Solution Found!
Refer to Exercise 12 in Section 3.2. Assume that ?0 = 50 ±
Chapter 3, Problem 11E(choose chapter or problem)
Refer to Exercise 12 in Section 3.2. Assume that \(\tau_{0}=50 \pm 1 \mathrm {\ M P a}\), and \(k=0.29 \pm 0.05 \mathrm{~mm}^{-1}\).
a. Estimate \(\tau\), and find the uncertainty in the estimate.
b. Which would provide the greatest reduction in the uncertainty in \(\tau\): reducing the uncertainty in \(\tau_{0}\) to 0.1 MPa, reducing the uncertainty in to
, or reducing the uncertainty in
to \(0.025 \mathrm{~mm}^{-1}\)?
c. A new, somewhat more expensive process would allow both \(\tau_{0}\) and to be measured with negligible uncertainty. Is it worthwhile to implement the process? Explain.
Equation Transcription:
Text Transcription:
tau_0=50{+/-}1 MPa
w=1.2{+/-}0.1 mm
k=0.29{+/-}0.05 mm^-1
tau
tau
tau_0
0.025 mm^-1
tau_0
Questions & Answers
QUESTION:
Refer to Exercise 12 in Section 3.2. Assume that \(\tau_{0}=50 \pm 1 \mathrm {\ M P a}\), and \(k=0.29 \pm 0.05 \mathrm{~mm}^{-1}\).
a. Estimate \(\tau\), and find the uncertainty in the estimate.
b. Which would provide the greatest reduction in the uncertainty in \(\tau\): reducing the uncertainty in \(\tau_{0}\) to 0.1 MPa, reducing the uncertainty in to
, or reducing the uncertainty in
to \(0.025 \mathrm{~mm}^{-1}\)?
c. A new, somewhat more expensive process would allow both \(\tau_{0}\) and to be measured with negligible uncertainty. Is it worthwhile to implement the process? Explain.
Equation Transcription:
Text Transcription:
tau_0=50{+/-}1 MPa
w=1.2{+/-}0.1 mm
k=0.29{+/-}0.05 mm^-1
tau
tau
tau_0
0.025 mm^-1
tau_0
ANSWER:
Answer :
Step 1 of 4 :
Given,
The maximum shear stress of cracked concrete member is given to be
=
(1 - kw)
We have = 50
1 MPa, w = 1.2
0.1 mm and k = 0.29
0.05m
.
-
We have to find the estimate of
and the uncertainty in the estimate.
-
If reducing the uncertainty in
to 0.1 MPa, w to 0.01 mm and k to 0.025 m
In these which would provide the greatest reduction in the uncertainty in .
c) more expensive process would allow both and w to be measured with negligible
uncertainty, the claim is to check that is it worthwhile to implement the process.