• Steel and Composite Structures
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• v.24 no.1
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• pp.65-77
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• 2017

The purpose of this research is to study the nonlinear free vibration and post-buckling analysis of functionally graded carbon nanotube reinforced composite (FG-CNTRC) beams resting on a nonlinear elastic foundation. Uniformly and functionally graded distributions of single walled carbon nanotubes as reinforcing phase are considered in the polymeric matrix. The modified form of rule of mixture is used to estimate the material properties of CNTRC beams. The governing equations are derived employing Euler-Bernoulli beam theory along with energy method and Hamilton's principle. Applying von $K\acute{a}rm\acute{a}n's$ strain-displacement assumptions, the geometric nonlinearity is taken into consideration. The developed governing equations with quadratic and cubic nonlinearities are solved using variational iteration method (VIM) and the analytical expressions and numerical results are obtained for vibration and stability analysis of nanocomposite beams. The presented comparative results are indicative for the reliability, accuracy and fast convergence rate of the solution. Eventually, the effects of different parameters, such as foundation stiffness, volume fraction and distributions of carbon nanotubes, slenderness ratio, vibration amplitude, coefficients of elastic foundation and boundary conditions on the nonlinear frequencies, vibration response and post-buckling loads of FG-CNTRC beams are examined. The developed analytical solution provides direct insight into parametric studies of particular parameters of the problem.

• Steel and Composite Structures
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• v.42 no.5
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• pp.685-697
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• 2022

In this paper, a vibration-based method using the change ratios of modal data and the experience-based learning algorithm is presented for quantifying the position, size, and interface layer of delamination in laminated composites. Three types of objective functions are examined and compared, including the ones using frequency changes only, mode shape changes only, and their combination. A fine three-dimensional FE model with constraint equations is utilized to extract modal data. A series of numerical experiments is carried out on an eight-layer quasi-isotropic symmetric (0/-45/45/90)s composited beam for investigating the influence of the objective function, the number of modal data, the noise level, and the optimization algorithms. Numerical results confirm that the frequency-and-mode-shape-changes-based technique yields excellent results in all the three delamination variables of the composites and the addition of mode shape information greatly improves the accuracy of interface layer prediction. Moreover, the EBL outperforms the other three state-of-the-art optimization algorithms for vibration-based delamination detection of composites. A laboratory test on six CFRP beams validates the frequency-and-mode-shape-changes-based technique and confirms again its superiority for delamination detection of composites.

• Steel and Composite Structures
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• v.50 no.6
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• pp.689-703
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• 2024

Construction of high-rise structures, formwork systems that can be installed quickly, resistant to external loads, can be used more than once, have become a necessity. Timber and composite timber materials are preferred in the formation of such formwork systems due to their durability, ease of assembly, light weight and easy to use more than one time. Formwork beams are the most commonly used structural component in the formation of such formwork systems, and these beams can be damaged for different reasons during their lifetime. In this study, H20 top P type timber formwork beams with 1800 and 2450 mm length which is among the products of DOKA(c) company is damaged under the effect of static loading up to a high load level of 85% of the maximum ultimate capacity and after being retrofitted using anchored CFRP strips, performance and behavior of the beams under the influence of various loading types such as static, fatigue and impact are investigated experimentally. Two different lengths of retrofitted timber formwork beams were tested by applying monotonic static, fatigue and impact loading and comments were made about the effects of the retrofit method on performance under different loading types.

• Composites Research
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• v.13 no.1
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• pp.89-97
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• 2000

Fatigue damage detection and vibration sensing for a laminated composites and impact location detection for a steel beam have been carried out using optical fiber sensor. Intensity based optical fiber sensor is constructed by placing two cleaved fiber end in a hollow glass tube, and multiple reflection within the cavity is considered. Fatigue signals are measured by embedded optical fiber, surface mounted optical fiber sensor and strain gage simultaneously. For vibration sensing, optical fiber sensor is mounted on the carbon fiber composite beam and its response to free vibration and forced vibration is investigated. In impact location detection, two optical fiber sensors are used and the information obtained from two sensors is arrival time delay of vibration caused by impact. Impact location can be calculated from this time delay. The obtained results show that the intensity based optical fiber sensor provide reliable data during long-term fatigue loading, unlike strain gage which deteriorate during the early part of the fatigue test. Optical fiber sensor signals coincide with gap sensor in vibration sensing. The precise locations of impact can be detected within 4.1% error limit.

• Steel and Composite Structures
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• v.21 no.2
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• pp.411-427
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• 2016

While the cyclic behaviour of fiber-reinforced polymer (FRP)-confined columns is studied rather extensively, the cyclic response especially the energy dissipation of FRP-confined damaged and undamaged square RC columns is not yet fully understood. In this paper, an experimental and numerical investigation was conducted to study the cyclic behavior of two different types of Carbon FRP (CFRP)-confined square RC columns: strengthened and repaired. The main variables investigated are initial damage, confinement of CFRP, longitudinal steel reinforcement ratio. The experimental results show that lower initial damage, added confinement with CFRP and longitudinal reinforcement enhance the ductility, energy dissipation capacity and strength of the columns, decrease the stiffness and strength degradation rates of all CFRP-confined square RC columns. Two hysteretic constitutive models were developed for confined damaged and undamaged concrete and cast into the non-linear beam-column fiber-based models in the software Open System for Earthquake Engineering Simulation (OpenSees) to analyze the cyclic behavior of CFRP-confined damaged and undamaged columns. The results of the numerical models are in good agreement with the experiments.

• Steel and Composite Structures
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• v.26 no.3
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• pp.347-360
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• 2018

The aim of this paper is to evaluate the accuracy and reliability of the available bond-slip laws which are being used for the numerical modeling of Fiber Reinforced Polymer (FRP)/concrete interfaces. For this purpose, a set of Reinforced Concrete (RC) beams retrofitted with external FRP were modeled using the 3D nonlinear Finite Element (FE) approach. All considered RC beams have been previously tested and the corresponding experimental data are available in the literature. The failure modes of these beams are concrete crushing, steel yielding and FRP debonding. Through comparison of the numerical and experimental results, the effectiveness of each FRP/concrete bond-slip model for the prediction of the structural behavior of externally retrofitted RC beams is assessed. The sensitivity of the numerical results against different modeling considerations of the concrete constitutive behavior and bond-slip laws has also been evaluated. The results show that the maximum allowable stress of FRP/concrete interface has an important role in the accurate prediction of the FRP debonding failure.

• Structural Engineering and Mechanics
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• v.5 no.6
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• pp.803-815
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• 1997

It is well understood that concentrated forces applied in the plane of a beam or panel (such as a wall or slab) lead to splitting forces developing within a disturbed region forming beyond the bearing zone. In a linearly elastic material the length of the disturbed region is approximately equal to the depth of the member. In concrete structures, however, the length of the disturbed region is a function of the orthotropic properties of the concrete-steel composite. In the detailing of steel reinforcement within the disturbed regions two limit states must be satisfied; strength and serviceability (in this case the serviceability requirement being acceptable crack widths). If the design requires large redistribution of stresses, the member may perform poorly at service and/or overload. In this paper the results of a plane stress finite element investigation of concentrated loads on reinforced concrete panels are presented. Two cases are examined (i) panels loaded concentrically, and (ii) panels loaded eccentrically. The numerical investigation suggests that the bursting force distribution is substantially different from that calculated using elastic design methods currently used in some codes of practice. The optimum solution for a uniformly reinforced bursting region was found to be with the reinforcement distributed from approximately 0.2 times the effective depth of the member ($0.2D_e$) to between $1.2D_e$ and $1.6D_e$. Strut and tie models based on the finite element analyses are proposed herein.

• Steel and Composite Structures
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• v.49 no.2
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• pp.245-255
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• 2023

The present paper summarizes the results of an experimental program on the influence of using waste lathe scraps in the concrete mixture on the shear behavior of RC beams with different amounts of shear reinforcement. Three different volumetric ratios (1, 2 and %3) for the scraps and three different stirrup spacings (160, 200 and 270 mm) were adopted in the tests. The shear span-to-depth ratios of the beams were 2.67 and the stirrup spacing exceeded the maximum spacing limit in the building codes to unfold the contribution of lathe scraps to the shear resistances of shear-deficient beams, subject to shear-dominated failure (shear-tension). The experiments depicted that the lathe scraps have a pronounced contribution to the shear strength and load-deflection behavior of RC beams with widely-spaced stirrups. Namely, with the addition of 1%, 2% and 3% waste lathe scraps, the load-bearing capacity escalated by 9.1%, 21.8% and 32.8%, respectively, compared to the reference beam. On the other hand, the contribution of the lathe scraps to the load capacity decreases with decreasing stirrup spacing, since the closely-spaced stirrups bear the shear stresses and render the contribution of the scraps to shear resistance insignificant. The load capacity, deformation ductility index (DDI) and modulus of toughness (MOT) values of the beams were shown to increase with the volumetric fraction of scraps if the stirrups are spaced at about two times the beam depth. For the specimens with a stirrup spacing of about the beam depth, the scraps were found to have no considerable contribution to the load capacity and the deformation capacity beyond the ultimate load. In other words, for lathe scrap contents of 1-3%, the DDI values increased by 5-23% and the MOT values by 63.5-165% with respect to the reference beam with a stirrup spacing of 270 mm. The influence of the lathe scraps to the DDI and MOT values were rather limited and even sometimes negative for the stirrup spacing values of 160 and 200 mm.

• Steel and Composite Structures
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• v.28 no.5
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• pp.589-606
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• 2018

The previous studies reflected the significant effect of neutral-axis position and coupling of in-plane and out-of-plane displacements on behavior of functionally graded (FG) nanobeams. In thin FG beam, this coupling can be eliminated by a proper choice of the reference axis. In shear deformable FG nanobeam, not only this coupling can't be eliminated but also the position of neutral-axis is dependent on through-thickness distribution of shear strain. For the first time, in this paper it is avoided to guess a shear strain shape function and the exact shape function and consequently the exact position of neutral axis for arbitrary gradation of higher order nanobeam are obtained. This paper presents new methodology based on differential transform and collocation methods to solve coupled partial differential equations of motion without any simplifications. Using exact position of neutral axis and higher order beam kinematics as well as satisfying equilibrium equations and traction-free conditions without shear correction factor requirement yields to better results in comparison to the previously published results in literature. The classical rule of mixture and Mori-Tanaka homogenization scheme are considered. The Eringen's nonlocal continuum theory is applied to capture the small scale effects. For the first time, the dependency of exact position of neutral axis on length to thickness ratio is investigated. The effects of small scale, length to thickness ratio, Poisson's ratio, inhomogeneity of materials and various end conditions on vibration and buckling of local and nonlocal FG beams are investigated. Moreover, the effect of axial load on natural frequencies of the first modes is examined. After degeneration of the governing equations, the exact new formulas for homogeneous nanobeams are computed.

• Steel and Composite Structures
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• v.49 no.5
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• pp.487-502
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• 2023

In the realm of nanotechnology, the nonlocal strain gradient theory takes center stage as it scrutinizes the behavior of spinning cantilever nanobeams and nanotubes, pivotal components supporting various mechanical movements in sport structures. The dynamics of these structures have sparked debates within the scientific community, with some contending that nonlocal cantilever models fail to predict dynamic softening, while others propose that they can indeed exhibit stiffness softening characteristics. To address these disparities, this paper investigates the dynamic response of a nonlocal cantilever cylindrical beam under the influence of external discontinuous dynamic loads. The study employs four distinct models: the Euler-Bernoulli beam model, Timoshenko beam model, higher-order beam model, and a novel higher-order tube model. These models account for the effects of functionally graded materials (FGMs) in the radial tube direction, giving rise to nanotubes with varying properties. The Hamilton principle is employed to formulate the governing differential equations and precise boundary conditions. These equations are subsequently solved using the generalized differential quadrature element technique (GDQEM). This research not only advances our understanding of the dynamic behavior of nanotubes but also reveals the intriguing phenomena of both hardening and softening in the nonlocal parameter within cantilever nanostructures. Moreover, the findings hold promise for practical applications, including drug delivery, where the controlled vibrations of nanotubes can enhance the precision and efficiency of medication transport within the human body. By exploring the multifaceted characteristics of nanotubes, this study not only contributes to the design and manufacturing of rotating nanostructures but also offers insights into their potential role in revolutionizing drug delivery systems.