1. Non-uniform Bending

Try these first

1. 1.

   Define non-uniform bending.

   Hint

   Consider how bending moment differs from pure bending.

2. 2.

   What happens to shear force when bending moment varies?

   Hint

   Think about the relationship between bending moment and shear force.

3. 3.

   In non-uniform bending, shear force must be:

   • Zero
   • Constant
   • Non-zero

   Hint

   Think about what happens when the moment changes.

4. 4.

   True or False: In pure bending, shear stress is always zero.

   • True
   • False

   Hint

   Recall the definitions of pure vs non-uniform bending.

5. 5.

   A simply supported beam of length L experiences a distributed load varying linearly from 0 to w across its length. Calculate the shear force and bending moment at a distance 'x' from the clamped end.

   Hint

   Consider the load's distribution when calculating reactions and internal diagrams.

6. 6.

   For an I-beam with varying flange widths, derive an expression for the shear stress at several locations and discuss the implications on structural integrity.

   Hint

   Compare stress distributions at different points, particularly near flanges versus the web.