Shape of Bending Moment Diagram for a Uniform Cantilever Beam carrying a Uniformly Distributed Load

The bending moment diagram for a beam represents how the bending moment varies along the length of the beam. In the case of a uniform cantilever beam carrying a uniformly distributed load over its length, the shape of the bending moment diagram is a parabola.

Explanation:

- A cantilever beam is a type of beam that is fixed at one end and free at the other end. It is supported only at one point, and the load is applied at the free end.
- When a uniform load is applied to a cantilever beam, it means that the load is distributed evenly over the entire length of the beam.
- The bending moment at any point along the beam is given by the equation M = w*x^2/2, where M is the bending moment, w is the uniformly distributed load per unit length, and x is the distance from the fixed end.
- As we can see from the equation, the bending moment is directly proportional to the square of the distance from the fixed end. This means that the bending moment increases quadratically as we move away from the fixed end.
- Therefore, the shape of the bending moment diagram for a uniform cantilever beam carrying a uniformly distributed load is a parabola.
- The vertex of the parabola represents the maximum bending moment, which occurs at the fixed end of the beam.
- The bending moment gradually decreases as we move towards the free end of the beam, resulting in a downward-sloping parabolic shape.

Conclusion:

In conclusion, the shape of the bending moment diagram for a uniform cantilever beam carrying a uniformly distributed load over its length is a parabola. This is because the bending moment varies quadratically with the distance from the fixed end of the beam. Understanding the shape of the bending moment diagram is important in structural analysis as it helps engineers design beams and determine the maximum bending moment and shear forces acting on the beam.