Problem No$.1[15$ marks$]$

In a $4-$storey hospital building, a one$-$way structural system is used for the roof of the building.

This system consists of a $120$ mm thick reinforced concrete slab supported by concrete beams

spaced at $4\mathrm{.}0m\frac{o}{c}$ along the length of the roof. Each concrete beam has a self$-$weight of $2\mathrm{.}4$

$k\frac{N}{m}.$ There arefour beams in total, supported by columns at each end. Along the width of

the roof, there are only two columns, spaced $9\mathrm{.}0$ meters o$/$c $($i$.$e$.,$ otal eight columns$).$ The floor

slab extends $0\mathrm{.}5$ meters beyond the exterior beams as a cantilever.

A roofing membrane weighing $0\mathrm{.}6$ kPa is applied on top of the slab. There is also a $1\mathrm{.}2k\frac{N}{m}$

parapet wall along the cantilevered edge. A rooftop HVAC unit weighing $12$ kN is mounted

directly on top of one of the interior beams, located $3\mathrm{.}0$ m from the centerline of a supporting

column.

The roof is subjected to snow and rain loads $(S)$ of $4\mathrm{.}0$ kPa $,$ and the wind pressure $(P)$ is $-1\mathrm{.}5$

kPa $.$

To design the roof beams, calculate the factored bending moment and shear force, assuming

all beams are of the same size.

Hint:

a$)$ Calculate the loads for both interior and exterior beams. Determine the governing load

and proceed with further calculations.

b$)$ Draw shear force and bending moment diagrams to determine the maximum factored

shear force and bending moment.