A New Method for Determining the Buckling Resistance in the Nonlinear Range of Strains for a Column Supported by Rotational Stiffeners

An innovational method for solving the Euler–Bernoulli problem of an overall buckling of the uniform column supported by rotational springs of stiffnesses γ₁, γ₂, N ∙ m free from traditional simplifications (invariable flexural rigidity and length) is given. It is based on a natural and comprehensive constraint on the restored axis length. A system of algebraic equations relating the critical stress σ_cr to the nonlinear compression diagram ε(σ) of the material, the slenderness of the column λ and the values γ₁, γ₂ has been obtained, solved and verified in important special cases. It is shown that columns of the same material with the same so-called the reduced spring stiffnesses have identical dependencies σ_cr(λ). It is shown that columns with λ ≤ λ_min(γ₁, γ₂) cannot be buckled by any axial load F for various types of ε(σ) (Ramberg-Osgood, rational fraction, polynomial, etc.).