Document
docx
keyboard_arrow_up
School
The University of Tennessee, Chattanooga *
*We aren’t endorsed by this school
Course
2460
Subject
Industrial Engineering
Date
Jan 9, 2024
Type
docx
Pages
10
Uploaded by ash77hem
Shear Strength of Bolts: Data Analysis and Reporting Specifications
XI.
Analysis of Data
Recall the objective of Mini Lab: Validate the formula, equation 1, predicting the critical load to failure for a bolt loaded in double shear. This will be accomplished by experimentally observing the failure load then comparing that to the load predicted by theory.
XII.
Prepare Mini Lab Report
Prepare a mini lab report in accordance with the following guidelines: Refer to Sample Mini Report at end of this document.
Format: Memo style as follows:
Date: mo/day/year
To: Instructor
From: Student name
Subject: Lab ID and Lab Name
Content
The mini lab report shall contain three sections only: Results, Q&A, and Appendix as specified below: I.
Results:
This section shall present results in the form of Tables and Captioned Figures as specified:
Tables One table required;
Table 1: Compare predicted and observed of: P
CRIT
:
Failure loads (4 specimens)
τ
ULT
:
Ultimate shear strength
Table shall report the uncertainties in the observed and predicted values
±
Δ
OBS’D
and ±
Δ
PRED’D
Table shall report the % deviation
%deviation=(observed-predicted)predicted100
Table shall report the Total Error as a % %Total Error
=∆ObservedObserved+∆PredictedPredicted*100
Tables shall report values with appropriate significant figures.
Refer to Table 1 at the end of this document for an example of the typical comparative table.
Captioned Figures: One captioned figure is required: Figure 1 One chart shall contain two plots:
One plot of the observed P
CRIT
vs. Area
Observed: plot with ‘markers’ NO LINES
One plot of the predicted P
CRIT
vs. Area
Predicted: plot with smooth solid lines NO MARKERS
ALL captioned figures shall be numbered and captioned Axes of plots shall be labeled with appropriate units
Markers will describe observed data
Solid lines will describe theoretical, predicted or published behaviors
Captions shall contain three to four descriptive sentences to identify the plots and to highlight the significance of the information revealed in the plot. Refer to Figure 2 below for an example of the typical captioned figure. II.
Q&A
This section gives you an opportunity to demonstrate the extent that you know, understand and are able to apply the principles associated with the Mini Lab. Please keep your responses short, concise
and thoughtful. Please reply in complete sentences. Bulleted lists are fine if appropriate. Number each response using the Q#.# below and please re-
state each question immediately prior to each response. Issue 1: Assumptions: Don’t these make an ass out of u and me??
The objective of this lab is to experimentally validate the formulas for predicting the load to failure of bolts in shear. The main assumption is that failure load is proportional to the cross section area. See eq. 1above.
Q1.1
Is the observed behavior consistent with the assumed dependence on area? Explain. Now consider the test fixture. It is intended to load the bolt in pure shear. Inspect the fixture. Inspect the bolt specimens after failure.
Q1.2.a
What evidence would suggest the bolt was in pure shear when loaded to failure? Q1.2.b
What evidence would suggest the bolt was not
in pure shear when loaded to failure? Q1.2.c
To what extent were the bolts specimens actually loaded in pure shear? Explain. Take note of differences between smaller diameter and larger diameter specimens.
Issue 2 Conclusions: Is the Theory, Prediction or Publication Valid??
Criterion for validation of a prediction by experimental observation is somewhat arbitrary. In this lab (ENGR2460L)
a prediction is deemed validated if the %Deviation < 25% AND if the %Total Error <25%. Even if arbitrary, this quantification
provides a sound basis for Conclusions
related to validation.
The Objective(s) of the Mini Lab cited in II above is to experimentally validate the formulas for predicting the torsional spring constant for straight and tapered shafts. Have the objectives been met? Depending on your assessment of the lab results, you might conclude that 1) All Objectives were achieved or 2) No Objectives were achieved or 3) Some Objectives were achieved and others were not. Therefore, answer a or b or c, below.
Q2.1.a If you conclude that All objectives were achieved, explain how the results reported in the Tables including the % deviation and total error are evidence of the validations.
Q2.1.b If you conclude that No objectives were achieved, explain how the results reported in the Tables including the % deviation and total error are evidence of the failure to validate.
Q2.1.c If you conclude that some objectives were achieved and some were not, explain how the quantified results reported in the Tables including the % deviation and total error are evidence of the validations or evidence of failure to validate.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
Issue 3 Recommendations: How Can This Study Be Improved??
Think of Recommendations
as advice you would give to the next inquisitive person who might repeat the study, advice that would improve the usefulness or strength of the study. One path to improvement lies in reducing total error. The queries below seek identification of specific recommendations to reduce the error and uncertainty in the predicted and observed results. Q3.1.a Identify the largest single source of error/uncertainty in the Predicted
? Q3.1.b Estimate the magnitude of 3.1.a with respect to the Δ
Predicted?
Q3.1.c Make a recommendation aimed to reduce the magnitude of the error in 3.1.a. Q3.2.a Identify the largest single source of error/uncertainty in the Observed
? Q3.2.b Estimate the magnitude of 3.2.a with respect to the Δ
Observed?
Q3.2.c Make a recommendation aimed to reduce the magnitude of the error in 3.2.a. REMEMBER: Experiment Validates Predictor:
If Maximum Error is reasonable (say < 20%) AND
If Deviation (%) < Maximum Error (%)
Appendix
Appendix A
Measurements & Observations:
Include tabulations of all measurements Copy/paste Excel templates, Remove the color used to fill the fields
Appendix B
Formulas and Sample Computations
Estimation of Predicted and Observed Parameter(s)
Estimation of Uncertainties in Predicted and Observed Parameter(s)
Partial Derivative Method
High Low Method
Save Lab Report and Convert to PDF
a.
Save properly named Lab Report in PDF format
b.
Save a copy for your own use
XIII.
Submit Mini Lab Report and Excel file (the template filled in with your data)
Date: 07/19/2022
To: Dr. Goulet
From: Ashkon Hemmati - Arass
Section: Wednesday
Subject: Strength of Bolts
Results:
Table 1. Comparison of Observed and Predicted Properties of Bolts In Shear
Bolt Type
PRED
PRED
OBS’D
OBS’D
Deviation
(%)
Total Error
(%)
PCRIT of
1/4”-20
(lbs)
10699
89
10660
185
0.36
2.6
ULT of
1/4”-20
(ksi)
112.5
8
112.1
2
0.36
8.9
PCRIT of
16830
545
16060
330
4.6
5.3
5/16”-18
(lbs)
ULT of
5/16”-18
(ksi)
112.5
8
107.35
5
4.6
11.8
PCRIT of
3/8”-16
(lbs)
24368
398
23060
482
5.4
3.7
ULT of
3/8”-16
(ksi)
112.5
8
106.46
6
5.4
12.7
PCRIT of
7/16”-14
(lbs)
32636
119
32150
636
1.5
2.3
ULT of
7/16”-14
(ksi)
112.5
8
110.82
3
1.5
9.8
Figure 1: Plot displaying observed Strain vs Sress for aluminum. The linear heavy solid black line indicates the predicted value for the Modulus of Elasticity, E
PRED
= 68.9 GPa. The heavier solid blue line indicates the observed behavior. The Trendline estimation of the E
OBS
is 46.6 GPa. The deviation is 32% between the observed and predicted.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
Figure 2: Plot displaying observed Strain vs Sress for acrylic. The linear heavy solid black line indicates the predicted value for the Modulus of Elasticity, E
PRED
= 3.3 GPa. The heavier solid blue line indicates the observed behavior. The Trendline estimation of the E
OBS
is 1.12 GPa. The deviation is 67% between the observed and predicted.
II.
Q&A
Q1.1
Which model most closely agrees with the observed behavior of acrylic? Explain.
Answer: The linear elastic model follows the observed behavior of acrylic more so than the other model. When examining the plotted graph for acrylic the strain vs stress plot resembles a linear line. Q1.2
Which model most closely agrees with the observed behavior of aluminum? Explain.
Answer: The linear elastic-perfectly plastic model follows the observed behavior of aluminum more so than the other model. When examining the plotted graph for aluminum the strain vs stress plot resembles a curve that then straightens out for the continuation of the plot which is characteristic of the linear elastic-perfectly plastic model.
Q2.1
Compare the Trendline result for E
OBS
based on: (a) 100% of the points in the linear region; (b) the “first” 20% of the points in the linear region and (c) “last” 20% of the points.
Answer: (a) Based off of 100% of the points the trendline will remain the same for both aluminum and acrylic; (b) Based off of the first 20% of the points the trendline for aluminum will be higher than the observed trend and for
acrylic it will be similar to the observed; (c) Based off of the last 20% the trendline for aluminum will be within the range of the observed and for acrylic it will be a bit outside of the range of the observed values.
Q2.2
Estimate the error/uncertainty in E
OBS
that is introduced in the arbitrary selection of data points and enter this into the Table. Answer: Please see Tables 1 & 2, under the “E” row, labeled as Q2.2.
Q3.1.a If you conclude that All objectives were achieved, explain how the results reported in the
tables including the % deviation and total error are evidence of the validations.
Answer: Not all objectives were achieved so please see Q3.1.c.
Q3.1.b If you conclude that No objectives were achieved, explain how the results reported in the
tables including the % deviation and total error are evidence of the failure to validate.
Answer: Some objectives were achieved so please see Q3.1.c.
Q3.1.c If you conclude that some objectives were achieved and some were not, explain how the
quantified results reported in the Tables including the % deviation and total error are
evidence of the validations or evidence of failure to validate.
Answer: If the deviation and total error are below 25%, for the specific variable, then the objective has been achieved to prove that the experiment proves said equation/theory. In this lab the YLD & ULT for aluminum and TEN for acrylic are all below 25%, however, all the other variables predicted and quantified are above 25%.
Q4.1.a Identify the largest single source of error/uncertainty in the Predicted
?
Answer: For the predicted the largest source of error is in the % Elongation as evidence by
the deviation and total error.
Q4.1.b Estimate the magnitude of 4.1.a with respect to the Δ
Predicted?
Answer: The magnitude is 16% (low) and 20% (high) for aluminum, and 3.5% (low) and
5.5% (high) for acrylic.
Q4.1.c Make a recommendation aimed to reduce the magnitude of the error in 4.1.a. Answer: I would recommend that a range be given for the % Elongation that way the error/
uncertainty can be more accurate. This may involve using a different type of material for the
acrylic and aluminum.
Q4.2.a Identify the largest single source of error/uncertainty in the Observed
?
Answer: In the observed, again the % Elongation is completely off in both aluminum and
acrylic. This can either be an error in reading the data and/or an error in using the Instron
5566.
Q4.2.b Estimate the magnitude of 4.2.a with respect to the Δ
Observed?
Answer: The magnitude is 38.8% (low) and 49.2% (high) for aluminum, and 74% (low) and
94% (high) for acrylic.
Q4.2.c Make a recommendation aimed to reduce the magnitude of the error in 4.2.a. Answer: I would recommend instructions for finding the % elongation and uncertainty. I went off of the excel file provided and followed how it was determined from the template. There isn’t really a direct way of quantifying what the correct value of error/uncertainty is, at least I couldn’t figure it out.
III.
Appendix
Appendix A
Measurements & Observations:
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
Appendix B
Formulas and Sample Computations
Estimation of Predicted Parameter(s)
Estimation of Uncertainties in Predicted Parameter(s)
Partial Derivative Method
High Low Method