Step 1: Understanding the Concept:
Bending stress (\(\sigma\)) in a beam is determined by the bending moment (\(M\)) at a specific section.
According to the flexure formula \(\sigma = \frac{M \cdot y}{I}\), the stress is directly proportional to the bending moment.
Step 2: Detailed Explanation:
In a simply supported beam:
1. The bending moment at the supports is always zero because they cannot resist rotation.
2. Under a Uniformly Distributed Load (\(w\)), the maximum bending moment occurs at the center (\(L/2\)) and is equal to \(\frac{wL^2}{8}\).
3. Under a central point load (\(P\)), the maximum bending moment also occurs at the center and is equal to \(\frac{PL}{4}\).
Since the bending moment is maximum at the mid-span, the maximum bending stress along the length of the beam will also occur at the mid-span.
Step 3: Final Answer:
The maximum bending stress occurs at the mid-span of the beam.