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Buckling Calculators







Buckling of Polygonal Plate

In this calculation, a polygonal plate with side a, thickness s is considered. The plate edges are simply supported. The set number of edges n may vary from 3 to 8. Based on the results of calculations, the minimum critical load for 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 polygon plate
Elastic stability of polygon plate

INITIAL DATA

а - Edge length;


n - Number of the plate edges (from 3 to 8);


s - Plate thickness;


E - Young's modulus;


ν - Poisson's ratio.

RESULTS DATA

σ - Critical compression stress of buckling.

Edge length (a)

Plate thickness (s)

Number of edges (n)

Young's modulus (Е)

Poisson's ratio (ν)

Critical stress (σ)

BASIC FORMULAS

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

σ = KEs2 / a2(1 - ν2);

K - coefficient, depending on the number of the edges.

INITIAL DATA

а - Edge length;


n - Number of the plate edges (from 3 to 8);


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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