• Structural Engineering and Mechanics
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• 제53권3호
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• pp.537-573
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• 2015

Multiple-step beams carrying intermediate lumped masses with/without rotary inertias are widely used in engineering applications, but in the literature for free vibration analysis of such structural systems; Bernoulli-Euler Beam Theory (BEBT) without axial force effect is used. The literature regarding the free vibration analysis of Bernoulli-Euler single-span beams carrying a number of spring-mass systems, Bernoulli-Euler multiple-step and multi-span beams carrying multiple spring-mass systems and multiple point masses are plenty, but that of Timoshenko multiple-step beams carrying intermediate lumped masses and/or rotary inertias with axial force effect is fewer. The purpose of this paper is to utilize Numerical Assembly Technique (NAT) and Differential Transform Method (DTM) to determine the exact natural frequencies and mode shapes of the axial-loaded Timoshenko multiple-step beam carrying a number of intermediate lumped masses and/or rotary inertias. The model allows analyzing the influence of the shear and axial force effects, intermediate lumped masses and rotary inertias on the free vibration analysis of the multiple-step beams by using Timoshenko Beam Theory (TBT). At first, the coefficient matrices for the intermediate lumped mass with rotary inertia, the step change in cross-section, left-end support and right-end support of the multiple-step Timoshenko beam are derived from the analytical solution. After the derivation of the coefficient matrices, NAT is used to establish the overall coefficient matrix for the whole vibrating system. Finally, equating the overall coefficient matrix to zero one determines the natural frequencies of the vibrating system and substituting the corresponding values of integration constants into the related eigenfunctions one determines the associated mode shapes. After the analytical solution, an efficient and easy mathematical technique called DTM is used to solve the differential equations of the motion. The calculated natural frequencies of Timoshenko multiple-step beam carrying intermediate lumped masses and/or rotary inertias for the different values of axial force are given in tables. The first five mode shapes are presented in graphs. The effects of axial force, intermediate lumped masses and rotary inertias on the free vibration analysis of Timoshenko multiple-step beam are investigated.

• Steel and Composite Structures
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• 제30권5호
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• pp.483-492
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• 2019

In the current study, the influence of the initial lateral (sweep) shape and the cross-sectional twist imperfection on the lateral torsional buckling (LTB) response of doubly-symmetric steel I-beams was investigated. The material imperfection (residual stress) was not considered. For this objective, standard European IPN 300 beam with different unbraced span was numerically analyzed for three imperfection cases: (i) no sweep and no twist (perfect); (ii) three different shapes of global sweep (half-sine, full-sine and full-parabola between the end supports); and (iii) the combination of three different sweeps with initial sinusoidal twist along the beam. The first comparison was done between the results of numerical analyses (FEM) and both a theoretical solution and the code lateral torsional buckling formulations (EC3 and AISC-LRFD). These results with no imperfection effects were then separately compared with three different shapes of global sweep and the presence of initial twist in these sweep shapes. Besides, the effects of the shapes of initial global sweep and the inclusion of sinusoidal twist on the critical buckling load of the beams were investigated to unveil which parameter was considerably effective on LTB response. The most compatible outcomes for the perfect beams was obtained from the AISC-LRFD formulation; however, the EC-3 formulation estimated the $P_{cr}$ load conservatively. The high difference from the EC-3 formulation was predicted to directly originate from the initial imperfection reduction factor and high safety factor in its formulation. Due to no consideration of geometric imperfection in the AISC-LFRD code solution and the theoretical formulation, the need to develop a practical imperfection reduction factor for AISC-LRFD and theoretical formulation was underlined. Initial imperfections were obtained to be more influential on the buckling load, as the unbraced length of a beam approached to the elastic limit unbraced length ($L_r$). Mode-compatible initial imperfection shapes should be taken into account in the design and analysis stages of the I-beam to properly estimate the geometric imperfection influence on the $P_{cr}$ load. Sweep and sweep-twist imperfections led to 10% and 15% decrease in the $P_{cr}$ load, respectively, thus; well-estimated sweep and twist imperfections should considered in the LTB of doubly-symmetric steel I-beams.

• Structural Engineering and Mechanics
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• 제89권1호
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• pp.1-11
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• 2024

This article introduces a novel analytical model for examining the impact of porosity on shear correction factors (SCFs) in functionally graded porous beams (FGPB). The study employs uneven and logarithmic-uneven modified porosity-dependent power-law functions, which are distributed throughout the thickness of the FGP beams. Additionally, a modified exponential-power law function is used to estimate the effective mechanical properties of functionally graded porous beams. The correction factor plays a crucial role in this analysis as it appears as a coefficient in the expression for the transverse shear stress resultant. It compensatesfor the assumption that the shear strain is uniform across the depth of the cross-section. By applying the energy equivalence principle, a general expression for static SCFs in FGPBs is derived. The resulting expression aligns with the findings obtained from Reissner's analysis, particularly when transitioning from the two-dimensional case (plate) to the one-dimensional case (beam). The article presents a convenient algebraic form of the solution and provides new case studies to demonstrate the practicality of the proposed formulation. Numerical results are also presented to illustrate the influence of porosity distribution on SCFs for different types of FGPBs. Furthermore, the article validates the numerical consistency of the mechanical property changesin FG beams without porosity and the SCF by comparing them with available results.

• 산업기술연구
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• 제15권
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• pp.71-75
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• 1995

A method of calculating the natural frequency corresponding to the first mode of vibration of beams and tower structures, with irregular cross-sections and with arbitrary boundary conditions was developed and reported by D. H. Kim in 1974. This method has been developed for two-dimensional problems including the laminated composite plates and was proved to be very effective for the plates with arbitrary boundary conditions and irregular sections. In this paper, the result of application of this method to the clamped composite plates with non-uniform cross-section and with attached point mass/masses is presented.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2003년도 추계학술대회논문집
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• pp.994-999
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• 2003

A modeling method for the modal analysis of a rotating cross-ply composite beam based on Timoshenko beam theory is presented. To analyze the composite beam exactly, the effects of shear deformation and rotary inertia are included. Linear differential equations of motion are derived using the assumed mode method. For the modeling, hybrid deformation variables are employed and approximated to derive the equations of motion. The effects of the dimensionless angular velocity and the slenderness ratio parameter on the variations of modal characteristics are investigated

• Steel and Composite Structures
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• 제18권1호
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• pp.149-163
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• 2015

Orthotropic steel highway bridges exist almost everywhere in world, especially in Europe. The design of these bridges started very early in 20th century and ended with a conventional orthotropic steel bridge structure, which is today specified in DIN FB 103. These bridges were mostly built in 1960's and exhibit damages in steel structural parts. The primary reason of these damages is the high pressure that is induced by wheel- loads and therefore damages develop especially in heavy traffic lanes. Constructive rules are supplied by standards to avoid damages in orthotropic steel structural parts. These rules are first given in detail in the standard DIN 18809 (Steel highway- and pedestrian bridges- design, construction, fabrication) and then in DIN- FB 103 (Steel bridges). Bridges built in the past are today subject to heavier wheel loads and the frequency of loading is also increased. Because the vehicles produced today in 21st century are heavier than before and more people have vehicle in comparison with 20th century. Therefore dimensioning or strengthening of orthotropic steel bridges by using stiffer dimensions and shorter spans is an essence. In the scope of this study the complex geometry of conventional steel orthotropic bridge is generated by FE-Program and the effects of cross beam web thickness and cross beam span on steel bridge are assessed by means of a parameter study. Consequently, dimensional and constructional recommendations in association with cross beam thickness and span will be given by this study.

• Structural Engineering and Mechanics
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• 제43권4호
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• pp.411-437
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• 2012

In this paper, we propose a continuum mechanics based 3-D beam finite element with cross-sectional discretization allowing for warping displacements. The beam element is directly derived from the assemblage of 3-D solid elements, and this approach results in inherently advanced modeling capabilities of the beam element. In the beam formulation, warping is fully coupled with bending, shearing, and stretching. Consequently, the proposed beam elements can consider free and constrained warping conditions, eccentricities, curved geometries, varying sections, as well as arbitrary cross-sections (including thin/thick-walled, open/closed, and single/multi-cell cross-sections). We then study the modeling and predictive capabilities of the beam elements in twisting beam problems according to geometries, boundary conditions, and cross-sectional meshes. The results are compared with reference solutions obtained by analytical methods and solid and shell finite element models. Excellent modeling capabilities and solution accuracy of the proposed beam element are observed.

• 항공우주시스템공학회지
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• 제12권6호
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• pp.41-49
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• 2018

이번 연구에서는 복합재료 박벽보(thin-walled beam)에서 시위 방향으로 단일 셀의 비대칭성 단면을 가지는 모델을 선정하여, 단면의 형상에 대한 이론적인 동특성을 연구하였다. 이를 위해 전단 변형 효과(transverse shear effect)와 와핑 구속 효과(warping restraint effect), 보의 길이 방향으로 일정한 테이퍼비와 기하학적 단면비 등을 고려하고, 비대칭 단면의 와핑 함수 보정을 통해 수학적 모델링을 수행하였다. 그 결과에 따라, 고려한 단면의 질량 계수와 강성 계수 및 고유 진동수 등의 특성을 조사하였다. 특히, 단면의 비대칭성, 와핑 함수를 보정하지 않은 경우, 모델의 테이퍼비와 단면비 등이 고유 진동수에 미치는 영향을 비교 분석하였다.

• Structural Engineering and Mechanics
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• 제16권6호
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• pp.695-712
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• 2003

The non-linear structural analysis of reinforced concrete beams in fire consists of three separate steps: (i) The estimation of the rise of surrounding air temperature due to fire; (ii) the determination of the distribution of the temperature within the beam during fire; (iii) the evaluation of the mechanical response due to simultaneous time-dependent thermal and mechanical loads. Steps (ii) and (iii) are dealt with in the present paper. We present a two-step computational procedure where a 2D transient thermal analysis over the cross-sections of beams are made first, followed by mechanical analysis of the structure. Fundamental to the accuracy of the mechanical analysis is a new planar beam finite element. The effects of plasticity in concrete, and plasticity and viscous creep in steel are taken into consideration. The properties of concrete and steel along with the values of their thermal and mechanical parameters are taken according to the European standard ENV 1992-1-2 (1995). The comparison of our numerical and full-scale experimental results shows that the proposed mechanical and 2D thermal computational procedure is capable to describe the actual response of reinforced concrete beam structures to fire.

• Computers and Concrete
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• 제16권6호
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• pp.919-932
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• 2015

This paper presents a new method for assessing the three-point-bending (3PB) strength of mortar beams in a non-destructive manner, based on neural network (NN) models. The models are based on the radial basis function (RBF) architecture and the fuzzy means algorithm is employed for training, in order to boost the prediction accuracy. Data for training the models were collected based on a series of experiments, where the cement mortar beams were subjected to various bending mechanical loads and the resulting pressure stimulated currents (PSCs) were recorded. The input variables to the NN models were then calculated by describing the PSC relaxation process through a generalization of Boltzmannn-Gibbs statistical physics, known as non-extensive statistical physics (NESP). The NN predictions were evaluated using k-fold cross-validation and new data that were kept independent from training; it can be seen that the proposed method can successfully form the basis of a non-destructive tool for assessing the bending strength. A comparison with a different NN architecture confirms the superiority of the proposed approach.