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

Working principle of ignition system , Working Principle of Ignition System...

Working Principle of Ignition System: An alternating current (AC) is generated when a magnet moves between two stationary coils. In a magneto, a coil of wires moves between two m

Screw jack and friction, Give the equivalence of screw jack and friction on...

Give the equivalence of screw jack and friction on an inclined plane

What is full-scale loading for load cell, A load cell based on a simply-sup...

A load cell based on a simply-supported beam with rectangular cross-section is shown below. The beam is made using a tool steel alloy with E = 200 GPa, ν = 0.285. Two strain gages

Determine of poissons ratio, a) Show that if E is assumed to be correctly c...

a) Show that if E is assumed to be correctly calculated, an error of 1% in the evaluation of C will involve an error of about 6% in the determine of Poisson's ratio when its correc

If engine does not start at cranking speed troubleshooting , If Engine Does...

If Engine Does Not Start at Cranking Speed Causes of Problem Remedy Incorrect electrode gap of spark plug Fouled spar

What do you mean by vibration, (a) What do you mean by vibration and the te...

(a) What do you mean by vibration and the terminology used in it to be defined? (b) A body is subjected to two Harmonic motions as provided below x 1 = 10 sin (wt + π/6) and x

Evaluate thickness of leaves, A semi-elliptical laminated vehicle spring to...

A semi-elliptical laminated vehicle spring to took a load of 6000 N is to consist of seven leaves 65 mm wide, two of the leaves extending the full length of the spring. The spring

Complete outer clutch lugs for deep cuts, Complete outer clutch lugs for de...

Complete outer clutch lugs for deep cuts: Visually check for any deep cuts formed on the outer complete clutch lugs.

Wind induced vibration of vertical vessels, Q. Wind Induced Vibration of Ve...

Q. Wind Induced Vibration of Vertical Vessels? Vertical vessels having a height-to-diameter ratio (h/D) (does not include insulation thickness but does include skirt height) gr

Explain the heterogeneous system - thermodynamic, Explain the Heterogeneous...

Explain the Heterogeneous System - Thermodynamic Heterogeneous System: A system, which involves two or more phase, is known as heterogeneous system. Such as, Water plus steam,

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