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

Simple Mechanisms, I have an assignment on kinematic chains.I have to tell ...

I have an assignment on kinematic chains.I have to tell the type of chain whether it is locked,constrained or unconstrained?? I am facing problem in counting number of joints,pair

Qualifications of welding procedures, Q. Qualifications of Welding Procedur...

Q. Qualifications of Welding Procedures? The Fabricator shall prepare and submit for review by Welding Procedure Specifications (WPS) and Procedure Qualification Records (PQR),

Working of drum type brake , Working of Drum Type Brake: When we apply br...

Working of Drum Type Brake: When we apply brake to the motorcycle that means we are applying force 'F' to the brake shoes. This force pushes the brake shoes towards the drum surf

Super charger, types of compressor used in super chasrger

types of compressor used in super chasrger

Flange assembly with bolt elongation measurement, Q. Flange Assembly with B...

Q. Flange Assembly with Bolt Elongation Measurement? Bolt elongation measurement may be used, with COLT engineering approval, at flanges where Hydraulic Bolt Tensioners are imp

Define the skid fabrication, Q. Define the skid fabrication? Unless not...

Q. Define the skid fabrication? Unless noted otherwise in this specification, skid fabrication shall be in accordance with GS-904-0510, GS-904-0511 and GS-904-0515. Dimensio

Chemical machining., chemical milling is used in aircraft plant to create p...

chemical milling is used in aircraft plant to create pockets in wing sections made of an aluminium alloy. the starting thickness of one work part is 20 mm.a series of rectangular s

Determine steady state error, Derive mathematical equation for the time res...

Derive mathematical equation for the time response of a first order system subjected to ramp input. Draw the response curve and determine steady state error. Give some examples of

Horizontal hinge, 2 x 2 m square gate opens clockwise on a horizontal hinge...

2 x 2 m square gate opens clockwise on a horizontal hinge located at point A, which is 100 mm below the centroid of the gate. The gate sits against solid rubber blocks which create

Shear force and bending moment, question no 2,page no 84 of strenght of mat...

question no 2,page no 84 of strenght of materials by G H Ryder

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