• Structural Engineering and Mechanics
• /
• v.35 no.2
• /
• pp.141-173
• /
• 2010

In this paper a boundary element method is developed for the general flexural-torsional buckling analysis of Timoshenko beams of arbitrarily shaped cross section. The beam is subjected to a compressive centrally applied concentrated axial load together with arbitrarily axial, transverse and torsional distributed loading, while its edges are restrained by the most general linear boundary conditions. The resulting boundary value problem, described by three coupled ordinary differential equations, is solved employing a boundary integral equation approach. All basic equations are formulated with respect to the principal shear axes coordinate system, which does not coincide with the principal bending one in a nonsymmetric cross section. To account for shear deformations, the concept of shear deformation coefficients is used. Six coupled boundary value problems are formulated with respect to the transverse displacements, to the angle of twist, to the primary warping function and to two stress functions and solved using the Analog Equation Method, a BEM based method. Several beams are analysed to illustrate the method and demonstrate its efficiency and wherever possible its accuracy. The range of applicability of the thin-walled theory and the significant influence of the boundary conditions and the shear deformation effect on the buckling load are investigated through examples with great practical interest.

• Structural Engineering and Mechanics
• /
• v.5 no.3
• /
• pp.269-281
• /
• 1997

The overall buckling mode in a composite steel-concrete beam over an internal support is necessarily lateral-distortional, in which the bottom compressive range displaces laterally and twists, since the top flange is restrained by the nearly rigid concrete slab. An efficient finite element method is used to study elastic lateral-distortional buckling in composite beams whose steel portion is tapered. The simplified model for a continuous beam that is presented herein is a fixed ended cantilever whose steel portion is tapered, and is subjected to moment gradient. This is intended to give an insight into distortion in a continuous beam that occurs in the negative bending region, and the differences between the cantilever representation and the continuous beam are highlighted. An eigenproblem is established, and the buckling modes and loads are determined in the elastic range of structural response. It is found from the finite element study that the buckling moment may be enhanced significantly by using a vertical stiffener in the region where the lateral movement of the bottom range is greatest. This enhancement is quantified in the paper.

• Smart Structures and Systems
• /
• v.21 no.3
• /
• pp.349-358
• /
• 2018

This paper investigates the free vibration analysis of double-beam system coupled by a two-degree-of-freedom mass-spring system. In order to generalize the model, the main beams are assumed to be elastically restrained against translation and rotation at one end and free at the other. Furthermore, the mass-spring system is elastically connected to the beams at adjustable positions by means of four translational and rotational springs. The governing differential equations of the beams and the mass-spring system are derived and analytically solved by using the Fourier transform method. Moreover, as a second way, a finite element solution is derived. The frequency parameters and mode shapes of some diverse cases are obtained using both methods. Comparison of obtained results by two methods shows the accuracy of both solutions. The influence of system parameters on the free vibration response of the studied mechanical system is examined.

• Structural Engineering and Mechanics
• /
• v.26 no.6
• /
• pp.673-685
• /
• 2007

Reinforced concrete beams can be strengthened in a structural retrofit process by attaching steel plates to their sides by bolting. Whilst bolting produces a confident degree of shear connection under conditions of either static or seismic overload, the plates are susceptible to local buckling. The aim of this paper is to investigate the local buckling of unilaterally-restrained plates with point supports in a generic fashion, but with particular emphasis on the provision of the restraints by bolts, and on the geometric configuration of these bolts on the buckling loads. A numerical procedure, which is based on the Rayleigh-Ritz method in conjunction with the technique of Lagrange multipliers, is developed to study the unilateral local buckling of rectangular plates bolted to the concrete with various arrangements of the pattern of bolting. A sufficient number of separable polynomials are used to define the flexural buckling displacements, while the restraint condition is modelled as a tensionless foundation using a penalty function approach to this form of mathematical contact problem. The additional constraint provided by the bolts is also modelled using Lagrange multipliers, providing an efficacious method of numerical analysis. Local buckling coefficients are determined for a range of bolting configurations, and these are compared with those developed elsewhere with simplifying assumptions. The interaction of the actions in bolted plates during buckling is also considered.

• The Transactions of The Korean Institute of Electrical Engineers
• /
• v.66 no.12
• /
• pp.1852-1865
• /
• 2017

The vibration of the structures with restrained motion has long been observed in various engineering fields. When the motion of vibrating structure is restrained due to the adjacent objects, the frequencies and the mode shapes of the structure change and its vibration characteristics becomes unpredictable, in general. Although the importance of the study on this type of vibration model increases in many engineering areas, most studies conducted so far are limited to the theoretical study on dynamic responses of the structure with stops, including some experimental works. Specially, the study on the nonlinear phenomena due to the impact between the structure and the stops have been mainly performed theoretically. In the paper, both numerical analyses and experiments are conducted to study the chaotic vibration characteristics of the nonlinear motion and the dynamic response of a cantilevered beam which has restrained motion at the free end by the stops. Results are presented for various magnetic forces and gaps between the beam and stops. The conclusions are as follows : Firstly, Numerical simulation results have a good agreement with experimental ones. Secondly, the effect of higher modes of beams are increased with increasing magnitude of exciting force, and displacement and velocity curves become more complicated shapes. Thirdly, nonlinear characteristics tend to appear greatly with increasing magnitude of exciting force, and fractal dimension is increased.

• Journal of the Earthquake Engineering Society of Korea
• /
• v.7 no.4
• /
• pp.1-13
• /
• 2003

For spatial free vibration of non-symmetric thin-walled curved beams with shear deformation, an improved formulation is proposed in the present study. The elastic strain and the kinetic energies are first derived by considering constant curvature and shear deformation effects due to shear forces and restrained warping torsion. Next equilibrium equations and force-deformation relations are obtained using a stationary condition of total potential energy. And the finite element procedures are developed by using isoparametric curved beam element with arbitray thin-walled sections. Particularly not only shear deformation and thickness-curvature effects on vibration behaviors of curved beams but also mode transition and crossover phenomena with change in curvatures of beams are parametrically investigated. In order to illustrate the accuracy and the reliability of this study, various numerical solutions for spatial free vibration are compared with results by available references and ABAQUS's shell element.

• Steel and Composite Structures
• /
• v.29 no.4
• /
• pp.423-435
• /
• 2018

There are presently two general ways of accounting for hazardous metal creep in structural fire analyses: either we incorporate creep strains implicitly in hardening model ('implicit-creep' plasticity) or we account for creep explicitly ('explicit-creep' plasticity). The first approach is simpler and usually used for fast engineering applications, e.g., following proposals of EN 1993-1-2. Prioritizing this approach without consideration of its limitations, however, may lead to significant error. So far the possible levels of such error have been demonstrated by few researchers for individual structural elements (i.e., beams and columns). This paper, however, presents analyses also for selected beam-girder assemblies. Special numerical models are developed correspondingly and they are validated and verified. Their important novelty is that they do not only account for creep in individual members but also for creep in between-member connections. The paper finally shows that outside the declared applicability limits of the implicit-creep plasticity models, the failure times predicted by the applied alternative explicit-creep models can be as much as 40% shorter. Within the limits, however, the discrepancies might be negligible for majority of cases with the exception of about 20% discrepancies found in one analysed example.

• Journal of the Earthquake Engineering Society of Korea
• /
• v.3 no.1
• /
• pp.41-54
• /
• 1999

For free vibration of non-symmetric thin-walled circular arches including restrained warping effect, the elastic strain and kinetic energy is derived by introducing displacement fields of circular arches in which all displacement parameters are defined at the centroid axis. The cubic Hermitian polynomials are utilized as shape functions for development of the curved thin-walled beam element having eight degrees of freedom. Analytical solution for in-plane free vibration behaviors of simply supported thin-walled curved beams with monosymmetric cross-sections is newly derived. Also, a finite element formulation using two noded curved beams element is presented by evaluating elastic stiffness and mass matrices. In order to illustrate the accuracy and practical usefulness of this study, analytical and numerical solutions for free vibration of circular arches are presented and compared with solutions analyzed by the straight beam element and the ABAQUS's shell element.

• Journal of Korean Society of Steel Construction
• /
• v.23 no.5
• /
• pp.595-606
• /
• 2011

This study was conducted to investigate the seismic behavior of steel member resisting frames considering the relative stiffness of the connection and beams. Six-story steel moment frames were designed to study the seismic behavior. The connections were classified into Double Web-Angle connections (DWAs), Top- and Seat-angles with double Web-angles (TWSs), FEMA-Test Summary No. 28, Specimen ID: UCSD-6 (SAC), and Fully Restrained (FR). The rotational stiffness of the semi-rigid connections was estimated using the Three-Parameter Power Model adopted by Chen and Kishi. The relative stiffness, which is the ratio of the rotational stiffness of the connections to the stiffness of the beams, was used. Push-over, repeated loading, and time history analysis were performed for all the frames. The seismic behavior of each frame was analyzed with the story drift, plastic hinge rotation, and hysteretic energy distribution.

• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.13 no.1
• /
• pp.1-12
• /
• 1993

Tangent stiffness matrices are derived for the torsional and lateral stability analysis of the space beams and framed structures with the symmetric thin-walled section by using the principle of virtual displacement. In the cases of restrained torsion and unrestrained torsion, the elastic and geometric stiffness matrices are evaluated by using the Hermitian polynomials which represent the displacement field of the beam element in simple flexure. Numerical examples illustrate the accuracy and convergence characteristics of the derived formulations.