homework_8_2005

# homework_8_2005 - (b If the column has a 0.40 m x 0.40 m...

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Homework Set #8 A plain concrete column is subjected to a random axial load W with lognormal distribution, mean value kN 3000 m W = [kN = Kilo Newton, a unit of force] and coefficient of variation . The resulting compressive stress is given by 2 . 0 V W = σ A W = σ , where A is the cross-sectional area of the column. The crushing strength of concrete f c also has lognormal distribution, with mean value (m = meter) and coefficient of variation 2 f kN/m 000 , 35 m c = 2 . 0 V c f = . (a) Obtain the probability density function (PDF) of the applied stress σ (which depends on A).
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Unformatted text preview: (b) If the column has a 0.40 m x 0.40 m square cross-section, what is the probability P F that it fails i.e. ] f [ P P c F > σ = ? Assume W and f c are independent. Hint: c f ln 1 c f c f < ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ σ ⇔ < σ ⇔ σ < (c) Determine the required cross-sectional area of the column for a target failure probability of 10-3 . (d) Find the mean stress A m m W = σ as a function of the failure probability P F . Plot against for between 10 ) P ( m F σ ) P log( F F P-4 and 10-1 ....
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