Theoretical Modal Analysis of Freely and Simply Supported RC Slabs

This paper focuses on the dynamic behavior of
reinforced concrete (RC) slabs. Therefore, the theoretical modal
analysis was performed using two different types of boundary
conditions. Modal analysis method is the most important dynamic
analyses. The analysis would be modal case when there is no external
force on the structure. By using this method in this paper, the effects
of freely and simply supported boundary conditions on the
frequencies and mode shapes of RC square slabs are studied. ANSYS
software was employed to derive the finite element model to
determine the natural frequencies and mode shapes of the slabs.
Then, the obtained results through numerical analysis (finite element
analysis) would be compared with the exact solution. The main goal
of the research study is to predict how the boundary conditions
change the behavior of the slab structures prior to performing
experimental modal analysis. Based on the results, it is concluded
that simply support boundary condition has obvious influence to
increase the natural frequencies and change the shape of the mode
when it is compared with freely supported boundary condition of
slabs. This means that such support conditions have the direct
influence on the dynamic behavior of the slabs. Thus, it is suggested
to use free-free boundary condition in experimental modal analysis to
precisely reflect the properties of the structure. By using free-free
boundary conditions, the influence of poorly defined supports is
interrupted.

• M. S. Ahmed
• F. A. Mohammad

• Natural frequencies
• Mode shapes
• Modal analysis
• ANSYS software
• RC slabs.

[1] S.C. Dutta, and P. Mukhopadhyay, Improving Earthquake and Cyclone
Resistance of Structures: Guidelines for the Indian Subcontinent”, TERI,
New Delhi, 2011.
[2] A. E., Abdelnaby, Multiple Earthquake Effects ON Degrading
Reinforced Concrete Structures. A thesis submitted for the Degree of
Doctor of Philosophy in Civil Engineering in the Graduate College,
University of Illinois at Urbana-Champaign, 2012.
[3] S. N. Mokhatar, and R. Abdullah, Computational Analysis of Reinforced
Concrete Slabs Subjected to Impact Loads. International Journal of
Integrated Engineering, vol. 4, Issue 2, 2012, pp. 70-76.
[4] S. N. Mokhatar, Y. Sonoda, and , Z. M. Jaini, Nonlinear Simulation of
Beam Elements Subjected to High Mass Low Velocity Impact Loading
using the Smoothed Particle Hydrodynamics (SPH) Method.
International Journal of Integrated Engineering, vol. 5, Issue 2, 2013, pp.
37-42.
[5] T. Kabeyasawa, H. Shiohara, S. Otani, and H. Aoyama, Analysis of the
Full-scale Seven-story Reinforced Concrete Test Structure. Journal (B),
The Faculty of Engineering, University of Tokyo, vol. 37, Issue 2,
1983,pp. 432 – 478.
[6] R. Pinho, and A. S. Elnashai , Dynamic Collapse Testing of A Full-Scale
Four Story RC Frame. ISET Journal of earthquake Technology, vol. 37,
Issue 4, 2000, pp. 143 - 163.
[7] J. M. M. Silva, and N. M. M. Maia, Modal Analysis and Testing:
Proceedings of the NATO Advanced Study Institute, NATO Science
Series: E: Applied Science, Sesimbra. 1998.
[8] M.SH. El-Nagar, Static and Dynamic Analysis of Cellular Raft
Foundation, Ph.D. Thesis, Faculty of Engineering, Menofia University,
2009.
[9] D. Roylance, Finite Element Analysis. Department of Material Science
and Engineering, Massachusetts Institute of Technology Cambridge,
MA 02139 .February 28, 2001.
[10] G. C. Martins, J. A. Cordioli, and R. Jordan. An Analysis Of Mesh
Parameters Of A Viscothermal Acoustic FE Model. ICSV18, 18th
International Congress on Sound and Vibration, Rio De Janero, Brazil,
2011.
[11] R. D. Blevins, Formulas for natural frequency and mode shape. Krieger
Pub. California 95327, 2001.