Pipes and Shells Calculators

Corrugated Tube Under Axial Load

In this calculation, a corrugated tube with a mean diameter D, corrigation diameter d and wall thickness t is considered. The shell is under tensile force of magnitude F, acting along the shell axis. For the calculation, the elastic modulus E, Poisson's ratio ν and number of corrigations n should be specified.

As a result of calculation, membrane stress σ₁ and bending stress σ₂ in the shell are determined. The total deformation of the shell X in the axial direction is also calculated.

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INITIAL DATA

D - Corrugated tube diameter;

d - Corrugation diameter;

t - Wall thickness;

F - Axial force;

E - Young's modulus;

ν - Poisson's ratio;

n - Number of corrugations (five shown at figure).

RESULTS DATA

σ₁ - Maximum circumferential membrane stress;

σ₂ - Maximum meridional bending stress;

Х - Total deformation the of tube in the axial direction.

Metric Imperial

Diameter (D)

Diameter (d)

Wall thickness (t)

Axial force (F)

Young's modulus (E)

Poisson's ratio (ν)

Number of corrugationd (n)

Membrane stress (σ₁)

Bending stress (σ₂)

Deformation (Х)

BASIC FORMULAS

Maximum circumferential membrane stress:

σ₁ = [0.925F / πD*t]*[D*d*(1 - ν²) / 4t²]^1/3;

Maximum meridional bending stress:

σ₂ = [1.63F / πD*t]*[D*d / ((1 - ν²)^0.5*4t²)]^1/3;

Deformation:

X = 0.58*F*D*n*(1 - ν²)^0.5 / 2Et².

INITIAL DATA

D - Corrugated tube diameter;

d - Corrugation diameter;

t - Wall thickness;

F - Axial force;

E - Young's modulus;

ν - Poisson's ratio;

n - Number of corrugations (five shown at figure).

RESULTS DATA

σ₁ - Maximum circumferential membrane stress;

σ₂ - Maximum meridional bending stress;

Х - Total deformation the of tube in the axial direction.

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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