• Steel and Composite Structures
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• 제44권4호
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• pp.451-471
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• 2022

In the present paper, the static bending and buckling responses of functionally graded carbon nanotubes-reinforced composite (FG-CNTRC) beam under various boundary conditions are investigated within the framework of higher shear deformation theory. The significant feature of the proposed theory is that it provides an accurate parabolic distribution of transverse shear stress through the thickness satisfying the traction-free boundary conditions needless of any shear correction factor. Uniform (UD) and four graded distributions of CNTs which are FG-O, FG-X, FG- and FG-V are selected here for the analysis. The effective material properties of FG-CNTRC beams are estimated according to the rule of mixture. To model the FG-CNTRC beam realistically, an efficient Hermite-Lagrangian finite element formulation is successfully developed. The accuracy and efficiency of the present model are demonstrated by comparison with published benchmark results. Moreover, comprehensive numerical results are presented and discussed in detail to investigate the effects of CNTs volume fraction, distribution patterns of CNTs, boundary conditions, and length-to-thickness ratio on the bending and buckling responses of FG-CNTRC beam. Several new referential results are also reported for the first time which will serve as a benchmark for future studies in a similar direction. It is concluded that the FG-X-CNTRC beam is the strongest beam that carries the lowest central deflection and is followed by the UD, V, Λ, and FG-O-CNTRC beam. Besides, the critical buckling load belonging to the FG-X-CNTRC beam is the highest, followed by UD and FG-O.

• Steel and Composite Structures
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• 제38권5호
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• pp.583-597
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• 2021

This article develops a nonclassical model to analyze bending response of squared perforated microbeams considering the coupled effect of microstructure and surface stress under different loading and boundary conditions, those are not be studied before. The corresponding material and geometrical characteristics of regularly squared perforated beams relative to fully filled beam are obtained analytically. The modified couple stress and the modified Gurtin-Murdoch surface elasticity models are adopted to incorporate the microstructure as well as the surface energy effects. The differential equations of equilibrium including the Poisson's effect are derived based on minimum potential energy. Exact closed form solution is obtained for bending behavior of the proposed model considering the classical and nonclassical boundary conditions for both uniformly distributed and concentrated loads. The proposed model is verified with results available in the literature. Influences of the microstructure length scale parameter, surface energy, beam thickness, boundary and loading conditions on the bending behavior of perforated microbeams are investigated. It is observed that microstructure and surface parameters are vital in investigation of the bending behavior of perforated microbeams. The obtained results are supportive for the design, analysis and manufacturing of perforated nanobeams that commonly used in nanoactuators, nanoswitches, MEMS and NEMS systems.

• 한국산학기술학회논문지
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• 제10권8호
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• pp.2038-2043
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• 2009

본 연구는 유한요소해석을 이용하여 순수 휨이 작용하는 T형 단면보의 탄성 횡-비틀림 좌굴강도에 대해 기술하고 있다. 유한요소해석을 통해 얻어진 결과는 AISC-LRFD(2007)설계기준과 비교되었으며, 검토결과 AISC-LRFD 제안식을 이용하여 얻어지는 값들이 유한요소해석 결과보다 큰 값을 나타내고 있어 안전측 설계를 유도하고 있지 못하고 있다. 이에 본 연구에서는 수정된 설계 계산식을 제안하고 예제를 통해 활용성을 검토하였다. 새로운 설계 계산식은 T형보의 횡-비틀림 좌굴강도 산정에 쉽게 적용될 수 있으며, 다양한 하중이 작용하는 경우 T형보의 연구에 적극 활용 될 수 있을 것이다.

• Steel and Composite Structures
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• 제9권4호
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• pp.349-366
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• 2009

The composite slim beam has become popular throughout Europe in recent years and has also been used on some projects in China. With its steel section encased in a concrete slab, the steel-concrete composite slim beam can provide the floor construction with minimum depth and high fire resistance. However, the design method of the T-shape steel-concrete composite beam is no longer applicable to the composite slim beam with deep deck for its special construction, of which the present design models are not available but mainly depend on experiences. The elevation of the flexural stiffness and bending capacity of composite slim beams with deep deck is rather complicated, because the influences of many factors should be taken into account, such as the variable section dimensions, development of cracks and non-linear characteristics of concrete, etc. In this paper, experimental investigations have been conducted into the flexural behavior of two specimens of simply supported composite slim beam with deep deck. The emphases were laid on the bonding force on the interface between steel beam and concrete, the stress distribution of beam section, the flexural stiffness and bending capacity of the composite beams. Based on the experimental results, the reduction factor of equivalent stress distribution in concrete flange is suggested, and the calculation method of flexural stiffness and bending capacity of simply supported slim beams are proposed.

• Steel and Composite Structures
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• 제39권2호
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• pp.215-228
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• 2021

This paper investigates the effect of micromechanical models on the bending behavior of bidirectional functionally graded (BDFG) beams subjected to different mechanical loading. The material properties of the beam are considered to be graded in both axial and thickness directions according to a power law. The beam's behavior is modeled by the mean of quasi 3D displacement field that contain undetermined integral terms and involves a reduced unknown functions. Navier's method is employed to determine and compute the displacements and stress for a simply supported beam. Different homogenization schemes such as Voigt, Reus, and Mori-Tanaka are employed to analyze the response of the BDFG beam subjected to linear, uniform, exponential and sinusoidal distributed loading. The results obtained by the present method are compared with available results in the literature and a good agreement was found. Several numerical results are presented in tabular form and in figures to examine the effects of the material gradation, micromechanical models and types of loading on the bending response of BDFG beams. It can be concluded that the present theory is not only accurate but also simple in predicting the bending response of BDFG beam subjected to different static loads.

• Steel and Composite Structures
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• 제10권2호
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• pp.109-128
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• 2010

The expediency of using tubular composite steel and concrete columns of annular cross-sections in construction is discussed. The new type space framework with tubular composite columns of multi-storey buildings and its rigid beam-column joints are demonstrated. The features of interaction between the circular steel tube and spun concrete stress-strain states during the concentrical and eccentrical loading of tubular composite members are considered. The modeling of the bearing capacity of beam-columns of composite annular cross-sections is based on the concepts of bending with a concentrical force and compression with a bending moment. The comparison of modeling results for the composite cross-sections of beam-columns is analysed. The expediency of using these concepts for the limit state verification of beam-columns in the methods of the partial safety factors design (PSFD) legitimated in Europe and the load and resistance factors design (LRFD) used in other countries is presented and illustrated by a numerical example.

• 한국강구조학회 논문집
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• 제19권6호
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• pp.611-620
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• 2007

일반적인 중력하중 재하상태의 라멘구조에서는 보-기둥의 이음부에 최대 부모멘트가 발생하며, 일반적으로 이음부의 최대 부모멘트가 보 중앙의 최대 정모멘트보다 크게 나타나므로 보와 기둥의 이음부에서의 모멘트에 의하여 보의 단면이 결정된다. 그러나 보와 기둥의 이음부에 의하여 라멘구조물의 단면을 설계하면 보의 중앙부는 단면과대설계가 되어 단면의 효율성이 낮아지므로, 이음부의 부모멘트를 감소시켜 보 전체의 응력을 고르게 분포시키면 보다 효율적인 단면설계가 가능하게 된다. 본 연구에서는 라멘구조물의 최대 부모멘트 구간에 부재력 재분배 효과로써 보 전체의 응력을 고르게 분포시키고 단면을 감소시킬 수 있는 새로운 시공방법으로써 반력모멘트를 이용한 라멘구조물의 프리스트레싱 공법을 제안하고자 한다. 반력모멘트는 프리스트레싱에 의하여 휨모멘트가 도입된 보부재를 기둥과 연결한 후, 도입된 프리스트레스를 제거할 시에 라멘구조물에 발생하는 반력을 이용하여 보와 기둥의 이음부에서 발생하는 최대 부모멘트를 감소시키고 부재력을 보 전체에 고르게 분배하여 구조물의 내하성능을 증진시키는 공법이다. 본 연구에서는 제안된 반력모멘트를 이용한 철골구조물의 프리스트레싱 도입 공법의 검증을 위하여 실험적 검증 및 구조해석을 실시하여, 반력모멘트에 의한 라멘구조물의 부재력 재분배 효과 및 효율성을 확인하였다.

• Smart Structures and Systems
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• 제30권3호
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• pp.245-253
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• 2022

A two-layer beam consisting of an elastoplastic layer and a functional layer made of shape memory alloy (SMA) TiNi is considered. Constitutive relations for SMA are set by a microstructural model capable to calculate strain increment produced by arbitrary increments of stress and temperature. This model exploits the approximation of small strains. The equations to calculate the variations of the strain and the internal variables are based on the experimentally registered temperature kinetics of the martensitic transformations with an account of the crystallographic features of the transformation and the laws of equilibrium thermodynamics. Stress and phase distributions over the beam height are calculated by steps, by solving on each step the boundary-value problem for given increments of the bending moment (or curvature) and the tensile force (or relative elongation). Simplifying Bernoulli's hypotheses are applied. The temperature is considered homogeneous. The first stage of the numerical experiment is modeling of preliminary deformation of the beam by bending or stretching at a temperature corresponding to the martensitic state of the SMA layer. The second stage simulates heating and subsequent cooling across the temperature interval of the martensitic transformation. The curvature variation depends both on the total thickness of the beam and on the ratio of the layer's thicknesses.

• Advances in materials Research
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• 제11권4호
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• pp.279-298
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• 2022

In this paper, the important novelty and the defining a physical phenomenon of the resent research is the development of nonlocal stress and strain parameters on the porous sandwich beam with functionally graded materials in the top and bottom face sheets.Also, various beam models including Euler-Bernoulli, Reddy and the generalized formulation of two-variable beam theories are obtained in this research. According to a nonlocal strain elasticity theory, the strain at a reference point in the body is dependent not only on the stress state at that point, but also on the stress state at all of the points throughout the body. Thus, the nonlocal stress-strain elasticity theory is defined that can be actual at micro/nano scales. It can be seen that the critical buckling load and transverse deflection of sandwich beam by considering both nonlocal stress-strain parameters is higher than the nonlocal stress parameter. On the other hands, it is noted that by considering the nonlocal stress-strain parameters simultaneously becomes the actual case.

• Structural Engineering and Mechanics
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• 제48권4호
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• pp.519-545
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• 2013

An outline of the Timoshenko beam theory is presented. Two differential equations of motion in terms of deflection and rotation are comprised into single equation with deflection and analytical solutions of natural vibrations for different boundary conditions are given. Double frequency phenomenon for simply supported beam is investigated. The Timoshenko beam theory is modified by decomposition of total deflection into pure bending deflection and shear deflection, and total rotation into bending rotation and axial shear angle. The governing equations are condensed into two independent equations of motion, one for flexural and another for axial shear vibrations. Flexural vibrations of a simply supported, clamped and free beam are analysed by both theories and the same natural frequencies are obtained. That fact is proved in an analytical way. Axial shear vibrations are analogous to stretching vibrations on an axial elastic support, resulting in an additional response spectrum, as a novelty. Relationship between parameters in beam response functions of all type of vibrations is analysed.