When a rectangular beam is loaded transversely, the maximum compressive stress develops on
- ABottom fibre
- BTop fibreCorrect
- CNeutral axis
- DEntire cross section
Solution
Concept
In a sagging beam, fibres above the neutral axis are compressed and fibres below are stretched. Stress is largest at the fibre farthest from the neutral axis.
Formula
σ = M y / I
Step-by-step solution
1. Take the usual case: a simply supported beam with downward load, so the beam sags. 2. In sagging, the top fibres shorten (compression) and the bottom fibres extend (tension). 3. From σ = M y / I, stress is maximum where y is maximum, that is at the extreme fibres. 4. So maximum compressive stress is at the top fibre.
Explanation
Bending stress changes linearly with distance from the neutral axis. For a sagging beam, the top fibre has the maximum compression and the bottom fibre has the maximum tension. At the neutral axis, the bending stress is zero.
Why the other options are wrong
A: The bottom fibre has maximum tension in sagging, not compression. C: Bending stress is zero at the neutral axis. D: Stress is not uniform. It varies linearly over the depth.
Shortcut
Sagging means top compression and bottom tension. Hogging means the opposite.
Common mistake
Thinking stress is maximum at the neutral axis. That is true for shear stress, not bending stress.
Correct answer: B) Top fibre