Equation for principal stresses and principal planes, Mechanical Engineering

Assignment Help:

Equation for principal stresses and principal planes:

Derive equation for principal stresses and principal planes for the element subjected to compound stresses.

Sol.: For state of stress shown in the given figure the normal stress and shear stress on any oblique plane inclined at angle θ is determined by,
445_Equation for principal stresses and principal planes.png 
1474_Equation for principal stresses and principal planes1.png 
As the principal plane should carry normal stress, shear stress acting on it is to be zero.
That is,
   1017_Equation for principal stresses and principal planes2.png 
This provides one of the principal planes, other principal plane shall be perpendicular to this plane.

Substituting value of θ in σn expression by rearranging as below.
343_Equation for principal stresses and principal planes3.png 
It provides the values of principal stresses. The largest one is called as major and smaller is called as minor principal stress.


Related Discussions:- Equation for principal stresses and principal planes

Working of torsion dynamometer, Can you explain the principal on which a to...

Can you explain the principal on which a torsion Dynamometer works ? Illustrate with details the evaluation involved in finding the power transmitted.

Types of coated electrodes-iron powder electrodes, Iron Powder Electrodes ...

Iron Powder Electrodes Iron powder is a widely used covering ingredient. It is incorporated in certain coverings to the extent of one half of the total weight. Iron Powder impart

Mechanical properties of materials, A tensile test on a specimen having an ...

A tensile test on a specimen having an initial diameter of 13.11 mm and an initial gauge length of 200.0 mm, gave the following data:

The welding arc, THE WELDING ARC The heat that is developed at the cath...

THE WELDING ARC The heat that is developed at the cathode and anode of an arc discharge is able to melt most of the metals and alloys. Hence, the arc is used as an intense heat

What is hybrid sweep, Hybrid Sweep It combines linear and/or non-linear...

Hybrid Sweep It combines linear and/or non-linear sweep via set operations. In this case, two point sets are swept in two different directions and the two resulting swept volum

Explain the methods of solid modeling, Explain the Methods of solid modelin...

Explain the Methods of solid modeling The various methods for representing the solids are : (i)  Half-space method (ii)  Boundary representation method (b-rep) (iii)

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd