$3\mathrm{.}1.$ A rigid pavement has the following design:

a$.$ Thickness, $9$ inches uniform.

b$.$ Slab dimensions, $40$ feet $($contraction joints$)$ by $24$ feet $(12-$ft lanes$).$

c$.$ Tie bars at longitudinal joint, $\frac{1}{2}$ inch round by $36$ inches long, spaced $30$ inches $c-c$

$($center$-$to$-$center$).$

d$.$ Longitudinal distributed steel, No$.3$ wires spaced at $6$ inches $($diameter of wire $0\mathrm{.}2437$

in$.).$

e$.$ Transverse distributed steel, No$.4$ wires spaced at $12$ inches $($diameter of wire $0\mathrm{.}2253in.).$

$f.$ Dowel bars, $\frac{3}{4}$ inch round by $18$ inches long, spaced $12$ inches on centers, first dowel $6$

inches from edge.

g$.$ Modulus of subgrade reaction, $100$pci.

Determine the complete stresses in the pavement for a $12,000-$pound dual wheel, tire pres$-$

sure $75.$

a$.$ Calculate the warping stress for a $12-$foot wide slab with various lengths, assuming tem$-$

perature differential to be$,$ day $+3\mathrm{.}0F$ per inch of slab thickness, and night $-1\mathrm{.}0F$ per

inch of slab thickness. Plot a curve of stress versus distance.

$b.$ Calculate the warping stress for various slab widths. Plot a curve of stress versus dsitance.

c$.$ Assume a transverse crack develops at the center of the slab. Calculate the stresses in

the distributed steel.

d$.$ Calculate the moment, shear, and bearing stresses on the dowels.

e$.$ Determine the tensile and bond stresses in the tie bars.

$f.$ Determine the loading stresses at the edge, and interior of the slab.

g$.$ Determine the maximum critical stress $($load plus temperature$)$ in the concrete.