ALL GATE CONCEPTS MECH DEFINITIONS MECHANICAL THEORY

Principal Stresses,Principal planes,Maximum Shear stress,Maximum Shear Stress Planes with Formulas

Principal Stresses,Principal planes,Maximum Shear stress,Maximum Shear Stress Planes with Formulas:When you are going for any interview or writing any competitive exam then a compulsory question will be asked on either of the above terms interms of a Definition or a Numerical.If it is a numerical question,it generally carries 2 marks and if it is a theory question,it may be 1 mark or 2 marks.So in this article,I am focussing on the definitions as well as formulas related to those terms i.e.Principal Stresses,Principal planes,Maximum Shear stress,Maximum Shear Stress Planes with Formulas so that we can solve any type of problem in an easier manner.

Principal Stresses,Principal planes,Maximum Shear stress,Maximum Shear Stress Planes with Formulas
Principal Stresses,Principal planes,Maximum Shear stress,Maximum Shear Stress Planes with Formulas

Principal Stresses,Principal planes,Maximum Shear stress,Maximum Shear Stress Planes with Formulas:

The definitions and their representation was presented below either in the form of text or in the form of Images.If you want formulas,then try to copy from the images.

Principal Stresses:

  • The maximum or minimum normal stress is the principal stress.
  • These principal stresses are used in design.
 principal stress
principal stress

 Principal planes:

  • The plane on which principal stresses will be acting is called as principal plane.
  • On the principal plane,shear stress must be zero.
  • Any plane in the material without shear stress is by default principal plane.
  • In a 2-D system, there are two principal planes separated by 90 degrees.On these planes,shear stress is zero.
principal planes
principal planes

 Maximum Shear stress(in 2D plane stress system):

 The Maximum Shear Stress in 2D Plane stress system is presented below.

max shear stress and max shear stress planes
max shear stress and max shear stress planes

 Maximum Shear Stress Planes:

The plane on which maximum shear stress is acting called as maximum shear stress plane and the formula of  Maximum Shear Stress Planes will be collected from the above image placed in maximum shear stress section.

  • In a 2D system there are two (Tow max) planes separated by 90 degrees.
  • The angle between any one principal plane and the nearest (Tow max) plane is 45°.
  • On (Tow max) plane, there will be a normal stresses and which is in the middle of (Sigma 1) and (Sigma 2) by magnitude.
  • The magnitude of shear stress on mutually perpendicular planes must be the same.
  • The sum of normal stresses on mutually perpendicular planes must be constant.

This is the complete explanation of Principal Stresses,Principal planes,Maximum Shear stress,Maximum Shear Stress Planes with Formulas in a detailed manner.If you have any doubts,then you can ask us from the comments section.

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