• Structural Engineering and Mechanics
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• v.72 no.4
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• pp.433-441
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• 2019

In this paper, geometrically nonlinear static analysis of laminated composite beams is investigated under hygrothermal effect. In the solution of problem, the finite element method is used within the first shear beam theory. Total Lagrangian approach is used nonlinear kinematic model. The geometrically nonlinear formulations are developed for the laminated beams with hygro-thermal effects. In the nonlinear solution of the problem, the Newton-Raphson method is used with incremental displacement. In order to verify of obtained formulations, a comparison study is performed. The effects of the fiber orientation angles, the stacking sequence of laminates, temperature rising and moisture changes on the nonlinear static displacements and configurations of the composite laminated beam are investigated in the numerical results.

• Smart Structures and Systems
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• v.21 no.4
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• pp.493-519
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• 2018

This article presents a finite element (FE) model to assess the free vibration and static response of a functionally graded skew magneto-electro-elastic (FGSMEE) plate. Through the thickness material grading of FGSMEE plate is achieved using power law distribution. The coupled constitutive equations along with the total potential energy approach are used to develop the FE model of FGSMEE plate. The transformation matrix is utilized in bringing out the element matrix corresponding to the global axis to a local axis along the skew edges to specify proper boundary conditions. The effect of skew angle on the natural frequency of an FGSMEE plate is analysed. Further, the study includes the evaluation of the static behavior of FGSMEE plate for various skew angles. The influence of skew angle on the primary quantities such as displacements, electric potential, and magnetic potential, and secondary quantities such as stresses, electric displacement and magnetic induction is studied in detail. In addition, the effect of power-law gradient, thickness ratio, boundary conditions and aspect ratio on the free vibration and static response characteristics of FGSMEE plate has been investigated.

• Journal of Navigation and Port Research
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• v.27 no.5
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• pp.519-526
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• 2003

For preliminary structural analysis of superstructures on very large floating structures(VLFS), superstructures are analyzed considering elastic deformations of barge type lower-structures subjected to wave loads. In this case, to consider the effect of wave loads on the superstructure, initial displacements at the support points of superstructures are evaluated as input data for the analysis. However, the evaluation and application of displacement loads are tedious and very time-consuming processes. Therefore, this paper proposes a simplified static analysis method to analyze the structural behaviors of superstructures on very large floating structures subjected to wave loads. In this study, the member forces due to the variation of beam span and the amplitude and period of wave load are analyzed by using an example 4 span -3 story structure and the amplification factors for beam moments are represented by the specific regression equation.

• Structural Engineering and Mechanics
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• v.35 no.6
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• pp.677-697
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• 2010

This paper focuses on geometrically non-linear static analysis of a simply supported beam made of hyperelastic material subjected to a non-follower transversal uniformly distributed load. As it is known, the line of action of follower forces is affected by the deformation of the elastic system on which they act and therefore such forces are non-conservative. The material of the beam is assumed as isotropic and hyperelastic. Two types of simply supported beams are considered which have the following boundary conditions: 1) There is a pin at left end and a roller at right end of the beam (pinned-rolled beam). 2) Both ends of the beam are supported by pins (pinned-pinned beam). In this study, finite element model of the beam is constructed by using total Lagrangian finite element model of two dimensional continuum for a twelve-node quadratic element. The considered highly non-linear problem is solved by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. In order to use the solution procedures of Newton-Raphson type, there is need to linearized equilibrium equations, which can be achieved through the linearization of the principle of virtual work in its continuum form. In the study, the effect of the large deflections and rotations on the displacements and the normal stress and the shear stress distributions through the thickness of the beam is investigated in detail. It is known that in the failure analysis, the most important quantities are the principal normal stresses and the maximum shear stress. Therefore these stresses are investigated in detail. The convergence studies are performed for various numbers of finite elements. The effects of the geometric non-linearity and pinned-pinned and pinned-rolled support conditions on the displacements and on the stresses are investigated. By using a twelve-node quadratic element, the free boundary conditions are satisfied and very good stress diagrams are obtained. Also, some of the results of the total Lagrangian finite element model of two dimensional continuum for a twelve-node quadratic element are compared with the results of SAP2000 packet program. Numerical results show that geometrical nonlinearity plays very important role in the static responses of the beam.

• Geomechanics and Engineering
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• v.18 no.2
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• pp.141-151
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• 2019

In this paper, it is aimed to present a detail investigation about the comparison of static and dynamic behavior of historical masonry arch bridges considering different arch curvature. $G{\ddot{o}}derni$ historical masonry two-span arch bridge which is located in Kulp town, Diyarbakir, Turkey is selected as a numerical application. The bridge takes part in bowless bridge group and built in large measures than the others. The restoration projects were approved and rehabilitation studies have still continued. Finite element model of the bridge is constituted with special software to determine the static and dynamic behavior. To demonstrate the arch curvature effect, the finite element model are reconstructed considering different arch curvature between 2.86 m-3.76 m for first arch and 2.64 m-3.54 m for second arch with the increment of 0.10 m, respectively. Dead and live vehicle loads are taken into account during static analyses. 1999 Kocaeli earthquake ground motion record is considered for time history analyses. The maximum displacements, principal stresses and elastic strains are compared with each other using contour diagrams. It is seen that the arch curvature has more influence on the structural response of historical masonry arch bridges. At the end of the study, it is seen that with the increasing of the arch heights, the maximum displacements, minimum principal stresses and minimum elastic strains have a decreasing trend in all analyses, in addition maximum principal stresses and maximum elastic strains have unchanging trend up to optimum geometry.

• Earthquakes and Structures
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• v.8 no.2
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• pp.443-462
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• 2015

Some model building codes stipulate that the design displacement of a building can be computed using the elastic static analysis results multiplied by the deflection amplification factor, $C_d$. This approach for estimating the design displacement is essential and appealing in structural engineering practice when nonlinear response history analysis (NRHA) is not required. Furthermore, building codes stipulate the consideration of accidental torsion effects using accidental eccentricity, whether the buildings are symmetric-plan, or asymmetric-plan. In some model building codes, the accidental eccentricity is further amplified by the torsional amplification factor $A_x$ in order to minimize the discrepancy between statically and dynamically estimated responses. Therefore, this warrants exploration of the reliability of statically estimated design displacements in accordance with the building code requirements. This study uses the discrepancy curves as a way of assessing the reliability of the design displacement estimates resulting from the factors $C_d$ and $A_x$. The discrepancy curves show the exceedance probabilities of the differences between the statically estimated design displacements and NRHA results. The discrepancy curves of 3-story, 9-story, and 20-story example buildings are investigated in this study. The example buildings are steel special moment frames with frequency ratios equal to 0.7, 1.0, 1.3, and 1.6, as well as existing eccentricity ratios ranging from 0% to 30%.

• Smart Structures and Systems
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• v.5 no.4
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• pp.495-505
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• 2009

Bridges form crucial links in the transportation network especially in high seismic risk regions. This research aims to provide a quantitative methodology for post-earthquake performance evaluation of the bridges. The experimental portion of the research involved shake table tests of a 4-span bridge which was subjected to progressively increasing amplitudes of seismic motions recorded from the Northridge earthquake. As part of this project, a high resolution long gauge fiber optic displacement sensor was developed for post-seismic evaluation of damage in the columns of the bridge. The nonlinear finite element model was developed using Opensees program to simulate the response of the bridge and the abutments to the seismic loads. The model was modified to predict the bent displacements of the bridge commensurate with the measured bent displacements obtained from experimental analysis results. Following seismic events, the tangential stiffness matrix of the whole structure is reduced due to reduction in structural strength. The nonlinear static push over analysis using current damaged stiffness matrix provides the longitudinal and transverse ultimate capacities of the bridge. Capacity loss in the transverse and longitudinal directions following the seismic events was correlated to the maximum displacements of the deck recorded during the events.

• Structural Engineering and Mechanics
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• v.17 no.5
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• pp.641-654
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• 2004

This paper presents a theoretic model of a smart structure, a transversely isotropic piezoelectric thick square plate constructed with three laminas, piezoelectric-elastic-piezoelectric layer, by adopting the first order shear deformation plate theory and piezoelectric theory. This model assumes that the transverse displacements through thickness are linear, and the in-plane displacements in the mid-plane of the plate are not taken to be account. By using Fourier's series expansion, an exact Navier typed analytical solution for deflection and electric potential of the simply supported smart plate is obtained. The electric boundary conditions are being grounded along four vertical edges. The external voltage and non-external voltage applied on the surfaces of piezoelectric layers are all considered. The convergence of the present approach is carefully studied. Comparison studies are also made for verifying the accuracy and the applicability of the present method. Then some new results of the electric potentials and displacements are provided. Numerical results show that the electrostatic voltage is approximately linear in the thickness direction, while parabolic in the plate in-plane directions, for both the deflection and the electric voltage. These results are very useful for distributed sensing and finite element verification.

• Proceedings of the Korea Concrete Institute Conference
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• 2004.05a
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• pp.60-63
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• 2004

The paper deals with the damage assessment of the concrete beam using static displacements and the flexural stiffness reduction of the beam was evaluated. Simply supported concrete beams were loaded at the mid-span, and the applied load level ranged $20\%,\;40\%,\;80\%$ of the flexural strength of the beam. When the displacements from the tests were increased more than $10\%$ of the initial values, flexural cracks occured. Judging from the observed cracks, damaged area of the beams were assumed and the stiffness reduction using the smeared-cracking concept was estimated to minimize the error between the test results and analytical results. Four stages of the behavior of a RC beam, which are uncracked, initial cracking, stabilized cracking and post-yielding, can be considered to assess the damage of RC beams. Main parameters for the assessment were cracking area and the stiffness reduction ratio. In each stage, damaged elements and their stiffness reduction were estimated to minimized the error.

• International Journal of Safety
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• v.9 no.2
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• pp.16-21
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• 2010

In this study, the variations of transformed impact factors and load carrying capacity of highway bridges measured from the state of expansion joint are evaluated. the field loading tests were performed on the highway bridge with damaged expansion joint to investigate the variation of the load carrying capacity. From the field loading tests in case that damaged expansion joint exist or do not exist, the static displacements and dynamic displacements were measured, and TIF were calculated, respectively. dynamic test is performed in order to estimate dynamic displacement and TIF according to the level of damage of expansion joint. From the results of TIF, the load carrying capacity of highway bridges with damaged expansion joint were estimated.