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

Storage and handling of epoxy powder, Q. Storage and Handling of Epoxy Powd...

Q. Storage and Handling of Epoxy Powder? Coating materials shall be stored, handled and applied in strict accordance with procedures as outlined by the coating manufacturer, ex

Pliers tool and equipment , Pliers: Pliers are used just for gripping or w...

Pliers: Pliers are used just for gripping or wire cutting and should never be used as substitute for spanners. The following types of plier are used : (a) Side cutting pliers

Angular dimensions-autocad, Angular Dimensions There is only one comman...

Angular Dimensions There is only one command in this section and it is used to annotate angular measurements. The Angular Dimension Command The Angular command is amazi

Determine the net rate of work output, A piston and a cylinder machine obta...

A piston and a cylinder machine obtains a fluid system, which passes through a complete cycle of four processes. In the mean while a cycle the sum of all heat transfer is 150KJ and

Hot and cold working, What is the difference between hot and cold working

What is the difference between hot and cold working

Determine the convection coefficient associated with airflow, An experiment...

An experiment to determine the convection coefficient associated with airflow over the surface of a thick stainless steel casting involves insertion of thermocouples in the casting

Laser sources-lasers with solid state lasing mediums, Lasers with Solid Sta...

Lasers with Solid State Lasing Mediums For an active medium, the solid state laser uses lasing ions which are suspended in a rod shaped solid matrix. These "dopants" in the rod

Essay, which topics i should take from mechanical engineering to compare th...

which topics i should take from mechanical engineering to compare them

Explain the electron beam machining, Explain the Electron Beam Machining ...

Explain the Electron Beam Machining Electron Beam Machining is the metal removal process by a high velocity focused stream of electrons which heats, melts and vaporizes the

White worth quick return mechanism, Which mechanism more efficiency? What i...

Which mechanism more efficiency? What is the reason ?

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