Activity YM1
Pupil
Sheet
NAME…………………………………………………………………………
Young’s Modulus
Experimental details
The device used in this experiment to determine Young’s Modulus and
Poisson’s ratio is the electrical resistance strain gauge. This is the most widely
used device for measuring elastic strains. It is essentially a str
ip of metal foil
which is firmly glued to the surface where the strain is to be measured, so that
when the material is strained, the strain at the surface is fully transmitted to the
metal foil. Elastic strain along the length of the strip causes a small c
hange in
resistance of the gauge, largely because of the change in length and cross

sectional area of the strip,
although there is also a slight change in its
resistivity. Small changes in resistance are easy to measure accurately, and so
the gauge gives a
n accurate reading of the small elastic strain along the
direction of the strip in the gauge. The change in resistance, and hence the
voltage across the strain gauge for a constant current, is proportional to the
strain; the gauge manufacturer supplies the
value of the constant of
proportionality.
For the strain gauges and current used here
ε = 3.803×10

7
V (a conversion factor provided by the
manufacturer),
where
ε = strain (No units
–
a dimensionless quantity)
and
V =
voltage across strain gauge (mea
sured in microvolts).
This practical uses a simulation, based on a University experiment, of the
simple cantilever bending of the beam to which the strain gauges are attached.
The sidearm is not used in this experiment.
Identify the 3 strain gauges on
the
cantilever arm. For this experiment
you will use only two gauges; the one
that is lined up along the cantilever,
the “x” direction and the one lined up
laterally across the cantilever, the “y”
direction. These are represented in
the diagram, above, by
the strain
gauges on the left and right respectively.
Measurements are taken using a single meter, which is attached in turn to
different strain gauges on the top and bottom of the beam. You will use four of
these.
TOP
–
denotes the gauges measuring ten
sion on the upper surface.
BOTTOM
–
denotes the gauges measuring compression on the lower surface.
ALONG
–
denotes the strain in the x direction, along the beam.
LATERAL
–
denotes the strain in the y direction, across the beam.
Activity
YM1
Pupil Sheet
page
2
of
4
http//outreach.materials.ox.ac.uk
The experimental work in t
his practical is very simple and proper working out of
the results will take some time. A results table is provided at the back of this
booklet for you to record your results. To make calculations easier, a
spreadsheet is available to enter your data and
process the results.
Alternatively you can use graph paper to plot graphs manually.
Method
–
Measurements
1.
Select the strain gauge labeled TOP,
ALONG
–
x direction in tension
2.
Take a reading with no load. There may be some drift in this value.
Wait until
a steady reading is obtained, or estimate the average value.
3.
Suspend weights from point
“A”,
and apply successively larger loads to
the end of the beam. Record the strain gauge outputs (in μV) produced
in each case. It may be useful to remove some weights
from time to
time to check that you get the same (or almost the same) readings.
4.
Repeat the method selecting the following strain gauges:
TOP, LATERAL
–
y direction in tension.
BOTTOM, ALONG
–
x direction in compression.
BOTTOM, LATERAL
–
y direction in co
mpression.
Treatment of Results
To verify Hooke’s Law for this material
Plot suitable graphs of the gauge readings as a function of the applied
load
.
The linearity of the graphs will demonstrate the validity of Hooke's law.
To determine Young’s Modul
us for this material
Convert the strain gauge readings to strains ε
x
and ε
y
, (Use the conversion
factor provided by the manufacturer) and the loads to Newtons (1 kg = 9.81N).
From the ε
x
and ε
y
readings (no units), the loads applied (in Newtons) and the
d
imensions of the beam (measure these yourself), calculate the Young's
modulus E and Poisson's ratio v of the beam. Use the gradients of the
stress/strain lines, rather than individual readings.
NOTE: T
he
LINEST
function in Excel is useful here; or you cou
ld plot the
graphs on graph paper.
Make an estimate of the accuracy of your values.
The
theory for this part of the practical is given in the Information Sheet.
Activity
YM1
Pupil Sheet
page
3
of
4
http//outreach.materials.ox.ac.uk
Results Tables
–
Use the Interactive Young’s Modulus simulation to
collect data. Enter your r
eadings in these tables, then transfer them to
the Excel Spreadsheet
To convert μV to measurements of elastic strain (ε), these readings are
multiplied by 3.803 x 10

7
. This is done for you on the spreadsheet.
Enter your data in the corresponding blue columns in the Excel spreadsheet.
As time is very short, much of the rou
tine calculation is done for you in the
spreadsheet
–
this includes
correction of results for the zero reading and
the
plotting of the graphs. You will, however, need to print your graphs.
Explain from the shape of the graphs whether your material demons
trates the
validity of Hooke’s Law. You then need to calculate Young’s Modulus and
Poisson’s ratio for your material, using the formulae shown on page 3
of the
Information Sheet
, and by comparing your value to
published data confirm
which material you
tested
.
A website you may find useful :

http://schools.matter.org.uk/
Dimensions of material tested
1
(cm)
2
(cm)
3
(cm)
Distance of weights to strain gauge
=
l
Width of the beam
=
w
Thickness of the beam
=
h
Direct Readings from Strain G
auges (microvolts)
Load / g
TOP
BOTTOM
ALONG (x)
LATERAL (y)
ALONG (x)
LATERAL (y)
0
100
150
200
250
300
350
400
450
500
Activity
YM1
Pupil Sheet
page
4
of
4
http//outreach.materials.ox.ac.uk
Using the
Information Sheet provided
, and
the results
obtained from
experimental work,
answer the questions below.
What is Hooke’s law?
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Explain what is meant by Young’s Modulus:
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Explain what is meant by Poisson’s ratio:
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