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Chapter: Civil - Mechanics Of Solids - Thin Cylinders, Spheres And Thick Cylinders

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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.

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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