Column Compression Stress

Compression stress in a short column

When a short column carries an axial load, the normal compression stress comes out to σ = P/A. Here P is the axial load and A the cross-sectional area. You check it against σ_max ≤ σ_allowable, and because the column is short there's no buckling reduction to worry about. Take P = 300 kN and A = 400 cm². That gives σ = 300·10³ / (400·10⁻⁴) = 7.5 MPa. With concrete f_ck = 25 MPa, the admissible stress lands around 18 MPa (roughly 0.85·f_ck/γ_c, taking γ_c = 1.4).

A column counts as short when its slenderness λ = K·L/r stays below the limit set by NBR 6118 §15 (for unbraced concrete columns that's usually λ < 35). Once you go past that, second-order effects and buckling need their own separate check. Keep the units lined up: P in N, A in m², σ in Pa.

Applications

Use it to dimension short reinforced-concrete columns under NBR 6118, to size pedestals and short steel posts, and to verify precast slab supports and bearing walls. It also works for a quick axial-load check before you bring in moment and slenderness effects.

FAQ

When is a column considered short? When λ = K·L/r stays below the code limit. NBR 6118 §15.8 puts that around 35 for typical concrete columns. Go past it and you have to add the second-order moment.

Does this include the rebar contribution? No. The full capacity of an RC column is N_d = 0.85·f_cd·A_c + f_yd·A_s. What this tool reports is the gross-concrete stress, meant as a quick check.

Why is the admissible stress so much lower than f_ck? NBR 6118 applies γ_c = 1.4 and then a 0.85 factor for sustained loading (the Rüsch effect). So σ_allow works out to roughly 0.85·f_ck/1.4 ≈ 0.6·f_ck, and that's before any safety margin on the load side.