2.2. Analysis

Try these first

1. 1.

   Define non-uniform bending.

   Hint

   Think about what happens to the bending moment.

2. 2.

   What is the relationship between bending moment and curvature?

   Hint

   Recall the formula we discussed.

3. 3.

   What happens to shear force when the bending moment is non-constant?

   • It becomes zero
   • It is constant
   • It becomes non-zero

   Hint

   Think about what varying moments imply.

4. 4.

   True or False: An I-beam experiences the same shear stresses throughout its length.

   • True
   • False

   Hint

   Consider how loads affect different points along the beam.

5. 5.

   Given a cantilever beam with a point load of 100 N at the free end and length 2 m, calculate the shear stress at a section 0.5 m from the fixed end.

   Hint

   Use the bending moment equation first to derive V.

6. 6.

   Analyze a simply supported beam with a varying distributed load. Derive the equations for stress distribution at various sections.

   Hint

   Remember to balance forces and moments at each section.