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IS 456:2000 · Slabs

One-Way Slab Design as per IS 456 — Complete Guide with 3 Worked Examples

⏱ 18 min read📅 June 2026✅ IS 456:2000🎓 GATE relevant

A one-way slab is the simplest structural slab — it bends in one direction only and transfers load to two opposite supporting beams or walls. If the ratio of longer span to shorter span (Ly/Lx) is greater than 2, the slab is classified as one-way because the load predominantly flows along the short span. This guide covers the full design process — from span-depth ratio to bar spacing — with three worked examples and 10 GATE MCQs.

1. Introduction — One-Way vs Two-Way

Hold a playing card by two opposite edges and press down at the centre — it bends into a cylindrical shape along the short span. Now hold it by all four edges and press — it forms a dish shape bending in both directions. A one-way slab behaves like the first case. When the long span is more than twice the short span, practically all the load travels along the shorter direction, and the longer direction carries negligible bending.

In Indian residential construction, one-way slabs are common in verandahs, passages, narrow rooms, and cantilevered balconies. The typical thickness is 100–150mm for spans of 2–4m, making them economical for moderate spans. For larger, more square panels, two-way slabs are more efficient.

2. Concept and Theory

How does a one-way slab work?

A one-way slab works exactly like a very wide beam. If you imagine cutting a 1-metre-wide strip from the slab parallel to the short span, that strip behaves as a beam of width 1000mm and depth equal to the slab thickness. The top surface goes into compression, the bottom into tension — exactly like a beam. The main reinforcement runs along the short span (carrying the bending moment) and distribution steel runs along the long span (handling shrinkage, temperature effects, and spreading any concentrated loads).

Why Ly/Lx > 2 makes it one-way

When Ly/Lx > 2, the stiffness in the short direction is dramatically higher than in the long direction (stiffness varies inversely as the cube of span). This means the short span attracts almost the entire load — over 95% flows along Lx. The remaining 5% along Ly is negligible for design purposes. IS 456 recognises this by saying: if Ly/Lx > 2, design as one-way slab.

The span-depth ratio approach

Instead of calculating deflection explicitly, IS 456 uses a beautifully simple shortcut — the span-to-depth ratio. If you keep L/d within a certain limit (modified by factors for steel stress and compression reinforcement), the deflection will automatically be within acceptable limits (span/250 for total deflection). This saves an enormous amount of calculation and is the primary tool for selecting slab depth.

3. IS Code Background

Clause	Subject	Plain English
22.2	Effective span	For simply supported: lesser of (clear span + d) or (c/c of supports). For continuous: clear span between support faces.
23.2	Span-depth ratio	Simply supported = 20, Cantilever = 7, Continuous = 26. Multiply by modification factor (based on steel stress and pt) from Fig. 4 of IS 456.
24.1	One-way slab	When Ly/Lx > 2, the slab bends in one direction. Design a 1m strip as a beam.
26.5.2.1	Min reinforcement	0.12% of bD for Fe415/Fe500, 0.15% for Fe250.
26.5.2.2	Max spacing	Main bars: min(3d, 300mm). Distribution bars: min(5d, 450mm).
26.3.3	Max bar diameter	Bar diameter ≤ D/8 where D = slab thickness.

4. Key Formulas

Formula 1 — Depth from Span-Depth Ratio

d = L / (basic ratio × modification factor)

Basic ratio: Simply supported = 20, Cantilever = 7, Continuous = 26
Modification factor from IS 456 Fig. 4 — depends on pt and fs
For preliminary design with Fe415: assume factor ≈ 1.3–1.5
D = d + cover + bar dia/2 (round up to nearest 10mm)

Formula 2 — Load on 1m Strip

Self weight = 25 × D × 1.0 (kN/m per metre width)
Floor finish = 1.0–1.5 kN/m² typically
Live load from IS 875 Part 2 (2–5 kN/m² depending on use)
w_u = 1.5 × (DL + LL) per metre width

Formula 3 — BM and Steel for Simply Supported Slab

M_u = w_u × L² / 8 (simply supported)
M_u = w_u × L² / 12 (one end continuous, negative moment at support)
Ast = [0.5 fck/fy × {1 − √(1 − 4.6Mu/(fck·b·d²))}] × b × d
where b = 1000mm (for 1m strip width)

5. Important Tables

Table 1: Span-Depth Ratios (IS 456 Cl 23.2)

Support Condition	Basic L/d	With Fe415 (typical mod factor 1.3)	Effective L/d
Simply supported	20	20 × 1.3 = 26	≈ 26
Continuous	26	26 × 1.3 = 33.8	≈ 34
Cantilever	7	7 × 1.3 = 9.1	≈ 9

How to use: For a simply supported slab of span 3m with Fe415: d = 3000/26 ≈ 115mm. Assume 20mm cover + 10mm bar: D = 115 + 20 + 5 = 140mm → use 150mm.

Table 2: Distribution Steel Requirements

Steel Grade	Min % of bD	For 150mm slab, 1m width
Fe250	0.15%	225 mm²/m
Fe415	0.12%	180 mm²/m
Fe500	0.12%	180 mm²/m

6. Step-by-Step Design Procedure

Check Ly/Lx > 2. If yes → one-way slab.
Assume depth using span-depth ratio. Round D to nearest 10mm.
Calculate loads on a 1m-wide strip: self-weight + finish + live load. Apply 1.5 factor.
Calculate BM. Use wL²/8 for SS, IS 456 Table 12/13 for continuous slabs.
Check depth. Verify M_u ≤ M_u,lim = 2.76 × 1000 × d² (Fe415, M20). If not, increase d.
Calculate Ast using the standard flexure formula for a 1m strip (b=1000mm).
Check minimum steel: 0.12% of bD for Fe415.
Select bar diameter and spacing. Max spacing = min(3d, 300mm).
Provide distribution steel along the longer span: 0.12% of bD. Max spacing = min(5d, 450mm).
Check deflection using modified span-depth ratio (IS 456 Fig. 4).

7. Worked Examples

Example 1 — Simply Supported One-Way Slab (Beginner)

Design a simply supported slab for a room 3m × 7m (clear spans). LL = 3 kN/m², floor finish = 1 kN/m². M20, Fe415.

Step 1 — Check Type

Ly/Lx = 7/3 = 2.33 > 2 → One-way slab

Step 2 — Depth

d = 3000/(20×1.4) = 107mm → assume d = 120mm
D = 120 + 20 + 5 = 145mm → Use D = 150mm, d = 125mm

Step 3 — Loads (per m width)

Self wt = 25 × 0.15 = 3.75 kN/m²
Finish = 1.0 kN/m²
LL = 3.0 kN/m²
Total = 7.75 kN/m²
w_u = 1.5 × 7.75 = 11.625 kN/m per m

Step 4 — Bending Moment

M_u = 11.625 × 3² / 8 = 13.08 kN·m per m width
M_u,lim = 2.76 × 1000 × 125² / 10⁶ = 43.1 kN·m > 13.08 ✅ Singly reinforced OK

Step 5 — Main Steel

Ast = [0.5×20/415 × {1−√(1−4.6×13.08×10⁶/(20×1000×125²))}] × 1000 × 125
Ast = 307 mm²/m
Min Ast = 0.12% × 1000 × 150 = 180 mm²/m → 307 > 180 ✅
Provide 8mm @ 160mm c/c (Ast = 1000/160 × 50.3 = 314 mm²/m) ✅

Step 6 — Distribution Steel

Ast,dist = 0.12% × 1000 × 150 = 180 mm²/m
Provide 8mm @ 270mm c/c (Ast = 186 mm²/m) ✅
Check: max spacing = min(5×125, 450) = 450mm → 270 < 450 ✅

Example 2 — Continuous One-Way Slab (Intermediate)

Design a continuous slab spanning 4m (3 equal spans). LL = 4 kN/m², finish = 1.5 kN/m². M25, Fe500.

Step 1 — Depth

d = 4000/(26×1.3) = 118mm → Use D = 160mm, d = 132mm

Step 2 — Factored Load

DL = 25×0.16 + 1.5 = 5.5 kN/m²
w_u = 1.5 × (5.5 + 4.0) = 14.25 kN/m

Step 3 — BM Coefficients (IS 456 Table 12)

Near middle of end span: M_u = w_uL²/12 = 14.25 × 16/12 = 19.0 kN·m (positive)
At support next to end: M_u = w_uL²/10 = 14.25 × 16/10 = 22.8 kN·m (negative)

Step 4 — Steel at Support (negative moment)

Ast = 425 mm²/m
Provide 10mm @ 180mm c/c at top (Ast = 436 mm²/m) ✅

Step 5 — Steel at Midspan

Ast = 353 mm²/m
Provide 10mm @ 220mm c/c at bottom (Ast = 357 mm²/m) ✅

Example 3 — Cantilevered Slab / Balcony (Advanced)

Design a cantilevered balcony slab projecting 1.5m. LL = 3 kN/m², finish = 1 kN/m². M20, Fe415.

Step 1 — Depth

d = 1500/(7×1.2) = 179mm → Use D = 200mm, d = 170mm

Step 2 — Factored Load

w_u = 1.5 × (25×0.2 + 1 + 3) = 1.5 × 9 = 13.5 kN/m

Step 3 — BM at Fixed End

M_u = w_uL²/2 = 13.5 × 1.5²/2 = 15.19 kN·m/m

Step 4 — Steel

Ast = 263 mm²/m
Min = 0.12% × 1000 × 200 = 240 mm²/m → 263 > 240 ✅
Provide 10mm @ 290mm c/c at top (main steel in cantilever is at top!) ✅

8. GATE MCQs

Q1. A slab panel 3m × 7m is classified as:

(a) Two-way slab
(b) One-way slab
(c) Flat slab
(d) Cannot be determined

Answer: (b)
Ly/Lx = 7/3 = 2.33 > 2 → one-way slab. The critical ratio is 2.

Q2. The basic span-depth ratio for a simply supported slab as per IS 456 is:

(a) 7
(b) 20
(c) 26
(d) 32

Answer: (b)
20 for simply supported, 26 for continuous, 7 for cantilever. These are fundamental values to memorise.

Q3. Minimum reinforcement in a slab with Fe500 bars as per IS 456 is:

(a) 0.15% of bD
(b) 0.12% of bD
(c) 0.8% of bD
(d) 0.85bd/fy

Answer: (b)
0.12% for HYSD (Fe415 and Fe500), 0.15% for mild steel (Fe250). Option (c) is for columns, option (d) is for beams.

Q4. Maximum spacing of main reinforcement in a slab is:

(a) 3d or 300mm
(b) 5d or 450mm
(c) 2d or 200mm
(d) 4d or 400mm

Answer: (a)
Main bars: min(3d, 300mm). Distribution bars: min(5d, 450mm). These are from IS 456 Cl 26.3.3.

Q5. Distribution steel in a one-way slab is provided in the direction of:

(a) Short span
(b) Long span
(c) Both spans equally
(d) Diagonal

Answer: (b)
Main steel runs along the short span (carries bending). Distribution steel runs along the long span (handles shrinkage, temperature, and load distribution).

Q6. A one-way slab 150mm thick spanning 3m (SS) with w_u = 12 kN/m has a midspan moment of:

(a) 13.5 kN·m
(b) 9.0 kN·m
(c) 27.0 kN·m
(d) 4.5 kN·m

Answer: (a)
M_u = wL²/8 = 12 × 9/8 = 13.5 kN·m. Option (b) uses L²/12, (c) uses L²/4, (d) uses L²/2×L. Simple formula application — know wL²/8 for SS.

Q7. In a cantilever slab, the main reinforcement is placed at:

(a) Bottom face
(b) Top face
(c) Both faces equally
(d) Middle of slab depth

Answer: (b)
A cantilever has hogging (negative) moment — tension at the top. So main steel goes at the top. This is a fundamental concept question that catches students who always assume steel is at the bottom.

Q8. The minimum thickness of a slab as per IS 456 is:

(a) 50mm
(b) 75mm
(c) 100mm
(d) No minimum specified

Answer: (b)
IS 456 Cl 23.1 specifies minimum 75mm for general slabs. However, practical minimum is 100–120mm for residential and 150mm for most commercial buildings.

Q9. For a continuous slab, the BM coefficient at the first interior support (IS 456 Table 12) is approximately:

(a) 1/8
(b) 1/10
(c) 1/12
(d) 1/16

Answer: (b)
IS 456 Table 12 gives coefficient of 1/10 at the support next to the end support for DL+LL on all spans. Midspan of end span = 1/12.

Q10. The modification factor for span-depth ratio depends on:

(a) Concrete grade only
(b) Steel stress at service load and pt
(c) Applied load only
(d) Bar diameter

Answer: (b)
IS 456 Fig. 4 plots modification factor vs steel stress (fs) for different values of tension reinforcement percentage (pt). Higher pt or higher fs → lower modification factor → shallower slab not permitted.

9. Common Mistakes

Mistake 1: Forgetting self-weight. Slab self-weight = 25 × D kN/m². For a 150mm slab, this is 3.75 kN/m² — often comparable to the live load itself.

Mistake 2: Main steel in the wrong direction. Main steel goes along the SHORT span (carrying the load). Distribution steel along the LONG span. For cantilevers, main steel is at the TOP.

Mistake 3: Using beam minimum steel formula for slabs. Slabs use 0.12% of bD (Fe415). Beams use 0.85bd/fy. These are different clauses and different values.

Mistake 4: Exceeding maximum spacing. Even if calculated Ast gives a spacing of 400mm, the maximum allowed is min(3d, 300mm). Must not exceed this.

10. Quick Revision Summary

Memorise:

One-way when Ly/Lx > 2
Basic L/d: SS = 20, Continuous = 26, Cantilever = 7
BM for SS: wL²/8 | Cantilever: wL²/2
Min steel: 0.12% bD (Fe415/500), 0.15% bD (Fe250)
Max spacing: Main = min(3d, 300mm), Distribution = min(5d, 450mm)
Distribution steel = 0.12% of bD (same as minimum)
Design a 1m strip (b = 1000mm) as a beam
Load factor = 1.5 for DL + LL
Clear cover for slab = 15mm (mild), 20mm (moderate exposure)
Cantilever: main steel at TOP

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