2.2. Bending energy

Try these first

1. 1.

   Define bending energy in your own words.

   Hint

   Think about how beams store energy under loads.

2. 2.

   What formula relates stress to bending moment?

   Hint

   Focus on the relationships between forces and geometry.

3. 3.

   What is the primary factor affecting bending energy in a beam?

   • A. Axial force
   • B. Bending moment
   • C. Shear force

   Hint

   Think about what causes beams to store energy in bending.

4. 4.

   True or False: The curvature of a beam increases with higher bending moments.

   • True
   • False

   Hint

   Consider how loads affect the geometry of beams.

5. 5.

   A simply supported beam with a point load at its center stores how much energy when it bends? Calculate using appropriate bending moment and curvature relations.

   Hint

   Use the load to determine the maximum moment and apply it to the energy equation.

6. 6.

   Given a beam with varying cross-section, derive the general expression for bending energy considering the moment of inertia's variation.

   Hint

   Reflect on how integration over varying cross-sections influences overall energy.