Calculating Maximum Bending Moment in a Cantilever Beam

Let's figure out how to find the maximum bending moment for the given cantilever beam problem.

A cantilever beam is a beam that is fixed at one end and free at the other. When a load is applied to a cantilever beam, it bends, and internal forces and moments develop within the beam to resist this bending. The bending moment is one of these internal actions.

The question specifies a uniformly distributed load (UDL). This means the load is spread evenly along the length of the beam, with a constant intensity per unit length.

For a cantilever beam of span \(L\) subjected to a uniformly distributed load of intensity \(w\) per unit length, the maximum bending moment occurs at the fixed support. The formula for the maximum bending moment (\(M_{max}\)) in this specific case is:

\(M_{max} = \frac{wL^2}{2}\)

Now, let's use the values given in the question:

• Span of the beam, \(L = 4 \text{ m}\)
• Uniformly distributed load intensity, \(w = 2 \text{ kN/m}\)

Substitute these values into the formula:

\(M_{max} = \frac{(2 \text{ kN/m}) \times (4 \text{ m})^2}{2}\)

\(M_{max} = \frac{2 \times 16}{2} \text{ kN.m}\)

\(M_{max} = \frac{32}{2} \text{ kN.m}\)

\(M_{max} = 16 \text{ kN.m}\)

So, the maximum bending moment in the cantilever beam is 16 kN.m. This maximum bending moment occurs at the fixed end of the beam.

Understanding the concept of bending moment and how it varies along the beam is crucial in structural analysis and design. The maximum bending moment is particularly important as it dictates the maximum stress the beam will experience due to bending, which is a key factor in determining the required size and material of the beam.