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  Module 4: Pavement Design
Lecture 29 Rigid pavement design
  

Wheel load stresses - Westergaard's stress equation

The cement concrete slab is assumed to be homogeneous and to have uniform elastic properties with vertical sub-grade reaction being proportional to the deflection. Westergaard developed relationships for the stress at interior, edge and corner regions, denoted as $\sigma_i,~\sigma_e,~\sigma_c$ in kg/cm$^2$ respectively and given by the equation 1-3.
\begin{displaymath}
\sigma_i=\frac{0.316~P}{h^2}\left[4~\log_{10}\left(\frac{l}{b}\right)+1.069\right]
\end{displaymath} (1)


\begin{displaymath}
\sigma_e=\frac{0.572~P}{h^2}\left[4~\log_{10}\left(\frac{l}{b}\right)+0.359\right]
\end{displaymath} (2)


\begin{displaymath}
\sigma_c=\frac{3~P}{h^2}\left[1-\left(\frac{a\sqrt{2}}{l}\right)^{0.6}\right]
\end{displaymath} (3)

where $h$ is the slab thickness in cm, $P$ is the wheel load in kg, $a$ is the radius of the wheel load distribution in cm, $l$ the radius of the relative stiffness in cm and $b$ is the radius of the resisting section in cm
Figure 1: Critical stress locations
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