Sistem rijitlik matrisinin kurulurken indirgenmesi ve basit kazıklı temelleriçin bir uygulama

Abstract

Çalışmanın birinci bölümü olan giriş bölümünde, çalışmanın amaçları açıklanmıştır. Ayrıca, çalışmanın ikinci bölümünde yapılan uygulamalarda ve üçüncü bölümünde yazılan programda kullanılan yöntemlerden bahsedilmiştir. Çalışmanın, ikinci bölümünde sistem rijitlik matrisinde kurarken eleme yöntemi ve alt sistem kullanımı, örneklerle açıklanmıştır. Sistem rijitlik matrisini bu yolla kurmaktaki a- maç bilgisayarların çevre belleklerini kullanarak, büyük sistemleri de, düşük bellek kapasiteli bilgisayarları kullanarak çözebilmektir, özellikle, özdeş çerçevelerin üst üste gelme siyle oluşan sistemlerde alt sistem kullanımı, işlemlere hız kazandırmaktadır. İkinci bölümde ayrıca, yukarıda bahsedilen yöntemler kullanı larak elde edilen sistem rijitlik matrislerinde, gerekli satır ve sütun değişikleri yapılarak yatay rijitlik matrisine nasıl geçildi ği, bu matrisin nasıl küçüldüğü, tek katlı ve iki katlı çerçeveler için hazırlanılan örnekler üzerinde açıklanmıştır. Yatay rijitlik matrisi, çerçeve elemanlarında eksenel boy değişiminin göz önüne alındığı ve alınmadığı durumlar için elde edilmiş olup, yatay yükler altında sistemin davranışı, bütün bu durumlar için incelenmiştir. Bölüm 3 ' te ise, üzerinde sonsuz rijit cisim gibi davranan, yani düzlemine dik ve düzlemi içinde rijitlikleri çok büyük sayılan bir başlığı bulunan kazıklı temellerde, kazıkların ara düğüm noktalarına ait deplasmanlarını ve eleman uç kuvvetlerini hesaplayan bir bilgisayar programı yazılmış tır. Program ayrıca, malzeme yönünden lineerleştirilmiş bir elâstoplastik hesap için, kazığın, rijit başlığa bağlandığı bölgedeki elemanı, istendiği kadar daha küçük elemana otomatik olarak ayırıp, her bir küçültülmüş elemanın uç kuvvetlerini ve düğüm noktalarına ait deplasmanlarını hesaplayacak düzeydedir. Son bölüm olan dördüncü bölümde ise, çalışmanın sonuçları ve yorumlanması yer almaktadır.

In the Introduction part of this study, the aim of this work and the summary of the methods which are explained in the second and the third part, are included. In the second part of this study, the analysis of the frames subjected to lateral loads have been examined by using the frontal technique and substructure in matrix displacement method. The results have been checked by the very well known program called shortly SAP90. The aim of using the substructure and frontal technique is, to solve more complex systems by using computers with a relatively low central memory capacity. The lateral displacements of the system shown in figure a have been calculated for the following cases: * Axial deformations allowed in all members. * No axial deformations allowed on the beam. *No axial deformations allowed on the beam and on the columns. *There is no Diagonal member in the system The period of the system has been calculated by using the lateral displacements to see the effect of the axial deformations. Two methods have been used in the second part of this study. These methods are: o.5t^(D ıra**» m©°^5t 9m Y| \ioo.ioo.io (J IPB400 5 IPB400 6m *x *y Figure a i)Matrlx Displacement Method Based on Frontal Technique ii)Slope Deflection Method The system shown In figure a has been solved first by matrix displacement method. For this, each Joints and element has been numbered and stiffness matrices have been written by taking cross-sectional properties of each element into account. For each element, the stiffness matrices written for local axes have been transformed to stiffness matrices written for global axes by using transformation matrices. By inserting the transformed element matrix according to the related joints into 12*12 system stiffness matrix which has 4 joints and summing the values which are overlapping, system stiffness matrix has been formed. By using the Gauss Elimination Method, the displacements corresponding to the first and second joints have been calculated. In the analysis, axial deformations in the elements xi have been taken into account. While making these calculations, frontal technique has been used Then the system has been analysed by using slope deflection method and SAP90 software program. Then the calculated displacements have been compared. After required arrangements have been made in 6*6 stiffness matrix containing first and second joints, first and second rows and columns have corresponded to rotations, third and forth rows and columns have corresponded to vertical displacements, fifth and sixth rows and columns have corresponded to lateral displacements. Then the reordered stiffness matrix has been reduced by the unknowns belonging to rotations and vertical displacements, a 2*2 lateral stiffness matrix has been formed. This matrix has been calculated for the following cases: * Axial deformations allowed in all members. * No axial deformations allowed on the beam. * No axial deformations allowed on the columns. * No axial deformations allowed on the beam and on the columns. *There is no Diagonal member in the system In section 2.6 and section 2.7, a 2-storey system has been formed and analysed by adding an identical 1 storey system on top of the 1 storey system. This system shown in Figure b has been solved again by means of two methods and then the results have been compared with the results of SAP 90 software program. These are : i)Matrix Displacement Method Based on Frontal Technique ii)Sub Structuring Method xii 9m 9m Q1X ® TPR500 rn 0 IPB4(Ki olr 1PB40C 0 TPR^nofFl 6m [PB400 ®> 0.5t IPB400 T Oİf* 9m 9m Q2X © TPRsnn rn Q> ?} \ıoo.ıoo.ıo u IPB40C IPB40C IPB400 © TPRSnfttTI ^ooıodo m ÖÜt IPB400 6m 1 1 Figure b In the solution of this system, the system stiffness matrix composed for 1-storey system had been made use of and the dimensions of system stiffness matrix have been aimed not to be changed. The reason for this is: i) In the execution of programs the operations can be made faster. ii) To analyze relatively big systems in the computers with low memory capacity In the third section of this study, the analysis of rigid foundations on piles have been examined and a software program has been written to calculate the displacements at determined joints and forces on rigid system and piles by talcing variation of soil properties along the pile length on piles that are on elastic soil. The stiffness matrix of the piles In the system shown in figure c has been formed by using the frontal technique and by the xiii Figure c method which has been found for the special systems like this one, the displacements of the rigid system and piles have been calculated.