Design of Reinforced Concrete Balcony with Dwarf Wall
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| Plan of Balcony Slab |
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| Section through Balcony Slab |
Moment and Shear
Slab Geometry
Span of slab = 1200 + (225/2) = 1312.5 mm = 1.3125 m
Design width = 1000 mm = 1 m
Slab Details
Thickness of slab = 150 mm
Characteristic strength of concrete; fcu = 20 N/mm2
Characteristic strength of reinforcement; fy = 460 N/mm2
Material safety factor; γm = 1.05
Cover to bottom reinforcement; c = 20 mm
Cover to top reinforcement; c’ = 20 mm
Loading details
Slab loading
Dead load
Self weight of slab = 0.15 × 24 = 3.6 kN/m2
Finishes @ 0.6 kN/m2 = = 0.6 kN/m2
Characteristic dead load; gk = 4.2 kN/m2
Dwarf wall loading
Wall is 150 mm hollow block wall (BS 648:1964, Schedule of weights of building materials)
Load per m run (Point load) = 1.52 × 1 = 1.52 kN/m
Characteristic dead load; gk = 1.52 kN/m
Imposed load (Office general use = 2.5 kN/m2 ,BS 6399-1:1996, Table 1)
Characteristic imposed load; qk = 2.5 kN/m2
Design loading factors
Dead load factor; γG = 1.4
Imposed load factor; γQ = 1.6
Moment redistribution ratio; βb = 1.0
Design loads
Dead loads
Slab
Slab load = 1.4 × 4.2× 1 = 5.88 kN/m
Dwarf wall load = 1.4 × 1.52 = 2.13 kN
Imposed loads
Slab
Slab load = 1.6 × 2.5× 1 = 4.00 kN/m
Moment and Shear
Service Moment
Mudl = (0.5 × 4.2 × 1.31252) + (0.5 × 2.5 × 1.31252) = 5.77kNm
Mpoint = 1.52 × 1.3125 = 2.00 kNm
Design Moment
Mudl = (0.5 × 5.88 × 1.31252) + (0.5 × 4.00 × 1.31252) = 8.51kNm
Mpoint = 2.13 × 1.3125 = 2.80 kNm
Design Shear force
V = (5.88 × 1.3125) + (4.00 × 1.3125) + 2.13 = 15.10 kN
Slab Design (Per metre run of balcony)
Using 12 mm main bars and 10 mm distribution bars
Effective depth of reinforcement; d = 150 – 20 + (12/2) = 124 mm
Support moment; m’ = 8.51 + 2.80 = 11.31 kNm/m
Design reinforcement
(3.4.4.4)
Lever arm; K’ = 0.402 × (βb – 0.4) – 0.18 × (βb – 0.4)2 = 0.176
K = m / (d2 × fcu) = 0.036778 < 0.176
Compression reinforcement is not required
(3.4.4.4)
z = min((0.5 + √(0.25 – (K / 0.9))), 0.95) × d = 117.8 mm
Area of reinforcement designed; Asreqd = m / (z × fy / γm) = 219.70 mm2/m
Minimum area of reinforcement required; Asmin = 0.0013 × h = 195 mm2/m
Area of reinforcement required; Asreq = max(Asreqd, Asmin) = 219.70 mm2/m
Provide 12 mm dia bars @ 200 mm centres
Area of main reinforcement provided; Asprov = 566 mm2/m
Provide 10 mm dia bars @ 200 mm centres
Area of distribution reinforcement provided; Asprov = 393 mm2/m
Shear Check
Maximum allowable shear stress; vmax = min(0.8 × √(fcu), 5) = 3.58 N/mm2
shear stress; v = V / (b × d) = 15.10 ×103 / (1000 × 124) = 0.122 N/mm2
Shear capacity of Slab; vc = (min(fcu,40)/25)1/3×0.79×min(100×Asprov/(b×d),3)1/3×max(400/d,1)1/4/1.25
Shear capacity of Slab; vc = 0.756 N/mm2 > 0.122 N/mm2
Shear Capacity Okay
Check deflection
Basic span/d ratio = 7
Kudl = 0.25
Kpoint = 0.33
Adjusted basic ratio = Basic ratio× (Mudl + Mpoint × Kudl/ Kpoint)/( Mudl + Mpoint )
Adjusted basic ratio = 7× (5.77 + 2.00 × 0.25/ 0.33)/( 5.77 + 2.00 ) = 6.56
Design service stress; fs = 2 × fy × Asreq / (3 × Asprov × βb) = 119.04 N/mm2
Modification factor; k1 = min(0.55+(477N/mm2-fs)/(120×(0.9N/mm2+(m/d2))),2) = min (2.38, 2.00)
Modification factor; k1 = 2.00
Allowable span to depth ratio; = 6.56 × k1 = 13.12
Actual span to depth ratio; L / d = 1312.5/124 = 10.58
L/d ratio Okay
Check Cracking
Clear spacing of bars = 200 – 12 = 188 mm
3d = 3 × 124 = 372 mm
47000/fs = 47000/119.04 = 394 mm
Bar spacing Okay
Anchorage length
Ultimate anchorage bond stress, fbu = β√fcu = 0.5√20
fbu = β√fcu = 2.24 N/mm2
L = (0.95fy) × f/ (4 fbu)f = (0.95×460×12)/ (4× 2.24) = 585.26 mm
L = 0.58526 m
However, ISTRUCTE detailers’ manual recommends
L = (1.5 × span) + 0.1125 = (1.5 × 1.3125) + 0.1125
L = 2.08125 m
Also L = 0.3 × span preceding cantilever span
In this case we take 4.5 m
L = 0.3 × 4.5 = 1.35 m
Therefore we adopt L = 2.08125m
i.e. 2.1 m from the centerline of the support
