Extending the Response Spectrum Method for the General Case of Spatial Integrated Seismic Load
Abstract
The response spectrum method (RSM) is the most commonly used technique for seismic design of structures. However, the description of this method that is given in dedicated literature applies in the majority of cases to analysis arrangements involving a diagonal matrix of masses and for horizontal seismic ground motions. The aim of this article is to show the possibility of applying the RSM to the most general case of spatial integrated ground motion, which includes three translational and three rotational components, and for arbitrary analysis structures. The integrated seismic load is specified in the form of a six-component vector of ground motion averaged over the ground volume under the structure. The seismic load intensity is defined as the maximum value of the seismic load vector modulus. The article presents the spectral method theory, the essence of which lies in the following. The equations of relative motion written in the space of main coordinates are solved; a quasistatic approach is used taking into account spectral dynamic amplification factors; the seismic force directions are determined from the condition of maximum dynamic response corresponding to each natural vibration mode; and expressions for the modal internal forces written in compact matrix form are derived (in so doing, it is assumed that the inertia matrix is not necessarily a diagonal one). An example of calculating the dynamic response for a simple spatial model using the RSM is given. A rigid plate resting on four columns having different stiffness values and subjected to a two-component seismic load is considered. The modal and full calculated forces along each generalized coordinate are obtained taking into account the dangerous directions of seismic ground motion.
References
2. Trifunac M.D. Biot Response Spectrum // Ibid. Pp. 491—500.
3. Завриев К.С. Динамика сооружений. Тбилиси: Трансжелдориздат, 1946.
4. Назаров А.Г. Метод инженерного анализа сейсмических сил. Ереван: Изд-во АН АрмССР, 1959.
5. Корчинский И.Л. Колебания высотных зданий. М.: Гос. изд-во литературы по строительству и архитектуре, 1953.
6. Назаров Ю.П. Аналитические основы расчета сооружений на сейсмические воздействия. М.: Наука, 2010.
7. Nazarov Y.P., Poznyak E.V., Filimonov A.V. Seismic Data Analysis in Odyssey Software // Int. J. of Emerging Technologies in Computational and Appl. Sci. 2014. V. 7. No. 4. Pp. 114—115.
8. Назаров Ю.П., Позняк Е.В. Оценка ротационных компонент сейсмического движения грунта // Основания, фундаменты и механика грунтов. 2015. № 6. C. 22—26.
9. Nazarov Yu.P., Poznyak E.V., Filimonov A.V. Earthquake Eng. 2015. V. 71. Pp. 31—41.
10. Назаров Ю.П., Позняк Е.В. Определение коэффициента динамичности в расчетах на сейсмостойкость [Электронный ресурс]. http://www.nso-journal.ru (дата обращения 25.04.2016).
11. Назаров Ю.П, Позняк Е.В. О пространственной изменчивости сейсмических движений грунта при расчете сооружений // Основания, фундаменты и механика грунтов. 2014. № 5. C. 17—20
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Для цитирования: Позняк Е.В., Новикова О.В. Обобщение линейно-спектрального метода для общего случая пространственного интегрального сейсмического воздействия // Вестник МЭИ. 2017. № 4. С. 28—35. DOI: 0.24160/1993-6982-2017-4-28-35.
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1. Trifunac M.D. Brief history Of Computation Of Earthquake Response Spectra. Soil Dynamics and Earthquake Eng. 2006;26;6—7:501—508.
2. Trifunac M.D. Biot Response Spectrum. Ibid:491—500.
3. Zavriev K.S. Dinamika Sooruzhenii. Tbilisi: Transzheldorizdat, 1946. (in Russian).
4. Nazarov A.G. Metod Inzhenernogo Analiza Seismicheskikh Sil. Erevan: Izd-vo AN Arm SSR, 1959. (in Russian).
5. Korchinskii I.L. Kolebaniia Vysotnykh Zdanii. M.: Gos. Izd-Vo Literatury po Stroitelstvu i Arkhitekture, 1953. (in Russian).
6. Nazarov Yu.P. Analiticheskie Osnovy Rascheta Sooruzhenii na Seismicheskie Vozdeistviia. M.: Nauka, 2010. (in Russian).
7. Nazarov Y.P., Poznyak E.V., Filimonov A.V. Seismic Data Analysis in Odyssey Software. Int. J. of
Emerging Technologies in Computational and Appl. Sci. 2014;7;4:114—115.
8. Nazarov Iu.P., Pozniak E.V. Otsenka Rotatsionnykh Komponent Seismicheskogo Dvizheniia Grunta. Osnovaniia, Fundamenty i Mekhanika Gruntov. 2015;6:22—26. (in Russian).
9. Nazarov Yu.P., Poznyak E.V., Filimonov A.V. A Brief Theory and Computing of Seismic Ground Rotations for Structural Analyses. Soil Dynamics and Earthquake Eng. 2015;71:31—41.
10. Nazarov Iu.P., Pozniak E.V. Opredelenie Koeffitsienta Dinamichnosti v Raschetakh na Seismostoikost [Elektron. Resurs] http://www.nso-journal.ru. (Data Obrashcheniia 25.04.2016). (in Russian).
11. Nazarov Iu.P, Pozniak E.V. O Prostranstvennoi Izmenchivosti Seismicheskikh Dvizhenii Grunta pri Raschete Sooruzhenii. Osnovaniia, Fundamenty i Mekhanika gruntov. 2014;5:17—20. (in Russian).
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For citation: Poznyak E.V., Novikova O.V. Extending the Response Spectrum Method for the General Case of Spatial Integrated Seismic Load. MPEI Vestnik. 2017; 4: 28—35. (in Russian). DOI: 10.24160/1993-6982-2017-4-28-35.
