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

Thermodynamics, define the first and second law of thermodynamics.

define the first and second law of thermodynamics.

Performance criterion of a steam power plant, Performance criterion of a st...

Performance criterion of a steam power plant: Sol. :   The design of power plant can be determined largely by the consideration of capital cost and operating cost; the forme

Brass is an alloy of which materials, Brass is an alloy of (A) Copper ...

Brass is an alloy of (A) Copper and zinc.  (B) Copper and iron. (C) copper and Aluminium.  (D) Copper and tin. Ans: Brass is an alloy of copper and zin

Machine design 1, Our sir asked us to design a knuckle joint...they gave us...

Our sir asked us to design a knuckle joint...they gave us only the tensile force applied on the joint as 50kn...and told us to find the appropriate material..so what can we use???

What is a cotter joint, These parts of joints are used to connect two rods,...

These parts of joints are used to connect two rods, which are under compressive or tensile stress. The ends of the rods are in the manner of a socket and shaft that fit together an

What are the types of interface, What are the Types of interface An int...

What are the Types of interface An interface can be regarded as an aggregate of conditions, rules and conventions which describes the information exchange, between two communic

Ultrasound bolt load monitoring, Q. Ultrasound Bolt Load Monitoring? Ul...

Q. Ultrasound Bolt Load Monitoring? Ultrasound measurement of bolt stresses, using ‘Bolt Scope', should be used on: • All bolts tightened by tensioning. • All bolts in hy

Find out load carried and compressive stress - steel bar, Find out load car...

Find out load carried and compressive stress: The concrete column 300mm x 300mm in section can be reinforced by 10 longitudinal 20mm diameter round steel bars. The column car

Determine the brake power of an engine, Determine the Brake power of an Eng...

Determine the Brake power of an Engine which is running at a fixed speed of 300 r.p.m. and carries a rope brake Dynamometer. The Dead weight on the spring balance and engine readin

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