Complete generalization of the Ayrton-Perry formula for beam-column buckling problems

Szalai, József

doi:10.1016/j.engstruct.2017.10.031

Cited by 22 publications

(18 citation statements)

References 18 publications

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“…(1) and it is linearly dependent on the actual amplitude so the equivalency relationship of Eq. Important to note that the buckling mode shape ( ( )) can have arbitrary amplitude when calculating ( ) of Eq.…”

Section: Overall Imperfection Methods (Oim)mentioning

confidence: 99%

“…The theoretical background of the two components are described in detail in (1) and (2). It has been shown that the two versions of the methodology -the OIM (Overall Imperfection Method) and the OSRM (Overall Strength Reduction Method) -have common mechanical background based on the generalized Ayrton-Perry formulation and a universal transformation method.…”

Section: Overall Imperfection Methods (Oim)mentioning

confidence: 99%

“…In Table 1. the active loads are the first order compression and/or strong axis bending moment whichever are present at the equivalent point and directly generate the actual buckling mode (1). When the fundamental buckling mode type is defined the equivalency relationship can be used to calculate the member length of the ERM, which can be written in the following form:…”

Section: The Forward Model Transformationmentioning

confidence: 99%

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New stability design methodology through overall linear buckling analysis

Szalai¹,

Papp

2019

ce papers

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Two new stability design methods are presented: the Overall Strength Reduction Method (OSRM) and the Overall Imperfection Method (OIM). Both methods are based on the linear buckling analysis (LBA) of global structural models and use the standard reduction curves. The OSRM is formulated in the classic way using generalized slenderness and reduction factors while the OIM uses equivalent amplitude for the buckling mode based geometrical imperfection. It is shown that both methods have the same mechanical background which is built on two essential components: (1) the generalized form of an Ayrton-Perry (or Perry-Robertson) type strength reduction method for basic reference members and (2) a generalized transformation technique connecting the real members of the global structural model with the proper basic reference member. The first component is a mechanically consistent extension of the model behind the traditional buckling curves used only for specific stability cases like flexural buckling of columns or lateral-torsional buckling of beams so far. The second component can be regarded as the generalization of the well-known effective length approach. The new design methods cover all types of buckling modes (flexural, torsional, flexural-torsional, lateral-torsional or any interaction), which can be calculated by LBA of structural models composed of uniform or non-uniform members with arbitrary cross-sections and support conditions and subjected to any complex loading (e.g. biaxial bending with moment gradient, direct torsion effects etc.). There is no need for any additional input for the calculations (like effective length factors, unrestrained lengths of beams, moment gradient factors, equivalent length for the imperfection amplitude etc.) since all the necessary information is received from the elastic critical load and buckling mode shape. This paper clarifies the mechanical interpretation and proper calculation of all the components of the two methods and shows some comprehensive validation study on the performance.

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Section: Overall Imperfection Methods (Oim)mentioning

confidence: 99%

Section: Overall Imperfection Methods (Oim)mentioning

confidence: 99%

Section: The Forward Model Transformationmentioning

confidence: 99%

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New stability design methodology through overall linear buckling analysis

Szalai¹,

Papp

2019

ce papers

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“…In literature [12], the researchers examined the simply supported steel member with uniform cross section subjected to uniform forces. e results showed buckling resistance for such members and were standardized by the reduction factor based on the Ayrton-Perry formula [19] and calibrated by strong theoretical and empirical background. e local and overall stability of the columns through simulating their geometric and material nonlinear behavior was investigated [11].…”

Section: Introductionmentioning

confidence: 99%

Buckling Analysis and Stability of Compressed Low‐Carbon Steel Rods in the Elastoplastic Region of Materials

Partskhaladze

Mshvenieradze

Medzmariashvili

et al. 2019

Advances in Civil Engineering

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is paper presents new approaches for solving a problem of the stability of compressed rods in the elastoplastic working region of materials. It is known that the columns of buildings, supports of engineering devices, drill rods of oil, and gas extraction industry may be subjected to significant risk of stability loss. Nowadays, there are design methods based on test results defining the relations (e.g., critical stresses-slenderness) to avoid this risk due to stability loss, but the precision and limits of definition are not always known. e main objectives of the study were to develop new approaches that would allow specifying the values of critical stresses of compressed elements beyond the proportional limit. e problem of stability of the compressed elements in the elastoplastic region was studied according to the stability theory. e authors suggested an original approach to the issue; in particular, the determination of values of the critical stresses and the finding of the points of the bifurcation were carried out by the tangent established by experimental results and by the approximation of the so-called double modulus. Comparative analysis showed the advantage of the proposed approach, particularly that the new critical curves were located below the curves of Engesser-Karman and Shanley and above the critical curves established by building codes. A new approach for the determination of critical stresses in the elastoplastic region was developed through which the structural reliability and economic efficiency was increased by almost 12% compared to the existing approaches.

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“…Recent international research with the use of various proposals is also related to the assessment of the beamcolumn resistance. The first of them is based on a direct application of the Ayrton-Perry approach [10][11][12] where a generalised slenderness concept is applied. The second proposal [13] is the so-called Overall Imperfection Method and it is adequate for computer-aided design methodology which is based on advanced elastic beamcolumn finite element method.…”

mentioning

confidence: 99%

Buckling resistance evaluation of steel beam-columns using refined General Method approach

Stachura

Giżejowski

2019

MATEC Web Conf.

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Different aspects of Eurocode 3 General Method (GM) approaches are discussed in this paper. The purpose of present study is to improve the application of GM approach for both beam-columns without intermediate lateral-torsional restraints and with these restraints. The results from the proposed GM are compared with those from Eurocode 3-1-1 interaction equations according to Method 1 and Method 2. A better consistency between the developed GM approach and the Eurocode's interaction equation approach than Eurocode 3 GM approach is observed.

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Complete generalization of the Ayrton-Perry formula for beam-column buckling problems

Cited by 22 publications

References 18 publications

New stability design methodology through overall linear buckling analysis

New stability design methodology through overall linear buckling analysis

Buckling Analysis and Stability of Compressed Low‐Carbon Steel Rods in the Elastoplastic Region of Materials

Buckling resistance evaluation of steel beam-columns using refined General Method approach

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