---
title: "Short note: radius of relative stiffness"
subject: "Transportation Engineering II"
chapter: 2
key: "semester_7/transportation_engineering_ii:short-note-radius-relative-stiffness"
source: https://www.bctengineer.com/q/semester_7/transportation_engineering_ii/short-note-radius-relative-stiffness
site: BCT Engineering
---

# Short note: radius of relative stiffness

Transportation Engineering II · Chapter 2: Highway Pavement

- Asked in: 2068 Baisakh, 4 marks
- Video: [radius of relative stiffness](https://www.youtube.com/watch?v=S8Uwg-eThqc) — sreehari pulaganti
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/transportation_engineering_ii/short-note-radius-relative-stiffness
- Whole chapter: https://www.bctengineer.com/md/semester_7/transportation_engineering_ii/chapter-2

## Question

Write a short note on radius of relative stiffness.

## Short answer

Radius of relative stiffness l = [E h^3/(12(1-μ^2)k)]^1/4, expressed in cm. It measures slab stiffness relative to subgrade support; larger l means wider load distribution. Used in Westergaard stress equations, warping coefficient ratios, and joint spacing.

## Answer

The radius of relative stiffness $l$ is a measure of how stiff the slab is compared with the subgrade support. It defines the area of slab that takes part in resisting a load (Westergaard).

$$
l=\left[\frac{E\,h^{3}}{12\,(1-\mu^{2})\,k}\right]^{1/4}
$$

where $E$ is the modulus of elasticity of concrete (kg/cm2), $h$ slab thickness (cm), $\mu$ Poisson's ratio and $k$ modulus of subgrade reaction (kg/cm3). The unit of $l$ is cm.

- A thicker slab or higher $E$ gives a larger $l$ (stiffer slab spreads load over a wider area); a higher $k$ gives smaller $l$.
- Typical values for 20-30 cm slabs are about 60-100 cm.
- It is used in all stress equations (Westergaard, Kelly, Bradbury) and in the ratio $L/l$ and $B/l$ for the warping coefficient, and to decide joint spacing and the spread of dowel load transfer (about $1.8\,l$).

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What does the radius of relative stiffness express?
   A. The radius of the wheel contact area
   B. The stiffness of the slab compared with the subgrade support
   C. The distance between dowel bars
   D. The radius of curling of the slab
   Answer: B. l measures slab stiffness relative to the subgrade and defines the area of slab resisting a load. (Key point: Meaning of l)

2. What happens to l if the slab thickness h is increased or the modulus of subgrade reaction k is increased?
   A. Thicker h gives larger l; higher k gives smaller l
   B. Both give a larger l
   C. Thicker h gives smaller l; higher k gives larger l
   D. Neither changes l
   Answer: A. l = [E h^3/(12(1-mu^2)k)]^(1/4): h is in the numerator, k in the denominator. (Key point: Effect of parameters)

3. Where is the radius of relative stiffness used?
   A. Only to find the CBR of subgrade
   B. Only in bituminous mix design
   C. To compute the vehicle damage factor
   D. In stress equations, L/l and B/l for the warping coefficient, and spread of dowel load transfer
   Answer: D. l appears in the Westergaard, Kelly and Bradbury equations and in joint and dowel design (dowel spread about 1.8 l). (Key point: Uses of l)

## Related in Transportation Engineering II

- [Flexible vs rigid; radius of relative stiffness, k](https://www.bctengineer.com/question.md?key=semester_7%2Ftransportation_engineering_ii%3Aflexible-rigid-differences-relative-stiffness-k) — Transportation Engineering II, chapter 2