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

Show application to gyroscope, Q. Show Application to Gyroscope? A fibe...

Q. Show Application to Gyroscope? A fiber optic Gyroscope is used to detect the mechanical rotation of the interference of light. Two beams travel along the fiver in opposite d

Water jet machining, Water jet machining is an advanced method for cutting ...

Water jet machining is an advanced method for cutting plates using a high-velocity water jet mixed with abrasive powder. The jet comes out of a nozzle A of diameter d and follows t

Shielding gas, SHIELDING GAS The primary function of the shielding gas ...

SHIELDING GAS The primary function of the shielding gas is to exclude the atmospheric air from the arc zone. However, the shielding gas has significant influence on the arc cha

A circumferential fin rectangular profile is constructed , A circumferentia...

A circumferential fin rectangular profile is constructed of Cu and surrounds a tube having a diameter of 1.25 cm.  The fin length is 6 mm and its thickness is 0.3 mm. The fin is ex

Forces, what are the practical applications and use of finding uniform dist...

what are the practical applications and use of finding uniform distributed load, concentrated point load, inclined point load, roller supported beam.

Find the resultant hydrostatic force, Question. Consider the triangular lam...

Question. Consider the triangular laminar D for given b and h shown below. (a) Find x L (s) and x R (s), the left and right ends of the elementary strip, of thickness ds, a

About water engines, when the water is artificially pressurized in a water ...

when the water is artificially pressurized in a water turbine, what is its power and the speed of rotation of a rotor?

Vibration, what is vibration in terms of mechanical term

what is vibration in terms of mechanical term

Compute the total force which shall be acting on the springs, Compute the t...

Compute the total force which shall be acting on the springs: An automobile of mass 1300 kg, travelling at a speed of 60 kmph hits a depression in the road that has a radius 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