Wind Event Probabilities 3

[Martin.H]

If a structure is designed for a 1 in 10 year wind event, but is only installed for 2 years, what is the likelihood of the structure receiving a 1 in 10 year wind event?

And what is the likelihood of the 2 year installation receiving a 1 in 50 year wind event?

I'm not sure if these are simple or complex questions. I think I might be missing something....

Martin.

 

[bones206]

10 year wind: 1 - 0.90[sup]2[/sup] = 0.19, 19% chance
50 year wind: 1 - 0.98[sup]2[/sup] = 0.04, 4% chance

Funny you ask because I'm sitting in my 2 year old house right now, experiencing probably the 3rd or 4th 10 year wind event since we moved in. Probabilities don't mean much when the historical data no longer describes current weather trends...

 

[Martin.H]

Hi bones206, thank you for your reply.

I see you're based in the US (I'm UK), but those figures (0.9, 0.98) look very similar to the c[sub]prob[/sub] values in the Eurocodes, although for 50 year return according to the formula in EN 1991-1-4, c[sub]prob[/sub] would be 1.00 (our wind speed data is based on 1 in 50 year event, if that explains anything).

Is the following interpretation of your probabilities correct:
If a building stands for 50 years, the probability it will experience a 1-in-50 year wind event is 98%.
If a building stands for 10 years, there's a 81% chance it will experience a 1-in 10 year wind event.

What I would really like to get my head around is, if a building stands for 2 years, what is the chance it will experience a 1 in 10 year event?

Is it 81% x (2/10) = 16.2%?

Eurocode EN 1991-1-6 gives the table below - one of the things I'm trying to understand is the relationship between Duration and Return Period in terms of probability of wind design force being exceeded.

Martin.

 

[Martin.H]

I think this might answer my questions, I'll take a deep dive when I get the time!

https://en.wikipedia.org/wiki/Return_period

Martin.

 

[bones206]

The probability of the 10 year wind event occurring in any given year is 1/10 = 0.10.

The probability of the 10 year wind event NOT occurring in any given year is (1 - 1/10) = 0.90.

The probability of the 10 year wind event NOT occurring in any given year, over a 2 year duration is (1 - 0.10)[sup]2[/sup].

The probability of the 10 year wind event occurring ONCE [correction] AT LEAST ONCE over a 2 year duration is then: 1 - (1 - 0.10)[sup]2[/sup].

 

[Martin.H]

Thank you very much bones.

Martin.

 

[Martin.H]

And if I was looking at occurrence over a 3 year period, the powers in those formulas would be 3, rather than 2, is that correct?


Martin.

 

[jayrod12]

Correct. Therefore the chance of having a 1 in 10 year event once in a 3 year period would be 27%

 

[Martin.H]

The penny hath droppethed.

Martin.

 

[EdStainless]

But if we consider these to be random events then the chances of a such an event are the same every day.
It does not matter what yesterday's wind was, or how long it has been since the last 'event'.
The chances are same on day 1 as they are on day 15,000.

= = = = = = = = = = = = = = = = = = = =
P.E. Metallurgy, consulting work welcomed

 

[jayrod12]

That's also correct. Technically you could have a 1 in 100 year event every day for 3 months. Extremely highly unlikely, but possible nonetheless. It's all on the probability.

 

[dik]

It's coming...

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

 

[1503-44]

Since it is more interesting to know if the building will survive the return period event, we must know the probability of the event with the given return period plus all those events of greater magnitude happening during any given year. Fortunately a return period event probability is the probability not only of the return period' event, but includes all greater events, those with higher return periods. It is the probability of at least an event of the given return period happens. It doesn't change the answer you're looking for, but it does change the question. The question then becomes, "What is the probability that an event with at least a return period of X occurs during time Y.

Pretend it's a flood. Here's the online calculator

https://www.weather.gov/epz/wxcalc_floodperiod

Dik, that's Murphy's Laws of Probability. Plus "it will happen precisely when it can do the most damage."

 

[HTURKAK]

Dera Mr. Martin.H (Structural),

My points are;

- EN 1991-1-6 at Table 3.1 ( Recommended return periods for the determination of the characteristic values of climatic actions ) specifies 50 year return period if the duration is > 1 year.

- NOTE 2 A ( at the same page ) minimum wind velocity during execution may be defined in the National Annex or for the individual project. The recommended basic value for durations of up to 3 months is 20 m/s in accordance with EN 1991-1-4.

- The fundamental basic wind velocity could be found at NA.

Dear Mr bones206 (Civil/Environmental)

.........

-The probability of the 10 year wind event NOT occurring in any given year is (1 - 1/10) = 0.90. ( TRUE )

-The probability of the 10 year wind event NOT occurring in any given year, over a 2 year duration is (1 - 0.10)2. ( TRUE )

-The probability of the 10 year wind event occurring ONCE over a 2 year duration is then: 1 - (1 - 0.10)^2. (NOT TRUE !!!)


The expression 1 - (1 - 0.10)^2 covers the probability of occurence of the 10 year wind event occurring AT LEAST ONCE over a 2 year duration.

For two year duration;

- Probability of occurence of the 10 year wind event only first year = (1/10)*(9/10)=9/100
- Probability of occurence of the 10 year wind event only second year = (9/10)*(1/10)=9/100
- Probability of occurence of the 10 year wind event for both years = (1/10)*(1/10)=1/100

So , probability of occurence of the 10 year wind event at least once over a 2 year duration =19/100 which is equivalent of the expression ( 1 - (1 - 0.10)^2 )

p.s. this probability calculation is based on that the subject event will occur only once at a year if occurs.. nowadays, with climate change and global warming, it will not be surprize if the design wind event occurs three times in a year ..

 

[Martin.H]

Many thanks for your input HTURKAK, interesting and useful.

Martin.

 

[bones206]

HTURKAK - thanks for pointing out that important semantic distinction. I wasn't precise enough with my wording. I've made the correction in my original post.