# Lognormal Distribution

1. Dec 5, 2004

### omgitsroy326

I'm quite confused bout lognormal distribution and normal distribution

Consider a three-span continuous beam. All supports are pinned supports. Each span has a length of l. The beam
has a modulus of elasticity E and a moment of inertia I. All spans are subjected to a uniformly distributed load W.
The maximum deflection of the beam occurs in the outer spans and is equal to

0.0069Wl^4 / (EI)

(a) Your job is to evaluate the probability pF that the deflection will exceed the code-specified limit of l/360
assuming that W, E, and I are statistically independent lognormal random variables and given the following
information:
l = 5 m (deterministic)
W has a mean value of 10 kN/m and a coefficient of variation of 0.4.
E has a mean value of kN/m2 and a coefficient of variation of 0.25.
I has a mean value of m4 and a standard deviation of m4.

I have the solution for it but i'm lost on when

Variables W E I are all lognormal distribution.
Now to solved for the mean you would do
d = 0.0069Wl^4 / (EI)

Now since you can't divide or multiply lognormal distributions you would have to ln the entire formual of d to be:

ln d = ln .0069 +lnW + 4ln L - ln E - ln I

since you're takin the natural log of a lognormal distribution it becomes a normal distribution ... Why is this ??? i'm confused on this part .