Skip to main content

Reliability-Based Optimum Structural Design

  • Chapter
Probabilistic Structural Mechanics Handbook

Abstract

Today, in modern structural design the ultimate goal is generally to find the best possible solution without compromising structural reliability. Toward this aim several reliability-based design codes have been proposed and are currently used in the United States, Canada, Asia, Australia, and Europe for buildings, bridges, and offshore platforms. These codes are calibrated using advanced structural reliability techniques to provide uniform and consistent safety levels over all structural elements (e.g., beams, columns, connections) that are designed by the same code provisions. However, uniform reliability of structural elements does not assure uniform reliability of structural systems. Depending on the type of structural topology, material, configuration, joint behavior, and correlations, the reliability of a structural system can be vastly different (Ang, 1989). Therefore, considerable research has been focused on structural system reliability assessment both in code work and in specific structural investigations for design criteria selection, concept evaluation, as well as on inspection and maintenance strategies. It is assumed in this chapter that we know how to evaluate both element (also referred to as component) and system reliabilities with respect to various limit states.1

The financial support of the National Science Foundation under Grants MSM-8618108, MSM-8800882, and MSM-9013017 for RBSO research at the University of Colorado at Boulder is gratefully acknowledged. Also gratefully acknowledged is the collaboration and support of the writer’s associates: A. Al-Harthy, G. Fu, S. Hendawi, M. Iizuka, S. Katsuki, M. Klisinski, Y.-H. Lee, R. Nakib, and K. Yoshida, all of whom made contributions to the development of RBSO theory, software, and/or applications.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 299.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 379.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 379.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  • Aashto (American Association for State Highway and Transportation Officials) (1983). Standard Specifications for Highway Bridges, 13th edition. Washington, D.C.: American Association for State Highway and Transportation Officials.

    Google Scholar 

  • Ang, A. H.-S. (1989). Foreword. In: New Directions in Structural System Reliability. D. M. Frangopol, Ed. Boulder, Colorado: University of Colorado, p. xi.

    Google Scholar 

  • Ang, A. H.-S., and C. A. Cornell (1974). Reliability bases of structural safety and design. Journal of the Structural Division, ASCE 100(9): 1755–1769.

    Google Scholar 

  • Ano, A. H.-S., and W. H. Tang (1984). Probability Concepts in Engineering Planning and Design, Vol. II. New York: John Wiley & Sons.

    Google Scholar 

  • Arora, J. S. (1989a). Introduction to Optimum Design. New York: McGraw-Hill.

    Google Scholar 

  • Arora, J. S. (1989b). Computational design optimization: A review and future directions. In: New Directions in Structural System Reliability. D. M. Frangopol, Ed. Boulder, Colorado: University of Colorado, pp. 29–44.

    Google Scholar 

  • Arora, J. S., D. F. Haskell, and A. K. Govill (1980). Optimal design of large structures for damage tolerance. AIAA Journal 118(5):563–570.

    Google Scholar 

  • Ashley, H. (1982). On making things the best-aeronautical uses of optimization. Journal of Aircraft 19:5–28.

    Google Scholar 

  • Atrek, E., R. H. Gallagher, K. M. Ragsdell, and O. C. Zienkiewicz, Eds. (1984). New Directions in Optimum Structural Design. New York: John Wiley & Sons.

    MATH  Google Scholar 

  • August, G., A. Baratta, and F. Cascjatri (1984). Probabilistic Methods in Structural Engineering. London: Chapman and Hall.

    Google Scholar 

  • Bjerager, P. (1989). On computation methods for structural reliability analysis. In: New Directions in Structural System Reliability. D. M. Frangopol, Ed. Boulder, Colorado: University of Colorado, pp. 52–67.

    Google Scholar 

  • Bjerager, P., and S. Krenk (1989). Parametric sensitivity in first order reliability theory. Journal of Engineering Mechanics, ASCE 115(7):1577–1582.

    Google Scholar 

  • Borkowski, A., and S. Jendo (1990). Structural Optimization--Mathematical Programming, Vol. 2. M. Save and W. Prager, Eds. New York: Plenum.

    Google Scholar 

  • Bourgund, U. (1987). Reliability-based optimization of structural systems. In: Stochastic Structural Mechanics, Lecture Notes in Engineering, Vol. 31. Y. K. Lin and G. I. Schuëller, Eds. Berlin: Springer-Verlag, pp. 52–65.

    Google Scholar 

  • Carmichael, D. G. (1981). Probabilistic optimal design of framed structures. Computer Aided Design 13:261–264.

    Google Scholar 

  • Casciatti, F., and L. Faravelli (1985). Structural reliability and structural design optimization. In: Proceedings of the 4th International Conference on Structural Safety and Reliability, (Kobe, Japan), Vol. 3. I. Konishi, A. H.-S. Mg, and M. Shinozuka, Eds. Kyoto, Japan: Shinko Printing Company, pp. 261–264.

    Google Scholar 

  • Cohn, M. Z. (1972). Analysis and Design of Inelastic Structures: Problems, Vol. 2. Waterloo, Ontario, Canada: Solid Mechanics Division, University of Waterloo.

    Google Scholar 

  • Cornell, C A (1967). Bounds on the reliability of structural systems. Journal of the Structural Division, ASCE 93(1): 171–200.

    Google Scholar 

  • Cornell, C. A. (1969a). A probability-based structural code. Journal of the American Concrete Institute 66(12): 974–985.

    Google Scholar 

  • Cornell, C A (1969b). Structural safety specifications based on second moment reliability analysis. In: Final Report of the Symposium on Concepts of Safety and Methods of Design. London, England: International Association for Bridge and Structural Engineering, pp. 235–245.

    Google Scholar 

  • Der Kiureghian, A., and P. Thoft-Christensen, Eds. (1991). Reliability and Optimization of Structural Systems ’80. (Proceedings of the 3rd IFIP WG 7.5 Conference on Reliability and Optimization of Structural Systems). Lecture Notes in Engineering, Vol. 61. Berlin: Springer-Verlag.

    Google Scholar 

  • Dhillon, B. S., and C.-H. Kuo (1991). Optimum design of composite hybrid plate girders. Journal of Structural Engineering, ASCE 117(7):2088–2098.

    Google Scholar 

  • Ditlevsen, O. (1973). Structural Reliability Analysis and the Invariance Problem. Copenhagen, Denmark: Department of Civil Engineering, Danish Engineering Academy.

    Google Scholar 

  • Ditlevsen, O. (1979). Narrow reliability bounds for structural systems. Journal of Structural Mechanics 7(4):453–472.

    Google Scholar 

  • Ditlevsen, O. (1981). Uncertainty Modeling with Applications to Civil Engineering Systems. New York: McGraw-Hill.

    MATH  Google Scholar 

  • Ditlevsen, O., and Bjerager, P. (1986). Methods of structural systems reliability. Structural Safety 3:195–229.

    Google Scholar 

  • Duckstein, L. (1984). Multiobjective optimization in structural design: The model choice problem. In: New Directions in Optimum Structural Design. E. Atrek, et al., Eds. Chichester, England: John Wiley & Sons, pp. 459–481.

    Google Scholar 

  • Enevoldsen, I. (1991). Reliability-Based Structural Optimization. Ph.D. Thesis. Aalborg, Denmark: Department of Building Technology and Structural Engineering, Aalborg University.

    Google Scholar 

  • Enevoldsen, I., and J. D. Sorensen (1990). Reliability-Based Optimization of Series Systems of Parallel Systems. Structural Reliability Theory Paper No. 82. Aalborg, Denmark: Aalborg University.

    Google Scholar 

  • Enevoldsen, I., J. D. Sorensen, and P. Thoft-Christensen (1989). Shape optimization of mono-tower offshore platform. In: Proceedings of the International Conference on Computer Aided Design of Structures: Applications. C. A. Brebbia and S. Hernandez, Eds. Southampton, England: Computational Mechanics Publications, pp. 297–308.

    Google Scholar 

  • Enevoldsen, I., J. D. Sorensen, and G. Sigurdsson (1990). Reliability-Based Shape Optimization Using Stochastic Finite Element Methods. Structural Reliability Theory Paper No. 73. Aalborg, Denmark: Institute of Building Technology and Structural Engineering, Aalborg University.

    Google Scholar 

  • Eschenauer, H. A., J. kosxt, and A. Osyczka, Eds. (1990). Multicriteria Design Optimization: Procedures and Applications. Berlin: Springer-Verlag.

    MATH  Google Scholar 

  • Farkas, J. (1984). Optimum Design of Metal Structures. Chichester, England: Ellis Horwood.

    Google Scholar 

  • Feng, Y. S., and F. Moses (1986a). A method of structural optimization based on structural system reliability. Journal of Structural Mechanics 14(4):437–453.

    Google Scholar 

  • Feng, Y. S., and F. Moses (1986b). Optimum design, redundancy and reliability of structural systems. Computers and Structures 24(2):239–251.

    Google Scholar 

  • Ferry-Borges, J. (1954). O Dimensionamento de Estruturas. Lisbon, Portugal: Ministry of Public Works, National Laboratory of Civil Engineering.

    Google Scholar 

  • Forssell, C. (1924). Ekonomi och byggnadsvasen (economy and construction). Sunt Fornoft 4:74–77 (in Swedish) (Translated to English in excerpts in Lind, N. C. [1970]. Structural Reliability and Codified Design. Waterloo, Ontario, Canada: Solid Mechanics Division, University of Waterloo.)

    Google Scholar 

  • Frangopol, D. M. (1984a). A reliability-based optimization technique for automatic plastic design. Computer Methods in Applied Mechanics and Engineering 44:105–117.

    MATH  Google Scholar 

  • Frangopol, D. M. (1984b). Interactive reliability-based structural optimization. Computers and Structures 19(4): 559–563.

    Google Scholar 

  • Frangopol, D. M. (1985a). Sensitivity of reliability-based optimum design. Journal of Structural Engineering, ASCE 111(8):1703–1721.

    Google Scholar 

  • Frangopol, D. M. (1985b). Multicriteria reliability-based optimum design. Structural Safety 3(1):23–28.

    Google Scholar 

  • Frangopol, D. M. (1985c). Structural optimization using reliability concepts. Journal of Structural Engineering, ASCE 111(11):2288–2301.

    Google Scholar 

  • Frangopol, D. M. (1985d). Towards reliability-based computer aided optimization of reinforced concrete structures. Engineering Optimization 8(4):301–313.

    Google Scholar 

  • Frangopol, D. M. (1986a). Computer-automated design of structural systems under reliability-based performance constraints. Engineering Computations 3(2):109–115.

    Google Scholar 

  • Frangopol, D. M. (1986b). Structural optimization under conditions of uncertainty, with reference to serviceability and ultimate limit states. In: Recent Developments in Structural Optimization. F. Y. Cheng, Ed. New York: American Society of Civil Engineers, pp. 54–71.

    Google Scholar 

  • Frangopol, D. M. (1986c). Computer-automated sensitivity analysis in reliability-based plastic design. Computers and Structures 22(1):63–75.

    MATH  Google Scholar 

  • Frangopol, D. M. (1987). Unified approach to reliability-based structural optimization. In: Dynamics of Structures. J. M. Roesset, Ed. New York: American Society of Civil Engineers, pp. 156–167.

    Google Scholar 

  • Frangopol, D. M., Ed. (1989). New Directions in Structural System Reliability. Boulder, Colorado: University of Colorado.

    Google Scholar 

  • Frangopol, D. M. (1991). Reliability-based optimization research at the University of Colorado: A brief retrospective. In: Progress in Structural Engineering. D. E. Grierson, A. Franchi, and P. Riva, Eds. Dordrecht, The Netherlands: Kluwer Academic, pp. 481–491.

    Google Scholar 

  • Frangopol, D. M. (1993). How to include reliability constraints in structural optimization. In: Structural Engineering in Natural Hazards Mitigation, Vol. 2. A. H.-S. Ang and R. Vilaverde, Eds. New York: American Society of Civil Engineers, pp. 1632–1637.

    Google Scholar 

  • Frangopol, D. M., and R. B. Corotis, Eds. (1990). System Reliability in Structural Analysis, Design and Optimization [Special Issue of Structural Safety (Journal). 7(2–4)].

    Google Scholar 

  • Frangopol, D. M., and G. Fu (1989). Optimization of structural systems under reserve and residual reliability requirements. In: Reliability and Optimization of Structural Systems ’88 (Lecture Notes in Engineering, Vol. 48). P. Thoft-Christensen, Ed. Berlin, Germany: Springer-Verlag, pp. 135–145.

    Google Scholar 

  • Frangopol, D. M., and G. fu (1990). Limit states reliability interaction in optimum design of structural systems. In: Structural Safety and Reliability, Vol. III. A. H.-S. Mg, M. Shinozuka, and G. I. Schuëller, Eds. New York: American Society of Civil Engineers, pp. 1879–1886.

    Google Scholar 

  • Frangopol, D. M., and M. Iizuka (1991a). Multiobjective decision support spaces for optimum design of non-deterministic structural systems. In: Probabilistic Safety Assessment and Management, Vol. 2. G. Apostolakis, Ed. New York: Elsevier, pp. 977–982.

    Google Scholar 

  • Frangopol, D. M., and M. Itzuxa (1991b). Pareto optimum solutions for nondeterministic systems. In: Proceedings of the 6th International Conference on Applications of Statistics and Probability in Civil Engineering (ICASP6), Vol. 1. L. Esteva and S. E. Ruis, Eds. pp. 216–223, Mexico City, Mexico.

    Google Scholar 

  • Frangopol, D. M., and M. Iizutca (1992a). Structural system design under uncertainty via Pareto optimization. In: Probabilistic Mechanics and Structural and Geotechnical Reliability. Y. K. Lin, Ed. New York: American Society of Civil Engineers, pp. 551–554.

    Google Scholar 

  • Frangopol, D. M., and M. Iizuica (1992b). Probability-based structural system design using multicriteria optimization. In: Proceedings of the 4th AIAA/USAF/NASA/OAI Symposium on Multidisciplinary Analysis and Optimization. AIAA-92–4788-CP Paper, Part 2, pp. 794–798, Cleveland, Ohio.

    Google Scholar 

  • Frangopol, D. M., and M. Klisinsxi (1992). Design for safety, serviceability and damage tolerability. In: Designing Concrete Structures for Serviceability and Safety. SP 133–12. E. G. Nawy and A. Scanlon, Eds. Detroit, Michigan: American Concrete Institute, pp. 225–254.

    Google Scholar 

  • Frangopol, D. M., and F. Moses (1994). Reliability-based structural optimization In: Advances in Design Optimization. H. Adeli, Ed. London: Chapman and Hall (in press), pp. 492–570.

    Google Scholar 

  • Frangopol, D. M., and R. Naxib (1990). Examples of system optimization and reliability in bridge design. In: Structural Safety and Reliability, Vol. II. A. H.-S. Mg, M. Shinozuka, and G. I. Schuëller, Eds. New York: American Society of Civil Engineers, pp. 871–878.

    Google Scholar 

  • Frangopol, D. M., and J. Rondal (1976). Considerations on optimum combination of safety and economy. In: Final Report of the 10th Congress of the International Association for Bridge and Structural Engineering, Zurich, Switzerland: International Association for Bridge and Structural Engineering, pp. 45–48.

    Google Scholar 

  • Frangopol, D. M., M. Klisinski, and M. Iizuica (1991). Computational experience with damage-tolerant optimization of structural systems. In: Proceedings of the 1st International Conference on Computational Stochastic Mechanics. P. D. Spanos and C. A. Brebbia, Eds. Southampton, England: Computational Mechanics Publications/London: Elsevier Applied Science, pp. 199–210.

    Google Scholar 

  • Freudenthal, A. M. (1956). Safety and the probability of structural failure. Transactions. ASCE, 121:1337–1375.

    Google Scholar 

  • Freudenthal, A. M., J. M. Garrelts, and M. Shinozuxa. (1966). The analysis of structural safety. Journal of the Structural Division, ASCE 92(1):267–325.

    Google Scholar 

  • Fu, G., and D. M. Frangopol (1988). Reliability-Based Multiobjective Structural Optimization. Phase 2: Applications to Frame Systems. Structural Research Series, No. 88–01. Boulder, Colorado: Department of Civil Engineering, University of Colorado.

    Google Scholar 

  • Fu, G., and D. M. Frangopol (1990a). Balancing weight, system reliability and redundancy in a multiobjective optimization framework. Structural Safety 7(2–4):165–175.

    Google Scholar 

  • Fu, G., and D. M. Frangopol (1990b). Reliability-based vector optimization of structural systems. Journal of Structural Engineering, ASCE 116(8):2141–2161.

    Google Scholar 

  • Furuta, H. (1980). Fundamental Study on Geometrical Configuration and Reliability of Framed Structures Used for Bridges. Ph.D. Thesis. Kyoto, Japan: Department of Civil Engineering, Kyoto University.

    Google Scholar 

  • Gellalty, R. A., and R. H. Gallagher (1966). A procedure for automated minimum weight structural design. Part I-Theoretical bases, Part II-Applications. Aeronautics Quarterly 17(3):216–230 and 17(4):332–342.

    Google Scholar 

  • Gill, P. E., W. Murray, and M. H. Wright (1981). Practical Optimization. New York: Academic Press.

    MATH  Google Scholar 

  • Grierson, D. E. (1983). The intelligent use of structural analysis. Perspectives in Computing 3(4):32–39.

    Google Scholar 

  • Grierson, D. E., and C. E. Cameron (1984). Computer Automated Synthesis of Building Frameworks. Paper No. 189. Waterloo, Ontario, Canada: Solid Mechanics Division, University of Waterloo.

    Google Scholar 

  • Grimmelt, M., and G. I. Schuller (1982). Benchmark study on methods to determine collapse failure probabilities of redundant structures. Structural Safety 1(2):93–106.

    Google Scholar 

  • Haftka, R. T., and M. P. Kamat (1985). Elements of Structural Optimization. Amsterdam: Martinius Nijhoff.

    MATH  Google Scholar 

  • Hasofer, A. M., and N. C. Lind (1974). Exact and invariant second moment code format. Journal of the Engineering Mechanics Division, ASCE 100(1):111–121.

    Google Scholar 

  • Haug, E. J., and J. S. Arora (1979). Applied Optimal Design: Mechanical and Structural Systems. New York: Wiley-Interscience.

    Google Scholar 

  • Hendawi, S., and D. M. Frangopol (1993). Reliability-based optimization of composite-hybrid plate girders. In: Proceedings of the 6th International Conference on Structural Safety and Reliability. ICOSSAR ’83, Innsbruck, Austria. G. I. Schuëller, M. Shinozuka, J. T. P. Yao, and A. A. Balkema, Eds. (in press).

    Google Scholar 

  • Hilton, H. H., and M. Feigen (1960). Minimum weight analysis based on structural reliability. Journal of the Aerospace Sciences 27:641–653.

    MathSciNet  MATH  Google Scholar 

  • Iizuka, M. (1991). Time Invariant and Time Variant Reliability Analysis and Optimization of Structural Systems. Ph.D. Thesis. Boulder, Colorado: Department of Civil Engineering, University of Colorado.

    Google Scholar 

  • Ishikawa, N., and M. Itzuka (1987). Optimum reliability-based design of large framed structures. Engineering Optimization 10(4):245–261.

    Google Scholar 

  • Johnson, A. I. (1953). Strength, Safety and Economical Dimensions of Structures. Stockholm, Sweden: Division of Building Statistics and Structural Engineering, Royal Institute of Technology.

    Google Scholar 

  • Kalaba, R. E. (1962). Design of minimum weight structures given reliability and cost. Journal of the Aerospace Sciences 29:355–356.

    Google Scholar 

  • Kim, S. H., and Y. K. Wen (1987). Reliability-Based Structural Optimization under Stochastic Time Varying Loads. Civil Engineering Studies, Structural Research Series No. 533. Urbana, Illinois: University of Illinois.

    Google Scholar 

  • Kim, S. H., and Y. K. Wen (1990). Optimization of structures under stochastic loads. Structural Safety 7(2–4): 177–190.

    Google Scholar 

  • Kirsch, U. (1981). Optimum Structural Design. New York: McGraw-Hill.

    Google Scholar 

  • Koski, J. (1984). Multicriterion optimization in structural design. In: New Directions in Optimum Structural Design. E. Atrek, R. H. Gallagher, K. M. Ragsdell, and O. C. Zienkiewicz, Eds. Chichester, England: John Wiley & Sons, pp. 483–503.

    Google Scholar 

  • Lee, Y.-H., S. Hendawi, and D. M. Frangopol (1993). RELTRAN: A Structural Reliability Analysis Program: Version 2.0. Report No. CU/SR-93/6. Boulder, Colorado: Department of Civil Engineering, University of Colorado.

    Google Scholar 

  • Lev, O. E., Ed. (1981). Structural Optimization: Recent Developments and Applications. New York: American Society of Civil Engineers.

    Google Scholar 

  • Levy, R., and O. Lev (1987). Recent developments in structural optimization. Journal of Structural Engineering, ASCE 113(9): 1939–1962.

    Google Scholar 

  • Lind, N. C. (1971). Consistent partial safety factors. Journal of the Structural Division,ASCE 97(6):1651–1670.

    Google Scholar 

  • Liu, Y, and F. Moses (1991). Bridge design with reserve and residual reliability constraints. Structural Safety 11(1):29–42.

    Google Scholar 

  • Madsen, H. O., S. Krenk, and N. C. Lind (1986). Methods of Structural Safety. Englewood Cliffs, New Jersey: Prentice-Hall.

    Google Scholar 

  • Mahadevan, S., and A. Haldar (1991). Reliability-based optimization using SFEM. In: Reliability and Optimization of Structural Systems ‘90 (Lecture Notes in Engineering, Vol. 61), A. Der Kiureghian and P. Thoft-Christensen, Eds. Berlin: Springer-Verlag, pp. 241–250.

    Google Scholar 

  • Mau, S. T., and R. G. Sexsmith (1972). Minimum expected cost optimization. Journal of the Structural Division, ASCE 98(9):2043–2058.

    Google Scholar 

  • Melchers, R. E. (1987). Structural Reliability Analysis and Prediction. Chichester, England. Ellis Horwood.

    Google Scholar 

  • Moses, E (1969). Approaches to structural reliability and optimization. In: An Introduction to Structural Optimi-zation. M. Z. Cohn, Ed. Waterloo, Ontario, Canada: Solid Mechanics Division, University of Waterloo, pp. 81–120.

    Google Scholar 

  • Moses, F. (1973). Design for reliability-concepts and applications. In: Optimum Structural Design. R. H. Gallagher and O. C. Zienkiewicz, Eds. London: John Wiley & Sons, pp. 241–265.

    Google Scholar 

  • Moses, F. (1974). Reliability of structural systems. Journal of the Structural Division, ASCE 100(9):1813–1820.

    Google Scholar 

  • Moses, F. (1977). Structural system reliability and optimization Computers and Structures 7:283–290.

    Google Scholar 

  • Moses, F. (1979). Sensitivity studies in structural reliability. In: Structural Reliability and Codified Design. Wa-terloo, Ontario, Canada: Solid Mechanics Division, University of Waterloo, pp. 1–17.

    Google Scholar 

  • Moses, F. (1982). System reliability developments in structural engineering. Structural Safety 1(1):3–13.

    MathSciNet  Google Scholar 

  • Moses, F., and D. E. Kinser (1967). Optimum structural design with failure probability constraints. AMA Journal 5(6):1152–1158.

    Google Scholar 

  • Moses, F., and J. D. Stevenson (1970). Reliability-based structural design. Journal of the Structural Division, ASCE 96(2):221–244.

    Google Scholar 

  • Mota Soares, C. A., Ed. (1987). Computer-aided optimal design: Structural and mechanical systems. In: Pro-ceedings of the NATO Advanced Study Institute. Series F, Vol. 27. New York: Springer-Verlag.

    MATH  Google Scholar 

  • Murotsu, Y., and S. Shag (1990). Optimum shape design of truss structures based on reliability. Structural Optimization 2(2):65–76.

    Google Scholar 

  • Murotsu, Y., M. Mita, and S. Shag (1992). Optimal configuration for fiber reinforced composites under uncer-tainties of material properties and loadings. In: Probabilistic Mechanics and Structural and Geotechnical Reliability. Y. K. Lin, Ed. New York: American Society of Civil Engineers, pp. 547–550.

    Google Scholar 

  • Nakib, R., and D. M. Frangopol (1990a). RSBA and RSBA-OPT: Two computer programs for structural system reliability analysis and optimization. Computers and Structures 36(1):13–27.

    MATH  Google Scholar 

  • Nam, R., and D. M. Frangopol (1990b). Reliability-based structural optimization using interactive graphics. Computers and Structures 37(1):27–34.

    Google Scholar 

  • Osyczka, A. (1984). Multicriterion Optimization in Engineering. Chichester, England- Ellis Horwood.

    Google Scholar 

  • Paez, A., and E. Torroja (1959). La Determination del Coefficiente de Seguridad en las Distintas Obras. Madrid, Spain: Instituto Technic de la Construcion y del Cemento.

    Google Scholar 

  • Parimi, S. R., and M. Z. Conty (1978). Optimum solutions in probabilistic structural design. Journal of Applied Mechanics 2(1):47–92.

    Google Scholar 

  • Rackwitz, R., and R. Cuntze (1987). Formulations of reliability-oriented optimization Engineering Optimization 11(1,2):69–76.

    Google Scholar 

  • Rackwitz, R., and P. Thoft-Christensen, Eds. (1992). Reliability and optimization of structural systems ’91. In: Proceedings of the 4th IFIP WG 7.5 Conference on Reliability and Optimization of Structural Systems. Lecture Notes in Engineering, Vol. 76. Berlin: Springer-Verlag.

    Google Scholar 

  • Rao, S. S. (1984). Optimization: Theory and Applications, 2nd ed. New York: John Wiley & Sons.

    MATH  Google Scholar 

  • Reklaitis, G. V., A. Ravindran, and K. M. Ragsdell (1983). Engineering Optimization. New York: WileyInterscience.

    Google Scholar 

  • Rojiani, K. B., and G. L. Bailey (1984). Reliability-based optimum design of steel structures. In: New Directions in Optimum Structural Design. E. Atrek, et al., Eds. Chichester, England: John Wiley & Sons, pp. 332–57.

    Google Scholar 

  • Rosenblueth, E. (1986). Optimum reliabilities and optimum design. Structural Safety 3(1):69–83.

    Google Scholar 

  • Rosenblueth, E., and L. Esteva (1972). Reliability basis for some Mexican codes. In: Probabilistic Design of Reinforced Concrete Buildings. ACI Publication SP-31. Detroit, Michigan: American Concrete Institute, pp. 1–41.

    Google Scholar 

  • Rosenblueth, E., and E. Mendoza (1971). Reliability optimization in isostatic structures. Journal of the Engineering Mechanics Division, ASCE 97(6):1625–1640.

    Google Scholar 

  • Save, M., and W. Prager (1985). Structural Optimization-Optimality Criteria, Vol. 1. New York: Plenum.

    Google Scholar 

  • Schmrr, L. A. (1960). Structural design by systematic synthesis. In: Proceedings of the 2nd ASCE Conference on Electronic Computation. pp. 105–122, Pittsburgh, Pennsylvania.

    Google Scholar 

  • Schmit, L. A. (1984). Structural optimization-some key ideas and insights. In: New Directions in Optimum Structural Design. E. Atrek, et al., Eds. Chichester, England: John Wiley & Sons, pp. 1–45.

    Google Scholar 

  • Sci-Imrr, L. A., and K. J. Cheng (1982). Optimum design sensitivity based on approximation concepts and dual methods. In: Proceedings of the 23rd AIAA/ASMEIASCE/AHS Structures, Structural Dynamics and Materials Conference. AIAA Paper No. 82–0713-CP, New Orleans, Louisiana.

    Google Scholar 

  • Shag, S. (1991). Reliability-Based Shape Optimization of Structural and Material Systems. Ph.D. Thesis. Osaka, Japan: Division of Engineering, University of Osaka Prefecture.

    Google Scholar 

  • Swnozuka, M. (1983). Basic analysis of structural safety. Journal of Structural Engineering, ASCE 109(3):721–740.

    Google Scholar 

  • Sobieszczanski-Sobieski, J., J. E. Bartiielemy, and K. M. Riley (1982). Sensitivity of optimum solutions to problem parameters, AIAA Journal 20(9):1291–1299.

    MATH  Google Scholar 

  • Soltani, M., and R. B. Corot’s (1988). Failure cost design of structural systems. Structural Safety 5:238–252.

    Google Scholar 

  • Sørensen, J. D. (1986). Reliability-Based Optimization of Structural Elements. Structural Reliability Theory Paper No. 18. Aalborg, Denmark: Institute of Building Technology and Structural Engineering, Aalborg University.

    Google Scholar 

  • Sørensen, J. D. (1987). Reliability-Based Optimization of Structural Systems. Structural Reliability Theory Paper No. 32. Aalborg, Denmark: Institute of Building Technology and Structural Engineering, Aalborg University.

    Google Scholar 

  • Sørensen, J. D. (1988). Optimal Design with Reliability Constraints. Structural Reliability Theory Paper No. 45. Aalborg, Denmark: Institute of Building Technology and Structural Engineering, Aalborg University.

    Google Scholar 

  • Sørensen, J. D., and I. Enevoldsen (1989). Sensitivity Analysis in Reliability-Based Shape Optimization. Structural Reliability Theory Paper No. 69. Aalborg, Denmark. Institute of Building Technology and Structural Engineering, Aalborg University.

    Google Scholar 

  • Sørensen, J. D., and P. Thoft-Christensen (1987). Integrated Reliability-Based Optimal Design of Structures. Structural Reliability Theory Paper No. 29. Aalborg, Denmark: Institute of Building Technology and Structural Engineering, Aalborg University.

    Google Scholar 

  • Spillers, W. R. (1975). Iterative Structural Design. Amsterdam: North-Holland.

    MATH  Google Scholar 

  • Surahman, A., and K. B. Rojiiani (1983). Reliability-based optimum design of concrete frames. Journal of Structural Engineering, ASCE 109(3):741–757.

    Google Scholar 

  • Swrrzky, H. (1964) Minimum weight design with structural reliability. In: Proceedings of the 5th AIAA Annual Structures and Materials Conference, Palm Springs, California, pp. 316–322.

    Google Scholar 

  • Tao, Z., J. H. Ellis, and R. B. Corons (1992). Markov decision processes in structural optimization. In: Probabilistic Mechanics and Structural and Geotechnical Reliability. Y. K. Lin, Ed. New York: American Society of Civil Engineers, pp. 539–542.

    Google Scholar 

  • Templeman, A. B. (1983). Optimization methods in structural design practice. Journal of Structural Engineering, ASCE 109(12):2420–2433.

    Google Scholar 

  • Thoft-Christensen, P., Ed. (1987a). Reliability and optimization of structural systems. In: Proceedings of the 1st IFIP W7.5 Working Conference on Reliability and Optimization of Structural Systems. Lecture Notes in Engineering, Vol. 33. Berlin: Springer-Verlag.

    MATH  Google Scholar 

  • Thoft-Christensen, P. (1987b). Application of Optimization Methods in Structural Systems Reliability Theory. Structural Reliability Theory Paper No. 33. Aalborg, Denmark: Institute of Building Technology and Structural Engineering, Aalborg University.

    Google Scholar 

  • Thoft-Christensen, P., Ed. (1989). Reliability and optimization of structural systems ‘88. In: Proceedings of the 2nd IFIP WG 7.5 Conference on Reliability and Optimization of Structural Systems. Lecture Notes in Engineering, Vol. 48. Berlin: Springer-Verlag.

    MATH  Google Scholar 

  • Thoft-Christensen, P. (1991). On reliability-based structural optimization. In: Reliability and Optimization of Structural Systems ‘80 (Lecture Notes in Engineering, Vol. 61), A. Der Kiureghian and P. Thoft-Christensen, Eds. Berlin: Springer-Verlag, pp. 387–402.

    Google Scholar 

  • Thoft-Christensen, P. (1992). Risk-based structural optimization. In: Probabilistic Mechanics and Structural and Geotechnical Reliability. Y. K. Lin, Ed. New York: American Society of Civil Engineers, pp. 535–538.

    Google Scholar 

  • Thoft-Christensen, P., and M. J. Baker (1982). Structural Reliability Theory and Its Applications. Berlin: Springer-Verlag.

    MATH  Google Scholar 

  • Thoft-Christensen, P., and Y Murotsu (1986). Applications of Structural Systems Reliability Theory. Berlin: Springer-Verlag.

    Google Scholar 

  • Thoft-Christensen, P., and J. D. Sorensen (1987). Optimal strategy for inspection and repair of structural systems. Civil Engineering Systems 4:94–100.

    Google Scholar 

  • Turkstra, C. J. (1970). Theory of Structural Design Decisions. SM Study No. 2. N. C. Lind, Ed. Waterloo, Ontario, Canada: Solid Mechanics Division, University of Waterloo.

    Google Scholar 

  • Vanderplaats, G. N. (1982). Structural optimization: Past, present, and future. AIAA Journal 20:992–1000.

    MathSciNet  MATH  Google Scholar 

  • Vanderplaats, G. N. (1984a). Numerical Optimization Techniques for Engineering Design. New York: McGraw-Hill.

    MATH  Google Scholar 

  • Vanderplaats, G. N. (1984b). Efficient calculation of optimum design sensitivity. In: Proceedings of the 25th AIAAIASME/ASCE/AHS Structures, Structural Dynamics and Materials Conference, Palm Springs, California. AIAA Paper No. 84–0855-CP, 1. pp. 34–40.

    Google Scholar 

  • Vanderplaats, G. N. (1986). ADS-a Fortran Program for Automated Design Synthesis: Version 1:10. Santa Barbara, California: Engineering Design Optimization.

    Google Scholar 

  • Vanmarcke, E. (1971). Matrix formulation of reliability analysis and reliability-based design. Computers and Structures 3:757–770.

    Google Scholar 

  • Vanmarcke, E. (1984). Random Fields: Analysis and Synthesis. Cambridge, Massachusetts: MIT Press.

    Google Scholar 

  • Yao, J. T. P. (1985). Safety and Reliability of Existing Structures. Boston: Pitman.

    Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1995 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Frangopol, D.M. (1995). Reliability-Based Optimum Structural Design. In: Sundararajan, C. (eds) Probabilistic Structural Mechanics Handbook. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-1771-9_16

Download citation

  • DOI: https://doi.org/10.1007/978-1-4615-1771-9_16

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-5713-1

  • Online ISBN: 978-1-4615-1771-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics