İdeal göçme mekanizması için enerji esaslı yapı taban kesme kuvvetinin belirlenmesi

Abstract

Bu çalışmada, klasik iş-enerji bağıntısı ve yapı için önceden hedeflenen ideal bir göçme mekanizmasının esas alınması ile deprem etkileri altında doğrusal elastik ötesi davranış gösteren betonarme çerçeve türü yapılar için genel enerji denkleminden hareketle taban kesme kuvveti hesaplanmaktadır. Yapısal sönümden dolayı, depremle birlikte yapı sistemlerine giren enerji bir katsayı ile modifiye edilmekte ve enerji denge denklemi değiştirilmiş şekli ile yazılmaktadır. Enerji denkleminde yer alan plastik enerji, yapısal elemanların çevrimsel davranışlarının daha gerçekçi bir şekilde hesaba katılmasının gerekliliğinden, belirlenen bir katsayı ile azaltılmaktadır. Plastik ve giren enerjiler için azaltma faktörleri literatürdeki farklı çalışmaların esas alınması ile belirlenmektedir. Yapı için belirlenen taban plastik dönmesi için yatay dış yükler tarafından yapılan dış iş, Türk Deprem Yönetmeliği’ndeki eşdeğer statik yatay yük dağılımının dikkate alınması ile hesaplanmaktadır. Plastik enerji ifadesi ile dış iş ifadelerinin eşitlenmesi sonucunda enerji esaslı taban kesme kuvvetlerini veren denklemler, farklı azaltma faktörleri için türetilmektedir. Enerji esaslı tasarım taban kesme kuvveti değerleri dört ve yedi katlı betonarme çerçeve yapılar için hesaplanmaktadır. Aynı çerçeveler için Z2 yerel zemin sınıfına ait elastik tasarım ivme spektrumuna uyumlu olacak şekilde ölçeklenen deprem ivme kayıtları ile gerçekleştirilen zaman tanım alanında doğrusal olmayan analizlerden elde edilen en büyük taban kesme kuvvetlerinin ortalaması enerji esaslı taban kesme kuvvetleri ile karşılaştırılmakta ve sonuçlar yorumlanmaktadır

Keywords

• İdeal göçme mekanizması, enerji denge denklemleri, plastik enerji, enerji esaslı taban kesme kuvveti, zaman tanım alanında doğrusal olmayan analiz

Determination of energy-based base shear for global collapse mechanism

Abstract

Depending upon different geophysical and structural factors, earthquakes cause several damages to buildings. The duration and the magnitude of the ground motion, soil type or fault properties may affect the structural damage. However, the most important parameter for the damage is to build structures poorly engineered. Even though there may exist moderate, heavy or major damages on structures under seismic effects, the crucial aspect for structural engineering is to prevent the total collapse. Therefore, when new structures are designed the yield mechanism of structures under seismic effects should be considered in detail. A nonlinear static procedure to estimate base shears of reinforced concrete frame structures is presented in the study considering global collapse state and energy concepts. Since global failure mechanism, where plastic hinges occur at beam ends and column bases, is a preferable collapse mode for structures under seismic effects to prevent the total collapse, this type of failure mechanism is targeted at the beginning of derivation of equations. Given the preselected failure mechanism, the energy-balance equality is written for frames. Earthquake resistant structural design procedures in current seismic design codes are traditionally strength-based and direct displacement-based. The strength and displacement capacity of structural members are not desired to be less than seismic demands of earthquakes in these procedures. However, energy-based structural design which considers the earthquake as an energy input to structures may be a more rational approach. In energy-balance equality written for frames, the seismic input energy and plastic energy is modified with a factor. Input energy is modified due to structural damping and the energy which contributes to structural damage is considered in the equality. The plastic energy is decreased with a factor, too, to consider the reduced hysteretic properties. The reduction factors are obtained from literature which are expressed by former researchers. Four different factors are considered and sixteen different base shear forces are obtained for RC frames by taking combinations of these factors. Plastic target drift needs to be estimated while the energy balance equality is set up. It can be obtained from the difference of maximum drift between the yield drift for the structure. For the probability level of exceedance 10% in fifty years period, the maximum story drift ratio is suggested as 2% for the design earthquake within the study. This is the performance criteria of the considered procedure. Selecting a suitable post-yield stiffness ratio is an important issue for performance-based structural design. The appropriate post-yield stiffness ratios for structural members are selected for calculation of energy-based base shears. From literature and experimental studies, the post-yield stiffness ratio is assumed as 0.10 for RC members. Seven real earthquake records, which are scaled in time domain according to the Z2 type soil class, are chosen to perform nonlinear time history analyses of four- and seven-story RC frames. The maximum base shear forces are compared with the results of the energy-based method. It can be seen from the study that the energy-based base shears are directly proportional with the input energy modification factor and inversely proportional with the plastic energy modification factor. Proportions of plastic and input energy modification factors are obtained very close to proportions of base shear forces, which are calculated by using these modification factors. Design base shear forces in current seismic codes are generally calculated for a constant displacement ductility of structures. Therefore, hysteretic behaviors of structural members and hysteretic damping are not included directly in these type of calculations. However, in this study, the design base shear forces for structures are obtained from energy balance concept and nonlinear properties of structural members are considered more detailed.

Keywords

• Failure mechanism, energy-balance equality, plastic energy, energy-based base shear force, RC frame.