RC Slab Design — IS 456:2000

Limit State Method · Plain & Reinforced Concrete, Fourth Revision

2 · One-Way Slab Design

Limit state design of a 1 m wide strip spanning in the short direction.

Cross-section A–Adimension & reinforcement details
D = 200 mmd = 174 mmb = 1,000 mm design stripclear cover = 20 mmmain ø12 @ 150 c/cdistribution ø8 @ 200 c/cSECTION A–A · slab cross-section (all bar positions to Cl. 26.4 cover)
Bending moment diagramcoefficient wu·leff² × 0.1250
+35.933 kN·m/mspan = 4.174 mDesign moment · Simply Supported
wu = 16.50 kN/m² (factored UDL along span)R = 34.44 kN/mR = 34.44 kN/mBOTTOM ø12 @ 150 c/cnominal top steel 0.15·Lcritical section, d from face (Cl. 22.6.2.1)clear span = 4.000 meffective span leff = 4.174 mD = 200 mm
Clear span + effective depth
4,000 + 174 mm
4.174m
Centre-to-centre of supports
4,000 + 300 mm
4.300m
Effective span, leff (governing)Cl. 22.2(a)
lesser of the two — clear+d
4.174m
Design ultimate load, wuTable 18
from load combinations
16.50kN/m²
Design strip width, b
1,000mm
Effective depth, d
174mm
Design moment, MuCl. 22.5
0.1250 · wu · leff² = 16.50 × 4.174²
35.933kN·m/m
Mu,lim = 0.36·fck·b·xu,max·(d − 0.42·xu,max)Annex G
Ru,lim = 0.1336 · fck
101.126kN·m/m
Check Mu ≤ Mu,lim
Singly reinforced — OKOK
Ru = Mu / (b·d²)
35,933,444 / (1000 × 174²)
1.187N/mm²
Required pt
fck/(2·fy)·[1 − √(1 − 4.598·Ru/fck)] × 100
0.2896%
Minimum reinforcement, pt,minCl. 26.5.2.1
0.12 % of gross section b·D
0.12%
Design pt
max(required, minimum)
0.2896%
Ast required
pt/100 · b · d
504mm²/m

Detailing — main steel

Area of one bar
π·ø²/4, ø = 12 mm
113.10mm²
Spacing required
1000 · Ab / Ast,req
224.4mm
Maximum spacingCl. 26.3.3
min(3d, 300 mm)
300mmOK
Ast provided
1000 · Ab / 150
754mm²/mOK
Minimum ptCl. 26.5.2.1
0.12 % of b·D (HYSD bars)
0.12%
Ast,dist required
0.0012 × 1000 × 200
240mm²/m
Area of one bar
ø = 8 mm
50.27mm²
Spacing required
1000 · Ab / Ast,req
209.4mm
Maximum spacingCl. 26.3.3
min(5d, 450 mm)
450mmOK
Ast,dist provided
251mm²/mOK
Shear at support, VuCl. 22.6
wu · leff / 2 = 16.50 × 4.174 / 2
34.436kN/m
Shear at critical section (d from face)Cl. 22.6.2.1
Vu − wu·(bsup/2 + d)
29.090kN/m
Nominal shear stress, τvCl. 40.1
Vu / (b·d) = 34,436 / (1000 × 174)
0.198N/mm²
100·Ast/(b·d)
100 × 754 / (1000 × 174)
0.433
τc from Table 19Table 19
0.85·√(0.8fck)·(√(1+5β) − 1)/(6β)
0.461N/mm²
Depth factor, kCl. 40.2.1.1
D = 200 mm
1.20
k · τc
0.553N/mm²
τc,maxTable 20
M25
3.10N/mm²
Verdict
τv ≤ k·τc
No shear reinforcement required (Cl. 40.2.3)OK

Design shear strength table — M25

Table 19
100Ast/bd0.150.250.500.751.001.251.501.752.002.252.502.753.00
τc (N/mm²)0.290.360.490.570.640.700.740.780.820.850.880.900.92
Basic l/dCl. 23.2.1
Simply Supported
20
pt provided
100·Ast,prov/(b·d)
0.433%
Service steel stress, fs
0.58·fy·(Ast,req / Ast,prov)
193.8N/mm²
Modification factorFig. 4
1/(0.225 + 0.00322·fs − 0.625·log₁₀(1/pt))
1.6073
Allowable l/d
basic × MF
32.146
Provided l/d
leff / d
23.989OK
Main bar spacing ≤ min(3d, 300)Cl. 26.3.3
150 ≤ 300 mm
OKOK
Bar diameter ≤ D/8Cl. 26.5.2.2
12 ≤ 25.0 mm
OKOK
Distribution spacing ≤ min(5d, 450)Cl. 26.3.3
200 ≤ 450 mm
OKOK
LocationBarSpacingAst req.Ast prov.Status
Main steel — bottom, short directionø12150 mm c/c504 mm²/m754 mm²/mOK
Distribution steel — bottom, transverseø8200 mm c/c240 mm²/m251 mm²/mOK
Design adequate