Nonlinear dynamic buckling of thin-walled beam-columns under ground excitations (original) (raw)
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Finite element solutions for the buckling of columns and beams
International Journal of Mechanical Sciences, 1971
The accuracy of the finite element method in dealing with problems of the buckling of columns and beams is demonstrated by providing solutions to a variety of examples. Among the subjects included in the study are the influence of restraints and of partial plasticity of the cross-section. In all cases agreement with existing solutions is good. NOTATION B torsional stiffness of restraint C lateral stiffness of restraint E Young's modulus F intensity factor G shear modulus I minor second moment of area J torsion constant [K] stiffness matrix M~ fully plastic moment t thickness Wcr critical load F warping constant
Elastic buckling of thin-walled beam-columns based on a refined energy formulation
Modern Trends in Research on Steel, Aluminium and Composite Structures, 2021
The paper discusses the effects of both in-plane displacements and second order P-δ bending on the elastic flexural-torsional buckling of beam-columns. An energy based solution of the elastic flexural-torsional buckling limit curves under arbitrary proportion between the major axis bending moment and the axial force is presented. The novelty of the approach is related to the development of an improved closed-form solution, in which the equivalent uniform moment modi fication factor should vary not only with the minor axis buckling force utilization ratio N/N z but also with that of major axis buckling N/N y represented by the factored ratio N/N z (1-k 1). Investiga tions include the effect of in-plane displacements resulting from an arbitrary moment gradient on the elastic flexural-torsional buckling of thin-walled narrow flange and wide flange double-tee sec tion members. The obtained solution is illustrated by elastic flexural-torsional buckling curves for different values of the factor k 1 of a beam-column subjected to unequal end moments.
Study of Buckling Behavior of Beam and Column
The objective of this work is to study the buckling behavior of beam and column and effect of buckling behavior of beam and column. These structural members are subjected to heavy loads and can experience failure due to buckling. The method includes the effects of flange and web interaction, residual stresses, and elastic and inelastic behavior.
Numerical analysis of local and global buckling of a stiffened beam-column
Tehnicki vjesnik - Technical Gazette
Preliminary communication The linear buckling phenomenon is obviously very important for stability of compressed supports. The determination of buckling resistance is an important characteristic of the design of steel structure. Besides, the presence of stiffeners in structural plate elements has a vital role in order to increase critical buckling load capacity. However, these stiffeners cause a redistribution in buckling behaviour in terms of local and global buckling. In this paper the transverse and longitudinal stiffeners were employed on a real beam-column structure to maximize the critical buckling loads. The objective is to find the optimum geometry of stiffeners. Based on the finite element method, a numerical model is made using the Abaqus program in order to observe the critical buckling capacity. The results showed that the local critical buckling has been significantly affected by stiffener's position in the case of transverse stiffeners, but little effect is observed on the critical local and global buckling in the case of longitudinal stiffeners.
INELASTIC LATERAL BUCKLING OF BEAM-COLUMNS
An accurate line model based on the finite-element method is developed for analyzing the inelastic lateral buckling of I-section beams and beam-columns. The prebuckling in-plane bending is analyzed using a geometrically nonlinear finite-element method that accounts for the effects of prebuckling displacements and residual stresses on yielding. The results of the prebuckling analysis allow the distributions of yielding and strain-hardening throughout the beam to be determined. The out-of-plane flexural-torsional buckling of the inelastic beam is analyzed by adapting an elastic tapered monosymmetric finite element. For this element, the deflections and twists are referred to an arbitrary straight-line axis along the midheight of the web, instead of the shear center or centroidal axes. The elastic element is adapted for inelastic buckling by using reduced out-of-plane stiffnesses that allow for yielding and strain-hardening. The method is used to give some indications of the accuracy of earlier studies based on less accurate assumptions.
Torsional vibrations and buckling of thin-walled beams on elastic foundation
Thin-Walled Structures, 1989
The problem of free torsional vibration and buckling of doubly symmetric thin-walled beams of open section, subjected to an axial compressive static load and resting on continuous elastic foundation, is discussed in this paper. An analytical method based on the dynamic stiffness matrix approach is developed, including the effects of warping. The resulting transcendental equation is solved for thin-walled beams clamped at one end and simply supported at the other. A computer program is developed, based on the dynamic stiffness matrix approach. The software consists of a master program to set up the dynamics stiffness matrix and to call specific subroutines to perform various system calculations. Numerical results for natural frequencies and buckling load for various vahtes of warping and elastic foundation parameter are obtained attd presented.
Local–global interactive buckling of built-up I-beam sections
Thin-Walled Structures, 2012
According to the Specification for structural steel buildings (AISC-LRFD 360-10), the nominal flexural capacity of I-beam sections having compact webs and noncompact or slender flanges can be estimated as the lower value obtained for the limit states of lateral-torsional buckling (LTB) and compression flange local buckling (FLB). The main assumption behind the approach is that there is no interaction between LTB and FLB limit states and they can be considered as two independent phenomena. In this paper a three dimensional finite-element model using ABAQUS is developed for the inelastic nonlinear analysis of I-beams having noncompact or slender flanges. The model is used to investigate the applicability of the AISC-LRFD approach in estimating the moment capacity of locally buckled steel built-up I-beams with various flange slendernesses. It was found that as the distance between the global and local buckling capacities becomes larger, there would be an interaction between the FLB and LTB limit states; indicating a considerable post-local-buckling capacity for such cases.
Buckling analysis of non-prismatic columns based on modified vibration modes
Communications in Nonlinear Science and Numerical Simulation, 2008
In this paper, a new procedure is formulated for the buckling analysis of tapered column members. The calculation of the buckling loads was carried out by using modified vibrational mode shape (MVM) and energy method. The change of stiffness within a column is characterized by introducing a tapering index. It is shown that, the changes in the vibrational mode shapes of a tapered column can be represented by considering a linear combination of various modes of uniformsection columns. As a result, by making use of these modified mode shapes (MVM) and applying the principle of stationary total potential energy, the buckling load of tapered columns can be obtained. Several numerical examples on tapered columns demonstrate the accuracy and efficiency of the proposed analytical method.
Numerical Methods in Civil Engineering
This paper presents a generalized numerical method to evaluate element stiffness matrices needed for the free vibration and stability analyses of non-prismatic columns resting on oneor two-parameter elastic foundations and subjected to variable axial load. For this purpose, power series approximation is used to solve the fourth-order differential equation of nonprismatic columns with variable geometric parameters. Then, the shape functions are obtained exactly by deriving the deformation shape of the column as power series form. Finally, the element stiffness matrices are determined by means of the principle of virtual work along the columns axis. In order to demonstrate the accuracy and the efficiency of presented method, several numerical examples including in the free-vibration and buckling analysis of non-prismatic columns, portal frame, and gable frame are presented and obtained results compared with the results of other available numerical and theoretical approaches. The method can be applied for the buckling load and natural frequencies computation of uniform members as well as non-prismatic members.