Structural reliablity : a probabilistic approach to the design of mechanical components

This thesis deals essentially with the new probabilistic design approach, which bas largely replaced the classical deterministic point of view. The latter is based upon the concept of a factor of safety, while the probabilistic approach is based upon the criterion of structural reliability. Structural reliability is normally evaluated using stress-strength interference theory, whereby the knowledge of the stress and strength distributions becomes a fundamental factor for such calculations. A new method of obtaining these distributions is developed, Basically, however, the degree of overlap of the stress and strength distributions determines the probability of non-failure of the structure, otherwise termed the reliability of the structure. Some new numerical techniques are suggested here for evaluating this reliability, and which ought prove especially valuable for cases where the stress and/or strength distributions are other than normal. In an effort to elucidate the connection between the probabilistic and the classical approaches, the research has been extended to determine the relationship between the reliability of the design and the factor of safety involved. A nomogram has been constructed which permits the practicing engineer to find the factor of safety for his design once the design reliability level and the parameters of the stress and strength distributions are known. An especially useful point concerns the bounds of the reliability, if the actual value of the latter cannot be accurately determined. Some new bounding techniques are derived whereby the lower and/or upper confidence bounds of the reliability value may be found. Further, investigation of the reliability concept shows that the value obtained from the interference theory, as mentioned above, is valid only for the case of static loading. For a mechanical structure submitted in general to a dynamic load, this value is only a local or instantaneous measure of the safety of the design, and thus does not reflect the time parameter. A more realistic measure of safety would be furnished by a "Probability of Survival" or a "Reliability Function". Consideration of survival probability should be based, among other things, on the concept of "Failure Rate" or the Mean Time Between Failures (MTBF), which is not normally available for mechanical components. In an effort to overcome this difficulty, a convenient "Reliability Function" is proposed. The development is based on the assumption that the probability of failure of a structural component, as derived from the stress-strength interference theory, may be considered numerically equal to the instantaneous failure rate of the component. Different expressions for the Reliability Function are derived for different models of strength degradation