Home > MEG 302 Lab "Materials Testing"

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Dr. Brendan O'Toole, Ph.D., Associate Professor of Mechanical Engineering SEB 2218, (702) 895 – 3885, bj@me.unlv.edu

Mr. Jeff Markle, jmarkle@me.unlv.edu TBE B-162, (702) 895 - 5597

All labs are performed in TBE B-150. The Teaching Assistants (TA��s) usually run the entire lab including: instruction, grading, and evaluation of student performance. Contact the laboratory coordinator if there is a problem that cannot be resolved directly between the student and the TA.

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Vishay Measurements Group Strain Gage Website Strain Gage Installation Manual

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• Planning the lab schedule each semester • Coordinating the lab schedule with the lecture schedule as much as possible • Revising and updating the laboratory manual • Helping the Teaching Assistants (TA��s) prepare for the labs • Resolving conflicts between students and TA��s (if necessary)

• Maintenance of laboratory equipment (planned and emergency) • Keeping track of laboratory supplies:

o Strain gages and accessories o Test Samples o Soldering irons

• Keeping copies of equipment manuals • Upgrading and installing new equipment • Training students, staff, and faculty on new equipment as needed

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ME 302 (CEE 370L) Course Objectives

The primary objective for this course is to provide hands on experimental experience in characterizing mechanical properties of materials. Students will learn:

• Laboratory safety procedures • Uncertainty analysis of data (error propagation) • Statistical analysis of data • Laboratory report writing skills • Tensile Testing Procedures for finding: Young��s Modulus, yield strength and strain, ultimate

strength and strain, and failure strength and strain of metallic materials

• Procedure for determining Poisson��s ratio of materials • Flexure testing procedures for determining Young��s modulus • Torsion testing procedures for determining shear modulus • Flexure test procedures for determining beam deflections • Column compression procedures for investigating buckling behavior

Students will also perform a group project where they will propose and conduct their own laboratory experiment.

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Reports are due on the date indicated in the lab schedule (one week after completion of the laboratory)

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All lab reports are to be word processed, except the original data which will be included as an appendix.

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All graphs are to be computer generated. Provide a graph title, and label the axis and major graduations. Always provide units where applicable.

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Lab reports are to be structured as shown on the Laboratory Report Contents Sheet.

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All equations, graphs, tables, and figures are to be numbered, with the appropriate "call-out" reference within the text. Also provide a Table of Graphs and Figures immediately following the Table of Contents if the report has many figures.

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The reports will be graded on format, content, and grammar, so be sure you proofread (and spell check) your reports.

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Late lab reports are accepted at a penalty of 10% per day (excluding Saturday & Sunday). Reports will not be accepted more than one week late.

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All students will participate in a Laboratory group project. The objective of this project is to provide an opportunity for all students to participate in the process of designing an experiment. All topics must be approved by the Teaching Assistants. The groups must have between 4 and 5 members. You cannot work alone; you must work in a group.

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The project should be a simple experiment that can be performed in 1-2 hours.

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Lab projects must make use of the principles learned in ME 302 and must involve material testing using knowledge obtained in ME 302L.

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The project will require one written report for each group.

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Projects must be performed and reports submitted by

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All laboratory reports (except Lab # 1)

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Necessary if the report has more than 5 figures or 5 tables..

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State the lab objectives.

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Provide a brief summary of the results.

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Provide background information regarding the experiment.

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Include the application of the experiment to theory.

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Indicate what the anticipated results of the experiment are, if known. In most cases, theoretical values (from the tables in the book) are the anticipated results.

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Engineering students need to know how to include computer generated equations in reports. Use Microsoft equation editor for generating equations in your lab reports. o The equation editor can be accessed by selecting the ��Insert�� tab from the menu bar, then select ��Object��, then select ��Microsoft Equation��. Equation symbols are selected from the various menus.

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Describe the specimens tested (type of material, physical dimensions, etc.).

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Identify the instruments used, including manufacturer and model number.

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Provide a

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Include a sketch of the experiment setup. This may be hand drawn, but be neat.

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Identify the equations used to obtain the results.

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Present the results.

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Provide appropriate plots, graphs, and tables.

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Make sure the report "flows" from the beginning to the end of the experiment; don��t present final results prior to intermediate calculations.

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( )

s. prediction al theoretic from determined are results expected or the (textbook) source reliable ain data tabulated from found are results expected the where, 100 Error %

Results Expected Results al Experiment - Results Expected

⊗ =

.

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Indicate sources of error. Do not just say, "human error." Be specific.

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•

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State what the results mean.

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Was the experimental method used a valid one? Explain why or why not.

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Did you accomplish the objectives of the lab? This is not a "yes/no" question. You must explain how the objectives were or were not met.

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Remember that you may not always get the "proper results" even though you followed the procedure and performed the experiment properly.

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Provide all raw data collected in the lab (In other words, your original data sheet. This is hand written, and will not be graded for neatness).

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Provide a list of references.

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Prepared For: ��Your Laboratory TA��, ME 302L Department of Mechanical Engineering University of Nevada, Las Vegas Prepared By: Your Name Your Group Members Date Laboratory Performed: Date Submitted:

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University of Nevada Las Vegas

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(MEDICAL OR FIRE)

then give them: A. YOUR NAME, B. BUILDING, (THOMAS BEAM ENGINEERING) C. ROOM NUMBER (ROOM TBE-B-_ _ _ ) D. TELL THEM CALMLY AND CLEARLY WHAT THE EMERGENCY IS. E. FOLLOW THEIR DIRECTIONS. If there is a need to evacuate the building, pull the fire alarm and exit the building and meet at the designated meeting place. The designated location for everyone to meet immediately after exiting the building during an emergency is on the sidewalk near the parking lot and just east of the loading ramp leading to the back entrance to the Artemus W. Ham Concert Hall. Make sure that the instructor or TA writes your name on a list before you depart the area. If you are injured and do not need 911 assistance, immediately notify your supervisor and the department��s Management Assistant and follow their standard procedures. If neither of those are immediately available, notify any professor of any shop staff.

UNLV PUBLIC SAFETY (POLICE) EMERGENCY # 911 NOTE - Do not dial ��O�� first for on campus emergencies. NON-EMERGENCY 895-3668

Ms. Becky Delacruz 895-4226 Occupational Safety Technician (OSHA) bdelacruz@ccmail.nevada.edu Mr. Ed Gannon 895-1791 Fire Safety Compliance gannon@ccmai.nevada.edu Mr. Courtney Kerr 895-42265 HAZMAT Compliance courtney kerr/UNLV@UNLV

MECHANICAL ENGINEERING DEPARTMENT OFFICE 895-1331 Machinist/Modeler: KEVIN NELSON TBE-B-162A, 895-4285, kevinn@me.unlv.edu Lab Director: Jeff Markle TBE-B-162A, 895-5597, jmarkle@me.unlv.edu CIVIL AND ENVIRONMENTAL ENGINEERING DEPARTMENT OFFICE 895-3701 TECHNICIAN: ALLEN SAMPSON TBE-B-162A, 895-4300, sampson@ce.unlv.edu

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I ________________________________________(Name) have read and understood the laboratory safety procedures and policies. I am responsible for following these procedures while in the laboratories. ______________________________ __________ (Signature) (Date)

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Calculate the arithmetic mean, median, and mode of a data set.

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Identify the range of a set of data.

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Calculate the variance and standard deviation of a data set.

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Perform a simple linear regression on a data set.

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Create a plot showing the data set and the linear regression lines on the same plot.

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Determine the uncertainty in reported experimental data by calculating the error propagation from measured variables. All required materials will be handed out and discussed in class, so no background preparation is required before this lab.

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Statistics is the science of collection, classifying, and interpreting information based on the number of samples. The primary purpose of using statistics when reporting laboratory data is to determine the average value and repeatability of the experimental results between multiple specimens. The minimum number of specimens need to conduct statistical analysis is three.

�� =

��

, where

( )2

2

�� ��

- =

��

for a population or

( )2

2

1

�� ��

- = -

��

for a sample. Use the first equation (for a population) is the entire set (or population) of data is used to calculate the variance. Use the second equation if only part of the data set is used to calculate the variance.

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= +

To obtain a best fit model, we will use the least square method, which minimizes the Sum of the Squared Errors (SSE) to the best fit line. In this method, the best fit line is given by:

1 0

= + , where

( )

( ) ( )

1 2 2

- = -

�� �� �� �� ��

and 0

1

= -

Also:

( )

( ) ( ) ( ) (

)

2 2 2 2

- = ⌈ ⌉ ⌈ ⌉ - - �� �� �� �� ⌊ ⌋ ⌊ ⌋

�� �� �� �� �� �� ��

The coefficient of determination is defined as

2

.

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th

and 6

th

value. The median value of production is (121 + 163)/2 = 142.

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2

was calculated for each production value in this column; �� is the arithmetic mean, which was calculated previously. The sum of all these values was determined and the variance was found by dividing by n (10). ��n�� was used instead of ��n-1�� because the entire population of data was used to determine variance. The calculations lead to a variance (��2 ) value of 12,625 and a standard deviation (��) of 112. The same numbers were determine using the built in MS Excel functions VARP() for ��variance of a population�� and STDEVP() for ��standard deviation of a population��. Line Production units (y) # of workers (x) (y-��)

2

6 61 14

14738

9 79 14

10692

3 95 16

7639

7 121 20

3770

4 121 21

3770

10 163 22

376

1 179 24

12

8 240 37

3318

5 352 50

28764

2 413 53

53176 sum 1824 271 126254 mean (��) 182.4 27.1 range 352 Variance (n) (my calcs) 12625 Stand. Dev. (n) (my calcs) 112 Variance (Excel) 12625 Standard dev (Excel) 112

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1 0

= + , where

( )

( ) ( )

1 2 2

- = -

�� �� �� �� ��

and 0

1

= -

Also:

2

x*y x

2

6 61 14

14738 854 196

9 79 14

10692 1106 196

3 95 16

7639 1520 256

7 121 20

3770 2420 400

4 121 21

3770 2541 441

10 163 22

376 3586 484

1 179 24

12 4296 576

8 240 37

3318 8880 1369

5 352 50

28764 17600 2500

2 413 53

53176 21889 2809 number of data points, n 10 sum 1824 271 126254 64692 9227 mean (��) 182.4 27.1 range 352 Variance (n) (my calcs) 12625 Stand. Dev. (n) (my calcs) 112 Variance (Excel) 12625 Standard dev (Excel) 112 Sum(x) * Sum(y) 494304 n * Sum (x*x) 92270 [Sum (x)]2 73441 n * Sum(x) * Sum (y) 646920 b1 8.11 b0 -37.3

So the best fit equation of the line to fit the data is:

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y = 8.1054x - 37.256 R2 = 0.9798 0 50 100 150 200 250 300 350 400 450 0 10 20 30 40 50 60

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( )

( ) ( ) ( ) (

)

2 2 2 2

- = ⌈ ⌉ ⌈ ⌉ - - �� �� �� �� ⌊ ⌋ ⌊ ⌋

�� �� �� �� �� �� ��

A few more lines and columns are added to the MS Excel table in order to calculate r and r

2

, which are shown at the bottom of this table. Both values match the values shown in the trendline equation calculated with the built in functions of MS Excel. Line Production units (y) # of workers (x) (y-��)

2

x*y x

2

y

2

6 61 14

14738 854 196 3721

9 79 14

10692 1106 196 6241

3 95 16

7639 1520 256 9025

7 121 20

3770 2420 400 14641

4 121 21

3770 2541 441 14641

10 163 22

376 3586 484 26569

1 179 24

12 4296 576 32041

8 240 37

3318 8880 1369 57600

5 352 50

28764 17600 2500 123904

2 413 53

53176 21889 2809 170569 number of data points, n 10 sum 1824 271 126254 64692 9227 458952 mean (��) 182.4 27.1 range 352 Variance (n) (my calcs) 12625 Stand. Dev. (n) (my calcs) 112 Variance (Excel) 12625 Standard dev (Excel) 112 Sum(x) * Sum(y) 494304 n * Sum (x*x) 92270 [Sum (x)]2 73441 n * Sum(x) * Sum (y) 646920 b1 8.11 b0 -37.3 n * Sum (y*y) 4589520 [Sum (y)]2 3326976 denominator inside SQRT 2.38E+10 coefficient of correlation, r 0.9898 coefficient of determination, r2 0.9798

2

. It is shown at the bottom of the previous table.

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th

inch marks as the smallest measuring increment. When you hold the paper up to the ruler, you could see that the paper is much thinner than 1/8 inch (0.125 inches). You may estimate that the paper is about 1/10 of the smallest increment of measurement of your ruler or 0.0125 inches. However, you really cannot say that this is an accurate measurement. At best, you could say you could measure to half the smallest increment on your ruler, or �� 0.0625 inches. Therefore the best way to report the measured thickness of that sheet of paper is 0.0125 inches �� 0.0625 inches. The ���� 0.0625�� inches is the uncertainty of your measurement. In this case your uncertainty is huge compared to the actual measured value. You should use a measuring tool with a much smaller resolution in this case. A micrometer that reads values to �� 0.0001 inches would be a much better tool to measure the thickness of a piece of paper since the average thickness of a sheet of copy paper is about 0.004 inches. Results from some experiments are calculated from several different measured values. The strength of a tensile specimen is equal to the measured ��force�� at failure divided by the cross-sectional area of the specimen. The cross-sectional area is proportional to the specimen diameter squared. Both the diameter and force measurements will have different uncertainties.

2 1 2 2 2 2 2 1 1

�� �� ⌋ ⌉ �� �� ⌊ ⌈ �� �� ⎠ ⎞ �� �� ⎝ ⎛ ∂ ∂ +∙ ∙∙∙ + �� �� ⎠ ⎞ �� �� ⎝ ⎛ ∂ ∂ + �� �� ⎠ ⎞ �� �� ⎝ ⎛ ∂ ∂ =

(Eq. 1) Where, WR = the uncertainty in the experimental results R = the given function of the independent variables x1, x2, ����xn R = R(x1, x2, ����xn) w1, w2, ����wn = the uncertainty in the independent variables

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2 2 4

4

��

�� ��

= = =

Using Equation 1 to determine the uncertainty in the stress,

1 2 1 2

2 2 2 2 2 3

4 8

�� ��

�� �� �� ��

⌈ ⌉ ∂ ∂ ⎛ ⎞ ⎛ ⎞ = + �� �� �� �� �� �� ∂ ∂ ⎝ ⎠ ⎝ ⎠ �� �� ⌊ ⌋ ⌈ ⌉ ⎛ ⎞ ⎛ ⎞ - ⎛ ⎞ ⎛ ⎞ = + �� �� �� �� �� �� �� �� �� �� ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ �� �� ⌊ ⌋

�� = 111 ksi

Corresponding average yield load (YL) P = 5449 lbs Uncertainty in Load Value

( ) ( ) ( ) ( ) ( )

1 2 1 2 1 2

2 2 2 3 2 2 2 3 2 2 4 4 2

4 8 8 5449 lbs 4 7 lbs 0.001 in 0.25 in 0.25 in lbs lbs 20,336 788,631 in in lbs 899 in

�� �� �� ��

�� �� �� ��

⌈ ⌉ ⎛ ⎞ ⎛ ⎞ - ⎛ ⎞ ⎛ ⎞ = + �� �� �� �� �� �� �� �� �� �� ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ �� �� ⌊ ⌋ ⌈ ⌉ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ - �� �� �� �� �� �� �� �� �� �� = + �� �� �� �� �� �� �� �� �� �� ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ �� �� ⌊ ⌋ ⌈ ⌉ = + �� �� ⌊ ⌋ =

Therefore the uncertainty in the yield stress calculation due to experimental error is 899 psi. The yield stress can be reported as: YS = 111 ksi �� 0.899 ksi or YS = 111 ksi �� 0.8% (since 0.899/111 = 0.008099 or 0.8 %)

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100

∆ ∙

The uncertainty in % Elongation is calculated using Equation 1:

( )

( ) ( ) ( ) ( )

( )

1 2 1 2

2 2 % 2 2 % 2

% % 100 100

∆ ∆

⌈ ⌉ ⎛ ⎞ ⎛ ⎞ ∂ ∂ �� �� = + �� �� �� �� �� �� �� �� ∂ ∆ ∂ �� �� ⎝ ⎠ ⎝ ⎠ ⌊ ⌋ ⌈ ⌉ ⎛ ⎞ ⎛ ⎞ - ∆ ⎛ ⎞ ⎛ ⎞ = + �� �� �� �� �� �� �� �� �� �� ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ �� �� ⌊ ⌋

( ) ( )

( ) ( ) ( ) ( )

( )

[ ]

( )

1 2 1 2 1 2

2 2 % 2 2 2 % 2 % %

100 100 100 0.2107 in 100 0.001 in 0.001 in 1 in 1 in 0.01 0.00044 0.102

∆

⌈ ⌉ ⎛ ⎞ ⎛ ⎞ - ∆ ⎛ ⎞ ⎛ ⎞ = + �� �� �� �� �� �� �� �� �� �� ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ �� �� ⌊ ⌋ ⌈ ⌉ ⎛ ⎞ ⎛ ⎞ - ⎛ ⎞ ⎛ ⎞ �� �� �� �� �� �� = + �� �� �� �� �� �� �� �� �� �� ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ �� �� ⌊ ⌋ = + =

Therefore the uncertainty in the % Elongation due to experimental error is 0.102 %. The percent elongation can be reported as: %El = 21.1 % �� 0.102 %

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Homework

Eight sales people (a population) were monitored in transactions to determine the relationship of dollar sales (y) generated to customer interactions (x) within a set time frame. The experimental values obtained were: Salesperson Dollar Sales (y) Customer Interactions (x) 1 9890 52 2 6774 38 3 10234 49 4 8892 44 5 4312 31 6 15997 56 7 9015 44 8 8320 47 Perform the following (you must show all work): 1. Find the median dollar sales. 2. Find the arithmetic mean of the dollar sales. 3. Find the mode of the customer visits. 4. Find the range of the dollar amount. 5. Find the variance and standard deviation of the dollar amount. 6. Perform a least squares regression of y on x. 7. Plot both the raw data and the linear regression equation on the same graph. Label all axes. 8. Find the coefficient of correlation. 9. Find the coefficient of determination. 10. Determine the estimated dollar sales for 50 customer interactions. 11. Discuss your results.

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*

: Jack P. Holman, ��Experimental Methods for Engineers,�� McGraw-Hill Book Company

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• Connect strain gages and a clip-on extensometer to a strain indicator box. • Use the Tinius-Olsen Universal Testing Machine (TOUTM) to test specimens in axial tension. • Create a stress-strain graph from laboratory data and determine the following properties:

o Modulus of Elasticity o Yield Strength and Yield Strain o Ultimate Strength and Ultimate Strain o Failure Strength and Failure Strain (% Elongation), o % Reduction of Cross-Sectional Area

• Use statistics to obtain mean and standard deviation for these values. • Use uncertainty analysis to determine measurement error in the calculated values. • Compare the measured properties from laboratory experiments to expected values obtained

from reference sources such as the textbook or internet. A good source of material property data on the internet is: http://www.matweb.com

• Metal specimens with attached strain gages (steel, aluminum, brass, copper, ��) • Tinius-Olsen Universal Testing Machine (TOUTM) • Calipers (for measuring dimensions of the specimens) • Epsilon Model 3542 clip-on axial extensometers • VISHAY P3 Data Acquisition Box • Calculator

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Obtain specimens from the laboratory teaching assistant (TA). The specimens should be cylindrical dogbone shaped specimens. Measure the total length, LT, the gage length, LG, and the gage section diameter, dG. The diameter and total length should be easy measurements. The gage length may be difficult because the transition from straight section to curved section may be difficult to find. Make your best measurement and use an appropriate uncertainty value based on your confidence of the measurement. Use calipers provided in the lab for these measurements. Check with the TA about the proper use of the calipers if you need help making the length measurement. A minimum of 3 measurements should be obtained and averaged for each dimension. LT LG dG

Measured Dimensions #1 #2 #3 Average Uncertainty

Specimen #1 Total Length Length of Gage Section Diameter of Gage Section Specimen #2 Total Length Length of Gage Section Diameter of Gage Section Specimen #3 Total Length Length of Gage Section Diameter of Gage Section

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A strain gage should be mounted to each of your three specimens. Visually inspect the strain gage. It should be mounted flush to the specimen with the grid lines in the axial direction of the specimen. Two small lead wires should be soldered from the small pads on the gage to larger pads mounted next to the gage. There are many different types of strain gages but they all work using the same principal. A small voltage is applied to the gage from the data acquisition box. And the gage provides some measurable resistance. The electrical resistance of the gage is proportional to the length of the small wire grid that makes up the gage. As the specimen is strained, the length of the wire grid increases and the resistance changes. The resistance is proportional to the strain in the specimen. The following strain gage information is needed in order to obtain the proper strain values. Ask the TA for this information if it is not marked on the specimen.

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Beginning in the spring 2010 semester; an axial clip-on extensometer will also be used to measure strain on each specimen. Manufacturer: Epsilon Technology Corp. Model: 3542-0200-030-ST Gage Length: 2 in Travel: +0.600 in (+30%), -0.200 in (-10%)

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o Make sure the strain gage is working while waiting for your turn to test the specimens. o Place the specimen flat on a table. o Connect the lead wires to the practice strain gage box following the instructions on the inside cover of the box. The TA will be able to assist with this. o Make sure the ��Amp zero�� has been zeroed. o Enter the correct gage factor. o Set the box to ��Run�� and try to zero out the strain reading by adjusting the balance dial. Most gages should be able to reach a zero reading when there is no load applied. Occasionally the gage cannot be set to zero but it still may be functioning properly. Make a note of the strain reading prior to testing if the gage will not go all the way to zero. This will be used as a reference value for the strain readings during the test. o Disconnect your specimen from the practice box.

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o What is the uncertainty in your specimen dimension measurements? ___________ o What is the uncertainty in the strain readings? ___________

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1) Insert Specimen, Connect Strain Gages, and Balance Strain Gages a) Place the specimen flat on a table and connect the strain gage lead wires to the Vishay P3 strain gage indicator and recorder attached to the TOUTM. b) Read the Vishay P3 operating instructions before the lab. See the file on the course website. The TA��s will help with the operation of the P3. c) Balance and zero the strain reading on the Vishay P3 indicator/recorder before mounting the specimen in the Tinius Olsen grips. d) Balance and zero the force reading on the Vishay P3 indicator/recorder (and on the dial indicator of the Tinius Olsen machine) before mounting the specimen in the Tinius Olsen grips. e) Mount the specimen into the grips of the Tinius-Olsen machine. f) Note: Mounting the specimen in the grips of the Tinius Olsen may impart a small preload and prestrain on the specimen. This is an actual load and strain on the specimen so do not re-zero the strain or load on the P3 indicator at this point. 2) Mount and Balance the Clip-On Extensometer a) Attach the extensometer to the specimen b) Connect the lead wires to the Vishay P3 recorder. c) Set the extensometer strain value to zero.

3) Set the Tinius Olsen controls to "lower" and "slower". 4) Set the P3 to record mode. 5) Slowly increase the speed of the crosshead to the desired testing speed. This machine can not be set to a specific testing cross-head velocity. The TA��s will help set the speed based on prior experience. The speed will be set so that each specimen will be loaded to failure in approximately 3-5 minutes. 6) The Vishay P3 indicator/recorder will be displaying and recording the force and strain readings at approximately 1 second intervals. a) The strain gages will only function up to about 2 % strain (0.02 in/in or 20,000 �̦�). The failure strain may be much higher than this for some specimens so you may not have enough strain data to construct an entire stress-strain curve. b) The extensometer should record strain up to 30%. 7) Stop the test after the specimen fails. 8) Save the data file to the hard drive of the computer in TBE B-150. Use a unique folder/file name to clearly identify this specimen. This may include a series of folders like: C:\MEG_302L\F_06\Sect_01\steel_specimen_01.dat 9) Carefully remove the specimen and inspect the shape near the failure surface. Make notes about the appearance of the failure surface. Take a picture and include it in the report if a digital camera is available. If you take a picture or pictures; make sure you can match the picture to a specific specimen and data file later on when you are working on your report. 10) Carefully put the two pieces of the specimen together and measure the final length of the specimen. Use this length to determine the failure strain of the specimen. 11) Measure the diameter of the specimen at the failure location. Use this measurement to determine the % reduction in cross-sectional area. 12) Repeat the experiment with the next specimen. Your group should be testing three specimens of the same material. The material type is identified by colored markings on the ends of the specimen.

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• Description of specimens including dimensions, materials, and preparation procedures. • Description of equipment and testing procedures. • Description of data reduction methods. The data file should have 3 columns of data for each

specimen: force, strain from the strain gage, and strain from the extensometer. Create separate stress-strain curves from the strain gage and extensometer data. If the experiment runs smoothly, these curves should match well for low strains but you may only get extensometer data at the higher strains. You must determine the following calculations for at least 3 specimens of the same material: 1. Copy the raw data from the computer, which should have 4 columns (time, force, and strain gage strain, and extensometer strain). Make sure you know the units used in the data file before you leave the lab. 2. Add another column for stress and calculate the engineering stress (�� = P/A0) for each force reading. A0 is the original cross-sectional area of the gage section of the specimen. 3. Create a graph of stress vs. strain from the strain gage data and another one from the extensometer data. Clearly label the title identifying the material and specimen number. Clearly label the axes with the correct units. Remember that the strain gage will probably stop working at some time during the test. The indicator may show a very high constant value at some point after the gage fails. Do not include these values in the graph. 4. Determine the Modulus of Elasticity by measuring the slope of the initial linear portion of the stress-strain curve (from strain gage and extensometer). ▪ MS Excel can do this by displaying the equation of a line fit through a portion of the stress- strain curve. ▪ NOTE: The curve may have an initial non-linear portion that is due to the slipping and tightening of the grips as the specimen is initially loaded. Ignore this part of the curve when determining the Modulus of Elasticity. ▪ If using MS Excel, you may need to create a full stress strain graph with all the data. Make a copy of this graph and then delete the initial data points that are outside the linear region. Also delete any data points near the end of the file if they are outside the linear region. Then use the curve fitting tool to find the equation of the line and determine its slope. 5. Determine the Yield point (Yield Stress and Yield Strain) in the curve using the 0.2% offset method discussed in class and in the textbook. You may need to make another graph with a close-up view of the initial portion of the data.

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This lab will consist of experimentally determining the value of Poisson��s Ratio for three different materials (steel, copper, and aluminum) by performing a bending experiment on a flat bar and measuring the axial and transverse strain. At the conclusion of this lab, you should:

• Know the definition of Poisson��s Ratio and expected values for Poisson��s Ratio. • Be able to determine Poisson��s Ratio from lab data.

Prior to reporting to the lab, prepare for this lab by obtaining "published" values of Poisson��s Ratio for steel, copper, and aluminum.

�� �� ��

= -

This experiment uses a bending specimen to create axial and transverse strains in a specimen. It is not necessary to fully understand bending stresses and strains in order to conduct this experiment. It is important to realize that the applied force in the bending test configuration shown below causes stress in the specimen in the axial direction. Therefore, there will be an axial strain due to the applied load. There will also be a transverse strain due solely to the Poisson��s Ratio effect in the material since there is no load in the transverse direction of the specimen. Axial gage Transverse gage Thickness Width Applied Force

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• Three metal specimens (steel, copper, aluminum) with attached strain gages • Strain Indicator Box (2 channels) • Micrometer

• Measure the width and thickness of the specimen. • Attach the strain gages to the indicator boxes, and determine which box is measuring axial

strain and which is measuring transverse strain.

• Clamp the specimen to the table, with most of the specimen hanging over the edge of the table.

Make sure the strain gages are not close to the table edge.

• Mark a point on the specimen at which to hang the weights. Place the weight hanger on the

specimen, and record the strain data.

• Load the weights. After hanging each weight, record the strain data. Continue until all weights

have been placed on the weight hanger.

• Repeat the procedure for each specimen.

• The test setup and detailed procedures. • Calculate the value of Poisson��s Ratio at each increment, then average to obtain ��. • Compare the calculated value of �� to the published values for each of the materials. • Make a plot of the data with ��x on the

compared to the value of �� calculated above.

• Include all other data, equations, calculations, and discussion you believe is necessary to

demonstrate that you have achieved the objectives of this lab.

Tables on the following page can be used to record data during experiments.

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The objective of this lab is to experimentally explore the relationships between several different variables in an experiment that applies torsional load to a circular cross-section rod of length L. Variables that will be investigated include the applied torque, angular deflection, length of rod, polar moment of inertia, and shear modulus. The TQ Products STR6 experimental apparatus is used for this experiment. See the following pages for a complete description of the experiments to be performed as part of this lab. The experiments described on the following pages mention the use of steel and brass specimens. The experiments usually work better with the brass specimens. The teaching assistant for your section may opt to use only the brass specimens and test a wider range of specimen lengths. If you use the steel specimens and the results do not come out as expected; think about and discuss possible causes. Steel has a higher shear modulus than brass. Is the specimen slipping in the grips? Could the specimen have been overloaded beyond its yield point?

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This lab will use the bending equations to find the Modulus of Elasticity of a specimen. At the conclusion of this lab, you should:

• Be familiar with the equation for bending stress. • Be able to calculate the bending stress at any point along a beam. • Use laboratory results to construct a stress-strain graph of a beam in bending. • Find the Modulus of Elasticity from lab data collected from a cantilever beam in bending.

To prepare for this lab, look up the equation for calculating bending stress. Next, assume the following: h = 0.258 inches b = 1.00 inches L = 4.40 inches M = 1916 grams

��x = 0.000112

where h is the bar thickness, b is the bar width, L is the distance from the application of the force to the strain gage, M is the mass in grams, and ��x is the strain recorded from the strain box. Using the data provided, calculate the stress at the strain gage, then calculate the Modulus of Elasticity for this single data point using Hooke��s Law. (hint: units, units, units, units, units)

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• Three metal specimens (steel, copper, aluminum) with strain gages attached • Strain Indicator Box • Micrometer • Ruler

•

Measure and record the width and thickness of the specimen.

•

Attach the strain gage leads to the strain indicator box. Zero the box.

•

Clamp the specimen to the edge of the table with the axial strain gage facing up. Make sure the strain gage is not near any support.

•

Place the mass hanger near the end of the specimen.

•

Measure and record the distance from the mass hanger to the strain gage.

•

Record the strain reading resulting from the mass hanger.

•

One at a time, place each of the 500-g masses in the mass hanger. After each mass is added, record the resulting strain reading.

•

Repeat for all specimens.

•

Calculate stress for each load reading for each specimen.

•

Calculate E using Hooke��s Law for each load reading for each specimen.

•

Plot stress versus strain for each specimen.

•

Calculate E using linear regression for each specimen. Set the y-intercept to zero for the linear regression.

•

For each specimen, compare the results to each other and to the published values of E. Calculate percent error and cite source of published value.

•

Include all other data, equations, calculations, and discussion you believe is necessary to demonstrate that you have achieved the objectives of this lab.

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1) What is purpose of the many specimen preparation procedures? 2) Briefly summarize how to test if your gage is working properly. 3) What experiments besides tensile testing could benefit from a properly installed strain gage? 4) What was the most difficult step in applying a strain gage and why?

• Strain gage supply cart from the machine shop

o Strain gages o Bonding supplies o Soldering supplies

• Soldering Irons from the ME 302 Supply cabinet • Tensile test specimens

o Variety of specimens stored in the machine shop

• Portable Strain Gage Reader (Vishay P3 or equivalent)

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The Vishay student strain gage manual and the P3 user manual can be downloaded from the course website located at the following site:

http://www.me.unlv.edu/~bj/MEG_302L_web/SYLLABUS.html

A large amount of information regarding strain gages can be found directly from the Vishay website:

www.vishay.com

The strain gage techniques section of the Vishay website can be found here:

Strain Gage Installation Information

Hardcopy booklets of the strain gage manual are available in the lab for use in the lab.

We have booklets in the lab that provide details of the strain gage installation process. We also have a video describing the process.

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This lab will involve loading specimens in bending to obtain deflection and strain data. Two 12-in specimens will be loaded within the elastic region of the material. Strain data and deflection data will be obtained, and compared to the experimental deflection and stress obtained from calculations. At the conclusion of this lab, you should:

•

Be familiar with the equation for bending stress.

•

Be able to calculate bending stress at any point along a beam.

•

Be able to derive the deflection equation for a beam in 3-point bending.

•

Be able to calculate the deflection at any point along a beam in 3-point bending.

•

Be able to compare theoretical deflection to actual measured deflections. Prior to reporting to the lab, prepare for the lab by completing the following exercise: A 12-in long rectangular beam is simply supported. The beam is made of 6061 Aluminum, with outside dimensions of 1.00 in. x 1.00 in. and inside dimensions of 0.760 in. x 0.760 in. A load of 100 lbf is applied to the center of the beam. The measured deflection at the center of the beam is 0.007 in., and a strain gage located at

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•

Measure the thickness, width, length, and wall thickness (as applicable) of the specimen.

•

Measure the distance from the support to the strain gages.

•

Mount the specimen in the Tinius-Olsen Universal Testing Machine (TOUTM). Center the specimen, and lower the cross-head until the cross-head is close to the specimen.

•

Place the ball-bearing on the centerline of the specimen. Lower the cross-head until it just contacts the ball bearing, then raise the cross-head slightly until no load is shown.

•

Set the dial indicator to the cross-head, and zero the dial indicator.

•

Connect both strain gages to strain indicator boxes.

•

Slowly load the specimen, recording strain and deflection data at 25-lb increments. Continue to increase the load until you have enough data points (approximately 10) to make a good graph of load versus deflection.

•

Repeat the procedures for the other specimen.

•

Calculate the stress at the strain gages and compare the stress obtained using the strain gage data. Plot theoretical and experimental stress vs. load on the same graph.

•

Calculate the deflection at the centerline of the specimen, and compare to the recorded deflection data.

•

Determine the percentage difference for each load interval.

•

For each specimen, plot load versus theoretical deflection and load versus actual deflection on the same graph.

•

Include all other data, equations, calculations, and discussion you believe is necessary to demonstrate that you have achieved the objectives of this lab.

•

In some lab sections, the experimental and theoretical strain values are reasonably close but the experimental and theoretical deflections have huge discrepancies. Provide reasons for this large error if it occurs.

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Strut Machine Aluminum Specimens of Different Lengths Yardstick or Tape Measure Calculator

2 2 2

��

=

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• Prior to starting the experiment, measure the aluminum specimens of different lengths. • Assuming that E = 69 GPa for aluminum, calculate the values of the critical load, Pcr, for

pinned-pinned, pinned-fixed, and fixed-fixed end conditions for the five specimens of different lengths.

• Place the column in the strut machine. • Apply load slowly until the specimen buckles. • Record the buckling load for each specimen and end condition.

• Calculations for determining the critical load (Pcr) of each specimen for each end condition. • Plot a graph of Pcr versus 1/L

2

for the three end conditions for five different lengths on the same graph.

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