One-way Ribbed Slab Design as Per BS8110

Project Details:

Page #

Ribbed Slab Designs to BS 8110-97:

Prepared: Y.A

Continuous 6m Long Spans & Imposed Loading 2.5kPa

Checked:

REF

CALCULATIONS

1 of

OUTPUT

► Slab Geometry:

6m

6m

6m

- Design a one-way ribbed slab with 3 equal continuous spans BS8110§3.5.2.3 & §3.5.2.4

- It satisfies the criteria of BS8110 for using Table 3.12 For +ve moment, design the most critical section: i.e. End Span, Span (upport c-r) L=

6

m

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

fy = fcu = RCC Weight =

460 N/mm² (main & shear reinforcement) 30 N/mm² (C25/30 Concrete) 25 kN/m³

► Loading:

BS6399-1

Floor Finishes & Services (SDL) =

1.20 kN/m2

Rapidwall Formwork (SDL) =

0.4 kN/m2

Characteristic Imposed Load =

2.50 kN/m2

► Slab Sizing:

Let topping thickness, hf =

100 mm

Rib width, bw =

230 mm

Flange Width b = BS8110§3.4.6.3 Table 3.9

500 mm (Rib spacing)

bw/b =

0.46 > 0.3

Interpolating Basic L/d =

26 -4.01

Let modification factor =

1.6 (to be confirmed later)

Allowable L/d ratio = Therefore, dmin= Bottom cover to links =

= 22.0

35.2 170.5 mm 25 mm (includes 5mm for deviation)

Rapidwall bottom skin =

15 mm

Dia of main bars =

14 mm

Dia of links =

8 mm

hreq =

225.5 mm Try an overall depth of slab h =

224 mm

Project Details:

Page #

Ribbed Slab Designs to BS 8110-97:

Prepared: Y.A

Continuous 6m Long Spans & Imposed Loading 2.5kPa

Checked:

REF

CALCULATIONS

2 of

OUTPUT

► Ulitmate Load & Moment Calculation:

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 = BS8110§3.5.2.3 & §3.5.2.4

34.48 kN

Ultimate bending moment and shear force as per Table 3.12

0.086FL

0.063FL BMD

0.063FL

0.086FL

0.4F

0.5F

0.5F

0.5F

0.6F

SFD

► Design of End Span (Bottom Reinforcement):

Ultimate Moment M = 0.086 FL = T section, b =

500

mm, d =

Assume 0.9x = hf =

100

mm

Mf = 0.45 fcu b hf (d - 0.5hf) = 80.325

169

mm

kNm

>M

17.8

kNm

∴Neutral axis lies in the flange; treat as a rectangular section, having width b = BS8110§3.4.4.4

500

mm, h =

224

mm

K = M/(fcu b d2) = 0.042 < 0.156 ∴ hence compression reinforcement is not required z/d = 0.5+√(0.25 - K/0.9) =

0.95

≯ 0.95

∴ z = 0.95d = 160.55 As req = M/(0.87 fy z) = BS8110Table 3.25

277

mm2

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

∴ Provide Bottom Reinforcement 2Y 14

BS8110Table 3.25

Asmin =

0.13% bw h =

67

mm2

1Y 14 Asprov(mm )= 462 2

Project Details:

Page #

Ribbed Slab Designs to BS 8110-97:

Prepared: Y.A

Continuous 6m Long Spans & Imposed Loading 2.5kPa

Checked:

REF

CALCULATIONS

3 of

OUTPUT

► Design of First Interior Support (Top Reinforcement):

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 = BS8110§3.5.2.3 & §3.5.2.4

230

mm, h =

224

Table coefficient include 20% redistribution of moment at support ∴ βb = 0.8 K' = 0.402(bb – 0.4) – 0.18(bb – 0.4)2 =

BS8110§3.4.4.4

mm

0.132

K = M/(fcu b d2) = 0.051 < K' ∴ hence compression reinforcement is not required z/d = 0.5+√(0.25 - K/0.9) =

0.94

≯ 0.95

∴ z = 0.95d = 160.55 As req = M/(0.87 fy z) = BS8110Table 3.25 §3.12.11.2

277

mm2

Minimum reinforcement check: for rectangular sections Asmin =

0.13% b h =

67

mm2

∴ Provide Top Reinforcement 2Y 10 +1Y 12 Asprov(mm2)= 270

► Shear Check:

Max. shear force at first interior support = 0.6F = Ribs are not terminated before the support, hence critical section is at the face of the load-bearing Rapidwall: x=

62

20.3

BS8110Eq. 22

Calculate design applied shear stress:

BS8110Table 3.8

Calculate design concrete shear stress:

v = V/bvd =

0.52

kN N/mm² < vcmax=

100 As/bvd =

0.70

≯3

(400/d)1/4 =

1.24

≰ 0.67

vc = (0.79/gm)*{100As/(bwd)}

kN

mm from support centerline

Shear Force V = (0.6F) - (wx) =

BS8110§3.6.4.7

20.7

1/3

(400/d)

1/4

(fcu/25) =

0.74

4.38

N/mm²

v < vc , no shear links required

BS8110§3.6.4.7

v < vc , no shear links required

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 ∴ Provide Double the links can generally be of the order of 1 m to 1.5 m depending on the Legged Links size of the main bars' Y8@500mm c/c

Project Details:

Page #

Ribbed Slab Designs to BS 8110-97:

Prepared: Y.A

Continuous 6m Long Spans & Imposed Loading 2.5kPa

Checked:

REF BS8110§3.4.6.3 Table 3.9

BS8110Eq. 8

CALCULATIONS

4 of

OUTPUT

► Deflection Check (Middle of End Span): 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"

bw/b =

0.46

Interpolated Basic L/d =

22.0

M/bd2 =

1.25

∴ βb ≈ fs =

0.95 194

N/mm²

tension m.f =

1.65

≯2

As'prov =

157

mm²

compression m.f =

1.06

≯1.5 =

> 0.3, N/mm²

BS8110Eq. 7

=

Allowable L/d = Basic L/d*m.f =

38.4

Actual L/d =

35.5

1.65

As'prov/bd =

0.19

1.06 < Allowable L/d

No further checks are required.

∴ Deflection Check Satisfactory

► Reinforcement in Topping:

Single layer of welded steel fabric is needed for the topping: ∴ Use Mesh A252 BS8110§3.6.6.2

Taking 1m width of the topping, b = As = 0.12% b hf = Maximum spacing Smax = rib spacing/2 = ► Detailing Diagram:

1000 mm 120 mm2/m 250 mm

Y8 bars S = 200 mm As = 252 mm2/m