9.2.1. Internal Work

Try these first

1. 1.

   What is strain energy?

   Hint

   Think about how much energy a material can hold as it bends or stretches.

2. 2.

   What does the Modulus of Elasticity (E) represent?

   Hint

   Consider how stretching affects the material.

3. 3.

   What is the primary formula for calculating strain energy in axial members?

   • U = ∫(σ²/(2E) dVol)
   • U = ∫(τ²/(2G) dVol)
   • U = σ * ε

   Hint

   Remember, this relates directly to how much force is distributed over an area.

4. 4.

   True or False: Shear modulus has no influence on strain energy calculations for torsional members.

   • True
   • False

   Hint

   Think about how materials respond to twisting.

5. 5.

   A steel beam is subjected to an axial load of 150 kN. If the beam has a cross-sectional area of 0.01 m² and an elastic modulus of 210 GPa, calculate the strain energy stored in the beam if it elongates by 1 mm.

   Hint

   Use the relationships established for stress and strain to formulate the solution.

6. 6.

   A circular shaft with a radius of 50 mm is subjected to a torsional moment that generates a shear stress of 60 MPa. Calculate the strain energy per unit volume if the shear modulus is 80 GPa.

   Hint

   Make sure to reference the relationship for torsional strain energy derivation.