Examination of Two Distinct Integration Techniques Used in Pseudo-Dynamic Test Method by Means of Experimental and Numerical Studies

Abstract

Experimental techniques are of great importance in determination of earthquake behavior of structures and structural members. Structural behavior could be determined by means of quasi-static tests in which prescribed displacement protocols are applied, by real time shake table tests realized with real acceleration records or by pseudo-dynamic tests in which experimental and numerical simulation efforts work together. In pseudo-dynamic test, the reactional forces measured from test specimen (stiffness matrix) are utilized for the numerical solution of dynamic equilibrium equation and for the determination of target displacement vector to be applied to test specimen in the next step. In pseudo-dynamic test method, the through interaction of the analytical and experimental parts is very effective on the success. For the success of the test; in addition to the sensitivity of the measuring devices used, the stability of the numerical integration technique to be used in the solution of the dynamic equilibrium equation is also of great importance. In order to ensure the stability of the numerical integration, the selected time interval should be small enough. In this study, the central difference method (CDM) and linear acceleration-based force separation method (Li-OSM) used as a numerical integration tool in pseudo-dynamic test method are compared with numerical and experimental studies. The performed numerical studies; regardless of the constitutive model used, showed that Li-OSM method produces more stable results than CDM method in the case of the integration step interval selected up to half of the earthquake record interval. From the experimental studies; instead of using “quarter” integration step interval in CDM method, it was concluded that in case of using “half” integration step interval in Li-OSM method, the total testing time will decrease by half and the stability of the test will increase.

Keywords

• Pseudo-dynamic test method
• Central difference method
• Linear acceleration-based operator splitting method
• Dynamic equilibrium equation
• Numerical integration

Benzeşik Dinamik Deney Tekniğinde Kullanılan iki Farklı İntegrasyon Tekniğinin Deneysel ve Sayısal Çalışmalar ile İrdelenmesi

Abstract

Yapı sistemlerinin ve yapı elemanlarının deprem etkisindeki davranışlarının belirlenmesinde, deneysel yöntemler çok önemlidir. Yapısal davranış; öngörülen bir yerdeğiştirme protokolü etkisinde gerçekleştirilen statik karakterli deneyler ile ivme kayıtlarının kullanılabildiği gerçek zamandaki sarsma masası deneyleri ile ya da analitik çözümlerin etkileşimli olarak gerçekleştirildiği statik karakterli benzeşik dinamik deneyler ile belirlenebilmektedir. Benzeşik dinamik deneyde, numuneden ölçülen reaksiyon kuvvetleri (rijitlik matrisi) dinamik denge denkleminin çözümünde ve bir sonraki deney adımında numuneye etkitilecek hedef yerdeğiştirme vektörünün hesabında kullanılmaktadır. Benzeşik dinamik deney tekniğinde, analitik ve deneysel bölümlerin doğru etkileşimi deneyin başarısı üzerinde çok etkilidir. Deneyin başarısı için; kullanılan ölçüm cihazlarının hassasiyeti yanında dinamik denge denkleminin çözümünde kullanılacak sayısal integrasyon yönteminin kararlılığı da büyük önem taşımaktadır. Sayısal hesapta kararlılık sağlanabilmesi için, integrasyon için seçilen hesap adım aralığının yeterli düzeyde küçük olması gerekmektedir. Bu çalışmada, benzeşik dinamik deney metodunda sayısal integrasyon aracı olarak kullanılan merkezi farklar yöntemi (CDM) ile lineer ivme tabanlı kuvvet ayırımı yöntemi (Li-OSM) sayısal ve deneysel çalışmalar ile karşılaştırılmıştır. Gerçekleştirilen sayısal çalışmalar; davranış modelinden bağımsız olarak, deprem kaydı adım aralığının yarısı kadar seçilen hesap adım aralığı durumunda, Li-OSM yönteminin CDM yöntemine göre daha kararlı sonuçlar ürettiğini göstermiştir. Deneysel çalışmalardan; CDM yönteminde “dörtte birlik” hesap adım aralığı ile çalışmak yerine, Li-OSM yönteminde “yarım” hesap adım aralığının kullanımı durumunda, toplam deney süresinin yarıya düşeceği ve deneyin kararlılığının artacağı sonucuna ulaşılmıştır.

Keywords

• Benzeşik dinamik deney tekniği
• Merkezi farklar yöntemi
• Lineer ivme yöntemi tabanlı kuvvet ayırımı metodu
• Dinamik denge denklemi
• Sayısal integrasyon

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