A SEMI-RIGOROUS APPROACH FOR INTERACTION BETWEEN LOCAL AND GLOBAL BUCKLING IN STEEL STRUCTURES

Transcription

1 A SEMI-RIGOROUS APPROACH FOR INTERACTION BETWEEN LOCAL AND GLOBAL BUCKLING IN STEEL STRUCTURES KULDEEP VIRDI METNET Seventh International Seminar, Izmir, October

2 OUTLINE Stiffened Plate Panels Interaction between Local and Overall Buckling Overall Buckling of Stiffened Plate Effect of Lack of Straightness Effect of Residual Stresses Local Plate Buckling Load-Deflection response Interactive Local-Global Failure Conclusion 2

3 STIFFENED PLATE PANELS 3

4 STIFFENED PLATE PANELS Ships Aircraft Bridges 4

5 STIFFENED PLATE PANELS Plate panels are strengthened with stiffeners. 5

6 STIFFENED PLATE PANELS Compression in the stiffened plate gives rise to instability. C T 6

7 STIFFENED PLATE PANELS Compression in the plate panels between stiffeners results in local buckling. The stiffeners, together with associated plate widths, fail by overall buckling as columns. Actual failure involves interaction between local and overall buckling. 7

8 OVERALL BUCKLING OF STIFFENED PLATE 8

9 OVERALL BUCKLING OF STIFFENED PLATE Parametric study on a single stiffener together with an associated plate width treated as column between cross-frames. 9

10 OVERALL BUCKLING OF STIFFENED PLATE Ultimate failure load by finite difference method Elastic-perfectly plastic stress-strain curve Simply supported ends with zero eccentricity of axial load Initial lack of straightness 10

11 SOLUTION BY FINITE DIFFERENCE METHOD Solution of two sub-problems 1. Internal Equilibrium Evaluation of stress resultants using numerical integration 2. External Equilibrium Calculation of deflections using finite differences and second-order iteration 11

12 INTERNAL EQUILIBRIUM Stresses need to be integrated over appropriate areas, using nonlinear stress-strain relations, to satisfy internal equilibrium Numerical Methods must be used 12

13 INTERNAL EQUILIBRIUM The equilibrium deflected shape is determined by the finite difference method combined with the Newton-Raphson method of iteration for nonlinear problems. Thus, starting with an approximate solution {uk} for the deflections at the finite difference stations, a better solution is obtained by: { uk+1 } = { uk } - [I - K]-1 { uk - Uk } [K] is determined numerically 13

14 STABILITY ANALYSIS The method described is applied repeatedly, starting with a small applied load and solving for the deflected shape, and then increasing the load until no convergence for the deflected shape is obtainable. Load Notional Elastic Critical load Ultimate Load The maximum load obtained is taken as the ultimate strength of the composite column Deflection 14

15 OVERALL BUCKLING OF STIFFENED PLATE Two modes of failure Plate in compression Plate in tension 15

16 OVERALL BUCKLING OF STIFFENED PLATE Plate in tension gives much lower strength than the case of plate in compression. 16

17 EFFECT OF RESIDUAL STRESSES 17

18 RESIDUAL STRESSES DUE TO WELDING At the weld location, the residual stresses approach yield stress of steel in tension. This zone is limited by the size of the plate and the size of the weld. The magnitude of stress in compression is determined by force equilibrium. 18

19 RESIDUAL STRESS PATTERN An empirical relation [Ref 1] gives the width of tension yield zone: Where, CA t y t t is the sum of plate thicknesses meeting at the weld, C A y is a constant (6000 N/mm2) is the cross-section of the added weld metal, and is the yield strength of the plate 19

20 RESIDUAL STRESS PATTERN For the stiffener-plate combination this results in the residual stress pattern 20

21 RESIDUAL STRESS PATTERN This pattern has no moment equilibrium 21

22 RESIDUAL STRESS PATTERN Corrected residual stress pattern 22

23 EFFECT OF RESIDUAL STRESSES Failure stresses for the two modes of buckling, including initial lack of straightness and residual stresses. 23

24 EFFECT OF RESIDUAL STRESSES The cusps are attributed to the sharp change of residual stress from tension to compression. 24

25 LOCAL PLATE BUCKLING 25

26 LOCAL PLATE BUCKLING Plate buckling is characterised mainly by the plate width to plate thickness ratio. Buckling stress does not depend significantly on the length of the plate panel. 26

27 LOCAL PLATE BUCKLING Plate buckling response in terms of load-deflection curves. Load-deflection response can also be interpreted as overall stress- strain characteristic. 27

28 LOCAL PLATE BUCKLING Experimental curves interpolated for the stiffened plate chosen in the parametric study. 28

29 EFFECT OF LOCAL AND GLOBAL BUCKLING The interaction between local and global buckling results in significant reduction in strength up to a certain slenderness ratio. 29

30 EFFECT OF LOCAL AND GLOBAL BUCKLING The UK standard for bridges handles the problem of local plate buckling by using an effective width of the plate acting together with the stiffener. Comparison shows that the approach described in this paper gives valid results. 30

31 CONCLUSIONS AND FUTURE WORK 31

32 CONCLUSIONS The paper describes how interaction between local and global buckling of stiffened plates can be studied by adopting the loaddeflection response of the plate as its stress-strain curve. The reduction in the failure load for a specific plate-stiffener geometry has been shown to be comparable with that estimated from a typical existing standard. The method described can handle lack of straightness, residual stresses and local plate buckling alongside the overall buckling of the stiffener-plate combination. 32

33 FUTURE WORK The method described above will be used to develop design buckling curves for columns made of high strength steel. Local buckling characteristics of walls of rectangular tubular columns, or flanges of I- or H- sections, can be considered in the same way as for stiffened plates. These computations, based on a finite-difference approach, will be validated against full-scale experiments as well as the alternative finite-element approach. 33

34 THANK YOU 34