Buckling Calculators

Buckling of Tube

In this calculation, a cylindrical shell with a diameter D and thickness s is considered. 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. The edges of the shell are fixed and retain their circular shape when loaded.

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

Buckling of cylindrical shell

Elastic stability of cylindrical shell

INITIAL DATA

D - Tube diameter;

s - Tube wall thickness;

L - Tube length. Tube ends held circular;

E - Young's modulus;

ν - Poisson's ratio.

RESULTS DATA

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

Metric Imperial

Tube diameter (D)

Wall thickness (s)

Tube length (L)

Young's modulus (E)

Poisson ratio (ν)

Critical pressure (P)

BASIC FORMULAS

Critical pressure P:

P = [1.6Es² / LD]*[(1 / (1-ν²))³*(s² / 0.25D²)]^0.25

INITIAL DATA

D - Tube diameter;

s - Tube wall thickness;

L - Tube length. Tube ends held circular;

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)	-

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