5. Theory of Bending of Beams

Try these first

1. 1.

   Define homogeneous material.

   Hint

   Think about how the material looks and behaves in all parts.

2. 2.

   What is the bending moment?

   Hint

   Consider the force applied and its distance from the pivot point.

3. 3.

   What type of material is assumed to be the same throughout according to beam bending theory?

   • Homogeneous
   • Inhomogeneous
   • Anisotropic

   Hint

   Remember the definition of homogeneous.

4. 4.

   The neutral plane in a beam is where:

   • Stress is maximum
   • Stress is zero

   Hint

   Think about where tension and compression balance out.

5. 5.

   A cantilever beam of length 4 m is subjected to a point load of 2000 N at its free end. Calculate the bending stress at a point 1 m from the fixed end. Assume the moment of inertia is 0.001 m^4.

   Hint

   First, determine the bending moment at that distance.

6. 6.

   Discuss the effects on the design of a beam if the assumptions of homogeneous and isotropic materials were not satisfied.

   Hint

   Consider how material inconsistencies can affect structural performance.