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IS 456:2000 · Slabs

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

⏱ 20 min read📅 June 2026✅ IS 456:2000🎓 GATE relevant
When a slab panel has its longer-to-shorter span ratio (Ly/Lx) ≤ 2, the load bends the slab in both directions simultaneously. This is a two-way slab — the most common type in Indian buildings for rooms, halls, and commercial spaces. The design uses IS 456 Table 26 to get bending moment coefficients based on edge conditions, and the procedure is significantly different from one-way slabs. This guide covers the full theory, all nine edge-condition cases, three complete worked examples, and 10 GATE MCQs.

📋 Table of Contents

  1. Introduction
  2. Concept and Theory
  3. IS Code Background
  4. Key Formulas
  5. BM Coefficient Tables
  6. Design Procedure
  7. Worked Examples (3)
  8. GATE MCQs (10)
  9. Common Mistakes
  10. Revision Summary
  11. Related Articles

1. Introduction

Most rooms in Indian buildings are roughly square or moderately rectangular — a 4m × 5m room (Ly/Lx = 1.25) or a 3m × 4m room (ratio = 1.33). These panels bend in both directions, and the load distributes to all four supporting beams or walls, not just two. Two-way slabs are more structurally efficient than one-way slabs because they spread load in two directions, resulting in lower bending moments and thinner slabs for the same span.

The behaviour depends heavily on the edge conditions — whether each edge is simply supported (resting on a masonry wall) or continuous (monolithic with adjacent slabs). IS 456 recognises nine distinct cases (numbered 1 through 9 in Table 26), each with different BM coefficients for positive and negative moments in both the short and long span directions.

2. Concept and Theory

How does a two-way slab bend?

Place a sheet of card on four pencils forming a rectangle and press at the centre. The sheet curves into a dish shape — bending along both the short and long directions simultaneously. The shorter span attracts a larger share of the moment because it is stiffer (stiffness ∝ 1/L³). A perfectly square slab splits the load equally between both directions; as the panel becomes more rectangular, the short span carries progressively more until, at Ly/Lx > 2, the long span carries so little that we treat it as one-way.

IS 456 vs Rankine-Grashoff approach

The Rankine-Grashoff method splits load between two perpendicular one-way strips based on span ratio. IS 456 does not use this directly — instead, Table 26 gives bending moment coefficients derived from yield-line theory and elastic plate theory. These coefficients account for the continuity of edges and give separate values for positive (midspan) and negative (support) moments in each direction. The yield-line basis means the code implicitly allows some moment redistribution, which is why the coefficients differ from pure elastic analysis.

Nine edge-condition cases

IS 456 Table 26 covers all possible combinations of simply supported and continuous edges for a rectangular panel. Case 1 is the simplest (interior panel — all four edges continuous), and Case 9 is the other extreme (all four edges simply supported). The negative moment coefficient at a continuous edge is always higher than the positive midspan coefficient — this is consistent with elastic theory where supports attract more moment than midspans.

3. IS Code Background

ClauseSubjectPlain English
24.4Two-way slabsApplies to slabs with Ly/Lx ≤ 2. Moments in each direction obtained from Table 26 coefficients.
Table 26BM coefficientsGives αx and αy for positive and negative moments. M = α × w × lx². Note: always use lx (short span) in the formula, even for long-direction moments.
24.4.1Torsion reinforcementAt corners where a simply supported edge meets another SS edge, provide torsion steel. Each layer = 0.75 × Ast for maximum midspan moment. Extends Lx/5 in each direction.
Cl 23.2Span-depth ratioUse the shorter span for checking L/d ratio. Basic ratio = 20 (SS) or 26 (continuous).

4. Key Formulas

Bending Moments in Two-Way Slab
Short span: Mx = αx × w × lx²
Long span: My = αy × w × lx²

αx, αy = coefficients from IS 456 Table 26
w = total factored load per unit area (kN/m²)
lx = shorter span (m) — used for BOTH directions
Note: Separate coefficients for positive (+ve midspan) and negative (−ve support) moments
Torsion Reinforcement at Corners
At corner where two simply supported edges meet:
Ast per layer = 0.75 × max midspan Ast (short direction)
Provide in 4 layers (top and bottom in both directions)
Extend lx/5 from corner in each direction
At corner with one continuous and one SS edge: half the above
At corner with two continuous edges: not required

5. BM Coefficient Table (IS 456 Table 26 — extract)

Values shown for selected Ly/Lx ratios. Full table has 9 cases.

Case 4: One Short Edge Discontinuous (very common in Indian buildings)

Ly/Lxαx(+ve)αx(−ve)αy(+ve)αy(−ve)
1.00.0350.0470.0350.047
1.20.0440.0590.0370.049
1.50.0570.0750.0400.052
2.00.0680.0890.0430.056

Case 9: All Four Edges Simply Supported

Ly/Lxαxαy
1.00.0620.062
1.20.0840.059
1.50.1040.046
2.00.1180.029

How to use: Find your Ly/Lx ratio (interpolate if needed). Pick the case matching your edge conditions. Read off αx and αy. Multiply by w × lx² to get the moment per metre width. Then design steel for a 1m strip in each direction.

6. Step-by-Step Design Procedure

  1. Check Ly/Lx ≤ 2. If yes → two-way slab.
  2. Identify edge conditions — which edges are continuous (monolithic with adjacent panels) and which are discontinuous (simply supported on walls). Pick the case number from IS 456 Table 26.
  3. Assume depth using span-depth ratio based on shorter span.
  4. Calculate factored load w = 1.5 × (self-weight + finish + live load).
  5. Read coefficients αx and αy (both positive and negative) from Table 26 for your Ly/Lx and case.
  6. Calculate moments: Mx = αx × w × lx², My = αy × w × lx².
  7. Design steel for each moment (4 values typically: +ve and −ve in x and y).
  8. Check minimum steel = 0.12% of bD for each direction.
  9. Check bar spacing ≤ min(3d, 300mm) for main, min(5d, 450mm) for distribution.
  10. Provide torsion reinforcement at corners per Cl 24.4.1 if SS edges meet.

7. Worked Examples

Example 1 — Interior Panel, All Edges Continuous (Case 1)
A slab panel 4m × 5m (all edges continuous). LL = 3 kN/m², finish = 1 kN/m². M20, Fe415.
Step 1
Ly/Lx = 5/4 = 1.25 ≤ 2 → Two-way slab. Case 1 (interior panel).
Step 2 — Depth
d = 4000/(26×1.4) = 110mm → D = 135mm → Use D = 140mm, d = 115mm
Step 3 — Loads
w = 1.5 × (25×0.14 + 1 + 3) = 1.5 × 7.5 = 11.25 kN/m²
Step 4 — Coefficients (Ly/Lx=1.25, Case 1, interpolated)
αx(+ve) = 0.032, αx(−ve) = 0.042
αy(+ve) = 0.024, αy(−ve) = 0.032
Step 5 — Moments
Mx(+ve) = 0.032 × 11.25 × 4² = 5.76 kN·m/m
Mx(−ve) = 0.042 × 11.25 × 16 = 7.56 kN·m/m
My(+ve) = 0.024 × 11.25 × 16 = 4.32 kN·m/m
My(−ve) = 0.032 × 11.25 × 16 = 5.76 kN·m/m
Step 6 — Steel (for maximum: Mx−ve = 7.56 kN·m)
Ast = 193 mm²/m
Min = 0.12% × 1000 × 140 = 168 mm²/m → 193 > 168 ✅
Provide 8mm @ 250mm c/c (Ast = 201 mm²/m) both directions as minimum
At supports: 8mm @ 200mm c/c top steel
Example 2 — One Long Edge Discontinuous (Case 3)
Slab panel 3.5m × 4.5m. Three edges continuous, one long edge on masonry wall. LL = 4 kN/m², M25, Fe500.
Step 1
Ly/Lx = 4.5/3.5 = 1.29. Case 3 — one long edge discontinuous.
Step 2 — Depth
D = 150mm, d = 122mm
Step 3 — Load
w = 1.5 × (25×0.15 + 1 + 4) = 1.5 × 8.75 = 13.125 kN/m²
Step 4 — Coefficients (interpolated for Ly/Lx = 1.29, Case 3)
αx(+ve) = 0.039, αx(−ve) = 0.051, αy(+ve) = 0.030, αy(−ve) = 0.040
Step 5 — Moments (lx = 3.5m)
Mx(−ve) = 0.051 × 13.125 × 3.5² = 8.20 kN·m/m (governs depth)
Step 6 — Steel
Ast for Mx(−ve) = 157 mm²/m
Min = 0.12% × 1000 × 150 = 180 mm²/m → use minimum
Provide 8mm @ 270mm c/c (186 mm²/m) ✅
Example 3 — All Four Edges Simply Supported (Case 9)
A room 3m × 4m resting on masonry walls on all sides. LL = 2 kN/m². M20, Fe415.
Step 1
Ly/Lx = 4/3 = 1.33. Case 9 — all edges SS.
Step 2 — Depth
D = 130mm, d = 105mm (SS ratio = 20)
Step 3 — Load
w = 1.5 × (25×0.13 + 1 + 2) = 1.5 × 6.25 = 9.375 kN/m²
Step 4 — Coefficients (Case 9, Ly/Lx=1.33 interpolated)
αx = 0.091, αy = 0.051 (Case 9 has only +ve moments — no continuous edges)
Step 5 — Moments
Mx = 0.091 × 9.375 × 9 = 7.67 kN·m/m
My = 0.051 × 9.375 × 9 = 4.30 kN·m/m
Step 6 — Torsion Reinforcement
All corners have two SS edges → full torsion steel required.
Ast = 0.75 × max midspan Ast = 0.75 × 214 = 161 mm²/m per layer
Provide in 4 layers at each corner, extending 3000/5 = 600mm from corner.

8. GATE MCQs

Q1. A two-way slab is one where:
  1. (a) Ly/Lx > 2
  2. (b) Ly/Lx ≤ 2
  3. (c) Ly/Lx = 1
  4. (d) Ly/Lx > 3
Answer: (b)
When Ly/Lx ≤ 2, load bends the slab in both directions → two-way slab.
Q2. In the formula Mx = αx × w × lx², the dimension lx refers to:
  1. (a) Longer span
  2. (b) Shorter span
  3. (c) Average of both spans
  4. (d) Diagonal span
Answer: (b)
IS 456 Table 26 always uses the shorter span lx in the formula — even for My (the long-direction moment). This is a very common GATE trap.
Q3. For an interior panel (Case 1) of a two-way slab, torsion reinforcement at corners is:
  1. (a) Required at all corners
  2. (b) Required at no corners
  3. (c) Required at two corners
  4. (d) Required at half value
Answer: (b)
Case 1 = all edges continuous. Torsion reinforcement is needed only where two simply supported (discontinuous) edges meet. Interior panels have no SS edges.
Q4. The torsion reinforcement at a corner where two SS edges meet should have Ast per layer equal to:
  1. (a) 0.50 × max midspan Ast
  2. (b) 0.75 × max midspan Ast
  3. (c) 1.0 × max midspan Ast
  4. (d) 0.25 × max midspan Ast
Answer: (b)
IS 456 Cl 24.4.1 specifies 0.75 times the maximum midspan reinforcement. At a corner with one continuous and one SS edge, use half of this (0.375 × max midspan Ast).
Q5. In IS 456 Table 26, as Ly/Lx increases from 1.0 to 2.0:
  1. (a) αx increases, αy decreases
  2. (b) Both increase
  3. (c) Both decrease
  4. (d) αx decreases, αy increases
Answer: (a)
As the panel becomes more rectangular, the short span carries more load (αx increases) and the long span carries less (αy decreases). At Ly/Lx = 2.0, αy becomes very small.
Q6. For a square interior panel (Ly/Lx=1.0, Case 1), the short-span and long-span moments are:
  1. (a) Equal
  2. (b) Short span is twice long span
  3. (c) Long span is twice short span
  4. (d) Depends on concrete grade
Answer: (a)
For a square panel, by symmetry, αx = αy. The moments in both directions are identical.
Q7. The edge condition "one short edge discontinuous" corresponds to IS 456 Table 26 Case:
  1. (a) Case 2
  2. (b) Case 4
  3. (c) Case 6
  4. (d) Case 8
Answer: (b)
Case 4 = one short edge discontinuous (3 edges continuous, 1 short edge SS). Students must memorise the case numbering or have the table available.
Q8. At a continuous edge of a two-way slab, the moment is:
  1. (a) Zero
  2. (b) Positive (sagging)
  3. (c) Negative (hogging)
  4. (d) Depends on span ratio only
Answer: (c)
Continuous edges have negative (hogging) moments — tension at the top. Steel must be provided at the top face at continuous supports.
Q9. Torsion reinforcement extends from the corner by a distance of:
  1. (a) lx/3
  2. (b) lx/4
  3. (c) lx/5
  4. (d) lx/2
Answer: (c)
IS 456 Cl 24.4.1 — torsion steel extends lx/5 from the corner in both directions.
Q10. A panel 5m × 5m (all edges continuous) has factored load 12 kN/m². With αx = 0.032, the midspan short-span moment is:
  1. (a) 9.6 kN·m/m
  2. (b) 4.8 kN·m/m
  3. (c) 19.2 kN·m/m
  4. (d) 7.2 kN·m/m
Answer: (a)
Mx = 0.032 × 12 × 5² = 0.032 × 12 × 25 = 9.6 kN·m/m. Straightforward application.

9. Common Mistakes

Mistake 1: Using Ly instead of Lx in the BM formula. Even for My (long-direction moment), the formula uses lx (short span). Both directions use the SAME span in the formula.
Mistake 2: Wrong case selection. A "discontinuous" edge is simply supported (not monolithic with adjacent slab). If a slab panel is bordered by a beam with another panel on the other side cast monolithically, that edge is continuous.
Mistake 3: Forgetting torsion reinforcement. Wherever two SS edges meet at a corner, torsion steel is mandatory. Omitting it can lead to cracking at corners — a very common site defect.
Mistake 4: Not providing top steel at continuous edges. The negative moment at continuous supports is often larger than the positive midspan moment. Top steel is essential.

10. Quick Revision Summary

Memorise:

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