Principal planes and principal stresses, Mechanical Engineering

Assignment Help:

Principal Planes and Principal Stresses:

Define the Principal Planes and Principal Stresses.
Sol.:
When an element in strained body is under action of plane stresses, it is found that there exist 2 mutually perpendicular planes of element on which normal stresses are maximum and minimum and no shear stress is acting on these planes. These planes are called as principal planes.

From the figure given below; the principle planes is determined by
1303_Principal Planes and Principal Stresses.png 
As shear stress on these plane is zero, thus they are also called as shear free plane.

The maximum and minimum principal stresses which are acting on principal planes are called as principal stress.
1255_Principal Planes and Principal Stresses1.png 
The principal stress which is having maximum value is called as "major principal stress" and principal stress having minimum value is called as "minor principal stress".
145_Principal Planes and Principal Stresses2.png 
Where  σx,  σy be direct stresses in  x and y direction and   σxy be the shear stress normal to xy plane.

Resultant stress can be given as follows
1391_Principal Planes and Principal Stresses3.png


Related Discussions:- Principal planes and principal stresses

Bodies stick together after collision the heat liberated, Two bodies of mas...

Two bodies of mass 1 kg and 2 kg move towards each other in mutually perpendicular direction with velocities 3m/s and 2 m/s respectively. If the bodies stick together after collisi

Determine atomic packing factor, Determine APF of BCC and theoretical densi...

Determine APF of BCC and theoretical density in g/cm 3 , assuming the value of r=1.28A 0 and atomic weight is 60g/mol. Determine APF of FCC and theoretical density in g/cm 3 ,

Trusses, Differentiate between perfect, deficient and redundant trusses

Differentiate between perfect, deficient and redundant trusses

Conversion of pressure reading into kpa, Conve r t following reading of p...

Conve r t following reading of pressure to kPa, supposing that the barometer reads 760mm Hg. (1) 90cm Hg gauge (2) 40cm Hg vacuum (3) 1.2m H 2 O gauge Sol: Given

Sewage treatment, Q. Sewage Treatment? Unless located in a metropolitan...

Q. Sewage Treatment? Unless located in a metropolitan area, it is common for plants to have sewage treatment facilities for disposal of sewage and grey water generated in the p

Tempering, TEMPERING: The hardening treatment specified to steel rais...

TEMPERING: The hardening treatment specified to steel raises the hardness but initiates internal stresses due to different cooling rates. The internal stresses are created al

Induction heating, Induction Heating: Alternating current throughout i...

Induction Heating: Alternating current throughout induction coil adjacent the part to be treated induces eddy current via the part that is so heated. The benefit of such heati

Industrial applications of ultrasonics, Industrial applications of ultraso...

Industrial applications of ultrasonics-cleaning, welding, soldering, drilling

Reasons of attribution of raft foundations by rigid method, What are the re...

What are the reasons of attribution of raft foundations by rigid method? The overdesign of raft foundations by rigid method can be attributed to three major reasons: a. Ther

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