Triaxial stress refers to a cond ition where only normal stresses act on an element and all shear.

**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*=2*r*
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.

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