Column Base Plate Preliminary Design

What does a base plate do?

A steel column has a small cross section and would crush the concrete if it bore on it directly. The base plate spreads the column load over a larger area. Preliminary design asks two questions: is the plate large enough not to crush the concrete, and is it thick enough not to bend under that pressure?

Bearing pressure and concrete check

Under concentric compression the bearing pressure is σ = N / (B × L). It is compared with the design bearing strength of the concrete: f_jd = β_j × α × f_ck / γ_c. β_j accounts for the grout layer and is 2/3 when its conditions are met. α is the gain from load spreading in the concrete when the foundation is larger than the plate, and is at most 3.

Plate thickness

The plate bends as a cantilever where it projects beyond the column. The cantilever lengths are m = (L − 0.95 h) / 2 and n = (B − 0.8 b) / 2, and for the area between the flanges n′ = √(h × b) / 4. The largest one governs. The required thickness is t = l × √(2 σ / (0.9 f_y)). It comes from setting the bending moment of a unit strip, σ l² / 2, equal to its plastic bending resistance, 0.9 f_y t² / 4.

Example

An HEB 200 column (h = b = 200 mm) on a 360 × 360 mm plate, 1000 kN design load, C25 concrete, S235 plate. Bearing pressure is 1 000 000 / (360 × 360) = 7.72 MPa. Bearing strength is 0.667 × 25 / 1.5 = 11.1 MPa, so utilisation is 69 percent. The cantilevers are m = 85 mm, n = 100 mm and n′ = 50 mm, so 100 mm governs. Thickness is 100 × √(2 × 7.72 / (0.9 × 235)) = 27.0 mm, and a 30 mm plate is chosen.

Limits

The tool covers concentric compression only. In moment resisting column bases the pressure is not uniform and the anchors go into tension, so this calculation is not enough. Thickness follows the cantilever method of American practice and the bearing limit follows the Eurocode expression. This combination is meant for preliminary sizing. Anchors, welds and shear transfer are designed separately.