• Steel and Composite Structures
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• 제52권3호
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• pp.343-356
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• 2024

This paper presents an analytical solution for correctly predicting the Lateral-Torsional Buckling critical moment of simply supported castellated beams, the solution covers uniformly distributed loads combined with compressive loads. For this purpose, the castellated beam section with hexagonal-type perforation is treated as an arrangement of double "T" sections, composed of an upper T section and a lower T section. The castellated beam with regular openings is considered as a periodic repeating structure of unit cells. According to the kinematic model, the energy principle is applied in the context of geometric nonlinearity and the linear elastic behavior of materials. The differential equilibrium equations are established using Galerkin's method and the tangential stiffness matrix is calculated to determine the critical lateral torsional buckling loads. A Finite Element simulation using ABAQUS software is performed to verify the accuracy of the suggested analytical solution, each castellated beam is modelled with appropriate sizes meshes by thin shell elements S8R, the chosen element has 8 nodes and six degrees of freedom per node, including five integration points through the thickness, the Lanczos eigen-solver of ABAQUS was used to conduct elastic buckling analysis. It has been demonstrated that the proposed analytical solution results are in good agreement with those of the finite element method. A parametric study involving geometric and mechanical parameters is carried out, the intensity of the compressive load is also included. In comparison with the linear solution, it has been found that the linear stability underestimates the lateral buckling resistance. It has been confirmed that when high axial loads are applied, an impressive reduction in critical loads has been observed. It can be concluded that the obtained analytical solution is efficient and simple, and offers a rapid and direct method for estimating the lateral torsional buckling critical moment of simply supported castellated beams.

• Advances in aircraft and spacecraft science
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• 제1권3호
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• pp.253-271
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• 2014

A linearised buckling analysis of thin-walled beams is addressed in this paper. Beam theories formulated according to a unified approach are presented. The displacement unknown variables on the cross-section of the beam are approximated via Mac Laurin's polynomials. The governing differential equations and the boundary conditions are derived in terms of a fundamental nucleo that does not depend upon the expansion order. Classical beam theories such as Euler-Bernoulli's and Timoshenko's can be retrieved as particular cases. Slender and deep beams are investigated. Flexural, torsional and mixed buckling modes are considered. Results are assessed toward three-dimensional finite element solutions. The numerical investigations show that classical and lower-order theories are accurate for flexural buckling modes of slender beams only. When deep beams or torsional buckling modes are considered, higher-order theories are required.

• Journal of Advanced Marine Engineering and Technology
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• 제18권5호
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• pp.68-77
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• 1994

The authors apply the transfer influence coefficient method to the 3-dimensional vibration analysis of beam with multi-joints and formulate a general algorithm to analysis the longitudinal, flexural and torsional coupled free vibration. In this paper, the structure, which is mainly founded in the robot arms, cranes and so on, has some crooked parts, subsystems and joints but has no closed loop in this system. It is modeled as the beam of a distributed mass system with massless translational, rotational and torsional springs in each node, and joint elements of release or roll at which node the displacement vector is discontinuous. The superiorty of the present method to the transfer matrix method in the computation accuracy was confirmed by the numerical computation results. Moreover, we confirmed that boundary and intermediate conditions could ve controlled by varying the values o the spring constants.

• Steel and Composite Structures
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• 제4권1호
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• pp.23-36
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• 2004

The inelastic lateral-distortional buckling of doubly-symmetric hot-rolled I-section beam-columns subjected to a concentric axial force and uniform bending with elastic restraint which produce single curvature is investigated in this paper. The numerical model adopted in this paper is an energy-based method which leads to the incremental and iterative solution of a fourth-order eigenproblem, with very rapid solutions being obtained. The elastic restraint considered in this paper is full restraint against translation, but torsional restraint is permitted at the tension flange. Hitherto, a numerical method to analyse the elastic and inelastic lateral-distortional buckling of restrained or unrestrained beam-columns is unavailable. The prediction of the inelastic lateral-distortional buckling load obtained in this study is compared with the inelastic lateral-distortional buckling of restrained beams and the inelastic lateral-torsional buckling solution, by suppressing the out-of-plane web distortion, is published elsewhere and they agree reasonable well. The method is then extended to the lateral-distortional buckling of continuously restrained doubly symmetric I-sections to illustrate the effect of web distortion.

• Journal of Advanced Marine Engineering and Technology
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• 제21권3호
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• pp.256-266
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• 1997

The authors apply the transfer influence coefficient method to the 3. dimensional vibration analysis of beam with multi - joints and formulate a general algorithm to analyse the longitudinal, flexural and torsional coupled forced vibration. In this paper, a structure which is mainly found in the robot arms, cranes and so on, has some crooked parts, subsystems and joints, but has no closed loop in this system. It is modeled as the beam of a distributed mass system with massless translational, rotational and torsional springs in each node, and joint elements of release or roll at node which the displacement vector is discontinuous. The superiority of the present method to the transfer matrix method in the computation accuracy was confirmed from the numerical computation results. Moreover, we confirmed that boundary and intermediate conditions could be controlled by varying the values of the spring constants.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 한국전산구조공학회 2007년도 정기 학술대회 논문집
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• pp.223-226
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• 2007

In current specification, modification factor(B) for web-tapered beam is used to account for the stress gradient and the restraining effect for adjacent spans. However, because these effects are considered together in modification factor, this paper revaluate the accuracy of the modification factor used in current specification. Also this paper investigate the flexural torsional buckling strength of laterally fixed thin-walled arch with doubly symmetric section using the analytical and numerical method. From this investigate the concept of effective length to consider the out-of-plane boundary condition for straight column or beam is not applicate for the flexural-torsional buckling of laterally fixed arches.

• Structural Engineering and Mechanics
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• 제38권2호
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• pp.195-210
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• 2011

Bernoulli-Euler beam theory is used to develop an exact dynamic stiffness matrix for the flexural-torsional coupled motion of a three-dimensional, axially loaded, thin-walled beam of doubly asymmetric cross-section. This is achieved through solution of the differential equations governing the motion of the beam including warping stiffness. The uniform distribution of mass in the member is also accounted for exactly, thus necessitating the solution of a transcendental eigenvalue problem. This is accomplished using the Wittrick-Williams algorithm. Finally, examples are given to confirm the accuracy of the theory presented, together with an assessment of the effects of axial load and loading eccentricity.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 한국소음진동공학회 2000년도 추계학술대회논문집
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• pp.540-545
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• 2000

This paper presents the exact dynamic element for composite Timoshenko beam, which is inherently subject both to bending and torsional vibration. The coupling effect between bending and torsional vibrations is rigorouly considered in the derivation of the exact dynamic element. Two examples are provided to validate and illustrate the proposed exact dynamic element matrix for composite Timoshenko beam.

• Steel and Composite Structures
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• 제43권2호
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• pp.271-278
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• 2022

Buckling is one of the most critical phoneme in the design of steel structures. Lateral torsional buckling (LTB) is particularly significant for slender beams generally subjected to loading in plane. The web distortion effects on LTB are not addressed explicitly in standards for flexural design of steel I-section members. Hence, the present study is focused to predict the influence of the web distortion on the elastic (L_r) limiting lengths given in American Institute of Steel Construction (AISC) code for the lateral torsional buckling (LTB) behavior of steel beams due to no provision in the code for consideration of web distortion. For this aim, the W44x335 beam is adopted in the buckling analysis carried out by the ABAQUS finite element (FE) program since it is one of the most critical sections in terms of lateral torsional buckling (LTB). The strain results at mid-height of the web at mid-span of the beam are taken into account as the monitoring parameters. The web strain results are found to be relatively greater than the yield strain value when L/L_r is equal to 1.0. In other words, the ratio of L/L_r is estimated from the numerical analysis to be about 1.5 when the beam reaches its first yielding at mid-span of the beam at mid-height of the section. Due to the effect of web distortion, the elastic limiting length (L_r) from the numerical analysis is obtained to be considered as greater than the calculated length from the code formulation. It is suggested that the formulations of the limiting length proposed in the code can be corrected considering the influence of the web distortion. This correction can be a modification factor or a shape factor that reduces sectional slenderness for the LTB formulation in the code.

• Structural Engineering and Mechanics
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• 제18권6호
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• pp.745-757
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• 2004

Lateral-torsional buckling moment resistances of I-shaped stepped beams with continuous lateral top-flange bracing under a single point load on the top flange and negative end moments were investigated. Stepped beam factors and a moment gradient correction factor suggested by Park et al. (2003, 2004) were used to develop new lateral buckling formula for beam designs. From the investigation of finite element analysis (FEA), new lateral buckling formula of beams with singly or doubly stepped member changes and with continuous lateral top-flange bracing subjected to a single point load on top flange and end moments were developed. The new design equation includes the length-to-height ratio factor to account for the increase of lateral-torsional buckling moment resistance as the increase of length-to-height ratio of stepped beams. The calculation examples for obtaining lateral-torsional buckling moment resistance using the new design equation indicate that engineers should easily determine the buckling capacity of the stepped beams.