Short note: radius of relative stiffness

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 $1.8\,l$).