1 / 15

Reliability – Based Design

b.  Design m R = m S + b  s S 2 + s R 2. Reliability – Based Design. Observe for Case 1 in which R and S are both Normal. If b   P S   Reliability   b = Reliability index = F -1 (P S ). What makes a structure safer?. Normally we cannot control loading

kieran-witt
Download Presentation

Reliability – Based Design

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. b  Design mR = mS + bsS2 + sR2 Reliability – Based Design Observe for Case 1 in which R and S are both Normal If b PS Reliability  b = Reliability index = F-1(PS)

  2. What makes a structure safer? • Normally we cannot control loading Building as ex, we can’t control wind • We can only control on resistance side We can build a larger column • Two ways: 1) higher μR higher mean capacity 2) lower σR  better quality control to reduce variation of strength of a column How about correlation between failure modes, or loading?

  3. Case 3: If R is discrete, S is continuous P(R = r) 0.6 0.3 0.1 r 5 6 7 Example on Case 3 S = N(5, 1)

  4. P(R = r) 1 r 5 6 7 P(R = r) 1 .8 .6 .4 .2 r 6 5 7 Challenge 1 • What if R is not discrete? Example on Case 4 S = N(5, 1) Cut into strips trapezium

  5. Challenge 1 • If we use 5 strips,

  6. Challenge 1

  7. Central Limit Theorem S will approach a normal distribution regardless the individual probability distribution of Xiif N is large enough More importantly, S will have a mean of And Variance of Or a Variance of

  8. fE(e) (a) E(E) = 0 1/2 -1 0 +1 e P4.27

  9. (b) P(E < 0.01% of length of segment) (area under rectangular curve) (c) T = total mean = E1 + E2 +…+ E124 E(T) = 124  0 = 0 Var(T) = Var(E1) + Var(E2) +…+ Var(E124) = 124Var(E) = 124  1/3 = 41.33 sT = 6.43 Distribution of T  Normal (C.L.T) \ P(T < 0.01% of 2 miles) Assume s.i. if not S.I., P ?  By making more measurements, the % error is decreasing  P(within given tolerance limit) 

  10. … X g(X) g’(mX) (X – mX) mx - mx Var(X) g(mX) mX X Taylor Series Approximation First order approximation:

  11. If mK = 400 ; sK = 200 If M = 100  Example

  12. K M M S.I. What if M is also random?  mM = 100; sM = 20 then What if not S.I.?

  13. Challenge 2 Product of many normal is log-normal? Transform Take log on both sides, and let S = ln P, X = ln Y with N (λ,ξ) And find μx, σx (This is “moments” of r.v. but we are NOT transforming to normal) By CLT, S is Normal with Then P can be calculated using the transformation formulae

  14. 4.17

  15. 4.17

More Related