Radial stress is

stress Stress may refer to: Science and medicine * Stress (biology), an organism's response to a stressor such as an environmental condition * Stress (linguistics), relative emphasis or prominence given to a syllable in a word, or to a word in a phrase ...

towards or away from the central

axis An axis (plural ''axes'') is an imaginary line around which an object rotates or is symmetrical. Axis may also refer to: Mathematics * Axis of rotation: see rotation around a fixed axis * Axis (mathematics), a designator for a Cartesian-coordinat ...

of a component.

Pressure vessels

The walls of

pressure vessel A pressure vessel is a container designed to hold gases or liquids at a pressure substantially different from the ambient pressure. Construction methods and materials may be chosen to suit the pressure application, and will depend on the size o ...

s generally undergo triaxial loading. For cylindrical pressure vessels, the normal loads on a wall element are: * the longitudinal stress * the circumferential (hoop) stress * the radial stress. The radial stress for a thick-walled

cylinder A cylinder (from ) has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes. In elementary geometry, it is considered a prism with a circle as its base. A cylinder may also be defined as an ...

is equal and opposite to the

gauge pressure Pressure measurement is the measurement of an applied force by a fluid ( liquid or gas) on a surface. Pressure is typically measured in units of force per unit of surface area. Many techniques have been developed for the measurement of pre ...

on the inside surface, and zero on the outside surface. The circumferential stress and longitudinal stresses are usually much larger for pressure vessels, and so for thin-walled instances, radial stress is usually neglected.

Formula

The radial stress for a thick walled pipe at a point

r

from the central axis is given by :

\sigma_r(r) = \frac+\frac\

where

r_i

is the inner radius,

r_o

is the outer radius,

p_i

is the inner absolute pressure and

p_o

is the outer absolute pressure. Maximum radial stress occurs when

r = r_i

(at the inside surface) and is equal to gauge pressure, or

p_i - p_o

References

Solid mechanics {{Engineering-stub