Footing Size Calculator

An isolated spread footing exists to convert a concentrated column force into a soil pressure the ground can tolerate. Its plan area follows directly from the service load divided by the allowable bearing pressure, with roughly 10 percent added for the self-weight of the concrete pad and any soil resting on it. Allowable bearing values are not soil constants but design outputs: geotechnical engineers compute an ultimate capacity and divide by a factor of safety of about 2.5 to 3.0. Typical allowable values run near 75 to 100 kPa for soft to firm clay, 150 to 200 kPa for medium dense sand, 300 kPa or more for dense sand and gravel, and well over 1,000 kPa for sound rock. Concrete unit weight is taken as 24 kN per cubic meter and soil around 18 kN per cubic meter. Once the plan dimensions are set, the pad thickness is governed by shear rather than bending, because adding shear reinforcement to a footing is impractical. Two checks apply. Two-way or punching shear examines a perimeter at half the effective depth from the column face, where the column can push a truncated cone through the slab; the limit used here is 0.33 times the square root of the concrete strength in MPa. One-way shear treats the cantilever as a wide beam with a critical section one effective depth from the column face and a lower limit of 0.17 times the square root of fc. Flexural steel is placed in the bottom face to resist the cantilever moment, with minimum ratios around 0.0018 to 0.0020 and at least 75 mm of cover when cast against soil. The output is a preliminary size only. It presumes a concentric load with no applied moment, uniform bearing pressure, no groundwater or frost penetration, and soil properties from an actual site investigation rather than assumption.

Spread footings are as old as monumental construction, but their proportions were set by precedent rather than analysis until soil behavior itself became a quantitative subject. That change is attributed to Karl Terzaghi, whose 1925 book Erdbaumechanik established soil mechanics as a discipline by showing that the strength and settlement of a soil depend on effective stress and pore water pressure. In his 1943 work Theoretical Soil Mechanics he presented the bearing capacity equation with its cohesion, surcharge, and unit weight terms that still frames shallow foundation design. George Geoffrey Meyerhof extended the theory through the 1950s and 1960s with factors for footing shape, embedment depth, and inclined loading, and Terzaghi and Ralph Peck's 1948 Soil Mechanics in Engineering Practice tied capacity estimates to standard penetration test blow counts. The concrete side of the problem developed alongside. The American Concrete Institute published reinforced concrete regulations from 1910 onward, with the ACI 318 designation appearing in 1941, and successive editions codified footing detailing. Punching shear proved to be the difficult case, since it fails abruptly and was implicated in several flat slab and footing collapses. Systematic laboratory work in the mid twentieth century, consolidated in the 1962 report of joint ACI-ASCE Committee 326 on shear and diagonal tension, produced the critical perimeter located at half the effective depth from the loaded face and the square-root-of-fc stress limit that codes still use in modified form. Eurocode 7, first issued in the 1990s and revised in 2004, later reformulated the same problem in partial factor terms, applying separate factors to actions and to soil strength parameters.