Mathematics and Language

Yunus, Adanur,Oktay, Yagiz,Ahmet, Isik 한국수학교육학회 2004 수학교육연구 Vol.8 No.1

This study explores the relations between mathematics and the natural human language. At the very outset, a general definition of language was, given while it was attempted to make some comparisons between the words of natural language and mathematical symbols at that. Besides, the occupation of natural language functions within mathematics was handled. Consequently, it was tried to manifest that the language of mathematics enjoys the features of natural language as well. Mathematics makes use of many functional and structural features. The fact that fundamental ingredient of mathematics is symbols does not change this reality.

Wave-Passage Effect on the Seismic Response of Suspension Bridges Considering Local Soil Conditions

Süleyman Adanur,Ahmet Can Altunışık,Hasan Basri Başağa,Kurtuluş Soyluk,A. Aydın Dumanoğlu 한국강구조학회 2017 International Journal of Steel Structures Vol.17 No.2

In this study, a comprehensive investigation of the stochastic analysis of a suspension bridge subjected to spatially varying ground motions is carried out for variable local soil cases and wave velocities. Bosphorus Suspension Bridge built in Turkey and connects Europe to Asia in Istanbul is selected as a numerical example. The spatial variability of the ground motion is considered with the incoherence, wave-passage and site-response effects. The incoherence effect is examined by taking into account Harichandran and Vanmarcke model, the site-response effect is outlined by using firm, medium and soft soil types, and the wave-passage effect is investigated by using 1000-2000, 500-1000, and 300-500 m/s wave velocities for the firm, medium and soft soils, respectively. Mean of maximum response values obtained from the spatially varying ground motions are compared with those of the specialized cases of the ground motion model. At the end of the study, it is seen that total displacements are dominated by dynamic component. The response values obtained for SMFF soil condition are generally the largest. When the varying local soil condition is considered, the variation of relative contributions of response components to the total response values for varying wave velocity cases is insignificant. Also, the variation of the wave velocity has important effect on the deck and towers total response values as compared with those of the constantly travelling wave velocity case. It is concluded that the site-response effect of ground motion on the response of suspension bridges is more important than that of the wave-passage, and the variation of the wave velocities depending on the local soil conditions, has important effects on the dynamic behavior of suspension bridge.

Construction stage analysis of fatih sultan mehmet suspension bridge

Gunaydin, Murat,Adanur, Suleyman,Altunisik, Ahmet Can,Sevim, Baris Techno-Press 2012 Structural Engineering and Mechanics, An Int'l Jou Vol.42 No.4

In this study, it is aim to perform the construction stage analysis of suspension bridges using time dependent material properties. Fatih Sultan Mehmet Suspension Bridge connecting the Europe and Asia in Istanbul is selected as an example. Finite element models of the bridge are modelled using SAP2000 program considering project drawing. Geometric nonlinearities are taken into consideration in the analysis using P-Delta large displacement criterion. The time dependent material strength variations and geometric variations are included in the analysis. Because of the fact that the bridge has steel structural system, only prestressing steel relaxation is considered as time dependent material properties. The structural behaviour of the bridge at different construction stages has been examined. Two different finite element analyses with and without construction stages are carried out and results are compared with each other. As analyses result, variation of the displacement and internal forces such as bending moment, axial forces and shear forces for bridge deck and towers are given with detail. It is seen that construction stage analysis has remarkable effect on the structural behaviour of the bridge.

Construction stage analysis of fatih sultan mehmet suspension bridge

Murat Günaydin,Süleyman Adanur,Ahmet Can Altunisik,Baris Sevim 국제구조공학회 2012 Structural Engineering and Mechanics, An Int'l Jou Vol.42 No.4

In this study, it is aim to perform the construction stage analysis of suspension bridges using time dependent material properties. Fatih Sultan Mehmet Suspension Bridge connecting the Europe and Asia in Istanbul is selected as an example. Finite element models of the bridge are modelled using SAP2000 program considering project drawing. Geometric nonlinearities are taken into consideration in the analysis using P-Delta large displacement criterion. The time dependent material strength variations and geometric variations are included in the analysis. Because of the fact that the bridge has steel structural system, only prestressing steel relaxation is considered as time dependent material properties. The structural behaviour of the bridge at different construction stages has been examined. Two different finite element analyses with and without construction stages are carried out and results are compared with each other. As analyses result, variation of the displacement and internal forces such as bending moment, axial forces and shear forces for bridge deck and towers are given with detail. It is seen that construction stage analysis has remarkable effect on the structural behaviour of the bridge.

Determination of structural behavior of Bosporus suspension bridge considering construction stages and different soil conditions

Murat Günaydin,Süleyman Adanur,Ahmet Can Altunişik,Barış Sevım,Emel Türker 국제구조공학회 2014 Steel and Composite Structures, An International J Vol.17 No.4

In this paper, it is aimed to determine the structural behavior of suspension bridges considering construction stages and different soil conditions. Bosporus Suspension Bridge connecting the Europe and Asia in Istanbul is selected as an example. Finite element model of the bridge is constituted using SAP2000 program considering existing drawings. Geometric nonlinearities are taken into consideration in the analysis using P-Delta large displacement criterion. The time dependent material strength of steel and concrete and geometric variations is included in the analysis. Time dependent material properties are considered as compressive strength, aging, shrinkage and creep for concrete, and relaxation for steel. To emphases the soil condition effect on the structural behavior of suspension bridges, each of hard, medium and soft soils are considered in the analysis. The structural behavior of the bridge at different construction stages and different soil conditions has been examined. Two different finite element analyses with and without construction stages are carried out and results are compared with each other. At the end of the analyses, variation of the displacement and internal forces such as bending moment, axial forces and shear forces for bridge deck and towers are given in detail. Also, displacement and stresses for bridge foundation are given with detail. It can be seen from the analyses that there are some differences between both analyses (with and without construction stages) and the results obtained from the construction stages are bigger. It can be stated that the analysis without construction stages cannot give the reliable solutions. In addition, soil condition have effect on the structural behavior of the bridge. So, it is thought that construction stage analysis using time dependent material properties, geometric nonlinearity and soil conditions effects should be considered in order to obtain more realistic structural behavior of suspension bridges.

Comparison of uniform and spatially varying ground motion effects on the stochastic response of fluid-structure interaction systems

Bilici, Yasemin,Bayraktar, Alemdar,Adanur, Suleyman Techno-Press 2009 Structural Engineering and Mechanics, An Int'l Jou Vol.33 No.4

The effects of the uniform and spatially varying ground motions on the stochastic response of fluid-structure interaction system during an earthquake are investigated by using the displacement based fluid finite elements in this paper. For this purpose, variable-number-nodes two-dimensional fluid finite elements based on the Lagrangian approach is programmed in FORTRAN language and incorporated into a general-purpose computer program SVEM, which is used for stochastic dynamic analysis of solid systems under spatially varying earthquake ground motion. The spatially varying earthquake ground motion model includes wave-passage, incoherence and site-response effects. The effect of the wave-passage is considered by using various wave velocities. The incoherence effect is examined by considering the Harichandran-Vanmarcke and Luco-Wong coherency models. Homogeneous medium and firm soil types are selected for considering the site-response effect where the foundation supports are constructed. A concrete gravity dam is selected for numerical example. The S16E component recorded at Pacoima dam during the San Fernando Earthquake in 1971 is used as a ground motion. Three different analysis cases are considered for spatially varying ground motion. Displacements, stresses and hydrodynamic pressures occurring on the upstream face of the dam are calculated for each case and compare with those of uniform ground motion. It is concluded that spatially varying earthquake ground motions have important effects on the stochastic response of fluid-structure interaction systems.

Stochastic response of suspension bridges for various spatial variability models

Ahmet C. Altunışık,Süleyman Adanur,Kurtuluş Soyluk,A. Aydın Dumanoğlu 국제구조공학회 2016 Steel and Composite Structures, An International J Vol.22 No.5

The purpose of this paper is to compare the structural responses obtained from the stochastic analysis of a suspension bridge subjected to uniform and partially correlated seismic ground motions, using different spatial correlation functions commonly used in the earthquake engineering. The spatial correlation function employed in this study consists of a term that characterizes the loss of coherency. To account for the spatial variability of ground motions, the widely used four loss of coherency models in the literature has been taken into account in this study. Because each of these models has its own characteristics, it is intended to determine the sensitivity of a suspension bridge due to these losses of coherency models which represent the spatial variability of ground motions. Bosporus Suspension Bridge connects Europe to Asia in Istanbul is selected as a numerical example. The bridge has steel towers that are flexible, inclined hangers and a steel box-deck of 1074 m main span, with side spans of 231 and 255 m on the European and Asian sides, respectively. For the ground motion the filtered white noise model is considered and applied in the vertical direction, the intensity parameter of this model is obtained by using the S16E component of Pacoima Dam record of 1971 San Fernando earthquake. An analytically simple model called as filtered white noise ground motion model is chosen to represent the earthquake ground motion. When compared with the uniform ground motion case, the results obtained from the spatial variability models with partial correlation outline the necessity to include the spatial variability of ground motions in the stochastic dynamic analysis of suspension bridges. It is observed that while the largest response values are obtained for the model proposed by Harichandran and Vanmarcke, the model proposed by Uscinski produces the smallest responses among the considered partially correlated ground motion models. The response values obtained from the uniform ground motion case are usually smaller than those of the responses obtained from the partially correlated ground motion cases. While the response values at the flexible parts of the bridge are totally dominated by the dynamic component, the pseudo-static component also has significant contributions for the response values at the rigid parts of the bridge. The results also show the consistency of the spatial variability models, which have different characteristics, considered in this study.

Static and dynamic responses of Halgavor Footbridge using steel and FRP materials

M. Gunaydin,S. Adanur,A.C. Altunisik,B. Sevim 국제구조공학회 2015 Steel and Composite Structures, An International J Vol.18 No.1

In recent years, the use of fiber reinforced polymer composites has increased because of their unique features. They have been used widely in the aircraft and space industries, medical and sporting goods and automotive industries. Thanks to their beneficial and various advantages over traditional materials such as high strength, high rigidity, low weight, corrosion resistance, low maintenance cost, aesthetic appearance and easy demountable or moveable construction. In this paper, it is aimed to determine and compare the geometrically nonlinear static and dynamic analysis results of footbridges using steel and glass fiber reinforced polymer composite (GFRP) materials. For this purpose, Halgavor suspension footbridge is selected as numerical examples. The analyses are performed using three identical footbridges, first constructed from steel, second built only with GFRP material and third made of steel- GFRP material, under static and dynamic loadings using finite element method. In the finite element modeling and analyses, SAP2000 program is used. Geometric nonlinearities are taken into consideration in the analysis using P-Delta criterion. The numerical results have indicated that the responses of the three bridges are different and that the response values obtained for the GFRP composite bridge are quite less compared to the steel bridge. It is understood that GFRP material is more useful than the steel for the footbridges.

Perturbation Based Stochastic Finite Element Analysis of the Structural Systems with Composite Sections under Earthquake Forces

Özlem Çavdar,Alemdar Bayraktar,Ahmet Çavdar,Süleyman Adanur 국제구조공학회 2008 Steel and Composite Structures, An International J Vol.8 No.2

This paper demonstrates an application of the perturbation based stochastic finite element method (SFEM) for predicting the performance of structural systems made of composite sections with random material properties. The composite member consists of materials in contact each of which can surround a finite number of inclusions. The perturbation based stochastic finite element analysis can provide probabilistic behavior of a structure, only the first two moments of random variables need to be known, and should therefore be suitable as an alternative to Monte Carlo simulation (MCS) for realizing structural analysis. A summary of stiffness matrix formulation of composite systems and perturbation based stochastic finite element dynamic analysis formulation of structural systems made of composite sections is given. Two numerical examples are presented to illustrate the method. During stochastic analysis, displacements and sectional forces of composite systems are obtained from perturbation and Monte Carlo methods by changing elastic modulus as random variable. The results imply that perturbation based SFEM method gives close results to MCS method and it can be used instead of MCS method, especially, if computational cost is taken into consideration.

Experimental Study of the Effect of Different Insulation Schemes on Fire Performance of FRP Strengthened Concrete: FIRECOAT and REALROCK

Ahmet Can Altunişik,Yunus Emrahan Akbulut,Süleyman Adanur,Murat Günaydin,Sara Mostofi,Ayman Mosallam 한국콘크리트학회 2024 International Journal of Concrete Structures and M Vol.18 No.1

The past two decades have witnessed rapid advances in the use of fiber-reinforced polymer (FRP) composites in different engineering fields. Advantages such as high strength-to-weight ratio, corrosion resistance, and tailority have led to immense interest in the use of FRPs in wide spectrum repair and strengthening of structures. Despite their many advantages, FRPs are highly sensitive to high temperatures, which pose a major concern for fire potential structures such as buildings. Applying proper thermal insulation can enhance the fire performance of FRP and reduce the possible fire damage to the FRP strengthened element. This study set out to experimentally investigate the effectiveness of two insulation systems, “FIRECOAT” and “REALROCK” on fire performance of CFRP and GFRP strengthened concrete specimens. Various configurations and exposure durations were considered to evaluate the effectiveness of insulating materials. To perform the experiments, cylindrical concrete specimens were fabricated and strengthened using CFRP or GFRP. After insulating the specimens, they were exposed to a standard fire curve for two different durations of 30 and 60 min. The results indicate that less than 30 min of fire, both insulation systems can provide the required protection. During long exposure duration of 60 min, only REALROCK can provide the required thermal resistance for FRP-strengthened concrete. Within the tested materials, Fire Set 60 outperformed other insulating materials. It was observed that implementing Fire Set 60 in the innermost layer of thermal insulations has crucial importance in preventing the fire induced reductions in strength of FRP-strengthened concrete elements.