Üstyapı zemin ortak sisteminin dinamik etkileşim problemi
Başlık çevirisi mevcut değil.
- Tez No: 75187
- Danışmanlar: DOÇ. DR. NECMETTİN GÜNDÜZ
- Tez Türü: Yüksek Lisans
- Konular: İnşaat Mühendisliği, Civil Engineering
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 1998
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Yapı Ana Bilim Dalı
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: 85
Özet
Bu çalışmada, üstyapı ile zeminden oluşan ortak sistemin deprem hesabı için bazı matematik modellerin üzerinde durulmuştur. Bu modellerin çerçevesinde üstyapı ile zemin arasındaki karşılıklı dinamik etki olayı incelenmiştir. Çalışma altı bölümden oluşmaktadır. Birinci bölümde konunun tanımı yapılmakta, üstyapı ile zeminden oluşan ortak sistemin deprem hesabı için yapılan çalışmalar iki grup halinde incelenerek özetlenmiştir. ikinci bölümde, üstyapı-zemin ortak sisteminin dinamik analizi için çeşitli yöntemlere ait kısa açıklamalara yer verilmiştir. Bu bölümde, ayrıca ortak sistemin idealleştirilmesi için kullanılan modeller eleştirilmiş, geliştirilen modellerin özellikleri ve problemin çözümünde sağladığı olanaklar açıklanmıştır. Üçüncü bölümde, zeminin homojen ve lineer elastik olması durumunda deprem etkisi altında ortak sistemin dinamik hareket denklemlerine yer verilmiştir. Dinamik hareket denklemlerinin elde edilmesi maksadı ile alt sistemlere ayırma metodundan (Substructure Method) yararlanılmış olup, böylece yöntemin esası hakkında genel bir fikir verilmeye çalışılmıştır. Dördüncü bölümde, üstyapı ile zemin arasındaki dinamik etkileşimi ifade eden empedans (etkileşim) fonksiyonlarına bağlı olarak ortak sistemin deprem hesabı açıklanmıştır. Bu fonksiyonların boyutsuz frekans değerine bağlı olmasından dolayı ortak sisteme ait dinamik denge denklemlerinin frekans alanındaki ifadelerine yer verilmiştir. Beşinci bölümde, sekiz katlı bir betonarme çerçeve ve zeminden oluşan ortak sistemin dinamik davranışı SAP90 programı incelenmiştir. Bu amaç ile, zeminde kayma dalgası hızına bağlı olarak, birim genlikli harmonik yer ivmesi etkisi altındaki ortak sistemin üstyapıya ait zemin kat kolonu uç kuvvetlerinin (kesme kuvveti ve eğilme momenti) ve en üst katın yatay yer değiştirmesinin 0-100 rad/s'lik frekans bölgesinde frekansa bağlı değişimi elde edilmiş, eğriler ile gösterilmiştir. Altıncı bölümde, bu çalışmada elde edilen genel sonuçlar açıklanmıştır.
Özet (Çeviri)
This work deals with the analysis of earthquake response of structures including soil structure interaction. In recent years, many important structures such as tall buildings, dams, nuclear power plants etc., have been constructed in seismic zones on weak or strong soil conditions. It is evident that, in the earthquake response analysis of such structures, the characteristics of the soil medium have to be considered in addition to the dynamic characteristics of the superstructures. It is evident that the soil conditions affect the seismic waves transmitted through the soil medium from the structure. Soil effect, which is independent of existing structure, causes in response an opposite effect, due to the transmission of the stress waves from the vibrating structure into the soil. This dynamic interactive behaviour of soil and structure constitutes the subject of soil-structure interaction. In the first chapter of this study, the problem is defined and a detailed review of the previous work is given. The previous investigations can be separeted mainly into two groups which are different idealization procedures for the soil medium. In the first group of investigations, the structure is assumed to be founded on a half space or a stratum through an infinitely rigid foundation plate. This approach makes use of the solution of steady state vibration of rigid circular or rectangular plates bonded on a half space. The force-displacement relationship of the rigid plate is expressed by the compliance matrix. The imaginary part of the compliance matrix states the energy loss due to the infinite soil medium. This model has some important restrictions: a) Under actual soil conditions, homogeneous and linearly elastic soil assumption seems to be unrealistic. b) Earthquake analysis of the soil-structure systems can be done in frequency domain using Fourier Transform Technique because of the elements of complex compliance matrix are frequency dependent. In the second model, the soil medium is assumed to be finite and composed of some discrete elements. The finite element method is used for the discretization. The finite element method has many advantages in the solution of soil-structure system: a) Geometrical, mechanical discontinuities and irregularities of the soil medium can be taken into account.b) Earthquake analysis of soil-structure systems can be made directly in the time domain. Nonlinear soil and structure conditions can be taken into account using step by step integration. c) It is not necessary that the foundation plate is rigid. Although the discrete model is efficient and provides some flexibilities, it has also some drawbacks for the solution of the problem: a) Large computer storage is needed for sufficient idealization. Since the discrete model has to contain enough number of nodal points. b) Because of the model is finite, radiation energy loss can not be taken into consideration due to reflection of waves from the boundaries of the model. In the second chapter of this study, it is not only investigated the methods for analyzing soil-structure interaction but also two types mathematical models. Complete interaction analysis must account for the variation of soil properties with depth, give appropriate consideration to the material nonlinear behaviour of soil, consider three dimensional nature of the problem, consider the complex nature of wave propagation which produced the ground motions, consider possible interaction with neighboring structures. Idealized interaction analysis is used when researchers are encountered with complex problem. The soil deposit is represented by a series of horizontal layers, and the patterns of ground motion in the near-surface soils are considered to be the result of simple mechanisms. Idealized problems can be solved by the Direct and Multistep Methods. Direct methods evaluate the dynamic response of the structure in a single analysis step. The equation of motion resulting from the formulation of the soil-structure system with finite elements can be solved by two methods. Solution in the time domain in which the system of differential equations is solved directly by the step by step integration. Solution in the frequency domain, in which the impedance function of any effect is obtained by solving at each frequency a system of linear algebraic equations, and the time history response is then computed by using Fourier transfoms. Multistep methods are based on the principle of superposition and are restricted to linear systems. The basic idea is to perform the analysis of the interaction problem in several steps whose solution might be easier. The two step solution can be explained in the following two steps. In the first step, it is assumed that the structure has no mass but has stiffness and damping. The acceleration time history of each point of the structure is computed as well as the forces in the structure. In the second step, time varying inertial forces are applied at each point of the structure; the force at each point is the product of the mass at the point, and the acceleration is determined in the fist step to the base rock acceleration. The motions and forces in the structure are computed and added to those computed in step one. The nature and amount of this interaction depends not only the soil stiffness, but also on the stiffness and mass properties of the structure. The interaction effect associated with the stiffness of thestructure is termed kinematic interaction and the corresponding mass related effect is called inertial interaction. Two different models are developed; the first intended to be used in the earthquake response analysis and the second to obtain qualitative results about the dynamic behaviour of soil-structure systems. In the first model, the soil medium is idealized as two subsystems. The soil is discretized by means of two dimensional finite elements whereas the rest of the medium is assumed to be a linear elastic and homogenous stratum. The major soil deformations caused by the vibrating structure occur near the foundation. On the other hand, the soil deformations decrease in the far region of the structure, this part of the soil is idealized as a stratum. In the second model, the whole soil medium is idealized as a linear elastic and homogenous stratum. In both models, the soil deposit is discretized by means of nodal points which are defined on the surface of the medium. In the third chapter, the equations of motion of soil-structure systems are obtained. The problem is considered in a general manner. In order to obtain the equations, the soil and the structure are thought separetely. In the soil-structure systems, total displacements can be separeted into two parts as follows; [u] = [u]a + [u]b where [u]a represents earthquake free field displacement vector which can be calculated anywhere in the soil medium. [u]b represents the interaction displacements due to structure's vibration. In the fourth chapter, an efficient method, based on the Ritz concept, for dynamic analysis of response of multistorey buildings including foundation interaction to earthquake ground motion is presented. The system considered is a shear building on a rigid circular disc footing attached to the surface of a linearly elastic halfspace. The mass of the building is considered to be concentrated at the floor levels. The floor systems are assumed to be rigid so that the relative displacements are due to the deformations in the columns. In this method, the structural displacements are transformed to normal modes of vibration of the building on a rigid foundation. Numerical results show that excellent results can be obtained by considering only the first few modes of vibration. This method can be applied to all types of linear structure-foundation systems and multistorey buildings. The governing equations of motion for a structure including foundation interaction as well as the methods are complex. The foundation stiffness and damping terms relating forces and displacements for the rigid disc on a linear elastic halfspace depend on the frequency excitation. The governing equations for the structure-foundation system must be written in the Fourier transformed frequency domain. The steady-state response to harmonic ground motion at a particular excitation frequency is determined by solving the frequency domain equations.For each frequency, the solution of a set of simultaneous algebraic equations is obtained. Such a procedure, called as a direct method, requires a large computational effort for structures with many degrees-of-freedom. Sufficiently accurate solutions for structural displacements should result when the number of modes included, is much smaller than the number of degrees-of-freedom of the building excluding those at the base. The efficiency in the solution process is of great significance because the process has to be repeated for many values of excitation frequency. If all the modes are included, it is reached the exact results. In the Fourier analysis, the effect of the soil on the structure can be expressed in terms of a set of dimensionless influence functions P and R derived by Oien. These functions chracterize the interaction forces between an elastic soil half space with a shear wave velocity Vs and density p and a rigid, infinitely long strip of width 2b bonded to it which diffracts normally incident harmonic seismic waves. For a building foundation of plan dimensions 2b and d undergoing harmonic translation and rotation, Oien' s solution yields, M9=pVs2bd(R,5,U0+bR,7le) Fb=pVs2d(p,5lU0+bP,7,e) in which Me, Fb, U0 and 9 are all funtions of excitation frequency and are the Fourier transform of the interaction rocking moment at the interface, interaction translation force at the interface, interaction translation of the base and the interaction rotation of the base. In this method, the system is considered as a shear-type structure-foundation system possessing N+2 degrees of freedom (N: degree of freedom of the shear type structure). The rocking of the system about a horizontal axis and the horizontal translation of the base and the floors. In the dynamic equilibrium equations of a structure including interaction, after placing displacement and derivatives' Fourier transform in these equations and separete real and imaginary part of these equations, is obtained equations in the frequency domain. These equations contain influence functions and are to be calculated for each excitation frequency. For given structural parameters, base geometry, and soil properties, the desired solution to the earthquake interaction problem requires finding: a) Base translation, base rotation, and floor horizontal translation transfer functions. b) The time history response of the interaction rotation of the base, the interaction horizontal translation of the base and floor horizontal translation for a specified free field acceleration by using inverse Fourier transform. Earthquake response of tall buildings founded on various soils, the following general conclusions can be drawn: a) The amount of interaction increases when the value of shear wave velocity decreases. The motion associated with the higher modes of vibration may be attenuated for massive structures.b) The natural frequency of the fundamental mode of the structure decreases when shear wave velocity decreases. c) Rocking motions contributes to the total displacement response of tall buildings founded on soft soil. d) The floor accelerations or displacements are largest when the dominant frequency of the earthquake matches the fundamental frequency of the structures, and when the founding soil is very stiff; the interaction caused by soils can reduce accelerations or displacements. e) If the dominant frequency of the earthquake is as high as the second-mode natural frequency of the structure, the maximum accelerations or displacements responses of the structure are generally independent of shear wave velocity. In the fifth chapter, a numerical example is presented. A eight-story framed building with a rigid footing is considered. This model has the value of a height of 24m and having base dimensions 24m, damping ratio 0.05, the fundamental frequency of this building neglecting interaction effects in 11.33 rad/s. The values of the shear wave velocity are taken into account as 100,200,400,800,1000,5000 m/s. The earthquake input used for this interaction system was the unit amplitude harmonic ground motion. The duration of the earthquake is 30s and the accelerogram is recorded the values of the ground acceleration at 600 data points. It has been shown that soil properties affect the natural frequencies of vibration. As a consequence of the decreasing shear wave velocity, the frequencies of vibrations decrease. The displacement of the roof and ground floor column's shear force and bending moment are plotted versus frequency. It is noticed that the horizontal displacements of the eight (roof) floor and the bending moment, shear force of the ground floor's column are largest when dominant frequency of the earthquake matches the fundamental frequency of the soil-structure system, and when the soil is very stiff; the interaction caused by soils can reduces the values of the eigth (roof) floor displacement and bending moment, shear force of the ground floor's column. In the sixth chapter, the conclusions of this study are presented.
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