Documents

Strain Energy

Categories
Published
of 14
All materials on our website are shared by users. If you have any questions about copyright issues, please report us to resolve them. We are always happy to assist you.
Related Documents
Share
Description
Strain Energy
Transcript
  Strain Energy. Variational Theorems. Concept of Minimum Potential Energy. The Ritz Method. Strain Energy    energy  –   capacity to do work    potential  energy  –   stored energy as a result of work previously done e.g. wind-up toys, spinning tops    strain energy is a form of potential energy that is stored in materials that have undergone/ been subjected to strain    when the strained material returns to its srcinal dimensions, it does work strain energy  –   energy stored within a material when work has been done on the material    assumption: material remains within elastic region so that all the energy is recovered i.e. no permanent deformations    thus         with reference to the diagram above: work done by (a gradually applied load) in straining material = area under the load-extension curve    the area above the curve is known as the complementary energy   Strain Energy due to Normal (direct) Stress    consider the elemental length of bar,  , with coss-sectional area              Young’s modulus,          From which we get,        Substituting this into      gives         For a bar of length  , total strain energy is          If the bar has constant c/s area           Normal stress,    so                 Strain Energy due to Shear    Putting the above expressions together gives shear strain energy,                Strain energy    Shear modulus    From which we get                  Total energy from shear                Now                     Strain Energy due to Bending    Strain energy becomes          Total strain energy from bending            For constant bending moment                                 Bending theory equation:    Strain energy =work done= now So  Strain Energy due to Torsion    From simple torsion theory          Total strain energy from torsion          Since T is constant in most practical applications    Also from simple torsion theory           So we have            Now the polar moment of inertia for a shaft          Also the volume for a bar is           Substituting these into the above expression for strain energy gives                     Torsion theory    Angle of twist   is in radians    Strain energy = work done =
We Need Your Support
Thank you for visiting our website and your interest in our free products and services. We are nonprofit website to share and download documents. To the running of this website, we need your help to support us.

Thanks to everyone for your continued support.

No, Thanks