Question

Please upload the excel sheet steps also so we can do it on our excel.

1. The settlement of each footing shown in the figure below follows a normal distribution with a mean of 2 in. and a coefficient of variation of 30%. Suppose the settlements between two adjacent footings are correlated with a correlation coefficient of 0.7; that is, the differential settlement is: D = |S1-S2 Where S1 and S2 are the settlements of footings 1 and 2, respectively. 777 77TTTTTTTTTT Footing 1 Footing 2 (a) Determine the mean and variance of D. (b) What is the probability that the magnitude of the differential settlement will be less than 0.5 in.? * Please attach the Excel spreadsheet or provide the Matlab code you used to solve the problem.

Answer 1

solution - from the given dater, as find the mean of differential settlement ! M = Ms. - Ms. there, mean of Settlement of footing I is. Ms, and mean of settlement of footing 2 is a Substitute 2 in for day, and a in. for M82, to find us u=2in. – ain a Hence, the mean of differential sttlement is a) find the variance of differential Settlements Var(D) = var (S.) + var (S2) - 2pvarcs) var (s)- Find the variance of settlement of footing 1. Var (S.) = (Ms, x Cov,2 Belstitute 2 for Ms, and 0.3 for coovito find Var (S.). var (S.) = (Ms, x C.O.V.) 2. var (s) = (2x0.3)2 - 0.36

find the variance of settlement of footing 2 var (S2) - (Ms, & Co. U6) ² substitute 2 for use and 0.3 for con to Eind var (S2) Var (S2) = (2x 0.32 -0.36 Now, find the variance of differential settlement using Equation (1) Substitute 0.36 for var (S.), 0.36 for var (s) and 0.7 for p in equation (1), to find var (D) var (D)= 0.36+ 0.36-260.7 (0.36) (036) = 0.72-0.504 = 0.216 Hence, the variance of differential settlement in 0.216) find the probability that the magnitude of the ditterential settlement will be less than osin. PC-05 20 20.5)= ( 0.5-4.) - (0.5 M ) - 12) The standard deviation of differential Settlement is so- Svar Co.

find the probability that the magnitude of the differential Settlement will be less than 0.5 in. using equation 42). substitute o for us and Jo. 216 for 6, in Equation (2) PC-0.52D<0:9)= od = 5 (1-076) - 0 (-1.076) = 3 (1.076)- 1 + $ (1.076) - 28(1.076)-1 from the standard normal probabilities & values is 1.076 and interpret the value of (1.076) as 0.858. P(-0.5LD20.5 - 2 (0.858) - 1 - 0.716 Hence, the probability that the magnitude of the differential Settlement will be less than 0.5 cis (0.716)