a$)$ An arterial road has existing concrete pavement containing doweled joints and concrete shoulders. The concrete slab thickness is $6\mathrm{.}5$ inches on a $6-$inch cementtreated subbase. The pavement was designed for a service life of $20$ years. The truck axle weight distribution is as follows:

$\backslash$table$[[\frac{\text{S}\text{i}\text{n}\text{g}\text{l}\text{e}\text{A}\text{x}\text{l}\text{e}\text{s}}{(1000lb)},$Expected Repetitions$],[26,6,200],[24,163,200],[22,639,740],[\frac{\text{T}\text{a}\text{n}\text{d}\text{e}\text{m}\text{A}\text{x}\text{l}\text{e}\text{s}}{(10001b)},],[44,150,500],[42,171,400]]$

The modulus of subgrade reaction $=100$pci, Modulus of rupture of concrete $=600.$ Is this a safe and economic design for a $20-$year design period? Why or why not? $($use PCA erosion criteria only$).$

b$)$ For the pavement in part $($a$),$ determine the maximum stress due to loading the pavement with $12,000lb$ on a single tire that has a circular contact area with radius $=5$ inches. Use $k=100$pci.

c$)$ Determine the corresponding deflection from the stress in part $($b$).$

d$)$ For the pavement information in parts $($a$)$ and $($b$),$ determine the curling stress $($thermal$)$ at the interior of the slab for a temperature difference of $30F.$ The slab is $40ft$ long and $12ft$ wide.