• Steel and Composite Structures
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• v.19 no.4
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• pp.897-916
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• 2015

A procedure for critical buckling moment of a tapered beam is proposed with the application of potential energy calculations using Ritz method. Respective solution allows to obtain critical moments initiating lateral buckling of the simply supported, modestly tapered steel I-beams. In particular, lateral-torsional buckling of beams with simultaneously tapered flanges and the web are considered. Detailed, numerical, parametric analyses are carried out. Typical engineering, uniformly distributed design loads are considered for three cases of the load, applied to the top flange, shear centre, as well as to the bottom flange. In addition simply supported beam under gradient moments is investigated. The parametric analysis of simultaneously tapered beam flanges and the web, demonstrates that tapering of flanges influences much more the critical moments than tapering of the web.

• Steel and Composite Structures
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• v.39 no.5
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• pp.599-614
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• 2021

This study deals with the Lateral-Torsional Buckling (LTB) of a mono-symmetric tapered I-beam, in which the cross-section is varying longitudinally. To obtain the buckling moment, two concentrated bending moments should be applied at the two ends of the structure. This structure is made of Functionally Graded Material (FGM). The Young's and shear modules change linearly along the longitudinal direction of the beam. It is considered that this tapered beam is laterally restrained continuously, by using torsional springs. Furthermore, two rotational bending springs are employed at the two structural ends. To achieve the buckling moment, Ritz solution method is utilized. The response of critical buckling moment of the beam is obtained by minimizing the total potential energy relation. The lateral and torsional displacement fields of the beam are interpolated by harmonic functions. These functions satisfy the boundary conditions. Two different support conditions are considered in this study. The obtained formulation is validated by solving benchmark problems. Moreover, some numerical studies are implemented to show the accuracy, efficiency and high performance of the proposed formulation.

• Steel and Composite Structures
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• v.28 no.4
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• pp.403-414
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• 2018

In this paper, the lateral-torsional buckling of axially-transversally functionally graded tapered beam is investigated. The structure cross-section is assumed to be symmetric I-section, and it is continuously laterally supported by torsional springs through the length. In addition, the height of cross-section varies linearly throughout the length of structure. The proposed formulation is obtained for the case that the elastic and shear modulus change as a power function along the beam length and section height. This structure carries two concentrated moments at the ends. In this study, the lateral displacement and twisting angle relation of the beam are defined by sinusoidal series. After establishing the eigenvalue equation of unknown constants, the beam critical bending moment is found. To validate the accuracy and correctness of results, several numerical examples are solved.

• Magazine of the Korean Society of Agricultural Engineers
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• v.41 no.1
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• pp.106-114
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• 1999

This paper explores the geometrical non-linear behavior of the simply supported tapered beams subject to the trapezoidal distributed load and end moments. In order to apply the Bernoulli -Euler beam theory to this tapered beam, the bending moment equation on any point of the elastical is obtained by the redistribution of trapezoidal distributed load. On the basis of the bending moment equation and the BErnoulli-Euler beam theory, the differential equations governging the elastical of such beams are derived and solved numerically by using the Runge-Jutta method and the trial and error method. The three kinds of tapered beams (i.e. width, depth and square tapers) are analyzed in this study. The numerical results of non-linear behavior obtained in this study from the simply supported tapered beams are appeared to be quite well according to the results from the reference . As the numerical results, the elastica, the stress resultants and the load-displacement curves are given in the figures.

• Structural Engineering and Mechanics
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• v.10 no.5
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• pp.479-489
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• 2000

Based on the stiffness equation of the tapered beam element involving the effects of axial force and shear deformation, numerical investigations are carried out on elastic instability for web-linearly tapered columns with I-section of steel portal frames. Effects of shear deformation on the effective length of the tapered columns with I-section are studied. An efficient approach for determining the effective length of the tapered portal frame columns considering effects of shear deformation is proposed.

• Journal of the Korean Society of Hazard Mitigation
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• v.8 no.2
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• pp.45-49
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• 2008

This paper investigated the accuracy of the current design formulae for the elastic buckling strength of web-tapered I-beams in AISC-LRFD specification. The basic concept is to replace a tapered beam by an equivalent prismatic beam with a different length, but with a cross section identical to that of the smaller end of the tapered beam. The modification factor, B, is used to account for the stress gradient within the unbraced length and the lateral restraining effects offered by the adjacent segments. The modification factor(B) suggested in AISC-LRFD specification was compared with the finite element method(FEM) results. This paper presented a redefined method to calculate the modification factor(B).

• Steel and Composite Structures
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• v.13 no.3
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• pp.225-238
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• 2012

Steel structural elements with web-tapered I cross section, are usually made of welded thin plates. Due to the nonrectangular shape of the element, thin web section may be obtained at the maximum cross section height. The buckling strength is directly influenced by lateral restraining, end support and initial imperfections. If no lateral restraints, or when they are not effective enough, the global behaviour of the members is characterized by the lateral torsional mode and interaction with sectional buckling modes may occur. Actual design codes do not provide a practical design approach for this kind of elements. The paper summarizes an experimental study performed by the authors on a relevant number of elements of this type. The purpose of the work was to evaluate the actual behaviour of the web tapered beam-columns when applying different types of lateral restraints and different web thickness.

• Steel and Composite Structures
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• v.4 no.4
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• pp.281-301
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• 2004

The paper begins by presenting a unified variational approach to the lateral-torsional buckling (LTB) analysis of doubly symmetric prismatic and tapered thin-walled beams with open cross-sections, which accounts for the influence of the pre-buckling deflections. This approach (i) extends the kinematical assumptions usually adopted for prismatic beams, (ii) consistently uses shell membrane theory in general coordinates and (iii) adopts Trefftz's criterion to perform the bifurcation analysis. The proposed formulation is then applied to investigate the influence of the pre-buckling deflections on the LTB behaviour of prismatic and web-tapered I-section simply supported beams and cantilevers. After establishing an interesting analytical result, valid for prismatic members with shear centre loading, several elastic critical moments/loads are presented, discussed and, when possible, also compared with values reported in the literature. These numerical results, which are obtained by means of the Rayleigh-Ritz method, (i) highlight the qualitative differences existing between the LTB behaviours of simply supported beams and cantilevers and (ii) illustrate how the influence of the pre-buckling deflections on LTB is affected by a number of factors, namely ($ii_1$) the minor-to-major inertia ratio, ($ii_2$) the beam length, ($ii_3$) the location of the load point of application and ($ii_4$) the bending moment diagram shape.

• Structural Engineering and Mechanics
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• v.90 no.3
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• pp.273-285
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• 2024

Tapered girders emerged as an economical remedy for the challenges associated with constructing long-span buildings. From an economic standpoint, these systems offer significant advantages, such as wide spans, quick assembly, and convenient access to utilities between the beam's shallow sections and the ceiling below. Elastic-local buckling is among the various failure modes that structural designers must account for during the design process. Despite decades of study, there remains a demand for efficient and comprehensive procedures to streamline product design. One of the most pressing requirements is a better understanding of the tapered web plate girder's local buckling behavior. This paper conducts a comprehensive numerical analysis to estimate the critical buckling coefficient for simply supported tapered steel web plates, considering loading conditions involving compression and bending stresses. An eigenvalue analysis was carried out to determine the natural frequencies and corresponding mode shapes of tapered web plates with varying geometric parameters. Additionally, the study highlights the relative significance of various parameters affecting the local buckling phenomenon, including the tapering ratio of the panel, normalized plate length, and ratio of minimum to maximum compressive stresses. The regression analysis and optimization techniques were performed using MATLAB software for the results of the finite element models to propose a separate formula for each load case and a unified formula covering different compression and bending cases of the elastic local buckling coefficient. The results indicate that the proposed formulas are applicable for estimating the critical buckling coefficient for simply supported tapered steel web plates.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2011.06a
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• pp.149-150
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• 2011