The flexural rigidity value is reduced in middle half portion of the second case fixed end moments which have developed in a beam section will be increases.

Answer:

Introduction: The problem statement discusses the effect of reducing the moment of inertia of the middle half-length of a fixed beam of uniform section carrying a point load at its mid-span. The aim is to determine the change in fixed end moment due to this reduction.

Analysis: The following steps can be used to determine the change in fixed end moment.

1. Determine the moment of inertia of the original beam: The moment of inertia of a fixed beam of uniform section can be calculated using the formula I = (bh^3)/12, where b is the breadth and h is the depth of the beam.

2. Determine the moment of inertia of the middle half-length of the beam: The middle half-length of the beam can be determined as L/4, where L is the length of the beam. The moment of inertia of the middle half-length of the beam can be calculated using the same formula as above.

3. Determine the new moment of inertia of the middle half-length of the beam: Since the moment of inertia of the middle half-length of the beam is reduced to half its previous value, the new moment of inertia can be calculated as I_new = I_original/2.

4. Determine the new fixed end moment: The new fixed end moment can be calculated using the formula M = PL/4, where P is the point load and L is the length of the beam.

5. Determine the change in fixed end moment: The change in fixed end moment can be calculated as ΔM = M_new - M_original.

Conclusion: In conclusion, the change in fixed end moment due to the reduction in the moment of inertia of the middle half-length of a fixed beam of uniform section carrying a point load at its mid-span can be determined using the above steps. The reduction in moment of inertia will result in an increase in the fixed end moment.