The analysis of piping under pressure, weight and thermal expansion is
complex. This complexity can be understood by knovledge of Principal
Axis System.
Stress is considered as the ratio of Force to Area. To find the stress
in the small element, say cube of a piece of pipe, construct a
three-dimensional, mutually perpendicular principal axis system with
each axis perpendicular to the face of the cube it intersects.
Each force, acting on the cube can be resolved into force components,
acting along each of the axis. Each force, acting on the face of the
cube divided by area of the cube face is called the principal stress.
The principal stress acting along the centerline of the pipe is called
Longitudinal principal stress. This stress is caused by longitudinal
bending, axial force loading or pressure.
Radial principal stress acts on a line from a radial line from center of
pipe through the pipe wall. This stress is compressive stress acting on
pipe inside diameter caused by internal pressure or a tensile stress
caused by vacuum pressure.
Circumferential principal stress, some times called Hoop or tangential
stress, acts along the circumference of the pipe. This stress tends to
open-up the pipe wall and is caused by internal pressure.
When two or more principal stresses act at a point on a pipe, a shear stress will be generated.
Longitudinal Principal stress, LPS = PD/4T
Circumferential Principal stress, CPS (Hoop) = PD/2T
Radial Principal stress, RPS = P
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