Given: The beam and loading shown below made with concrete strength $f_c^{\text{'}}=5,500$ psi and Grade $60$ steel. Assume the unit weight of the concrete is $150pcf$ for purposes of finding the self$-$weight.

Dead load is equal to the self$-$weight of the beam, which you need to compute, plus a point load of $15$ kips at midspan. Live load of $1\mathrm{.}5ki\frac{p}{f}t$ is distributed along the entire length of the beam. These loads are unfactored $($i$.$e$.,$ service loads$)$ and should remain so when computing the deflections.

Determine:

Compute the gross moment of inertia $I_g$ and the location of the centroid $y_{\frac{?}{\text{b}\text{a}\text{r}}}.$ You may neglect the steel. $[2$ pts$]$

Compute the cracking moment $M_{cr}.1pt$

Compute the cracked moment of inertia $I_{cr}.[1$ pt$]$

Find the immediate midspan deflection of the beam due to the live loading. $[4$ pts$]$

Assume that only the dead load is sustained. Find the additional long$-$term $(>5$ years out$)$ midspan deflection due to creep and shrinkage. $[1$ pt$]$

Assume the beam supports nonstructural elements that are not likely to be damaged by large deflections. Are the deflections of this beam permissible according to ACI $318-19?$