The vertical displacement v of a cracked slurry infiltrated fiber concrete member at maximum shear stress is given by v = a + b w, where w is the crack Width, and a and b are estimated from data to be a = 2.5 ± 0.1 mm and b = 0.05 ± 0.01. Assume that w= 1.2 ± 0.1 mm.

a. Estimate v. and find the uncertainty in the estimate.

b. Of the uncertainties in w, a, and b, only one has a non-negligible effect on the uncertainty in v. Which one is it?

Answer:

Step 1 of 4:

Given the vertical displacement v of a cracked slurry infiltrated fiber concrete member at maximum shear stress is given by v = a+ b w, where w is the crack width, and a, b are estimated from data. Then,

Step 2 of 4:

a). We have to estimate v and to find the uncertainty in the estimate.

First we have to estimate v.

That is,

v = a+ b w

= 2.5 + 0.05(1.2)

v = 2.56

To compute , we first compute partial derivatives of v, we get

=

= 1

= w

= 1.2 mm

= b

= 0.05.