Pipes and Shells Calculators

Double-walled Pipes

The maximum stresses in a pipe loaded with internal pressure cannot be less than twice value of the loading pressure, regardless of the pipe wall thickness. If the nominal allowable stresses are below this value, jointed pipes may be used. In this case, the outer pipe is press-fitted to the inner pipe thus unloading its inner layers and taking a part of the applied load.

In this calculation, a double-walled pipe with an inner diameter D₁, outer diameter D₃ and mating diameter D₂ is considered. The outer and inner pipes are installed with an interference fit Δ. These dimensions are used for calculation of the contact pressure σ on the mating surface.

When setting the value of the internal pressure P, the optimal amount of interference Δ₀ by conditions of equal strength of inner and outer tubes, and also optimal adjacent diameter D₀ by minimal stress conditions can be calculated.

For the calculation, the elastic modulus E of the pipe should be specified.

Pipe stresses can be calculated here.

Calculation of double-walled pipes

Calculation of double-walled pipes

INITIAL DATA

D₁ - Pipe inner diameter;

D₂ - Nominal adjacent diameter;

D₃ - Pipe outer diameter;

Δ - Amount of interference (difference between outer radius of inner tube and inner radius of outer tube);

P - Internal pressure;

E - Young's modulus.

RESULTS DATA

σ - Contact pressure on the adjacent surfaces;

Δ₀ - Optimal interference on the condition of equal strength of the inner and outer pipes;

D₀ - Optimal adjacent diameter by minimal stress condition.

Metric Imperial

Diameter (D₁)

Diameter (D₂)

Diameter (D₃)

Amount of interference (Δ)

Pipe pressure (Р)

Young'a modulus (E)

Contact pressure (σ)

Optimal interference (Δ₀)

Optimal diameter (D₀)

BASIC FORMULAS

Contact pressure:

σ = Δ*E*(D₃²/4 - D₂²/4)*(D₂²/4 - D₁²/4) /
[(D₂³/4)*(D₃²/4 - D₁²/4)];

Optimal amount of interference:

Δ₀ = 2P*D₂*(D₃²/4)*(D₂²/4 - D₁²/4)/
[E*((D₃²/4) * (D₂²/4 -D₁²/4) + (D₂²/4) * (D₃²/4 - D₂²/4))];

Optimal adjacent diameter:

D₀ = 2[(D1 / 2) × (D3 / 2)]^1/2.

INITIAL DATA

D₁ - Pipe inner diameter;

D₂ - Nominal adjacent diameter;

D₃ - Pipe outer diameter;

Δ - Amount of interference (difference between outer radius of inner tube and inner radius of outer tube);

P - Internal pressure;

E - Young's modulus.

RESULTS DATA

σ - Contact pressure on the adjacent surfaces;

Δ₀ - Optimal interference on the condition of equal strength of the inner and outer pipes;

D₀ - Optimal adjacent diameter by minimal stress condition.

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