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Thick-walled Pipes Under Pressure and Axial Load

If the pipe wall thickness exceeds 1 / 10 of the mean radius of the cross section, the pipe is considered to be thick-walled, and it is not allowed to make the strength calculation by the method for thin-walled pipes calculation. The reason for this is the change in the circumferential stresses along the pipe wall thickness (in thin-walled pipes it is assumed to be constant), as well as the fact that the radial stresses in the outer layers of the pipe wall are comparable with the circumferential stresses by value, and their effect cannot be neglected anymore.

In this calculation, a thick-walled pipe with an inner radius R1 and outer radius R2 is considered. The pipe is under the influence of internal pressure P1, external pressure P2, and axial load F. Loads can take on both positive and negative values.

As a result of calculation, internal stresses σr, σt, σz are determined in the circumferential, meridional and axial directions at a given point lying on a circle with a radius r. Equivalent stresses σmizes and deformation X in the radial direction are also calculated.

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

Thick-walled pipe calculator
Thick-walled pipe calculation

INITIAL DATA

R1 - Inner radius of the pipe;


R2 - Outer radius of the pipe;


r - Radius of the pipe wall in calculated point;


P1 - Internal pressure;


P2 - External pressure;


F - Axial load;


E - Young's modulus;


ν - Poisson's ratio.

RESULTS DATA

σr - Radial stress in the calculated point;


σt - Circumferential stress in the calculated point;


σz - Axial stress in the calculated point;


σmizes - Equivalent stress in the calculated point;


X - Deformation of pipe wall in the radial direction.

Inner radius (R1)

Outer radius (R2)

Point radius (r)

Internal pressure (P1)

External pressure (P2)

Axial load (F)

Young'a modulus (E)

Poisson's ratio (ν)

Radial stress (σr)

Circumferential stress (σt)

Axial stress (σz)

Equivalent stress (σmizes)

Deformation (Х)

BASIC FORMULAS

Radial stress:

σr = [(P1*R12 - P2*R22) / (R22 - R12)] - [(P1 - P2)*R12*R22 / (R22 - R12)]*(1/r 2);

Circumferential stress:

σt = [(P1*R12 - P2*R22) / (R22 - R12)] + [(P1 - P2)*R12*R22 / (R22 - R12)]*(1/r 2);

Axial stress:

σz = F/[π*(R22 - R12)].

INITIAL DATA

R1 - Inner radius of the pipe;


R2 - Outer radius of the pipe;


r - Radius of the pipe wall in calculated point;


P1 - Internal pressure;


P2 - External pressure;


F - Axial load;


E - Young's modulus;


ν - Poisson's ratio.

RESULTS DATA

σr - Radial stress in the calculated point;


σt - Circumferential stress in the calculated point;


σz - Axial stress in the calculated point;


σmizes - Equivalent stress in the calculated point;


X - Deformation of pipe wall in the radial 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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