Study on Natural Frequency of Frame Structures

Document Type : Research Note

Authors

1 Department of Civil Engineering, Pabna University of Science & Technology (PUST), Pabna-6600, Bangladesh

2 Department of Civil Engineering, Rajshahi University of Engineering & Technology (RUET), Rajshahi-6204, Bangladesh

Abstract

Moment resisting frame (MRF) structures are gaining popularity for their high lateral stiffness. This study investigates the parameters which affecting the natural frequency of moment resisting frame structures. Steel and concrete MRF structures were studied theoretically, analyzed numerically to obtain their mode shapes and frequency of vibration for each mode. From the theoretical and analytical results, a model equation for approximation of natural frequency of these types of MRF structures is proposed. The proposed model expressed the relationship of natural frequency of MRF structure with its total mass, lateral dimension in the direction of vibration and total height. The proposed equation will be helpful and easy to calculate the fundamental frequency for study on dynamic behavior of structures. Comparison between the current guidelines and proposed model is also discussed. The proposed model is satisfying the general concept of free vibrational response, and can be applied for analyzing small and full scale structures. 

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[1]      Al-Aasam HS, Mandal P. Simplified Procedure to Calculate by Hand the Natural Periods of Semirigid Steel Frames. J Struct Eng 2013;139:1082–7. doi:10.1061/(ASCE)ST.1943-541X.0000695.
[2]      El-saad MNA, Salama MI. Estimation of period of vibration for concrete shear wall buildings. HBRC J 2017;13:286–90. doi:10.1016/j.hbrcj.2015.08.001.
[3]      Gaile L, Tirans N, Velicko J. Evaluation of Highrise Building Model Using Fundamental. 4th Int. Conf. Civ. Eng. 2013, Proc. Part I, Struct. Eng., 2013, p. 15–20.
[4]      Rezaee M, Yam GF, Fathi R. Development of “modal analysis free vibration response only” method for randomly excited systems. Acta Mech 2015;226:4031–42. doi:10.1007/s00707-015-1467-3.
[5]      Alavi A, Rahgozar R, Torkzadeh P, Hajabasi MA. Optimal design of high-rise buildings with respect to fundamental eigenfrequency. Int J Adv Struct Eng 2017;9:365–74. doi:10.1007/s40091-017-0172-y.
[6]      Karakale V. Use of Structural Steel Frames for Structural Restoration of URM Historical Buildings in Seismic Areas. J Earthq Tsunami 2017;11:1750012. doi:10.1142/S1793431117500129.
[7]      AlHamaydeh M, Abdullah S, Hamid A, Mustapha A. Seismic design factors for RC special moment resisting frames in Dubai, UAE. Earthq Eng Eng Vib 2011;10:495–506. doi:10.1007/s11803-011-0084-y.
[8]      Asteris PG, Repapis CC, Tsaris AK, Di Trapani F, Cavaleri L. Parameters affecting the fundamental period of infilled RC frame structures. Earthquakes Struct 2015;9:999–1028. doi:10.12989/eas.2015.9.5.999.
[9]      Oliveira CS, Navarro M. Fundamental periods of vibration of RC buildings in Portugal from in-situ experimental and numerical techniques. Bull Earthq Eng 2010;8:609–42. doi:10.1007/s10518-009-9162-1.
[10]    Asteris PG, Repapis CC, Repapi E V., Cavaleri L. Fundamental period of infilled reinforced concrete frame structures. Struct Infrastruct Eng 2017;13:929–41. doi:10.1080/15732479.2016.1227341.
[11]     Aghayari R, Ashrafy M, Tahamouli Roudsari M. Estimation the base shear and fundamental period of low-rise reinforced concrete coupled shear wall structures. Asian J Civ Eng 2017;18:547–66.
[12]    Guminiak M. Free vibrations analysis of thin plates by the boundary element method in non-singular approach. Pr Nauk Inst Mat i Inform Politech Częstochowskiej 2007;6:75–90.
[13]    Nilesh VP, Desai AN. Effect of height and number floors to natural time period of a multi- storey building. Int J Emerg Technol Adv Eng 2012;2.
[14]    Lengvarský P, Bocko J, Hagara M. Modal Analysis of Titan Cantilever Beam Using ANSYS and SolidWorks. Am J Mech Eng 2013;1:271–5. doi:10.12691/ajme-1-7-24.
[15]    Christopher Arnold. Chapter 4 - Earthquake Effects on Buildings. Des. Earthquakes A Man. Archit. | FEMA.gov, 2006.
[16]    Goel RK, Chopra AK. Period Formulas for Moment-Resisting Frame Buildings. J Struct Eng 1997;123:1454–61. doi:10.1061/(ASCE)0733-9445(1997)123:11(1454).
[17]    FEMA. 310-Handbook for seismic evaluation of buildings- A pre-standard. 1998.
[18]    IS1893:2002. Part 1: Criteria for earthquake resistant design of structures, general provisions and buildings. 2002.
[19]    BNBC. Bangladesh National Building Code. Hous Build Res Inst 2014;Part 6(2).
[20]    Naeim F. Dynamics of structures: Theory and applications to earthquake engineering, 2nd edition. Earthq Spectra 2001;17:549. doi:10.1193/1.1586188.
[21]    Beer FP (Ferdinand P. Mechanics of materials. McGraw-Hill Higher Education; 2009.
[22]    Sandra Brown. Seismic analysis and shake table modeling: using a shake table for building analysis. University of Southern California; 2007.
[23]    Christovasilis IP, Filiatrault A, Wanitkorkul A. Seismic testing of a full-scale wood structure on two shake tables. 14th World Conf. Earthq. Eng., Beijing, China: 2008.
[24]    Tiziano S, Daniele C, Roberto T, Maurizio P. Shake table test on 3-storey light-frame timber building. World Conf. Timber Eng., Auckland, No. 77, I-38123: 2012.
[25]    Kim S-E, Lee D-H, Ngo-Huu C. Shaking table tests of a two-story unbraced steel frame. J Constr Steel Res 2007;63:412–21. doi:10.1016/j.jcsr.2006.04.009.
[26]    Siddika A, Awall MR, Mamun MA Al, Humyra T. Free vibration analysis of steel framed structures. J Rehabil Civ Eng 2019;7:70–8. doi:10.22075/jrce.2018.12830.1224.
[27]    Ghaffarzadeh H, Talebian N, Kohandel R. Seismic demand evaluation of medium ductility RC moment frames using nonlinear procedures. Earthq Eng Eng Vib 2013;12:399–409. doi:10.1007/s11803-013-0181-1.
[28]    Srinivasan R, Suresh Babu S, Itti S V. A study on performance of 3D RC frames with masonry in-fill under dynamic loading conditions. KSCE J Civ Eng 2017;21:322–8. doi:10.1007/s12205-016-0537-y.
[29]    Liu S, Warn GP, Berman JW. Estimating Natural Periods of Steel Plate Shear Wall Frames. J Struct Eng 2013;139:155–61. doi:10.1061/(ASCE)ST.1943-541X.0000610.
[30]    Tomasiello S. A Simplified Quadrature Element Method to compute the natural frequencies of multispan beams and frame structures. Mech Res Commun 2011;38:300–4. doi:10.1016/j.mechrescom.2011.04.002.
[31]    Zalka K. A simplified method for calculation of the natural frequencies of wall–frame buildings. Eng Struct 2001;23:1544–55. doi:10.1016/S0141-0296(01)00053-0.