Sonlu elemanları yöntemi ile elastik zemine oturan plakların analizi ve yapı sistemlerinin hesap yöntemlerinin karşılaştırılması
Başlık çevirisi mevcut değil.
- Tez No: 55812
- Danışmanlar: PROF.DR. AHMET I. SAYGIN
- Tez Türü: Yüksek Lisans
- Konular: İnşaat Mühendisliği, Civil Engineering
- Anahtar Kelimeler: Karşılaştırmalı analiz, Levhalar, Sonlu elemanlar yöntemi, Yapı sistemleri, Comparative analysis, Plates, Finite element method, Structure systems
- Yıl: 1996
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: Belirtilmemiş.
Özet
ÖZET Yüksek lisans tezi olarak sunulan bu çalışmanın birinci bölümünde düşey kolon yükleri altında, elastik zemine oturan plaklarda çeşitli süreklilik koşullarına bağlı olarak, zemin gerilmesi ve iç kuvvet dağılımı Sonlu Elemanlar Yöntemi ile incelenmiştir. Aynı yatak katsayısı altında zeminin İki Parametreli alınmasının, Winkler kabulüne göre zemin gerilmesi ve iç kuvvet dağılımını önemli ölçüde değiştirdiği görülmüştür. İkinci bölümde Yapı Sistemlerinin Hesap Yöntemlerinin karşılaştırılması yapılmıştır. Bu bölümde seçilen örnek bir düzlem sisteminin boyutlandırılmasında ve değişik yükleme durundan için farklı yöntemler kullanılarak bulunan en elverişsiz kesit zorlarına göre betonarme kesit hesabı yapılmıştır. Bu çalışmada son olarak, hareketli yükler için iki kesitte M,N,T kesit tesirlerine ait tesir çizgileri endirekt deplasman yöntemi ile çizilmiştir.
Özet (Çeviri)
SUMMARY THE ANALYSIS OF THE PLATE ON ELASTIC FOUNDATION BY USING FINITE ELEMENT METHOD AND COMPARISON OF THE CALCULATION METHODS FOR STRUCTURAL SYSTEM The object of structural engineering is to realize structures, which provide safety and economy factors together. It has known that these both, safety and economy factors are effective on each other. Because of the real behavior of structures and the uncertainty of applied loadings; safety factors has the upmost importance in design of structures. Because of the development of the structural analysis methods and computer technology, the behavior of the structures is determined more precisely and the structures are designed more economically. This study consists of two main parts for the plate on elastic foundation, under the vertical column loads, calculation of the base tension and internal force dispersion by using finite element method and comparison of the methods for structural analysis.. In the first part of this study, finite element method has been applied to compare the plate on Winkler foundation and the plate on two parameter foundation and it is applied to examine these plates on elastic foundations in the different boundary conditions. For the plate on elastic two parameter soil the vertical displacement at any point in compressible soil below the plate can be expressed as follows. wz - (a{x,y) $(z) w(x,y) : The surface displacement of the soil 0(z) : The displacement which is varying with depth The boundary condition for 0(z) are z - 0 - $(z) - 1 XVz = H- 4>(z) - 0 The effect of base reaction can be obtained as follows qz - CMU>y)-2Cr[yt)(x'y) + Ü2İ2&ZL] dx2 dy2 where c-“*y. 7 (i«£L)»<i. (1+v.) 1-v, J dz 3 s 2-0 H 2CT - Ga f $2(z)dz Where Es, v. are material properties of the soil. Taking the reaction of the soil and the external loading q into account, the differential equation of the plate on two parameter foundation can be written as follows D A Ao-2CjAcıî+Co)-g- At any point of the plate domain the following differential equation will be valid -2CjA(jİ+Cü> - q C : The Winkler coefficient Op : The shear parameter which depends on the shear deformation of the soil. C and &p depend on the material properties, the thickness of compressible layer of the soil and the function of 0(z). xviThe function of 0(z), which satisfy the boundary condition at z=0 and z=H can be given as follows £hy(l- §) 4>(z) = - H Shy y : The soil surface parameter It can be obtained as follows: 2 m h2u-2vs) L L dx dy 2 (1-V _) j \<&2dxdy If the function <p(z) is substituted into the expression for C, and Cj, it yields c_ Es(l-vs) _y_ (Sh2y+2y) ”(l+vfl) (l-2vs) H 4Sh2y m H (SH2y-2y) s Y 45İ22Y As seen in these expressions C and Ct, depend on the material properties, the thickness of compressible layer of the soil, the coefficient of y. y depends on the dimension and stiffness of plate and the external loads. The parameter y can be evaluated after determining o(x,y) which satisfies differential equation, below and around the plate, by integrating the numerator and denominator in expression of y for below and around of the foundation domain. Approximate methods are used to evaluate the parameter y. In finite element two parameter soil effect can be expressed by adding the matrices [C] and [Cp] to the stiffness matrices. The terms of these matrices can be computed as follows, xvuC^cffa ±a jdxdy The differential equation which is valid at the point out of the plate region where no external load is considered can be given as follows: ox2 ay2 The wideness of the soil region around the plate which is divided into finite element has to be as much as the computed deflection on this boundary is close to zero. This region can be chosen as the thickness of the compressible layer of soil. By assuming the differential equation, the outside soil region of the plate has the same behavior of the shear plate having shear rigidity 2Cji=Gh' If [d] shows the nodal vertical displacement of the soil element then and the nodal forces of the elements depend on the displacements as follows [C] [d] + [CJ [d]-[P] The displacement field of the rectangular finite element will be expressed depending on vertical displacement of the nodes can be written as [Ad] z- [12 (x) 12 (y) l1(x)l2(y) l1(y)l2(x) l1(x)l1(y)] The matrices of the soil can be obtained by integrating the functions as it was explained before. When the nodal freedom of the element are known, the integral terms of the expression in y can be obtained for each elements as follows xvmJfa'dA-± idi TICİ [d] //[(^)2+(J^)2]dxdy._^[d]r[Cr][d] By using this equations, an example plate is examined and solved by Genson computer program. In the second part, the analysis of a three-span frame subjected to various external effects is presented. Different analysis method have been used for each external loading. Firstly the cross sectional dimensions of the frame have been designed by using Slope- deflection Method. In symmetrical structures, it is able to use half of the unknowns when the loads are symmetrical or antisymmetrical. It has shown that the results can be get more quick and easily by using this way. In the second chapter of this section the structure is analyzed by the Matrix Displacement Method for dead weight acting on the structure. In the Matrix Displacement Method, the unknowns are displacements of the joints. This method is more useful for the system having more members united at joints forming system. The band with is limited and there is no elasticity in choosing the unknowns. Equation can be obtained automatically. But when the equations are not good in stability, returning is restricted because of the lackness elasticity in choosing unknowns. And this method is more suitable for computer programming. In the third chapter of this section, the structure is analyzed by slope-deflection Method for live loads P*, P** P3 an(* W. In Slope-deflection Method, the unknowns are the rotation of joints and inde endence displacement of the ends of members forming the system. In this system the equation can be obtained automatically. In the fourth chapter of this section, the structure is analyzed by Matrix Force Method for uniform temperature changes. In Matrix Force Method, the unknowns are the forces acting at the ends of the members. In this method number of forces released are equal to number of unknowns. Analysis can be made with lesser unknowns for the system, having more members in a frame. The writing of these equations are systematic, however it can be done automatically of its elasticity in choosing unknowns. XIXIn the fifth chapter of this section, the structure is analyzed by Cross Method for different support settlements and external effect. In this method a part the simultaneous equations are solved by successive iterations. At the end of these calculations, the dimensions of the critical cross-section obtained from the firstly analysis are checked under the most unsuitable loading combinations which consider different external effect actions in certain proportions according to Turkish Design Code. In the second part finally, the influence lines for bending moment, axial force and shear force of two given section are obtained by means of the Indirect Displacement Method. xx
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