Buckling

Industry Presentation

September 2012

Philippe Baumans & Åge BøeProject Management Team (PMT)

CSR Harmonisation

Buckling presentation: Contents

• General

• Application

• Closed form method

• Utilization factor

• Interaction formulae

• Overall stiffened panel capacity

• Plate capacity

• Ultimate stiffener capacity

• Method A and B

General

• Failure modes:– Global elastic buckling of stiffened

panel (eigen values)

– Ultimate limit state = ultimate capacity of the panel

– Stress redistribution within the panels, between plate & stiffeners is considered

• For various type of structural elements:

– Local supporting members (LSM)

– Primary supporting members (PSM)

– Pillars, corrugated bulkheads & brackets

• Buckling strength defined as the most critical buckling failure mode

• Net scantling considered for buckling capacity: tgr - tc

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1.0

• Overall stiffened panel capacity

• Plate capacity• Stiffener capacity

Application

• Slenderness requirements• Plates, longitudinal and transverse stiffeners,

primary supporting members and brackets

Section 2

• Prescriptive buckling requirements• Plates, longitudinal and transverse stiffeners, primary

supporting members (PSM) and other structures

Section 3

• Buckling requirements of the FE analysis• Plates, stiffened panels and other structures

Section 4

• Buckling capacity• Prescriptive and FE buckling requirements

Section 5

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New Closed Form Method (CFM) considers the following buckling failure modes:

Overall stiffened panel capacityPlate capacityStiffener buckling capacity

One single buckling assessment method : Closed Form Method (CFM)

Closed Form Method

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CFM adjustment method - Load cases

Pressure

6September 2012 CSR-H Buckling

Load Case 1 Load Case 2

Load Case 3 Load Case 4

CFM adjustment method: 18 panels considered for each stiffener type

• 4 stiffener types

– Flat bar

– Bulb bar

– Angle bar

– Tee bar

• Different scantling combinations

– Plate thickness

– Stiffener scantling (size and thickness)

• Method 1 : Ultimate strength

• Method 2 : Ultimate and elastic

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CFM adjustment method: Result comparisons on Load case 1

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CFM adjustment method: Result comparisons on Load case 3

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Utilization Factor

• CSR-H based on CSR-OT approach:

• Definition:

– Failure calculated by increasing/decreasing actual stress combination proportionally (γ stress multiplier factor) until interaction formulas are equal to 1

– Limit state when γ = γc (stress multiplier factor at failure)

– Highest buckling utilization factor of different failure modes is considered : η = 1 / γc

• Criteria allowableact ηη ≤

u

act

WW

=η

222 τσσ ++= yxactW

222ccycxuW τσσ ++=

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UTILIZATION FACTOR η

Interaction formulae

Overall stiffened panel capacity

Stiffener ultimate limit statePlate limit state

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Overall stiffened panel capacity

• Limit state

• Pz represents the equivalent applied axial stress from longitudinal, transverse and shear stress:

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Plate capacity

• New interaction formulae based on Von Mises ellipse

• No Poisson Effect Correction

• Limit State :

• Calculation of critical stresses based on DIN / CSR-BC with some modifications based on FEM calibration:

• F1 removed compared to CSR-BC. F1 depends on the type of stiffener to take into account the stiffness of the stiffener).

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• Flong =1 in CSR BC

Ultimate stiffener capacity

• Ultimate stiffener capacity is based on DIN & CSR BC

• Combination of lateral and torsional buckling capacity

Axial stress

• At mid span• Efficient

breadth of attach plate

Bending stress

• Lateral load• In-plane

loads

Warping stress

• depends on the scantling

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Method A and B

• All the edges of the elementary plate panel are forced to remain straight (but free to move in the in-plane directions) due to the surrounding structure/neighbouring plates

• Equivalent to SP-M1 of CSR OT

Method A

• The edges of the elementary plate panel are not forced to remain straight due to low in-plane stiffness at the edges and/or no surrounding structure/neighbouring plates

Method B

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MB

“pull-in”effect

Keep straight Free pull-in

Method A and B

• Carried out Non Linear FE Analysis (NLFEA) study on “free pull-in” boundary condition

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Method A and BComparison with CSR-OT M2

• Non-linear FE results are between M2 and integrated panels

• Method 2 found to be too conservative and replace by Method B (Free pull-in)

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THANK YOU FOR YOUR ATTENTION !