MEP-Technical Manual CDN 0408.qxd - Hambro

DESIGN PRINCIPLES AND CALCULATIONS
4.1.5 SLAB DESIGN EXAMPLE METRIC
Verify the standard Hambro slab under various limit states
(strength and serviceability) for residential loading.
Dead load: 3 kPa
Live load: 2 kPa
Slab thickness: 70 mm
Joist spacing: 1 250 mm
Concrete strength (f’ c ): 20 MPa at 28 days
Area of steel: 152 x 152 MW18.7 x MW18.7
As = 123 mm2 /m
1- Analysis (Per Meter of Slab)
a) Factored Load
Wf = 1.25 x 3 + 1.5 x 2 = 6.75 kN/m2 b) Maximum Positive Moment at �
M f + = 6.75 x 1.20 2 /11 = 0.88 kN•m
c) Maximum Negative Moment at �
M f – = 6.75 x 1.20 2 /10 = 0.97 kN•m
d) Maximum Shear
Vf = 6.75 x 1.15 x 1.25 = 4.85 kN
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2- Resistance
a) Moment Capacity
√
ø = 4 x Awire π
ø = 4 x 18.7 √ = 4.88 mm
π
where ø = wire diameter
at mid-span: 20 mm concrete cover
d = t - (20 + ø/2)
= 70 - (20 + 4.88/2) = 47.6 mm
at support: 38 mm depth of embedded top chord
d = 38 + ø/2
d = 38 + 4.88/2 = 40.4 mm governs
� 1 = 0.85 - 0.0015f’ c = 0.82 ≥ 0.67 OK
a = øs As Fy 0.85 x 123 x 400
=
�1øc f’ c b 0.82 x 0.65 x 20 x 1 000
a = 3.92 mm
Mr = øs As Fy (d - a/2)
M r = 0.85 x 123 x 400 (40.4 - 3.92) x 10-6 2
Mr = 1.61 kN•m > Mf = 0.97 kN•m OK
b) Shear Capacity
Vr = ß � øc f’ c bwd = 0.21 x 1 x 0.65 x 20 x 1 000 x 40.4 x 10-3 √
√
= 24.66 kN >> Vf = 4.85 kN OK
3- Serviceability
a) Crack Control
dc = t - 38 - ø/2 = 29.6 mm ≤ 50.0 mm OK
A = 2 x dc x 152 = 9 000 mm2 fs = 0.6 x 400 = 240 MPa
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Z = fs dc A x 10-3 Z = 240 x 3 29.6 x 9 000 x 10-3 √
√
Z = 15.5 kN/mm < 25.0 kN/mm exterior exposure OK
< 30.0 kN/mm interior exposure OK
b) Deflection Control
Span/depth = 1 250/70 = 18
Exterior span = 18 < 24 OK
Interior span = 18 < 28 OK
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