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This paper presents a statistical procedure for expressing factors or margins of safety in terms of failure probabilities. The procedure involves identifying the basic variables in a structural or stress analysis and evaluating the statistical measurements of these variables in terms of mean, standard deviations and variances. An approximate rule of statistical algebra is then applied to obtain the relationship between margins of safety and failure probabilities. The present paper is restricted to variables that exhibit a normal probability distribution. A discussion is given on the advantages and limitations of the present statistical approach and an example is used to illustrate the calculation procedure.

Despite recent improvements in finite element applications, random vibration problems encountered in practical design situations continue to be tackled by a traditional simplified approach based on a single mode and single degree of freedom response. This paper presents an outline of this approach and examines its accuracy and validity by correlating its results against a finite element program for two specific examples. The correlation indicates that stress predictions using the traditional approach based on equivalent static loads are acceptable for design purposes, but displacement velocity and acceleration response estimates can be dangerously optimistic. The effects of damping and modal interactions on structural response are studied and the difficulties associated with accurate damping selection are also discussed from a practical standpoint.