Bending between supports in a simply supported beam with equal overhanging lengths and equal point loads at the ends

When a simply supported beam has equal overhanging lengths and carries equal point loads at the ends, the bending between the supports will be symmetrical. This means that the beam will experience the same bending moment and shear force at both supports. Let's explore this in detail:

Bending Moment:
- The bending moment in a simply supported beam is maximum at the mid-span and zero at the supports.
- Since the overhanging lengths are equal, the midpoint of the beam coincides with the midpoint between the two supports.
- As a result, the bending moment at both supports will be equal and maximum.

Shear Force:
- The shear force in a simply supported beam is constant across the length of the beam, except at the supports where it changes abruptly.
- Since the point loads at the ends are equal, the shear force at both supports will be equal and opposite in direction.

Deflection:
- The deflection of a simply supported beam is influenced by the bending moment and shear force.
- Since the bending moment and shear force are symmetrical in this case, the deflection between the supports will also be symmetrical.

Conclusion:
In conclusion, when a simply supported beam has equal overhanging lengths and carries equal point loads at the ends, the bending between the supports will be symmetrical. This means that the bending moment, shear force, and deflection at the supports will be equal and opposite. Understanding the behavior of the beam under these conditions is crucial for designing and analyzing structures to ensure their stability and safety.