CEEN $5303$ Homework #$1($due: January $24{?}^{th},2024)$

Name:

Estimate the maximum curling stress in the longitudinal and transverse directions in the middle of the slab when the slab, which is $12-$ft wide and $15-ft$ long with a thickness $10-$in$,$ is subject to the $30F$ linear temperature differential between top and bottom of the slab $($top is lower than the bottom$).$ Determine the maximum stresses for $3$ different slab support conditions $(k$ values of $100,300,$ and $500\frac{}{i}n).$ The material properties are as follows:

a$)$ Concrete coefficient of thermal expansion: $5$ microstrain $\frac{?}{?}F$

b$)$ Modulus of elasticity of concrete: $5$ million psi

c$)$ Poisson's ratio of concrete: $0\mathrm{.}15$

Discuss the effect of slab support on curling stresses and potential cracking in concrete slab.

To prevent transverse cracking problems due to temperature variation in plain jointed concrete pavement, you would like to limit the maximum curling stress at $300.$ You estimate that the maximum temperature difference between the top and bottom of a $12-$in slab will be $30F$ with a linear distribution. For $12-$ft slab width, determine the maximum allowable transverse joint spacing for three slab support conditions as discussed in Problem #$1.$ The material properties are as shown in problem #$1.$

Discuss what you, as a material and pavement engineer, would do to minimize the potential for cracking in concrete slab.