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# Principal Stress Calculator

Principal stress refers to the extreme values of normal stress that a plane can possess at some point. It is a measurement of maximum normal and minimum normal stress in a plane. In other words, it is the magnitude of normal stress acting on a principal plane. Use this Online Solid Mechanics Calculator to find the maximum and minimum principal stress. Enter the input values in the principal stress calculator and find the maximum, minimum and angle of shear stress.

## Solid Mechanics Calculator

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Principal stress refers to the extreme values of normal stress that a plane can possess at some point. It is a measurement of maximum normal and minimum normal stress in a plane. In other words, it is the magnitude of normal stress acting on a principal plane. Use this Online Solid Mechanics Calculator to find the maximum and minimum principal stress. Enter the input values in the principal stress calculator and find the maximum, minimum and angle of shear stress.

#### Formula:

Maximum Principal Stress = ((σx+ σy)/2) + √(((σx - σy)/2) 2+ h2) Minimum Principal Stress = ((σx + σy)/2) - √(((σx - σy)/2) 2+ h2) Maximum Shear Stress = √(((σx - σy)/2)2+h2) Angle of Principal Stress = (tan-1((2×h) / (σx - σy)))/2 Angle of Maximum Shear Stress = (tan-1((2×h) / (σx - σy)))/2+ 45 Angle of Minimum Shear Stress =(tan-1((2×h) / (σx - σy)))/2- 45 Where, σx = Normal Stress σy = Normal Stress h = Shear Stress

### Example

Find the principal stress using the solid mechanics formula, if normal stress (σx and σy values are 12, 15 Pa and shear stress is 8 Pa.

#### Maximum Principal Stress

= ((12+15) / 2) - √(((12 - 15)/2)2+ 82)
= 21.6394 Pa

#### Minimum Principal Stress

= ((12 + 15)/2) - √(((12 - 15)/2)2)+ 82)
= 5.3606

#### Maximum Shear Stress

= √(((12 - 15) / 2) 2+ 82)
=8.1394 Pa

#### Principal Angle

= (tan-1((2×8) / (12 - 15)))/2
=50.3098 °

#### Angle of Maximum Shear Stress

= (tan-1((2×8) / (12 - 15)) )/2+ 45
= 95.3098 °

#### Angle of Minimum Shear Stress

= (tan-1((2×8) / (12 - 15)))/2 - 45
= 5.3098°