How to use this calculator
Choose the cross-section and end conditions, then enter the length, modulus, axial load and eccentricity. Add the yield stress to find the load that first yields the column, solved numerically because the formula is nonlinear in P.
Formulas
Worked example
100 × 150 mm steel bar, 3 m pinned–pinned, P = 200 kN at e = 20 mm (the default)
- A = 15 000 mm², I = 28.1 × 10⁶ mm⁴, r = 43.3 mm, Le/r = 69.3.
- (Le/2r)√(P/EA) = 0.283 rad, sec = 1.042; ec/r² = 0.80.
- σmax = 13.33 MPa × [1 + 0.80 × 1.042] = 24.4 MPa; vmax = 0.83 mm.
- With σY = 250 MPa, the column first yields at PY = 1717 kN, a load safety factor of 8.6.
Frequently asked questions
Why is the safety factor on load smaller than σ_Y/σ_max?
Stress grows faster than load in the secant formula, because the deflection itself adds moment. Doubling the load more than doubles the stress, so design is done on the load.
What happens when e = 0?
The formula reduces to σ = P/A until P reaches the Euler load. Any real column has some eccentricity, which is why the secant formula is used for design curves.
Which axis should I use?
The axis of bending caused by the eccentricity: c and r are taken in the plane of e. Check the Euler load about the weak axis separately.