• Structural Engineering and Mechanics
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• 제56권6호
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• pp.1003-1020
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• 2015

In this study, free vibration analysis of an edge cracked multilayered symmetric sandwich beams made of functionally graded materials are investigated. Modelling of the cracked structure is based on the linear elastic fracture mechanics theory. Material properties of the functionally graded beams change in the thickness direction according to the power and exponential laws. To represent functionally graded symmetric sandwich beams more realistic, fifty layered beam is considered. Composition of each layer is different although each layer is isotropic and homogeneous. The considered problem is carried out within the Timoshenko first order shear deformation beam theory by using finite element method. A MATLAB code developed to calculate natural frequencies for clamped and simply supported conditions. The obtained results are compared with published studies and excellent agreement is observed. In the study, the effects of crack location, depth of the crack, power law index and slenderness ratio on the natural frequencies are investigated.

• Computers and Concrete
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• 제15권3호
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• pp.373-389
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• 2015

The development of a finite element model for the geometric and material nonlinear analysis of bonded prestressed concrete continuous beams is presented. The nonlinear geometric effect is introduced by the coupling of axial and flexural fields. A layered approach is applied so as to consider different material properties across the depth of a cross section. The proposed method of analysis is formulated based on the Euler-Bernoulli beam theory. According to the total Lagrangian description, the constructed stiffness matrix consists of three components, namely, the material stiffness matrix reflecting the nonlinear material effect, the geometric stiffness matrix reflecting the nonlinear geometric effect and the large displacement stiffness matrix reflecting the large displacement effect. The analysis is capable of predicting the nonlinear behaviour of bonded prestressed concrete continuous beams over the entire loading stage up to failure. Some numerical examples are presented to demonstrate the validity and applicability of the proposed model.

• Steel and Composite Structures
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• 제43권1호
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• pp.79-90
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• 2022

In this study, the dynamic behavior of functionally graded layered deep beams with viscoelastic core is investigated including the porosity effect. The material properties of functionally graded layers are assumed to vary continuously through thickness direction according to the power-law function. To investigate porosity effect in functionally graded layers, three different distribution models are considered. The viscoelastically cored deep beam is exposed to harmonic sinusoidal load. The composite beam is modeled based on plane stress assumption. The dynamic equations of motion of the composite beam are derived based on the Hamilton principle. Within the framework of the finite element method (FEM), 2D twelve -node plane element is exploited to discretize the space domain. The discretized finite element model is solved using the Newmark average acceleration technique. The validity of the developed procedure is demonstrated by comparing the obtained results and good agreement is detected. Parametric studies are conducted to demonstrate the applicability of the developed methodology to study and analyze the dynamic response of viscoelastically cored porous functionally graded deep beams. Effects of viscoelastic parameter, porosity parameter, graduation index on the dynamic behavior of porous functionally graded deep beams with viscoelastic core are investigated and discussed. Material damping and porosity have a significant effect on the forced vibration response under harmonic excitation force. Increasing the material viscosity parameters results in decreasing the vibrational amplitudes and increasing the vibration time period due to increasing damping effect. Obtained results are supportive for the design and manufacturing of such type of composite beam structures.

• 콘크리트학회논문집
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• 제11권5호
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• pp.131-137
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• 1999

The use of higher strength materials with the strength methed of design has resulted in more slender member and shallower sections. For this reason, it is necessary to satisfy the requirements of serviceability even though the structural safety is the most important limit state. This paper is only concerned with the control of deflections in the serviceability. In this study, an analytical model is presented to predict the deflections of reinforced concrete beams to given loading and environmental conditions. This model is based on the finite element approach in which a finite element is generally divided into a number of stiffening effect due to cracking, creep and shrinkage. Comparisons are made with available measured deflections reported by others to assess the capability of the layered beam model. The calculated values of instantaneous and long-term deflection show good agreement with experimental results in the range of tension stiffening parameter $\beta$ between 2.5 and 3.0.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 1998년도 춘계학술대회논문집; 용평리조트 타워콘도, 21-22 May 1998
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• pp.438-443
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• 1998

In this paper, the axial-bending coupled equations of motion for an elastic layered beam are derived. From this equation of motion, the spectral element is formulated for the vibration analysis by use of the spectral element method (SEM). The modal analysis methodology for the present coupled field equations of motion is then developed. As an illustrative example, a cantilevered beam is considered. The correctness of the equations of motion developed herein is verified by gradually reducing the thickness of upper elastic layer to converge to the single layered elastic beam solutions. Also, the accuracy of spectral element is confirmed by comparing its results with the result by modal analysis.

• 비파괴검사학회지
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• 제29권3호
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• pp.242-247
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• 2009

The ability of time reversal techniques to focus ultrasonic beams on the source location is important in many aspects of ultrasonic nondestructive evaluation. In this paper, we investigate the time reversal beam focusing of ultrasonic array sensors on a defect in layered media. Numerical modeling is performed using the commercially available software which employs a time domain finite difference method. Two different time reversal approaches are considered - the through transmission and the pulse-echo. Linear array sensors composed of N elements of line sources are used for signal reception/excitation, time reversal, and reemission in time reversal processes associated with the scattering source of a side-drilled hole located in the second layer of two layer structure. The simulation results demonstrate the time reversal focusing even with multiple reflections from the interface of layered structure. We examine the focusing resolution that is related to the propagation distance, the size of array sensor and the wavelength.

• Structural Engineering and Mechanics
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• 제57권4호
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• pp.657-680
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• 2016

Reinforced concrete (RC) deep beams are structural members that predominantly fail in shear. Therefore, determining the shear strength of these types of beams is very important. The strut-and-tie method is commonly used to design deep beams, and this method has been adopted in many building codes (ACI318-14, Eurocode 2-2004, CSA A23.3-2004). In this study, the efficiency of artificial neural networks (ANNs) in predicting the shear strength of RC deep beams is investigated as a different approach to the strut-and-tie method. An ANN model was developed using experimental data for 214 normal and high-strength concrete deep beams from an existing literature database. Seven different input parameters affecting the shear strength of the RC deep beams were selected to create the ANN structure. Each parameter was arranged as an input vector and a corresponding output vector that includes the shear strength of the RC deep beam. The ANN model was trained and tested using a multi-layered back-propagation method. The most convenient ANN algorithm was determined as trainGDX. Additionally, the results in the existing literature and the accuracy of the strut-and-tie model in ACI318-14 in predicting the shear strength of the RC deep beams were investigated using the same test data. The study shows that the ANN model provides acceptable predictions of the ultimate shear strength of RC deep beams (maximum $R^2{\approx}0.97$). Additionally, the ANN model is shown to provide more accurate predictions of the shear capacity than all the other computed methods in this study. The ACI318-14-STM method was very conservative, as expected. Moreover, the study shows that the proposed ANN model predicts the shear strengths of RC deep beams better than does the strut-and-tie model approaches.

• Structural Engineering and Mechanics
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• 제51권1호
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• pp.111-130
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• 2014

The aim of this study is to investigate the effects of the beam aspect ratio(L/h), hole diameter, hole location and stacking layer sequence ($[0/45/-45/90]_s$, $[45/0/-45/90]_s$ and $[90/45/-45/0]_s$) on natural frequencies of glass/epoxy perforated beams under room and high (40, 60, 80, and $100^{\circ}C$) temperatures for the common clamped-free boundary conditions (cantilever beam). The first three out of plane bending free vibration of symmetric laminated beams is studied by Timoshenko's first order shear deformation theory. For the numerical analyses, ANSYS 13.0 software package is utilized. The results show that the hole diameter, stacking layer sequence and hole location have important effect especially on the second and third mode natural frequency values for the short beams and the high temperatures affects the natural frequency values significantly. The results are presented in tabular and graphical form.

• Computers and Concrete
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• 제13권6호
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• pp.799-827
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• 2014

In this paper, a theoretical and experimental study of the sectional behaviour of reinforced concrete beams subjected to short-term loads is carried out. The pure bending behaviour is analysed with moment-curvature diagrams. Thus, the experimental results obtained from 24 beams tested by the authors and reported in literature are compared with theoretical results obtained from a layered model, which combines the material parameters defined in Model Code 2010 with some of the most recognized tensions-tiffening models. Although the tests were carried out for short-term loads, the analysis demonstrates that rheological effects can be important and must be accounted to understand the experimental results. Another important conclusion for the beams tested in this work is that the method proposed by EC-2 tends to underestimate the tension-stiffening effects, leading to inaccuracies in the estimations of deflections. Thus, the actual formulation is analysed and a simple modification is proposed. The idea is the separation of the deflection prediction in two parts: one for short-term loads and other for rheological effects (shrinkage). The results obtained are in fairly good agreement with the experimental results, showing the feasibility of the proposed modification.

• Computers and Concrete
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• 제10권3호
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• pp.307-330
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• 2012

This work intends to contribute for the improvement of the procedure suggested by Brazilian Technical Code that takes into account the cracked concrete stiffness in the estimative of the displacement of reinforced concrete beams submitted to service loads. A damage constitutive model accounting for induced anisotropy, plastic deformations and bimodular elastic response is used in order to simulate the concrete behaviour, while an elastoplastic behaviour is admitted for the reinforcement. The constitutive models were implemented in a program for bars structures analysis with layered finite elements. Initially, the damage model is briefly presented as well as the parametric identification of the materials that have been used in the reinforced concrete beams. After that, beams with different geometries and reinforcement area are analyzed and a statistical method (ANOVA) is employed in order to identify the main variables in the problem. Soon after, the same procedure is used with another resistance of concrete, where the compression strength is changed. The numerical responses are compared with the ones obtained by Brazilian Technical Code and experimental tests in order to validate the use of the damage model. Finally, some remarks are discussed based on responses presented in this work.