Meccanica

, Volume 6, Issue 3, pp 168–171

# Upper and lower bounds for the optimum design of structures with random resistance

• Giannantonio Sacchi
Article

## Summary

The expected value of the minimum weight of material necessary for a structure in order to support assigned loads is considered, when the « resistance » of each element is a random quantity.

By going back to a theorem which gives a lower bound for this expected value, a way to compute an upper bound is shown.

A way of evaluating the variation of the interval of the existence of the average is then set out.

Such bounds are functions of random variables but are evaluated on the basis of a deterministic limit design.

### Keywords

Mechanical Engineer Civil Engineer Lower Bound Optimum Design Alla

## Sommario

Richiamato un teorema[4] che fornisce un minorante del valore medio del volume minimo di strutture soggette a carichi noti e dotate di elementi costituiti da materiale a resistenza aleatoria, si dimostra l'esistenza di un maggiorante.

Si dimostra poi come sia possibile stabilire un maggiorante ed un minorante della varianza del minimo volume, e quindi come si possa apprezzare il rischio d'errore connesso alla aleatorietà delle resistenze, nella valutazione del volume minimo.

I limiti indicati, benchè derivati da elaborazioni statistiche sulle resistenze, risultano da un progetto ottimale sviluppato con soli calcoli deterministici.

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### References

1. [1]
A. Castellani,Average Value of the Safety Coefficient in a Framed Structure Corresponding to Randon Distributions of Yield Stresses, Meccanica no. 4, 1969.Google Scholar
2. [2]
G. Sacchi,Limit Analysis and Design of Structurss Having Elements with Randon Distribution of Yield Stresses with Associated and Non-associated Flow-Laws, Meccanica no. 1 1971.Google Scholar
3. [3]
C. Gavarini,Calcolo a rottura e programmazione stocastica, Giornale del Genio Civile, August 1969.Google Scholar
4. [4]
G. Sacchi,Upper and Lower Bounds for the Average and for for the Safety Coefficients of Structures with Random Resistance, Meccanica no. 2, 1971.Google Scholar
5. [5]
A. Zavelani Rossi,Minimum-Weight Design for Two-dimensional Bodies, Meccanica, Vol. 4, no. 4, 1969.Google Scholar
6. [6]
A. Pugsley,The Safety of Structures, Edward Arnold, London, 1966.Google Scholar
7. [7]
R. E. Rowe,Current European Views on Structural Safety, ASCE., S.T.3, March 1970.Google Scholar
8. [8]
J. L. Jorgenson, J. E. Golderg,Probability of Collapse Failure, ASCE. S.T.8., Aug. 1968.Google Scholar
9. [9]
A. H. S. Ang, M. Amin,Reliability of Structures and Structural Systems, ASCE. E.M.2, Apr. 1968.Google Scholar
10. [10]
A. H. S. Ang, M. Amin,Safety Factors and Probability in structural design, ASCE. S.T.7, July 1969.Google Scholar
11. [11]
A. H. S. Ang,Extended Reliability Basis of Structural Design under Uncertainties. 9th Reliability and Maintainability Conference., Detroit, July 1970.Google Scholar

## Authors and Affiliations

• Giannantonio Sacchi
• 1
1. 1.Istituto di Scienza e Tecnica delle CostruzioniPolitecnico di MilanoItaly