Buckling Calculators

Buckling of Curved Shell

In this calculation, a cylindrical open shell with a diameter D, central bending angle α and thickness s is considered. Calculations are performed for shells with hinged (scheme I) and fixed (scheme II) edges. 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 shell is determined.

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

Buckling of curved shell

Elastic stability of curved shell

INITIAL DATA

D - Shell mean diameter;

α - Shell center angle;

s - Shell thickness;

E - Young's modulus;

ν - Poisson's ratio.

RESULTS DATA

P - Critical pressure of buckling on the external surface of the shell.

Metric Imperial

Shell diameter (D)

Angle (α)

Shell thickness (s)

Young's modulus (E)

Poisson's ratio (ν)

Scheme # 1

Scheme # 2

Critical pressure (P)

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BASIC FORMULAS

Critical pressure P is determined by parametric equations of the form:

P = Es³(K - 1) / 1.5D³(1 - ν²);

K - coefficient, depending on angle α.

INITIAL DATA

D - Shell mean diameter;

α - Shell center angle;

s - Shell thickness;

E - Young's modulus;

ν - Poisson's ratio.

RESULTS DATA

P - Critical pressure of buckling on the external surface of the shell.

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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ELASTIC CONTACT

IMPACT LOADS

NATURAL FREQUENCIES

PRESSURED SHELLS

FLUID DYNAMIC

COMPOSITES

SPRINGS

THREAD CONNECTIONS

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BEARINGS

DRIVES

FATIGUE

HEAT TRANSFER