

63 Comparison of predicted and measured connection rotations for Group 2: B22, B24 (Al-Jabri et al 25) 8 Beam bottom flange temperature ( C) B22 (tested) B22 (predicted) B24 (tested) B24 (predicted) Connection rotation

64 4. CONCLUSIONS The current model has the advantages of both the previous simple and component-based models. The current model is robust and has a capability to predict the behaviour of bolted end-plate connection under fire attac with reasonable accuracy. Compared to the tested results the predictions of the current model were mainly on conservative side. The model can be used for structural fire engineering design on steel-framed composite buildings. The idea described in this paper can also easily be applied to develop other ind of connections.

ON THE DESIGN OF A STEEL END-PLATE BEAM-TO-COLUMN BOLTED JOINT ACCORDING TO PN-EN

ON THE DESIGN OF A STEEL END-PLATE BEAM-TO-COLUMN BOLTED JOINT ACCORDING TO PN-EN CZASOPISMO INŻYNIERII LĄDOWEJ, ŚRODOWISKA I ARCHITEKTURY JOURNAL O CIVIL ENGINEERING, ENVIRONMENT AND ARCHITECTURE JCEEA, t. XXXV, z. 65 (2/18), kwiecień-czerwiec 2018, s. 187-196, DOI:10.7862/rb.2018.35