Principal planes and principal stresses, Mechanical Engineering

Principal Planes and Principal Stresses:

Define the Principal Planes and Principal Stresses.
Sol.:
When an element in strained body is under action of plane stresses, it is found that there exist 2 mutually perpendicular planes of element on which normal stresses are maximum and minimum and no shear stress is acting on these planes. These planes are called as principal planes.

From the figure given below; the principle planes is determined by
1303_Principal Planes and Principal Stresses.png 
As shear stress on these plane is zero, thus they are also called as shear free plane.

The maximum and minimum principal stresses which are acting on principal planes are called as principal stress.
1255_Principal Planes and Principal Stresses1.png 
The principal stress which is having maximum value is called as "major principal stress" and principal stress having minimum value is called as "minor principal stress".
145_Principal Planes and Principal Stresses2.png 
Where  σx,  σy be direct stresses in  x and y direction and   σxy be the shear stress normal to xy plane.

Resultant stress can be given as follows
1391_Principal Planes and Principal Stresses3.png

Posted Date: 10/23/2012 2:56:07 AM | Location : United States







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