Calculation and procedure for constructing cantilever slabs
Design of cantilever slabs according to Eurocode 2
- Plate span 1.5m
- Variable load 4kN/mm2
- Plate thickness 175mm
- Fck 25N/mm2 to 500N/mm2
- Coverage for 25mm reinforcements
- Office building
Slab loading
Dead weight = 175x25x10-3 = 4.375kN/mm2
Breaking load = 1.35gk+1.5qk = 1.35×4.375+1.5×4 = 11.91 kN/mm2
bending moment
n = 11.91kN/mm2
bending moment
M = 11.91*1.5*1.5/2 = 13.4 kNm
Suppose T10 bars are used for the span
Effective depth = 175-25-5 = 145 mm
Reinforcement
K = M/bd2fck=13.4×10^6/(1000×145^2×25)=0.0255
K' = 0.60δ-0.18δ2-0.21
No redistribution, therefore
δ =1
k'=0.21
k'>k No compressive reinforcement required
Z = (d/2)*(1+(1-3.53k)^0.5) ≤ 0.95
d = (145/2)*(1+(1-3.53*0.0255)^0.5) ≤ 0.95*145= 141.66 > 137.75 Therefore
Z = 137.75
As = M/0.87fyk*Z= 13.4*10^6/(0.87*500*137.75) = 224 mm2/m
Provides T10 at 200 mm C/C (as per. = 393 mm2/m
Check deflection (same method as bi-directional plate)
Span/d eff allowed. = (l/d)*F1*F2*F3
ρ = As needed /bd
For cantilever panels
K = 0.4
ρ o = (fck ^ 0.5)/1000 = (25 ^ 0.5)/1000 = 0.005ρ= 224/ (1000*145) = 0.00154
Ρ0 > Ρ
Then
l/d = K{11+(1.5*(fck^0.5) ρ o/ ρ )+ 3.2*(fck^0.5)*(( ρ0/ ρ)-1)^1, 5}= K{11+( 1.5*(25^0.5)0.005/0.00154)+ 3.2*(25^0.5)**((0.005/0.00154) – 1) ^1.5} = 35.69
Normal dish
F1 = 1
The wingspan is less than 7 m
F2 = 1
F3 = 310/σ S ≤ 1.5
σ S = (fyk/γ S )(As,req/As,prov)(SLS Loads / ULS Loads)(1/δ)
= (fyd)(As,erf/As,vor)(gk+ Ψ2qk) /(γ G gk + γ P qk)(1/δ)
σ S = (500/1.15)(224/393)(4.375+0.3*4) /(1.35*4.375 + 1.5*4)(1/1) = 116.1 N/mm2
F3 = 310/116.1 = 2.67 ≥ 1.5
That's why,
F3 = 1.5
Span/d eff allowed. = 35.69*1*1*1.5 = 53.54
Actual range/d eff. = 1500/145 = 10.34
The deflection test is ok.
