HW#5_f08_sol - CE 3102 Fall 2008 Homework #5 Due: 9:45 AM...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
CE 3102 Fall 2008 Homework #5 Due: 9:45 AM October 28, 2008 This is a team assignment. You may work together in teams of up to, but not exceeding, three people. Only one written submission is required from each team. However, every team member is responsible for knowing all of the material. 1. Problem 4.15, p. 194 A&T. (a) P=(1/2)CRV 2 Ln(P)=ln(1/2)+ln(C)+ln(R)+2ln(V) Since C, R, and V are lognormal random variables, ln(C), ln(R), ln(V) are normal random variables, ln(P) is a linear combination of normal random variables, so ln(P) is also normal, which means P is a lognormal random variable. The pdf for P then has the form = σ μ π ) ln( ) 2 / 1 ( exp 2 1 ) ( p p p f where )] [ln( 4 )] [ln( )] [ln( )] [ln( )] [ln( 2 )] [ln( )] [ln( ) 2 / 1 ln( )] [ln( 2 V VAR R VAR C VAR p VAR V E R E C E P E + + = = + + + = = Let )] [ln( )] [ln( 2 C VAR s C E m C C = = Since C is a lognormal random variable, we (ought to) know that 1 ) exp( 20 . 0 2 exp ] [ 80 . 1 2 2 = = + = = C C C C s s m C E δ or 568 . 0 2 0392 . ) 8 . 1 ln( 2 ]) [ ln( 0392 . 0 ) 1 2 ln(. ) 1 ln( 2 2 2 2 = = + = + = C C C C s C E m s
Background image of page 1

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

View Full DocumentRight Arrow Icon
Similarly 1844 . 0 695 . 4 00995 . 0 08 . 6 2 2 V V R R s m s m so finally 787 . 0 ) 1844 (. 4 00995 . 0392 . 185 . 3 ) 695 . 4 ( 2 08 . 6 568 . ) 2 / 1 ln( 2 = + + = + + σ μ (b) 404 . 0 596 . 1 ) 244 . 0 ( 1 ) 244 . 0 ( 787 . 185 . 3 ) 30 ln( 787 . 185 . 3 ) ln( )) 30 ln( ) (ln( ) 30 ( = = > = ⎛− > = > = > Z P Z P P P P P P P (c) Let S denote the strength of the tower. Failure occurs if the load exceeds the strength, so ) 0 ) ln( ) (ln( 1 ) ( ) ( > = > = > = S P P S P P S P P failure P S is lognormal so ln(S) is normal, and ln(P)-ln(S) is also normal. 489 . 4 ) 2 / 0225 (. ) 90 ln( )] [ln( 0225 . ) 1 ) 15 ln((. )] [ln( 2 = + = S E S VAR so 0735 . 9265 . 1 ) 45 . 1 ( 1 ) 45 . 1 ( ) 45 . 1 ( 0225 . 787 . ) 489 . 4 185 . 3 ( 0 0225 . 787 . ) 489 . 4 185 . 3 ( ) ln( ) ln( ) ( = = = > > = + > + = Z P Z P Z p S P P failure P (d) Suppose Let N denote the number of windstorms in 25 years, and let X be the number of those that are strong enough to cause failure. The probability a windstorm causes failure
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This document was uploaded on 02/05/2011.

Page1 / 7

HW#5_f08_sol - CE 3102 Fall 2008 Homework #5 Due: 9:45 AM...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online