Similarly the difference of two gaussian random

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Unformatted text preview: f of also follows a Gaussian distribution having mean and variance as: n n Z ai X and 2 ai2 X 2 respectively. i 1 i Z i 1 i Problem 1. For the safety of a building, the total force acting on the columns of the building should be examined. The total force acting on the columns are the effects of the dead load ( D ) , the live load ( L ) , and the wind load ( W ) . If the load effects acting on the individual columns are statistically independent and Normally distributed with mean and standard deviation as given, D 22kN and D 1.5 kN L 30 kN and L 3.5 kN W 18 kN and W 3.0 kN Determine the mean and standard deviation of the load acting on the column (i) The strength of the column also follows normal distribution with a mean equals to 1.5 times the total mean force. The coefficient of variation of the strength is 15% and the strength and load effects are statically independent. Determine the probability of the column. Solution. (i) Let the total load be represent as T , then T D L W It follows a normal distribution, therefore T D L W 22 30 18 70 kN and, 2 2 2 T D L W 1.5 2 3.5 2 3.0 2 4.85 kN (ii) Let the strength of column be represented as S and if the strength of the column S is less than the total load, T , then the column will fail. If R represents the difference between strength and total...
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This note was uploaded on 03/18/2014 for the course CE 5730 taught by Professor Dr.rajibmaity during the Spring '13 term at Indian Institute of Technology, Kharagpur.

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