Lec16_Structural_Reliability_Example

# Lec16_Structural_Reliability_Example - R – 0.5 Var[ln(R =...

This preview shows pages 1–4. Sign up to view the full content.

Lecture 16; page 12 Structural Reliability - Revisited S = load effect (lognormal) lognormal) R = resistance of structure to load lognormal) V = R/S = safety factor for structure < 1 failure > 1 no failure P[ V < 1 ] = P[ R S < 1]

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Lecture 16; page 13 SOLUTION STRATEGY: Resistance Load Safety Factor Real Space variables R S R/S = exp[ U ] | | /\ \/ \/ | Log Space variables lnR lnS —> U = lnR – lnS ~ N
Lecture 16; page 14 Let R and S be independent and lognormal where E[R] = 120 E[S] = 75 Var[R] = (10) 2 Var[S] = (15) 2 Find mean and variance of ln(R) Var[ ln(R) ] = ln[ 1 + σ R 2 R 2 ] = ln[ 1 + (10) 2 /120 2 ] = 0.00692 = (0.0832) 2 E[ ln(R) ] = ln[μ R ] – 0.5 Var[ln(R)]

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: R ] – 0.5 Var[ln(R)] = ln[120] – 0.5 (0.0832) 2 = 4.78 Doing the same for ln[S] Var[ ln(S) ] = ln[ 1 + σ S 2 /μ S 2 ] = ln[ 1 + (15) 2 /75 2 ] = 0.0392 = (0.2) 2 E[ ln(S) ] = ln[μ S ] – 0.5 Var[ln(S)] = ln[75] – 0.5 (0.2) 2 = 4.30 Lecture 16; page 15 The variable of interest is U = ln(R) – ln(S) ~ N(μ lnR – μ lnS , σ lnR 2 + σ lnS 2 ) = N( 4.78 – 4.30, (0.0832) 2 + (0.2) 2 ) = N( 0.486, 0.046 ) = N( 0.486, (0.21) 2 ) P[ R/S < 1] = P[ ln(R) – ln(S) < 0 ] = P[ (U-μ U )/ σ U < –0.486/0.21 ] = P[ Z < –0.486/0.21 ] = P[ Z < – 2.26 ] = 0.012 = 1.2% (using tables) Using bivariate normal model obtained failure probability of 0.6% —> model choice matters....
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern