Abstract
The stability of load-bearing members is a challenging issue for designers. The avoidance of possible stability troubles is a mandatory step of the overall design process. The paper presents and discusses two simplified methods based on the Technical Stability Theory (TSTh) of loss of stability of lateral buckling in elastic-plastic states of semi-slender columns axially compressed by force. It is assumed that in the critical elastic-plastic transverse cross-section there are the elastic and plastic parts of the area, keeping strength. To simplify the calculations, there are assumed the simplifications that the whole moment of inertia of a cross-section area is taken into account Jz = Jzall, the plastic module equals compress module Epl = Ec taken from experimental researches and as the next bigger simplification, the plastic module equals compressing module Epl = 0. The graphs of functions of the curved axes, their slopes, deflections of the columns, stresses and strains in thin-walled columns and compressing critical stresses depending on the cross-section areas and slenderness ratios are presented as the theoretical examples of thin-walled cylindrical columns and compared to results obtained from experiments with columns made of steel St35.
Highlights
IntroductionThe problem of the stability was searched and analyzed with a focus on many other relevant aspects for various engineering applications.Many research contributions were related to the stability issues of a multitude of load-bearing systems and members, including plates (Raheem et al, 2013; Hosseinpour et al, 2015; Hedayat et al, 2018; Than et al, 2018; Civalek and Avcar, 2020; Zhang et al, 2020) and bracing systems (Solazzi, 2010; Alencar et al, 2018; Mohabeddine et al, 2020), or Functionally Graded Material (FGM) structures (Sofiyev et al, 2008; Sofiyev and Avcar, 2010; Sofiyev et al, 2012; Nam et al, 2019; Cuong-Le et al, 2021), etc.The buckling of beams was searched by (Maraveas et al, 2018; Wankhade and Bendine, 2017; Toufik et al, 2018; Mansour et al, 2019; Mondal and Chatterjee, 2021; Zaki, 2021) and microbeams (Demir and Civalek, 2017).Single-layer graphene sheets have been examined in (), while polymer-confined concrete columns have been discussed in () and hyperelastic tubes are analyzed by ().The buckling of structures composed of various constructional materials was searched by (Broujerdian et al, 2018; Rostami and Kolahdooz, 2019; Esmaeili et al, 2020; Hassan and Al-Zaidee, 2020; Kılıç and Çinar, 2020; Taraghi et al, 2021).In the case of very slender columns, this refers to the problem of stability in elastic states
On the assumption that in the critical elastic-plastic transverse cross-section area, strength keep both parts, i.e., elastic and plastic and by simplifications that whole moment of inertia of a cross-section area is taken into account Jz = Jzall, the equation of the elastic lines y(x)el, elastic slopesel (Fig. 8) and function of maximal deflection yL/2(P)el in the elastic state (Fig. 9), for the cylindrical column in the elastic states with both pinned ends, according to Murawski (2018), were determined
To check the possibility of a bigger simplification of a computing, next to the assumption that in the critical elastic-plastic transverse cross-section area keep a resistance both parts, i.e., elastic and plastic, with simplification that in elastic-plastic states the moment of inertia is taken of whole transverse critical cross-section Jz = Jzall, was taken the assumption that the plastic module equals zehro Epl = 0
Summary
The problem of the stability was searched and analyzed with a focus on many other relevant aspects for various engineering applications.Many research contributions were related to the stability issues of a multitude of load-bearing systems and members, including plates (Raheem et al, 2013; Hosseinpour et al, 2015; Hedayat et al, 2018; Than et al, 2018; Civalek and Avcar, 2020; Zhang et al, 2020) and bracing systems (Solazzi, 2010; Alencar et al, 2018; Mohabeddine et al, 2020), or Functionally Graded Material (FGM) structures (Sofiyev et al, 2008; Sofiyev and Avcar, 2010; Sofiyev et al, 2012; Nam et al, 2019; Cuong-Le et al, 2021), etc.The buckling of beams was searched by (Maraveas et al, 2018; Wankhade and Bendine, 2017; Toufik et al, 2018; Mansour et al, 2019; Mondal and Chatterjee, 2021; Zaki, 2021) and microbeams (Demir and Civalek, 2017).Single-layer graphene sheets have been examined in (), while polymer-confined concrete columns have been discussed in () and hyperelastic tubes are analyzed by ().The buckling of structures composed of various constructional materials was searched by (Broujerdian et al, 2018; Rostami and Kolahdooz, 2019; Esmaeili et al, 2020; Hassan and Al-Zaidee, 2020; Kılıç and Çinar, 2020; Taraghi et al, 2021).In the case of very slender columns, this refers to the problem of stability in elastic states. The basic theory of slender columns losing stability in elastic states, as known, has been originally formulated by Euler (1744). He first introduced the concept of critical load Pcr and presented, according to his theory, the differential equation of an elastic deflected central line. Later it was searched by many others like (Khalil, 2004; Noaman, 2011; Avcar, 2014; Melo and Barbosa, 2020; Selvaraj and Madhavan, 2021)
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