Optimal Criteria in Probabilistic Structural Design

  • S. R. Parimi
  • M. Z. Cohn
Part of the International Union of Theoretical and Applied Mechanics book series (IUTAM)


The design of a statically indeterminate structure is, of necessity, iterative in nature since its safety is a function of the component strengths. The design consists of assuming an initial set of values for the design parameters, determining the safety level of the structure thus obtained by analysis, and then suitably adjusting the design parameters over a series of reanalyses, until the safety level of the design is equal to or slightly larger than that specified. The number of iterations required to arrive at a satisfactory design increases with the number of the design parameters involved and with the complexity of the functional relationship between structural safety and design parameters.


Failure Mode Optimal Criterion Reliability Level Structural Weight Safety Concept 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



coefficient indicating the relative influence of the economic criterion in the total cost criterion, Eq. (3)


cost of failure in mode i


initial erection cost of a structure


coefficient indicating the relative influence of the i-th mode of failure on the combined optimality criterion, Eq. (3)


total cost of a structure allowing for the expected costs of various failure modes


index referring to the modes of failure considered in design; in two-criteria design i = 1 refers to unserviceability and i = 2 refers to plastic collapse

\({\overline M _p}\)

mean member strength

\(\overline M _p^*\)

optimal value of \({\overline M _p}\)


probability of structural failure in mode i


probability of structural survival in failure mode i


probability of survival for the structure with optimal member strengths


specified reliability of structure against failure in mode i


structural weight (proportional to the initial erection cost)


specified limit on the structural weight, Z


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  1. 1.
    Moses, F.: Approaches to Structural Reliability and Optimization, SM Study-No. 1, Solid Mechanics Division, University of Waterloo, Waterloo, Ontario, Canada, April 1969, pp. 81–120.Google Scholar
  2. 2.
    Vasco Costa, F.: Optimization of Structures, 8th Congress, IABSE, New York, September 1968.Google Scholar
  3. 3.
    Turkstra, C. J.: Choice of Failure Probabilities. Journal of the Structural Division, ASCE 93, No. ST6, Proc. paper 5678, December 1967.Google Scholar
  4. 4.
    Shinozuka, M., Yang, J. N.: Optimum Structural Design Based on Reliability and Proof-Load Test. Annals of Reliability and Maintainability 8, 375 – 391 (1969).Google Scholar
  5. 5.
    Mau, S.: Optimum Design of Structures with a Minimum Expected Cost Criterion, Report No. 340, Dept. of Structural Engineering, Cornell, University, Ithaca, New York, June, 1971.Google Scholar
  6. 6.
    Sawyer, H. A., Jr.: Status and Potentialities of Nonlinear Design of Concrete Frames, Flexural Mechanics of Reinforced Concrete, Proceedings of the International Symposium held in Miami, Fla., November 1964, ASCE-ACI, 1965, pp. 7–28.Google Scholar
  7. 7.
    Freudenthal, A. M.: Safety, Safety Factors and Reliability of Mechanical Systems, Proceedings, 1st Symposium on Engrg. Applications of Random Function Theory and Probability, held at Purdue Univ., Lafayette, Ind., 1962, Edited by J. L. Bogdanoff and F. Kozin, New York: Wiley 1963, pp. 130–162.Google Scholar
  8. 8.
    Allen, D. E.: Limit State Design-A Unified Procedure for the Design of Structures, Paper presented at the 83rd Annual Meeting of EIC, Vancouver, September 1969.Google Scholar
  9. 9.
    Cohn, M. Z., Parimi, S. R.: Multi-Criteria Probabilistic Structural Design, ASCE National Structural Engineering Meeting, April 24–28, 1972, Cleveland, Ohio, Preprint No. 1840; Paper 19, Inelasticity and Non-Linearity in Structural Concrete, SM Study No. 8, University of Waterloo, Press 1973, pp. 471–492.Google Scholar
  10. 10.
    Parimi, S. R.: Multi-Criteria Probabilistic Design of Inelastic Framed Structures, Ph. D. Dissertation, Dept. of Civil Engineering, University of Waterloo, September, 1972.Google Scholar

Copyright information

© Springer-Verlag, Berlin/Heidelberg 1975

Authors and Affiliations

  • S. R. Parimi
    • 1
  • M. Z. Cohn
    • 1
  1. 1.University of WaterlooWaterlooCanada

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