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The vertical displacement v of a cracked slurry
Chapter 3, Problem 18E(choose chapter or problem)
The vertical displacement \(v\) of a cracked slurry infiltrated fiber concrete member at maximum shear stress is given by v = a + bw, where \(w\) is the crack width, and \(a\) and \(b\) are estimated from data to be \(a=2.5\pm0.1\mathrm{\ mm}\) and \(b=0.05 \pm 0.01\). Assume that \(w=1.2\pm0.1\mathrm{\ mm}\).
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?
Equation Transcription:
Text Transcription:
v
w
a
b
a = 2.5 pm 0.1 mm
b = 0.05 pm 0.01
w = 1.2 pm 0.1 mm
Questions & Answers
QUESTION:
The vertical displacement \(v\) of a cracked slurry infiltrated fiber concrete member at maximum shear stress is given by v = a + bw, where \(w\) is the crack width, and \(a\) and \(b\) are estimated from data to be \(a=2.5\pm0.1\mathrm{\ mm}\) and \(b=0.05 \pm 0.01\). Assume that \(w=1.2\pm0.1\mathrm{\ mm}\).
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?
Equation Transcription:
Text Transcription:
v
w
a
b
a = 2.5 pm 0.1 mm
b = 0.05 pm 0.01
w = 1.2 pm 0.1 mm
ANSWER: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,