On the Accuracy of Basic Modal Displacement Method Considering Various Earthquakes

Authors: Seyed Sadegh Naseralavi, Sadegh Balaghi, Ehsan Khojastehfar

Abstract:

Time history seismic analysis is supposed to be the most accurate method to predict the seismic demand of structures. On the other hand, the required computational time of this method toward achieving the result is its main deficiency. While being applied in optimization process, in which the structure must be analyzed thousands of time, reducing the required computational time of seismic analysis of structures makes the optimization algorithms more practical. Apparently, the invented approximate methods produce some amount of errors in comparison with exact time history analysis but the recently proposed method namely, Complete Quadratic Combination (CQC) and Sum Root of the Sum of Squares (SRSS) drastically reduces the computational time by combination of peak responses in each mode. In the present research, the Basic Modal Displacement (BMD) method is introduced and applied towards estimation of seismic demand of main structure. Seismic demand of sampled structure is estimated by calculation of modal displacement of basic structure (in which the modal displacement has been calculated). Shear steel sampled structures are selected as case studies. The error applying the introduced method is calculated by comparison of the estimated seismic demands with exact time history dynamic analysis. The efficiency of the proposed method is demonstrated by application of three types of earthquakes (in view of time of peak ground acceleration).

Keywords: Time history dynamic analysis, basic modal displacement, earthquake induced demands, shear steel structures.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1125471

References:

[1] S. Gholizadeh, and E. Salajegheh, “Optimal design of structures for time history loading by swarm intelligence and an advanced metamodel,” Comput. Methods Appl. Mech. Eng. vol. 198, pp. 2936–2949, (2009).
[2] Rosenblueth, E. (1951). A basis for aseismic design. PhD thesis, Univ. of Illinois, Urbana, Ill.
[3] E. L Wildon, A. Der Kiureghiant, and E P. Bayot, “A replacement for the SRSS method in seismic analysis”, Earthquake Engineering and Structural Dynamics, vol. 9, pp. 187-194, 1981.
[4] S. Gholizadeh, J. Salajegheh, and E. Salajegheh, “An intelligent neural system for predicting structural response subject to earthquakes”, Advances in Engineering Software, vol. 40, pp. 630–639, 2009.
[5] E Salajegheh, and A Heidari, “Optimum design of structures against earthquake by wavelet neural network and filter banks,” Earthquake Engineering & Structural Dynamics, vol. 34, pp. 67-82, 2005.
[6] L. Su, S. L. Dong, S. Kato, “A new average response spectrum method for linear response analysis for structure to spatial earthquake ground motions,” Engineering Structures. Vol. 28, pp. 1835-1842, (2006).
[7] N.D. Lagaros, M. Fragiadakis, M. Papadrakakis, and Y. Tsompanakis, “Structural optimization: a tool for evaluating dynamic design procedures”, Engineering Structures, vol. 28, pp. 1623–1633, 2006.
[8] X.K. Zou, and C.M. Chan, “An optimal resizing technique for dynamic drift design of concrete buildings subjected to response spectrum and time history loadings”, Computers and Structures, vol. 83, pp. 1689–1704, 2005.
[9] F.Y. Kocer, and J.S. Arora, “Optimal design of H-frame transmission poles for earthquake loading”, ASCE Journal of Structural Engineering, vol. 125, pp. 1299–1308, 1999.
[10] M.B. Prendes Gero, A. Bello García, and J.J. Coz Díaz. “Design optimization of 3D steel structures: Genetic algorithms vs. Classical techniques” Journal of Constructional Steel Research, vol. 62, pp. 1303–1309, 2006.
[11] M.B. Prendes Gero, A. Bello García, and J.J. Coz Díaz, “A modified elitist genetic algorithm applied to the design optimization of complex steel structures”. Journal of Constructional Steel Research, vol. 61, pp. 265–280, 2006.
[12] F.Y. Cheng, D. Li, J. Ger, Multiobjective optimization of dynamic structures, in: M. Elgaaly (Ed.), ASCE Structures 2000 Conference Proceedings, 2000.
[13] A.K. Chopra, Dynamics of the Structures. New Jersey: Prentice Hall, Upper Saddle River, 3rd edition. 2007.