Abstract:In energy-based seismic design approach, earthquake ground motion is considered as an energy input to structures. The earthquake input energy is the total of energy components such as kinetic energy, damping energy, elastic strain energy and hysteretic energy, which contributes the most to structural damage. In literature, there are many empirical formulas based on the hysteretic model, damping ratio and ductility in order to estimate hysteretic energy, whereas they do not directly consider the ground motion characteristics. This paper uses nonlinear time history (NLTH) analysis for energy calculations and presents the distribution of earthquake input energy and hysteretic energy of single-degree-offreedom (SDOF) systems over the ground motion duration. Seven real earthquakes recorded on the same soil profile and three different bilinear SDOF systems having constant ductility ratio and different natural periods are selected to perform NLTH analyses. As results of nonlinear dynamic analyses, input and hysteretic energies per unit masses are graphically obtained. The hysteretic energy to input energy ratio (EH/EI) is investigated, as well as the ratio of other energy components to energy input. EH/EI ratios of NLTH analysis are compared to the results of empirical approximations related EH/EI ratio and a reasonable agreement is observed. The average of EH/EI ratio is found to be between 0.468 and 0.488 meaning nearly half of the earthquake energy input is dissipated through the hysteretic behavior.
ÖZETGerçek malzeme davranışları esas alınarak veya deneysel yoldan elde edilen eğilme momenti-eğrilik ilişkisi yardımıyla kesitlerin elastik ötesi davranışı ile ilgili birçok soruya cevap bulunabilmektedir. Kesit akma eğriliğinden en büyük eğrilik değerine kadar olan eğilme momenti-eğrilik grafiğinin alanı, elastik ötesi davranışta kesitte tüketilen enerjiyi ifade etmektedir. Tüketilen enerjideki artış kesit sünekliğindeki artışa da karşılık gelmektedir. Bu çalışma kapsamında, monotonik yükleme altındaki betonarme kesitlerin doğrusal olmayan davranışta tükettikleri enerji hesaplanmış ve kesit enerji tüketimlerine boyuna donatı oranının, enine donatı adım aralığının ve eksenel yükün etkisi araştırılmıştır. Seçilen betonarme kesitlerde pratikteki mühendislik uygulamalarında sıkça karşılaşılan farklı boyuna donatı oranları, farklı sargı donatısı aralıkları ve farklı eksenel yükler için eğilme momenti-eğrilik ve enerji analizleri gerçekleştirilmiştir. Enerji tüketimi açısından enine donatı adım aralığı ile kesit sünekliği arasında ters orantılı bir ilişki olduğu, eksenel yükteki artışın genel olarak sünekliği azalttığı ve betonarme elemandaki enerji tüketiminin eksenel yükteki artışla birlikte azaldığı sonucu elde edilmiştir.Anahtar Kelimeler: Boyuna donatı oranı, sargı donatısı aralığı, eksenel yük, enerji tüketimi, süneklik
EFFECTS OF LONGITUDINAL REINFORCEMENT RATIO, TRANSVERSE REINFORCEMENT SPACING AND AXIAL LOAD ON THE INELASTIC ENERGY CONSUMPTION OF REINFORCED CONCRETE SECTIONS ABSTRACTMany questions about nonlinear behavior of RC sections can be answered by the help of moment-curvature relations which can be obtained from experimental ways or theoretical approach by considering material stressstrain curves. Area of the moment-curvature relation of the section from yield curvature to ultimate curvature expresses the inelastic energy consumption of the section in its unit length. Increase in inelastic energy consumption of the section corresponds to the increase in ductility of the section with the same time. Within the scope of this study, the inelastic energy consumption of RC sections under monotonic loading is calculated and the effect of longitudinal reinforcement ratio, transverse reinforcement spacing and axial load of the section to the inelastic energy consumption is researched analytically. Moment-curvature and inelastic energy consumption analyses of the RC sections which are frequently used in engineering applications are performed for different longitudinal reinforcement ratios, different transverse reinforcement spacing's and different axial loads. It is obtained from the study that there is inversely proportional relation between transverse reinforcement spacing and inelastic energy consumption of the section. Increase in axial load of the section decreases the section ductility and energy consumption of the section and this result can be seen from the inelastic energy
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