Two-Way Slab Design Example (IS 456:2000)

Two-way slab design is one of the most important topics in RCC design. A slab is called a two-way slab when the ratio of longer span to shorter span is less than 2.

Problem Statement

Design a Two-Way Slab Design for a room of size:

Length = 4.5 m
Width = 3.5 m

Given:

Live load = 4 kN/m²
Concrete grade = M30
Steel grade = Fe415

Consider two cases:

Edges simply supported, corners free
Edges simply supported, corners held down

Case (A): Edges Simply Supported & Corners Free

Basic Assumptions

Thickness of slab = 150 mm
Clear cover = 15 mm
Bar diameter = 10 mm

Effective depth:

d = 150 − 15 − (10/2) = 130 mm

Effective Span Calculation

Short span (lx) = 3.5 + 0.13 = 3.63 m
Long span (ly) = 4.5 + 0.13 = 4.63 m

Ratio:

ly / lx = 4.63 / 3.63 = 1.28 < 2

Hence, it is a two-way slab

Load Calculation

Self weight = 0.15 × 25 = 3.75 kN/m²
Live load = 4 kN/m²
Finishes = 1 kN/m²

Total load:

= 3.75 + 4 + 1 = 8.75 kN/m²

Factored load:

= 1.5 × 8.75 = 13.125 kN/m²

Bending Moment Calculation

From IS 456 coefficients:

Mx = αx × wu × lx²
My = αy × wu × lx²

αx = 0.0912
αy = 0.0558

Moments:

Short span:

Mx = 15.77 kNm/m

Long span:

My = 9.65 kNm/m

Depth Check

Using limit state design:

Required depth:

d = √(Mu / (0.138 × fck × b))

d ≈ 61.7 mm

Adopt:

Overall depth = 100 mm
Effective depth = 80 mm

Reinforcement Design

Ast = (pt / 100) × b × d

Short Direction

Steel % ≈ 0.763%
Ast ≈ 610 mm²/m

Provide:

10 mm bars @ 120 mm c/c

Long Direction

Steel % ≈ 0.445%
Ast ≈ 356 mm²/m

Provide:

10 mm bars @ 200 mm c/c

Minimum Reinforcement Check

As per IS 456:

Ast(min) = 0.12% × b × D

Minimum = 0.12% = 96 mm²/m

Provided steel is safe

Case (B): Edges Simply Supported & Corners Held Down

Slab Thickness

Overall depth = 130 mm
Effective depth = 110 mm

Effective Span

lx = 3.61 m
ly = 4.61 m

Ratio:

ly / lx = 1.28 → Two-way slab

Load Calculation

Self weight = 3.25 kN/m²
Live load = 4 kN/m²
Finishes = 1 kN/m²

Factored load:

= 12.375 kN/m²

Bending Moments

(IS 456 Table values)

αx = 0.0776
αy = 0.056

Moments:

Mx = 12.51 kNm/m
My = 9.03 kNm/m

Reinforcement

Short Direction

Provide 10 mm bars @ 150 mm c/c

Long Direction

Provide 10 mm bars @ 200 mm c/c

Shear Check

Shear stress = 0.27 N/mm²
Shear capacity = 0.72 N/mm²

Slab is safe in shear

Corner Reinforcement (Important for Held Corners)

Provide 75% of mid-span steel
Required ≈ 392 mm²

Provide:

10 mm bars @ 100 mm c/c (top)

Length of reinforcement:

= 1/5 of span ≈ 950 mm

Final Reinforcement Summary

Direction	Spacing
Short span	10 mm @ 120–150 mm
Long span	10 mm @ 200 mm
Corner steel	10 mm @ 100 mm