Barlow's formula

The boiler formula (DIN 2413) is a formula of engineering mechanics. She has a fundamental importance in the calculation and design of steam boilers, pressure vessels and piping.

Application

Boilers formula specifies the mechanical stresses in loaded by internal pressure rotationally symmetrical bodies, such as are for example encountered in pipes or pressure vessels. As it is based on a membrane stress balance of forces, so even elasticity sizes are used to calculate the stresses neither deformation assumptions necessary.

The boiler formula is valid only for thin and curved pressure vessel. For boilers, which are made of flat metal sheets, and for thick-walled containers, boilers formula does not apply.

A pressure vessel can be considered as a thin wall, when its dimensions (diameter ) is much greater than its wall thickness (ie, outer diameter / inner diameter = D / d < 1.2). The greatest stress is the tangential stress, which is why pipes and similar shaped container always burst in the longitudinal direction in cylindrical bodies. For pressure loaded on flat plates, the boiler formula, however, not applicable.

Calculation

The hoop and axial stress in a loaded by pressure cylinder which is closed at the ends:

• P = internal pressure
• D = inside diameter - outside diameter D - average diameter
• S = wall thickness
• = Tangential stress in the wall
• = Axial stress (longitudinal direction ) in the wall

In this form the boiler formula is also known as sausage formula. The term serves as a mnemonic to remember which is the larger of the two voltages. The circumferential stress is twice as large as the tension in the longitudinal direction, so burst sausages with improper heating always in the longitudinal direction.

From the shear stress hypothesis follows in the final analysis as a " boiler formula " designated comparison voltage with

• = Radial stress; is attached to the container's interior side to the exterior side ( non-loaded surface), in the middle of the wall, the arithmetic mean is used

Or

Includes wall thickness surcharges calculated the minimum wall thickness using the following formula:

• Allowance for corrosion
• Supplement for tolerance errors

In spherical containers there are no tangential stresses; the axial stresses match those of the cylinder. Therefore, the minimum wall thickness is halved: