# Optimal Criteria in Probabilistic Structural Design

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

## Abstract

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.

## Keywords

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.

## Notation

A

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

CFi

cost of failure in mode i

CI

initial erection cost of a structure

Ci

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

CT

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

i

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 $${\overline M _p}$$

pFi

probability of structural failure in mode i

PSi

probability of structural survival in failure mode i

PS*

probability of survival for the structure with optimal member strengths

Ri

specified reliability of structure against failure in mode i

Z

structural weight (proportional to the initial erection cost)

Z0

specified limit on the structural weight, Z

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