MEEN 3210 MEASUREMENTS LABORATORY
Spring 2023
Instructions and Samples for Technical Report
The grade sheet must be attached to the front of each written laboratory report. The
sample report cover sheet and grade sheets are included in this document. The report will
be graded on two parts: technical content, and writing style and format.
Report Sections
Grade Sheet:
See Sample
Cover Sheet:
Abstract:
Table of Content:
Nomenclature:
Introduction:
Objectives:
Apparatus:
Theory: (if needed)
Results:
Discussion:
Conclusions:
Citations:
Appendix:
Format and Style
See Sample
200-300 words, no citation, no detail results
Each Section and corresponding page number, no leading character
for page number
Symbols and units, Alphabetical (Upper, then lower), Greek, Sub
and Super-scripts
Brief description of the lab, problem statement
List the main objectives of the lab
List/Tabulate the equipments and instruments used for the lab
Gives a short summary of theory and equations used
Raw data collected during the lab, sample calculation (in
Appendix), final results
Discuss the results in terms of accuracy, agreement with theory,
achievement of objectives, experimental errors
final thoughts on experiments and results, recommendations for
improvements
Use the style in the textbook.
Sample calculation
Write in third person past tense, and present tense.
Use a standard font and font size, e.g. Times New Roman 11 points.
Check spelling and grammar, usage of words, repetition, redundancy, etc.
Arrange sections to improve readability.
Include page numbers.
Number each equation and define the symbols in Nomenclature.
Caption tables and label figures.
Label each axis clearly in a figure and include unit of the variables.
Include Legends in graphs if there is more than one data set.
Show only data points, unless there is a trend line (least-square-fit) involved.
If the trend line is used, include the goodness of fit measure (R or R²) and the regression
equation of the line. SAMPLE GRADE SHEET FOR A LAB REPORT
MEEN 3210 MEASUREMENTS LABORATORY
SPRING 2023
Grade Sheet
Name:
John Doe
Lab No. and Title:
Laboratory 4 Strain Measurement
Content (70%)
Abstract
Table of Contents
Nomenclature
Introduction
Objectives
Experimental Apparatus
Results
Raw Data Sheet
Sample Calculation
Final Results
Points Allocated
Point Received
10
10
1555i5
Discussion
Conclusion
10
55595
Format and Style (30%)
Heading, Citations, Readability
10
Grammar, Usage
10
Tables/Figures
10
100
TOTAL
Instructor's Comment: SAMPLE COVER SHEET FOR A LAB REPORT
MEEN 3210
Measurements Laboratory
Department of Mechanical Engineering
Lab 4 Strain Measurement Laboratory
John Doe
Date of Experiment: 02/--/2023
Date of Submission: 02/--/2023/nTable 1: Dimensions of the Beams
Dimensions (unit)
Steel
Beam Material
Aluminum
Brass
Width
in
Tin
Lin
Length
Height
Location of a strain
15.8
10.75 in
21.8
Convert
403
P.25
0.125
0.2 S
gauge from an open end
9.06 in
5.5
in
11.25 in
Table 2: Strain Measurements of Three Beams
Brass
Steel
Nico
Aluminum
Weight
Strain
Weight
Strain
Weight
Strain
(unit)
(E) X/9
(unit)
(με) Χιο
(unit)
(H) x/
500 gm
31
100 gm
50
200 gm
46
1000 gm
69
200 gm
100
400 gm
90
1500 gm
2000 gm
2500 gm
300 gm
151
600 gm
133
136
400 gm
201
800 gm
176
174
500 gm
252
1000 gm
225
Table 3: Comparison of Experimental and Theoretical Stress Values
Material
Stress
from the
book
do calelution no
Result
Experimental Theoretical
(unit)
(unit)
Error
(unit)
Error (%)
Aluminum
from the
Steel
Brass
Table 4: Comparison of Experimental and Textbook Values of Modulus of Elasticity
Material
for each material
Modulus of Elasticity
Experimental
(unit)
Aluminum
Eeel
ass
Result
Textbook
Error
book
Error (%)
(unit)
(unit)
ba/nProcedure
1. Select the beam to be used and record the strain gage factor for future reference.
2. Measure the dimensions of the beam and record data in Table 6.
3. Place the beam onto the support bars and level it.
4. Connect the strain gage wires to the P3500 strain gage indicator and calibrate the
indicator as shown on the inside of the lid of the indicator unit.
5. Apply the weights at the designated distance (mid-point of the beam) and record
data (strain and deflection) in Table 7.
6. Compare the measured values of defection with the theoretical values obtained
using Eq. (7).
I
of incre
در
calcate
Sthin
σε
Mc
I
PL³
d =
48EL
is lood
Eq. (7)
Strain
Jraph
7. Discuss the differences between theoretical and experimental results.
Possible discussions: Does experimental and theoretical values of deflection agree with
each other? What are the sources of errors?
Table 6: Dimensions of the Beams
Dimensions (unit)
Width
Beam Material
Steel
34 in
Length
Height
34 in
0.25 in
defection
61
Location of a
strain gauge
Table 7: Strain and Deflection Measurements for the Beam
0.001
Load
(in lb)
Load
(in gm)
Strain
Deflection
61-49
(unit)
2
0907.18 gm
16
12
in
4
1814.37 gm
33
26
6
2721.55 gm
50
40
8
3628.74 gm
67
54
Table 8: Comparison of Experimental and Theoretical Deflection Values
Material
Load
(unit)
Deflection (unit)
Experimental
Theoretical
Steel
from text book
grap/n MEEN 3210 MEASUREMENTS
STRAIN MEASUREMENT LABORATORY
Robert Benton and Kendrick Aung
Introduction
Experimental determination of stress is important when designing components with
complex geometry and/or loading. To verify a given design, nondestructive tests of a
prototype may be performed using strain gages. Once strain is determined
experimentally, the stress may be calculated using the stress-strain relationship for the
material.
Although there are various failure theories for the ductile and brittle materials subjected
to static and dynamic loads, each of these theories predicts failure when the stress in a
given material exceeds various predetermined values. As such, stress is a major
consideration in design of mechanical components. Analytical methods exist for
relatively simple and common geometric cases such as shafts, beams, and cylinders.
However for cases with stress concentration or other complex geometry, these analytical
methods are not accurate. Numerical methods such as finite element analysis (FEA) may
be applied in such cases. However, finding the appropriate FEA model (or mesh) for a
given situation can be more of an art than an exact science. As such, strain measurements
should be used to verify stresses in physical prototypes of the design.
Strain Measurement
Three common tools are available for experimental determination of stress and strain,
namely, photoelasticity, stress coat application, and strain gage application.
Photoelasticity
Although photoelasticity is most easily applied in cases of two-dimensional components,
techniques also exist for more complex geometry. When polarized light is passed
through a transparent material, visible bands appear as contour lines within the material
to indicate the level of stress in the material. This is because the speed of light in the
medium is a function of stress. Determination of stress using photoelasticity requires
relatively expensive equipment when compared to the methods described below. In
addition, prototypes of the part must be prepared especially for photoelastic
measurement.
Stress Coat Application
The application of a stress coat is a fairly simple concept for which students should have
an intuitive sense. A stress coat is used to determine the principal stress directions by
observation. A brittle lacquer is applied to the surface of the prototype (note: the stress
coat is applied in liquid form and allowed to dry). Because the coating is brittle, the coating will crack perpendicular to the direction of maximum tensile stress (maximum
principal stress).
Strain Gage Application
Strain gages may be applied to any free surface of a prototype component. In many
cases, the component may be tested in service with the strain gages applied. The main
limitations include environmental limitations required to avoid corrosion motion
limitations due to the requirement that wire leads be connected between the strain gages
and measurement instruments (for example, rotating components would present a
challenge). In these cases, service conditions should be simulated on the prototype
during strain gage experiments. Strain gage measurements are based on small changes in
resistance of the gage when strained. As such, a bridge circuit is employed to measure
change in resistance. Although the bridge can be cheaply constructed from scratch using
precision resistors, specialized bridge-balancing units and strain indicators are most often
used in practice to ensure precise measurements. Specialized analog-to-digital-
conversion (AD) cards may also be purchased with built-in bridge circuits for dynamic
strain gage measurement and data logging via personal computer (PC). Because strain
gage resistance and prototype/gage strain are functions of temperature, temperature is an
important consideration in strain gage application. If used to determine stress, the
thermal growth in the component should not be measured by the strain-gage bridge
circuit. Bridges with more than one strain gage leg may be used to aid in temperature
compensation. In addition, self-temperature compensation gages are commonly available
for application with steel and aluminum alloys (designated 06 and 13, respectively).
Resistors in the bridge will also change resistance with temperature. Once the gage
system is connected, temperature tests can be performed to determine error due to
temperature in the measurement system. During any experiment where environmental
factors may affect the results, temperature variation and other environmental conditions
should be recorded along with strain measurements for future analysis.
Theory
The resistance in a wire in Equation (1)
PL
R =
Eq. (1)
where p is the wire material's resistivity, L is the wire's length, and A is the wire's cross
sectional area. When a strain is placed on the wire, its resistance changes due to changes
in resistivity, length, and cross-sectional area. As a result, measurement of the wire's
resistance can be used to indicate strain.
A strain gage is a specially designed metallic element that is very sensitive to strain in a
given direction (see discussion and figures in [1], [2], and [3]). Strain gage application
procedures are described on pages 17-23 of [1], which should be read at this time. Once the gage is applied and connection wires have been made, the gage must be placed in a
bridge circuit in order to measure changes in the gage's resistance (see page 24 of [1]).
For this lab, specially designed strain gage instruments described in [1] will be used to
implement the bridge circuits.
Often, specially oriented sets of strain gage “rosettes” are applied to measure strain in
various directions at a single location (see pages 31 and 32 of [1] for examples of various
strain gages and strain gage rosettes). Juvinal [3] gives equations necessary to find
principal strains from measured strains in chapter 5.
Objectives
The main objectives of the laboratory are:
1. To familiarize students with industry standard strain measurement techniques
2. To determine Modulus of Elasticity of three materials using a cantilever beam
3. To compare experimental and theoretical values of Modulus of Elasticity
4. To compare experimental and theoretical deflection values
Experiment 1: Application of a Strain Gage on a beam
Required Equipment and Supplies
Bulletin 309D: Student Manual for Strain Gage Technology [1]
Student Strain Gage Application Kit
"
◉
Sandpaper
Degreaser
◉
M-Prep Conditioner A
"
M-Prep Neutralizer 5A
Gauze and Cotton Swabs
•
◉
Cellophane tape
M-Bond 200 Kit
M-Coat A
Leadwire
Drafting tape
Soldering Station with Soldering Supplies
Student Strain Gage Practice Patterns and Student Strain Gages
Steel or Aluminum Bar Stock
Procedure
1. Select a piece of steel or aluminum bar stock.
2. Prepare the surface of the bar stock as described on pages 18 and 19 of [1].
3. Obtain a student strain gage practice pattern from the instructor and practice the strain
gage application procedure described on pages 20 and 21. Special care should be
taken to replace the caps on all chemicals to avoid spillage or evaporation.
4. Repeat steps 2 and 3 until the practice pattern in successfully applied to the bar stock
surface. 5. Obtain a student strain gage from the instructor and repeat the procedures described
on pages 18-21.
STRAIN GAUGE
LT-1
CSM-1
Figure 1 Materials and Soldering Station for Strain Gage Mounting
Possible discussions: Why is the cleaning process before mounting the strain gage
important?
Experiment 2: Strain Measurement and Application
Required Equipment and Supplies
•
Model P-3500 Portable Digital Strain Indicator
Connecting wires
Beam with Strain Gage
Calipers and/or Ruler
Test Weights
Procedure
1. Select a beam with strain gage (record the strain gage resistance and gage factor for
future reference).
2. Clamp the beam to the table or place the beam in a vice. Note that care should be
taken to clamp the beam far enough from the strain gage to minimize the strain
induced by the clamping forces. Recall that the vice forces may induce strain due to
the effects of Poisson's ratio.
3. Measure the dimensions of the beam required to calculate the stress at the location of
the strain gage. Record data in Table 1.
4. Connect the wires to the P-3500 Portable Digital Strain Indicator as indicated inside
the lid of the Indicator unit. 5. Use the procedure inside the lid of the P-3500 unit to set the appropriate gage factor
for the strain gage(s).
6. With no weight attached to the beam, use the procedure inside the lid of the P-3500
unit to balance the bridge circuit. To avoid unnecessary wear on the equipment,
please unlock the balance control knobs before attempting to adjust the knob
positions.
7. Once the bridge is balanced, lock the balance control knob on the P-3500 unit and do
not attempt to adjust the knob for the remainder of the lab period.
8. Apply weights supplied by instructor to the beam made of steel and record the strain
for each weight. Record data in Table 2.
9. Repeat the measurements in step 8 using the beam made of Plexiglas. Record the
measured data in Table 2.
C
000
Figure 2 An Experimental Setup for Measuring Strain
Results and Discussions
Result I: Comparison of Stress Using the Published Value of Young's Modulus
1. Use the stress strain relationship (Hooke's law) to calculate the experimental stress
(σexp) using the measured strain and Young's Modulus of the beam material from the
Machine Design text book.
σ
= E.
exp
text
*
E exp
Eq. (2)
where, σexp is the experimental stress, Etext is the value of modulus of elasticity from
the textbook and Ɛexp is the experimental strain.
