• Structural Engineering and Mechanics
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• 제52권5호
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• pp.1033-1049
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• 2014

The free vibration of functionally graded material (FGM) beams on an elastic foundation and spring supports is investigated. Young's modulus, mass density and width of the beam are assumed to vary in thickness and axial directions respectively following the exponential law. The spring supports are also taken into account at both ends of the beam. An analytical formulation is suggested to obtain eigen solutions of the FGM beams. Numerical analyses, based on finite element method by using a beam finite element developed in this study, are performed in order to show the legitimacy of the analytical solutions. Some results for the natural frequencies of the FGM beams are given considering the effect of various structural parameters. It is also shown that the spring supports show the greatest effect on the natural frequencies of FGM beams.

• Steel and Composite Structures
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• 제33권3호
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• pp.403-432
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• 2019

Axially functionally graded (AFG) beams are a new class of composite structures that have continuous variations in material and/or geometrical parameters along the axial direction. In this study, the exact analytical solutions for the free vibration of AFG and uniform beams with general elastic supports are obtained by using Euler-Bernoulli beam theory. The elastic supports are modeled with linear rotational and lateral translational springs. Moreover, the material and/or geometrical properties of the AFG beams are assumed to vary continuously and together along the length of the beam according to the power-law forms. Accordingly, the accuracy, efficiency and capability of the proposed formulations are demonstrated by comparing the responses of the numerical examples with the available solutions. In the following, the effects of the elastic end restraints and AFG parameters, namely, gradient index and gradient coefficient, on the values of the first three natural frequencies of the AFG and uniform beams are investigated comprehensively. The analytical solutions are presented in tabular and graphical forms and can be used as the benchmark solutions. Furthermore, the results presented herein can be utilized for design of inhomogeneous beams with various supporting conditions.

• 소음진동
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• 제8권2호
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• pp.297-305
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• 1998

The finite element method is used for the study of the eigenvalue problems of partially fixed end beams with intermediate elastic supports. The elastic critical loads and natural frquencies of the beams are investigated by changing the numbers of elastic supports and their stiffness, and also by changing Kinney's fixity factor, $f_a$. The relationship between two eigenvalues is established by calculating the corresponding values of $(w/w_n)^2$ through changing $(P/P_{cr})$ values. The results of this study are as follows : (1) The elastic critical loads and natural frequencies of beams increase with increases in Kinney's fixity factor, $f_a$ and with the increased numbers of intermediate elastic supports. (2) The relationship between elastic critical loads and the natural frequencies of partially fixed end beams with intermediated elastic supports is $P/P_{cr} + (w/w_n)^2/ = 1$ without regard to Kinney's fixity factor, the stiffness of elastic supports, or the number of elastic supports.

• Steel and Composite Structures
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• 제10권2호
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• pp.169-185
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• 2010

The present work describes the experimental tests on steel and lightweight concrete composite beams performed at University of Minho, Portugal. The study involves tests on simply supported composite beams of 4.5 m span, with the same geometrical disposition, supports and materials. The geometrical configuration for the cross section and supports is identical for every beam, varying the shear connectors' distribution and the loading conditions. Headed studs are used to provide the connection between the steel profile and the concrete slab. The parameters in study are the stud disposition and the load distribution. The main objective is to describe the composite beams behaviour, focused on its connection, and to analyse the contribution of the different components to the beams load and deformation capacity. All the tests explored the beams maximum load and deformation capacity and different types of failure were observed.

• Structural Engineering and Mechanics
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• 제70권6호
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• pp.751-763
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• 2019

Steel-concrete composition is widely used in the construction due to efficient utilization of materials. The service load behavior of composite structures is significantly affected by cracking, creep and shrinkage effects in concrete. In order to control these effects in concrete slab, an efficient and novel strategy has been proposed by use of fiber reinforced concrete near interior supports of a continuous beam. Numerical study is carried out for the control of cracking, creep and shrinkage effects in composite beams subjected to service load. A five span continuous composite beam has been analyzed for different lengths of fiber reinforced concrete near the interior supports. For this purpose, the hybrid analytical-numerical procedure, developed by the authors, for service load analysis of composite structures has been further improved and generalized to make it applicable for composite beams having spans with different material properties along the length. It is shown that by providing fiber reinforced concrete even in small length near the supports; there can be a significant reduction in cracking as well as in deflections. It is also observed that the benefits achieved by providing fiber reinforced concrete over entire span are not significantly more as compared to the use of fiber reinforced concrete in certain length of beam near the interior supports in continuous composite beams.

• 한국공간구조학회논문집
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• 제12권1호
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• pp.87-98
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• 2012

본 연구에서는 쉘의 테두리를 보가 둘러싸고 있는 전통적인 형태와 모서리보를 제거한 형태의 모임지붕형 쌍곡포물선쉘구조의 유한요소해석결과비교를 통해 모서리보의 역할을 확인하고, 또한 지붕의 경사도의 영향을 분석하였다. 유한요소해석에 의하면 쉘면에 작용하는 하중은 쉘 대각선 방향의 아치작용을 통해 모퉁이의 지점에 직접 전달되므로 막이론에 비해 테두리보에는 부재력이 작게 작용하고 모퉁이의 지점 부분의 쉘에는 응력이 증가되는 것으로 나타났다. 모서리보를 제거하면 지점 부근의 쉘에 더욱 응력이 집중되고 경사진 모서리 부분의 처짐이 증가하는데 이와 같은 현상은 지붕의 경사도가 낮아짐에 따라 현저해지는 것으로 나타났다. 따라서, 모임지붕형 쌍곡포물선쉘 구조에서는 지점 부분의 쉘두께를 보다 증가할 필요가 있으며 경사도가 낮은 쌍곡포물선쉘 구조의 모서리보 제거는 주의가 필요한 것으로 나타났다.

• Structural Engineering and Mechanics
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• 제70권3호
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• pp.367-380
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• 2019

The paper concerns topology and geometry optimization of statically determinate beams with arbitrary number of supports. The optimization problem is treated as a bi-criteria one, with the objectives of minimizing the absolute maximum bending moment and the maximum deflection for a uniform gravity load. The problem is formulated and solved using the Pareto optimality concept and the lexicographic ordering of the objectives. The non-dominated sorting genetic algorithm NSGA-II and the local search method are used for the optimization in the Pareto sense, whereas the genetic algorithm and the exhaustive search method for the lexicographic optimization. Trade-offs between objectives are examined and sets of Pareto-optimal solutions are provided for different topologies. Lexicographically optimal beams are found assuming that the maximum moment is a more important criterion. Exact formulas for locations and values of the maximum deflection are given for all lexicographically optimal beams of any topology and any number of supports. Topologies with lexicographically optimal geometries are classified into equivalence classes, and specific features of these classes are discussed. A qualitative principle of the division of topologies equivalent in terms of the maximum moment into topologies better and worse in terms of the maximum deflection is found.

• 한국건축시공학회:학술대회논문집
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• 한국건축시공학회 2014년도 추계 학술논문 발표대회
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• pp.203-204
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• 2014

Unlike other members, beams have various cross-sections and they have an important role of delivering the load of slabs. A beam form neighbors the columns and slabs, which makes it difficult to be installed. In a conventional way to exclusively use the form after concrete pouring, the form and a support should be both removed. Then, the support should reinstalled to sustain the stripping time of form, resulting in a structural issue. To solve such structural problem, the study proposes SMART beam form that uses filler panels and supports for filler. The floor filler panels and supports for filler are not removed after concrete curing, to conform to the stripping time of supports. Thus, any structural problem such as cracks and reduction of compressive strength owing to the gap of load bearing capacity can be prevented. The study results will be used as cases for studies on productivity analyses.

• Structural Engineering and Mechanics
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• 제8권6호
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• pp.531-546
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• 1999

The paper presents an experimental and theoretical study on the influence of steel fibers and longitudinal tension and compression reinforcements on immediate and long-term deflections of high-strength concrete beams of 85 MPa (12,300 psi) compressive, strength. Test results of eighteen beams subjected to sustained load for 180 days show that the deflection behavior depends on the longitudinal tension and compression reinforcement ratios and fiber content; excessive amount of compression reinforcement and fibers may have an unfavorable effect on the long-term deflections. The beams having the ACI Code's minimum longitudinal tension reinforcement showed much higher time-dependent deflection to immediate deflection ratio, when compared with that of the beams having about 50 percent of the balanced tension reinforcement. The results of theoretical analysis of tested beams and those of a parametric study show that the influence of steel fibers in increasing the moment of inertia of cracked transformed sections is most pronounced in beams having small amount of longitudinal tension reinforcement.

• Computers and Concrete
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• 제18권6호
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• pp.1113-1134
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• 2016

A methodology using neural networks has been proposed for rapid prediction of inelastic bending moments in reinforced concrete continuous beams subjected to service load. The closed form expressions obtained from the trained neural networks take into account cracking in concrete at in-span and at near the internal supports and tension stiffening effect. The expressions predict the inelastic moments (considering the concrete cracking) from the elastic moments (neglecting the concrete cracking) at supports. Three separate neural networks are trained since these have been postulated to represent all the beams having any number of spans. The training, validating, and testing data sets for the neural networks are generated using an analytical-numerical procedure of analysis. The proposed expressions are verified for example beams of different number of spans and cross-section properties and the errors are found to be small. The proposed expressions, at minimal input data and computation effort, yield results that are close to FEM results. The expressions can be used in preliminary every day design as they enable a rapid prediction of inelastic moments and require a computational effort that is a fraction of that required for the available methods in literature.