STUDENT'S GUIDE
e TQ Education and Training Ltd 2000
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TrainingLimited.
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discoveredpleaseinform TQ so the problemmay be rectified.
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checkthe contentsof the package(s)againstthe list. If any items
are missing or damaged, contact your local TQ agent or TQ
immediately.
TQ Edu~ation and Training Ltd
Products Division
Contents
Section
1
2
INTRODUCTION
Description
Computer Connection
Strain Sensors
How to set up the equipment
1
2
3
3
EXPERIMENTS
5
Background and Introduction to the Experiments
Experiment 1 - Thin Cylinder with Open Ends
Analysis of Results
Using the Method of Superposition to Find the Principle Strains
5
7
9
9
9
10
10
13
15
15
SOFTWARE OPERATION
17
The Main Page
The Menu Bar
The Tool Bar
Menu Bar Options
Short cut Keys
Using the Software
To zero all the gauges
To take a set of readings
To display the data table
To display a graph
Plotting Graphs using the SM1007 Software
To change the experiment
Normal Operation
17
17
17
18
18
19
19
19
19
20
20
21
21
THEORY
23
Analysis of Results
The Stress Strain Relationship
Conclusion
The Ratio of Hoop Strain to Longitudinal Strain in an Open Cylinder
Principle Strains and The Mohr's Circle
Experiment 2 - Thin Cylinder with Closed ends
3
4
Page
APPENDIX
Nomenclature
27
27
SECTION 1.0 INTRODUCTION
This guide describeshow to set up and perfonn several experimentsrelatedto the stresssystemsin a thin cylinder. It
clearly demonstratesthe principles involved and gives practical supportto your studies.The derivation of the theory
related to the stresssystemsin a thin cylinder is given in section4. You should read this prior to completing the
experimentsand useit asa referencewhenanalysingyour results.
Figure 1
Description
Figure 1 showsthe SMlOO7Thin Cylinder apparatus.It consistsof a thin walled aluminiumcylinder of 80 mm inside
diameterand 3 mm wall. Operatingthe hydraulic pumppressurisesthe cylinder with oil.
The cylinder hassix sensorson its surfacethat measurestrain. A mechanicalgaugeand electronicsensormeasurethe
hydraulicpressurein the cylinder. The cylinder is held in a sturdy frame in which it is free to move along its axis.The
strains(andthus the stress)can be measuredwith the cylinder in two configurations:
"Open" ends- wherethe axial loadsaretakenby the frame(not the cylinder), thereforethereis no direct axial stress
2. "Closed"ends- wherethe axial loadsaretakenby the cylinder, thereforetheremustbe direct axial stress
The two configurationsareachievedusingthe large handwheelat the end of the frame.
In the Openendscondition the handwheelis screwedfully in. This pushesthe two pistonsaway from the cylinder end
capsso that thereis no contactbetweenthem. Therefore,the axial force is transmittedfrom the pressurisedoil into the
frameratherthanthe cylinder. SeeFigure2.
In the Closed ends condition the hand wheel is wound out. This allows the pistons to move outward against the cylinder
end caps so that there is no contact with the frame. Therefore the axial force is transmitted from the pressurised oil into
the cylinder itself. See Figure 3.
Thin Cylinder. Student Guide
Pistons
(toud1ingframe)
I"-',
m
Frame
Pathof load
Gap
Figure 2 Open Ends Condition.
n
Platona
(bJd1W'O
end cepe)
..
n
r:
1
~
Frame
1
Figure 3 Closed Ends Condition
Computer Connection
To take and record readingsand plot graphs,the SMlOO7must be connectedto a PC. Dedicatedsoftware and the
connectingleadis suppliedwith the SMlOO7.
Page2
SM1007 Thin Cylinder. Student Guide
Strain Sensors
The sensorusedto measurethe strainsin the walls of the thin cylinder is called a Strain Gauge.
Strain gauges are sensors that experience a change in electrical resistance when they are stretched or compressed, this
change in resistance can be shown in terms of displacement (strain). Strain gauges are made from a metal foil cut in a
zigzag pattern, they are only a few microns thick so they are mounted on a backing sheet, this allows them to be handled
and electrically insulates the zigzag element. Gauges are bonded to the structural part under examination, thus the strain
gauge stretches and compresses the same amount as the surface of the part. To give an direct reading of strain we use a
constant called the gauge factor, this is to compensate for the slight differences in manufacture between each batch of
gauges, it usually varies between 1.8 and 2.2. It is usual to set this in the strain gauge readout.
There are six strain gaugeson the cylinder, arrangedat variousanglesto allow the study of how the strain varies at
different anglesto the axis. Strainsare shown on the P.C. screen,directly in microstrain on a schematicof the thin
cylinder. Note that a negativereadingis a compressivestrainand a positivereadingis a tensile strain
The technique of strain gauging is of great importance to structural engineers. This equipment gives you the opportunity
to understand their use.
How to set up the equipment
~
--- Cylinder
Figure 4 Layoutof the SM1007
Before usingthe equipment,always:
Visually inspectall parts,includingelectricalleads,for damageor wear.
Checkthat all electricalconnectionsandother partsare securedcorrectly and fasteningsare sufficiently tight.
Position the equipment safely on a solid, level surface, so that it is steady, easily accessible.
Never apply excessiveloadsto any part of the equipment.
In all of the experiments.the basicset up of the equipmentis the same.Refer to the relevantsectionfor the specific
informationyou will requireto do eachexperiment.
I. The main switch is at the rearof the unit. Move it to the on position.the greenLED on the front shouldilluminate.
2. Startthe SM 1007softwareon the PC (seeFigure 5). Refer to "Softwareoperation"on page17 if you are unsure.
3. Leavethe SMl007 for 5 minutesto allow the gaugesto WarD)up andreacha steadystate.
4. To checkthat the Hydraulic circuit is functioning,and familiariseyourselfwith the controls:
a). Openthe releasevalve on the pump (turn anticlockwise)
b). Wind the handwheelfully in
I
c). Fully closethe releasevalve on the pump
d). Operatethe pumpsteadilyobservingthe pressureon the gauge.Stop at a pressureof 3 MN/m2.
e). Leavethe unit for I minute. observingthe pressuregauge.the pressureshouldnot vary in this time
.
f). Openthe releasevalve on the pump.the pressureshouldfall to zero
Finally, to setup the unit with the computer,select'Options' (seeFigure5) from the menubar andset theGaugefactor
to that given on the SMIOO7front panel. Press'Test SM1007' to ensurethat the SMlOO7is communicatingwith the
PC. The PC shouldgive the message:'Communications with SM1007 OK'.
If all the stepsare completesuccessfullythen you are readyto begin the experiments,if not, refer to your lecturerfor
assistance.
.
f\
:~
1
Figure5 SM1007 Software Main Screen with Options box selected.
Page4
SECTION 2.0 EXPERIMENTS
Background and Introduction to the Experiments
In relation to stress analysis, cylinders are divided into two groups: thick and thin. The distinction between the two
relates to the ratio of internal diameter to wall thickness of a particular cylinder. A cylinder with a diameter to thickness
ratio of more than 20 is considered to be thin. A ratio of less than 20 is considered to be thick. This distinction is made
as the analysis of a cylinder can be simplified by assuming it is thin. The SMlOO7 cylinder has a ratio of approximately
27, which is well above the ratio for being considered thin.
Thin cylinders,or shells arecommonplacein engineering.Examplesof thin walled cylindersare:
.
.
.
pressurepipes,
aircraft fuselagesand
compressed gas containers.
Thick walledcylindersare lesscommon,an examplebeing a gun barrel.
For a closed cylinder with an internal pressure there can be three direct stressesacting upon it.
.
.
.
-
Longitudinal stress the cylindersresistanceto stretchingalongits length (axis).
Hoop or Circumferential stre~ - the cylindersresistanceto grow in diameter.
Radial stress - gasor fluid compressingthe walls of the cylinder. It is equalto the pressureon the insideand zero
on the outside
The longitudinal stress and hoop stressesare directly proportional to the pressure and the ratio of diameter to thickness
of the cylinder. However the radial stress is related to the pressure alone.
Becauseof their relationshipto the geometry,the Longitudinal and Hoop stressesare far greaterand more significant
than the radial stressin a thin cylinder. It is reasonableand recognisedto assumethat the radial stressis small enough
for it to be ignoredfor basiccalculations.
~
Figure 6 Stresses in a thin walled cylinder
~O7Thin Cylinder
-Student Guide
The individual direct sb'esses
are given by
0'H = pd/2t and
O'L= pdl4t
Where:
O'H
=Hoop
aL
=Longitudinal
Sb'eSS(Nm-2
Stress (Nm-2
p =Pressure in the cylinder (Nm-1
d
=Diameter of the cylinder (m:
t
=Thicknessof cylinder walls (m)
Nearly all applications of the thin cylinder will have closed ends with the biaxial stress system described previously.
However as outlined in the introduction, the equipment allows us to examine the stressesin the cylinder with open ends
i.e. with no direct longitudinal stress. Although there is no practical applications for a cylinder in this condition, the
experiment yields several useful relationships. We can use these relationships in the more complex closed ends
condition.
Page 6
~
SM1007 Thin Cylinder. Student Guide
-
Experiment 1 Thin Cylinder with Open Ends
In this experiment we will pressurise the cylinder in the open ends condition taking readings from all six strain gauges,
we will then analyse the results in various ways to establish some important relationships. Examine the cylinder and the
diagram on the front panel (or Figure 7) to understand the notation and placement of the strain gauges in relation to the
axis of the cylinder. The experimental method utilises the SMlOO7 software to display and take readings. A guide to
using the software is given in section 3.
-
n
Figure 7 Positions of the strain gauges.
.I
:8
-
I. Having set up and familiarised yourself with the equipmentby following the instructionsin section 1, open the
pumpreleasevalve and screwin the handwheelto set up the openendscondition.
2. In the SMlOO7softwarechoose'Open Ends Condition' from the 'Experiments' menuoption.Thenconnectto
the SMlOO7unit by selecting 'Connect to SM1007' from the samemenu. The virtual meterson the screen
shouldnow display valuesof pressureand strain.
n
NOn
~
If the 'Disconnect the SM1007' from
the 'Experiments'
menu option was not
selected the last time the equipment was used, the software may prompt you to
disconnect and then reconnect again when you change the experiment from closed to
open (or the other way round).
3. Close the pump release valve and zero the readings by selecting 'Zero All Gauges' from the 'Experiments'
menu option. All the virtual strain meters should now read 0:10.3 J.1E,
and the pressure meter should read 0:1:0.01
MN
-2
m
.
4. Take the first set of readings (at zero) into the data table by selecting 'Record Gauge Readings' from the
'Experiments'
menu option. Display the data table by selecting 'Data Table' in the 'Results'
menu.
8'
5. Pumpthe handleslowly until a pressureof around0.5 MNm-2 andrecordthe readingsinto the datatableagainby
selecting'Record Gauge Readings' from the 'Experiments' menuoption.Wait a few secondsbetweenpumps
for the gaugesto stabilize.
007 Thin Cylinder. Student Guide
6. Carefully increasethe pressurein 0.5 MNm-2 increments,recordingthe readingsinto thedatatable until you have
reacheda valueof 3 MNm-2.
WARNING
~
Do not exceeda cylinder pressureof 3.5 MNmo2
Try to get as close as possible to 3 MNm-2 as it will allow you to make direct comparisons with established theoretical
values at this pressure.
7. You may print the datatable if desiredby pressingthe printer button in the top left comer of the table.
8. Disconnectthe communicalionsbetweenthe PC and the apparatusby selecting'Disconnect the SM1007' from
the 'Experiments' menuoption.
.
ilri':
1
1
Page8
SM1007 Thin Cylinder. Student Guide
Analysis of Results
The Stress Strain Relationship
The datatable calculatesthe hoop stressfor eachpressurereading. Selectone pressurereading(other than zero) and
check the calculationof stressusing the equationsgiven in the previoussectionand the dataon the front panelof the
SMlOO7.
From your examination of the positioning of the strain gaugesyou will have noticed that gauges 1 and 6 have been placed
so that they are measuring the hoop strain in the cylinder. Examine the results for gauges 1 and 6, what can you say about
the magnitude of the hoop strain as you move along the axis of the cylinder?
You should conclude that the hoop strain remains constant along the length of the cylinder.
Plot a graphof AverageHoop StressversusHoop Straineither by hand(from the datatable),or by usingthe graphing
facility in the SMlOO7.
To plot the graphusingthe SMlOO7software.select'Hoop Stress v Hoop Strain' from the 'Results' menuoption.
A chart wi" appearwith crossesmarkingthe results.
What is the relationship between stress and strain?
Your graph should reveal a linear relationship between stress and strain. the gradient of which is a measure of stiffness
called the Youngs's Modulus.
Eade
Where:
E =Young's Modulus (Nm-2)
0"
=Stress (Nm-2)
E
=Strain (~)
Find a valueof the Young's Modulus for the cylinder materialfrom your graph.
To find the value of the gradient and therefore the Youngs Modulus from the graph plotted by the software, a line needs
to be drawn through the results. The slope of the line is indicated when you release the mouse button. (Refer to "Plotting
Graphs using the SMlOO7 Software" on page 20)
The Young's Modulus varies from materialto material,but is a constantfor eachmaterial, so long as it hasunifonn
properties(homogenousandisotropic). For the aluminiumalloy usedfor the SM I 007 cylinder the Young's modulusis
nominally 70 GNm-2 Doesthe valueof Young's modulusfrom your graphagreewith the theoreticalvaluestated? If
thereis a discrepancybetweenthe valuesthen nameany sourcesof error that may be present.
Steelis approximatelythreetimes stiffer than aluminiumhaving a Young's Modulus of 210 GNm-2.
If the cylinder hadbeenmadeof steelwould the measuredstrainbe higher or lower for the samestress?
Conclusion
The use of the apparatus has established the stress strain relationship and experimental value of Young's Modulus. Note
that since the Young's Modulus remains constant for any given homogenous isotropic material, strain gauges are a
reliable meansof measuringstresson the surfaceof a structuralpart.
7 Thin Cylinder. Student Guide
The Ratio of Hoop Strain to Longitudinal Strain in an Open Cylinder
In the introduction to the experiments it was stated that there is no Direct longitudinal strain in the open ends conditions.
With referenceto the small diagramon the front of the SM 1007, identify the gaugewhich measuresthe longitudinal
strain. Doesthis gaugeregisterzero?
You will find that the gaugedoesnot registerzero,in fact a significant compressivestrain is measured.This is because
thereis an Indirect Longitudinal strain which is a result of the hoopstress. This indirect strain is generatedby the fact
that as the cylinder increasesdiameterthe length decreases(the oppositecan be seento occur if you stretchan elastic
band)
To explorethis relationship,plot a graphof the Longitudinal Strain VersusAverageHoop Strain,either by hand(from
the datatable),or by using the graphingfacility in the SMlOO7.
To plot the graphusing the SM I 007 software,selectLongitudinal v Hoop Strain from the Results menu.A chart
will appearwith crossesmarking the results.
Find the gradient of your plot.
To find the value of the gradient from the graph plotted by the software, a line needs to be drawn through the results. The
slope of the line (gradient) is indicated when you release the mouse button. (Refer to "Plotting Graphs using the SM1OO7
Software" on page 20)
The magnitudeof the gradientof your plot is a calledPoisson'sratio it can be definedas the ratio of indirect strain to
direct strain. In mathematicaltermsit is given as:
v =-eI.JeHo
where
v =Poisson's Ratio
ELo
=Longitudinal
EHo
Strain (in the open ends condition)
=Hoop Strain (in the open ends condition)
The Poisson'sratio changesfrom materialto materialbut is constantfor any given homogenousisotropicmaterial.
Most metalshavea value of Poisson's ratio of around0.3. althoughthe rangeof valuesis 0.1 to 0.5 the extremesbeing
concreteandrubberrespectively.
Thecylinder is manufacturedfrom analuminiumalloy which hasa Poisson'sratio of 0.33. Comparethis to the gradient
of your graph.
Principle Strains and The Mohr's Circle
In the caseof a cylinder the maximum and minimum strainsare always at right anglesto eachother (seethe theory
section) Thesestrainsare called the principle strains. As discoveredpreviously,in the openendscondition, the thin
cylinder hasprinciple strainsof:
EHo
= uHJE (direct from the hoop stress)
ELo
=-vO'HoIE(indirectly
due to the Poisson effoct)
But how to we quantify strainsat other than right anglesto the axis of the cylinder?
The answerlies in a simple yet effective graphicalmethodknown as a Mohr's Circle. Mohr's circles can be u~ to
solvea varietyof strain,stressand deflectionproblems.
Page 10
SM1007 Thin Cylinder. Student Guide
First. constructa Mohr's Circle by handso that you understandhow themethodworks. The 8M 1007softwarewill also
constructa Mohr's circle from your results. You can usethis facility to checkyour work.
We have already established that the strain gauges give a very linear response to pressure so we will use only the values
for the maximum test pressure (3 MNm-2).
1. On graph paper constructan axis which allows for the minimum principle strain (gauge2) and the maximum
principle strain(the averageof gauges1 and6) on the x axis and a strainof around-400 to +400 on the y axis. The
x and y axesmust be to the samescale.
2. As canbe seenfrom the equationsin the theorysection,on a Mohr's Circle the strains are related to 29 where 9 =
the angle from the axis. This is an importantthing to remember.
Sincegauge2 is on the axis of the cylinder, thenthe angleis 0° on the Mohr's circle
SincegaugesI and6 are90° from the axis, thenthe angleis 180°on the Mohr's circle
3. Plot these 2 points on the axis as shown in sketch 1
go-
Figure8 Sketch 1
4. The two pointsarethe extremesof the Mohr's circle. On this basisfind the centreeither by calculationor by
construction,then draw a circle asshownin sketch2.
This is the Mohrs circle based on your results for the principle strains. You can now use this to find the direct strain
at any angle from the ws.
5. To find the direct strainat 60° from the axis,draw a line from the centreof the circle at 120°clockwisefrom 0°
(remember,twice the angle!) until it intersectsthe circle, thendraw a line vertically down to the x axis (seeFigure
10).
6. Readoff the valueof strainandcomparethis to the readingfor the straingaugewhich is placedat 60° from the axi!
(gauge5) you shouldfind that the two readingsare in closeagreement.
7. Repeatthe processfor 30° and45° andcomparethe readingsfrom your Mohr's Circle to thosemeasuredon the
equipment.Doesthe Mohr's circle accuratelypredict the direct ~trainat any angle?
As you know, the x axis on the Mohr's circle plot is the direct strain,but what is the y axis?
The answeris the shear strain, from which we canquantify the shear stress
Figure9 Sketch2
1
Figure 10 Sketch3
To plot the Mohr's circle using the SMlOO7 software, select Plot Mohr's Circle from the Results menu. A chart will
appear with crosses marking the results. Refer to "To display a graph" on page 20 for extra functions on the Mohr's
circle. Readings of strain may be taken from the graph by moving the mouse CUTSOf'
around the circle.
Find the values of shear strain for each of the angles on the cylinder in the same way you found the direct strain. At what
angle is the maximum shear strain? Will it always be this angle for a thin cylinder?
Calculatetheoreticalprinciple strains(using the equations~iven in the theory section)with a pressureof 3 MNm-2, a
Poisson'sratio of 0.33anda Young's Modulusof 69 MNm- . Constructa Mohr's circle usingthesevaluesandcompare
it to your experimentalone. Do the theoreticalandexperimentalMohr's circles agree?What are the sourcesof error?
Page 12
SM1007 Thin Cylinder. Student Guide
-
Experiment 2 Thin Cylinder with Closed ends
Having completedthe analysisof the openendscondition we will now test the cylinder taking the samereadingsas in
experiment1 but with the cylinder in the closedendscondition to showthe effect of the biaxial stresssystem.
. Openthe pumpreleasevalve andcarefully unscrewthe handwheelenoughto setup the closedendscondition.
NOTE
~
The handwheel is not fastened to the apparatus, if it is unscrewed too far, it will fall
out.
To check that the frame is not transmitting any load, close the pump release valve and pump the handle and observe
the pressure gauge, you may need to pump a number of times as the oil pushes the pistons outward.
2. Oncea pressureof around3 MNm-2hasbeenachieved,gently pushandpull the cylinder alongits axis,the cylinder
shouldmove in the frame indicatingthat the frame is nOllransmittingany load. If it doesn'tmove,wind the
handwheelout somemoreandtry again.
WARNING
~
Do not exceeda cylinder pressureof 3.5 MNm-2
3. In the SMlOO7 software choose 'Closed Ends Condition' from the 'Experiments'
menu option. Then connect
to the SMlOO7unit by selecting 'Connect to SM1007' from the samemenu. The virtual meterson the screen
should now display values of pressure and strain.
If the 'Disconnect
the SM1 007' from the 'Experiments'
menu option was not
selected the last time the equipment was used, the software may prompt you to
disconnect and then reconnect again when you change the experiment from closed to
open (or the other way round).
4. Closethe pumpreleasevalve andzero thereadingsby selecting'Zero All Gauges' from the 'Experiments'
menuoption. All the virtual strainmetersshouldnow read0:!:0.3~, andthe pressuremetershouldreadO:tO.Ol
MN
-2
m
.
5. Takethe first setof readings(at zero)into the datatable by selecting'Record Gauge Readings' from the
'Experiments' menuoption. Display the datatable by selecting'Data Table' in the 'Results' menu.
6. Pumpthe handleslowly until a pressureof around0.5 MNm-2 andrecordthe readingsinto the datatableagainby
selecting'Record Gauge Readings' from the 'Experiments' menuoption.Wait a few secondsbetweenpumps
for the gaugesto stabilize.
7. Carefully increasethe pressurein 0.5 MNm-2 increments,recordingthereadingsinto the datatable until you have
reacheda valueof 3 MNm-2.
WARNING
~
Do not exceeda cylinder pressureof 3.5 MNm-2
SM1007 Thin Cylinder. Student Guide
Try to get as close as possible to 3 MNm-2 as it will allow you to make direct comparisons with established theoretical
values at this pressure.
8. You may print the datatable if desiredby pressingthe printer button in the top left cornerof the table.
9. Disconnectthe communicationsbetweenthe PC andthe apparatusby selecting'Disconnect the SM1007' from
the 'Experiments' menuoption.
Page 14
SM1007 Thin Cylinder
-Student Guide
Analysis of Results
Examinethe datatable.With referenceto the stressequations,confirm that longitudinal stressis half the value of the
hoop stress. Check,using a methodof differences,or by sketchinggraphs,that the readingsfrom the gaugesare still
linear in the closedendscondition.
Using the Methodof Superpositionto Find the Principle Strains
In the previous experiment, we established that for the direct hoop stresswe created and indirect longitudinal strain, due
to the Poisson effect. It follows therefore, that if we created a purely longitudinal stress that we would have an indirect
hoop strain. If the cylinder were stretched it will have a tendency to reduce in diameter (which is exactly what happens
if you stretch an elastic band.) To find the principle strains we can use the idea of superposition. This means that we can
simply work out the principle strains for each stress case (hoop and longitudinal) in isolation and then sum them to give
the principle strains for the biaxial system.
I.e.
"The principle strain in the longitudinal direction is the sum of the direct longitudinal strain and the indirect
longitudinal strain"
and
'The principle strain in the circumfrencial direction is the sum of the direct hoop strain and the indirect hoop
strain."
In mathematical terms
The hoop stress will cause strains of:
EH= O'IIE
£L
=-vailE
(due to the Poisson effect)
Conversely, the longitudinal stress will cause strains of:
£L= ailE
EN
=-vO'LIE (due to the Poisson effect)
The algebraic sum of these strains is
EH= (O"JrvO"IJIE
£L
=(O"L-VO"H)/E
Construct a Mohr's circle from your results at 3 MNm-2 either by hand or by using the SM 1007 Software using the same
methodas usedin experiment1.
Readoff valuesfor the direct strainsand comparethem to valuesobtainedfrom the equipment. Your predictedand
experimentalvalue shouldbe in closeagreement.What do you notice aboutthe overall diameterof the Mohr's circle
comparedto the openendscondition? How doesthis affect the shearstrain?
Calculate theoretical principle strains using the equations given in the theory section with a pressure of 3 MNm-2, a
Poisson's ratio of 0.33 and a Young's Modulus of70 MNm-2. Construct a Mohr's circle using these values and compare
it to your experimental one. Do the theoretical and experimental Mohr's circles agree?
SECTION3.0 SOFTWAREOPERATION
The TQ SMlOO7 Thin Cylinder software only operates on computers which have the WindowsTM Operating System
Currently, WindowsTM 95, 98 and NT4 are supported.
To start the software:
Start the computer and allow the WindowsTM Operating System to load.
2. Click on the TQ SMlOO7icon or selectSM1007 Thin Cylinder from the SM1007 Programs
Group.
3. The main pagewill appear,asin Figure 11althoughsomeof the controlsmay be greyedout.
Figure 11 TO SM1007 Thin Cylinder Software
-Mainpage
The Main Page
The picture on the main page 'mimics' the actual apparatus.The text boxes around the cylinder are 'virtual meters' which
indicate the reading from each strain gauge and the pressure gauge, they do not respond immediately because the
software allows the gauges to stabilize before updating the readings.
The Menu Bar
Along the top of the page is the menu bar. You may click on any of the words in the menu bar to make them drop down
into a list of choices, or you may press the AL T button on your keyboard and at the same time, the letter which is
underlined.
The Tool Bar
Underneaththe menubar is a rangeof 'tool bar' buttons.The buttonson the tool bar are a user-friendlyshort cut to
commonlyusedchoicesfrom the menubar. Hover the mousecursorover eachtool button to discoverwhat action they
perform.
SM1007 Thin Cylinder. Student Guide
Menu Bar Options
The menubar optionsallow you to perform the following
File
This list allows you to opena new or previousfile, savethe currentfile or exit the program.
NOTE
~
If the program is exited (closed) before saving the experiment, the data will be lost.
Files aresavedby default into the Experiment Files folder underthe TQ Softwaredirectoryof theProgram Files in the
PC. All experimentfiles are given the extension*,SM7.
Experiments
This list allows you to selectOpenor Closedendsexperiments,connectthe communicationspath to the SMlOO7Thin
Cylinder apparatus,setup the gaugesandtakereadings.
Results
This list allows you to display the datatableandgraphsof stressand strainrelationships.
Only one graph may be displayed at a time.
When either the data table or graphsare selectedfrom the results option on the menu bar, a new page will open,
displayingthe datayou haveselected.Along the top of eachnew pagethereare more tool buttons,which allow you to
print the resultsor graph on the selectedprinter. The graphshavetool buttonswhich allow you to display or hide grid
lines, modify the graphsor copy the graph to the clipboardof the PC. Hover the mousecursor over the tool buttonsto
discoverwhat action they perform.
Options
This allows you to checkthe communicationpath to the Thin Cylinder apparatus,calibratethe gaugefactor and select
the COM port on the PC to which the serial communicationscableis connected.
1
Short cut Keys
On eoch of the drop down menu lists, a short cut key is indicated along side some commands. Pressing the short-cut key
indicated gives a quick one key press method of perfonning those commands.
The short-cutkeys in the TQ SMlOO7softwareare:
-
F3 Connect to SMIOO7
-
F4 Disconnect from SMlOO7
-
FS Record Gauge Readings
-
F6 Remove Last Reading
Page 18
Using the Software
Figure 12 The Tool Buttons.
To set up an experiment,
select 'New'
from the 'File'
menu option, or press the Create New File tool button.
2. Make sure the SMlOO7 apparatus is connected to the PC with the serial cable and that the apparatus is connected to
the mains supply and switched on. The green light next to the serial communication socket on the apparatus should
be on.
3. Select'Options' from the menubar.Checkthat the correctCOM port is selectedand that the gaugefactor is setto
the valueindicatedon the label at the front of the SM1007apparatus.
4. Press'Test SM1 007' to check that the communications are set up correctly. If the communications are faulty or the
wrong COM port is selected, the software will indicate an error, stating 'Could not Communicate'.
Otherwise
the softwarewill state'Communication with SM1007 OK'.
5. On the optionsbox, select'OK' (to saveany changes)or 'Cancel' (to discardany changes)andthenclosethe box.
6. Decidewhich experimentyou wish to do and selecteither 'Open ends Condition' or 'Closed ends
Condition' from the 'Experiments' menu.
7. Select'Connect to SM1007' from the 'Experiments'
menu, or press the Connect to SMlOO7 tool button.The
virtual meters will all display the current values of pressure and strain. The green light next to the serial
communication socket on the apparatus will start to flash slowly.
8. Conductthe experimentsasdetailed.
To zero all the gauges
Select'Zero All Gauges' from the 'Experiments' menuoption, or pressthe Zero All Gaugestool button.
To take a set of readings
Select 'Record Gauge Readings' from the 'Experiments'
menuoption,or presstheRecord GaugeReadingstool
button.
To display the data table
Select'Display Data Table' from the 'Results'
menu option, or pressthe Display Data Table tool button.
Incorrect readingsmay be removedby selecting'Remove Last Reading' or 'Remove All Readings' from the
'Experiments' menuoption.
SM1007 Thin Cylinder. Student Guide
To display a graph
Select 'Hoop Stress V Hoop Strain'. 'Plot Mohr's Circle', or 'Longitudinal
'Results' menuoption.
v Hoop Strain' from the
The Longitudinal v Hoop Strain graph will not operate for the closed ends condition
At the top of eachgraph. more tool buttons allow you to perform operations.such as printing the graph. or adding
horizontaland vertical grid lines.
Hoop Stressv Hoop Strain and Longitudinal v Hoop Strain Graphs
Thesegraphshavetool buttonswhich will eithercalculatethe gradientof a line drawn on the graphor display the x and
y coordinatesof the mousecursoron the graph.
Mohr's Circle
The Mohr's Circle is initially displayedin red and plotted from the principle strainsof gauges1.2and 6. Pressthe Plot
Experimental Values tool button to display the other gaugevalues.Pressthe Plot Theoretical Mohr's Circle tool
button to display a theoreticalcircle in blue.
Plotting Graphs using the SM1007 Software
The softwaresuppliedwith the SM 1007will automaticallyplot graphsfrom the resultsof eachexperiment.The graphs
show the x and y axis and the resultsas a seriesof crosses.Thereare tool buttonsat the top left comer of eachgraph
page,one of the buttonswill toggle betweentwo options:Calculate gradient of a line or display coordinates.When
the button is not pressedin, the coordinatesof the mousecursor are displayedin the bottom right comer of the page.
When the button is pressedin, the softwarewill automaticallycalculatethe gradientof the line, using the following
method:
Figure 13 Tool Buttons for graphs (not Mohr's Circle).
To automaticallycalculatethe slopeof the graph(gradient)a line must be drawn throughthe resultcrossesas follows;
r
Move the mousecursornearto the 0,0 origin of the graph,the cursorwill changeto a squarewith a pointer.
2. Click andhold the left mousebutton. movethe cursortowardsthe oppositecomer of the graph
:n
Release the mouse button when the line is at a good average of all the points.
n
Paae 20
To change the experiment
Savethe file for the currentexperiment,using 'Save As' from the 'File' menuoption, or pressthe SaveTo File
tool button.
2. Disconnectthe communicationsby selectingthe 'Disconnect SM1007' from the 'Experiments' menuoption,
or pressthe disconnectSMIO07 tool button.
NOTE
~
Always disconnectafter eachexperiment.
3. Select'New' from the 'File' menuor pressthe createnew file tool button.
4. Selectthe experimentyou wish to do from the 'Experiments' menuandselect'Connect To SM1007' from the
samemenu.
Normal Operation
When the PC and the SM 1007 apparatus are connected and the experiment is running:
a). The text boxes surrounding the picture on the main page will indicate the strain monitored by each gauge.
b). The indicator on the picture of the mechanical gauge will move in accordance with the real gauge on the
equipment.
c). The picture
experiments
of the hand wheel will
move in and out as the selection
between open and closed ends
is made.
d). The green light next to the serial communications socket will flash slowly.
Along the bottom of the main page. text boxes display the current status of the experiment. the COM port condition and
the last pressure reading.
SECTION 4.0 THEORY
The diagrams in Figure 14 and Figure 15 represent the stressand the forces acting upon an element of material under the
action of a two-dimensional stress system.
Gt
Oy
Figure 14 Stress diagram for two-dimensional stress systems
Figure
15 Forcediagramfor two-dimensionalstresssystem
AssumeFigure 15 to be a 'wedge' of materialof unit depthand the side AB to be of unit length.Resolvingalong 0'0
gives:
0',= (O'yOOS
8) COS8 + (O'xsin8)sin8+ ('fcos8)sin8+ ('fsin 8)oos 8
ug-
(1 +COS26)"
Uy
2
"
+ u1
(1-
Co828)
2
Tsin26
+
cos28 + -rsin28
(t)
Resolvingalong 1'8gives:
f9
= (O'ycosO)sinO- (O'xsin O)cosO+ (t"sin 0) sin 0-
(fCOSO)cos0
07 Thin Cylinder
-Student
Guide
'f9
1',
=
sin29
sin28
O'y~-O'x-r
(0:-0:)
= :':y~sin28-
. 2
9
+
'tSln
2
-
-rcos
9
'l'cos28
(2)
From Equation(2) it can be seenthat there are valuesfor 8 for which 1'8is zero, and the planeson which the shear
componentis zeroarecalled 'Principal Planes'.
From Equation (2):
0 =
!.5~
2
sin28- -rcos28
-rcos29= (a-o:)
::..:.l.rSin28
1'=
(3)
~~tan28
,
This will give two valuesof 28 differing by 1800and, therefore,two valuesof 8 differing by 9()0.This showsthat the
principal planesare at right anglesto eachother.
Figure 16 Diagrammatic representation of Equation (3)
From the diagram'
(4)
and
0' -,0'.
cas28 = :tJ<~:~i'~
-;
(S)
The Sb'eSseS
on the principal planes are nonnal to these planes and are called 'Principal Stresses'
From Equation (1) and substituting the above values:
(6)
Page 24
SM1007 Thin Cylinder. Student Guide
Principalstressesare the maximumand minimum valuesof normal stressin the system.The sign will denotethe type
of stress, i.e.
Negabve sign:
Posibve sign:
Compressive stress
Tensile stress
~
Figure 17 Force diagram for an element
Assuming BC and AC are principal planes, i.e. 'r= O. and 0'1 and ~ are the principal stresses:
(7)
Now maximum shear stress f9will be seen to occur when sin28
stress occurs on planes at 45° to the principal planes, and
A
-r, =
= I, i.e. when 8= 45°. Thereforethe maximumshear
(aa-a.)
2
(8)
or, usingEquation(6)
I, - .2 . _2
-r, = ~(ax
- ay>
+4-r
A
Figure 18 Diagram of principal stresses on an element
(9)
£1 = 0".
E-
0'2
~=E-
E
El andE2arethe valuesof the principal strains.A negativequantitydenotescomp~ve strainwhile a positivequantity
denotestensile strain.Thesestrainscan be usedto constructa Mohr's StrainCircle in the sameway as stresses.
Figure 19 Representation of strain on a Mohr's circle
Q
=Centreof the straincircle
-:--:
2
em
=~
+(~)cao26
+ l~)C0828
and
En
£D= (~
= ~+(~)-(~)C0828
+(Y)COS26
(12)
APPENDIX
Nomenclature
a
NonnalStress
MNm-2
If
Shear Suess
MNm-2
8
Angular Position
Degrees
InternalPresaure
MNm-2
e
DirectRtlain
(Ratioof &L)
E
Young's Modulus
GNm-2
v
Poisson's Ratio
(Ratio of LateralStrain/Axial Strain)
d
Cylinder Internal Diameter
m(ormm)
t
CyMnder Wall Thk:knes8
I
Denotes StraIn In the open ends condition
H
Denotes !he hoop or circumferential direction
L
Denotes the longitudinal direction
IP
IxandV
-
-
Denote particular directions
-
-
m (or mm)