Respuesta :
The principal stresses are those that act on the principal planes. There are three principal stresses on a point under force.
What is principal stress?
The principal stresses are those that act on the principal planes. The plane bearing the greatest normal stress is referred to as the principal plane, and the stress acting on it is referred to as the principal stress.
When a force is applied on an inclined plane, the force can be divided into two subparts, the first component of the force is perpendicular to the plane and is known as the normal force, while the second component of the force is parallel to the plane and is known as the shear stress.
The principal stresses at a point can be found using the following formulas, therefore, the principal stresses will be,
[tex]{\sigma}'_{xx}=\sigma_{xx}cos(2\theta)+\sigma_{yy}sin(2\theta)+2\tau_{xy}sin(\theta)cos(\theta)[/tex]
[tex]{\sigma}'_{yy}=\sigma_{xx}sin(2\theta)+\sigma_{yy}cos(2\theta)-2\tau_{xy}sin(\theta)cos(\theta)[/tex]
[tex]{\tau}'_{xy}=(\sigma_{yy}-\sigma_{xx})sin\theta cos\theta+\tau_{xy}(cos2\theta-sin2\theta)[/tex]
Hence, there are three principal stresses on a point under force.
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