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Buckling Analysis of Tapered Continuous Columns by Using Modified Buckling Mode Shapes

  • Sina ToosiEmail author
  • Akbar Esfandiari
  • Ahmad Rahbar Ranji
Research Article
  • 18 Downloads

Abstract

Elastic critical buckling load of a column depends on various parameters, such as boundary conditions, material, and cross-section geometry. The main purpose of this work is to present a new method for investigating the buckling load of tapered columns subjected to axial force. The proposed method is based on modified buckling mode shape of tapered structure and perturbation theory. The mode shape of the damaged structure can be expressed as a linear combination of mode shapes of the intact structure. Variations in length in piecewise form can be positive or negative. The method can be used for single-span and continuous columns. Comparison of results with those of finite element and Timoshenko methods shows the high accuracy and efficiency of the proposed method for detecting buckling load.

Keywords

Buckling analysis Tapered column Continuous columns Finite element method Modified buckling mode shapes 

Nomenclature

K

stiffness matrix

KG

geometric stiffness matrix

λi

eigenvalue of the structure

φi

mode shape of the structure

δij

Kronecker’s delta

δλi

variation of eigenvalue

δφi

variation of mode shape

δK

variation of stiffness matrix

αij

linear coefficient of jth mode shape

\( {\boldsymbol{\varphi}}_i^{\prime } \)

changes in mode shape of the structure

E

Young’s modulus of elasticity

I

column flexural moment of inertia

T

internal load of elements

L

beam length

Pcr

critical buckling load of column

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Copyright information

© Harbin Engineering University and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Sina Toosi
    • 1
    Email author
  • Akbar Esfandiari
    • 1
  • Ahmad Rahbar Ranji
    • 1
  1. 1.Department of Ocean EngineeringAmirKabir University of TechnologyTehranIran

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