Pipes and Shells Calculators

Thin Axisymmetric Shells Under Internal Pressure

When transporting and storing fluid media, organizing a technological process, using hydraulic drive and heat exchange systems, and in many other cases, it becomes necessary to operate technical objects under the influence of hydrostatic pressure.

From the point of view of strength and stiffness calculations, many of these structures may be classified as thin-walled axisymmetric shells of revolution. Mainly, these are various types of pressure vessels. Shells of this type are calculated according to the momentless theory, and only tensile stresses σ_m in the meridional (along the generatrix) and σ_t in circumferential (perpendicular to the meridional) directions are considered.

In this calculation, a thin-walled axisymmetric shell of arbitrary geometry with an internal axial radius r and a meridional radius R determined at the calculated point, and thickness t is considered. The shell is under hydrostatic pressure P. As a result of calculations, the equivalent stresses σ are found at any given point of the shell. In case of curved shell, in addition to the axial and meridional radiuses, this calculated point is characterized by a distance H to the center of the shell curvature in the meridional direction (along the shell axis).

In case of straight generatrix, the calculated point is characterized by the inner radius r and slope of the shell generatrix α (look at figure).

Pipe calculator

Pipe calculation

INITIAL DATA

P - Internal pressure;

r - Inner radius of the shell in calculated point;

R - Meridional radius of the shell in calculated point;

Н - Distance along axis of the shell from center of circle of radius R to calculated point. It can take values from 0 to R;

t - Wall thickness;

α - Angle of inclination of the shell generatrix (Applies only with straight generatrix. In this case the parameters R and H are ignored).

RESULTS DATA

σ - Equivalent stress in calculated point.

Metric Imperial

Internal pressure (P)

Inner radius (r)

Meridional radius (R)

Distance (Н)

Wall thickness (t)

Angle of inclination (α)

Equivalent stress (σ)

Meridional stress (σ_m)

Circumferential stress (σ_t)

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BASIC FORMULAS

Meridional stress:

σ_m = P*r / (2t*cosα),

Circumferential stress:

(σ_t*cosα / r) + (σ_m / R) = 1 - Laplace equation.

Equivalent stress:

σ - Largest of stresses σ_m and σ_t.

INITIAL DATA

P - Internal pressure;

r - Inner radius of the shell in calculated point;

R - Meridional radius of the shell in calculated point;

Н - Distance along axis of the shell from center of circle of radius R to calculated point. It can take values from 0 to R;

t - Wall thickness;

α - Angle of inclination of the shell generatrix (Applies only with straight generatrix. In this case the parameters R and H are ignored).

RESULTS DATA

σ - Equivalent stress in calculated point.

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