Triaxial Stress, Biaxial Stress, and Uniaxial Stress

Triaxial Stress, Biaxial Stress, and Uniaxial Stress

Triaxial stress refers to a cond ition where only normal stresses act on an element and all shear s An example of a triaxial stress state is hydrostatic pressure acting on a small element submerged i

A two-dimensional state of s tress in which only two normal stresses a re present is called b dimensional state of stress in w hich normal stresses act along one direction only is called a uniaxi

Pure Shear

Pure shear refers to a stress st ate in which an element is subjected to pla ne shearing stresses o shear occurs in elements of a circular shaft under a torsion load.

Thin cylindrical and sph erical shells

Thin-walled assumption

For the thin-walled assumptio n to be valid the vessel must have a wall thicckness of no more tha one twentieth) of its radius. Th is allows for treating the wall as a surface, an d subsequently using estimating the hoop stress created by an internal pressure on a thin wall cyli ndrical pressure vesse

where

·        P is the internal pressurre

·        t is the wall thickness

·        r is the inside radius of the cylinder.

·         Ro(Deta) is the hoop stress.

The hoop stress equation for thin shells is also approximately valid for spherical vessels, including plant which the internalturgor pressu re may reach several atmospheres.

Inch-pound-second system (IP S) units for P are pounds-force per square inch (psi). Units for t, and d are i for P are pascals (Pa), while t and d=2r are in meters (m).

When the vessel has closed ends the internal pressure acts on them to d evelop a force along the axis of t known as the axial stress and i s usually less than the hoop stress.