Konsol ''L'' plakların incelenmesi ve yapı sistemlerinin hesap yöntemlerinin karşılaştırılması
The solution of an ''L''shaped fix based thin plate by the finite element method and the comparison of methods of structural
- Tez No: 39645
- Danışmanlar: PROF.DR. AHMET İ. SAYGUN
- Tez Türü: Yüksek Lisans
- Konular: İnşaat Mühendisliği, Civil Engineering
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 1994
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: 129
Özet
Yüksek Lisans Tezi olarak yürütülen bu çalışma iki ana bölümden oluşmaktadır. Çalışmanın birinci bölümünde“L”biçimindeki dışbükey konsol ince plağın farklı genişlik oranlarına göre (Ly/Lx) hesaplanan uç deplasmanların ve iç kuvvetlerin değişimi incelenmiştir. Hesaplarda Sonlu Elemanlar Yöntemi 'nden yararlanılmıştır. Döşeme sistemi kendi içinde üç döşemeye bölünerek alt sistemler halinde çözüme gidilmiştir, iç kuvvetlerin hesabı için yaklaşık bir bağıntı önerilmiş ve sonuçlar karşılaştırılmıştır. Yapı sistemlerinin hesap yöntemlerinin karşılaştırılması bölümünde, düzlemi içinde çeşitli yükler etkisinde bulunan dört açıklıklı bir düzlem çerçeve seçilmiş ve değişik yükleme durumu için farklı hesap yükleri kullanılarak statik hesapları yapılmıştır. Çerçevenin ön boyutlandırılması Açı Yöntemi kullanılarak hesaplanmıştır. Daha sonra sırasıyla sabit yükler için Açı Yöntemi, Pl, P2 ve P3 ilave yükleri için Matris Deplasman Yöntemi, Düzgün Sıcaklık Değişimi için Matris Kuvvet Yöntemi, mesnet çökmeleri için Cross Metodu ve son olarak (W)Deprem Yükleri için Açı Yöntemi kullanılarak kesit tesirlerihesaplanmıştır. Ayrıca elde edilen kesit tesirlerinin en elverişsiz kombinezonlarına göre kesitler donatılmış ve Endirek Deplasman Metodundan yararlanılarak iki kesite ait M, N, T tesir çizgileri çizilmiştir.
Özet (Çeviri)
This M.Sci. thesis study consists of two parts : in the first part, an“L”shaped fix based thin plate is examined by the Finite Element Method and a comparison of the displacements and the strength of the joints for different length ratios (Ly/Lx) is presented. Instead of studying on öne plate, three subplates are used in the solution. The aim of this is to show that a system can be solved by dividing into subsystems. Dividing the plate into three subplates, shortens the width of the stifness matrix of the plate. By the help of this, the calculation is more simple than the calculation of whole plate. First of ali, the first and the second numbered subplates, as shoven in Fiğ.l are solved. The reactions of the last three joints of the subplates are calculated by the help of a basıc program. Then the third subplate is solved with the reactions from other two subplates and the displacements of the third subplate joints are calculated. By using the displacements of the joints that subplates have the same numbered joints, the ali system joints ' displacements are found.Jt I I } ıI 1 I1==\ lLy Second-^\Subplate Third Subplatezm. ı First Subplate Lx +j Figüre 1. The Subplates With the help of [a] Strength Matrix and the joints ' displacements, the strengths [Mx, My, Mxy] of the joints are solved. The results obtained through the numerical investigations are compared and an approximate forumla is proposed to calculate the strength of the joints. in the second part, the analysis and design of a four span reinforced concrete plane frame subjected to various external effects, is presented. Different method of analysis is used for each external effect. Application and comparison of these methods is also presented. The preliminary cross-sectional dimensions of the frame have been determined through the utilization of the Slope-Deflection Method. viiA sufficient result can be obtained in the preliminary design of the structural system by reducing the chracteristic strenghts of material. Both dead and live loadss are considered not only in the preliminary design but also in the definite design of the first chapter of the second part as well. in the second chapter, the frame is analysed by Matrix Displacement Method för live loads Pl, P2 and P3 acting on the structure. in the Matrix Displacement Method, unknovns are the displacements of the joints, forming the structural system. This method is more useful for the systems having high degrees of statical indeterminacy. in another saying, this method enables to operate with lesser unknovns in system having more members united, at joints forming the system. Although the band width of simulateneous eguations is limited because of no elasticity in choosing of unknowns, enable to have a good stability. But, when the eguations are not good in stability, returning in restricted because of the lackness elasticity in choosing unknovms. Thus, it is easy to formulate the Matrix Displacement Method and this method is more suitable for computer programming. in the third chapter of part two, the uniform temperature changes have been taken into account as an external effect on the structure. Uniform temperature change is the changing of the temperature at the upperside and underside of the Cross-Section. To determine the internal forces acting on the Cross- Sections, the structure is analysed by the Matrix Force Method. This method enables to operate with lesser unknovns in systems which having more members in frames forming the system. In addition, it is possible to optain equations in which the band width is kept small and system equations is stable, by means of independence in choosing unknowns. However the equations can be derived automatically because of its elasticity in choosing unknowns, they are also written systematically. In the fourth chapter, the structure is analysed by the Cross Method for different support settlements as an external effect. Structural systems are expected to have support settlements during its lifetime. If these settlements are some on every support of system, there will not be any reactions acting on structures members. But if they are different, some reactions acting on the structures Cross-Sections are expected. In Cross Method, the unknowns are the forces acting at the ends of the member. This forces can be obtained such as“ Mij = Mo + M1*S1 + + Mi*5i ”where Mo is the moment ends of the member due to only external forces, Ml is the end moments of the member due to while independent unit displacement 61 which can be choose by engineer. The structure is analysed by Slope Deflection Method for lateral loads (W) in the fifth chapter. In Slope Deflection Method, the unknowns are the conversions of joints and the independent displacements of the ends of members forming the system. In this method, the equations can be obtained automatically. At the end of these calculations, the dimensions of the critical Cross-Sections obtained from the preliminary analysis are checked under the most unsuitable loading conditions. These loading conditions are some combinations which considers different external effects action in some proportions. It is observed that the most unsuitable loading condition is obtained“1.4*G+1.6*Q”in which is Dead and Q is Live Load. Finally, in the seventh chapter of part two, the influence lines for bending moment, axial force and shear force of two given Cross-Sections are obtained by means of The Indirect Displacement Method which is an efficient and reliable method.
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