Introduction:
In structural engineering, beams are subjected to various types of loads such as vertical loads, horizontal loads, and moments. Bending moment is one of the important factors that affect the behavior and design of beams. It refers to the internal moment that develops within a beam due to the applied loads. The bending moment varies along the length of the beam, and its maximum value occurs at a specific location.

Bending Moment in Beams:
- Beams are structural members that resist loads by bending. When a beam is subjected to a load, the fibers on the top of the beam experience compressive stresses, while the fibers on the bottom experience tensile stresses. This results in the development of a bending moment within the beam.
- The bending moment is a measure of the internal resistance of the beam to bending. It is expressed in Newton-meters (Nm) or foot-pounds (ft-lb).
- The bending moment varies along the length of the beam and its magnitude depends on the type and distribution of the applied loads.
- The bending moment is maximum at certain locations, which are influenced by the type of load and the beam's support conditions.

Bending Moment in Sagging Beams:
- Sagging is a term used to describe the behavior of a beam when it bends downward under the action of a load. In sagging beams, the bending moment is maximum at the mid-span.
- When a load is applied to the mid-span of a beam, the beam deflects downward, resulting in tensile stresses on the bottom fibers and compressive stresses on the top fibers.
- The maximum bending moment occurs at the mid-span because it is the location farthest away from the supports, where the beam experiences the maximum deflection.
- The bending moment gradually decreases as we move towards the supports because the deflection reduces closer to the supports.

Conclusion:
In sagging beams, the bending moment is maximum at the mid-span. This is because the mid-span is the location farthest away from the supports, where the beam experiences the maximum deflection. Understanding the distribution of bending moment along a beam is crucial for designing safe and efficient structures. By identifying the location of the maximum bending moment, engineers can determine the required beam size and reinforcement to ensure structural integrity.