Determination of failure mechanisms and ductility of 3D steel frames under earthquake loads with three components

Üç boyutlu çelik çerçevelerin üç bileşenli deprem yükleri etkisinde göçme mekanizmaları ve sünekliğinin belirlenmesi

Abstract

In this study, it has been aimed to develop an algorithm that determines failure mechanisms and ductility capacities of 3D frames under earthquake loads with three components and a computer program which performs dynamic analysis according to this algorithm. In the first chapter, definitions concerning linear elastic system solution have been described. The member’s elastic stiffness matrix has been explained which is written both in the local and the global coordinate systems. Then, the system’s global stiffness matrix has been given with how it is formed by using the global stiffness matrix of each member. Modified Crout reduction procedure which is a kind of Gauss elimination method has been used for the solution of linear equation systems. In the second chapter, semi-rigid connection model has been described. The independent hardening model given by Kishi and Chen has been used to express the behaviour under cyclic loading. Because this model is simple to use and easily applicable to all type of steel frame connection models, it is often implemented in the frame analysis program. The moment-rotation curve under the first cycle of loading, unloading and reverse loading remain unchanged under the repetition of loading cycles. The skeleton curve used in the model was obtained from three parameter power models. In this procedure, the initial connection stiffness, ultimate moment capacity and shape parameter of the connection have been determined by an analytical model for top- and seatangle connection with double web angle. In the third chapter, material nonlinearity has been investigated. The inelastic moment-rotation and axial forcedeformation behaviour of structural members have been modeled by the inversion of the Ramberg-Osgood relation. Material nonlinearity is simulated by the formation of plastic zones of zero length at the ends of the elements. The plastic hinge does not form until all of the fibers in the cross-section reach the yield stress. Hysteresis behaviour of plastic hinges has been defined using skeleton and branch curves relating to moment-rotation and axial forcedeformation relations of members. Elasto-plastic correction factors have been obtained from finite incremental nonlinear member force-deformation relations and then, the member’s tangent stiffness matrix has been formed by using these factors. Interaction surfaces have been described with the lower bound yield surface equations suggested by Morris and Fenves, relating to the various neutral axis positions of common cross-sectional types. The internal force values obtained by employing the tangent stiffness generated at the beginning of a time interval do not satisfy the yield equations at the end of this time interval.In order to obtain results which satisfy this condition with reasonable time required, a method of modifying the member stiffness for each time increment has been used. Because direct shear deformations are usually neglected as being small for framed structures, direct shear forces parameters are not included in the yield conditions formulated. In the fourth chapter, the geometric nonlinearity including the second-order effects associated with P − $delta$ and P − $Delta$ has been investigated. While the geometric nonlinearity caused by axial force has been described by the use of the geometric stiffness matrix, the nonlinearity caused by the interaction between the axial force and bending moment has also been described by the use of the stability functions. In the fifth chapter, dynamic equation of motion has been built in the finite time increments for multi-story systems and the system mass, damping and tangent stiffness matrices which are a part of the system dynamic equation of motion have been described. El Centro acceleration record with three components has been applied to the dynamic equation of motion as external load. This equation of motion has been solved by Newmark’s constant acceleration method in time history domain. The input energy in the system due to seismic loading, dissipated energy by the hysteretic behaviour of the material at the location of plastic hinges, if they form, by viscous damping and by hysteretic behaviour of the semi-rigid connections, elastic strain energy and kinetic energy have been described. Member-level ductility demands including hysteretic behaviour of three dimensional members, system-level ductility demands and drift demands have been calculated. Using the written computer program which uses the developed algorithm, different structural models have been analyzed under ground motions with three components and the response quantities of structural models have been calculated.

Özet

Bu çalışmada üç boyutlu çerçeve sistemlerin üç bileşenli deprem yükleri altındaki göçme mekanizmalarının ve süneklik kapasitelerinin belirlenmesi için bir algoritmanın geliştirilmesi ve bu algoritmaya uygun dinamik analiz yapabilen bir bilgisayar programının üretilmesi amaçlanmıştır. Malzemenin lineer olmayan gerilme-şekil değiştirme bağıntısı, Ramberg-Osgood ifadesinin tersine karşı gelen bağıntı ile modellenmiştir. Sistem zamana bağlı değişken dış yüklerin etkisinde olduğu için, plastik mafsallarda eleman uç momenti-açısal uç deplasmanı ile eksenel uç kuvveti-eksenel uç deplasmanı arasındaki bağıntılara ait iskelet ve dal eğrileri kullanılarak histerik davranış tanımlanmıştır. Sonlu küçük uç kuvvet artımları ile uç deplasman artımları arasındaki lineer olmayan bağıntılardan elasto-plastik düzeltme katsayıları tanımlanarak elemanın elasto-plastik tanjant rijitlik matrisi oluşturulmuştur. Karşılıklı etki yüzeyi, Morris ve Fenves tarafından verilen, eleman enkesitindeki tarafsız eksenin herbir konumu için belirlenmiş olan alt-sınır akma yüzeyi ifadeleriyle tanımlanmıştır. Tekrarlı yükler altındaki birleşimin davranışını tanımlayabilmek için Kishi ve Chen tarafından önerilen bağımsız pekleşme modeli kullanılmıştır. Bu modele ait, birleşim başlangıç rijitliği, maksimum moment taşıma kapasitesi ve şekil parametresi değerleri, Üst ve Alt Flanşlar ile Gövdeden Çift Korniyerli birleşim tipi için hesaplanmıştır. Eleman uç noktalarının farklı yer değiştirmesi sonucu oluşan ikinci mertebe etkiler (P − $Delta$ etkisi) geometrik rijitlik matrisiyle, eleman uzunluğu boyunca elemanda oluşan ikinci mertebe etkiler (P − $delta$ etkisi) ise stabilite fonksiyonlarıyla tanımlanmıştır. Çok katlı uzay çerçeve sistemlerin sonlu küçük zaman artımları için hareket denklemleri oluşturulmuş ve sonlu küçük zaman artımları için Newmark’ın genelleştirilmiş ivme yöntemiyle adım-adım integre edilerek çözülmüştür. Seçilen uzay çerçeve sistemleri, yazılmış bilgisayar programı kullanılarak üç boyutlu deprem yükleri altında analiz edilmiş ve elde edilen sonuçlar grafikler ve tablolar ile gösterilmiştir.