• Proceedings of the KSME Conference
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• 2001.06b
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• pp.590-595
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• 2001

To improve the modeling accuracy for the finite element method, this paper proposes a method to make a combined use of finite elements and exact dynamic elements. Exact interpolation functions for a Timoshenko beam element are derived and compared with interpolation functions of the finite element method (FEM). The exact interpolation functions are tested with the Laplace variable varied. The exact interpolation functions are used to gain more accurate mode shape functions for the finite element method. This paper also presents a combined use of finite elements and exact dynamic elements in design problems. A Timoshenko frame with tapered sections is tested to demonstrate the design procedure with the proposed method.

• Coupled systems mechanics
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• v.10 no.1
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• pp.79-102
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• 2021

In this paper we deal with instability problems of structures under nonconservative loading. It is shown that such class of problems should be analyzed in dynamics framework. Next to analytic solutions, provided for several simple problems, we show how to obtain the numerical solutions to more complex problems in efficient manner by using the finite element method. In particular, the numerical solution is obtained by using a modified Euler-Bernoulli beam finite element that includes the von Karman (virtual) strain in order to capture linearized instabilities (or Euler buckling). We next generalize the numerical solution to instability problems that include shear deformation by using the Timoshenko beam finite element. The proposed numerical beam models are validated against the corresponding analytic solutions.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.6
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• pp.719-730
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• 2007

This study presents a thin-walled space frame element based on the classical Timoshenko beam theory. The element is derived according to the assumed strain field in order to resolve the shear-locking phenomenon. The shape function is developed in accordance with the strain field which is assumed to be constant at a 2-noded straight frame element. In this study, the geometrically nonlinear analysis applies the Corotational procedure in order to evaluate unbalanced loads. The bowing effect is also considered faithfully. Two numerical examples are given; monosymmetric curved and nonsymmetric straight cantilever. When these example structures behave lateral-torsional bucking, the critical loads are obtained by this study and ABAQUS shell elements. Also, the post-buckling behavior is examined. The results give good agreement between this study and ABAQUS shell.

• Structural Engineering and Mechanics
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• v.65 no.1
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• pp.9-17
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• 2018

This study concerns about calculating exact natural frequencies of frames using a single variable shear deformation theory (SVSDT) which considers the parabolic shear stress distribution across the cross section. Free vibration analyses are performed for multi-bay, multi-storey and multi-bay multi-storey type frame structures. Dynamic stiffness formulations are derived and used to obtain first five natural frequencies of frames. Different beam and column cross sections are considered to reveal their effects on free vibration analysis. The calculated natural frequencies are tabulated with the results obtained using Euler-Bernoulli Beam Theory (EBT) and Timoshenko Beam Theory (TBT). Moreover, the effects of inner and outer columns on natural frequencies are compared for multi-bay frames. Several mode shapes are plotted.

• Computers and Concrete
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• v.12 no.4
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• pp.519-536
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• 2013

This paper presents a mixed formulation frame element with the assumptions of the Timoshenko shear beam theory for displacement field and that accounts for interaction between shear and normal stress at material level. Nonlinear response of the element is obtained by integration of section response, which in turn is obtained by integration of material response. Satisfaction of transverse equilibrium equations at section includes the interaction between concrete and transverse reinforcing steel. A 3d plastic damage model is implemented to describe the hysteretic behavior of concrete. Comparisons with available experimental data on RC structural walls confirm the accuracy of proposed method.

• Structural Engineering and Mechanics
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• v.74 no.1
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• pp.33-54
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• 2020

The aim of this study is to calculate natural frequencies and harmonic responses of cracked frames with general boundary conditions by using transfer matrix method (TMM). The TMM is a straightforward technique to obtain harmonic responses and natural frequencies of frame structures as the method is based on constructing a relationship between state vectors of two ends of structure by a chain multiplication procedure. A single variable shear deformation theory (SVSDT) is applied, as well as, Timoshenko beam theory (TBT) and Euler-Bernoulli beam theory (EBT) for comparison purposes. Firstly, free vibration analysis of intact and cracked frames are performed for different crack ratios using TMM. The crack is modelled by means of a linear rotational spring that divides frame members into segments. The results are verified by experimental data and finite element method (FEM) solutions. The harmonic response curves that represent resonant and anti-resonant frequencies directly are plotted for various crack lengths. It is seen that the TMM can be used effectively for harmonic response analysis of cracked frames as well as natural frequencies calculation. The results imply that the SVSDT is an efficient alternative for investigation of cracked frame vibrations especially with thick frame members. Moreover, EBT results can easily be obtained by ignoring shear deformation related terms from governing equation of motion of SVSDT.

• Steel and Composite Structures
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• v.52 no.1
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• pp.77-87
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• 2024

Analytical methods for assessment of the out-of-plane buckling of unbraced top chords of truss bridges may look obsolete while comparing them to finite element analysis. However they are, usually, superior when rapid assessment is necessary. Analytical methods consider the top chord as a bar on elastic supports provided by bracing (Holt, Timoshenko). Correct assessment of the support elasticity (stiffness) is crucial. In the case of truss bridge spans of traditional structural layout (cross-beams at the truss chord nodes only), the elasticity may be set based on the analysis of the, so called, U-frame stiffness. Here the analyses consider the U-frame itself (a pair of verticals and a cross-beam) or the U-frame with adjacent diagonals or the pair of diagonals (in the absence of verticals) and the members of the bottom chord in the adjacent panels. For all the cases, the stability analysis of the chord as a bar in compression is necessary. Unfortunately, the method cannot be applied to contemporary truss bridges without verticals, that usually have independent cross-beam decks (the cross-beams attached to truss chords at their nodes and between them). This is the motivation for the analysis resulting in the method of setting the stiffness of the equivalent U-frame for the aforementioned truss bridges. Truss girders of both, gussetless and gusseted, joints are taken into account.

• Selected Papers of The Society of Naval Architects of Korea
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• v.1 no.1
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• pp.52-64
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• 1993

There exist many frame structural systems having some attachments reducible to damped spring-mass systems, concentracted masses and spring supports. For free and forced vibration analyses of such a system an analytical method based on the receptance method is presented. A framed structure having attachments is considered as a combined system composed of various Timoshenko beam and bar elements and the attachments. So, the vibration characteristics of the system are calculated by synthesizing receptances and Support Displacement Transfer Ratio (SDTR) of beam and bar elements In spectral and/or closed forms, and receptances of the attachments. In forced vibration analysis, arbitrary excitation forces at a point on the structure and displacement excitations at boundaries are considered. Numerical investigations are carried out for verification of the presented method, and the results show good accuracy and very high computational efficiency.

• Coupled systems mechanics
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• v.3 no.1
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• pp.111-145
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• 2014

In this paper we present a new model for computing the nonlinear response of reinforced concrete frame systems subjected to extreme thermomechanical loads. The first main feature of the model is its ability to account for both bending and shear failure of the reinforced concrete composites within frame-like model. The second prominent feature concerns the model capability to represent the total degradation of the material properties due to high temperature and the thermal deformations. Several numerical simulations are given to confirm these capabilities and illustrate a very satisfying model performance.

• Journal of the Society of Naval Architects of Korea
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• v.28 no.2
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• pp.174-186
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• 1991

There exist many frame structural systems which may be regarded as a combined structural system composed of beam/bar elements and attachments reducible to damped spring-mass systems. In this paper, analytical methods based on the receptance for the vibration analysis of such a system are presented. For the free vibration analysis and response calculations to point excitations, receptances of a uniform Timoshenko beam and a bar are derived in closed and spectral forms, and the method to obtain the system receptance by synthesizing the receptances of the elements and other subsystems is presented. The system damping property is also obtainable by sysnthesizing the components' damping properties. For calculations of the system responses to support motion, the Support Displacement Transfer Ratio(SDTR) of a uniform Timoshenko beam and a bar conceptually similar to the receptance is defined, and the method of synthesizing them with other subsystems' receptances is also presented. Such a method is very convenient especially in dynamic reanalysis subject to changes of some design variables.