Eigenvalues And Eigenvectors

Concept: Bending stress in a beam depends on the bending moment, which varies along the length of the beam.
Step 1: Relation of stress and bending moment.
Maximum bending stress occurs where bending moment is maximum.
Step 2: Simply supported beam behavior.
For a simply supported beam with uniform load, the bending moment is maximum at the center (mid-span).
Step 3: Evaluating the options.

• At supports Bending moment is zero (incorrect)
• At mid-span Maximum bending moment (correct)
• At quarter span Not maximum (incorrect)
• At free end Not applicable (incorrect)

Step 4: Conclusion.
Thus, maximum bending stress occurs at the mid-span.