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.

Metric Imperial

Edge length (a)

Plate thickness (s)

Number of edges (n)

Young's modulus (Е)

Poisson's ratio (ν)

Critical stress (σ)

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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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CIRCULAR FLAT PLATES

BUCKLING

ELASTIC CONTACT

IMPACT LOADS

NATURAL FREQUENCIES

PRESSURED SHELLS

FLUID DYNAMIC

COMPOSITES

SPRINGS

THREAD CONNECTIONS

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DRIVES

FATIGUE

HEAT TRANSFER