Calculating Loads and Member Forces on a Structure

The plan and elevation of a reinforced concrete building shown below is $7$ bays long by $4$ bays wide. The building has beams along building lines A through E and one$-$way slabs spanning between building lines A through E$.$ Concrete shear walls around the elevators $($between buildinglines $5$ and $6)$ provides the resistance to lateral wind and earthquake forces. Construction is withnormal weight concrete with an assumed density of $150$ pcf$.$Assume the building is used for residential space and the slab is $6$ in$.$ thick. The beams are $14$ in$.$ wide and have a total depth $($i$.$e$.,$ including the depth of the slab$)$ of $18$ in$.,$ the bay dimensions are$20$ ft in the X direction and $30$ ft in the Y direction, and the superimposed dead load is $18$ psf$.$ Refer to Table $1\mathrm{.}1$ in the Darwin text $($also in Lecture $2$ notes$)$ for live loads $($you may ignore live loadreduction factors$).$

For designing the one$-$way slab $($framing in the North$-$South direction$)$:

$($i$)$ calculate the critical $($governing$)$ factored gravity load combination $($psf$)$

$($ii$)$ sketch the moment diagram and calculate$*$ the maximum positive and negative bendingmoments on a $1-$ft wide strip of slab. Indicate where these maximum moments occur along the slab span.

$($iii$)$ assuming a concrete modulus of Ec $=3500$ ksi and using an effective moment of inertia equal to half of the gross moment of inertia $($i$.$e I$\_$eff$=0\mathrm{.}5$I$\_$g$),$ calculate$*$ the maximum deflection of the slab under the service live load.$*$NOTE for calculating the moments, shears and deflections you will need to make some assumptions to relate the ideal boundary conditions in the design charts to the building frame