Footings transfer loads from columns to the soil. An isolated (pad) footing is the most common type for individual columns. IS 456:2000 Clause 34 governs its design. The process integrates geotechnical parameters (SBC) with structural design (bending, shear, punching).
Types of Foundations
| Type | Used When | Typical Load Range |
|---|---|---|
| Isolated (Pad) Footing | Individual column, good soil | Up to ~2000 kN |
| Combined Footing | Two columns close together or near boundary | Variable |
| Strap Footing | Eccentric loading, boundary column | Variable |
| Raft / Mat | Weak soil, high loads, many columns | Any |
| Strip Footing | Load-bearing walls | Linear loads |
Design Philosophy
Footing design involves two stages:
- Geotechnical design: Size the footing so gross soil pressure ≤ Safe Bearing Capacity (SBC)
- Structural design: Design the footing as a cantilever slab for the net upward soil pressure
Worked Example — Isolated Square Footing
Given Data
- Column size: 400 mm × 400 mm
- Column load: P = 1200 kN (service load)
- SBC of soil: q_safe = 200 kN/m²
- Depth of footing: Df = 1.5 m, Unit weight of soil: γ = 18 kN/m³
- fck = 25 N/mm², fy = 415 N/mm²
Step 1: Net Safe Bearing Capacity
Net SBC = q_safe − γ × Df = 200 − 18 × 1.5 = 200 − 27 = 173 kN/m²
Allow 10% extra for self-weight of footing: Net = 173 / 1.1 = 157 kN/m²
Step 2: Footing Area Required
A = P / Net q = 1200 / 157 = 7.64 m²
Side of square footing B = √7.64 = 2.76 m → Provide 2.8 m × 2.8 m
Step 3: Net Upward Soil Pressure (for structural design)
Factored load = 1.5 × 1200 = 1800 kN
Net upward pressure qu = 1800 / (2.8 × 2.8) = 229.6 kN/m²
Step 4: Depth from Punching Shear (Two-Way Shear)
Critical perimeter at d/2 from column face: bo = 4 × (400 + d)
Punching shear force Vp = qu × [B² − (400 + d)²] / 10⁶
Permissible punching shear stress τvp = ks × τc where ks = 1.0 (square column), τc = 0.25√fck = 0.25 × 5 = 1.25 N/mm²
Solving: d ≥ 420 mm → Provide d = 450 mm, D = 500 mm (cover = 50 mm)
Step 5: Bending Moment Design
Critical section for BM = at face of column (Clause 34.2.3.2)
Cantilever projection from column face: a = (B − c) / 2 = (2800 − 400) / 2 = 1200 mm
Mu = qu × B × a²/2 = 229.6 × 2.8 × 1.2²/2 = 463.6 kN·m
Step 6: Reinforcement
Ast = (0.5 × fck / fy) × [1 − √(1 − 4.6Mu/(fck × b × d²))] × b × d
b = 2800 mm, d = 450 mm, Mu = 463.6 × 10⁶ N·mm
= (0.5 × 25 / 415) × [1 − √(1 − 4.6 × 463.6×10⁶ / (25 × 2800 × 450²))] × 2800 × 450
= 3125 mm²
Minimum Ast = 0.12% × 2800 × 500 = 1680 mm² (less, so use calculated value)
Provide 16 mm bars: n = 3125/201 = 15.6 → 16 bars of 16 mm dia
Spacing = (2800 − 2×50) / (16−1) = 180 mm c/c ✓ (less than 3d = 1350 mm)
Step 7: One-Way (Beam) Shear Check
Critical section at d from column face: x = a − d = 1200 − 450 = 750 mm
Vu = qu × B × x = 229.6 × 2.8 × 0.75 = 482.2 kN
τv = Vu / (b × d) = 482200 / (2800 × 450) = 0.382 N/mm²
Pt = 100 × 3125 / (2800 × 450) = 0.248%
From IS 456 Table 19 for M25, pt = 0.25%: τc = 0.36 N/mm²
τv (0.382) > τc (0.36) → Increase d to 480 mm, D = 530 mm. Recheck → OK
Reinforcement Detailing — IS 456 Clause 34.3
| Item | Requirement |
|---|---|
| Cover to bottom bars | 50 mm (soil face, IS 456 Clause 26.4.1) |
| Development length Ld | Must be ≥ Ld from the critical section of maximum BM |
| Available length | a − cover = 1200 − 50 = 1150 mm; check Ld for 16 mm bar |
| Ld (Fe 415, M25) | 47φ = 47 × 16 = 752 mm < 1150 mm ✓ |
| Distribution in central band | For rectangular footing: 2/(β+1) of total steel in central band of width B |
Eccentrically Loaded Footing
When the column transfers both axial load P and moment M, the soil pressure varies linearly:
q_max = P/A + M/Z; q_min = P/A − M/Z
where Z = B³/6 for square footing. Condition: q_min ≥ 0 (no tension). If q_min < 0, increase footing size. Design for the trapezoidal pressure diagram.
Pedestal or Column Stub
A pedestal (short column with h < 3 × least lateral dimension) is provided above the footing to:
- Limit bar development length requirements
- Provide an easy construction joint
- Protect column bars from soil
Common Errors in Footing Design
- Using gross load (including self-weight) for structural design — should use factored column load only
- Using gross SBC without deducting overburden weight for footing sizing
- Forgetting punching shear check (most critical for thick footings)
- Not checking bar development length — bar must extend Ld beyond critical section
- Providing shear reinforcement in footing — IS 456 prefers increasing depth
Frequently Asked Questions
Why is the critical section for shear at d from column face?
IS 456 adopts the ACI approach where the diagonal tension crack forms at approximately 45° from the column-footing interface, placing the critical section at depth d from the loaded area.
What is the difference between one-way and two-way shear in footings?
One-way (beam) shear: wide beam action across full width B, critical at d from column face. Two-way (punching) shear: column punches through footing, critical perimeter at d/2 from column face. Punching is more critical for deeper footings with large column loads.
What is the minimum depth of a footing as per IS 456?
IS 456 Clause 34.1.2 requires minimum depth of 150 mm for plain concrete and generally 300–500 mm for RCC isolated footings to ensure adequate punching shear resistance.