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51_HWKTTE 4004c - (5-14 42 In Equation 5-14 the values of...

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41 Probability density function For the LRFD design, the probability of failure to occur for a given load and resistance distribution is of fundamental importance. The latter is calculated with the “probability density function” which is defined as the probability that X occurs in the interval x to x + d x as f x (x)dx (see Figure 5-1). The total area under the curve f x (x) must be equal to unity because a probability of 1 includes all possible outcomes. Figure 5-1. Lognormal Probability Density Function Based on the distribution of the resistance data, a lognormal probability distribution was recommended for the resistance data by the AASHTO Specification. A normal function was used to represent the observed distribution of load data. Equation 5- 14 presents the lognormal probability density equation. ( 29 - - = 2 ln 2 1 exp 2 1 ξ θ ξ π x
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Unformatted text preview: (5-14) 42 In Equation 5-14 the values of θ and ζ are the lognormal mean and lognormal standard deviation respectively, + = 2 2 2 1 ln R R λ σ ξ (5-15) 2 2 1 ln θ-= R (5-16) Where σ R and λ R are the standard deviation and the mean of the resistance as defined in prior sections. LRFD components Probability of failure. The LRFD approach defines the probability of failure of a structure based on the load and resistance distribution curves. Figures 5-2 shows the probability density functions for normally distributed load and resistance. The shaded area represents the region of failure where the resistance is smaller than the loads. For the load and resistance curves, the margin of safety can be defined in terms of the probability of survival as ( 29 Q R P p s = (5-17)...
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