tailieunhanh - A variable separation method for the calculation of the reliability of construction

In this paper, a variable separation method for determining the reliability of construction is proposed. Therefore, the reliability is a multiflication of two probabilities: The probability of the occurrance of load and the probability of construction in the condition the load has a determined value. | Vietnam Journal of Mechanics, NCST of Vietnam Vol. 23, 2001, No 3 (167 - 172) A VARIABLE SEPARATION METHOD FOR THE CALCULATION OF THE RELIABILITY OF CONSTRUCTION NGUYEN VAN PHO University of Civil Engineering ABSTRACT. In this paper, a variable separation method for determining the reliability of construction is proposed. Therefore, the reliability is a multiflication of two probabilities: The probability of the occurrance of load and the probability of construction in the condition the load has a determined value. 1. Introduction Linearization method and iterative method have been used in the reliability theory for determining the safety probability Ps or the reliability index /3. But it is not applicable; in many important problems, because of the great value of standard deviations or deficiency of characteristic probabilities of some random variables. Some simple cases of variable separation method were considered in (1, 2]. In this paper, a variable separation method for determining the safety probability Ps in construction is proposed. For illustration, a simple axample is considered. 2. Some existing methods for determining the safety probability . Linearization method [3] Let the safety margin M be non-linear and given by M = f(x) = f (x1, X2, . , Xn), () where xi are basic variables. Then by expanding M in a series about the linearization point r o o . ,xno]T x o = LX1,X2, (x 0 is usually chosen as the expectation point) and retaining only the linear terms one gets. () 167 · · wh ere t h e d envat1ves xg. 81 ~ UXj j = 1, 2, . . . , n, are evai uat ed. at t h e i inearization point Approximate values for the mean value µMand the standard deviation be calculated from (). aM can () () Finally, the reliability index /3 is defined from () and () by /3 = µM.