Point Protection of Primary Beams of Steel Grillages Against Lateral Torsional Buckling

Piotrowski, Rafał; Siedlecka, Monika

doi:10.12913/22998624/121532

Cited by 3 publications

(3 citation statements)

References 4 publications

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“…The next stage involved the analysis of the limit states of the single layer ribbed dome, in which a full probabilistic description was utilized. In the literature, many studies can be found in which the deterministic approach was adopted to describe the ultimate and serviceability limit states [ 48 , 49 , 50 , 51 , 52 , 53 , 54 ]. According to the deterministic approach, loads, material, and geometry features of the structure are described with code-specified characteristic values and relevant safety factors.…”

Section: Resultsmentioning

confidence: 99%

Probabilistic Approach to Limit States of a Steel Dome

2021

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In this paper, Numpress Explore software, developed at the Institute of Fundamental Technological Research of the Polish Academy of Sciences (IPPT PAN), was used to conduct reliability analyses. For static-strength calculations, the MES3D module, designed by the authors, was employed. Ultimate limit state was defined as condition of non-exceedance of the capacity value, resulting from the stability criterion of the bent and compressed element. The serviceability limit state was defined as the condition of non-exceedance of allowable vertical displacement. The above conditions constitute implicit forms of random variable functions; therefore, it was necessary to build an interface between the Numpress Explore and MES3D programs. In the study, a comparative analysis of two cases was carried out. As regards the first case, all adopted random variables had a normal distribution. The second case involved a more accurate description of the quantities mentioned. A normal distribution can be adopted for the description of, e.g., the randomness in the location of the structure nodes, and also the randomness of the multiplier of permanent loads. In actual systems, the distribution of certain loads deviates substantially from the Gaussian distribution. Consequently, adopting the assumption that the loads have a normal distribution can lead to gross errors in the assessment of structural safety. The distribution of loads resulting from atmospheric conditions is decidedly non-Gaussian in character. The Gumbel distribution was used in this study to describe snow and wind loads. The modulus of elasticity and cross-sectional area were described by means of a log-normal distribution. The adopted random variables were independent. Additionally, based on an analysis of the elasticity index, the random variables most affect the failure probability in the ultimate limit state and serviceability limit state were estimated.

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Section: Resultsmentioning

confidence: 99%

Probabilistic Approach to Limit States of a Steel Dome

2021

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“…The literature on the interaction of component beams in grillages or similar structures (e.g., system of beams braced against torsion) focuses on, among others, (1) lateral torsional buckling of I-girders discretely braced against torsion and/or against translation [ 14 , 15 , 16 , 17 , 18 , 19 ], including lateral torsional buckling of beams with point bracing [ 20 , 21 ], (2) the numerical analysis of two- and four-beam structural systems transversely braced with coupling beams [ 22 ], (3) the assembly of beam systems in skewed bridge structures [ 23 ], (4) global stability loss in two-beam systems (beams connected by cross-frames) [ 24 , 25 ], (5) modelling of curvilinear composite bridges, in which the grillage structure made of full-wall I-beam girders was approximated by an equivalent 3D truss model [ 26 ], (6) taking into account, in the global analysis, the actual stiffness of the component beam joints (stringer-to-crossbeam) of the deck members of old railway bridges [ 27 ]. A considerable number of studies are available in the technical literature that deal with various grillage systems.…”

Section: Introductionmentioning

confidence: 99%

Elastic Critical Resistance of the Simple Beam Grillage Resulting from the Lateral Torsional Buckling Condition: FEM Modelling and Analytical Considerations

2023

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Transversely loaded beam grillages are quite often used in industrial construction. In order to produce a safe design of such structures, it is necessary to account for the lateral torsional buckling phenomenon, which reduces load-bearing capacity. To be able to calculate the relevant reduction factor, the elastic critical load must be determined. As regards the existing design practice for such structures, simplified conditions are assumed for the mutual restraint of the component beams. However, this approach does not correspond to reality. This study discusses the results of numerical investigations and analytical calculations concerning the effect of the elastic action of simple beam grillage (SBG) joints on the critical load, which results from the lateral torsional buckling (LTB) condition. The SBG was defined as a flat system of interconnected beams, unstiffened laterally and loaded perpendicularly to the grillage plane. The analysis covered H-shaped grillages with different span ratios of component beams, in which the main (coupling) beam was decisive for instability. The effectiveness of the use of closed-section stiffeners at the grillage joints was also investigated. The grillage elastic critical resistances (ECR) were determined for two variants of joint stiffening. The computations were performed by means of FEM numerical simulations. The spatial models were discretised with the following elements: (1) solid ones in Abaqus, (2) shell ones in ConSteel, and (3) thin-walled bars in ConSteel. The LTB critical moments of the weakest beam (critical beam), elastically restrained against warping and against lateral rotation (in the LTB plane), were computed using the analytical methods developed by the authors. To this end, the methods were proposed to determine the indexes of the critical beam elastic restraint in the adjacent stiffening beams. In the study, it was demonstrated that (1) taking into account the conditions of mutual elastic restraint and interaction of the component beams provides a more accurate assessment of the grillage ECR, (2) the use of closed-section stiffeners in the grillage joints increase the ECR compared with classic flat stiffeners, (3) the grillage ECR can be estimated based on the critical moment Mcr of the weakest beam (critical beam) when the conditions of its elastic restraint in joints are accounted for.

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“…Such an approach facilitates an analysis of other parameters that affect the LTB critical moment. Idealised boundary conditions of that type were taken into account to investigate the effect of the following: (a) the distribution of the bending moment over the beam length, e.g., [1][2][3][4][5][6], (b) the coordinates of the points of transverse load application over the height of the cross section, e.g., [1,[7][8][9][10], (c) discrete (point-based) restraint against displacement and/or the cross sections' torsion over of the beam length, e.g., [11][12][13][14][15][16][17][18], (d) LTB of monosymmetric cross sections [2,4,8,19], (e) the use of complete and incomplete (inserted) end plates [20][21][22], (f) coped beams [20,21,[23][24][25][26][27], effect on the LTB critical moment, (g) modification of the energy equation leading to a nonlinear analysis of eigenvalue problem [28], and (h) interaction between buckling and LTB of beam columns [29][30][31][32].…”

Section: Introductionmentioning

confidence: 99%

The Effect of Steel Beam Elastic Restraint on the Critical Moment of Lateral Torsional Buckling

Piotrowski

Szychowski

2022

Materials

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This paper reports the results of the next stage of the authors’ investigations into the effect of the elastic action of support nodes on the lateral torsional buckling of steel beams with a bisymmetric I-section. The analysis took into account beam elastic restraint against warping and against rotation in the bending plane. Such beams are found in building frames or frame structures. Taking into account the support conditions mentioned above allows for more effective design of such elements, compared with the boundary conditions of fork support, commonly adopted by designers. The entire range of variation in node rigidity was considered in the study, namely from complete freedom of warping to complete restraint, and from complete freedom of rotation relative to the stronger axis of the cross section (free support) to complete blockage (full fixity). The beams were conservatively assumed to be freely supported against lateral rotation, i.e., rotation in the lateral torsional buckling plane. Calculations were performed for various values of the indexes of fixity against warping and against rotation in the beam bending plane. In the study, formulas for the critical moment of bilaterally fixed beams were developed. Also, approximate formulas were devised for elastic restraint in the support nodes. The formulas concerned the most frequent loading variants applied to single-span beams. The critical moments determined in the study were compared, with values obtained using LTBeamN software (FEM). Good compliance of results was observed. The derived formulas are useful for the engineering design of this type of structures. The designs are based on a more accurate calculation model, which, at the same time offers simplicity of calculation.

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Point Protection of Primary Beams of Steel Grillages Against Lateral Torsional Buckling

Cited by 3 publications

References 4 publications

Probabilistic Approach to Limit States of a Steel Dome

Probabilistic Approach to Limit States of a Steel Dome

Elastic Critical Resistance of the Simple Beam Grillage Resulting from the Lateral Torsional Buckling Condition: FEM Modelling and Analytical Considerations

The Effect of Steel Beam Elastic Restraint on the Critical Moment of Lateral Torsional Buckling

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