Buckling Calculators

Buckling of Circular Plate

In this calculation, a circular plate with a diameter D and thickness s is considered. Calculations are performed for plates with hinged (scheme I) and fixed (scheme II) edges. 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

Elastic stability of Circular plate

INITIAL DATA

D - Plate diameter;

s - Plate thickness;

E - Young's modulus;

ν - Poisson's ratio.

RESULTS DATA

σ - Critical compression stress of buckling.

Metric Imperial

Diameter (D)

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 Poisson's ratio and support type.

INITIAL DATA

D - Plate diameter;

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)	-

OTHER CALCULATORS

AREA MOMENTS OF INERTIA

BEAM CALCULATORS

TORSION OF BARS

CIRCULAR FLAT PLATES

BUCKLING

ELASTIC CONTACT

IMPACT LOADS

NATURAL FREQUENCIES

PRESSURED SHELLS

FLUID DYNAMIC

COMPOSITES

SPRINGS

THREAD CONNECTIONS

SHAFT CONNECTIONS

BEARINGS

DRIVES

FATIGUE

HEAT TRANSFER