• Journal of KSNVE
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• v.9 no.5
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• pp.1012-1018
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• 1999

This paper deals with the coupled flexural-torsional vibrations of Timoshenko beams with monosymmetric cross-section. The governing differtial equations for free vibration of such beams are derived and solved numerically to obtain frequencies and mode shapes. Numerical results are calculated for three specific examples of beams with free-free, clamped-free, hinged-hinged, clamped-hinged and clamped-clamped end constraints. The effect of warping stiffess on the natural frequencies and mode shapes is discussed and it is concluded that substantial error can be incurred if the effect is ignored.

• 한국방재학회:학술대회논문집
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• 2010.02a
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• pp.83.2-83.2
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• 2010

Stepped I-beams having increased moment of inertia at one end(singly stepped beam) or both ends(doubly stepped beams) can often be seen in construction of bridges due to material economy and easy fabrication of the section. This paper presents the results of the parametric study of lateral torsional buckling of monosymmetric stepped I-beams with constant depth subjected to equal and opposite end moments applied at the end of the beam. Design recommendations were made based on the finite element results of the models having different combinations of monosymmetric ratio, stepped length ratio, flange thickness ratio and flange width ratio,. The proposed approximation is acceptable based on the parameters given having mostly conservative results. The proposed equation can be further used to extend the study to different loading conditions.

• Journal of the Earthquake Engineering Society of Korea
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• v.2 no.2
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• pp.57-68
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• 1998

For free vibration of monosymmetric 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 free vibration behaviors of simply supported thin-walled curved beam 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 FEM using straight beam element.

• Journal of the Korean Society of Hazard Mitigation
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• v.10 no.2
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• pp.7-13
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• 2010

Stepped I-beams having increased moment of inertia at one end (singly stepped beam) or both ends (doubly stepped beams) can often be seen in construction of bridges due to material economy and easy fabrication of the section. This paper presents the results of the parametric study of lateral torsional buckling of monosymmetric stepped I-beams with constant depth subjected to uniform moment. Design recommendations were made based on the finite element results of the models having different combinations of monosymmetric ratio, stepped length ratio, flange thickness ratio and flange width ratio. The proposed approximation is acceptable based on the parameters given having mostly conservative results. The proposed equation can be further used to extend the study to different loading conditions.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1998.04a
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• pp.465-472
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• 1998

In this study, analytic solution and finite element formulation for the free vibration analysis of thin-walled circular arch, based on linearized virtual work and Vlasov's assumption, including restrained warping effect and second order terms of finite semitangential rotations, is presented. The total potential energy is derived by applying the Hellinger-Reissner principle. In this formulation, all displacement parameters of deformation are defined at the centroid axis. For the finite element formulation, the two node cubic Hermitian polynomials are utilized as shape functions. In special case, potential energy functional of thin-walled curved beam with monosymmetric cross section is derived. From this methodology, analytic solution for the free vibration of monosymmetric circular arch with simply supported is derived. In order to illustrate the accuracy of this study, various parameter studies for free vibration of circular arches are presented and compared with numerical solution analyzed by the FEM using straight beam element.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.11a
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• pp.709-712
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• 2004

A study of the coupled flexural-torsional vibrations of thin-walled beams with monosymmetric cross-section is presented. The governing differential equations for free vibration of such beams are solved numerically to obtain natural frequencies and their corresponding mode shapes. The beam model is based on the Bernoulli-Euler beam theory and the effect of warping is taken into consideration. Numerical results are given for two specific examples of beams with free-free, clamped-free, hinged-hinged, clamped-hinged and clamped-clamped end constraints both including and excluding the effect of warping stiffness. The effect of warping stiffness on the natural frequencies and mode shapes is discussed and it is concluded that substantial error can be incurred if the effect is ignored.

• Journal of Korean Society of Steel Construction
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• v.25 no.2
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• pp.153-164
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• 2013

In this paper, lateral-torsional buckling(LTB) strength of HSB800 high strength steel plate girder with monosymmetric section under uniform moment was evaluated by nonlinear analysis. The unbraced length in inelastic LTB range was considered for the sections whose smaller or larger flange is in compression with slender, noncompact and compact web. Analyses of SM490 steel girders were first performed with the single-panel and three-panel model to judge the validity of the constructed models by comparing those results with Eurocode 3, AASHTO and AISC codes. By using the same models, LTB strength of HSB800 girder was evaluated and it was found that the sections whose smaller flange is in compression with noncompact flange-slender/noncompact web could not reach the flexural strength of the design codes.

• Structural Engineering and Mechanics
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• v.52 no.4
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• pp.787-813
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• 2014

Starting with Hamilton's variational principle, the governing field equations for the steady state response of thin-walled beams under harmonic forces are derived. The formulation captures shear deformation effects due to bending and warping, translational and rotary inertia effects and as well as torsional flexural coupling effects due to the cross section mono-symmetry. The equations of motion consist of four coupled differential equations in the unknown displacement field variables. A general closed form solution is then developed for the coupled system of equations. The solution is subsequently used to develop a family of shape functions which exactly satisfy the homogeneous form of the governing field equations. A super-convergent finite element is then formulated based on the exact shape functions. Key features of the element developed include its ability to (a) isolate the steady state response component of the response to make the solution amenable to fatigue design, (b) capture coupling effects arising as a result of section mono-symmetry, (c) eliminate spatial discretization arising in commonly used finite elements, (d) avoiding shear locking phenomena, and (e) eliminate the need for time discretization. The results based on the present solution are found to be in excellent agreement with those based on finite element solutions at a small fraction of the computational and modelling cost involved.

• Journal of Korean Society of Steel Construction
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• v.20 no.1
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• pp.175-181
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• 2008

Finite element buckling analyses of the monosymmetric I-beams subjected to t ransverse loading applied at different heights with respect to the mid-height of the cross section were conducted. Transverse loads consisting of a mid-span point load and a uniformly distributed load were considered in the investigation. The method suggested in the SRC Guide was compared with the finite element method (FEM) results. This paper presents a more accurate moment gradient correction factor for monosymetric I-beams considering the load height effect. The applicability of this new design method is limited to monosymmetric I-beams in which the degree of monosymetry, ${\rho}$, is from 0.1 to 0.9.

• Journal of Korean Society of Steel Construction
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• v.26 no.6
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• pp.581-594
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• 2014

In this paper, flexural resistance of hybrid girder under uniform bending moment was evaluated, which is composed of HSB800 and HSB600 steel for the flange and web, respectively. Doubly-symmetric and monosymmetric sections with noncompact or compact flange and slender, noncompact or compact web were considered. Nonlinear analyses with 3-dim. shell element model were performed to determine the 'flexural resistance of section' and the 'lateral torsional buckling strength' by taking initial imperfection and residual stress into account. The numerical results were compared with the AASHTO LRFD and Eurocode 3 specifications and also the applicability of AASHTO LRFD appendix A6 was examined for the sections with noncompact and compact web.