a semi-rigorous approach for interaction between local …...

KULDEEP VIRDI

AARHUS UNIVERSITET

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

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METNET Seventh International Seminar, Izmir, 11-12 October 2012

AARHUS UNIVERSITET

METNET SEVENTH INERNATIONAL SEMINAR IZMIR TURKEY

11-12 OCTOBER 2012

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

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STIFFENED PLATE PANELS

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Ships

Aircraft

Bridges

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Plate panels are strengthened with stiffeners.

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Compression in the stiffened plate gives rise to instability.

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C

T

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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.

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OVERALL BUCKLING OF STIFFENED PLATE

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Parametric study on a single stiffener together with an associated

plate width treated as column between cross-frames.

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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

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SOLUTION BY FINITE DIFFERENCE METHOD

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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

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INTERNAL EQUILIBRIUM

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Stresses need to be integrated over appropriate areas, using non-

linear stress-strain relations, to satisfy internal equilibrium

Numerical

Methods must be

used

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INTERNAL EQUILIBRIUM

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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

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STABILITY ANALYSIS

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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.

The maximum load

obtained is taken as the

ultimate strength of the

composite column

Notional Elastic Critical load

Deflection

Load

Ultimate Load

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Two modes of

failure

Plate in

compression

Plate in tension

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Plate in tension gives much lower strength than the case of

plate in compression.

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EFFECT OF RESIDUAL STRESSES

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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.

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RESIDUAL STRESS PATTERN

An empirical relation [Ref 1] gives the width of tension yield zone:

Where, is the sum of plate thicknesses meeting at the weld,

is a constant (6000 N/mm2)

is the cross-section of the added weld metal, and

is the yield strength of the plate

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t

CAt

y

t

C

A

y

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For the stiffener-plate combination this results in the residual

stress pattern

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This pattern has no moment equilibrium

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Corrected residual stress pattern

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Failure stresses for

the two modes of

buckling, including

initial lack of

straightness and

residual stresses.

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The cusps are

attributed to the

sharp change of

residual stress from

tension to

compression.

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LOCAL PLATE BUCKLING

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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.

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Plate buckling

response in terms of

load-deflection

curves.

Load-deflection

response can also be

interpreted as overall

stress- strain

characteristic.

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Experimental curves

interpolated for the

stiffened plate

chosen in the

parametric study.

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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.

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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.

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CONCLUSIONS AND FUTURE WORK

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CONCLUSIONS

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The paper describes how interaction between local and global

buckling of stiffened plates can be studied by adopting the load-

deflection 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.

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FUTURE WORK

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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.

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11-12 OCTOBER 2012

THANK YOU

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