Simple bending equation (with usual notation) is
- AM/I = R/E = F/Y
- BM/I = E/R = F/YCorrect
- CI/M = E/R = Y/F
- DI/M = E/R = F/Y
Solution
Concept
The simple bending (flexure) equation relates moment, moment of inertia, Young's modulus, radius of curvature, bending stress and distance from the neutral axis.
Formula
M/I = E/R = σ/y (F = σ, Y = y)
Step-by-step solution
1. The standard flexure formula is M/I = E/R = σ/y. 2. Here F is the bending stress σ and Y is the distance y from the neutral axis. 3. So M/I = E/R = F/Y. 4. This matches option B.
Explanation
The bending equation is M/I = E/R = σ/y. Here M is the bending moment, I is the moment of inertia, E is Young's modulus, R is the radius of curvature, σ (F) is the bending stress and y (Y) is the distance from the neutral axis. Option B shows exactly this form.
Why the other options are wrong
A: R/E is inverted. It should be E/R. C: I/M and Y/F are inverted, so the ratios do not match. D: I/M is inverted and does not equal E/R.
Shortcut
Remember 'M by I, E by R, σ by y'. All terms are 'top/bottom' in this order.
Common mistake
Writing R/E instead of E/R.
Correct answer: B) M/I = E/R = F/Y