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 radial dimension commands, The Radial Dimension Commands There are ...

The Radial Dimension Commands There are 2 main radial dimension commands, DIMDIAMETER & DIMRADIUS. Both commands result in  similar looking dimension so AutoCAD automatically i

Design varies with scale of operation, Design varies with scale of operatio...

Design varies with scale of operation The design of a fermenter varies with scale of operation from lab (1-20L), to pilot (up to 5000L) to production (to >200,000L) scales. Th

Refrigeration, In a steam jet refrigeration system, the ejector extracts 3....

In a steam jet refrigeration system, the ejector extracts 3.3 m3/s of saturated water vapor at a temperature of 7.2 °C from the flash chamber. The return water from the cooling coi

determine the minimum cross section area of graph, To design a cantilevere...

To design a cantilevered truss to support the loads shown in the figures, two layouts are proposed as shown in Figs. A and B. All truss members are steel with allowable stress of 2

Two coplanar forces are acting on the rigid body, Steps for solving the pro...

Steps for solving the problems when more than two coplanar forces are acting on the rigid body: The steps are as; 1. Check the Problem for the concurrent or Non concurren

Explain the disadvantages of automation, Explain the Disadvantages of Autom...

Explain the Disadvantages of Automation? a) Initial cost is higher providing additional features in machine tools. b) Skilled personnel's are required for maintenance of aut

Flow work - thermodynamics , Flow work: Flow work is energy possessed ...

Flow work: Flow work is energy possessed by the fluid by virtue of its pressure. Displacement Work: When piston moves in cylinder from position 1 to 2 with vo

Define the ideal surface roughness, Define the Ideal Surface Roughness ...

Define the Ideal Surface Roughness The ideal surface roughness represents the best possible finish which may be obtained for a given tool shape and can only be approached if bu

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