PLANE STRESS AND TRANSFORMATIONS
Plane stress transformation tool was developed to calculate normal stresses and
shear stress at a specific point for plane stress state (σ_{z}=τ_{zx}=τ_{zy}=0)
after the element is rotated by θ around the Zaxis. Results are also shown with Mohr's Circle representation.
If the plane stresses are known for a member, then plane stresses for different orientation
(in the same plane) can be
calculated with this calculator.
The formulas used for the calculations are given in the List of Equations
section.
Calculator:
Note: Use dot "." as decimal separator.
RESULTS 
Parameter 
Symbol 
Value 
Unit 
Normal stress
after transformation 
σ_{x}' 


MPa

Normal stress
after transformation 
σ_{y}' 


Shear stress
after transformation 
τ_{xy}' 


Definitions:
Mohr’s Circle: A graphical method to represent the plane stress (also strain) relations.
It’s a very effective way to visualize a specific point’s stress states, stress transformations for an angle,
principal and maximum shear stresses.
Normal Stress: Stress acts perpendicular to the surface (cross section).
Plane Stress: A loading situation on a cubic element where two faces the element is free of any stress.
Such a situation occurs on free surface of a structural element or machine component, at any point of the
surface of that element which is not subjected to an external force. Another example for plane stress is structures which are built from sheet metals where stresses across the thickness are negligible.

Plane stress example  Free surface of structural element 
Shear stress: A form of a stress acts parallel to the surface (cross section) which has a cutting nature.
Stress: Average force per unit area which results strain of material.
List of Equations:
Parameter 
Symbol 
Formula 
Normal stress
after transformation 
σ_{x}' 
(σ_{x}+σ_{y})/2+Cos(2θ)(σ_{x}σ_{y})/2+τ_{xy}Sin(2θ) 
Normal stress
after transformation 
σ_{y}' 
(σ_{x}+σ_{y})/2Cos(2θ)(σ_{x}σ_{y})/2τ_{xy}Sin(2θ) 
Shear stress
after transformation 
τ_{xy}' 
Sin(2θ)(σ_{x}σ_{y})/2+τ_{xy}Cos(2θ) 
Examples:
Link 
Usage 
Pressure Vessel

An example about the calculation of stresses on a pressure vessel,
evaluation of yield criteria of material and stress transformation to find shear
and perpendicular stresses on welding of the cylindrical body of the pressure
vessel. 
Reference: