First Order Approximations and correlation

The shear strength. T . ofa soil is given by the expression T 2 C + S tan (D where (' denotes the cohesion, S denotes the effective normal stress, and (D is the friction angle. The quantities (7. S and (D are uncertain with the following rst and second moment properties: ______.__________4- Mean Jur' = 100 psi \"3 : 800 psi pm : 0.60 rad Standard deviation 5r = 40 psi Us = 100 p5; do = 0_15 rad Correlation coefcients p\". = 0 Pam = 0 pm. 2 -0.30 ______'_____-._____- 3) Compute the first-order approximation of the mean and standard deviation of T b) Compute the rst-order approximation of the correlation coefficient between T and (D