Buckling of Circular Plate with a Hole | Online Calculator

Buckling Calculators







Buckling of Circular Plate with a Hole

In this calculation, a circular plate with an outer diameter D, inner diameter d, and thickness s is considered. Calculations are performed for plates with hinged (scheme I) and fixed (scheme II) edges. For a fixed edge plate, the hole diameter should not exceed the outside radius of the plate.

Based on the results of calculations, the minimum critical load of the first form of stability loss acting on the edges of the plate and given by the compressive stresses σ is determined.

For the calculation, the elastic modulus E and Poisson's ratio ν of the plate should be specified.

Buckling of circular plate with hole
Elastic stability of circular plate with hole

INITIAL DATA

D - Plate outer diameter;


d - Plate hole diameter. For scheme #2 there must be condition d < D/2;


s - Plate thickness;


E - Young's modulus;


ν - Poisson's ratio.

RESULTS DATA

σ - Critical compression stress of buckling.

Outer diameter (D)

Inner diameter (d)

Plate thickness (s)

Young's modulus (E)

Poisson's ratio (ν)

Scheme # 1

Scheme # 2

Critical stress (σ)

BASIC FORMULAS

Critical stress σ is determined by parametric equations of the form:

σ = KE(s/0.5D)2 / (1 - ν2);

K - coefficient, depending on the d / D ratio.

INITIAL DATA

D - Plate outer diameter;


d - Plate hole diameter. For scheme #2 there must be condition d < D/2;


s - Plate thickness;


E - Young's modulus;


ν - Poisson's ratio.

RESULTS DATA

σ - Critical compression stress of buckling.

MATERIALS PROPERTIES

Material

Young’s modulus

Pa (psi)

Poisson’s ratio

Steel

1.86÷2.1×1011 (2.7÷3.05×107)

0.25÷0.33

Cast iron

0.78÷1.47×1011 (1.1÷2.1×107)

0.23÷0.27

Copper

1.0÷1.3×1011 (1.45÷1.9×107)

0.34

Tin bronze

0.74÷1.22×1011 (1.1÷1.8×107)

0.32÷0.35

Brass

0.98÷1.08×1011 (1.4÷1.6×107)

0.32÷0.34

Aluminum alloy

0.7×1011 (1.0×107)

0.33

Magnesium alloy

0.4÷0.44×1011 (5.8÷6.4×106)

0.34

Nickel

2.5×1011 (3.6×107)

0.33

Titanium

1.16×1011 (1.7×107)

0.32

Lead

0.15÷0.2×1011 (2.2÷2.9×106)

0.42

Zinc

0.78×1011 (1.1×107)

0.27

Glass

4.9÷5.9×1010 (7.1÷8.5×106)

0.24÷0.27

Concrete

1.48÷2.25×1010 (2.1÷3.3×106)

0.16÷0.18

Wood (along the grain)

8.8÷15.7×1010 (12.8÷22.8×106)

-

Wood (across the grain)

3.9÷9.8×1010 (5.7÷14.2×106)

-

Nylon

1.03×1010 (1.5×106)

-

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