One-way Ribbed Slab Design as Per BS8110

Project Details: Page # 1 of

Ribbed Slab Designs to BS 8110-97: Prepared: Y.A

Continuous 6m Long Spans & Imposed Loading 2.5kPa Checked:

REF CALCULATIONS OUTPUT

6m 6m 6m

- Design a one-way ribbed slab with 3 equal continuous spans - It satisfies the criteria of BS8110 for using Table 3.12

For +ve moment, design the most critical section:

6 m

For -ve moment, design the most critical section: i.e. First Interior Support

460N/mm² (main & shear reinforcement) 30N/mm² (C25/30 Concrete)

RCC Weight = 25kN/m³

Floor Finishes & Services (SDL) = 1.20 Rapidwall Formwork (SDL) = 0.4 BS6399-1 Characteristic Imposed Load = 2.50

100 mm 230mm

Flange Width b = 500mm (Rib spacing) 0.46

Interpolating Basic L/d = 26 -4.01 = 22.0

Let modification factor = 1.6(to be confirmed later) Allowable L/d ratio = 35.2

170.5 mm Bottom cover to links = 25 Rapidwall bottom skin = 15 mm

Dia of main bars = 14mm Dia of links = 8 mm 225.5 mm

Try an overall depth of slab h = 224mm

► Slab Geometry:

BS8110- §3.5.2.3 & §3.5.2.4

i.e. End Span, Span (upport c-r) L=

► Material Properties: f_y = f_cu = ► Loading: kN/m2 kN/m2 kN/m2 ► Slab Sizing:

Let topping thickness, h_f = Rib width, b_w = b_w/b = _{> 0.3} BS8110- §3.4.6.3 Table 3.9 Therefore, d_min= mm (includes 5mm for deviation) h_req =

Project Details: Page # 2 of

Ribbed Slab Designs to BS 8110-97: Prepared: Y.A

Continuous 6m Long Spans & Imposed Loading 2.5kPa Checked:

REF CALCULATIONS OUTPUT

Width of slab carried by one rib = 500 mm Self-weight of slab = 1.88 kN/m Design Dead Load = 1.4xDL = 3.75 kN/m Design Implosed Load = 1.6xLL = 2.00 kN/m Total Design Load, w = 5.75 kN/m

Total Design Load on a span, F = wL = 34.48 kN

Ultimate Moment M = 0.086 FL = 17.8 kNm

T section, b = 500 mm, d = 169 mm

100 mm

80.325 kNm > M ∴Neutral axis lies in the flange; treat as a rectangular section,

having width b = 500 mm, h = 224 mm 0.042 < 0.156

∴ hence compression reinforcement is not required 0.95

∴ z = 0.95d = 160.55 277

2Y 14

► Ulitmate Load & Moment Calculation:

BS8110- §3.5.2.3 & §3.5.2.4

► Design of End Span (Bottom Reinforcement):

Assume 0.9x = h_f = M_f = 0.45 f_cu b h_f (d - 0.5h_f) = BS8110- §3.4.4.4 K = M/(fcu b d2) = z/d = 0.5+√(0.25 - K/0.9) = ≯ 0.95 ∴ Provide Bottom Reinforcement A_{s req} = M/(0.87 f_y z) = mm2 BS8110-

Table 3.25 Minimum reinforcement check: web in tension, bw/b≥0.4

0.086FL 0.063FL 0.086FL _0.063FL 0.4F 0.6F 0.5F 0.5F 0.5F BMD SFD Ultimate bending moment and shear force as per Table 3.12

0.13% 67 1Y 14 462

Project Details: Page # 3 of

Ribbed Slab Designs to BS 8110-97: Prepared: Y.A

Continuous 6m Long Spans & Imposed Loading 2.5kPa Checked:

REF CALCULATIONS OUTPUT

Ultimate Moment M = 0.086 FL = 17.8 kNm

Hogging moment over support; slab bottom face in compression. Ribs are not terminated before the support, hence:

Solid section: b = 230 mm, h = 224 mm

Table coefficient include 20% redistribution of moment at support 0.8

0.132 0.051 < K'

∴ hence compression reinforcement is not required 0.94

∴ z = 0.95d = 160.55 277

Minimum reinforcement check: for rectangular sections 2Y 10

0.13% 67 +1Y 12

270 Max. shear force at first interior support = 0.6F = 20.7 kN

x = 62 mm from support centerline Shear Force V = (0.6F) - (wx) = 20.3 kN

Calculate design applied shear stress:

0.52 4.38

Calculate design concrete shear stress: 0.70 1.24 0.74 N/mm² BS8110- Table 3.25 As_min = b_w h = mm2 A_sprov(mm2)=

► Design of First Interior Support (Top Reinforcement):

BS8110- §3.5.2.3 & §3.5.2.4 ∴ β_b

=

K' = 0.402(b_b – 0.4) – 0.18(b_b – 0.4)2 ₌ BS8110- §3.4.4.4 K = M/(fcu b d2) = z/d = 0.5+√(0.25 - K/0.9) = ≯ 0.95 ∴ Provide Top Reinforcement A_{s req} = M/(0.87 f_y z) = mm2 BS8110- Table 3.25 §3.12.11.2 As_min = b h = mm2 A_sprov(mm2)= ► Shear Check:

Ribs are not terminated before the support, hence critical section is at the face of the load-bearing Rapidwall:

BS8110- Eq. 22 v = V/b_vd = N/mm² < v_cmax= BS8110- Table 3.8 100 A_s/b_vd = ≯ 3 (400/d)1/4 _{= ≰ 0.67} BS8110- §3.6.4.7 vc = (0.79/gm)*{100As/(bwd)}1/3 (400/d)1/4 (fcu/25) = v < vc , no shear links required

Y8@500mm c/c

Project Details: Page # 4 of

Ribbed Slab Designs to BS 8110-97: Prepared: Y.A

Continuous 6m Long Spans & Imposed Loading 2.5kPa Checked:

REF CALCULATIONS OUTPUT

0.46 > 0.3, Interpolated Basic L/d = 22.0 1.25 N/mm² 0.95 194 N/mm² tension m.f = 1.65 1.65 157 0.19 compression m.f = 1.06 1.06 Allowable L/d = Basic L/d*m.f = 38.4 Actual L/d = 35.5 < Allowable L/d No further checks are required.

Single layer of welded steel fabric is needed for the topping:

Use Mesh A252 ∴

Taking 1m width of the topping, b = 1000 mm Y8 bars

120 S = 200 mm

250 mm BS8110-

§3.6.4.7 v < v_{links required}c , no shear

BS8110-

§3.6.6.3 'Where two or more bars are used in a rib, the use of link reinforcement is recommended to ensure correct cover to reinforcement. The spacing of the links can generally be of the order of 1 m to 1.5 m depending on the size of the main bars'

∴ Provide Double Legged Links

► Deflection Check (Middle of End Span):

BS8110- §3.4.6.3 Table 3.9

Code says that Table 3.9 ratios "are based on limiting the total deflection to span/250 and this should normally ensure that the part of the deflection occurring after construction of finishes and partitions will be limited to span/500 or 20 mm, whichever is the lesser, for spans up to 10 m"

b_w/b = M/bd2 ₌ ∴ β_b

≈

BS8110- Eq. 8 fs = BS8110- Eq. 7 ≯2 = A_s'_prov = mm² A_s'_prov/bd = ≯1.5 = ∴ Deflection Check Satisfactory ► Reinforcement in Topping: BS8110- §3.6.6.2 A_s = 0.12% b h_f = mm2_/m

Maximum spacing S_max = rib spacing/2 = A_s = 252 mm2_/m