1
Part III
Lab Projects 5,6,7,8
ATTN: Stage II Report baseline
All the items listed below need to be completely addressed in your report. Those are considered
baseline for the second stage reports).
1) all tables and figures need to be numbered and referenced in the context;
- The title of a figure need to be descriptive and be placed below the figure;
- The title of a table need to be descriptive and be placed above the table;
- All figures need to be clear and clean;
2) all table or figure: a) first introduce it + and then b) interpret/making observations, and then
briefly conclude based on b);
3) all analysis questions listed in the lab material need to be answered/addressed in your Analysis
and Discussion section using (referring to) your data tables and figures (you are strongly
suggested to number your answers using the question numbers in your report if you prefer).
2
Lab 5 Effect of Heat Treatment and hardenability of Material
1. IntroductionHeat treatment affects materials properties. Heat treatment are commonly used to minimize thermal
stresses and distortion as well as to achieve other properties such as high hardness in manufacturing
components. Carbon steels are important materials widely used in engineering applications. Steel
hardenability is an important property and it is the ability of the steel to partially or to completely
transform from austenite to some fraction of martensite at a given depth below the surface when cooled
under a given condition from high temperature. It depends on the chemical composition of the steel and
can also be affected by processing conditions, such as the austenitizing temperature. Dependent on the
material constituents such as carbon percent, one may or may not be able to use heat treatment to
effectively harden the material owing to the hardenability of the material. This lab will involve in the
study of hardenability of the medium carbon steel. Heat treatment, quenching with water, will be used.
Hardness measurement will be performed on the sample.
2. Theory
̶ Time-Temperature-Transformation (TTT) Curve
When carbon steel is cooled down from austenite region, dependent on the cooling rate, difference micro
structure will be formed. Fig. 1. shows an example of the TTT curves for medium carbon steel cooling
down at various cooling rate. The hardenability of a steel is the property which determines the depth and
distribution of hardness induced by quenching from the austenitic condition. The hardness is dependent
on the formation of martensite which depends upon the quenching rate (cooling rate) of the material. As
shown in Fig. 1., in order to effectively achieve high hardness, the cooling curve need to avoid intercept
the nose of the TTT curve such that one can get martensite. The fast cooling rate can be achieved by
quenching the material with cooling resources, here we use water.
Fig. 1. TTT curve of medium carbon at various cooling rate
It is easy to understand that the surface of the part is cooled rapidly, resulting in high hardness, whereas
the interior cools more slowly and is not hardened. From the T-T-T diagram, the hardness does not
vary linearly from the outside to the center. In general medium carbon steel to low end of high carbon
steel can be heat treatment to form martensite, low carbon steel is not very responsive to heat treatment to
form martensite (or no good hardenability) since low carbon steel has a nose very close to the vertical axis
which requires extreme fast cooling rate in order to get martensite.
3
̶ Phase Diagram of Carbon Steel
The idea of heat treatment is to restructure material to achieve some desirable properties needed. In order
to restructure the material, the material need to be heated into austenite region and then cool down at a
rate necessary for obtain the micro constituent. Fig. 2 below shows the phase diagram for carbon steels.
From the figure, the temperature need to reach austenite region differs dependent on the carbon percent.
For example, for 1018 steel, one will need to rise the temperature to about 930 oC, but for medium carbon
steel like 1045 steel, one may use 910 oC.
Fig. 2. Phase diagram of carbon steel
Please notice, the steel sample may need to be normalized to eliminate differences in microstructure due
to previous hot working before austenitzing and quenching.
3. Procedures
̶ Material/Equipment (take pictures)
(List yours)
̶ Operation Procedure (ATTN: Hot sample, extreme caution is needed!)
A furnace as shown in Fig. 3 will be used for this lab project.
Fig. 3. Furnace for heat treatment
1) Get the furnace ready;
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2) Normalize the steel sample to eliminate previous hot or/and cold working effect and measure the
initial hardness of the sample material (or follow the instructor).
Note: To save time, the sample used in the lab has been normalized already. For cold rolled 1045
steel, this normalized sample has an average hardness HRC 8.
3) Place the sample into the furnace and set the target temperature to 900 oC or as instructed by the
instructor.
4) Close the door of the furnace and turn on the power;
5) Watch the temperature change. After the temperature reaching the target temperature, keep the
sample in the furnace for about 30 minutes at the temperature. This will allow full austenitizing of
the sample.
6) Turn off the furnace first and then open the furnace door when ready to take out the sample.
7) The test sample is quickly transferred to the test fixture (or as instructed), which quenches the
steel sample by spraying a controlled flow of water onto one end of the sample.
Note: The cooling rate varies along the length of the sample, from very rapid at the quenched end
where the water strikes the specimen to slower rates that are equivalent to air cooling at the other
end. The situation is shown in Fig. 4 below. Fig. 4(b) shows an example of the cooling rate from
the quenching end to the top end.
Cooling
rate:
o
( C/s)
(a)
(b)
Fig. 4. (a) Quenching setup and (b) an example of cooling rate from the quenching end to the top end of the steel
sample
8) Grind 0.25-0.3mm thickness of the heat treated sample to remove the carburized material
(oxidation) as shown in Fig. 5 (remove the washer first if applicable).
Fig. 5. Grinded steel sample with oxidation removed
5
Note: Be careful that this should not heat the sample to cause tempering to soften the steel.
9) Measure the hardness of the heat treated steel sample using Wilson Rockwell 574T at intervals
from the quenched end, typically at intervals 0.75 mm for carbon steels (and 1.5 mm for alloy
steels), beginning as close as possible to the quenched end to the other end. Rockwell regular C
scale (150kg major load) (or as instructed) is be used.
Note: Decrease in hardness with distance from the quenched end should be observed. High
hardness occurs where high-volume fractions of martensite develop. Lower hardness
indicates transformation to bainite or ferrite/pearlite microstructures.
The hardenability is described by a hardness curve for the steel or more commonly by reference to the
hardness value at a particular distance from the quenched end.
4. Results/Data
1) A table documenting the initial hardness number, and the hardness at various locations after heat
treatment;
2) Hardenability curve
(Present yours, you may combine with section 5 below)
5. Analysis/Discussion
1) Plot the hardenability curve for the steel sample using hardness change from to bottom (quenched side)
to the top, and Interpret your results;
2) Using your results explain whether the particular steel can be sufficiently hardened .
3) Can you predict the depth of hardenability of this material from the surface to the core (center)? Why?
4) Explain how to increase the machinability for a hardened steel by referring to your material science
and material processing texts.
6. Conclusions
Conclude what have been done and the conclusions drawn from your analysis.
7. References
[1] ……
[2] …….
[3] …….
(Note: These numbers need to be located in your report at the place you used the references)
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Lab 6 Buckling and Fatigue for Repaired Material
1. Introduction
Fatigue of structural members is strongly influenced by surface condition as well as microstructure. A
material that has been yielded and then repaired may see a change in fatigue life. This lab is related to Lab
4 where a new undamaged sample was tested.
2. Theory
A-Buckling of Column
For long column (which is the case for this lab), the critical load causing column buckling may be
estimated using Eq. (1),
 2E I
(1)
Pcr =
( K e L) 2
where, Ke is the end-condition constant; E is the modulus of elasticity; L is the length of the column ; and
I is the moment of Inertia and it can be calculated by using Eq. (2)
bh 3
(2)
I =
12
The end-condition constant for the column in Eq. (1) may be estimated using Fig. 1. Choose the one best
fits your case.
Fig. 1. Column end fixity conditions
B-Fatigue
(See Lab 4.)
3. Procedures
Material/Equipment (take pictures)
• MTS (Material Test Systems) 22 kip Fatigue Test Machine
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• Steel tension samples: 1018 Cold Drawn (? verify and report)
• Calipers
• AMSCOPE (Optional)(as shown in Figure 3.2)
Caution: Only the operator should run the MTS machine. Specimen edges are sharp – handle with
care. Use appropriate safety measures in EPL when straightening samples.
A-Buckling Test
1) Measure sample (length, cross section area, etc.);
(Note: complete the dimensions shown in Fig. 2)
2) Install in MTS machine and set the limit at 3/16-inch deflection for the machine to cut out;
3) Measure the column length between the fixed ends (Fig. 2);
4) Run the test. (the scenario is shown in Fig. 3)
The length L =
(the vertical distance between the two jaws’ ends upon installed)
Fig. 2. Sample dimensions
L = ? (original without buckling)
Fig. 3. Column buckling using MTS
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B-Fatigue Test
1) Straighten the sample as good as you can in the EPL (? verify). You may request help from the
person in charge of the EPL. Do not heat the part.
2) Conduct a fatigue test on the repaired part using the same loading and operating conditions as you
did in Lab4.
(Same as Lab 4)
4. Result/Data
1) Dimension Data of the sample;
2) Buckling data table/figure (s)
3) Fatigue data table showing the max load, min load, the point the failure cycle reached, a few data point
after the failure. (You may use Table1 and Table 2 below.)
Table 1: Fatigue Test - Undamaged
Stroke (in)
Load (Kip)
Count
Running time (s)
…
…
Fatigue failure cycles
…
…
Table 2: Fatigue Test – Damaged but Repaired Sample
Stroke (in)
Load (Kip)
Count
Running time (s)
…
…
Fatigue failure cycles
…
…
(Present yours, you may combine with section 5 below in your report)
5. Analysis/Discussion
1) Calculate the predicted buckling load using the theory of buckling, and explain the end conditions
used.
2) Compare the theoretically calculated buckling load with the experimentation data and explain your
observations.
3) Compare the fatigue life of the repaired sample with the one (unrepaired sample) you did in Lab 4, and
explain the differences in fatigue life. Also explain whether or not the Basquin’s equation can be
used to predict fatigue life directly using the same ultimate strength as you used in Lab 4.
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4) Discuss how to calculate the endurance limit (106 loading cycles) for the undamaged sample material
using the experimental result.
6. Conclusions
Conclude what have been done and the conclusions drawn from your analysis.
7. References
[1] ……
[2] …….
[3] …….
(Note: These numbers need to be located in your report at the place you used the references)
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Lab 7 Fatigue-Rotating beam
1. Introduction
The rotating beam test produces a fully reversed stress cycle for each revolution of the machine. The
machine is much simpler than a MTS machine, but is limited to cylindrical test specimens and fully
reversed stresses. Since the machine can run at 5000 RPM or more it is possible to produce hundreds of
thousands of cycles in less than one hour.
The schematics of the experimental setup is shown in Fig. 1 below. (Take a picture of yours and it may be
different.).
Fig. 1. Schematics of rotating beam fatigue testing apparatus
2. Theory
(Note: You may combine this part with the Analysis section.)
Cyclic Loading
For the experimental apparatus as shown in Fig. 1 one can see, fatigue due to completely reversed loading
cycle applies to this lab. The loading condition in the lab may be represented by using Fig. 2 below.
Fig. 2 Completely reversed loading cycle
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From Fig. 2, one can calculate
Average applied stress using Eq. (1),
 (
m
+
min
max
)/2
(1)
Range stress using Eq. (2),

range
=
max
−
(2)
min
Stress amplitude using Eq. (3)
 = (
a
max
-
min
)/2
(3)
Fatigue Prediction
With the stress, the fatigue life of the material may be estimated using Basquin’s equation.
(Refer to Lab 4 for details.)
S-N curve for steels
S-N curve shows the applied stress and the corresponding fatigue life. Fig. 3 below shows examples of
some selected carbon steel and their S-N curve. You may use it to determine a load you would like to use
for the lab. Higher load leads to lower loading cycles and lower load leads to higher loading cycles. To
estimate, the stress loading can be calculated using the so called flexure formula (Eq. (4)) for this lab,
𝜎=
𝑀𝑐
𝐼
(4)
Where M the applied moment, c is the radius at the neck of the sample, and I is the area moment of inertia
at the neck.
Fig. 3 S-N curve for some steel samples
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3. Procedures
Material/Equipment (take pictures)
- RBF-200
- Sample(s): 1018 steel ((?) Need to be confirmed with the tech. staff)
......
(List all you used as appropriate, pictures are suggested.)
(A) Sample machining and fabrication (Ask the instructor before doing it)
Use the following drawing to make a sample.
(B) Operation
1)
2)
3)
4)
Read the instruction about the RBF-200 in the appendix to get familiar with the machine;
Lightly sand the ends of the samples (if needed) so they slide into the collets;
Insert the end of the sample into collet located on the motor;
Make sure sample is inserted all the way into the collet and tighten the collet with the wrenches
provided (do not over tighten it);
(Best practice: run it for 30 seconds and further tight it after 4 (do not over tighten it).)
5) Insert the other end of the sample into the load arm and repeat step 4;
(Note: Make sure no load is applied when you do step 5).)
6) Setup the deflection gage for checking runout.
7) Rotate the system 360 degrees. Zero the gage at the lowest point.
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8) Keep rotating the system to find the point where the deflection is the highest; at this point slightly
press on the load arm near the deflection gage. (This is rearranging the collets).
9) Repeat steps 9 and 10 until the runout is less than 0.007 in.
10) Determine the moment load to cause failure at about 105 loading cycles using the S-N curve and
equation provided. Measure the specimen diameter at the groove and use this in the calculations;
11) Hold the load arm upward and set load;
12) Set safety bar so it doesn’t touch the specimen. (Avoid applying a false load with the safety bar)
13) Set cutoff switch.
(ATTN: Danger open circuit! Do not touch the bottom of the cutoff switch inside the machine!
14) Slowly start the machine with holding the load upward; (ask the instructor if not sure)
15) Reset the counter and remove your hand from holding the load arm simultaneously;
16) Work up speed to 3000 RPM until reach about 50,000 cycles (and then slowly increase up to
5000 RPM you prefer if the rotation can maintain smooth. Please notice, excessive vibration may
kill your sample and ruin your data), as you increase the speed use your hand at the load bearing
to dampen out the vibrations (do not push it to add additional load).
(ATTN: Stop the machine if the shaft pushes out to the safety bar side and reinsert the sample
and re-tight it.)
17) Maintain the speed until sample failure;
Record the data needed.
18) Insert new sample, repeat the steps from 2) to 17) above at 10% increase or decrease in load and
run to failure. (Increase or decrease the load dependent on the time (loading cycles) you spent for
the first sample.)
Record the data needed.
19). Use the scope provided in the lab to obtain images of the failure surface of each of the broken
samples.
4. Result/Data
1) Dimension Data of the sample;
2) Fatigue data recorded.
(Present yours, you may combine with section 5 below)
3) Image data from the lab scope
5. Analysis/Discussion
1) Calculate the fatigue life similar to what you did in Lab 4 using the load applied;
2) Compare your theoretical prediction and your testing results and explain your observations;
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3) Present a brief discussion about the appearance of the failure surface using the image data you obtained
from the lab scope.
6. Conclusions
Conclude what have been done and summarize what you have concluded from your analysis.
7. References
[1] ……
[2] …….
[3] …….
(Note: These numbers need to be located in your report at the place you used the references)
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Appendix
RBF-200 Machine
The RBF- 200 as shown in Fig. 4. is a compact, bench mounted machine designed to apply reversed
bending loads to unthreaded, straight shank specimen bars. Included a cycle counter (99,999,900
maximum count), adjustable spindle (500 to 10,000 RPM), and a calibrated beam and poise system which
can apply an infinitely adjustable moment of up to 200 inch-pounds to the cantilevered end of the
specimen bar. Collet sizes available include 1/4, 3/8, and ½ inch diameters. Unless specified otherwise, a
½ inch pair of collets is furnished with the machine. Other collet sizes are available on special order
within the range of ¼ to ½ inch diameter.
Fig. 4 RBF-200 Machine components
The description of the major parts in Fig. 4 is listed below:
Motor and spindle
The motor is a ½ HP, 115 volt, universal type which is powered by a variable transformer to control the
speed from 500 to 10,000 RPM. The motor drives a spindle assembly through a flexible coupling. The
spindle assembly consists of the shaft, bearings and oil filled housing. A sight gage is provided on the
back of the machine for maintaining the proper oil level in the spindle.
CAUTION: The motor must not be operated at a speed over 10,000 RPM
Moment Beam
The bending moment loading beam is numbered from 0 to 200 inch-pounds at successive 10 inch-pound
increments. The interval between each 10 inch- pound increment is marked with successive one inchpond divisions. A locking screw is provided in the poise weight to secure it at the desired bending
moment settling.
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Cutoff Switch
A snap action reset switch is furnished to automatically shut off the machine at specimen failure. It is
located under the end of the calibrated beam in such a manner that when the beam drops at specimen
failure, the bottom of the adjustable screw actuates the switch. The nuts on the screw are adjustable to
stop the beam from damaging the switch after actuation. The switch must be reset with the tab at the
outside end of the machine before testing can be resumed.
Cycle Counter
The six digit resettable counter (99,999,900 maximum count) is actuated by a switch which is directly
driven by the spindle through a 100: 1 ratio.
Load Estimation
The applicable inch- pound moment setting for the poise weight is generally determined on the basis of
some desired bending stress level in the specimen. This moment may be determined from the Eq. (5),
𝑀 = 3.1416
𝜎𝐷 3
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= 0.0982 𝜎𝐷 3
Where, M = the setting for poise weight in inch- pounds;
 = Desired bending stress level in specimen at minimum cross section in pounds
per square inch
D = Diameter of specimen at minimum cross section in inches
(5)
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Lab 8 Structure Deflections
1. Introduction
The objectives of this lab are to become familiar with structure testing and deflection measurements, and
to conduct an analysis of structure deflection and compare to measurements. Here the structure we will
use is a truss system.
Deflections in structures due to loading are an important design consideration. The structures may be a
classical truss, a vehicle suspension component, a transmission casing and many others. For the
transmission, deflection under torque affects bearing loads, and gear mesh geometry and noise. For
continuous structures, like a transmission case, deflections are typically analyzed by finite element
methods. For discrete structures, like a truss, closed from solutions exit to allow calculating- thus
predicting- the deflection. The Energy Method is such a method.
A key issue is structural deflection measurement, for comparison to calculations, is extraneous
deflections. These deflections are typically due to the fixture of the structure and attachments to ground.
Extraneous deflections typically result in a greater deflection than the structure alone. For example in the
structural testing apparatus, the frame has several reinforcements to reduce frame deflection.
The structure for this lab is a truss as shown in Figure 1 below. The idealizations for the truss are those
presented in your statics class. All members are two force with the force along the member axis. The
joints are viewed as frictionless pins with zero clearance. Both sides of the truss deflect the same amount.
Members will be either in compression or tension. The failure mode for the tension members is yielding.
The failure mode for the compression members is buckling.
Figure 1 Structural Testing Apparatus
As a structure is loaded, the force of the load is transmitted throughout the components of the structure. If
the components are binary (two force) members pinned together, each member will be subjected to a
single axial force. This force will cause the member to either stretch in tension or contract in compression.
As the member expands or compresses, it stores energy – just like a spring. Finally, the energies stored by
each member by be added together and used to calculate the total deflection of the point at which the
structure is loaded. Mechanical advantage of a moment arm (assumed rigid) is determined by simply
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dividing the distance from the fulcrum to the applied force by the distance from the fulcrum to the applied
load.
The structural testing apparatus shown above was designed to measure the deflection of a bridge
subjected to a point load. Weights (borrowed from the Brinell Hardness Tester) are hung from the end of
the moment arm, which is also connected to the base and the bridge. The moment arm transfers the force
of the weights to the bridge at a mechanical advantage. It is very important to level the moment arm after
each weight is added in order to keep the force on the bridge strictly vertical. This can be accomplished
by turning the leveling screw and checking the bubble level. Moving the leveling screw from the two L
positions to the two H positions on the base and moment arm will shift the system from the low load
range to the high load range. CAUTION: A maximum of 4 weights can be used in the high range.
More weight may cause the truss members to buckle.
The truss bridge consists of 8 solid ¼ inch diameter rods and 6 hollow 3/8 inch diameter by 0.035
inch thick tubes. All truss members are made from 6061 – T6 aluminum alloy with modulus of
elasticity of 10.16 Mpsi.
2. Theory
The theory background for this lab is force equilibrium for a truss system. For the given system in the lab
as show in Figure 2 below. Due to the symmetry of the system, you only need to use half of the system
for analysis. (Note: The load is half as well.)
(notice: you will need to fill some of the incomplete part below.)
Figure 2. Truss system
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Aluminum Modulus of Elasticity = 10.16 Mpsi
The indices for each member in the truss are shown in Figure 3.
Length of each member (1=2=3=…=7) = ___?___
in
Cross sectional area of solid member (2, 3, 5, 7) = 0.0491
Cross sectional area of hollow member (1, 4, 6) = 0.0374
Force applied at the center of Truss = P
lbf (P = ?)
in2
in2
Force Analysis:
To calculate P, the moment arm is needed.
P
Oy
Ox
W
Figure 3-1. FBD for moment arm
Use the FBD as shown in Fig. 3-2, P = ?
For the system:
RA
P/2
RB
Figure 3-2. FDB of the truss system (half of the truss)
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F = 0:
M = 0:
y
P
RA + RB = P 
P
 R A = RB =
4
R A = RB

Forces at the point P is applied:
(P/2)/2
Figure 4. FDB at point P applied (used half that’s why P/2)
F
y
= 0:
P

− F3 sin 60 = 0  F3 = F5 = ?
4

Next, at A:
F1
F2
Figure 5. FDB at point A
F
F
y
x
P
=0
4
= 0 : F2 − F1 cos60 = 0
= 0 : F1 sin 60 −


 F1 = F6 = ?, F2 = F7 = ?


Finally, at C:
Figure 6. FDB at point C
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F
x
= 0 : F4 − F1 cos60 − F3 cos60 = 0
F
4
=?
Strain Energy:
U =  kxdx =
=
1
1
kx  x =  F  x

2
2
1
FL
F

2
EA
F 2L L
F2
U =
=
A
2 EA 2 E
Deflection (y) by strain energy:
U = ( P / 2) y
for linear elastic
And y = 2U / (P)
The theoretically calculated spring constant K can be obtained using
𝑃
𝐾=
(2)
𝑦
for elastic deflection.
3. Procedure
Material/Equipment (take pictures)
(a)
(b)
(c)
(d)
(e)
Truss structural system,
Four Weight Plates with 19.7 pounds each
Dial Indicator (0.001’’ resolution (each minor mark), the range is from 0-1’’)
Spirit Level
Tape Measure
(a)
(b)
(c)
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(d)
(e)
Figure 7. Equipment used in the lab, (a) Truss structural system, (b)Four Weight Plates with 19.7 pounds each, (c)
Dial Indicator, (d) Spirit Level, (e) Tape Measure
3.1 Low Range Position (Perform loading/unloading 3 times)
a. Selected the low range position by pinning the leveling screw at the top and bottom to the
adjustment holes labeled “L”. (Figure 2)
b. Adjusted the leveling screw by rotating it until the level on the moment arm reads horizontal.
(Figure 2)
c. Zeroed the dial indicator measuring the deflection of the truss by loosening the locking screw,
turning the dial to the zero point, and retightening the locking screw.
d. Placed one weight plate (19.7 lbs.) securely onto the loading platform. (Figure 7(b))
e. Re-leveled the moment arm by turning the leveling screw until the level reads horizontal.
f. Read and recorded the deflection reading of the dial.
g. Repeated steps 1.d – 1.f until the last deflection reading is taken with all four weight plates loaded
on the loading platform.
h. Removed a single weight plate from the loading platform.
i. Re-leveled the moment arm by turning the leveling screw until the level reads horizontal.
j. Read and recorded the deflection reading of the dial.
k. Repeated steps 1.h – 1.j until all weights are removed and the last dial reading is taken.
l. Repeated steps 1.b – 1.k twice more, resulting in three total data sets at the low range position.
3.2 High Range Position (Perform loading/unloading 3 times)
a. Selected the high range position by pinning the leveling screw at the top and bottom to the
adjustment holes labeled “H”.
b. Adjusted the leveling screw by rotating it until the level on the moment arm reads horizontal.
c. Zeroed the dial indicator measuring the deflection of the truss by loosening the locking screw,
turning the dial to the zero point, and retightening the locking screw.
d. Placed one weight plate securely onto the loading platform.
e. Re-leveled the moment arm by turning the leveling screw until the level reads horizontal.
f. Read and recorded the deflection reading of the dial.
g. Repeated steps 2.d – 2.f until the last deflection reading is taken with all four weight plates loaded
on the loading platform.
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h.
i.
j.
k.
l.
Removed a single weight plate from the loading platform.
Re-leveled the moment arm by turning the leveling screw until the level reads horizontal.
Read and recorded the deflection reading of the dial.
Repeated steps 2.h – 2.j until all weights are removed and the last dial reading is taken.
Repeated steps 2.b – 2.k twice more, resulting in three total data sets at the low range position.
4. Results/Data
Low range position: Loading and unloading data
High range position: Loading and unloading data
To report the data, Table 1 and Table 2 below provide a thought (you may use your way to present them).
(Note: You need to record low range load and high range separately.
You also need to calculate the force applied using the momentum arm.)
Table 1. Deflection measurement for loading and unloading
Force
(lb)
1
2
Loading
3
Avg.
K
(lb/in)
3
2
Unloading
1
Avg.
K
(lb/in)
Loading and unloading curve can be plotted based on the data you obtained at low range and high range
position using Table 1.
The theoretically calculated data can be summarized into Table 2.
Note: You only need the table for one load on your choice. For theoretical calculation, the spring constant
K should be the same for different load as long as the deformation is in elastic domain.
The Deflection by strain energy and the deflection can be thus calculated. The spring constant K can be
estimated using the loading /unloading curve.
For theoretical calculation, Table 2 may be used.
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Table 2. Summary of the calculated results
Member
Force (lb)
Area
(in2)
FL/(EA) (in)
F2/A
Strain
F/(EA)
Ui=
L F2
( )
2E A
1
2
3
4
5
6
7
U = ∑Ui
y = U /(0.5P) (in)
K (lb/in) = (0.5P)/y
Note: You may combine section 4 and 5 together in the report.
A summary of the spring constant can be found in Table 3.
Table 3. Summary of the spring constant and loading conditions
Force
(lb)
Range
Spring Constant (lb/in)
loading
(from Table 1)
Unloading
(from Table 1)
Theoretically
Calculated
(from Table 2)
From loading
curve
From
unloading
curve
Low
High
5. Analysis/Discussion
1) Complete data tables.
2) Calculate the magnitudes of the deflection at the point P is applied for each loads (of loading
and unloading).
3) Calculate the gross effective spring constant K of the system using the deflection at the point
P is applied (of loading and unloading).
4) Graph deflection of the point force P is applied as a function of the force P for both loading
and unloading situation (each of the low and high range position).
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Attn: a) One chart for low range with both loading and unloading curve, use trend line do
not connect data points
b) One chart for high range with both loading and unloading curve, use trend line do
not connect data points
c) Estimate the spring constant for the system using the trend lines in 1) and 2).
5) Discuss your results obtained in 3) and 4).
6. Conclusions
Conclude what have been done and the conclusions drawn from your analysis.
7. References
[1] ……
[2] …….
[3] …….
(Note: These numbers need to be located in your report at the place you used the references)