Compressive stress

Input

F value

F

Effective buckling length

L

Young's modulus

E

Second moment of area

I

Cross-sectional area

A

Critical slenderness ratio

\Lambda

Radius of gyration

i

Slenderness ratio

\lambda

Short-term allowable compressive stress

\sigma_s

Long-term allowable compressive stress

\sigma_l

Notes

Based on 5.1(3) of the AIJ Standard for Allowable Stress Design of Steel Structures (2019). For long-term loading, Eq. (5.3) applies while $\lambda \leq \Lambda$ and Eq. (5.4) once $\lambda > \Lambda$ , and the safety factor is $\nu = 3/2 + (2/3)(\lambda/\Lambda)^2$ (constant at 13/6 = 2.17 where $\lambda > \Lambda$ ). The result field shows the equation actually used.
The short-term value is 50 % above the long-term one (5.6 of the same Standard). At $\lambda = 0$ the long-term value is $F/1.5$ , so the short-term value is $F$ , but it falls further below $F$ as $\lambda$ grows.
Where the Standard writes "stress intensity", this page writes simply "stress".

Reference strengths F, by material.