PROBABILISTIC DESIGN TECHNIQUES APPLIED TO MECHANICAL ELEMENTS

Abstract

ABSTRACTA little known stress analysis technique is applied to the design of a titanium tension member of a complex mechanical coupling in a situation where space limitations preclude the application of the conventional factor of safety. The computed safety factor for the critical section in this instance is a normally unacceptable 1.42 based on the tensile yield point and only slightly higher based on the ultimate tensile strength.The stress‐strength probability technique, applied here, is in some ways a more realistic design method in that it takes into account the potential for variability of the yield strength (or ultimate strength if desired) of the material as determined from a significant amount of test data. It also accounts for variations in the calculated stress by allowing for dimensional variations as expressed by dimensional tolerances as well as for any potential for variation of the maximum design loading.In this instance, each of these “random variables” can be expressed as a normal or Gaussian distribution in terms of a mean value and a standard deviation; the relatively uncomplicated mathematics of random variables is applied to determine the percentage of overlap between the calculated (Gaussian) stress distribution and the known strength (yield point) distribution. This overlap gives the probability of failure.The calculated probability of failure for the critical section of the tension member under study is less than 1 times 10‐7, or less than one failure in 107 such units that could be manufactured. The corresponding reliability for the section is 0.9999… to seven decimal places, a very safe value for this application, despite the low factor of safety.The paper discusses the significance of the reliability value vis‐a‐vis the “factor of safety” design approach as well as the limitations involved. Guidance is offered for establishing overall reliability goals for a unit or assembly with several significantly stressed sections.The probability design techniques are shown to be compatible with sophisticated stress analysis techniques such as finite element analysis, although a little ingenuity is required. An example is given.