IS 456:2000 · Foundations
Isolated Footing Design as per IS 456 — Complete Guide with 3 Worked Examples
⏱ 18 min read📅 June 2026✅ IS 456:2000🎓 GATE relevant
An isolated footing is the most common foundation type in Indian construction — it sits beneath a single column and spreads its concentrated load over a wider area of soil. Designing a footing means answering three questions: how big should it be (so the soil can carry the pressure), how deep (so it doesn't punch through or shear off), and how much steel (so it doesn't crack in bending). This guide covers all three from first principles, with three worked examples and 10 GATE MCQs.
1. Introduction — What Footings Do
Every structure ultimately rests on soil. A column in a G+3 building might deliver 800–1500 kN to a cross-section of just 230×450mm — that is a pressure of about 7000–14000 kN/m². No ordinary soil can withstand that; typical Indian soils have safe bearing capacities of 100–300 kN/m². The footing solves this mismatch by acting as a pressure spreader — it takes the concentrated column load and distributes it over a large enough area that the soil pressure stays within its safe limit.
Imagine standing on soft sand. Your shoes sink in because your weight acts on a small area. But if you stand on a wide plywood board, you stay on the surface — the board spreads your weight. An isolated footing is that plywood board for your column.
In Indian practice, isolated footings are used for individual columns in low-rise and mid-rise buildings, typically up to G+4 or G+5, where columns are spaced far enough apart that adjacent footings don't overlap. When footings start to overlap, you shift to combined footings, strap footings, or raft foundations.
2. Concept and Theory — Load Transfer to Soil
The three failure modes
A footing can fail in three distinct ways, and the design must guard against each:
Bearing failure (soil crushes): If the footing is too small, the soil pressure exceeds its bearing capacity. The soil squeezes out sideways and the footing sinks. This is prevented by making the footing large enough — a sizing check, not a structural check.
Punching shear (footing punches through): The column tries to punch through the footing like a cookie cutter through dough. A truncated cone of concrete around the column tends to push downward while the rest of the footing is pushed up by soil pressure. The critical section is at d/2 from the column face. This is a two-way shear failure and is usually the check that governs the footing depth.
One-way shear (footing acts as a wide beam): If you look at the footing as a wide cantilever beam projecting from the column face, it must resist the vertical shear from the soil pressure on the projecting portion. The critical section is at distance d from the column face.
Bending failure: The projecting portion of the footing bends upward like a cantilever due to the upward soil pressure. This creates tension on the bottom face, requiring reinforcement. The critical section for bending moment is at the face of the column.
Why footing design uses working loads for sizing but factored loads for structural checks
This is a point of confusion for many students. The soil bearing capacity is a serviceability parameter — it is the pressure the soil can carry under sustained loads without excessive settlement. Therefore, the footing size is determined using working (service) loads divided by the allowable SBC. However, the structural design of the footing itself (shear checks, bending steel) uses factored loads (1.5 × working load) because the concrete and steel must be designed to the limit state. The net upward pressure for structural design is qu = Pu / (B × L), where Pu is the factored load.
3. IS Code Background — Clause 34 of IS 456
| Clause | Subject | What it says (plain English) |
|---|
| 34.1 | General | Footings shall be designed to sustain applied loads and moments without exceeding safe bearing capacity and with adequate safety against sliding and overturning. |
| 34.2.3 | Bending moment | Critical section for bending moment is at the face of the column/pedestal. For concrete columns, at the column face. For masonry walls, at halfway between wall centre and wall face. |
| 34.2.4 | One-way shear | Critical section at distance d from the face of column. Footing acts as a wide beam — check τv ≤ τc from IS 456 Table 19. |
| 31.6 | Punching shear | Critical section at d/2 from column face. Permissible stress τc = ks × 0.25√fck. ks = 0.5 + βc but ≤ 1.0 (βc = short side / long side of column). |
| 34.5 | Minimum thickness | For footings on soil, minimum thickness at edge = 150mm. |
Formula 1 — Footing Plan Area
Areq = P / qsafe
P = working (unfactored) column load (kN)
qsafe = net safe bearing capacity = SBC − γsoil × Df (kN/m²)
This accounts for the weight of soil above the footing level
Add 10–15% extra area for self-weight of footing
Formula 2 — Net Factored Upward Pressure
qu = Pu / (B × L)
Pu = 1.5 × P (factored load)
B, L = footing width and length (m)
This uniform pressure acts upward on the footing base for all structural checks
Formula 3 — Punching Shear Check (Cl 31.6)
τv = Vu,punch / (bo × d) ≤ τc = ks × 0.25 × √fck
Vu,punch = Pu − qu × (column + d)² for square column/footing
bo = perimeter of critical section = 4 × (column side + d)
ks = 0.5 + βc ≤ 1.0, where βc = short/long side of column
d = effective depth of footing
Formula 4 — One-Way Shear Check (Cl 34.2.4)
Critical section at distance d from column face
Vu = qu × B × [(L − column length)/2 − d]
τv = Vu / (B × d) ≤ τc from IS 456 Table 19
Formula 5 — Bending Moment (Cl 34.2.3)
Mu = qu × B × [(L − column length)/2]² / 2
Critical section at face of column
The projecting cantilever of length (L − col)/2 carries uniform upward pressure qu
Calculate Ast using standard flexure formula or Mu = 0.87 fy Ast (d − 0.42xu)
5. Important Tables
Table 1: Typical SBC Values for Indian Soils
| Soil Type | SBC (kN/m²) | Common In |
|---|
| Soft clay | 50–100 | Coastal regions, river deltas |
| Medium clay / sandy clay | 100–150 | Indo-Gangetic plains |
| Stiff clay | 150–250 | Deccan plateau, central India |
| Medium dense sand | 150–250 | Rajasthan, coastal sand |
| Dense sand / gravel | 250–400 | River terraces, gravelly sites |
| Weathered rock | 300–500 | Hilly terrain, western ghats |
| Hard rock | 500+ | Granite/basalt regions |
Table 2: Permissible Shear Stress τc (IS 456 Table 19, extract)
| pt % | M20 | M25 | M30 |
|---|
| 0.15 | 0.28 | 0.29 | 0.29 |
| 0.25 | 0.36 | 0.36 | 0.37 |
| 0.50 | 0.48 | 0.49 | 0.50 |
| 0.75 | 0.56 | 0.57 | 0.59 |
| 1.00 | 0.62 | 0.64 | 0.66 |
How to use for footings: After calculating the steel percentage (pt) in the footing, look up τc for that pt and concrete grade. Compare with τv = Vu/(Bd). If τv ≤ τc, one-way shear is safe.
6. Step-by-Step Design Procedure
- Determine working load P from column design. Add 10% for footing self-weight.
- Calculate footing area = 1.1P / qsafe. Choose B × L (square if column is square, rectangular if column is rectangular — maintain same projection on all sides).
- Calculate factored upward pressure qu = Pu / (B × L).
- Assume depth: start with d = projection/1.5 as a trial (typically 400–600mm).
- Check punching shear at d/2 from column face. If it fails, increase d.
- Check one-way shear at d from column face. If it fails, increase d.
- Calculate bending moment at column face. Find Ast using flexure formula.
- Check minimum steel: 0.12% of bD for Fe415/Fe500 (IS 456 Cl 26.5.2.1).
- Select bar size and spacing. Maximum spacing ≤ 3d or 300mm.
- Check development length of footing bars from column face to footing edge.
7. Worked Examples
Example 1 — Square Footing for Square Column (Beginner)
Design an isolated square footing for a 300×300mm column. Working load P = 600 kN, SBC = 200 kN/m², M20 concrete, Fe415 steel.
Step 1 — Footing Size
Area = 1.1 × 600 / 200 = 3.3 m²
Side = √3.3 = 1.82m →
Provide 1.9m × 1.9m (area = 3.61 m²)
Step 2 — Net Factored Pressure
P
u = 1.5 × 600 = 900 kN
q
u = 900 / (1.9 × 1.9) =
249 kN/m²Step 3 — Punching Shear (try d = 400mm)
Critical perimeter b
o = 4 × (300 + 400) =
2800mm
Punching area = (300+400)² = 490,000 mm² = 0.49 m²
V
u = 900 − 249 × 0.49 = 900 − 122 =
778 kN
τ
v = 778 × 10³ / (2800 × 400) =
0.695 N/mm²
τ
c = 1.0 × 0.25 × √20 =
1.118 N/mm²
0.695 < 1.118
✅ Punching shear OKStep 4 — One-Way Shear
Projection from column face = (1900−300)/2 = 800mm
Critical section at d=400mm from face → cantilever = 800−400 =
400mm
V
u = 249 × 1.9 × 0.4 =
189.2 kN
τ
v = 189200 / (1900 × 400) =
0.249 N/mm²
For pt ≈ 0.25%, τ
c = 0.36 N/mm² (M20)
0.249 < 0.36
✅ One-way shear OKStep 5 — Bending Moment & Steel
Cantilever from column face = 0.8m
M
u = 249 × 1.9 × 0.8² / 2 =
151.4 kN·m
Ast = [0.5×20/415 × {1 − √(1 − 4.6×151.4×10⁶/(20×1900×400²))} ] × 1900 × 400
=
1112 mm²
Min steel = 0.12% × 1900 × 450 (total depth) = 1026 mm²
Provide
12mm bars @ 180mm c/c (Ast = 1900/180 × 113 = 1193 mm²)
✅
Example 2 — Rectangular Footing (Intermediate)
Design a footing for a 230×450mm column. Working load = 900 kN, SBC = 150 kN/m², M25 concrete, Fe500 steel.
Step 1 — Footing Size
Area = 1.1 × 900 / 150 = 6.6 m²
For equal projection: (B−0.23)/2 = (L−0.45)/2 → L = B + 0.22
B × (B+0.22) = 6.6 → B ≈ 2.5m, L = 2.72m →
Provide 2.5m × 2.75mStep 2 — Net Factored Pressure
P
u = 1.5 × 900 = 1350 kN
q
u = 1350 / (2.5 × 2.75) =
196.4 kN/m²Step 3 — Punching Shear (try d = 450mm)
b
o = 2×(230+450+450+450+450) = 2×(680+900) =
3160mm
Punch area = (0.23+0.45) × (0.45+0.45) = 0.68 × 0.90 = 0.612 m²
V
u = 1350 − 196.4 × 0.612 = 1350 − 120 =
1230 kN
τ
v = 1230×10³ / (3160×450) =
0.865 N/mm²
β
c = 230/450 = 0.511 → k
s = 0.5+0.511 = 1.011 → use 1.0
τ
c = 1.0 × 0.25 × √25 =
1.25 N/mm²
0.865 < 1.25
✅ Punching OKStep 4 — Bending & Steel (long direction)
Cantilever = (2750−450)/2 = 1150mm
M
u = 196.4 × 2.5 × 1.15² / 2 =
325 kN·m
Ast =
1782 mm²
Provide
16mm bars @ 160mm c/c along length (Ast = 2500/160 × 201 = 3141 mm²)
✅
Example 3 — Heavy Load with Deep Footing (Advanced)
Design a square footing for a 450×450mm column carrying working load = 1800 kN. SBC = 200 kN/m², M25 concrete, Fe500 steel.
Step 1 — Size
Area = 1.1 × 1800 / 200 = 9.9 m² → Side = √9.9 = 3.15m →
Provide 3.2m × 3.2mStep 2 — Factored Pressure
q
u = (1.5 × 1800) / (3.2²) = 2700 / 10.24 =
263.7 kN/m²Step 3 — Punching Shear (try d = 600mm)
b
o = 4 × (450+600) = 4200mm
V
u = 2700 − 263.7 × (1.05)² = 2700 − 290.7 =
2409 kN
τ
v = 2409×10³ / (4200×600) =
0.956 N/mm²
τ
c = 0.25√25 =
1.25 N/mm² →
✅ OKStep 4 — Bending Steel
Cantilever = (3200−450)/2 = 1375mm
M
u = 263.7 × 3.2 × 1.375² / 2 =
798 kN·m
Ast ≈
3290 mm²
Provide
20mm bars @ 150mm c/c both ways (Ast = 3200/150 × 314 = 6699 mm²)
✅
8. GATE Previous Year Style Questions
Q1. The critical section for punching shear in an isolated footing is located at:
- (a) Face of column
- (b) d from column face
- (c) d/2 from column face
- (d) 2d from column face
Answer: (c)
IS 456 Cl 31.6.1 specifies d/2 from the periphery of the column. This is the standard punching shear perimeter. Option (b) = d is for one-way shear. Mixing these up is the most common footing mistake in GATE.
Q2. The critical section for bending moment in a footing supporting a concrete column is at:
- (a) Centre of column
- (b) Edge of footing
- (c) Face of column
- (d) d from column face
Answer: (c)
IS 456 Cl 34.2.3.1 — for concrete columns, the critical section is at the face of the column. For masonry walls, it is at halfway between centre and face.
Q3. For footing size calculation, which load should be used?
- (a) Factored load
- (b) Working (service) load
- (c) Ultimate load × 1.5
- (d) It doesn't matter
Answer: (b)
SBC is a serviceability limit — it already includes a factor of safety (typically 2.5–3.0). So footing size uses working loads. Structural design (shear, bending) uses factored loads.
Q4. The permissible punching shear stress in M20 concrete is approximately:
- (a) 0.25 N/mm²
- (b) 1.12 N/mm²
- (c) 1.5 N/mm²
- (d) 0.75 N/mm²
Answer: (b)
τc = ks × 0.25√fck = 1.0 × 0.25 × √20 = 1.118 ≈ 1.12 N/mm². Option (a) uses the coefficient without √fck.
Q5. If the column is rectangular (230×450mm), the shape factor ks for punching shear is:
- (a) 0.511
- (b) 1.011
- (c) 1.0
- (d) 0.75
Answer: (c)
βc = 230/450 = 0.511. ks = 0.5 + 0.511 = 1.011, but IS 456 caps ks at 1.0. So ks = 1.0.
Q6. Minimum thickness at the edge of a footing on soil as per IS 456 is:
- (a) 100mm
- (b) 150mm
- (c) 200mm
- (d) 300mm
Answer: (b)
IS 456 Cl 34.5 specifies minimum 150mm at the edge for footings on soil. For pile caps, it is 300mm.
Q7. The critical section for one-way shear in a footing is at:
- (a) d/2 from column face
- (b) d from column face
- (c) Face of column
- (d) 1.5d from column face
Answer: (b)
IS 456 Cl 34.2.4 — one-way shear is checked at d from the column face, not d/2 (which is punching shear).
Q8. A square footing of side 2m carries a factored load of 800 kN. The net upward pressure is:
- (a) 400 kN/m²
- (b) 200 kN/m²
- (c) 100 kN/m²
- (d) 800 kN/m²
Answer: (b)
qu = 800 / (2×2) = 200 kN/m². Simple calculation — just don't use working load instead of factored.
Q9. In footing design, if punching shear stress exceeds permissible, the designer should:
- (a) Increase steel area
- (b) Increase footing plan size
- (c) Increase footing depth
- (d) Increase concrete grade
Answer: (c)
Punching shear stress = V/(bo×d). Increasing d reduces τv and simultaneously increases bo (since the critical perimeter depends on d). Steel area does not affect punching shear capacity directly. Increasing plan size reduces qu but is less efficient.
Q10. The minimum reinforcement in a footing slab (Fe415) as per IS 456 is:
- (a) 0.15% of bD
- (b) 0.12% of bD
- (c) 0.85bd/fy
- (d) 0.8% of bD
Answer: (b)
IS 456 Cl 26.5.2.1 specifies 0.12% of bD for HYSD bars (Fe415/Fe500) for slabs. Footings follow slab rules for minimum steel, not beam rules (0.85bd/fy) or column rules (0.8%).
9. Common Mistakes
Mistake 1: Using factored load for footing sizing. SBC already has a factor of safety built in. Using factored load makes the footing unnecessarily large and expensive.
Mistake 2: Confusing punching shear (d/2) and one-way shear (d) critical sections. This is the single most tested point in footing questions. Remember: punching is a two-way phenomenon (closer to column → d/2), one-way is like a beam (further out → d).
Mistake 3: Not checking development length. Footing bars must be long enough to develop full tensile stress. The available length = projection − cover. If insufficient, provide hooks or use smaller diameter bars.
Mistake 4: Using beam minimum steel (0.85bd/fy) instead of slab minimum (0.12% bD). A footing is designed like a slab, not a beam. The minimum steel rule for slabs applies.
10. Quick Revision Summary
Memorise these:
- Size: Use working loads ÷ SBC. Add 10% for self-weight.
- Structural design: Use factored loads (1.5× working).
- Punching shear critical section: d/2 from column face. τc = ks × 0.25√fck.
- One-way shear critical section: d from column face. τc from Table 19.
- Bending moment critical section: Face of column.
- Min steel: 0.12% of bD for Fe415/Fe500.
- Min edge thickness: 150mm on soil.
- Punching shear usually governs depth.
- ks = 0.5 + βc ≤ 1.0 (βc = short/long side of column).
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