Question

1. Problem 3, HW 4 revisited. An offshore structure with a design life of 20 me wave events mav occur with a return period of 100 years (i.e. the 100-year wave). The structure is de- signed to have a 0.99 probability of not suffering damage within its design years is planned for a site where extre life. Damage effects between wave events are statistically independent (a) You found in HW 4 that the yearly probability of exceedance of the design wave height is p 1/100 0.01. Here, using the information provided above and a r.v. for damage that follows a binomial distri- bution, find the probability of damage to the structure under a single extreme wave event (damage/exceedance) from your results of p wave events follows a Poisson process? (b) Using the damage probability (damage/year) that may be determined structure in the next 10 years assuming the occurrences of extreme c) How would your answer to part (b) differ had you assumed that ex- art (a), what is the probability of damage to the follow the binomial distribution? treme wave events

**Note: You do not need to use problem 3 from homework 4 (what the question references in the beginning) all necessary information is provided

Answer 1

Solution Given thab cith design life of zo yeass An offshose stductuse is planned fo a site ahc e c t eme ωαν e events may occud with a retuon pesiod oF 100 yeoas 0 poobability of eaeceedonce of the design wave heigh 100 use binomial distsibution sith pasomete n-O whese 20-f P(x:) : 20 i (oo') (ơ.qq) =0,1652 The peobobility of domage to the structure undes a Single extdeme wave event

2 (b The peobability f damage to the stoue ure ?n the next 10 yea8s n-10 Expected numbe np: 10% o-oi Nod, we use io distsibution caith podometer foo poisso distoibutiorn whede exp (A). PCx) o0905 :. The PdobQbility OF damage to the stouctuse and ез a Sinqle cxtaeme wave evento 0405 tdeme everrts (9hersobability of everrts is vedy loo) Ge should use Poisson distibution,