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Abstract <p>An innovational method for solving the Euler–Bernoulli problem of an overall buckling of the uniform column supported by rotational springs of stiffnesses γ<sub>1</sub>, γ<sub>2</sub>, 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<sub>cr</sub> to the nonlinear compression diagram ε(σ) of the material, the slenderness of the column λ and the values γ<sub>1</sub>, γ<sub>2</sub> 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<sub>cr</sub>(λ). It is shown that columns with λ ≤ λ<sub>min</sub>(γ<sub>1</sub>, γ<sub>2</sub>) cannot be buckled by any axial load <i>F</i> for various types of ε(σ) (Ramberg-Osgood, rational fraction, polynomial, etc.).</p>

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

  • 期刊论文

  • 发表日期：

    2025年4月1日

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  • V. V. Chistyakov,
  • S. M. Soloviev

摘要

Abstract

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 σcr 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 σcr(λ). It is shown that columns with λ ≤ λmin(γ1, γ2) cannot be buckled by any axial load F for various types of ε(σ) (Ramberg-Osgood, rational fraction, polynomial, etc.).