Week 6 Challenge

1) Given data

Factored live load=15KN/m²

The plate dimension = 1200x5000mm

Density of steel=78.5KN/m³

All edges fixed

i) Assume the thickness of plate=1mm

E=2X105 N/mm²

Self weight of plate=0.001x78.5=0.0785KN/m²

Total load=0.0785+15=15.07KN/m²

ii) At centre

σ=β2xqxb²/t²

From the roads chart table 11.4

a/b=5000/1200=4.166

Take β2 = 0.25, ∝=0.0284

β1=0.5

σ=0.25x15.07x10³x1.2²/0.001² =10850.4N/mm²

γmax=∝xqxb4/Ext³ =0.0284x15.x07x10³x1.2² /2x1050.001³ =3080mm

as per above we get ,

σ = 5425.2 N/mm²

σmax = 10850.4N/mm²

γmax=3080mm, hence ok

2) Depth of slab :

Lx = 8m, Ly = 10m

Live load =8KN/m²

let Pt=0.4% fs=240 N/mm² (Fe=415)

mf=1.3

l/d=20mf

8000/d = 20x1.3

d = 310mm

D = 310+20+10/2 =335mm

Effective span

Clear span+eff depth = 8000+310 =8310mm

lx=8310mm, ly=10310mm

Load calculation

Total load = 5+8 = 13KN/m

factored load = 1.5x13 = 19.5 KN/m

Bending moment

Case1: Four edges discontinuous

ly/lx = 1.25, lx = 0.075

Mux = ∝x Wu lx² = 100.9KN-m

Muy= ∝y Wu lx² = 75.4KN-m

Mu lim =0.138 fck b d²

100.9 x 106 = 0.138 x 25 x 1000 x d²

dreq = 171mm

Reinforcement

Along shorter span Pt = 0.2%

Ast = 0.2/100 x 1000x310 =620mm²

Consider 10mm Ø bars

Spacing = 78.3/620 x 1000 = 120mm

Ast prov = 654.41 mm²

Ast min =0.12/100 x 1000 x 33.5 =402 mm²<=Ast prov

Pt = 0.152%

Ast = 0.152/100 x 1000 x310 = 471.2 mm²

Consider 8mm Ø bars

Spacing = 50.26/471.2 x 1000 = 100mm

Ast prov = 502.6 mm²

Ast min = 0.152/100 x 1000 x 33.5 =500 mm²<Ast prov