Question $4$

A designer selects a $1-$in dowel bar size for contraction joints in a $10"$ concrete slab resting on a

subgrade material with a $250$ pci modulus of subgrade reaction. The design load is a $9,000-lb$

dual wheel load centered $6^{\text{'}\text{'}}$ from the slab edge. Assume a $12"$ dowel spacing. Assume that the

modulus of elasticity of concrete $=4\mathrm{.}7{10}^6,$ concrete compressive strength is $2800$ psi $,$ and

Poisson ratio of concrete $=0\mathrm{.}15.$ Determine the maximum bearing stress at the outermost dowel

bar and assess the safety of the design. Assume modulus of dowel support $(K)=1500ks\frac{i}{i}n,$

$E_{\text{s}\text{t}\text{e}\text{e}\text{l}}=29,000$ksi, and $z=0\mathrm{.}27in.$