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Çok katlı perde-çerçeve yapıların deprem yükleri altında dinamik analizi

Dynamic analysis of multistory walled-framed structures under load of the earthquake

  1. Tez No: 39657
  2. Yazar: HÜSEYİN ASLANBAŞ
  3. Danışmanlar: DOÇ.DR. ZEKİ HASGÜR
  4. Tez Türü: Yüksek Lisans
  5. Konular: İnşaat Mühendisliği, Civil Engineering
  6. Anahtar Kelimeler: Belirtilmemiş.
  7. Yıl: 1994
  8. Dil: Türkçe
  9. Üniversite: İstanbul Teknik Üniversitesi
  10. Enstitü: Fen Bilimleri Enstitüsü
  11. Ana Bilim Dalı: Belirtilmemiş.
  12. Bilim Dalı: Belirtilmemiş.
  13. Sayfa Sayısı: 92

Özet

ÖZET Bu çalışmanın amacı dolu veya boşluklu perde-çerçeve sistemlerden oluşmuş çok katlı yapıların deprem kuvvetleri altında dinamik hesabının yapılması ve bu konu ile ilgili bilgisayar programlarının geliştirilmesidir. Geliştirilen programlarda uç kuvvet ve deformasyonlar matris deplasman yöntemiyle bulunmuştur. Yöntemin amacı, dış etkilerden meydana gelen uç kuvvetlerin ve uç yerdeğiştirmeleri hesaplamaktır. Çünkü bunlara bağlı olarak uç kuvvetler, yer değiştirmeler, şekil değiştirmeler bulunabilir. Yapıya ait dinamik karakteristikler (frekans, periyot, mod şekilleri) Stodola metodu kullanlarak bulunmaktadır. Özdeğer probleminin çözümü için çeşitli algoritmalardan biri olan stodola yöntemi bir ardışık yaklaşım yöntemidir. Kullanımda yöntem, matris notasyonu şeklinde ifade edilebileceği için programlamaya uygundur. Dinamik analiz DINAN 1 programında spektral analiz, DINAN 2 programında ise adım adım integrasyon yöntemi kullanılarak yapılmaktadır. Bu çalışmada, DINAN 1 ve DINAN 2 programı değişik yapılar için uygulanmış, sonuçta spektral analiz metodunun, adım adım integrasyona göre bir yaklaşıklık içerdiği görülmüştür. Tezin birinci bölümünde yöntem seçiminin nedenleri ana hatlarıyla açıklanmıştır. İkinci bölümde ise matris deplasman metodu ve yapının modellenmesi hakkında ayrıntılı bilgi verilmiştir. Üçüncü bölümde ise dinamik hesapta kullanılan yöntemler ayrıntılı bir biçimde açıklanmıştır. Dördüncü bölümde programların çalışma düzeni ve programa veri girişinin nasıl olduğu anlatılmıştır. Beşinci bölümde bilgisayar programları ile sayısal uygulamalar yapılmış ve sonuçlar irdelenmiştir. Altıncı bölümde ise sonuçlar ve öneriler yer almaktadır. vii

Özet (Çeviri)

SUMMARY DYNAMIC ANALYSIS OF MULTISTORY WALLED-FRAMED STRUCTURES UNDER LOAD OF THE EARTHQUAKE In structural engineering, both safety and economic factors are considered in structural design. Therefore, these two basic factors considerably effect each other. Safety factor was the most important aspect in the design of structure due to the indeterminaney of real behavior of structures, before the use of computer technology in structural engineering. The behaviour of structures is determined more precisely, because of the devolopment of structural analysis methods and computer technology. So, the problem of economical design becomes more important. In this study dynamic analysis of structures composed of solid or coupled shear walls and frames is done by using both spectral analysis and step by step integration methods by means of two different computer programs, devoloped in Basic Programing Language. In programing the matrix displacement method is prefered. The unknowns are displacements and rotations of the joints: This method is more useful for the systems statically indeterminated (having degrees of statically in determinacy). In this method the story displacement of a joint effect only the members connects at the given joint. Therefore, it is easy to formulate the matrix displacement method which is available for computer programing. This study which has been carried out for M.Sc thesis, consists of six chapters and content of each chapter will be explained the following paragraphs in detail. In the first chapter, the method and preferency reasons for matrix displacement method and spectral analysis and step by step integration methods are briefly explained. In the second chapter matrix displacement method and modelling of walled-framed planar systems are explained. The stiftness equations for an element: viiiWe can express the matrix of nodal actions of an element as [P] = [A] + [PJ (1) where [A] is the matrix of nodal actions of the element when subjected only to its nodal displacement, and [P0] is the matrix of nodal action of the element when subjected to the given external disturbances with its ends fixed. [PJ is called the matrix of fixed-end actions of the element. If the structures subjected only to external loads equation (1) can be written as the following [P] = [A] (2) We express the local components of the nodal dispacements as a linear combination of its nodal displacement That is, [A] =[K] [D] (3) Relation (2) is called the stiffness equation for an element. The matrix [K] is called the local stiffness matrix of the element. Its terms are called the local stiffness coefficents of the element. The local stiffness coefficent Kmn represents the nodal action Am (the action in the m th row of the matrix [A]) of the element when it is subjected only to a nodal displacement Dn =1, while all other nodal displacement vanish. (Dn is the displacement in the n th row of the matrix [D]) Local stiffness matrix of an element of a planar beam or a planar frame: The physical significance of the stiffness coefficients of the second column of the stiffness matrix for a general planar element can be established by considering such an element only to the components of nodal actions which are required to induce the following nodal displacement, (see Fig. 1) IXK,, K12 K13 Kj4 Kj K 31 [A]- = 41 5 K16 ^21 ^22 ^23 ^4 ^5 ^26 K32 K33 K34 ^5 K: 42 43 44 45 36 K... K,, K., K... K,, K "46 K51 K52 K53 K54 K55 ^6 K61 K62 K63 K64 K65 K66 I>. EH, IX DJ. EH Dİ (4) K u=l -> (6) In matrix form, the complete set of elastic-force relation ships may be written symbolically, fş = k v (7) in which the matrix of stiffness coefficients k called the stiffness matrix of the structure and v is the displacement vector representing the displaced shape of the structure. Symbolically damping forces may be written 5> = £ v W In which the matrix of damping coefficients ç is called the damping matrix of the structure and v is the velocity vector. Symbolically, also inertia forces may be written 5. = m v (9) In which the matrix of mass coefficient m is called the mass matrix of the structure and v is its acceleration vector. Substituting Eqs. (7), (8), (9) into Eq. (6) gives the complete dynamic equilibrium of the structure, considering all degrees of freedom: mv + C.V + kv = p(t) (10) The normal coordinate transformation, which serves to change the set N coupled equations of motion of a MDOF system into a set of N uncoupled equations, is the basis of the mode-superposition method of dynamic analysis. The method can be used to evaluate the dynamic response of any linear structure for which the displacements have been expressed in terms of a set of N discrete coordinates and where the damping can be expressed by modal damping ratios. This method is XIIcalled the mode-superposition procedure and consists of the following steps. STEP 1 : For this class, the equations of motion may be expressed (Eq. (10)) as mv+ cv+ kv = p(t) STEP 2 : For undamped, free vibrations, this matrix equation can be reduced to the eigenvalue equation: [k-a>2m] a being used in turn, the generalized mass and generalized load for each mode can be computed M. = 2 Y2(t) + ^ Y3(t) + (16) that is, it merely represents the superposition of the various modal contributions; hence the name mode-superposition method. STEP 7 : The displacement history of the structure may be considered to be the basic measure of its response to dynamic loading. In general, other response parameters such as stress or forces developed in various structural components can be evaluated directly from the displacements. For example, the elastic forces fs which resist the deformation of the structure are given directly by fş(t) =k v(t) =k * Y(t) (17) The step by step integration can also be used for displacement history of the structure. For this reason numerical integration of Eq (10) is necessary. The technique employed here is simple in concept but has been found to yield excellent results with relatively little computational effort. The basic assumptation of process is that the accelaration varies linearly during each time increment while the proporties of the system remain constant during this interval. [2] In the fourth chapter, The details of computer programs called DINAN1 and DINAN2 are presented. We explain how to solve the planar systems by the programs. Especially how to compose of the data files is indicated. In the fifth chapter, applications which are solved by the programs are explained. In the sixth chapter the results and the comments are expressed. xivThe results, determined in this study can be explained as the following. a) Effect of axial deformations and shear deformations are very important at the structure, because these effects is induced to increase of period and displacements of the structure. The base shear force of the structure decreases, because flexibility of the structure increases. b) Dynamic analysis of structure has been done by using both spectral analysis method and step by step integration method. In step by step integration method base shear force of the structure is determined smaller than spectral analysis method. Moreover responses of the structures in step by step integration method determined smaller than spectral analysis method. Therefore the results, determined by using step by step integration method is exact and economical according to spectral analysis method. c) Although peak acceleration values of Erzincan 1992 N-S and El Centro 1940 N-S earthquakes are almost the same, responses of the structure, determined from Erzincan 1992 N-S is greater because Housner intensity of Erzincan earthquake greater. This result shows that Housner intensity of earthquakes are also very effective for dynamic analysis. xv

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