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

Production engineering, what are the finishing operation in construction of...

what are the finishing operation in construction of telephone receivers?

Flanged pressure vessel nozzles, Q. Flanged pressure vessel nozzles? Th...

Q. Flanged pressure vessel nozzles? The Designer is responsible for ensuring that the facings, bolt circle, number of bolts, and size of bolts of vessel nozzles, match the mati

Copper alloys, Copper Alloys Some alloys of copper are employed in ind...

Copper Alloys Some alloys of copper are employed in industry for varying causes. Copper forms alloys along with zinc or the brasses, tin or the bronzes, along with tin and pho

Tachometer-electrical instruments , Tachometer: This is used to measure th...

Tachometer: This is used to measure the speed (revolutions) of an engine in revolutions per minute (RPM). This is shown in Figure. Figure : Tachometer

Sketch merchants force diagram, Merchants force diagram. State the assumpti...

Merchants force diagram. State the assumptions made in development of such diagram.

Matlab question please help me, The salary calculation method for employees...

The salary calculation method for employees of a company is as follows: (1) If the number of working hours exceeds 120 hours, an additional 15% will be issued for the excess part;

Foil butt seam welding, Foil Butt Seam Welding This is a modification o...

Foil Butt Seam Welding This is a modification of seam welding, in which thin narrow strips of metal arc introduced between one or both of the circular electrodes and the work p

Illustrate the babcock and wilcox boiler, How the boiler are classified? Sk...

How the boiler are classified? Sketch and define the babcock & Wilcox boiler and also Compare the water tube boiler and fire tube?

Order quantity and reorder point, Example: Order Quantity and Reorder Point...

Example: Order Quantity and Reorder Point: Daily demand for a particular product manufactured by ABC company is distributed normally with a mean of 30 and standard deviation o

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