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

Comparison of disc and drum type brakes drum brake , Comparison of Disc and...

Comparison of Disc and Drum type Brakes Drum Brake Disc Brake Drum brakes have cooling problem because the friction occurs at internal surfaces,

Trusses, Differentiate between perfect, deficient and redundant trusses

Differentiate between perfect, deficient and redundant trusses

Determine time required to stop the automobile, Determine time required to ...

Determine time required to stop the automobile: A 20KN automobile is moving at speed of 70Kmph when brakes are fully applied causing all the four wheels to skid. Determine ti

Arc blow, ARC BLOW In certain cases depending upon where the return pa...

ARC BLOW In certain cases depending upon where the return path connections are given for the arc current, the arc may be deflected towards a direction of weaker electro magnet

Fracture mechanics, difference between stress intensity factor and stress c...

difference between stress intensity factor and stress concentration factor

Evaluate the speed of train, Evaluate the speed of train: A train of ...

Evaluate the speed of train: A train of mass 200KN has frictional resistance of 5N per KN. Speed of train, at the top of an inclined of 1 in 80 is 45 Km/hr. Find speed of tra

Varignon theorem - mechanics, Varignon theorem: State Varignon's theo...

Varignon theorem: State Varignon's theorem. How it helps in determining of the moments? In which type of condition is it used? Sol.: Varignon's theorem also called Law

Determine about the pier and well foundations, Pier and Well Foundations ...

Pier and Well Foundations Pier foundations are used when the loads to be transmitted are heavier than loads those can bc acconlplished by piles. They are essentially bearing i

Thermodynamics, microscopic and macroscopic view points

microscopic and macroscopic view points

.high lead copper alloy castings, I have faced a serious problem of Lead se...

I have faced a serious problem of Lead segregation and porosity in Copper Tin Zn alloy containing 26-30 % lead sand castings.Can anybody throw light on this

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