STUDENT'S GUIDE. TQ Edu~ation and Training Ltd Products Division

STUDENT'S GUIDE e TQ Education and Training Ltd 2000 No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording or any information storage and retrieval system without the express permission of TQ Education and Training Limited. All due care has been taken to ensure that the contents of this manual are accurate and up to date. However, if any errors are discovered please inform TQ so the problem may be rectified. A Packing Contents List is supplied with the equipment. Carefully check the contents of the package(s) against the list. If any items are missing or damaged, contact your local TQ agent or TQ immediately. TQ Edu~ation and Training Ltd Products Division

Section Contents Page 1 INTRODUCTION Description Computer Connection Strain Sensors How to set up the equipment 1 2 3 3 2 EXPERIMENTS 5 Background and Introduction to the Experiments Experiment 1 - Thin Cylinder with Open Ends 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 Analysis of Results Using the Method of Superposition to Find the Principle Strains 5 7 9 9 9 10 10 13 15 15 3 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 SM1 007 Software To change the experiment Normal Operation 17 17 17 18 18 19 19 19 19 20 20 21 21 4 THEORY 23 APPENDIX 27 Nomenclature 27

SECTION 1.0 INTRODUCTION This guide describes how to set up and perfonn several experiments related to the stress systems in a thin cylinder. It clearly demonstrates the principles involved and gives practical support to your studies. The derivation of the theory related to the stress systems in a thin cylinder is given in section 4. You should read this prior to completing the experiments and use it as a reference when analysing your results. Figure 1 Description Figure 1 shows the SMlOO7 Thin Cylinder apparatus. It consists of a thin walled aluminium cylinder of 80 mm inside diameter and 3 mm wall. Operating the hydraulic pump pressurises the cylinder with oil. The cylinder has six sensors on its surface that measure strain. A mechanical gauge and electronic sensor measure the hydraulic pressure in the cylinder. The cylinder is held in a sturdy frame in which it is free to move along its axis.the strains (and thus the stress) can be measured with the cylinder in two configurations: "Open" ends - where the axial loads are taken by the frame (not the cylinder), therefore there is no direct axial stress 2. "Closed" ends - where the axial loads are taken by the cylinder, therefore there must be direct axial stress The two configurations are achieved using the large hand wheel at the end of the frame. In the Open ends condition the hand wheel is screwed fully in. This pushes the two pistons away from the cylinder end caps so that there is no contact between them. Therefore, the axial force is transmitted from the pressurised oil into the frame rather than the cylinder. See Figure 2. 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 (toud1ing frame) I "', - m Frame Gap Path of load Figure 2 Open Ends Condition. Platona (bjd1w'o end cepe) n.. n r: Frame Figure 3 Closed Ends Condition 1 ~ 1 Computer Connection To take and record readings and plot graphs, the SMlOO7 must be connected to a PC. Dedicated software and the connecting lead is supplied with the SMlOO7. Page 2

SM1007 Thin Cylinder. Student Guide Strain Sensors The sensor used to measure the strains in 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 gauges on the cylinder, arranged at various angles to allow the study of how the strain varies at different angles to the axis. Strains are shown on the P.C. screen, directly in microstrain on a schematic of the thin cylinder. Note that a negative reading is a compressive strain and a positive reading is 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 Layout of the SM1007 Before using the equipment, always: Visually inspect all parts, including electrical leads, for damage or wear. Check that all electrical connections and other parts are secured correctly and fastenings are sufficiently tight. Position the equipment safely on a solid, level surface, so that it is steady, easily accessible. Never apply excessive loads to any part of the equipment. In all of the experiments. the basic set up of the equipment is the same. Refer to the relevant section for the specific information you will require to do each experiment.

I. The main switch is at the rear of the unit. Move it to the on position. the green LED on the front should illuminate. 2. Start the SM 1007 software on the PC (see Figure 5). Refer to "Software operation" on page 17 if you are unsure. 3. Leave the SMl007 for 5 minutes to allow the gauges to WarD) up and reach a steady state. 4. To check that the Hydraulic circuit is functioning, and familiarise yourself with the controls: a). Open the release valve on the pump (turn anticlockwise) b). Wind the hand wheel fully in c). Fully close the release valve on the pump d). Operate the pump steadily observing the pressure on the gauge. Stop at a pressure of 3 MN/m2. e). Leave the unit for I minute. observing the pressure gauge. the pressure should not vary in this time f). Open the release valve on the pump. the pressure should fall to zero Finally, to set up the unit with the computer, select 'Options' (see Figure 5) from the menu bar and set the Gauge factor to that given on the SMIOO7 front panel. Press 'Test SM1007' to ensure that the SMlOO7 is communicating with the PC. The PC should give the message: 'Communications with SM1007 OK'. If all the steps are complete successfully then you are ready to begin the experiments, if not, refer to your lecturer for assistance. I.. f\ :~ 1 Figure 5 SM1007 Software Main Screen with Options box selected. Page 4

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 are commonplace in engineering. Examples of thin walled cylinders are:. pressure pipes,. aircraft fuselages and. compressed gas containers. Thick walled cylinders are less common, an example being a gun barrel. For a closed cylinder with an internal pressure there can be three direct stresses acting upon it.. Longitudinal stress - the cylinders resistance to stretching along its length (axis).. Hoop or Circumferential stre~ - the cylinders resistance to grow in diameter.. Radial stress - gas or fluid compressing the walls of the cylinder. It is equal to the pressure on the inside and zero on the outside The longitudinal stress and hoop stresses are 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. Because of their relationship to the geometry, the Longitudinal and Hoop stresses are far greater and more significant than the radial stress in a thin cylinder. It is reasonable and recognised to assume that the radial stress is small enough for it to be ignored for basic calculations. ~ Figure 6 Stresses in a thin walled cylinder

~O7 Thin Cylinder - Student Guide The individual direct sb'esses are given by 0' H = pd/2t and O'L = pdl4t Where: O'H = Hoop Sb'eSS (Nm-2 al = Longitudinal Stress (Nm-2 p = Pressure in the cylinder (Nm-1 d = Diameter of the cylinder (m: t = Thickness of 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 stresses in 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

~ MN -2 m. 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 I. Having set up and familiarised yourself with the equipment by following the instructions in section 1, open the pump release valve and screw in the hand wheel to set up the open ends condition. :8-2. In the SMlOO7 software choose 'Open Ends Condition' from the 'Experiments' menu option. Then connect to the SMlOO7 unit by selecting 'Connect to SM1007' from the same menu. The virtual meters on the screen should now display values of pressure and 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 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. Pump the handle slowly until a pressure of around 0.5 MNm-2 and record the readings into the data table again by selecting 'Record Gauge Readings' from the 'Experiments' menu option. Wait a few seconds between pumps for the gauges to stabilize.

007 Thin Cylinder. Student Guide 6. Carefully increase the pressure in 0.5 MNm-2 increments, recording the readings into the data table until you have reached a value of 3 MNm-2. WARNING ~ Do not exceed a cylinder pressure of 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 data table if desired by pressing the printer button in the top left comer of the table. 8. Disconnecthe communicalions between the PC and the apparatus by selecting 'Disconnect the SM1007' from the 'Experiments' menu option.. ri il ': 1 1 Page 8

SM1007 Thin Cylinder. Student Guide Analysis of Results The Stress Strain Relationship The data table calculates the hoop stress for each pressure reading. Select one pressure reading (other than zero) and check the calculation of stress using the equations given in the previous section and the data on the front panel of the SMlOO7. From your examination of the positioning of the strain gauges you 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 graph of Average Hoop Stress versus Hoop Strain either by hand (from the data table), or by using the graphing facility in the SMlOO7. To plot the graph using the SMlOO7 software. select 'Hoop Stress v Hoop Strain' from the 'Results' menu option. A chart wi" appear with crosses marking the 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 value of the Young's Modulus for the cylinder material from 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 material to material, but is a constant for each material, so long as it has unifonn properties (homogenous and isotropic). For the aluminium alloy used for the SM I 007 cylinder the Young's modulus is nominally 70 GNm-2 Does the value of Young's modulus from your graph agree with the theoretical value stated? If there is a discrepancy between the values then name any sources of error that may be present. Steel is approximately three times stiffer than aluminium having a Young's Modulus of 210 GNm-2. If the cylinder had been made of steel would the measured strain be higher or lower for the same stress? 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 means of measuring stress on the surface of a structural part.

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 reference to the small diagram on the front of the SM 1007, identify the gauge which measures the longitudinal strain. Does this gauge register zero? You will find that the gauge does not register zero, in fact a significant compressive strain is measured. This is because there is an Indirect Longitudinal strain which is a result of the hoop stress. This indirect strain is generated by the fact that as the cylinder increases diameter the length decreases (the opposite can be seen to occur if you stretch an elastic band) To explore this relationship, plot a graph of the Longitudinal Strain Versus Average Hoop Strain, either by hand (from the data table), or by using the graphing facility in the SMlOO7. To plot the graph using the SM I 007 software, select Longitudinal v Hoop Strain from the Results menu. A chart will appear with crosses marking 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 magnitude of the gradient of your plot is a called Poisson's ratio it can be defined as the ratio of indirect strain to direct strain. In mathematical terms it is given as: where v = Poisson's Ratio ELo = Longitudinal Strain (in the open ends condition) EHo = Hoop Strain (in the open ends condition) v = -ei.jeho The Poisson's ratio changes from material to material but is constant for any given homogenous isotropic material. Most metals have a value of Poisson' s ratio of around 0.3. although the range of values is 0.1 to 0.5 the extremes being concrete and rubber respectively. The cylinder is manufactured from an aluminium alloy which has a Poisson's ratio of 0.33. Compare this to the gradient of your graph. Principle Strains and The Mohr's Circle In the case of a cylinder the maximum and minimum strains are always at right angles to each other (see the theory section) These strains are called the principle strains. As discovered previously, in the open ends condition, the thin cylinder has principle strains of: EHo = uhje (direct from the hoop stress) ELo = -vo'hoie (indirectly due to the Poisson effoct) But how to we quantify strains at other than right angles to the axis of the cylinder? The answer lies in a simple yet effective graphical method known as a Mohr's Circle. Mohr's circles can be u~ to solve a variety of strain, stress and deflection problems. Page 10

SM1007 Thin Cylinder. Student Guide First. construct a Mohr's Circle by hand so that you understand how the method works. The 8M 1007 software will also construct a Mohr's circle from your results. You can use this facility to check your 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 construct an axis which allows for the minimum principle strain (gauge 2) and the maximum principle strain (the average of gauges 1 and 6) on the x axis and a strain of around -400 to +400 on the y axis. The x and y axes must be to the same scale. 2. As can be seen from the equations in the theory section, on a Mohr's Circle the strains are related to 29 where 9 = the angle from the axis. This is an important thing to remember. Since gauge 2 is on the axis of the cylinder, then the angle is 0 on the Mohr's circle Since gauges I and 6 are 90 from the axis, then the angle is 180 on the Mohr's circle 3. Plot these 2 points on the axis as shown in sketch 1 go- Figure 8 Sketch 1 4. The two points are the extremes of the Mohr's circle. On this basis find the centre either by calculation or by construction, then draw a circle as shown in sketch 2. 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 strain at 60 from the axis, draw a line from the centre of the circle at 120 clockwise from 0 (remember, twice the angle!) until it intersects the circle, then draw a line vertically down to the x axis (see Figure 10). 6. Read off the value of strain and compare this to the reading for the strain gauge which is placed at 60 from the axi! (gauge 5) you should find that the two readings are in close agreement. 7. Repeathe process for 30 and 45 and compare the readings from your Mohr's Circle to those measured on the equipment. Does the Mohr's circle accurately predict the direct ~train at 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 answer is the shear strain, from which we can quantify the shear stress Figure 9 Sketch 2 1 Figure 10 Sketch 3 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? Calculate theoretical principle strains (using the equations ~iven in the theory section) with a pressure of 3 MNm-2, a Poisson's ratio of 0.33 and a Young's Modulus of 69 MNm-. Construct a Mohr's circle using these values and compare it to your experimental one. Do the theoretical and experimental Mohr's circles agree? What are the sources of error? Page 12

MN -2 m. SM1007 Thin Cylinder. Student Guide Experiment 2 - Thin Cylinder with Closed ends Having completed the analysis of the open ends condition we will now test the cylinder taking the same readings as in experiment 1 but with the cylinder in the closed ends condition to show the effect of the biaxial stress system.. Open the pump release valve and carefully unscrew the hand wheel enough to set up the closed ends condition. The handwheel is not fastened to the apparatus, if it is unscrewed too far, it will fall NOTE ~ 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. Once a pressure of around 3 MNm-2 has been achieved, gently push and pull the cylinder along its axis, the cylinder should move in the frame indicating that the frame is nollransmitting any load. If it doesn't move, wind the handwheel out some more and try again. WARNING ~ Do not exceed a cylinder pressure of 3.5 MNm-2 3. In the SMlOO7 software choose 'Closed Ends Condition' from the 'Experiments' menu option. Then connect to the SMlOO7 unit by selecting 'Connect to SM1007' from the same menu. The virtual meters on 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. 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:!:0.3 ~, and the pressure meter should read O:tO.Ol 5. 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. 6. Pump the handle slowly until a pressure of around 0.5 MNm-2 and record the readings into the data table again by selecting 'Record Gauge Readings' from the 'Experiments' menu option. Wait a few seconds between pumps for the gauges to stabilize. 7. Carefully increase the pressure in 0.5 MNm-2 increments, recording the readings into the data table until you have reached a value of 3 MNm-2. WARNING ~ Do not exceed a cylinder pressure of 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 data table if desired by pressing the printer button in the top left corner of the table. 9. Disconnecthe communications between the PC and the apparatus by selecting 'Disconnect the SM1007' from the 'Experiments' menu option. Page 14

SM1007 Thin Cylinder - Student Guide Analysis of Results Examine the data table. With reference to the stress equations, confirm that longitudinal stress is half the value of the hoop stress. Check, using a method of differences, or by sketching graphs, that the readings from the gauges are still linear in the closed ends condition. Using the Method of Superposition to Find the Principle Strains In the previous experiment, we established that for the direct hoop stress we 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: The algebraic sum of these strains is L= aile EN = -vo'lie (due to the Poisson effect) 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 method as used in experiment 1. Read off values for the direct strains and compare them to values obtained from the equipment. Your predicted and experimental value should be in close agreement. What do you notice about the overall diameter of the Mohr's circle compared to the open ends condition? How does this affect the shear strain? 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?

SECTION 3.0 SOFTWARE OPERATION 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 SMlOO7 icon or select SM1007 Thin Cylinder from the SM1007 Programs Group. 3. The main page will appear, as in Figure 11 although some of the controls may be greyed out. Figure 11 TO SM1007 Thin Cylinder Software - Main page 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 Underneath the menu bar is a range of 'tool bar' buttons. The buttons on the tool bar are a user-friendly short cut to commonly used choices from the menu bar. Hover the mouse cursor over each tool button to discover what action they perform.

SM1007 Thin Cylinder. Student Guide Menu Bar Options The menu bar options allow you to perform the following File This list allows you to open a new or previous file, save the current file or exit the program. NOTE ~ If the program is exited (closed) before saving the experiment, the data will be lost. Files are saved by default into the Experiment Files folder under the TQ Software directory of the Program Files in the PC. All experiment files are given the extension *,SM7. Experiments This list allows you to select Open or Closed ends experiments, connect the communications path to the SMlOO7 Thin Cylinder apparatus, set up the gauges and take readings. Results This list allows you to display the data table and graphs of stress and strain relationships. Only one graph may be displayed at a time. When either the data table or graphs are selected from the results option on the menu bar, a new page will open, displaying the data you have selected. Along the top of each new page there are more tool buttons, which allow you to print the results or graph on the selected printer. The graphs have tool buttons which allow you to display or hide grid lines, modify the graphs or copy the graph to the clipboard of the PC. Hover the mouse cursor over the tool buttons to discover what action they perform. Options This allows you to check the communication path to the Thin Cylinder apparatus, calibrate the gauge factor and select the COM port on the PC to which the serial communications cable is connected. Short cut Keys 1 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-cut keys in the TQ SMlOO7 software are: 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 menu bar. Check that the correct COM port is selected and that the gauge factor is set to the value indicated on the label at the front of the SM 1007 apparatus. 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 software will state 'Communication with SM1007 OK'. 5. On the options box, select 'OK' (to save any changes) or 'Cancel' (to discard any changes) and then close the box. 6. Decide which experiment you wish to do and select either '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. Conduct the experiments as detailed. To zero all the gauges Select 'Zero All Gauges' from the 'Experiments' menu option, or press the Zero All Gauges tool button. To take a set of readings Select 'Record Gauge Readings' from the 'Experiments' button. menu option, or press the Record Gauge Readings tool To display the data table Select 'Display Data Table' from the 'Results' menu option, or press the Display Data Table tool button. Incorrect readings may be removed by selecting 'Remove Last Reading' or 'Remove All Readings' from the 'Experiments' menu option.

SM1007 Thin Cylinder. Student Guide To display a graph Select 'Hoop Stress V Hoop Strain'. 'Plot Mohr's Circle', or 'Longitudinal 'Results' menu option. v Hoop Strain' from the The Longitudinal v Hoop Strain graph will not operate for the closed ends condition At the top of each graph. more tool buttons allow you to perform operations. such as printing the graph. or adding horizontal and vertical grid lines. Hoop Stress v Hoop Strain and Longitudinal v Hoop Strain Graphs These graphs have tool buttons which will either calculate the gradient of a line drawn on the graph or display the x and y coordinates of the mouse cursor on the graph. Mohr's Circle The Mohr's Circle is initially displayed in red and plotted from the principle strains of gauges 1.2 and 6. Press the Plot Experimental Values tool button to display the other gauge values. Press the Plot Theoretical Mohr's Circle tool button to display a theoretical circle in blue. Plotting Graphs using the SM1007 Software The software supplied with the SM 1007 will automatically plot graphs from the results of each experiment. The graphs show the x and y axis and the results as a series of crosses. There are tool buttons at the top left comer of each graph page, one of the buttons will toggle between two options: Calculate gradient of a line or display coordinates. When the button is not pressed in, the coordinates of the mouse cursor are displayed in the bottom right comer of the page. When the button is pressed in, the software will automatically calculate the gradient of the line, using the following method: Figure 13 Tool Buttons for graphs (not Mohr's Circle). To automatically calculate the slope of the graph (gradient) a line must be drawn through the result crosses as follows; r Move the mouse cursor near to the 0,0 origin of the graph, the cursor will change to a square with a pointer. 2. Click and hold the left mouse button. move the cursor towards the opposite comer 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 Save the file for the current experiment, using 'Save As' from the 'File' menu option, or press the Save To File tool button. 2. Disconnecthe communications by selecting the 'Disconnect SM1007' from the 'Experiments' menu option, or press the disconnect SMIO07 tool button. NOTE ~ Always disconnect after each experiment. 3. Select 'New' from the 'File' menu or press the create new file tool button. 4. Select the experiment you wish to do from the 'Experiments' menu and select 'Connect To SM1007' from the same menu. Normal Operation When the PC and the SM 1 007 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 of the hand wheel will move in and out as the selection between open and closed ends experiments 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 stress and the forces acting upon an element of material under the action of a two-dimensional stress system. Gt Figure 14 Stress diagram for two-dimensional stress systems Oy Figure 15 Force diagram for two-dimensional stress system Assume Figure 15 to be a 'wedge' of material of unit depth and the side AB to be of unit length. Resolving along 0'0 gives: 0',= (O'yOOS 8) COS 8 + (O'xsin 8)sin8+ ('fcos8)sin8+ ('fsin 8)oos 8 - (1 +COS26)" " (1- Co828) Tsin26 ug- Uy 2 + u1 2 + cos28 + -rsin28 (t) Resolving along 1'8 gives: f9 = (O'ycosO)sinO- (O'x sin O)cosO+ (t"sin 0) sin 0- (fcos O)cos 0

07 Thin Cylinder - Student Guide 'f9 sin28 = O'y~-O'x-r sin29. 29 2 + 'tsln - -rcos 9 (0:-0:) 1', = :':y~sin28- 'l'cos28 (2) From Equation (2) it can be seen that there are values for 8 for which 1'8 is zero, and the planes on which the shear component is zero are called 'Principal Planes'. From Equation (2): 0 =!.5~ 2 sin28- -rcos28 (a-o:) -rcos29 = ::..:.l.rsin28 1'= ~~tan28, (3) This will give two values of 28 differing by 1800 and, therefore, two values of 8 differing by 9()0. This shows that the principal planes are at right angles to each other. Figure 16 Diagrammatic representation of Equation (3) From the diagram' (4) and 0' -,0'. cas 2 8 = :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 Principal stresses are the maximum and minimum values of normal stress in the system. The sign will denote the 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 = I, i.e. when 8= 45. Therefore the maximum shear stress occurs on planes at 45 to the principal planes, and A (aa-a.) -r, = 2 (8) or, using Equation (6) A I, - -.2. _2 -r, = ~(ax - ay> +4-r (9) Figure 18 Diagram of principal stresses on an element

0". 1 = E- 0'2 ~=E- E El and E2 are the values of the principal strains. A negative quantity denotes comp~ve strain while a positive quantity denotes tensile strain. These strains can be used to construct a Mohr's Strain Circle in the same way as stresses. Figure 19 Representation of strain on a Mohr's circle Q = Centre of the strain circle -:--: 2 +(~)cao26 em =~ + l~)c0828 (12) and En = ~+(~)-(~)C0828 D = (~ + (Y)COS26

APPENDIX Nomenclature a If Nonnal Stress Shear Suess MNm-2 MNm-2 8 Angular Position Degrees IP e E Internal Presaure Direct Rtlain Young's Modulus MNm-2 (Ratio of &L) GNm-2 v Poisson's Ratio (Ratio of Lateral Strain/Axial Strain) d Cylinder Internal Diameter m(ormm) t I H L IxandV CyMnder Wall Thk:knes8 - - - - Denotes StraIn In the open ends condition Denotes!he hoop or circumferential direction Denotes the longitudinal direction Denote particular directions m (or mm)