>>14327253where defined for the secant formula (for short columns), use the Exponential Formula. You get the constant lambda based on the column dimensions length & radius, the degree of end fixity, the material properties [maximum fiber stress @ failure & modulus of elasticity. Then you choose between the Parqabolic, exponential, Rankine, & Secant based on lambda.
Now this is different for non-buckling beams, which utilize the compressive strength (The inverse modulus of elasticity) which shortened, but also as the extreme fiber stress on one side