Probability considerations in assessing the effects of structural out-of-plumbs

Design expressions based on statistics have been derived in earlier papers to account for the destabilizing effects of the gravity loads acting through the random out-of-plumbs of members in structures. The reliability of the predictions and the soundness of the theory itself depend on the basic assumptions that the out-of-plumb variables are uncorrelated and that the loads are deterministic.An examination of the nature and implications of these assumptions is presented in this paper. Of particular interest is the determination of the final safety obtained for "out-of-plumb" effects when the design is based on the limit states technique prescribed by the Canadian Standard CAN3-S16. 1-M78. It is demonstrated that the expected probability of failure is increased due to the existing dependence between the out-of-plumbs of adjacent members but is reduced due to the randomness of the factored gravity loads. As a result, the final probability of failure appears to be somewhat lower than that implied by the prob...