Stability of Monosymmetric Beams and Cantilevers

Anderson, John M.; Trahair, Nicholas S.

doi:10.1061/jsdeag.0003114

Cited by 102 publications

(13 citation statements)

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“…The dimensions and details of the tested specimens are displayed in Figure (5) and summarized in Table 2. Three meshes, coarse, intermediate, and fine, were built for the specimen D-8-1.5 and the total number of elements in these was 10968, 37592, and 119540, as shown in Figure (6). This is to explore the effect of mish size on the FE solution's accuracy and processing time.…”

Section: Validation Of Finite Element Modelsmentioning

confidence: 99%

“…The results showed that the lowest value of ultimate moment capacities was obtained when loads were applied at the top flange and the highest at the bottom flange. Anderson and Trahair [6] provided numerical solutions for beams with simply supported and cantilever boundary conditions and compared their predicted critical moments against experimental results. Kitipornchai and Trahair [7] proposed approximate expressions for the sectional properties required to determine critical moments for beams with I-sections having unequal flanges and lipped flanges.…”

Section: Introductionmentioning

confidence: 99%

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Generalized formula of moment gradient lateral torsional buckling factor for monosymmetric steel beams

Sharaf

Sayed²,

El-Ghandour³

et al. 2023

Port-Said Engineering Research Journal

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The lateral-torsional buckling (LTB) behavior of steel beams has been extensively reported. Most reports have been limited to study the doubly-symmetric beams besides a few other standard geometries. On the other hand, not so much research exists for monosymmetric steel beams, and LTB is one of the most critical design aspects for this type of beams. Codes allow the researchers to relate the critical moment to any in-plane loading to the standard uniform moment and members using the moment gradient factor. The moment gradient factor is an essential parameter in the design of steel cross-sections. Yet, it needs more to be applicable for cross-section shapes and boundary conditions. In this paper, a numerical model based on finite element analysis is presented, which is adopted to investigate the values of the moment gradient factor for different loading configurations. The model is developed to investigate the influence of load location with respect to the shear center of the beam section as well as the flange width ratio on the critical moment causing LTB. The numerical analysis results were validated, and new general equations for the moment gradient factor were developed to consider the effect of the different parameters.

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Section: Validation Of Finite Element Modelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Generalized formula of moment gradient lateral torsional buckling factor for monosymmetric steel beams

Sharaf

Sayed²,

El-Ghandour³

et al. 2023

Port-Said Engineering Research Journal

View full text Add to dashboard Cite

show abstract

“…) Note that I R is non-zero for bisymmetric sections and has an important influence in nonlinear torsion behaviour and lateral post buckling response. The geometric coefficients β y , β z and β ω are called Wagner's coefficients; β y , β z are associated with the bending curvature under pure torsion and β ω is associated with the modification to the torsional stiffness in the presence of a bimoment [4]. These geometric parameters are expressed by the following relationships:…”

Section: Local Equilibrium Equations and Constitutive Lawsmentioning

confidence: 99%

Three-dimensional beam element for pre- and post-buckling analysis of thin-walled beams in multibody systems

Jonker

2021

Multibody Syst Dyn

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This paper presents a three-dimensional beam element for stability analysis of elastic thin-walled open-section beams in multibody systems. The beam model is based on the generalized strain beam formulation. In this formulation, a set of independent deformation modes is defined which are related to dual stress resultants in a co-rotational frame. The deformation modes are characterized by generalized strains or deformations, expressed as analytical functions of the nodal coordinates referred to the global coordinate system. A nonlinear theory of non-uniform torsion of open-section beams is adopted for the derivation of the elastic and geometric stiffness matrices. Both torsional-related warping and Wagner’s stiffening torques are taken into account. Second order approximations for the axial elongation and bending curvatures are included by additional second order terms in the expressions for the deformations. The model allows to study the buckling and post-buckling behaviour of asymmetric thin-walled beams with open cross-section that can undergo moderately large twist rotations. The inertia properties of the beam are described using both consistent and lumped mass formulations. The latter is used to model rotary and warping inertias of the beam cross-section. Some validation examples illustrate the accuracy and computational efficiency of the new beam element in the analysis of the buckling and post-buckling behaviour of thin-walled beams under various loads and (quasi)static boundary conditions. Finally, applications to multibody problems are presented, including the stability analysis of an elementary two-flexure cross-hinge mechanism.

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“…Timoshenko used infinite series to study the singly symmetric cross-section cantilever beam and obtained the critical load of the lateral-torsional buckling [9]. Anderson and Attard [10,11] carried out LTB experiments on four types of I-shaped cantilever steel beams with different cross-sections. Andrade et al [12] extended the domain of application of C 1 , C 2 and C 3 factors to cantilevers.…”

Section: Introductionmentioning

confidence: 99%

“…Because the boundary conditions of cantilever beams are more complex than those of simply supported beams, the analytical solutions of M cr of the cantilever are highly complex. Therefore, the solution to M cr requires more approaches, such as the finite difference [17], finite element [18][19][20], energy method [21,22], finite integral [10] or the lateral-torsional buckling modification factor [1]. Among them, the energy method is one of the most common and basic methods.…”

Section: Introductionmentioning

confidence: 99%

Lateral–Torsional Buckling of Cantilever Steel Beams under 2 Types of Complex Loads

Cai

Ling

2023

Applied Sciences

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Cantilever steel beams are an essential structural element in civil engineering fields such as bridges and buildings. However, there is very little research on the critical moment (Mcr) of cantilever beams subjected to a concentrated load (CL) or a combination of concentrated load and uniformly distributed load (CUDL) when the concentrated load is not limited to the free end. Therefore, the focus of the current paper is the calculation of Mcr for cantilever steel beams under CL and CUDL. This paper proposes a program and a simple closed-form solution for Mcr that are applicable to the elastic buckling analysis of cantilever I-beams under CL and CUDL. Based on the Rayleigh–Ritz method, a matrix equation and the corresponding procedure about Mcr under CL and CUDL are derived by using infinite trigonometric series for the buckling deformation functions. The value of Mcr and the corresponding mode of buckling can be obtained efficiently by considering the symmetry of the section, the ratio of two load values and the load action position. Experimental results and finite element calculations validate the numerical solutions of the procedure. A closed-form solution for Mcr is derived according to the assumption of a small torsion angle and the specific values of each coefficient in the closed-form solution of Mcr are calculated by the proposed procedure. The results show that the procedure and closed-form solution for Mcr presented in this paper have a high degree of accuracy in calculating the Mcr of the cantilever beam under CL and CUDL. The deviations between the results calculated by the proposed procedure and data from existing literature are less than 8%. These conclusions are capable of solving the calculation problem of Mcr for cantilever beams under CL or CUDL, which are both significant load cases in engineering. The study provides a reference for the design of cantilever steel beams.

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Stability of Monosymmetric Beams and Cantilevers

Cited by 102 publications

References 0 publications

Generalized formula of moment gradient lateral torsional buckling factor for monosymmetric steel beams

Generalized formula of moment gradient lateral torsional buckling factor for monosymmetric steel beams

Three-dimensional beam element for pre- and post-buckling analysis of thin-walled beams in multibody systems

Lateral–Torsional Buckling of Cantilever Steel Beams under 2 Types of Complex Loads

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