Optimization of Elevated Concrete Foundations for Vibrating Machines
Publication: Journal of Structural Engineering
Volume 128, Issue 11
Abstract
The objective of this study is to describe a problem formulation and an optimization procedure for the design of elevated reinforced concrete foundations for vibrating machines. Special emphasis is placed on structures composed of footings, beams, and columns. The dimensions of the structure and its reinforcement are the design variables for the optimization problem. The objective function consists of costs of the concrete, the steel, the form, and the propping form. Constraints related to material and soil failure, as well as geometrical limits and human comfort are imposed. A new failure surface for columns and beams subjected to biaxial bending and axial loads is defined and used in the formulation. The main motivation of using the new failure surface is to save a large amount of computational effort in the solution of this dynamic response optimization problem. The problem of minimizing the structural cost while satisfying the operating and safety requirements is solved using an augmented Lagrangian method. A large number of constraints (time dependent and time independent) is treated without any difficulty in the method. The numerical methods used in the solution process are described. Optimal solutions for an example problem are obtained and discussed.
Get full access to this article
View all available purchase options and get full access to this article.
References
Arora, J. S. (1989). Introduction to optimal design, McGraw-Hill, New York.
Arora, J. S. (1999). “Optimization of structures subjected to dynamic loads.” Structural dynamic systems, computational techniques and optimization; optimization techniques, C. Leondes, ed., Gordon and Breach, New York, 1–72.
Arora, J. S., Burns, S. A., and Huang, M. (1997). “What is optimization.” Guide to structural optimization, J. S. Arora, ed., ASCE Manuals and Reports on Engineering Practice 90, Reston, Va., 1–24.
Arora, J. S., Chahande, A. I., and Paeng, J. K.(1991). “Multiplier methods for engineering optimization.” Int. J. Numer. Methods Eng., 32, 1485–1525.
Associação Brasileira de Normas Técnicas (ABNT). (1978). “Projeto e Execução de Obras de Concreto Armado (in Portuguese).” NB-1, Brazil.
Atkinson, K. (1993). Elementary numerical analysis, Wiley, New York.
Arya, S., O’Neill, M., and Pincus, G. (1979). Design of structures and foundations for vibrating machines, Gulf, Houston, Tex.
Balling, R. J., Gallup, S. S., and McGrath, C. S. (1997). “How to optimize a reinforced concrete column or beam.” Guide to structural optimization, J. S. Arora, ed., ASCE Manuals and Reports on Engineering Practice 90, Reston, Va., 55–73.
Balling, R. J., and Yao, X. (1997). “How to optimize a reinforced concrete frame.” Guide to structural optimization, J. S. Arora, ed., ASCE Manuals and Reports on Engineering Practice 90, Reston, Va., 123–138.
Bowles, J. E. (1996). Foundation analysis and design, 5th Ed., McGraw-Hill, New York.
Carter, M. (1983). Geotechnical engineering handbook, Pentech, London.
Chahande, A. I., and Arora, J. S.(1994). “Optimization of large structures subjected to dynamic loads with the multiplier method.” Int. J. Numer. Methods Eng., 37, 413–430.
Das, B. M. (1990). Principles of foundation engineering, PWS-KENT, Pacific Grove, Calif.
Dieterman, H. A., and Gajewski, R. R.(1996). “An improved viscous boundary for dynamic soil-structure interaction.” Comput. Assisted Mech. Eng. Sci., 3, 55–64.
Fletcher, R. (1985). Practical methods of optimization, Wiley, New York.
Goldenberg, P., Silva, M. A., Pimenta, P. M., and Brasil, R. M. L. R. F. (1997). “Augmented Lagrangian optimization of a portal frame with elastoplastic behavior under dynamic loading.” Proc., 5th Pan-American Congress on Applied Mechanics, San Juan, Puerto Rico, 373–376.
Haug, E. J., and Arora, J. S. (1979). Applied optimal design, Wiley-Interscience, New York.
Kocer, F., and Arora, J. S. (1999). “Optimal design of nonlinear structures subjected to dynamic loads with application to transmission line structures.” Technical Rep. No. ODL-99.02, Optimal Design Laboratory, College of Engineering, The University of Iowa, Iowa City, Iowa.
Llambias, J. M. (1993). “Validation of seismic soil structure interaction (SSI) methodology for a UK PWR power station.” Proc., 12th International Conf. on “Structural Mechanics in Reactor Technology,” Vol. A, Stuttgart, Germany, 213–218.
Roddis, W. M. K., and Chunnanond, V. (1996). “Genetic algorithms applied to single-criteria optimization of reinforced concrete design and detailing,” SL Rep. No. 96-1, University of Kansas Center for Research, Lawrence, Kan.
Roddis, W. M. K., Lucas, W. K., and Chunnonond, V. (1996). “Single-criteria genetic optimization for design and detailing of concrete structures.” Proc., Computing Congress III, ASCE, Anaheim, CA.
Shigueme, P. (1995). “Análise de vibrações livres em torno de configurações deformadas em placas de comportamento geometricamente não-linear pelo método dos elementos finitos.” PhD thesis (in Portuguese), Polytechnic School of The University of Sao Paulo, São Paulo, Brazil.
Silva, M. A., Arora, J. S., Swan, C. C., and Brasil, R. M. L. R. F. (1999). “Optimization of footing under vibratory loading.” Technical Rep. No. ODL-99.11, Optimal Design Laboratory, The University of Iowa, Iowa City, Iowa.
Silva, M. A., and Brasil, R. M. L. R. F. (1999a). “Augmented lagrangian optimization of steel plates under dynamic loading.” Technical Bulletin BT/PEF/9906 of Polytechnic School of The University of Sao Paulo, São Paulo, Brazil.
Silva, M. A., and Brasil, R. M. L. R. F. (1999b). “Optimization of concrete plates under dynamic loading.” XX CILAMCE-20th Iberian Latin-American Congress on Computational Methods in Engineering, Anais, São Paulo, Brazil.
Silva, M. A., Swan, C. C., Arora, J. S., and Brasil, R. M. L. R. F.(2001). “Failure criterion for RC members under biaxial bending and axial load.” J. Struct. Eng., 127(8), 922–929.
Stojko, S. (1989). “Soil structure interaction analysis in the time domain using DYNA3D/ABAQUS.” Proc., 10th International Conf. on “structural mechanics in reactor technology,” Vol K, Paper K04/3, Anaheim, Calif.
Stojko, S. (1990). “NNC/DYNA3D—a modified version of DYNA3D for general soil structure interaction analysis.” Proc., DYNA3D user group conference, Lawrence Livermore National Laboratory, Livermore, Calif.
Stojko, S. (1991). “Non-linear soil structure interaction analysis of a reactor building using NNC/DYNA3D.” Proc., DYNA3D user group conference, Lawrence Livermore National Laboratory, Livermore, Calif.
Stojko, S. (1993). “Application of DYNA3D to non-linear soil structure interaction (SSI) analyses of retaining wall structures.” Proc., 1st International LS-DYNA3D Conf., Livermore Software Technology Corp., Livermore, Calif.
Sussekind, J. C. (1979). Curso de concreto (in Portuguese), Editora Globo, Rio de Janeiro, Brazil.
Tedesco, J. W., McDougal, W. G., and Ross, C. A. (1999). Structural dynamics: Theory and applications, Addison-Wesley Longman, Menlo Park, Calif.
Wolf, J. P. (1994). Foundation vibration analysis using simple physical models, Prentice-Hall, Upper Saddle River, N.J.
Zhao, C. (1999). “Applications of infinite elements to dynamic soil-structure interaction problems.” Developments in geotechnical engineering, Elsevier Science, Elmont, N.Y., 83.
Zienkiewicz, C., and Taylor, R. L. (1989). The finite element method, 4th ed., McGraw-Hill, New York.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 128 • Issue 11 • November 2002
Pages: 1470 - 1479
Copyright
Copyright © 2002 American Society of Civil Engineers.
History
Received: Jan 3, 2001
Accepted: Apr 9, 2001
Published online: Oct 15, 2002
Published in print: Nov 2002
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.