Equation for principal stresses and principal planes, Mechanical Engineering

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.

Posted Date: 10/23/2012 2:58:25 AM | Location : United States







Related Discussions:- Equation for principal stresses and principal planes, Assignment Help, Ask Question on Equation for principal stresses and principal planes, Get Answer, Expert's Help, Equation for principal stresses and principal planes Discussions

Write discussion on Equation for principal stresses and principal planes
Your posts are moderated
Related Questions
Charpy impact tests, when required shall comply. Impact tests shall be conducted at the minimum design metal temperature or at a lower temperature and shall meet or exceed energ

Find out the velocity of the mass: A mass of weight 29.4 Newton is subjected into a time dependent force, F(t)  = (3t 3  + 5) along x direction. Find out the velocity of the

What is Conformance Testing Conformance Testing : There was no mechanism for testing processors or resolving errors between two processors.

what are the common application of statics in industry

Compute the coefficient of friction at block: The frame shown in Figure rotates about a vertical axis. The coefficient of friction under block A is 0.4. Compute the coefficien

Explain about the eccentrically loaded footings. ECCENTRICALLY LOADED FOOTINGS When footings have overturning moments and axial loads, the base pressure under the footing wi

how to find out hte optimal sequence and determine the minimun total elapsed time associated with a given problem

Q. Pressure and Temperature in Unfired pressure vessels? The design pressures and coincident maximum and minimum metal temperature, shall be determined by carefully considering

Illustration of CAM A cam rotating at consisted angular velocity operates an oscillating follower. Draw cam profile for the given data: Angular displacement of the follower