Search results for: infinite beams

Authors: Arifuzzaman Nayeem, Tafannum Torsha, Tanvir Manzur, Shaurav Alam

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Performance evaluation of reinforced concrete (RC) beams subjected to accidental fire is significant for post-fire capacity measurement. Mechanical properties of any RC beam degrade due to heating since the strength and modulus of concrete and reinforcement suffer considerable reduction under elevated temperatures. Moreover, fire-induced thermal dilation and shrinkage cause internal stresses within the concrete and eventually result in cracking, spalling, and loss of stiffness, which ultimately leads to lower service life. However, conducting full-scale comprehensive experimental investigation for RC beams exposed to fire is difficult and cost-intensive, where the finite element (FE) based numerical study can provide an economical alternative for evaluating the post-fire capacity of RC beams. In this study, an attempt has been made to study the fire behavior of RC beams using FE software package ABAQUS under different durations of fire. The damaged plasticity model of concrete in ABAQUS was used to simulate behavior RC beams. The effect of temperature on strength and modulus of concrete and steel was simulated following relevant Eurocodes. Initially, the result of FE models was validated using several experimental results from available scholarly articles. It was found that the response of the developed FE models matched quite well with the experimental outcome for beams without heat. The FE analysis of beams subjected to fire showed some deviation from the experimental results, particularly in terms of stiffness degradation. However, the ultimate strength and deflection of FE models were similar to that of experimental values. The developed FE models, thus, exhibited the good potential to predict the fire behavior of RC beams. Once validated, FE models were then used to analyze several RC beams having different strengths (ranged between 20 MPa and 50 MPa) exposed to the standard fire curve (ASTM E119) for different durations. The post-fire performance of RC beams was investigated in terms of load-deflection behavior, flexural strength, and deflection characteristics.

Keywords: fire durations, flexural strength, post fire capacity, reinforced concrete beam, standard fire

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Authors: Shahrad Ebrahimzadeh

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Nowadays, the main efforts of the researchers aim to constantly evolve new, optimized and efficient construction materials and methods related to reinforced concrete beams. Due to the fewer applied materials and offering a higher structural efficiency compared to solid concrete beams with the same concrete area, hollow reinforced concrete beams (HRCB) internally reinforced with steel rebars have been employed extensively for bridge structural members and high-rise buildings. Many experimental studies have been conducted to investigate the behavior of hollow beams subjected to bending loading and found that the structural performance of HRCBs is critically affected by many design parameters. While the proper design of the HRCBs demonstrated comparable behavior to solid sections, inappropriate design leads beams to be extremely prone to brittle failure. Another potential issue that needs to be further investigated is the replacement of steel bars with suitable materials due to their susceptibility to corrosion. Hence, to develop a reliable construction system, the application of GFRP bars as a non-corroding material has been utilized. Furthermore, this study aims to critically review the different design parameters that affect the flexural performance of the HRCBs and recognize the gaps of knowledge in the better design and more effective use of this construction system.

Keywords: design parameters, experimental investigations, hollow reinforced concrete beams, steel, GFRP, flexural strength

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Authors: Bakhtiar Azadbakht, Karim Adinehvand, Amin Sahebnasagh

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The purpose of this study was to evaluate dependence of PAGAT polymer gel dosimeter 1/T2 on different electron and photon energies as well as on different mean dose rates for a standard clinically used Co-60 therapy unit and an ELECTA linear accelerator. A multi echo sequence with 32 equidistant echoes was used for the evaluation of irradiated polymer gel dosimeters. The optimal post-manufacture irradiation and post imaging times were both determined to be one day. The sensitivity of PAGAT polymer gel dosimeter with irradiation of photon and electron beams was represented by the slope of calibration curve in the linear region measured for each modality. The response of PAGAT gel with photon and electron beams is very similar in the lower dose region. The R2-dose response was linear up to 30Gy. In electron beams the R2-dose response for doses less than 3Gy is not exact, but in photon beams the R2-dose response for doses less than 2Gy is not exact. Dosimeter energy dependence was studied for electron energies of 4, 12 and 18MeV and photon energies of 1.25, 4, 6 and 18MV. Dose rate dependence was studied in 6MeV electron beam and 6MV photon beam with the use of dose rates 80, 160, 240, 320, 400, and 480cGy/min. Evaluation of dosimeters were performed on Siemens Symphony, Germany 1.5T Scanner in the head coil. In this study no trend in polymer-gel dosimeter 1/T2 dependence was found on mean dose rate and energy for electron and photon beams.

Keywords: polymer gels, PAGAT gel, electron and photon beams, MRI

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Authors: Mohamed Sanad, Noha Hassan

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A low wind-load light-weight broad-band multi-beam base station antenna has been developed. It can generate any required number of beams with the required beamwidths. It can have horizontal and vertical sectorization at the same time. Vertical sectorization doubles the overall number of beams. It will be very valuable in LTE-A and 5G. It can be used to serve vertically split inner and outer cells, which improves system performance. The intersection between the beams of the proposed multi-beam antenna can be controlled by optimizing the design parameters of the antenna. The gain at the points of intersection between the beams, the null filling and the overlap between the beams can all be modified. The proposed multi-beam base station antenna can cover an unlimited number of wireless applications, regardless of their frequency bands. It can simultaneously cover all, current and future, wireless technology generations such as 2G, 3G, 4G (LTE), --- etc. For example, in LTE, it covers the bands 450-470 MHz, 690-960 MHz, 1.4-2.7 GHz and 3.3-3.8 GHz. It has at least 2 ports for each band in each beam for ±45° polarizations. It can include up to 72 ports or even more, which could facilitate any further needed capacity expansions.

Keywords: base station antenna, multi-beam antenna, smart antenna, vertical sectorization

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Authors: Kun-Peng Jin, Jin Liang, Ti-Jun Xiao

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In this work, we are concerned with the dynamic behaviors of solutions to some coupled systems with infinite memory, which consist of two partial differential equations where only one partial differential equation has damping. Such coupled systems are good mathematical models to describe the deformation and stress characteristics of some viscoelastic materials affected by temperature change, external forces, and other factors. By using the theory of operator semigroups, we give wellposedness results for the Cauchy problem for these coupled systems. Then, with the help of some auxiliary functions and lemmas, which are specially designed for overcoming difficulties in the proof, we show that the solutions of the coupled systems decay to zero in a strong way under a few basic conditions. The results in this dynamic analysis of coupled systems are generalizations of many existing results.

Keywords: dynamic analysis, coupled system, infinite memory, damping.

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Authors: Sandeep Kumar, Naveen Gupta

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Terahertz (THz) generation has been investigated by beating two cosh-Gaussian laser beams of the same amplitude but different wavenumbers and frequencies through rippled collisionless plasma. The ponderomotive force is operative which is induced due to the intensity gradient of the laser beam over the cross-section area of the wavefront. The electrons evacuate towards a low-intensity regime, which modifies the dielectric function of the medium and results in cross focusing of cosh-Gaussian laser beams. The evolution of spot size of laser beams has been studied by solving nonlinear Schrodinger wave equation (NLSE) with variational technique. The laser beams impart oscillations to electrons which are enhanced with ripple density. The nonlinear oscillatory motion of electrons gives rise to a nonlinear current density driving THz radiation. It has been observed that the periodicity of the ripple density helps to enhance the THz radiation.

Keywords: rippled collisionless plasma, cosh-gaussian laser beam, ponderomotive force, variational technique, nonlinear current density

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Authors: Ikram Slamani, Hicheme Ferdjani

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This study focuses on analyzing a Griffith crack situated at the center of an infinite strip. The problem is reformulated as a hyper-singular integral equation and solved numerically using second-order Chebyshev polynomials. The primary objective is to calculate the stress intensity factor in mode 1, denoted as K1. The obtained results reveal the influence of the strip width and crack length on the stress intensity factor, assuming stress-free edges. Additionally, a comparison is made with relevant literature to validate the findings.

Keywords: center crack, Chebyshev polynomial, hyper singular integral equation, Griffith, infinite strip, stress intensity factor

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Authors: Yeo Kyeong Lee, Hae Won Min, Ji Yeon Kang, Hee Sun Kim, Yeong Soo Shin

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Fire incidents have been steadily increased over the last year according to national emergency management agency of South Korea. Even though most of the fire incidents with property damage have been occurred in building, rehabilitation has not been properly done with consideration of structure safety. Therefore, this study aims at evaluating rehabilitation effects on fire damaged normal strength concrete beams through experiments and finite element analyses. For the experiments, reinforced concrete beams were fabricated having designed concrete strength of 21 MPa. Two different cover thicknesses were used as 40 mm and 50 mm. After cured, the fabricated beams were heated for 1hour or 2hours according to ISO-834 standard time-temperature curve. Rehabilitation was done by removing the damaged part of cover thickness and filling polymeric mortar into the removed part. Both fire damaged beams and rehabilitated beams were tested with four point loading system to observe structural behaviors and the rehabilitation effect. To verify the experiment, finite element (FE) models for structural analysis were generated using commercial software ABAQUS 6.10-3. For the rehabilitated beam models, integrated temperature-structural analyses were performed in advance to obtain geometries of the fire damaged beams. In addition to the fire damaged beam models, rehabilitated part was added with material properties of polymeric mortar. Three dimensional continuum brick elements were used for both temperature and structural analyses. The same loading and boundary conditions as experiments were implemented to the rehabilitated beam models and non-linear geometrical analyses were performed. Test results showed that maximum loads of the rehabilitated beams were 8~10% higher than those of the non-rehabilitated beams and even 1~6 % higher than those of the non-fire damaged beam. Stiffness of the rehabilitated beams were also larger than that of non-rehabilitated beams but smaller than that of the non-fire damaged beams. In addition, predicted structural behaviors from the analyses also showed good rehabilitation effect and the predicted load-deflection curves were similar to the experimental results. From this study, both experiments and analytical results demonstrated good rehabilitation effect on the fire damaged normal strength concrete beams. For the further, the proposed analytical method can be used to predict structural behaviors of rehabilitated and fire damaged concrete beams accurately without suffering from time and cost consuming experimental process.

Keywords: fire, normal strength concrete, rehabilitation, reinforced concrete beam

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Authors: Fernanda M. Bastos, Teógenes A. da Silva

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Extrapolation chambers were designed to be used as primary standard dosimeter for measuring absorbed dose in a medium in beta radiation and low energy x-rays. The International Organization for Standardization established series of reference x-radiation for calibrating and determining the energy dependence of dosimeters that are to be reproduced in metrology laboratories. Standardization of the low energy x-ray beams with tube potential lower than 30 kV may be affected by the instrument used for dosimetry. In this work, parameters of a 23392 model PTW extrapolation chamber were determined aiming its use in low energy x-ray beams as a reference instrument.

Keywords: extrapolation chamber, low energy x-rays, x-ray dosimetry, X-ray metrology

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Authors: Suleiman Bashir Adamu, Lawan Sani Taura

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We study the role of boundary conditions via -symmetric quantum mechanics, where denotes parity operator and denotes time reversal operator. Using the one-dimensional Schrödinger Hamiltonian for a free particle in an infinite square well, we introduce symmetric boundary conditions. We find solutions of the 1D Klein-Gordon equation for a free particle in an infinite square well with Hermitian boundary and symmetry boundary conditions, where in both cases the energy eigenvalues and eigenfunction, respectively, are obtained.

Keywords: Eigenvalues, Eigenfunction, Hamiltonian, Klein- Gordon equation, PT-symmetric quantum mechanics

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Authors: Ho Young Son, Bu Seog Ju, Woo Young Jung

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This study presents the seismic safety evaluation of weir structure subjected to strong earthquake ground motions, as a flood defense structure in civil engineering structures. The seismic safety analysis procedure was illustrated through development of Finite Element (FE) and InFinite Element (IFE) method in ABAQUS platform. The IFE model was generated by CINPS4, 4-node linear one-way infinite model as a sold continuum infinite element in foundation areas of the weir structure and then nonlinear FE model using friction model for soil-structure interactions was applied in this study. In order to understand the complex behavior of weir structures, nonlinear time history analysis was carried out. Consequently, it was interesting to note that the compressive stress gave more vulnerability to the weir structure, in comparison to the tensile stress, during an earthquake. The stress concentration of the weir structure was shown at the connection area between the weir body and stilling basin area. The stress both tension and compression was reduced in IFE model rather than FE model of weir structures.

Keywords: seismic, numerical analysis, FEM, weir, boundary condition

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Authors: Benalia Nadia, Bensiali Nadia, Zezouri Noura

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This paper studies the effects of voltage sags, both symmetrical and unsymmetrical, on the three-phase Synchronous Machine (SM) when powering an isolate load or infinite bus bar. The vast majority of the electrical power generation systems in the world is consist of synchronous generators coupled to the electrical network though a transformer. Voltage sags on SM cause speed variations, current and torque peaks and hence may cause tripping and equipment damage. The consequences of voltage sags in the machine behavior depends on different factors such as its magnitude (or depth), duration , the parameters of the machine and also the size of load. In this study, we consider the machine feeds an infinite bus bar in the first and the isolate load using symmetric and asymmetric defaults to see the behavior of the machine in both case the simulation have been used on SIMULINK MATLAB.

Keywords: power quality, voltage sag, synchronous generator, infinite system

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Authors: Mantai Chen, Johnny Ching Ming Ho

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The stress-strain relationship of concrete under flexure is one of the essential parameters in assessing ultimate flexural strength capacity of RC beams. Currently, the concrete stress-strain curve in flexure is obtained by incorporating a constant scale-down factor of 0.85 in the uniaxial stress-strain curve. However, it was revealed that strain gradient would improve the maximum concrete stress under flexure and concrete stress-strain curve is strain gradient dependent. Based on the strain-gradient-dependent concrete stress-strain curve, the investigation of the combined effects of strain gradient and concrete strength on flexural strength of RC beams was extended to high strength concrete up to 100 MPa by theoretical analysis. As an extension and application of the authors’ previous study, a new flexural strength design method incorporating the combined effects of strain gradient and concrete strength is developed. A set of equivalent rectangular concrete stress block parameters is proposed and applied to produce a series of design charts showing that the flexural strength of RC beams are improved with strain gradient effect considered.

Keywords: beams, equivalent concrete stress block, flexural strength, strain gradient

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Authors: Mazin Mohammed S. Sarhan

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This study presents the performance of concrete beams reinforced with steel plates as a technique of reinforcement. Three reinforced concrete beams with the dimensions of 200 mm x 300 mm x 4000 mm (width x height x length, respectively) were experimentally investigated under flexural loading. The deformed steel bars were used as the main reinforcement for the first beam. A steel plate placed horizontally was used as the main reinforcement for the second beam. The bond between the steel plate and the surrounding concrete was enhanced by using steel bolts (with a diameter of 20 mm and length of 100 mm) welded to the steel plate at a regular distance of 200 mm. A pair of steel plates placed vertically was used as the main reinforcement for the third beam. The bond between the pair steel plates and the surrounding concrete was enhanced by using 4 equal steel angles (with the dimensions of 75 mm x 75 mm and the thickness of 8 mm) for each vertical steel plate. Two steel angles were welded at each end of the steel plate. The outcomes revealed that the bending stiffness of the beams reinforced with steel plates was higher than that reinforced with deformed steel bars. Also, the flexural ductile behavior of the second beam was much higher than the rest beams.

Keywords: concrete beam, deflection, ductility, plate

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Authors: Falek Kamel

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Free vibration analysis of beams, based on the assumptions of Bernoulli-Euler theory, has been extensively studied. Many research works have focused on the study of transverse vibrations under the application of different boundary conditions where different theories have been applied. The stiffness and mass matrices considered are those obtained by assembling those resulting from the use of the finite element method. The Jacobi method has been used to solve the eigenvalue problem. These well-known concepts have been applied to the study of beams with constant geometric and mechanical characteristics having one to two overhangs with variable lengths. Murphy studied, by an algebraic solution approach, a simply supported beam with two overhangs of arbitrary length, allowing for an experimental determination of the elastic modulus E. The advantage of our article is that it offers the possibility of extending this approach to many interesting problems formed by transversely vibrating beams with various end constraints.

Keywords: beam, finite element, transverse vibrations, end restreint, Bernoulli-Euler theory

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Authors: Cut Maisyarah Karyati, Aries Muslim, Sulardi

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Digital image processing techniques to obtain detailed information from an image have been used in various fields, including in civil engineering, where the use of solid beam profiles in buildings and bridges has often been encountered since the early development of beams. Along with this development, the founded castellated beam profiles began to be more diverse in shape, such as the shape of a hexagon, triangle, pentagon, circle, ellipse and oval that could be a practical solution in optimizing a construction because of its characteristics. The purpose of this research is to create a computer application to edge detect the profile of various shapes of the castella beams hole. The digital image segmentation method has been used to obtain the grayscale images and represented in 2D and 3D formats. This application has been successfully made according to the desired function, which is to provide information on the type of castella beam hole.

Keywords: digital image, image processing, edge detection, grayscale, castella beams

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Authors: Asal Pournaghshband

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This paper presents the development of a finite element model to study the large deflection behavior of restrained stainless steel cellular beams at elevated temperature. Cellular beams are widely used for efficient utilization of raw materials to facilitate long spans with faster construction resulting sustainable design solution that can enhance the performance and merit of any construction project. However, their load carrying capacity is less than the equivalent beams without opening due to developing shear-moment interaction at the openings. In structural frames due to elements continuity, such beams are restrained by their adjoining members which has a substantial effect on beams behavior in fire. Stainless steel has also become integral part of the build environment due to its excellent corrosion resistance, whole life-cycle costs, and sustainability. This paper reports the numerical investigations into the effect of structural continuity on the thermo-mechanical performance of restrained steel beams with circle and elongated circle shapes of web opening in fire. The numerical model is firstly validated using existing numerical results from the literature, and then employed to perform a parametric study. The structural continuity is evaluated through the application of different levels of axial restraints on the response of carbon steel and stainless steel cellular beam in fire. The transit temperature for stainless steel cellular beam is shown to be less affected by the level of axial stiffness than the equivalent carbon steel cellular beam. Overall, it was established that whereas stainless steel cellular beams show similar stages of behavior of carbon steel cellular beams in fire, they are capable of withstanding higher temperatures prior to the onset of catenary action in large deflection, despite the higher thermal expansion of stainless steel material.

Keywords: axial restraint, catenary action, cellular beam, fire, numerical modeling, stainless steel, transit temperature

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Authors: Serge Provost, Abdous Saboor

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A q-analogue of the generalized extreme value distribution which includes the Gumbel distribution is introduced. The additional parameter q allows for increased modeling flexibility. The resulting distribution can have a finite, semi-infinite or infinite support. It can also produce several types of hazard rate functions. The model parameters are determined by making use of the method of maximum likelihood. It will be shown that it compares favourably to three related distributions in connection with the modeling of a certain hydrological data set.

Keywords: extreme value theory, generalized extreme value distribution, goodness-of-fit statistics, Gumbel distribution

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Authors: Shashi Kant Mishra

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In this paper, we consider semi-infinite mathematical programming problems with equilibrium constraints (SIMPEC). We establish necessary and sufficient optimality conditions for the SIMPEC, using convexificators. We study the Wolfe type dual problem for the SIMPEC under the ∂∗convexity assumptions. A Mond-Weir type dual problem is also formulated and studied for the SIMPEC under the ∂∗-convexity, ∂∗-pseudoconvexity and ∂∗quasiconvexity assumptions. Weak duality theorems are established to relate the SIMPEC and two dual programs in the framework of convexificators. Further, strong duality theorems are obtained under generalized standard Abadie constraint qualification (GS-ACQ).

Keywords: mathematical programming problems with equilibrium constraints, optimality conditions, semi-infinite programming, convexificators

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Authors: Merrimi El Bekkaye, El Bikri Khalid, Benamar Rhali

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In the present paper, the problem of geometrically non-linear free vibration of symmetrically and asymmetrically laminated composite beams (LCB) resting on nonlinear Pasternak elastic Foundation with immovable ends is studied. A homogenization procedure has been performed to reduce the problem under consideration to that of the isotropic homogeneous beams with effective bending stiffness and axial stiffness parameters. This simple formulation is developed using the governing axial equation of the beam in which the axial inertia and damping are ignored. The theoretical model is based on Hamilton’s principle and spectral analysis. Iterative form solutions are presented to calculate the fundamental nonlinear frequency parameters which are found to be in a good agreement with the published results. On the other hand, the influence of the foundation parameters on the nonlinear frequency to the linear frequency ratio of the LCB has been studied. The non-dimensional curvatures associated to the fundamental mode are also given in the case of clamped-clamped symmetrically and asymmetrically laminated composite beams.

Keywords: large vibration amplitudes, laminated composite beam, Pasternak foundation, composite beams

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Authors: Mohammed A. Sakr, Tarek M. Khalifa, Walid N. Mansour

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Fiber reinforced polymer (FRP) installation is a very effective way to repair and strengthen structures that have become structurally weak over their life span. This technique attracted the concerning of researchers during the last two decades. This paper presents a simple uniaxial nonlinear finite element model (UNFEM) able to accurately estimate the load-carrying capacity, different failure modes and the interfacial stresses of reinforced concrete (RC) continuous beams flexurally strengthened with externally bonded FRP plates on the upper and lower fibers. Results of the proposed finite element (FE) model are verified by comparing them with experimental measurements available in the literature. The agreement between numerical and experimental results is very good. Considering fracture energy of adhesive is necessary to get a realistic load carrying capacity of continuous RC beams strengthened with FRP. This simple UNFEM is able to help design engineers to model their strengthened structures and solve their problems.

Keywords: continuous beams, debonding, finite element, fibre reinforced polymer

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Authors: Babak Safaei, A. M. Fattahi

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In the present study we have investigated axial buckling characteristics of nanocomposite beams reinforced by single-walled carbon nanotubes (SWCNTs). Various types of beam theories including Euler-Bernoulli beam theory, Timoshenko beam theory and Reddy beam theory were used to analyze the buckling behavior of carbon nanotube-reinforced composite beams. Generalized differential quadrature (GDQ) method was utilized to discretize the governing differential equations along with four commonly used boundary conditions. The material properties of the nanocomposite beams were obtained using molecular dynamic (MD) simulation corresponding to both short-(10,10) SWCNT and long-(10,10) SWCNT composites which were embedded by amorphous polyethylene matrix. Then the results obtained directly from MD simulations were matched with those calculated by the mixture rule to extract appropriate values of carbon nanotube efficiency parameters accounting for the scale-dependent material properties. The selected numerical results were presented to indicate the influences of nanotube volume fractions and end supports on the critical axial buckling loads of nanocomposite beams relevant to long- and short-nanotube composites.

Keywords: nanocomposites, molecular dynamics simulation, axial buckling, generalized differential quadrature (GDQ)

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Authors: O. Vlcek

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The paper deals with current issues in the research of advanced methods to increase the reliability of traditional timber structural elements. It analyses the issue of strengthening of bent timber beams, such as ceiling beams in old (historical) buildings with the additional concrete slab in combination with externally bonded fibre-reinforced polymer. The study evaluates deflection of a selected group of timber beams with concrete slab and additional CFRP reinforcement using different calculating methods and observes differences in results from different calculating methods. An elastic calculation method and evaluation with FEM analysis software were used.

Keywords: timber-concrete composite, strengthening, fibre-reinforced polymer, theoretical analysis

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Authors: Ghada Diaa, Enas A. Khattab

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Ultra High Strength Concrete (UHSC) is a new advanced concrete that is being transferred from laboratory researches to practicable applications. In addition to its excellent durability properties, UHSC has high compressive and tensile strengths, and high modulus of elasticity. Despite of this low degree of hydration, ultra high strength values can be achieved by controlling the mixture proportions. In this research, an experimental program was carried out to investigate the shear behavior of ultra high strength concrete beams. A total of nine beams were tested to determine the effect of different parameters on the shear behavior of UHSC beams. The parameters include concrete strength, steel fiber volume, shear span to depth ratio, and web reinforcement ratio. The results demonstrated that nominal shear stress at cracking load and at ultimate load increased with the increase of concrete strength or the decrease in shear span-depth ratio. Using steel fibers or shear reinforcement increases the ultimate shear strength and makes the shear behavior more ductile. In this study, a simplified analytical model to calculate the shear strength of UHSC beams is introduced. Shear strength estimated according to the proposed method in this research is in good agreement with the experimental results.

Keywords: ultra high strength, shear strength, diagonal, cracking, steel fibers

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Authors: Nihal Abdel Hamid Taha

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Crack evaluation of flexure reinforced concrete (RC) member is considered an important step in the design process, since the formation of concrete cracks depends on the possibility of exposure to various conditions(pollution, humidity,..etc.). Because of the disparity between different grades of steel in the service load stresses, this affects the cracking behavior. This paper is concerned with the crack pattern and cracking load for concrete beams with T-section reinforced with two different grades of steel at the service load levels stages up to ultimate load. A practical program has been put up to investigate the difference between reinforced steel bars with yield strength 420 N/mm2 and 500 N/mm2 through six T-section reinforced beams. The beams were tested under static- monotonic two– point service loading up to ultimate failure under flexural stresses. The influence of parameters such as clear concrete cover and concrete compressive strength are considered for each of the two grades of steel used. Cracking load, spacing and width were determined. The experimental results demonstrated that increasing the concrete strength results in both of cracking and ultimate load increase, while no significant difference in yield load for the two steel grades used. It has also become obvious, that the number of cracks was more for the lower steel strength, which is followed by decrease in crack width and spacing.

Keywords: RC beams, cracking behavior, steel stress, crack width, crack spacing

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Authors: Seung-Yeon Kim

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The Ising model, consisting magnetic spins, is the simplest system showing phase transitions and critical phenomena at finite temperatures. The Ising model has played a central role in our understanding of phase transitions and critical phenomena. Also, the Ising model explains the gas-liquid phase transitions accurately. However, the Ising model in a nonzero magnetic field has been one of the most intriguing and outstanding unsolved problems. We study analytically the partition function zeros in the complex magnetic-field plane and the Yang-Lee edge singularity of the infinite-range Ising model in an external magnetic field. In addition, we compare the Yang-Lee edge singularity of the infinite-range Ising model with that of the square-lattice Ising model in an external magnetic field.

Keywords: Ising ferromagnet, magnetic field, partition function zeros, Yang-Lee edge singularity

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Authors: A. Selmi

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Free vibration analysis of homogenous and axially functionally graded simply supported beams within the context of Euler-Bernoulli beam theory is presented in this paper. The material properties of the beams are assumed to obey the linear law distribution. The effective elastic modulus of the composite was predicted by using the rule of mixture. Here, the complexities which appear in solving differential equation of transverse vibration of composite beams which limit the analytical solution to some special cases are overcome using a relatively new approach called the Differential Transformation Method. This technique is applied for solving differential equation of transverse vibration of axially functionally graded beams. Natural frequencies and corresponding normalized mode shapes are calculated for different Young’s modulus ratios. MATLAB code is designed to solve the transformed differential equation of the beam. Comparison of the present results with the exact solutions proves the effectiveness, the accuracy, the simplicity, and computational stability of the differential transformation method. The effect of the Young’s modulus ratio on the normalized natural frequencies and mode shapes is found to be very important.

Keywords: differential transformation method, functionally graded material, mode shape, natural frequency

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Authors: Ali Al-Ghalib, Fouad Mohammad

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The identification of damage in reinforced concrete structures subjected to incremental cracking performance exploiting vibration data is recognized as a challenging topic in the published and heavily cited literature. Therefore, this paper attempts to shine light on the extent of dynamic methods when applied to reinforced concrete beams simulated with various scenarios of defects. For this purpose, three different reinforced concrete beams are tested through the course of the study. The three beams are loaded statically to failure in incremental successive load cycles and later rehabilitated. After each static load stage, the beams are tested under free-free support condition using experimental modal analysis. The beams were all of the same length and cross-sectional area (2.0x0.14x0.09)m, but they were different in concrete compressive strength and the type of damage presented. The experimental modal parameters as damage identification parameters were showed computationally expensive, time consuming and require substantial inputs and considerable expertise. Nonetheless, they were proved plausible for the condition monitoring of the current case study as well as structural changes in the course of progressive loads. It was accentuated that a satisfactory localization and quantification for structural changes (Level 2 and Level 3 of damage identification problem) can only be achieved reasonably through considering frequencies and mode shapes of a system in a proper analytical model. A convenient post analysis process for various datasets of vibration measurements for the three beams is conducted in order to extract, check and correlate the basic modal parameters; namely, natural frequency, modal damping and mode shapes. The results of the extracted modal parameters and their combination are utilized and discussed in this research as quantification parameters.

Keywords: experimental modal analysis, damage identification, structural health monitoring, reinforced concrete beam

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Authors: A. Szekrényes

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This paper revisits the free vibration problem of delaminated composite beams. It is shown that during the vibration of composite beams the delaminated parts are subjected to the parametric excitation. This can lead to the dynamic buckling during the motion of the structure. The equation of motion includes time-dependent stiffness and so it leads to a system of Mathieu-Hill differential equations. The free vibration analysis of beams is carried out in the usual way by using beam finite elements. The dynamic buckling problem is investigated locally, and the critical buckling forces are determined by the modified harmonic balance method by using an imposed time function of the motion. The stability diagrams are created, and the numerical predictions are compared to experimental results. The most important findings are the critical amplitudes at which delamination buckling takes place, the stability diagrams representing the instability of the system, and the realistic mode shape prediction in contrast with the unrealistic results of models available in the literature.

Keywords: delamination, free vibration, parametric excitation, sweep excitation

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Authors: Belal Almassri, Amjad Kreit, Firas Al Mahmoud, Raoul François

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Corrosion of steel in reinforced concrete leads to several major defects. Firstly, a reduction in the crosssectional area of the reinforcement and in its ductility results in premature bar failure. Secondly, the expansion of the corrosion products causes concrete cracking and steel–concrete bond deterioration and also affects the bending stiffness of the reinforced concrete members, causing a reduction in the overall load-bearing capacity of the reinforced concrete beams. This paper investigates the validity of a repair technique using Near Surface Mounted (NSM) carbon-fibre-reinforced polymer (CFRP) rods to restore the mechanical performance of corrosion-damaged RC beams. In the NSM technique, the CFRP rods are placed inside pre-cut grooves and are bonded to the concrete with epoxy adhesive. Experimental results were obtained on two beams: a corroded beam that had been exposed to natural corrosion for 25 years and a control beam, (both are 3 m long) repaired in bending only. Each beam was repaired with one 6-mm-diameter NSM CFRP rod. The beams were tested in a three-point bending test up to failure. Overall stiffness and crack maps were studied before and after the repair. Ultimate capacity, ductility and failure mode were also reviewed. Finally some comparisons were made between repaired and non-repaired beams in order to assess the effectiveness of the NSM technique. The experimental results showed that the NSM technique improved the overall characteristics (ultimate load capacity and stiffness) of the control and corroded beams and allowed sufficient ductility to be restored to the repaired corroded elements, thus restoring the safety margin, despite the non-classical mode of failure that occurred in the corroded beam, with the separation of the concrete cover due to corrosion products.

Keywords: carbon fibre, corrosion, strength, mechanical testing

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