Effects of Structural Tests on Aircraft Safety

This paper investigates the effects of structural tests on aircraft safety. In particular, the paper focuses on the effect of the number of coupon tests and structural element tests on the final distribution of failure stress. The mean failure stress is assumed to be predicted by a failure criterion (e.g. Tsai-Wu), and the initial distribution of this mean failure stress reflects the uncertainty in the analysis procedure that uses coupon test data to predict structural failure. In addition to the uncertainty in the mean failure stress, there is also uncertainty in its variability due to the finite number of coupon tests. The Bayesian technique is used to update the failure stress distribution based on results of the element tests. Structural design following the FAA regulations is considered and the tradeoffs between the number of tests, weight and probability of failure in certification and in service are explored. We find that these are not very sensitive to the number of tests. Nomenclature A = load carrying area of a small part of the overall structure bt = bound of error in the design thickness, et bw = bound of error in the design width, ew eef = error associated with failure criterion used while predicting failure in the structural element tests ef = error in predicting failure of the entire structure in certification or proof test ep = error in load calculation eσ = error in stress calculation et = error in the design thickness due to construction errors ew = error in the design width due to construction errors E ( ) = expected value (i.e., mean value) Pcalc = calculated design load Pd = true design load based on the FAA specifications (e.g., gust load specification) Pf = probability of failure PFCT = probability of failing certification test σca = allowable stress (B-basis) from coupon testing σea = allowable stress (B-basis) from element testing σa = allowable stress (B-basis) of the entire structure σcf = failure stress from coupon testing σef = failure stress of the structural element (σef) test = element failure stress measured in tests (σef)calc = calculated (or predicted) element failure stress