Strain Energy

Strain Energy = Work done

Or, Force x Displacement

U = (σ2/2E) x Volume

Unit: Nm, or kNm, or Nmm

Strain Energy DUE TO1. Elastic

1. Resilience 2. Proof Resilience3. Modulus of Resilience

2. Loading 1. Gradual2. Sudden3. Impact4. Shock

3. Effects1. Shear2. Bending3. Torsion

Some definitions

• ‘Elasticity’ can be defined as the ability of a body to store energy

• ‘Resilience’ can be defined as the ability of a body to regain its original shape

Work Done = Work Stored

Work Done = ½ P δlWork Stored = ½ σ A δl

Strain Energy= ½ R δl

P

Rδl

Strain Energy DUE TO Action – Gradual

σ = P/A; u = (σ2/2E) V

– Suddenσ = 2P/A; u = (σ2/4E) V

– Impact

σ = P/A + √[(P/A)2 + (2EPh)/(Al)]; u = ?

– Shock

u = (σ2/2E) V

Strain Energy DUE TO Effect

• Shearu = (τ2/2G) x V

• Bendingu = 0∫l {(M2) dx / (2EI)}

• Torsionu = (τ2/4G) x V Solid Shaftu = (τ2/4G) x [(D2 + d2)/d2] x V Hollow Shaft

Draw Diagraames in

Tutorial books.

Tutorials

1. Define 1. Strain Energy2. Resilience3. Impact Factor4. Load Factor

2. State two differences between Proof Resilience (Up) and Modulus of Resilience (Um)

3. Derive to Work out ‘U’ i.e. strain energy due to Impact Loading4. Draw neat diagrammes for Strain energy due to Shear, Bending and Torsion5. Rethaliya Exercises. Page 463. Exercises 1, 2, 5 & 8