Empirical Formula for the Fundamental Period of Reinforced Concrete Moment Resisting Frames in Indonesia
DOI:
https://doi.org/10.5614/jts.2025.32.1.1Keywords:
Vibration period, building height, number of floors, moment-resisting frame, concreteAbstract
Abstract
In dynamic analysis, the vibration period of a structure is recognized as a crucial factor that determines the structural response to earthquakes. The value of the structural vibration period is closely related to the stiffness and mass of a building, both of which are associated with the height and number of floors in the building. This study aims to establish a relationship between the structural vibration period, building height, and the number of floors in Indonesia. This research employs eigenvalue calculations to determine the structural vibration period. The vibration periods of 27 buildings with varying heights and numbers of floors are calculated, followed by statistical analysis to derive an empirical formula for the structural vibration period. The research findings indicate that the obtained vibration period data and resulting equation fall within the range of previous studies that employed direct measurement methods. Furthermore, this study proposes empirical formulas for the structural vibration period developed based on the lower bound of this research's data, offering estimates of conservative design earthquake forces.
Keywords: Vibration period, building height, number of floors, moment-resisting frame, concrete
Abstrak
Di dalam analisis dinamis, periode getar struktur diketahui menjadi faktor penting yang menentukan perilaku struktur terhadap gempa. Nilai periode getar struktur erat kaitannya dengan kekakuan dan massa bangunan, dimana keduanya berhubungan dengan tinggi dan jumlah lantai bangunan. Penelitian ini bertujuan mencari hubungan antara periode getar struktur dengan tinggi dan jumlah lantai bangunan di Indonesia. Penelitian ini menggunakan perhitungan nilai eigen untuk mendapatkan periode getar struktur. Sebanyak 27 bangunan gedung dengan ketinggian dan jumlah lantai yang bervariasi dihitung periode getarnya. Selanjutnya dilakukan analisis statistik untuk mendapatkan rumus empirik periode getar struktur. Hasil penelitian menunjukan bahwa data nilai periode getar dan persamaan yang dihasilkan berada dalam rentang data penelitian sebelumnya yang menggunakan metode pengukuran langsung. Selain itu, penelitian ini mengusulkan rumus empirik periode getar struktur yang dikembangkan berdasarkan batas bawah dari data penelitian ini untuk memberikan perkiraan gaya gempa desain yang konservatif.
Kata-kata kunci: Periode getar, tinggi bangunan, jumlah lantai, rangk a pem ik ul m om en, beton.
References
ASCE. (2016). ASCE 7-16: Minimum Design Loads for Buildings and Other Structures.
CEN. (2004). Eurocode 8: Design of structures for earthquake resistance (Vol. 1, Issue 2004). European Committee for Standardization.
Chatterjee, S., & Hadi, A. S. (2012). Regression Analysis By Example (5th ed.). John Wiley & Sons Inc.
Crowley, H., & Pinho, R. (2004). Period-height relationship for existing European reinforced concrete buildings. Journal of Earthquake Engineering, 8 (May 2014), 93?119. https://doi.org/10.1080/13632460409350522
Ditommaso, R., Lamarucciola, N., & Ponzo, F. C. (2024). Prediction of the fundamental period of infilled RC framed structures considering the maximum inter-story drift at different design limit states. Structures, 63. https://doi.org/10.1016/j.istruc.2024.106422
Gallipoli, M. R., Mucciarelli, M., ?ket-Motnikar, B., Zupan?i?, P., Gosar, A., Prevolnik, S., Herak, M., Stip?evi?, J., Herak, D., Milutinovi?, Z., & Olum?eva, T. (2010). Empirical estimates of dynamic parameters on a large set of European buildings. Bulletin of Earthquake Engineering, 8(3), 593?607. https://doi.org/10.1007/s10518-009-9133-6
Gedam, B. A., Bhandari, N. M., & Upadhyay, A. (2016). Influence of Supplementary Cementitious Materials on Shrinkage, Creep, and Durability of High-Performance Concrete. Journal of Materials in Civil Engineering, 28(4), 04015173. https://doi.org/10.1061/(asce)mt.1943-5533.0001462
Goel, R. K., & Chopra, A. K. (1997). Period Formulas for Moment-Resisting Frame Buildings. Journal of Structural Engineering, 123(11).
Hong, L., & Hwang, W. (2000). Empirical formula for fundamental vibration periods of reinforced concrete buildings in Taiwan. Earthquake Engineering & Structural Dynamics, 29(3), 327?337. https://doi.org/10.1002/(sici)1096-9845(200003)29:3<327::aid-eqe907>3.3.co;2-s
Inqiad, W. Bin, Javed, M. F., Siddique, M. S., Alabduljabbar, H., Ahmed, B., & Alkhattabi, L. (2024). Predicting natural vibration period of concrete frame structures having masonry infill using machine learning techniques. Journal of Building Engineering, 96. https://doi.org/10.1016/j.jobe.2024.110417
Kaplan, O., Guney, Y., & Dogangun, A. (2021). A period-height relationship for newly constructed mid-rise reinforced concrete buildings in Turkey. Engineering Structures, 232(June 2020), 111807. https://doi.org/10.1016/j.engstruct.2020.111807
Kewate, S. P., & Murudi, M. M. (2019). Empirical Period-Height Relationship for reinforced Concrete Moment Resisting Buildings in India. IOP Conference Series: Materials Science and Engineering, 481(1), 1?11. https://doi.org/10.1088/1757-899X/481/1/012018
Kose, M. M. (2009). Parameters affecting the fundamental period of RC buildings with infill walls. Engineering Structures, 31, 93?102.
Michel, C., Guuen, P., Lestuzzi, P., & Bard, P. Y. (2010). Comparison between seismic vulnerability models and experimental dynamic properties of existing buildings in France. Bulletin of Earthquake Engineering, 8(6), 1295?1307. https://doi.org/10.1007/s10518-010-9185-7
Midas IT. (2023). Analysis Manual for Midas Gen. MIDAS Information Technology Co., Ltd.
Oliveira, C. S., & Navarro, M. (2010). Fundamental periods of vibration of RC buildings in Portugal from in-situ experimental and numerical techniques. Bulletin of Earthquake Engineering, 8(3), 609?642. https://doi.org/10.1007/s10518-009-9162-1
Pan, T.-C., Goh, K. S., & Megawati, K. (2014). Empirical relationships between natural vibration period and height of buildings in Singapore. Earthquake Engineering & Structural Dynamics, 43, 449?465. https://doi.org/10.1002/eqe
Paz, M., & Kim, Y. H. (2019). Structural Dynamics: Theory and Computation (6th ed.). Springer.
Salameh, C., Guillier, B., Harb, J., Cornou, C., Bard, P. Y., Voisin, C., & Mariscal, A. (2016). Seismic response of Beirut (Lebanon) buildings: instrumental results from ambient vibrations. Bulletin of Earthquake Engineering, 14(10), 2705?2730. https://doi.org/10.1007/s10518-016-9920-9
Sharma, N., Dasgupta, K., & Dey, A. (2020). Natural period of reinforced concrete building frames on pile foundation considering seismic soil-structure interaction effects. Structures, 27, 1594?1612. https://doi.org/10.1016/j.istruc.2020.07.010
Smith, B. S., & Crowe, E. (1986). Estimating Periods of Vibration of Tall Buildings. Journal of Structural Engineering, 112(5), 1005?1019. https://doi.org/10.1061/(asce)0733-9445(1986)112:5(1005)
UBC. (1997). UBC 97: Structural design requirements (Vol. 2).
