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Civil Engineering DISCUSSION
A 400 mm square column carries service loads of 450 kN dead and 250 kN imposed. The ground investigation report gives an allowable bearing pressure of 150 kPa at the founding level. I need the plan size of an isolated pad footing.
I am unsure whether to divide the factored load or the unfactored load by the 150 kPa, whether the weight of the footing itself counts, and what then decides the thickness of the pad.
With an allowable bearing pressure, the plan area comes from unfactored service loads, because the allowable value already contains the safety factor against bearing failure and is usually also limited by settlement. Add an allowance for the footing's own weight, about 10 percent of the column load to start with: 450 + 250 + 70 = 770 kN.
Required area = 770 / 150 = 5.13 m². A 2.3 m square pad gives 5.29 m² and a pressure of 770 / 5.29 = 146 kPa. If the report states a net allowable pressure, meaning the increase over the pressure of the soil that was removed, the weight of footing and backfill roughly cancels against the excavated soil and need not be added; read the report to see which it is.
The structural design of the pad is a separate step and uses factored loads. With Eurocode-style factors, 1.35 × 450 + 1.5 × 250 = 983 kN. The design pressure on the underside is 983 / 5.29 = 186 kPa; the footing's own weight is left out here because it is carried straight into the ground and causes no bending in the pad.
The pad projects (2.3 - 0.4) / 2 = 0.95 m beyond each column face and acts as a cantilever loaded from below. The bending moment at the column face across the full width is 186 × 2.3 × 0.95² / 2 = 193 kN·m, which sets the bottom reinforcement in each direction.
Thickness is normally governed by shear, not bending. Two checks are made: punching shear on a perimeter around the column, where the column tries to push through the pad, and one-way shear across the full width at a set distance from the column face. The aim is usually a depth that needs no shear reinforcement, since links in a pad footing are awkward to fix.
A pad of this size commonly ends up around 450 to 600 mm deep, but take that as a starting guess for the checks in your design code, not a result. Cover to the bottom steel is larger than in a superstructure member because the concrete is cast against the ground.
If the column also brings a moment down, the pressure is no longer uniform. It varies linearly: q = P / A × (1 ± 6 × e / L), where e = M / P is the eccentricity. As long as e is less than L / 6 the whole base stays in compression.
With M = 100 kN·m on your footing, e = 100 / 770 = 0.13 m, well inside 2.3 / 6 = 0.38 m, but the peak pressure is 146 × (1 + 6 × 0.13 / 2.3) = 195 kPa, which exceeds 150 kPa. The pad then has to grow, be made rectangular with the long side in the direction of the moment, or be offset under the column so the resultant lands near the centre.
Treat the 150 kPa as specific to the footing size and depth the ground report assumed. A wider footing stresses the ground to a greater depth, roughly one and a half to two times its width, so on compressible soil a large pad settles more than a small one at the same pressure. Differential settlement between neighbouring columns is what damages a structure, so it is good practice to size all pads for similar bearing pressures under the long-term load.
Bearing values must come from a site investigation for any real building, not from a generic table. And if the pads start to cover more than about half of the building footprint, or would overlap, a combined footing or a raft is usually the better solution.
