A warehouse structure incorporates a two$-$storey office portion: a bottom level for storage and top level

for workspaces $($offices$).$ The ground floor space consists of load bearing masonry walls and a

suspended RC floor slab. The suspended slab is only supported by the masonry walls and is separated

from the steel columns comprising the warehouse structure.

Figure $1.$ Plan view of masonry walls and suspended slab

Loading

$$ Unit weight of reinforced concrete: $25$ kN$/$m$3$

$$ Dead load for screed, services, finishes, and partitions: $1\mathrm{.}15$ kPa

$$ Live load on the slab surface: $4$ kPa $($increased per client$$s specification$)$

$$ Load factors: i$)$ dead load $=1\mathrm{.}2$ and ii$)$ live load $=1\mathrm{.}6$

Materials

$$ High yield steel $($Y bars, fy $=450$ MPa$)$

$$ Concrete cover: $30$ mm

$$ Concrete strength: fcu $=30$ MPa

Geometry of Slab A

$$ Short span $($a$)=5500$ mm $($center to center$)$

$$ Long span $($b$)=8250$ mm $($center to center$)$

$$ Thickness $($h$)=200$ mm

Assessment Questions

$($a$)$ Calculate the required moment capacities $($Mpx$,$ Mpy and Mnx$)$ for the suspended slab portion

denoted Slab A using Yield Line Analysis $($from first principles use virtual work method$).$ Note: the geometry of the

critical yield line pattern incorporates two $(2)$ variables. Assume isotropic reinforcement, with

equal moment capacity for hogging and sagging yield lines, i$.$e$.,$ Mpx $=$ Mpy $=$ Mnx$.$