TABLE OF CONTENTS Recently, many probabilistic studies on structural strength are reported in connection with reliability analysis. With regard to column strength, several investigations have been made since Dutheil (1950) evaluated column test results statistically. Most studies are limited to elastic column strength considering only the initial deflection of a column as the random variable (Boyce, 1961; Fraser and Budiansky, 1969). Probabilistic analyses in the plastic range, using tangent modulus theory with the modulus of elasticity and the yield stress being treated as random variables, were made by Chung and Lee (1971), Rokach( 1970), and Augusti and Baratta(1971). Some of them include the initial out-of-straightness of a column as a random variable. Common to all of the above mentioned solution procedures is their treatment of the random column strength parameters as independent, which is an assumption that is not correct in general.
In this chapter, first basic statistical equations which are necessary in the study of column strength reliability are summarized. Their derivations or proofs are not given here, for which readers can find many text books in this field (see for example, Haugen, 1968; Bolotin, 1969). It is assumed for simplicity in this chapter that all random variables governing the column strength follow the normal distribution. Design procedure for elastic columns is then discussed in connection with reliability analysis. Finally, probabilistic multiple column curves are introduced following Bj rhovde's work (1972).
Discrete random variable
Consider a random variable x which takes m discrete values
