Consider a bridge with two columns. As the foundation system settles, settlments of the two columns are denoted, respectively, byS

1

S

1

andS

2

S

2

. LetD

D

denote the differential settlement, expressed asD

=

|

S

1

?

S

2

|

.

D

=

|

S

1

?

S

2

|

.

Assume thatS

1

S

1

has a mean and variance of?

1

?

1

,?

2

1

?

1

2

, whileS

2

S

2

has a mean and variance of?

2

?

2

and?

2

2

?

2

2

. Also assume that they are correlated with a correlation coefficient denoted by?

?

.

1. What is the difference between the first order and the second order estimates of the mean ofD
2. D
3. ?
4. Give your best estimate of the variance ofD
5. D
6. ?

Consider a bridge with two columns. As the foundation system settles, settiments of the two columns are denoted, respectively, by S, and S,. Let D denote the differential settlement, expressed as D = 151 -52- Assume that S, has a mean and variance of , or, while S, has a mean and variance of us and dog. Also assume that they are correlated with a correlation coefficient denoted by p. 1. What is the difference between the first order and the second order estimates of the mean of D? 2. Give your best estimate of the variance of D