This document contains calculations for the design of a two-way residential slab continuous on four edges. It includes design data, loading information, bending moment calculations, reinforcement requirements for midspan and edges, shear checks, serviceability checks for deflection and cracking, and a note about detailing the slab according to standard methods. Reinforcement is specified as Y10 bars at 200mm spacing for midspan and edges and Y8 bars at 200mm for distribution. The slab passes all design checks for strength and serviceability.

1. FIRST FLOOR Job No: ST/001/13 Sheet No: 3
Calculations by: AJWANG Checked by:
Date: 28th JULY
PROPOSED RESIDENTIAL DEVELOPMENT
TWO WAY SLAB CONTINUOUS ON FOUR EDGES
BS 8110-1: 1997 DESIGN DATA
cl 3.4.1.3 Effective long span,Ly 4.2 m
Effective short span,Lx 3.3 m
BS 5328 Concrete Strength, fcu 25 N/mm²
cl 2.4.4.1 Steel strength, fy 460 N/mm²
Edge 1
Lx = 3.3m
Ly = 4.2m
Edge 3
Figure 3.2 Slab thickness,h 150 mm
Table 3.2 Exposure conditions MILD
Table 3.4 Fire resistance 1.5 hrs.
Table 3.3 Concrete cover, c 20 mm
(BS 5800-1) Concrete density 24.0 kN/m³
cl. 2.4.3.1.1 Dead load factor, ϒfd 1.4
Table 2.1 Live load factor, ϒfl 1.6
LOADING
cl 2.4.1.1 (a) Characteristic Dead Load, Gk
(BS 648) Slab self weight 3.6 kN/m²
Finishes/service 1 kN/m²
BS 6399-1 cl 5.1.4 Partitions 1 kN/m²
Additional dead load 0 kN/m²
5.60 kN/m²
cl 2.4.1.1 (b) Characteristic Live Load, Qk
BS 6399-1 Table 1 Minimum imposed floor load 2.5 kN/m²
Extra imposed Load 1 kN/m²
BS 6399-1 cl 6.1 Floor Number (OR 1 to ignore reduction) 4
BS 6399-1 Table 2 Imposed Load reduction factor 0.7
2.45 kN/m²
cl. 2.4.3.1.1 Design load, n 11.76 kN/m²
Ly/Lx 1.273
ULS BENDING MOMENTS (Rankine-Grashoff method with Marcus corrections)
cl 3.5.3.4 Section βs Moment
Equation 17 Short span 0.0339 4.34 kNm
Equation 16 Long span 0.0240 3.07 kNm
Edge 1 0.0452 5.78 kNm
Edge 2 0.0320 4.10 kNm
Edge 3 0.0452 5.78 kNm
Edge 4 0.0320 4.10 kNm
PANEL H d-e/ 2-3
REFERENCE CALCULATIONS OUTPUT
Edge4
Edge2
Qk = 2.45kN/m²
n = 11.76kN/m²
2 way spanning
Gk = 5.6kN/m²

2. Kraft Engineering Limited | TEL: +254 737 484882 Sheet No:
MIDSPAN MAIN STEEL (Moment distribution = 0%)
Critical midspan moment 4.34 kNm
Assumed bar diameter 10 mm
cl. 1.3.3.4 Effective depth, d = h-c-ϴ/2 125 mm
Design width, b 1000 mm
cl. 3.4.4.4 K = M/bd²/fcu 0.011 < 0.156 Take Z/d
Lever arm, Z/d = [0.5+√(0.25-K/0.9)] 0.988 > 0.95d 0.95
Asreq = M/0.95fyZ 84 mm²/m
Spacing 200 mm
Provide Y10@200B1 393 mm²/m
cl. 3.12.6.1 Max. reinforcement, 4.0%Ac 6000 mm²/m
Table 3.25 Min. reinforcement, 0.13%Ac 195 mm²/m
Midspan distribution steel (Nominal)
Bar diameter 8 mm
Spacing 200 mm
Provide Y8@200B2 251 mm²/m
EDGE MAIN STEEL (Moment distribution = 0%)
Critical edge moment 5.78 kNm
cl. 3.4.4.4 K = M/bd²/fcu 0.015 < 0.156 Take Z/d
Lever arm, Z/d = [0.5+√(0.25-K/0.9)] 0.983 > 0.95d 0.950
Asreq = M/0.95fyZ 111 mm²/m
Spacing 200 mm
Bar size 10 mm
Provide Y10@200T1 393 mm²/m
Edge distribution steel (Nominal)
Bar size 8 mm
Spacing 200 mm
Provide Y8@200T2 251 mm²/m
ULS SHEAR
Maximum shear force, V = nLx/2 19.40 (n per metre length)
cl. 3.5.5.2 Equation 21 Shear stress, v = V/bvd 0.155 N/mm²
Table 3.8, Table 2.2 Concrete shear stress, vc 0.575 N/mm²
vc + 0.4 0.975 N/mm²
0.8√fcu 4 N/mm²
v < vc < 0.8√fcu
Checks
Table 3.8 NOTE 2 100As/bd 0.314 < 3 OK
(400/d)^1/4 1.337 > 0.67 OK for member without shear reinf
Slab thickness,h 150 mm SHEAR REINF. NOT ADVISABLE
cl. 3.5.7 cl. 3.4.6 SLS DEFLECTION
Table 3.9 Span effective depth ratio 26 (Continuous slab)
M/bd² 0.278
Equation 8 fs = 2/3fyAsreq/Asprov 65.2 N/mm²
Table 3.10 Equation 7 Tension modification factor 3.46 > 2
Allowable span/eff. depth ratio 52.0 mm
Actual span/eff. depth ratio 26.4 mm
REFERENCE CALCULATIONS OUTPUT
Asprov = 393mm²/m
OK IN MAX. REINF
OK IN MIN. REINF.
d = 125mm
No comp. reinf.
No comp. reinf.
OK IN MIN. REINF.
Asprov = 393mm²/m
OK IN MIN. REINF
Asprov = 251mm²/m
M = 5.78kNm
vc = 0.575N/mm²
NO SHEAR REINF.
SAFE IN SHEAR
OK IN MIN. REINF.
Asprov = 251mm²/m
V = 19.4kN
v = 0.155N/mm²
fs = 65.2N/mm²
Factor = 2.0
PASSES IN DEFL.

3. Kraft Engineering Limited | TEL: +254 737 484882 Sheet No:
SLS CRACKING
Minimum spacing (Empirical) 100 mm
cl. 3.12.11.2.7 Max. bar spacing, 3d 375 mm 3d < 750mm
Actual bar spacing 190 mm
Actual spacing < max. spacing
cl. 3.12.11.2.7 a) 2) 150 mm No further check for fy=460
Crack widths < 0.3mm TRUE FALSE
APPROXIMATE DETAIL GUIDE
shape code: 01 shape code: 01
BS 8666
Y10@200T1 Y10@200T1
Y10@200T1
shape code: 01
Y10@200B1
shape code: 01
Y8@200T2
shape code: 01
Y10@200T1
shape code: 01
Y8@200T2 Y8@200B2
shape code: 01 shape code: 01
The drawing is to be detailed in accordance with the standard methods of structural
concrete detailing in accordance with The Institution of Structural Engineers (UK)
and The Concrete Society (UK)
NOTES
Depth of slab, h
REFERENCE CALCULATIONS OUTPUT
PASSES IN CRACKING