The total axial load, Y, that is acting on a column is the sum of the following load effects, which are listed in the table given below, together with their statistical parameters. All load effects are assumed to be statistically independent and normally distributed. 

a) Find the mean value, standard deviation and coefficient of variation of the total load, Y. 

b) If the coefficient of variation of the axial design capacity of the column, D, is 0.25 and if it is a normally distributed random variable statistically independent of Y, what is the reliability (i.e. survival probability) of this column, if it is designed for a mean safety factor (S.F.) of 1.75?

c) If the coefficient of variation of the axial design capacity of the column, D, is 0.25 and if it is a normally distributed random variable correlated with Y with a correlation coefficient p= 0.7, what is the reliability of this column, if it is designed for a mean safety factor (S.F.) of 1.75?

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Load Effect Expected Value (kN) Coefficient of Variation Dead Load (D) 50 0.03 Live Load (L) 80 0.20 Equivalent Wind Load (W) 20 0.25 Snow Load (S) 10 0.25 Equivalent Earthquake Load (E) 35 0.40 Load Effect Expected Value (kN) Coefficient of Variation Dead Load (D) 50 0.03 Live Load (L) 80 0.20 Equivalent Wind Load (W) 20 0.25 Snow Load (S) 10 0.25 Equivalent Earthquake Load (E) 35 0.40