Kuvvet yönteminin etkin kullanımı ve kolon-kiriş birleşim bölgesinin yapı davranışına etkisi
The Effective usage of the force method-the analysis of frame behavior affected by beam-column connections
- Tez No: 21789
- Danışmanlar: PROF. DR. FARUK KARADOĞAN
- Tez Türü: Yüksek Lisans
- Konular: İnşaat Mühendisliği, Civil Engineering
- Anahtar Kelimeler: Kiriş-kolon birleşimi, Kuvvet yöntemi, Yapı sistemleri, Beam-column collection, Force method, Structure systems
- Yıl: 1992
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: Belirtilmemiş.
Özet
ÖZET Bu çalışma iki ana bölümden oluşmaktadır: Kuvvet Yönteminin Etkin Kullanımı ve Kolon-Kiriş Birleşim Bölge¬ sinin İncelenmesi. Kuvvet yönteminin Etkin Kullanımı Bölümünde, düzlemi içerisinde çeşitli yüklerin etkisinde bulunan üç açıklıklı bir düzlem çerçeve seçilmiş ve değişik yükleme durumları için kuvvet yöntemi kullanılarak statik hesap yapılmıştır. Bütün yükleme durumları için hiperstatik esas sistem kul¬ lanılmıştır. Matris kuvvet yöntemi kullanılarak sabit yükler ve sıcaklık değişmesine göre hesap tekrar edilmiştir. Virtüel iş teoremi ve grup yüklemeler ile f kesitine ait M, N tesir çizgileri çizilmiştir. Ayrıca, elde edilen kesit tesirlerinin en elverişsiz kombinezonlarına göre kesitler donatılmışlardır. Çalışmanın ikinci kısmında 12 serbestlik dereceli düzlem levha eleman üzerine etkiyen değişik yükleme durum¬ larına ait yük fonksiyonları ve yük terimleri elde edilmiş¬ tir, daha sonra bu yük terimlerinin doğruluğu sabSO ile kontrol edilmiştir. Bu çalışmaya ilave olarak düğüm nok¬ tasını temsil eden iki matematik model üzerinde çalışılmış. Buradan sonsuz rijit kısımları bulunan çubuklara ait birim deplasman sabitleri elde edilmeye çalışılmıştır. vi"
Özet (Çeviri)
THE EFFECTIVE USAGE OF THE FORCE METHOD-THE ANALYSIS OF FRAME BEHAVIOR AFFECTED BY BEAM-COLUMN CONNECTIONS SUMMARY This study consists of two major parts. First of these is the effective usage of The Force Method and the second of these is the analysis, of reinforced concrete beam-column connection, which effects frame behaivour. In the first part, the analysis of a three-span reinforced concrete plane frame subjected to various external effects are presented. Here, the advantages of the Force Method has been explained and examlified. The preliminary cross-sectional dimensions of the frame have been determined through the Force Method thinking the combination of dead weight and live loads : 1.4G + 1.6Q Depending on this calculations d intensions of frame have been chosen. In the first chapter of the first part, the structure has been analysed by the Force Method for dead weight acting on the structure. Here, firstly the axial deformations of the tie has been ignored. A statically determinate base structure has been chosen for this load case. After that the unit loadings and external loads have been affected on this structure. To make lesser the degree of static indeterminancy, xt is convenient to use aproperly chosen indeterminate structure as a base structure. The terms of S ? T in the compatibility equations have been calculated using reduction theorem. According to the reduction theorem rotational deformations or any of the corresponding internal forces that exist in the compatibility equations can be taken from a statically determinate base structure. Because of the finucular form of the structure; at the end of this calculation it has been seen that the moments on the structure are relatively small in comparison to the axial forces. Vllin the second chapter of the first part, the şelf weight analysis of the structure for the second direction by means of the Force Method. in the third chapter of this part the calculations for dead weight have been repeated considering the axial deformations of the tie. The compatibility equation have been solved. And then the new moment diagram has been dravm. At the end of this calculation it has been seen that the moments on the structure became bigger. in the fourth chapter of this part the lateral loads due to earthguake have been taken account that the lateral loads have been concentrated at the nodes of the structure Since the lateral loads on the structure are antimetric, the symmetric unknowns became zero. The compatibility equations have been written again. So the antimetric unknovms have been obtained. After writing the superpositioı equations, M, N, T diagrams have been dravm. in the fifth chapter of this part, the structure has been affected by the uniform distrubuted snow load, P,. The coefficients matrix for P, is the same as the coefficıent matrix which is obtained for dead weight. The right hand side of compatibility equation have been calculated for P,. Then the new unknowns have been found. The diagrams of M, N, T have been dravm for this load case. The snow can be accumulated in the roof middle part of the structure. Hence it is necessary to consider a second snow loading, P« for middle part of the structure this loading is symmetric too. The right hand side of compatibility equation have been calculated in the sixth chapter of this part. in the seventh chapter of the first part the support settlements have been considered. Since öne bay öne story fixed frame have been used, the term of M in the superposition equations is different from zero. Since the support settlements haye been given as symmetric/ the coefficient matrix is the same as the öne for the other symmetric load cases. After calculating the right hand side of the compatibility equations the unknovms have been found for support settlements. Then the diagrams M, N, T have been dravm. in the eighth chapter of the first part the uniform temperature changes has been considered. Since öne bay öne story fixed frame has been used, the term of M in the superposition equations is different f rom zero. ¥he unknovms belong to this load case have been found. Then the diagrams M, N, T have been dravm. viiiin the sixth part, the structure has been reanalysed by the Matrix Force method för dead weight. Firstly redundont forces, the numbers of elements and connections have been specified. Axial deformations have been taken into account för ali elements except the middle part of the structure, which is öne bay öne story fixed frame and considered as a subsystem. The flexibility matrices have been obtained for each element. The flexibility matrix of substructure has been easily prepared using virtual work theorem. After having prepared homogenous and partial solutions, which are beiong to redundont forces and external loads/ end forces have been obtained using the algorithm given in [ 2] f.ör the Matrix Force Method'. in the seventh parth, the structure has been reanalysed by the Matrix Force Method for the uniform temperature changes.The way of calculation is the same as the vay which has been used for dead weight. in the eighth part, the influence lines for bending moment and axial force of section f have been obtained using virtual work theorem» A unit load has been affected on the structure at each 2 nü For each position of the unit load, the moments at section f have been found by a program called gos 411. Hence the influence lines have been checked. in the nineth part, the influence lines for bending moment and axial force of section f obtained using group loading and statically indeterminate system. in the tenth part, the dimensions of the critical cross-sections obtained from the preliminary analysis, have been checked using the most unsuitable loading conditions, which are some combinations of different external effects given by TS 500. After that the reinforcements for the sections have been chosen. in the second part in order to have better understanding of the beam-column connection regions, several attempts have been made depending on finite element solutions. After that idealisation a parametric work has been carried out to obtain global stiffness coefficients of beams with very rigid parts at the ends. The beam-column connections especially reinforced concrete of the plane-frame have been affected by the cyclic moments and shear forces. Due to this cyclic effect of internal forces, the beam-column connection will experience very big plastic deformations even total crushing during on earthguake if they are not well confined especially by stirrups. This is a kind of behaivour which can be totally opposite of assumption. And it has to be taken into account when it is dealt with earthguake response of systems. ixTo reduce the amount of finite elements used in a beam-column connection, elements with higher degrees of freedom can be employed with several different type load matrix for special load cases such as third order distrubuted tensile and their force distrubution and a concentrated load arbitrarily placed on any one of the edges of finite elements. Load matrices for each specified load case have been derived as much as in general formes. Using the displacement function which has been given [4] some terms of stiffness matrix have been obtained once more using the following integration. [K]=/ [B]T[Dj[B] dv V After that using virtual work the load matrices have been obtained for three different distrubuted loads [q] employing the following equations. T>0la - £ [ÜIT 9<x) dv A sample structure which present the beam-column connection has been chosen. distrubuted and concentrated loads have been affected on the structure. The Matrix Displacement Method has been used to solve the structure. Firstly the region has been divided into four rectangular elements. The element stifness matrices have been found, then system stiffness matrix have been obtained by hand calculations. The element load matrices calculated for each element using the formula found before. After that the load matrix' for the structure has been obtained. The nodal displacements have been found as a solution of the following linear equation. [S] [d] + [P J = oJ The stress in each element has been calculated. After that the avarage at nodes have been calculated for the structure. Using the program called SAP30 the results have been checked. In order to examplify the efficiency newly developed loading matrices a set of finite element analysis have been performed by means of the famous SAP80.- Equivalent results have been achieved with SAP80 for a particular example using only 27 unknown instead of 126 unknowns.The member element stiffness coefficients effected due to the existance of rigid parts at. the ends of beams have been obtained simply comparing the two kind of solutions namely the finite elements analysis of a beam loaded at the mid point by concentrated moment and simple eguilibrium equations (see Fiğ. 3.51). Using the same mathematical models, the modulus of elasticty within the connection decreased to represent the inelastic deformation of beam-column connections and fictitious beam stiffness coe^-Ficients have been obtained pararaetr-icaLly. -in addition to this a öne story öne bay frame have been analysed for lateral loads to demonstrate the influence of the decreasing rigidity of the beam-column connection on the response of the structure. At the end of this.analyses it has been concluded that the materially nonlinear beam-column connection has important the effect on the behaivour of the structures. This results coincied with behaviour of flexible framed structures observed in 13 th marchy 1992 Erzincan earthguake. The nonlinear behaivour:. of beam-column connections can be reflected to the design of the structures through the change of the stiffnesses of beam and column elements. Another mechanical model has also been employed especially to have the fictitious column stiffness coefficients taking in to account the nonlinear behaivour of beam to column connections.
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İnşaat Mühendisliğiİstanbul Teknik ÜniversitesiYapı Ana Bilim Dalı
PROF. DR. H. FARUK KARADOĞAN
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