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

Types of couple - mechanics, Types of couple: Explain about different...

Types of couple: Explain about different types of couple?  Sol.: There are mainly two types of couples: 1 . Clockwise Couple   A couple whose tendency

Concurrent force system - mechanics, Concurrent force system: It state...

Concurrent force system: It state that if force acting at a point on a rigid body, it can be considered to act at any other point on its line of action, given this point is ri

Categorization of geometric models, Q. Categorization of Geometric models? ...

Q. Categorization of Geometric models? Modern CAD systems define objects in 3-D. Thus, the designer can construct 3-D model of objects conveniently and store the database of th

Determine the acceleration of each block, Determine the acceleration of eac...

Determine the acceleration of each block: In the system of associated blocks shown in figure the coefficient of kinetic friction under blocks A and C is 0.20. Determine the ac

Predict the output of load - curved beam theory, A load cell based on a "pr...

A load cell based on a "proving ring" is shown below.  The circular portion of the load cell has an inner radius of 1.25 in and outer radius of 1.50 in.  The ring has a depth (i.e.

Requirement of temperature scale - thermodynamics, Requiremen t of Tempera...

Requiremen t of Temperature Scale: The temperature scale on which temperature of the system can be read is required to assign the numerical values to the thermal state of the

Computer aided visualization, There are various methods to visualize the ...

There are various methods to visualize the design process which can be summarized as given below: a. An automated drafting tool and presentation of graphics. b. A means

Concept of absolute thermodynamic temperature scale, (a) Write short note o...

(a) Write short note on steady flow energy equation and its applications. (b) A heat engine operating between two reservoirs at 1000k and 300k is used to drive a heat pump which

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