=RiskDiscrete(Mass!A33:A65,Mass!B33:B65)

short tons

=RiskLognorm(3.86,1.31)

degrees

Vox

=RiskLognorm(1.44,5.5,RiskTruncate(0,6))

feet per second

Voy

=RiskLognorm(0.048,0.083,RiskTruncate(0,1))

feet per second

Vn

=(B14*SIN($B*PI()/180)+B15*COS($B*PI()/180))

feet per second

Fm

=RiskOutput("Impact Force") + 0.435*($B*2/32.2)*(B14*SIN($B*PI()/180)+B15*COS($B*PI()/180))

kips

(1) The statistical results from the PBIA are

shown in Table D-4. This table shows the minimum,

maximum, mean, and standard deviation from the

simulation data for the impact force. However, since

Minimum

0.05

the PBIA is performed to calculate the return periods,

Maximum

978.89

the output needs to be expressed in terms of either the

Mean

47.21

histogram, cumulative probability distribution, or the

corresponding percentiles of the impact loads. These

Std Dev

67.52

are all derived from the output or graphing capabilities

Note: To convert force to kilonewtons, multiply by 4.448.

from with the @Risk simulation program.

(2) The histogram shows the range and distribution of expected annual impact forces. Figure D-9

shows the histogram for this example. The histogram shows that a majority of the impact forces (over

90 percent as shown in Figure D-9) from the simulation are below the mean value of 209.95 kN

(47.2 kips). From this histogram, a cumulative probability distribution of impact forces can be fit. Figure

D-10 shows the cumulative probability distribution for the PBIA. The cumulative probability distribution

is used to determine the percentage of distribution that is below a specified level. Figure D-10 shows that

90 percent of impact values below the mean value and 10 percent of the distribution lie above that value.

(3) For a PBIA, the simplest way to determine the return period is to use percentiles for the distribu-

tion of annual impact forces. Percentiles are defined as the percentage of annual impact force that occurs

at or below that impact force. The resulting percentiles can be used to determine the Probability of

Exceedence *P*(*E*), which is the converse of the percentile such that both should add up to unity. The return

period *RT *can be determined by using the equation

= 1/*P*(*E*)

The values for this PBIA example are shown in Table D-5.

D-8

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