PRINCIPAL & MAXIMUM SHEAR STRESS CALCULATOR FOR PLANE STRESS
Principal stress calculator is developed to calculate principal and maximum
shear stresses, principal and maximum shear stress angles and Von Mises stress at a
specific point for plane stress (σ_{z}=τ_{zx}=τ_{zy}=0). Mohr's Circle is also drawn
according to input parameters.
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 
Maximum principal stress 
σ_{max} 


MPa

Minimum principal stress 
σ_{min} 


Maximum shear stress* 
τ_{max} 


Average principal stress 
σ_{avg} 


Von Misses stress 
σ_{mises} 


Angle of principal stresses ** 
θ_{p} 


deg 
Angle of maximum shear stress ** 
θ_{s} 


Note 1:
*Maximum shear stress given in results is the maximum inplane shear stress. For
outplane shear stress, check 3D stress analysis.
Note 2:** There are 2 values for this parameter. The first value is shown in the table and the other value is 90°
apart from the first one.
Definitions:
Maximum Shear Stress Angle: The angle of orientation at which maximum
inplane shear stress occurs for
a specific point.
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 
Principal Stress: Maximum and minimum normal stress possible
for a specific point on a structural element. Shear stress is 0 at the orientation where principal stresses occur.
Principal Angle: The angle of orientation at which principal stresses occur for a specific point.
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.
Supplements:
List of Equations:
Step 
Parameter/Condition 
Symbol 
Equation 
1 
Maximum principal stress 
σ_{max} 

2 
Minimum principal stress 
σ_{min} 

3 
Principal angle 
θ_{p} 

4 
Maximum shear stress angle 
θ_{s} 

5 
Maximum shear stress 
τ_{max} 

Symbol 
Parameter 
σ_{x} 
Normal stress in X direction 
σ_{y} 
Normal stress in Y direction 
τ_{xy} 
Shear stress perpendicular to X axis and in Y direction. 
Examples:
Link 
Usage 
Torsion Of Solid Shaft

An example about the calculation of torsional stress on stepped shaft. After
calculation of torsional stress, principal stresses are calculated and
evaluation of yield criteria of material is done with these stresses. 
Reference:
 Beer.F.P. , Johnston.E.R. (1992). Mechanics of Materials , 2nd edition. McGrawHill