Binaların deprem etkisi altındaki lineer olmayan davranışının belirlenmesi için çok modlu uyarlamalı yük artımı yöntemi

Abstract

Çalışmada, binaların deprem etkileri altındaki lineer olmayan davranışının belirlenmesi için çok modlu uyarlamalı bir yük artımı yöntemi sunulmuştur. Yöntemde yığılı plastisite yaklaşımı kullanılmaktadır. Oluşan ardışık plastik kesitler arasındaki bölgelerde, sistemin geometri değişimi bakımından lineer olmayan davranışı (ikinci mertebe etkileri) ve bileşik eğilme etkisindeki kesitlerde akma koşulları lineerleştirilmekte ve bu bölgelerde geleneksel davranış spektrumu analizi esaslarından yararlanılarak yüksek mod etkileri göz önüne alınmaktadır. Yapılan lineerleştirmelerle, plastik kesitlerin oluşumu için gerekli yük artımları, ardışık yaklaşıma veya adımadım analize gerek kalmadan direkt olarak belirlenebilmektedir. Her yük artımındaki modal yüklerin belirlenmesinde, plastikleşen kesitler nedeniyle sistemin değişen dinamik özellikleri kullanılmaktadır. Böylece önemli rijitlik değişimleri, kısmi mekanizma vb. durumların modal yatay yükler üzerindeki etkileri de göz önüne alınabilmektedir. Çalışmada, modal yatay yüklerin hesabı için yeni bir yaklaşım da önerilmektedir. Önerilen yöntem ile yüksek modların etkili olduğu çok katlı betonarme bir bina çerçevesinin analizi yapılmış ve elde edilen sonuçlar, farklı deprem yer hareketi kayıtları için yapılan Lineer Olmayan Dinamik Analiz (LODA) sonuçları referans (kesin çözüm) alınarak birçok parametre ile değerlendirilmiştir. Ayrıca, FEMA 356’da önerilen üç farklı dağılım (birinci mod, SRSS ve üniform dağılım) için de lineer olmayan statik analizler yapılmış ve elde edilen sonuçlar karşılaştırılarak değerlendirmeler yapılmıştır. Buna göre, önerilen yöntemin, FEMA 356’daki prosedürlere göre LODA’e oldukça yakın sonuçlar verdiği belirlenmiştir.

Today, investigations on low-rise irregular buildings, high-rise regular and irregular buildings show that traditional non-linear static (pushover) analysis (T-NSA) procedures based on monotonically increasing lateral loads proportional to first mode or similar shapes are not sufficient in determination of the non-linear seismic behavior. In these buildings, higher modes besides fundamental modes are effective in structural behavior and/or modal properties of the buildings change extremely due to plastification (yielding with pure bending moment or bending moment and axial force) in structural system. Therefore, higher mode effects and/or change of dynamic properties due to plastification in system should be considered in NSA of these buildings. In order to consider these effects, it is stipulated that NSA are performed separately for least two different load distribution (pattern) in FEMA 356 and in Eurocode 8. Thus, consideration of all inertial effects occurred during earthquake are intended in the evaluation of buildings. In addition recently, improved pushover procedures including multi-mode and/or effect of plastification in system on mode shapes (adaptive procedures) have been developed by several researchers in order to overcome the deficiencies of T-NSA procedures. These improved procedures generally utilize from the essentials of traditional response spectrum analysis and use traditional load increment approaches (iterative approximations or step-by-step techniques). In these procedures, determination of formation of plastic sections and change of dynamic properties increase greatly computation process. Furthermore, some mathematical stability problems can arise in application of changing load distribution along the building height due to plastification. For this reasons, development of more effective load increment methods is needed for multi modal and adaptive non-linear static analysis of buildings. In this study, an effective multi modal adaptive load increment method is presented for determination of non-linear behaviour of building type structures under seismic effects. The scope of this study is restricted to plane frame systems. However, essentials of the proposed procedure are general and can be applied to three dimensional systems readily. In the method, lumped plasticity approach is adopted and geometrical non-linearities (second-order effects) are included. Geometrical non-linearity effects between successive plastic sections and non-linear yield conditions of column elements are linearized. Thus, load increment required for determination of the plastic sections can be determined directly without using the iterative or step-by-step techniques. After formation of each plastic section, the higher mode effects are considered by utilizing essentials of the traditional response spectrum analysis at the linearized regions between successive plastic sections. Changing dynamic properties due to plastification in structural system are used on the calculation of modal lateral loads. Thus, effects of stiffness changes and local mechanism at system on lateral load distribution are included. Earthquake characteristics and changes of modal effectiveness due to plastification in structural system are considered by scaling the modal load distributions with the elastic spectral accelerations. Different scaling approximations for modal loads can be used in each step without any mathematical stability problems in the method. In the study, a new approach is also proposed for the determination of modal lateral loads. In order to evaluate the proposed method, a 15 story RC building frame are analyzed by the proposed method, then compared with Non-linear Dynamic Analysis (NDA) results and FEMA 356 Non-linear Static Analysis (NSA) procedures based on fixed loads distributions (first mode, SRSS and uniform distribution) in terms of floor displacements, story drifts, max. beam plastic rotations, story shears and distribution of plastic sections in the system. Three ground motions that have different frequency content are used in the evaluation. At the end of the evaluations taking the NDA results as reference, it is determined that the proposed method yielded generally better results than all FEMA 356 procedures for all the investigated parameters. The first mode distribution in FEMA 356 yield generally good results at the lower stories, but it is not sufficient for determination of the response quantities at the upper stories. The SRSS distribution proposed in FEMA 356 to consider higher mode effects yield generally good results at the upper stories, but it is not sufficient for determination of the response quantities at the mid and lower stories of the frame. The uniform distribution in FEMA 356 is generally not sufficient for determination of the response quantities at all stories of the frame.