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 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.
- Spring '13
- Civil Engineering