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...
View
Full
Document
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
 Dr.RajibMaity
 Civil Engineering

Click to edit the document details