International Workshop on Connections in Steel Structures: 2008 Chicago, Illinois, USA June [1]

Transcription

1 2/5/21 International Workshop on Connections in Steel Structures: 28 Chicago, Illinois, USA June Authors: STRUCTURAL RESPONSE S OF K AND T TUBULAR JOINTS UNDER STATIC LOADING Luciano Rodrigues Ornelas de Lima [1] Pedro Colmar Gonçalves da Silva Vellasco [1] José Guilherme Santos da Silva [2] Luis Filipe da Costa Neves [3] Mateus Cunha Bittencourt [4] [1] Structural Engineering Department - UERJ Rio de Janeiro, Brasil [2] Mechanical Engineering Department - UERJ Rio de Janeiro, Brasil [3] Civil Engineering Depratment - FCTUC Coimbra, Portugal [4] MSc Student - PGECIV Post Graduate Program in Civil Engineering - UERJ Rio de Janeiro, Brasil Summary 2 Why study structural tubular joints in Brazil? Eurocode 3 Provisions Numerical Model Results Analysis and Discussion Parametrical Analysis Final Remarks 1

2 2/5/21 The intensive worldwide use tubular structural elements 3 Footbridge Pediatric Hospital Coimbra - Portugal The intensive worldwide use tubular structural elements 4 Footbridge Vila Nova de Gaia - Portugal 2

3 2/5/21 5 The intensive worldwide use tubular structural elements Footbridge Rio de Janeiro - Brazil 6 Aesthetical and structural advantages led designers to be focused on the technologic and design issues related to these structures Design methods accuracy is a fundamental aspect under the economical and safety points of view In Brazil initially, iti tubular space trusses After 2 V&M other structural types Design codes are required EC3 3

4 2/5/21 Connection design performed since their behaviour frequently governs the overall structural response Wardenier et al. (1991) 7 338kN top chord CHS219.1x7.1 diagonal 2 CHS139.7x4.5 diagonal 4 CHS88.9x kN kN 259kN Joint design: 382.5kN NO OK! Solve the problem two possibilities change the top chord thickness; use eccentricity in the joint introduction of bending in the joint but, more economical 8 259kN 432kN Joint design: 657.6kN OK! 4

5 2/5/21 Design rules HSS joints plastic analysis or on deformation limit criteria Plastic analysis joint ultimate limit state plastic mechanism corresponding to the assumed yield line pattern Each plastic mechanism is associated to an unique ultimate t load suitable for this particular failure mechanism 9 Deformation limits criteria ultimate limit state of the chord face to a maximum out of plane deformation of this component Justification for a deformation versus plastic criterion slender chord faces the joint stiffness is not exhausted after complete onset of yielding, and can assume quite large values due to membrane effects 1 5

6 2/5/21 Deformation limit proposed by Lu et al. [7] T Joints Ultimate strength (N u ) u =.3b Load (kn) 8 6 T1 - Lie et al. (26) Solid w eld 4 Without w eld Shell weld 2 EC3 Deformation limit Displacement (mm) Deformation limit proposed by Lu et al. [7] and reported by Choo et al. [8] K Joints 12 Ultimate strength (N u ) u =.3d Serviceability strength (N s ) s =.1d Se N u /N s >1.5 u and N u /N s >1.5 s right diagonal (compression) left diagonal (tension) EC3 ultimate load 4 Lu et al - ultimate strength Lu et al - serviciability strength Axial displacement (mm) 6

7 2/5/21 Eurocode 3 Provisions Geometrical properties T Joints 13 b.25 b 1.85 b 2t 1 35 b b t t 1 Eurocode 3 Provisions Geometrical properties K Joints 14 d d d 2t d di d di d t t i 7

8 2/5/21 Eurocode 3 Provisions Failure modes 15 plastic failure of the chord face chord side wall failure chord shear failure punching shear failure of a chord wall brace failure with reduced effective width local buckling failure of a member Eurocode 3 Provisions Chord face plastic load investigated T joint 16 N 1,Rd 2 knfyt sen 1 sen 1 8

9 2/5/21 Eurocode 3 Provisions Chord face plastic load investigated K joint 17 2 k gkpfyt d 1 N1,Rd / M5 sen 1 d with N sin 1 2,Rd N1, Rd sin 2 Numerical Model Tubular joints shell elements midsurfaces of the joint member walls Welds three-dimensional solid or shell elements (Lee [11] and Van der Vegte [13] ) T1 - Lie et al. [1] T1RA4Nx2MATWELDSOLID T1RA4Nx2MATWELDOUT T1RA4Nx2MATWELDSHELL EC3 Deformation limit Displacement (mm) 9

10 2/5/21 Numerical Model T joints SHELL 181 four-node thick shell elements bending, shear and membrane deformations Ansys 1. Material (three-linear x relationship) and Geometrical Non-linearity (Updated Lagrangian Formulation) 19 Numerical Model Considered T Joint Lie at al. [12] 2 Brace SHS2x16mm = 9º Bottom chord SHS35x15mm b b1 / t b b b / t t 1

11 2/5/21 Results Analysis and Discussion T joints Model Calibration performed on SHS T-joints tested by Lie et al. (26) ANSYS N 1,Rd = 77kN Loa ad (kn) EC3 T1 - Lie et al. [1] T1RA4Nx2MATWELDSOLID T1RA4Nx2MATWELDOUT T1RA4Nx2MATWELDSHELL EC3 Deformation limit N 1,Rd = 751kN Displacement (mm) Results Analysis and Discussion Von Mises Stress (in MPa) T1 - Lie et al. [1] T1RA4Nx2MATWELDSOLID T1RA4Nx2MATWELDOUT T1RA4Nx2MATWELDSHELL EC3 Deformation limit Displacement (mm) 11

12 2/5/21 Results Analysis and Discussion 23 Von Mises Stress (in MPa) T1 - Lie et al. [1] T1RA4Nx2MATWELDSOLID T1RA4Nx2MATWELDOUT T1RA4Nx2MATWELDSHELL EC3 Deformation limit Displacement (mm) Numerical Model 24 K joints also used SHELL181 (Ansys 1.) Material (bi-linear x relationship strain hardening) and Geometrical Non-linearity (Updated Lagrangean Formulation) Best identification of yielded points in the joint 12

13 2/5/21 Numerical Model Considered K Joint 25 Diagonal CHS162.4x11.28mm = 3º Bottom chord CHS46x11.28mm d 1.4 d d t 1 di / ti d / t di / d.4 1. Numerical Model Boundary conditions according to Lee (1999) T C NULL Model Calibration performed comparing with EC3 formulation 2 16 N s = 155kN T N u = 165kN right diagonal (compression) 2 - left diagonal (tension) EC3 N 1,Rd = 946kN EC3 ultimate load 4 Lu et al - ultimate strength Axial displacement (mm) 13

14 2/5/21 Results Analysis and Discussion 27 Von Mises Stress (in MPa) right diagonal (compression) 2 - left diagonal (tension) EC3 ultimate load Lu et al - ultimate strength Lu et al - serviciability strength Axial displacement (mm) Results Analysis and Discussion 28 Von Mises Stress (in MPa) right diagonal (compression) 2 - left diagonal (tension) EC3 ultimate load Lu et al - ultimate strength Lu et al - serviciability strength Axial displacement (mm) 14

15 2/5/21 Results Analysis and Discussion Von Mises Stress (in MPa) right diagonal (compression) 2 - left diagonal (tension) EC3 ultimate load Lu et al - ultimate strength Lu et al - serviciability strength Axial displacement (mm) Scale factor = 2 Parametrical Analysis T Joint Braces: SHS9x16mm ( =.25) SHS18x16mm ( =.5) SHS26x16mm ( =.75) SHS28x16mm ( =.8) SHS3x16mm ( =.857) 3 Same bottom chord SHS35x15mm 15

16 2/5/21 2 Parametrical Analysis T Joint b1 = 9 (beta =.25) 12 b1 = 18 (beta =.5) b1 = 26 (beta =.75) 8 b1 = 28 (beta =.8) 4 b1 = 3 (beta =.857) Deformation Limit (3%b) Displacement (mm) EC3 (kn) Ansys (kn) 3%b As expected, increasing the value of leads to a strong increase in the strength of the connection specially if.75. However, if.75, an increase of this parameter leads to an increase of strength with a magnitude much smaller than expected. This is due to the fact that for large values of the limit state related to bending does not control, while shear and punching shear begins to be the governing limit states. Parametrical Analysis K Joint 32 Diagonals: CHS125x11.28mm ( =27) CHS162x11.28mm ( =4) CHS25x11.28mm ( =31.2) CHS245x11.28mm ( =36) = 3º Same bottom chord CHS46x11.28mm 16

17 2/5/21 3 Parametrical Analysis K Joint d1 = 125 (beta =.31) 1 d1 = 162 (beta =.4) d1 = 25 (beta =.5) d1 = 245 (beta =.6) 5 Lu et al - ultimate strength Lu et al - serviciability strength Displacement (mm) Ansys (kn) EC3 (kn) 1%d 3%d As expected, increasing the value of leads to a substantial increase in the connection load carrying capacity. It may be observed that the joint resistance evaluated according to Eurocode 3 (23) provisions represents a lower limit for the analysed joints. Final Remarks FEM T and K tubular joints four-node thick shell elements bending, shear and membrane df deformations Deformation limits criteria were used to obtain the joint ultimate load The analysis results assess the EN [4] performance maximum load global load versus displacement curves fully joint structural response stiffness and ductility capacity 34 17

18 2/5/21 Final Remarks Observing analytical curves numerical results achieved a good agreement with the Eurocode 3 [4] previsions ii for the K joint resistance it combined with a deformation limit criterion for the deformation of the joint chord face For T joints with elevated values difference between numerical and EC3 results Ak Acknowledgements: ld CAPES/GRICES, CNPq, UERJ and FAPERJ financial support provided to enable the development of this research program 35 18