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,