Walk me through how you would calculate the bending stress in a simply supported beam with a central point load.
FoundationalHow to answer
What they’re really asking
They want to confirm you have a working grasp of fundamental beam mechanics and can connect loads, geometry, and material limits. This is a screening question for basic statics competence.
Strong answer structure
Identify reactions (P/2 at each support). Maximum bending moment at center M = P*L/4. Bending stress sigma = M*c/I, where c is distance from neutral axis to outer fiber and I is the second moment of area (for a rectangle, b*h^3/12). Mention checking sigma against yield with a factor of safety, and that max deflection occurs at center, delta = P*L^3/(48*E*I).
Likely follow-ups
- How does the answer change for a distributed load instead of a point load?
- What if the beam is fixed at both ends instead of simply supported?
- Where would the beam most likely fail and why?