If Vd is design speed (mph), emax is maximum rate of superelevation, fmax is co-efficient of side friction. What is the expression for minimum radius of curvature (Rmin) ?
- ARmin = Vd² / (0·01 emin − fmax)
- BRmin = Vd² / (15 (emin + fmax))
- CRmin = Vd² / (15 (emin − fmax))
- DRmin = Vd² / (15 (0·01 emin + fmax))Correct
Solution
Concept
AASHTO minimum radius
Formula
Rmin = V² / [15 (0.01 emax + fmax)] (V in mph, R in ft)
Step-by-step solution
1. Equilibrium on a banked curve: e + f = V²/(15 R) in US units. 2. With e expressed in percent, Rmin = V² / [15 (0.01 emax + fmax)].
Explanation
The minimum radius occurs when the maximum superelevation and the maximum side friction are both used.
Why the other options are wrong
Options with a minus sign or without 0.01 (e in percent) are not the AASHTO expression.
Shortcut
R = V²/15(0.01e + f).
Common mistake
Using e in percent without 0.01.
Correct answer: D) R_min = Vd² / (15 (0·01 e_min + f_max))