Buckling Calculators

Buckling of Sphere

In this calculation, a spherical shell with a mean diameter D and wall thickness s is considered. The calculation is performed for an ideal case (absolutely smooth surface, homogeneous material, and exact geometry), and an approximate calculation of stability is also performed for real structures. Based on the results of calculations, the minimum uniformly distributed critical load of the first form of stability loss P, acting on the outer surface of the sphere is determined.

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

Buckling of curved shell

Elastic stability of curved shell

INITIAL DATA

D - Mean sphere diameter;

s - Sphere wall thickness;

E - Young's modulus;

ν - Poisson's ratio.

RESULTS DATA

P₁ - Critical pressure of buckling on external surface for ideal case;

P₂ - Critical pressure of buckling on external surface for real structures.

Metric Imperial

Sphere diameter (D)

Thickness of wall (s)

Poisson's ratio (ν)

Young's modulus (Е)

Critical pressure (P₁)

Critical pressure (P₂)

BASIC FORMULAS

Critical pressure P₁:

P₁ = 8Es² / D²[3(1 - ν²)]^0.5.

INITIAL DATA

D - Mean sphere diameter;

s - Sphere wall thickness;

E - Young's modulus;

ν - Poisson's ratio.

RESULTS DATA

P₁ - Critical pressure of buckling on external surface for ideal case;

P₂ - Critical pressure of buckling on external surface for real structures.

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