Table of Contents
1. Introduction to Footing Design
Footings are the foundation elements that transfer column or wall loads to the soil. They must be designed to distribute the load over a sufficient area to keep soil pressures within allowable limits and to resist internal forces (moment, shear, and punching shear) without failure. ACI 318 Chapter 13 provides the governing design provisions for footings.
The design process involves three primary checks: (a) bearing pressure under service and factored loads must not exceed allowable and ultimate bearing capacities respectively, (b) the footing must have adequate thickness to resist punching shear (two-way) and beam shear (one-way), and (c) flexural reinforcement must be provided for bending moments with proper development length and detailing.
Key inputs include column load (axial load and moments), soil bearing capacity, concrete compressive strength f'c, steel yield strength fy, and geotechnical parameters. The Footing Size Calculator automates the initial sizing, and the Soil Bearing Capacity Calculator determines the allowable soil pressure.
2. Types of Footings
Isolated (pad) footings are the most common type, supporting a single column. They are typically square or rectangular and are economical for column loads up to approximately 2000 kN. The footing projects beyond the column face on all sides, with reinforcement in both directions at the bottom.
Combined footings support two or more columns, used when columns are closely spaced or when an isolated footing would extend beyond the property line. They are typically rectangular or trapezoidal in plan. The centroid of the footing should align with the resultant of the column loads to achieve uniform soil pressure.
Strip footings (wall footings) support continuous bearing walls. They are designed as one-way members spanning perpendicular to the wall, with reinforcement running perpendicular to the wall length. Strip footings are common for light structures, retaining walls, and basement walls.
Raft (mat) foundations cover the entire building footprint and are used when individual footings would cover more than 50% of the plan area, or when differential settlement must be minimized. Mat design is more complex and covered in separate resources. See the Foundation Types Explained article for a broader comparison.
3. Footing Sizing from Bearing Capacity
The required footing area is determined from the service loads and the allowable bearing capacity: A = P_service / qa. For isolated square footings, B = sqrt(A). For rectangular footings, the aspect ratio typically matches the column aspect ratio plus twice the required projection on each side.
Under factored loads, the maximum soil bearing pressure qu_max must not exceed the ultimate bearing capacity. For concentric loading, qu = Pu / A. For eccentric loading (presence of moment), the soil pressure distribution is trapezoidal or triangular: qu_max = Pu/A + M/S, qu_min = Pu/A - M/S, where S = BL^2/6 is the section modulus. If qu_min is negative (tension), use triangular pressure distribution over a reduced effective area.
For ACI 318, the factored soil pressure used for strength design is qu_factored = Pu / A (for concentric loading). For eccentric loading, use the maximum factored bearing pressure. The Soil Bearing Capacity Calculator provides allowable and ultimate bearing capacities for design.
4. Thickness Design — Two-Way and One-Way Shear
Footing thickness is governed by shear strength, not flexure. Two shear checks are required: punching shear (two-way) at a critical section d/2 from the column face, and beam shear (one-way) at a critical section d from the column face.
Punching shear (two-way): The critical perimeter bo = 2(c1 + c2 + 2d) for a rectangular column. The nominal shear strength Vc is the smallest of: (a) Vc = 0.17(1 + 2/beta)sqrt(f'c) bo d, (b) Vc = 0.083(alpha_s d/bo + 2)sqrt(f'c) bo d, and (c) Vc = 0.33sqrt(f'c) bo d. Where beta is the column aspect ratio, alpha_s = 40 for interior columns, 30 for edge, 20 for corner. The factored punching shear Vu = Pu - qu x (critical area within the perimeter). Must satisfy Vu less than or equal to phi Vc with phi = 0.75.
One-way shear (beam action): The critical section is at distance d from the column face. The shear force is the sum of factored soil pressures acting on the shaded area beyond the critical section. Vc = 0.17sqrt(f'c) b d. Must satisfy Vu less than or equal to phi Vc. One-way shear typically governs for slender footings (length/thickness greater than 5), while punching shear governs for thicker footings.
5. Flexural Reinforcement Design
The critical section for bending in an isolated footing is at the column face. The factored moment Mu is computed from the soil pressure acting on one side of the column: Mu = qu x (projection)^2 / 2 per unit width for a square footing. For rectangular footings, compute moments in both directions separately using the respective projections.
The required steel area per unit width is: As = Mu / (phi x fy x jd), with jd approximately 0.9d. Minimum reinforcement per ACI 318 for footings: As_min = 0.0018bh (for shrinkage and temperature, using Grade 420 steel). The maximum spacing of flexural reinforcement is 3h or 450 mm, whichever is smaller.
| Footing Type | Reinforcement | Distribution | Min. Ratio |
|---|---|---|---|
| Isolated (square) | Bottom mat both ways | Uniform spacing | 0.0018 |
| Isolated (rectangular) | Bottom mat both ways | Long direction: uniform; Short: banded center | 0.0018 |
| Strip (wall) | Bottom bars perpendicular to wall | Uniform across width | 0.0018 |
For rectangular footings, ACI 318 requires that reinforcement in the long direction be uniformly distributed. In the short direction, a portion of the reinforcement (2/(beta+1)) must be concentrated within a band equal to the footing width in the short direction, centered on the column. The Rebar Weight Calculator assists with reinforcement quantity estimation.
6. Development Length and Detailing
Reinforcement in footings must be developed beyond the critical section for flexure. For straight bars, the available development length is the distance from the column face to the end of the bar minus cover. This available length must be at least Ld per ACI 318. If the available length is insufficient, use standard 90-degree hooks at bar ends.
Concrete cover for footings: ACI 318 requires a minimum of 75 mm for concrete cast against earth and 50 mm for concrete exposed to weather. For interior footings (with a mud slab), 50 mm cover is typically acceptable. Cover is measured from the concrete surface to the outermost reinforcement.
Load transfer from column to footing is verified through bearing on the contact surface. The bearing strength of the column is phi(0.85f'c)A1, and the footing bearing strength can be increased by sqrt(A2/A1) up to 2.0, where A1 is the column area and A2 is the footing area. Dowels matching the column reinforcement are typically provided to ensure load transfer, with minimum area 0.005 times the column gross area.
7. Combined and Strip Footings
Combined footings are designed as a beam spanning between columns, with the centroid aligned with the resultant load for uniform soil pressure. The design involves: (a) determining the footing dimensions to achieve uniform pressure, (b) drawing the shear force and bending moment diagrams along the length, (c) designing longitudinal reinforcement for the maximum positive and negative moments, and (d) designing transverse reinforcement under each column for transverse bending. The footing thickness is governed by one-way shear at the critical section adjacent to the larger column.
Strip footings under walls are designed per unit length of wall. The projection beyond the wall face is typically 0.4 to 0.6 times the footing width. The bending moment at the wall face is Mu = qu x (projection)^2 / 2 per unit length. The depth is governed by one-way shear at distance d from the wall face: Vu = qu x (projection - d). Strip footings typically use less reinforcement than isolated footings for the same wall load.
For all footing types, construction joints should be located at least 300 mm above the footing base, and the top surface should be roughened to ensure shear transfer between the footing and the column or wall. The Footing Size Calculator provides preliminary dimensions for all footing types.
8. Worked Example
Design an Isolated Square Footing
Given: Column 400 mm x 400 mm with Pu = 2400 kN (factored), P_service = 1600 kN (service). f'c = 28 MPa, fy = 420 MPa. Allowable bearing capacity qa = 250 kPa. Soil unit weight = 18 kN/m3. Depth to footing base = 1.5 m.
Step 1 — Size footing. Required area = 1600 / 250 = 6.4 m2. Use B = 2.6 m (A = 6.76 m2). Net allowable bearing pressure (including overburden removal): qnet = 250 - 18(1.5) = 223 kPa. A = 1600 / 223 = 7.17 m2. Use B = 2.7 m (A = 7.29 m2). Factored soil pressure qu = 2400 / 7.29 = 329 kPa.
Step 2 — Thickness from punching shear. Assume h = 600 mm, cover = 75 mm, bar dia = 16 mm, d = 600 - 75 - 8 = 517 mm. Critical perimeter bo = 4(400 + 517) = 3668 mm. Vu = 2400 - 329(0.917)^2 = 2123 kN. Vc = 0.33sqrt(28)(3668)(517) x 10^-3 = 0.33(5.292)(3668)(517) x 10^-3 = 3312 kN. phi Vc = 0.75(3312) = 2484 kN > 2123 kN. OK.
Step 3 — One-way shear. Critical section at d from column face. Projection beyond = 1350 - 200 = 1150 mm. Critical distance = 1150 - 517 = 633 mm. Vu = 329 x 2.7 x 0.633 = 562 kN. phi Vc = 0.75 x 0.17 sqrt(28) x 2700 x 517 x 10^-3 = 0.75(0.17)(5.292)(2700)(517) x 10^-3 = 944 kN > 562 kN. OK.
Step 4 — Flexural reinforcement. Projection = 1.15 m. Mu = 329 x 2.7 x (1.15)^2 / 2 = 587 kN-m per 2.7 m width. Mu per m width = 587 / 2.7 = 217 kN-m/m. As = 217 x 10^6 / (0.9 x 420 x 0.9 x 517) = 1223 mm2/m. Try #16 @ 150 mm (As = 1340 mm2/m). Check As_min = 0.0018 x 1000 x 600 = 1080 mm2/m. 1340 > 1080. OK. Provide #16 @ 150 mm both ways.
Step 5 — Development length. Available length = 1150 - 75 = 1075 mm. Ld for #16: Ld = (fy x psi_t x psi_e x psi_s) / (1.7 sqrt(f'c)) x db, simplified: Ld = 420(1.0)(1.0)(0.8) / (1.7 x 5.292) x 16 = 597 mm. 1075 > 597. OK. Use the Footing Size Calculator for rapid iteration across different footing sizes.
Common Mistakes in Footing Design
Ignoring punching shear: Punching shear is the most common failure mode in footings. Always check the critical perimeter at d/2 from the column face, especially for heavily loaded columns on thin footings.
Using service loads for strength design: Footing sizing uses service loads (for bearing pressure), but reinforcement and thickness checks must use factored loads per ACI 318 load combinations.
Inadequate development length: Straight bars in footings often have limited available length. Always check Ld and use hooked bars when necessary.
Best Practices
- Always verify the allowable bearing capacity with a geotechnical engineer and factor in water table effects.
- For footings with moment, check that the minimum soil pressure is positive (no tension) under service loads.
- Provide a mud slab (50-75 mm) below footings to maintain cover and provide a clean working surface.
- Consider differential settlement between adjacent footings, especially in variable soil conditions.
- For corrosive soil conditions, increase cover to 75 mm and consider epoxy-coated reinforcement.
9. Frequently Asked Questions
What is the minimum footing thickness?
ACI 318 does not specify a minimum absolute thickness, but practical minimums are 300 mm for lightly loaded footings and 450 mm for typical building columns. Thickness is governed by shear strength, cover requirements, and development length needs.
What is the punching shear perimeter?
The critical section for punching shear is located at a distance d/2 from the column face. The perimeter bo = 2(c1 + c2 + 2d) for rectangular columns. For edge columns, the perimeter is reduced because part of the critical section falls outside the footing.
What is the difference between one-way and two-way shear?
One-way shear (beam action) acts across the full width of the footing at a distance d from the column face. Two-way shear (punching) acts around the column perimeter at d/2. Two-way shear capacity is higher because of the three-dimensional confinement effect.
How is reinforcement distributed in footings?
For square footings, reinforcement is uniformly spaced in both directions. For rectangular footings, long-span bars are uniform, while short-span bars have 2/(beta+1) of the total area concentrated in a band centered on the column (beta = L/B).
How is development length checked in footings?
The available length is the distance from column face to the bar end minus cover. This must equal or exceed Ld. Hooks are used when straight bar development is insufficient. For #16 bars and smaller in footings, Ld is typically 400-600 mm depending on grade.
How is the moment in footings calculated?
The critical section for moment is at the column face. For a square footing, the factored moment per meter width = qu x (projection)^2 / 2, where the projection is (B - c)/2. The moment acts on a cantilevered section of the footing.
How are combined footings designed?
Combined footings are designed as beams spanning between columns. Determine dimensions so the centroid aligns with the load resultant. Draw shear and moment diagrams, design longitudinal reinf. for max moments, and check one-way shear as the governing criterion for thickness.
How are eccentric footings designed?
For eccentric loading, the soil pressure distribution is trapezoidal. If eccentricity e exceeds B/6, part of the footing loses contact and pressure redistributes triangularly over effective width B' = 3(B/2 - e). Design reinforcement for the non-uniform pressure diagram.
How is soil pressure under footing calculated?
For concentric loads: q = P/A. For loads with moment: q = P/A +/- M/S, where S = BL^2/6. For combined footings, the pressure varies linearly along the length. Maximum pressure must not exceed allowable bearing capacity.
Are construction joints needed in footings?
Construction joints between footings and columns are typically required. ACI 318 requires the contact surface to be roughened to a full amplitude of 6 mm. Dowels extending from the footing into the column provide positive shear transfer. Avoid horizontal joints within the footing depth.
Related Calculators
Footing Size Calculator
Determine footing dimensions from loads and bearing capacity.
Soil Bearing Capacity Calculator
Compute allowable bearing pressure by multiple methods.
RC Column Calculator
Column design and load transfer to footings.
Rebar Weight Calculator
Reinforcement estimation for footing mats.
Related Articles
References & Standards
- ACI 318-19. Building Code Requirements for Structural Concrete. American Concrete Institute, 2019.
- IS 456:2000. Plain and Reinforced Concrete — Code of Practice. Bureau of Indian Standards.
- EN 1992-1-1:2004. Eurocode 2: Design of Concrete Structures. CEN, 2004.
- Bowles, J.E. Foundation Analysis and Design. 5th ed., McGraw-Hill, 1996.
- Coduto, D.P. Foundation Design: Principles and Practices. 3rd ed., Pearson, 2016.
- Civil Engineering Handbook — Foundation Engineering chapter.
- Engineering Formula Library — Footing design formulas.
- Engineering Standards Reference — ACI 318, IS 456, Eurocode 2.
- Engineering Glossary — Foundation and geotechnical terms.