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

Airport layout - planning a new airport, Airport Layout: The main com...

Airport Layout: The main components of an airport are: (a)        Runways (b)       Taxiways (c)        Apron (d)       Terminal area (i)        Terminal build

Steam engines, Steam engines: Steam engine is heat engine which conver...

Steam engines: Steam engine is heat engine which converts heat energy to mechanical energy. The pressure energy of steam acts on piston and piston is moved to and fro in a cyl

Frictionless pulley, Frictionless pulley: The frictionless pulley A ...

Frictionless pulley: The frictionless pulley A is being supported by two bars AB and AC which are hinged at points B and C to a vertical wall. The flexible cable D

Screw conveyors, Screw Conveyors: Screw conveyors are used principally f...

Screw Conveyors: Screw conveyors are used principally for transmitting materials in the form of powder or paste with the application of rotating screw. For example feedin

Describe organic binders and its working, Q. Describe Organic binders and i...

Q. Describe Organic binders and its working? Organic binders: The binders are most frequently used in core making. Cereal binders are obtained from wheat, corn or rye; resins

Quantitative Project Paper, Could I have 3 topic ideas with problem stateme...

Could I have 3 topic ideas with problem statement and research questions for each to pick one and send it to the expert? I have a project in Manufacturing Engineering, Master leve

Classification of welding based on mode of energy transfer , Classification...

Classification of welding Based on Mode of Energy Transfer Energy is converted from one form to another. Any form of energy can be converted to heat energy, which can be used f

Electric resistance welding, ELECTRIC RESISTANCE WELDING Electric resis...

ELECTRIC RESISTANCE WELDING Electric resistance welding is an important and widely applied non fusion welding process. This write up covers the basic principles of various resi

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