Keywords: earthquakes, optimisation, design, hard soils, reinforced concrete, structures.

The paper deals with the design optimisation for the case of reinforced concrete structures, erected on hard soils. These structures are investigated for the case of a near source earthquake occurrence. The paper focuses mainly on the definition of the objective mechanical criterion, based on the structural displacements, during the seismic response. The response spectrum provides a convenient means to summarize the peak response of all possible linear single-degree-of-freedom systems to a particular component of the ground motion. It also provides a practical approach to apply the knowledge of structural dynamics to the design of structures and development of lateral force requirements in building codes [1,2]. A classical software ECOgcW is used [3], in order to perform the modal analysis and derive the maximal displacements as well as the stresses from the structural response.

In the present paper, only the first mode is considered. The corresponding shear load at the structure base is then calculated in order to evaluate the structural response. With simulated earthquakes, see references [4,5], for adequate ranges of magnitudes and epicentral distances for the zone under study, the spectrum response (pseudo-accelerations) are compared to the design spectrum derived from the software Degtra [6]; the soil periods range from 0.06s up to 0.29s. This methodology is applied to several existing buildings erected near a subduction fault in Mexico, and concerns mainly the states of Jalisco, Colima, Michoacán, Guerrero, Oaxaca and Chiapas. This contribution identifies and evaluates the residual bearing capacities of the existing buildings.

A sensitivity analysis is performed in order to study the effect of structural typology and modelling on the maximum displacements and internal stresses. This numerical study is based on both real and simulated seismic inputs collected from the Michoacán earthquake in Mexico during 1985: the reinforced concrete structures under study have up to 10 storeys.

The collected results show that, for the structures investigated:

1. the structural flexibility governs the period variation
2. rigid walls might be avoided for buildings having less than five levels
3. the decrease in the column dimensions at upper levels leads to a decrease of the inertial forces and a change in the global stiffness as well as the fundamental period. The structural response falls therefore faroutside the soil period for flexible structures.

1

A.K. Chopra, "Dynamics of Structures", Premier Edition Prentice-Hall, 1995.

2

R.W. Clough and J. Penzien, "Dynamics of Structures", Second Edition Mc Graw-Hill, 1993.

3

C. Corona , ECOgcW, Análisis y diseño de Edificios de Concreto, Software, URL

4

J. Alamilla, L. Esteva, J. García and O. Díaz, "Evolutionary properties of stochastic models of earthquake accelerograms : their dependence on magnitude and distance", Journal of Seismology, 5, 1-21, 2001. doi:10.1023/A:1009892002555

5

J. Alamilla, L. Esteva, J. García and O. Díaz, "Simulating earthquake ground motion at a site for given intensity and uncertain source location", Journal of Seismology, 5(4), 475-485, 2001. doi:10.1023/A:1012062620566

6

Ordaz M. and Montoya C., Software Version 5.4.0, UNAM (25/07/2005), 1990-2002.

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