Deprem Etkisindeki TSD Yapılarda Histeretik Enerji Talebi: Analitik ve Ampirik Sonuçlar

Enerjiye dayalı sismik tasarımda deprem yer hareketi yapılara enerji girişi olarak dikkate alınmaktadır. Sisteme giren enerji kinetik enerji, sönüm enerjisi, elastik şekil değiştirme enerjisi ve histeretik enerji şeklindeki bileşenlerin toplamı olup histeretik enerji doğrudan yapısal hasar ile ilişkilidir. Literatürde histeretik enerjinin belirlenmesine yönelik histeretik modeli, sönüm oranını ve sünekliği esas alan çok sayıda ampirik bağıntı vardır. Buna karşın bu bağıntılar yer hareketinin özelliklerini dikkate almamaktadır. Bu çalışmada, enerjilerin hesabı için zaman tanım alanında doğrusal elastik olmayan analiz kullanılmış ve tek serbestlik dereceli (TSD) sisteme giren deprem enerjisi ile histeretik enerjinin yer hareketi süresi boyunca değişimi incelenmiştir. Dinamik analizlerde aynı zeminler üzerinde kaydedilmiş yedi adet yer hareketi ve farklı süneklik oranları ve doğal periyotları bulunan üç adet bilineer TSD sistem kullanılmıştır. Doğrusal olmayan dinamik analizlerin sonucunda birim kütle başına enerji girişi ve histeretik enerji grafiksel olarak elde edilmiştir. Histeretik enerji/toplam enerji oranı (EH/EI) ile diğer enerji bileşenlerinin giren enerjiye oranı araştırılmıştır. Doğrusal olmayan dinamik analizlerden elde edilen EH/EI oranları ile ampirik yaklaşımlara ait oranlarla karşılaştırılmış ve tutarlı sonuçlar elde edilmiştir. Ortalama EH/EI oranı 0.468 ile 0.488 arasında değişmektedir ki bu da toplam enerji girdisinin yarısına yakın kısmının doğrusal olmayan davranış yoluyla tüketildiğini göstermektedir.

Hysteretic Energy Demand in SDOF Structures Subjected to an Earthquake Excitation: Analytical and Empirical Results

In energy-based seismic design approach, earthquake ground motion isconsidered as an energy input to structures. The earthquake input energy is thetotal of energy components such as kinetic energy, damping energy, elastic strainenergy and hysteretic energy, which contributes the most to structural damage. Inliterature, there are many empirical formulas based on the hysteretic model,damping ratio and ductility in order to estimate hysteretic energy, whereas theydo not directly consider the ground motion characteristics. This paper usesnonlinear time history (NLTH) analysis for energy calculations and presents thedistribution of earthquake input energy and hysteretic energy of single-degree-offreedom(SDOF) systems over the ground motion duration. Seven real earthquakesrecorded on the same soil profile and three different bilinear SDOF systems havingconstant ductility ratio and different natural periods are selected to perform NLTHanalyses. As results of nonlinear dynamic analyses, input and hysteretic energiesper unit masses are graphically obtained. The hysteretic energy to input energyratio (EH/EI) is investigated, as well as the ratio of other energy components toenergy input. EH/EI ratios of NLTH analysis are compared to the results ofempirical approximations related EH/EI ratio and a reasonable agreement isobserved. The average of EH/EI ratio is found to be between 0.468 and 0.488meaning nearly half of the earthquake energy input is dissipated through thehysteretic behavior.

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