A Study on Shear Frame Structure by Modal Superposition Method

A Study on Shear Frame Structure by Modal Superposition Method

© 2023 by IJETT Journal
Volume-71 Issue-2
Year of Publication : 2023
Author : Dharmesh N, L. Govindaraju
DOI : 10.14445/22315381/IJETT-V71I2P247

How to Cite?

Dharmesh N, L. Govindaraju, "A Study on Shear Frame Structure by Modal Superposition Method," International Journal of Engineering Trends and Technology, vol. 71, no. 2, pp. 457-465, 2023. Crossref, https://doi.org/10.14445/22315381/IJETT-V71I2P247

The current study uses a normal mode to transform the coupled differential equation system into a set of uncoupled differential equations. As a result, the modal superposition method reduces the problem of determining the response of a multi-degree-of-freedom system to that of a single-degree-of-freedom system. The undamped multi-degrees-of-freedom system is analyzed using free modal vibrations. To determine the natural frequencies, mode shapes, time period, modal mass contribution, and mode participation factors of structures under free vibrations. Two cases are considered in the present study, first a single-storey, single-degree-of-freedom system (SDOF) & second case, a three-dimensional three-storey multi-degree of freedom (MDOF) building modeled as a shear building, idealized as a lumped spring-mass model. Modal analysis of shear frames for single and multi degrees of freedom (MDOF) structures are studied. The results are compared first theoretically, secondly by MATLAB program, and finally by ETABS software. The first case is a single-storey reinforced concrete 2D frame of 6m wide and 3m high & the dimension of each column and the beam is 300 mm square section. In the second case, a threedimensional three-storey is considered. The effective length of the beam in the X-direction is 3.6m and 4.7m along the Y-direction, and the column's height is 3m. The effective slab thickness is 120mm, and the grade of concrete fck=25N/mm2

ETABS, Lumped mass model, MATLAB, Mode period, Natural frequency.

[1] Anil K. Chopra, Dynamics of Structures–Theory and Applications to Earthquake Engineering, Eastern Economy Edition, Prentice Hall of India, New Delhi, 2002.
[2] Alvar M. Kabe, “Stiffness Matrix Adjustment Using Mode Data,” AIAA Journal, vol. 23, no. 9, pp. 1431-1436, 1985. Crossref, https://doi.org/10.2514/3.9103
[3] Aditya Raut, and D. N Kakade, "Study the Behaviour of G+36 Multistorey Building With and Without Transfer Slab Using Etabs & Safe," SSRG International Journal of Civil Engineering, vol. 9, no. 7, pp. 35-43, 2022. Crossref, https://doi.org/10.14445/23488352/IJCE-V9I7P106
[4] F. Garces et al., “Stiffness Identification of Framed Models under Controlled Damage,” 14th World Conference on Earthquake Engineering,China, 2008.
[5] I.S 1893, Part-1, Criteria for Earthquake Resistant Design of Structures, General Provisions and Buildings (Sixth Revision), 2016.
[6] Mario Paz, and Young-Hoon Kim, Structural Dynamics–Theory and Computation, Sixth Edition, Springer Nature Switzerland, 2019.
[7] Dhananjay Shrivastava, and Dr. Sudhir Singh Bhaduria, "Analysis of Multi-Storey RCC Frames of Regular and Irregular Plan Configuration Using Response Spectrum Method," SSRG International Journal of Civil Engineering, vol. 4, no. 6, pp. 70-78, 2017. Crossref, https://doi.org/10.14445/23488352/IJCE-V4I6P112
[8] Mohsen Shahrouzi, “A Quick Method for Eigenvalue Estimation of Multistorey Buildings,” 13th World Conference on Earthquake Engineering, Vancouver, 2004.
[9] Pankaj Agarwal, and Manish Shrikhande, Earthquake Resistant Design of Structures, Prentice-Hall of India, Private Limited, New Delhi, 2006.
[10] Nwofort.C., and Obianime, Tamunoene Sunday, "Stiffness Modifications for Vibration Solutions of Multistory Frames (An Approach From Buckling to Vibration)," SSRG International Journal of Civil Engineering, vol. 6, no. 1, pp. 25-36, 2019. Crossref, https://doi.org/10.14445/23488352/IJCE-V6I1P105
[11] Xianyue Gang L Li, and S Chai Li, “Fixed Boundary Mode Superposition Method for the Dynamic Analysis of Base Motion Excited Structures,” Journal of Mechanical Engineering, vol. 52, no. 13, pp. 87-93, 2016. Crossref, https://doi.org/10.3901/JME.2016.13.087
[12] Kavan S. Mistry, Snehal V. Mevada, and Darshana R. Bhatt, "Vibration Control of Building with Passive Tuned Liquid Column Damper," SSRG International Journal of Civil Engineering, vol. 8, no. 5, pp. 1-15, 2021. Crossref, https://doi.org/10.14445/23488352/IJCE-V8I5P101
[13] Xin Zhang et al., “Performance Assessment of Moment Resisting Frames during Earthquakes Based on Force Analogy Method,” Engineering Structures, vol. 29, no. 10, pp. 2792-2802, 2007. Crossref, https://doi.org/10.1016/j.engstruct.2007.01.024
[14] Gopal Dabhi, Vimlesh V. Agrawal, and Vishal B. Patel, "Soil Structure Interaction for Basement System of Multistorey Building for Different Soil Condition Using Static Analysis in Etabs," SSRG International Journal of Civil Engineering, vol. 7, no. 6, pp. 71-79, 2020. Crossref, https://doi.org/10.14445/23488352/IJCE-V7I6P109
[15] Ayesha Siddika et al., “Study on the Natural Frequency of Frame Structures,” Computational Engineering and Physical Modeling, vol. 2, no. 6, pp. 36-48, 2019. Crossref, https://doi.org/10.22115/cepm.2019.183201.1062
[16] Mohammed Siraj, “Modal Analysis of Plane Frames,” International Journal of Engineering Research & Technology (IJERT), vol. 1, no. 7, 2012.
[17] Vikhyati J. Zaveri et al., "Seismic Vibration Control of Non-Structural Elements Using Dampers," SSRG International Journal of Civil Engineering, vol. 8, no. 5, pp. 21-34, 2021. Crossref, https://doi.org/10.14445/23488352/IJCE-V8I5P103
[18] S. Rajasekaran, Structural Dynamics of Earthquake Engineering–Theory and Application Using Mathematica and Matlab, Woodhead Publishing Limited and CRC Press LLC, 2009.
[19] Edward L.Wilson, Three Dimensional Static and Dynamic Analysis of Structures - A Physical Approach with Emphasis on Earthquake Engineering, 3rd Edition, Computer and Structures Inc., Berkeley, CA, 2002