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.
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