Expression for strain energy, Mechanical Engineering

Assignment Help:

Expression for strain energy:

Derive an expression for strain energy because of torsion.                                         

Sol.: The work done in straining shaft within elastic limit is called as strain energy. Consider a shaft having diameter D, and Length L, subjected to gradually applied torque T. Let θ be angle of twist. Energy is stored in shaft because of this angular distortion. This is called as torsional energy or Torsional resilience.

Torsional energy or strain energy = Work done by the torque = average torque X angular twist.

384_Expression for strain energy.png

Thus; Strain energy per unit volume is 1/4th  ratio of square of shear stress to modulus of rigidity. For the hollow shaft: U = [ τ2.(D2  + d2)/4.G.D2].Volume of shaft

For the Solid shaft (d = : U = [ τ2/4.G].

Volume of shaft

For very thin hollow shaft (d = 0): U = [τ2/2.G].Volume of shaft

 


Related Discussions:- Expression for strain energy

The auto component sector-automobiles industry growth , The auto component ...

The auto component sector has also posted significant growth of 20 percent in 2003-04, and achieved a sales turnover of Rs. 30,640 crore (US$ 6.7 billion). Further, there is a pote

Direct current, Direct Current ( DC ) :  The direct current flows through...

Direct Current ( DC ) :  The direct current flows through a wire in one direction and it remains same over time. The current from battery is always direct current. Direc

Determine the maximum stress - thick cylinder, Determine the maximum stress...

Determine the maximum stress - thick cylinder: A thick cylinder of steel with an internal diameter of 100 mm & external diameter of 200 mm is subjected to an internal pressure

Theory of machine, analytical method for determining the acceleration and v...

analytical method for determining the acceleration and velocity?

Heat conduction duhamels method, Procedure for solving a problem using duha...

Procedure for solving a problem using duhamels method

Perform a beam analysis, You need to sketch shear force and bending moment ...

You need to sketch shear force and bending moment diagrams and estimate maximum bending and shear stresses acting on the beam using your knowledge in beam analysis.  Please note

Process of steam generation unit, Q. Process of Steam generation unit? ...

Q. Process of Steam generation unit? BFW from water treatment area is sent to the BFW Booster pumps at temperature around 105°C. The BFW is then heated and fed to the HP BFW Pu

Define the winged-edge representation, The Winged-Edge Representation P...

The Winged-Edge Representation Perhaps the oldest data structure for a b-rep is Baumgart's winged-edge data structure. It is quite different from that of a wire-frame model, be

Describe the break-even-analysis, What is Time-Study ? How the standard tim...

What is Time-Study ? How the standard time is determined in Time-Study ? What are the Merit-Rating ? Illustrate various methods of Merit-Rating. Describe the Break-Even-Analy

Numerical problems based on overhanging beam, Numerica l Problems Based on...

Numerica l Problems Based on Overhanging Beam: Q: Draw Shear force diagram for the simply supported beam loaded as shown in the figure given below. Sol.: Let the

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