EXPERIMENT A2                                 Strain Gage MeasurementsSummary:         Welcome to the ME-242 laboratory! I...
What’s a Strain Gage Used For?                                                Structural Element ofThe Birdman Contest is ...
There are many types of strain gages. The fundamental structure of a strain gage consists of agrid-shaped sensing element ...
The gage factor, F, differs depending on the material used for the resistive foil. Typically, the gagefactors of the strai...
zero the voltage.       Because conventional ohmmeters are not capable of measuring these small changes in resistanceaccur...
multiply and increase our strain sensitivity in applications where only very small strains are present.These are discussed...
Experimental Apparatus:      Strain gage and terminals      Aluminum beam (with no gage attached yet)      M-Line Neutrali...
Experimental Procedure:        This lab has two distinct portions.        In the first you will mount a strain gage on a b...
I.b) Testing of Strain Gage        Before proceeding perform the following tests to verify the gage and mounting procedure...
To prepare the experiment, back the micrometer out of the way and insert the beam into the Flexor, withthe gage on the top...
With the beam unloaded (except for its own weight), set the gage factor on the strain indicatorto the value given on the s...
PART II - PRINCIPAL STRESSES AND STRAINS ON A CANTILEVER BEAM        In this part of the experiment you will use a beam wh...
Figure 7 - Wire diagram for the connection between the                   BLH Switching and Balancing Unit and the Digital ...
EXPERIMENT A2 STRAIN GAGES                                       PRELIMINARY QUESTIONSGroup number (names):_______________...
3.        Using the variables defined for the cantilevered beam in Figure 2, write down an equation for     a)   displacem...
4.       Using the results of question 3, derive an expression for the axial strain gradient along thebeam’s upper surface...
APPENDIX 1: Model 1225 Specifications…                                         A2-17
APPENDIX 2: Model 1200B Specifications…                                     A2-18
APPENDIX 2: Model 1200B Specifications…                                     A2-18
APPENDIX 2: Model 1200B Specifications…                                     A2-18
APPENDIX 2: Model 1200B Specifications…                                     A2-18
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A2 strain gages_2003

  1. 1. EXPERIMENT A2 Strain Gage MeasurementsSummary: Welcome to the ME-242 laboratory! In this laboratory you will perform hands-on experiments withstrain gages. Strain gages are a key tool in the testing of materials. This includes everything from simpletest coupons to advanced and very complex structures. This experiment will provide you with anunderstanding of: • the principles involved in strain gage measurements • the factors to be considered in selecting a strain gage for an actual application This experiment will also use supplemental information contained in the Student Manual For StrainGage Technology booklet that is supplied by the Department of Mechanical Engineering. This experimentshould give you the tools necessary to instrument and conduct your own strain gage experiments if calledupon in future projects. In this experiment you will be examining the stress state in cantilever beams. You will also use astrain gage rosette that has already been mounted for you to calculate principal strains in the cantileveredbeam through the use of Mohr’s circle.Instructions:Your key to success in this lab is to come prepared! • Before arriving at the lab, read through this lab module so that you will understand what the lab procedure is and how the lab equipment is used. • Before coming to lab read through this handout to familiarize yourself with what will be expected of you in the lab. • Read also the ‘Student Manual for Strain Gage Technology’. It contains excellent descriptions of how to select, mount and attach (solder) strain gages. The mounting section has simple explanations with very good illustrations of these procedures. • Background material on strain gages and Wheatstone bridges can be found in most introductory textbooks dealing with mechanical measurements including your course textbook. A good reference is Introduction to Engineering Experimentation by Wheeler and Ganji. • Background material on the behavior of cantilever beams may be found in most introductory mechanics of materials texts such as Mechanics of Materials, by Hibbler, and your ME 242 textbook. • In your report discussion be sure to answer the questions included in the lab description below, as well as the points described at the end (i.e. calculation of Poissons ratio, etc.). • At key points in the discussion questions will be posed that you should answer. These questions will be numbered and the questions are in bold print surrounded by a frame. • In your report discussion be sure to answer the questions included in the lab description below, as well as the points described at the end (i.e. calculation of Poissons ratio, etc.). • Suggestions and reminders on report content are offered in the Report Notes sections. A2-1
  2. 2. What’s a Strain Gage Used For? Structural Element ofThe Birdman Contest is an annual event held on Lake Biwa near Benicia-Martinez Bridge inKyoto, Japan. In this contest cleverly designed human-powered Southern Californiaairplanes and gliders fly several hundred meters across the lake.Aside from the great spectacle of this event, it is a wonderful view of Undergoing a Load Testengineering experimentation and competition. Despite the carefuldesigns and well-balanced airframes occasionally the wings of thesevehicles fail and crash into the lake. There have been somespectacular crashes but few, if any, injuries to the contestants.Increasingly, each time a new airplane, automobile, or other vehicle isintroduced, the structure of such vehicles is designed to be lighter toattain faster running speeds and less fuel consumption. It is possibleto design a lighter and more efficient product by selecting light-weightmaterials. However, as with all technology, there are plusses andminuses to be balanced. If a structural material is made lighter orthinner the safety of the vehicle is compromised unless the requiredstrength is maintained. By the same token, if only the strength istaken into consideration, the vehicle’s weight will increase and itseconomic feasibility is compromised. Picture of A Strain Gage Attached to Bridge ElementIn engineering design the balance between safety and economics isone variable in the equation of creating a successful product. Whileattempting to design a component or vehicle that provides theappropriate strength it is important to understand the stress borne bythe various parts under different conditions. However, there is notechnology or test tool that allows direct measurement of stress.Thus, strain on the surface is frequently measured in order todetermine internal stress. Strain gages are the most commoninstrument to measure surface strain. Background: Introduction: Experimental stress analysis is an important tool in the design and testing of many products. Several practical techniques are available including photoelastic coatings and models, brittle coatings, moiré, and electrical resistance strain gages. In this experiment the strain gage will be utilized. There are three steps in obtaining experimental strain measurements using a strain gage: 1. Selecting a strain gage 2. Mounting the gage on the test structure and 3. Measuring strains corresponding to specific loads. The operation and selection criteria for strain gages will be discussed in this introduction. In Part I of this experiment, you will mount a strain gage on a beam and test its accuracy. Measurements will be made with a strain gage rosette in Part II of this experiment to obtain the principal stresses and strains on a cantilevered beam. Strain Gages: A2-2
  3. 3. There are many types of strain gages. The fundamental structure of a strain gage consists of agrid-shaped sensing element of thin metallic resistive foil (3 to 6 microns thick) that is sandwichedbetween a base of thin plastic film (12-16 micron thick) and a covering or lamination of thin film. Thin Film Laminate Figure 1: Strain Gage Construction Resistive Foil Plastic BaseStrain Gage Operation: When needed for testing the strain gage is tightly bonded to the structural element under test.This ensures that the sensing element (the metallic resistive foil at the center of the “sandwich”) mayelongate or contract in the same manner as the strain experienced by the test article. Typically thesensing element is made of a copper-nickel alloy foil. When experiencing a contraction or elongation,most metals undergo a change in electrical resistance. The alloy foil has a rate of resistance change that,with a certain constant, is proportional to the strain. The strain gage is therefore a measuring device thatapplies the principle of resistance change as a means to effectively sense strain.Strain MeasurementIt should be noted that there are various types of strain measuringmethods available. These may be roughly classified intomechanical, electrical, and even optical techniques.From a geometric perspective, strain recorded during any testmay be regarded as a distance change between two points on atest article. Thus all techniques are simply a way of measuringthis change in distance.If the elastic modulus of the test article’s constituent material isknown, strain measurement will allow calculation of stress. Asyou have learned from your studies and prior labs strainmeasurement is often performed to determine the stress created This LVDT, attached to a tensilein a test article by some external force, rather than to simply gain specimen, is also a common toolknowledge of the strain value itself. for measuring strain. A resistance strain gage consists of a thin strain-sensitive wire mounted on a backing that insulatesthe wire from the test structure. Strain gages are calibrated with a gage factor F, which relates strain tothe resistance change in the wire by F = ∆R/R F = ∆R/R ∆L/L ∆L/L where R is the resistance and L is the length of the wire. The change in resistance correspondingto typical values of strain is usually only a fraction of an ohm.(1) What parameters of the strain gage can be altered to increase its sensitivity? A2-3
  4. 4. The gage factor, F, differs depending on the material used for the resistive foil. Typically, the gagefactors of the strain gages you will use in this experiment are between 2 and 3. It should be noted that theresistance change caused by strain is extremely small. For example, assume a structural element in abridge is instrumented with a strain gage. The structural element experiences a strain of 1000 x 10 -6. If thestrain gage used to measure this has a resistance of 120Ω and a gage factor of 2 the followingrelationship is established: (∆R)/ 120Ω = 2 (1000 x 10-6) and (∆R)=120(2)(1000 x 10-6) = 0.24Ω and the rate of resistance change may be shown as: (∆R)/R = 0.24/120 = 0.002 = 0.2% It is very difficult to accurately measure such a small resistance change. Thus, these resistancechanges are typically measured with a dedicated strain amplifier that uses an electric circuit called aWheatstone Bridge.The Wheatstone BridgeA Wheatstone bridge is a measuring instrument that, despitepopular myth, was not invented by Sir Charles Wheatstone,but by Samuel H. Christie in 1833. The device was laterimproved upon and popularized by Wheatstone. The bridge isused to measure an unknown electrical resistance bybalancing two legs of a circuit, one leg of which includes theunknown component that is to be measured. The Wheatstonebridge illustrates the concept of a difference measurement,which can be extremely accurate. Variations on theWheatstone bridge can be used to measure capacitance,inductance, and impedence.In a typical Wheatstone configuration, Rx is the unknownresistance to be measured; R1, R2 and R3 are resistors ofknown resistance and the resistance of R2 is adjustable. Ifthe ratio of the two resistances in the known leg (R2/R1) isequal to the ratio of the two in the unknown leg (Rx/R3), thenthe voltage between the two midpoints will be zero and no Typical Wheatstone Bridgecurrent will flow between the midpoints. R2 is varied until this diagram with strain gage at Rxcondition is reached. The current direction indicates if R2 istoo high or too low.Detecting zero current can be done to extremely highaccuracy. Therefore, if R1, R2 and R3 are known to highprecision, then Rx can be measured to high precision. Verysmall changes in Rx disrupt the balance and are readilydetected.Alternatively, if R1, R2, and R3 are known, but R2 is notadjustable, the voltage or current flow through the meter canbe used to calculate the value of Rx. This setup is what youwill use in strain gage measurements, as it is usually faster toread a voltage level off a meter than to adjust a resistance to A2-4
  5. 5. zero the voltage. Because conventional ohmmeters are not capable of measuring these small changes in resistanceaccurately, a Wheatstone bridge is usually employed. It can be operated in either a balanced orunbalanced configuration. The configuration for an unbalanced bridge is shown in Figure 2. For anunbalanced bridge, a change in resistance is measured as a non-zero voltage Vo which, can becalibrated in standard strain units (∆L/L x 10-6) or micro strain. A balanced bridge is rebalanced aftereach load increment so that the output voltage Vo is zero. The appropriate changes in resistance arethen noted and strain calculated using the gage factor. Digital Strain Indicator 2.065 BLH P2 S1P2 D1-120 Figure 2 - An unbalanced Wheatstone bridge with strain gage(2) Does the BLH meter use a balanced or out- of-balance bridge?(3) In Figure 1, what is the relationship between R1, R2, R3, and R4 for Vo=0? Strain gage Wheatstone bridges are usually described by the number of active strain gageelements vs. the number of fixed resistors. The various common configurations and their relationship toFigure 1 are described in Table 1, below: Table 1: Wheatstone Bridge Summary Type of Bridge Active Resistance Precision Fixed Usual ApplicationTypical Designation Elements Resistances Quarter Bridge R1 R2, R3, R4 Easiest to use, requires material matching Half Bridge R1, R3 R2, R4 Cancels unwanted thermal effects or bending effects Full Bridge R1, R2, R3, R4 - Increased sensitivity There are many advantages and disadvantages with each of these systems. Theseinclude self compensation for resistance changes in the ‘active’ elements due to temperature and self-heating effects, cancellation of unwanted forces or bending effects in measurements, and the ability to A2-5
  6. 6. multiply and increase our strain sensitivity in applications where only very small strains are present.These are discussed in more detail in the strain gage manuals, in your textbook, and in the literature. In our experiment, quarter bridges will be used since we can use gages that arecompensating for temperature with respect to the tested material. In our case, an Al gage on an Al beam.For gages and materials that are not self-compensating (i.e. a poor match of thermal expansioncoefficients), a half bridge or full bridge could be used to compensate for temperature changes.(4) Briefly describe how to use the half bridge to compensate for temperaturechanges. To achieve temperature compensation with two active gages, whereshould the second strain- sensitive resistance be mounted?Strain Gage Selection: The process of selecting the proper strain gage for an application is not easy. Many interactingfactors must be considered together if accurate measurements are to be obtained. The following definethe general parameters that must first be considered. 1. The temperature range - This is the gage operating temperature range which can be a function of the ambient temperature of the experiment and the power dissipation and thermal conduction ratios of the substrate and base materials. 2. Magnitude of strain - The amount and type (elastic and/or inelastic) must be considered. 3. Principal axis of strain to be measured - An analysis of the stress vectors must be done to determine proper gage mounting axes. If the principal axes are not known, a 3-element rosette gage must be used. 4. Strain gradients - This effects the size of the selected gage in many cases. 5. Duration of measurement - Gages and substrate mounting materials have different degrees of durability. 6. Approximate number of cycles - All gages experience fatigue and are rated for various fatigue lives. 7. Accuracy requirements - All materials differ to some extent in linearity. 8. Any special ambient conditions which would adversely affect installation (magnetic fields, radiation, etc.)(5) What is the expression for the axial strain gradient along a cantileveredbeam’s upper surface? From observing this expression, explain why the straingage length is not an important factor here. A2-6
  7. 7. Experimental Apparatus: Strain gage and terminals Aluminum beam (with no gage attached yet) M-Line Neutralizer (or isopropyl alcohol) Cotton swabs and gauze sponges clean strain gage box (or glass slide) tweezers tape M-Bond 200 adhesive and catalyst degreaser sandpaper conditioner medium hard pencil and ruler wire micrometer BLH 1200B Portable Digital Strain Indicator Flexor Cantilever Flexure Frame BLH 1225 Switching and Balancing Unit Beam with pre-mounted strain gage rosette (Beam E-103) Ohmmeter A2-7
  8. 8. Experimental Procedure: This lab has two distinct portions. In the first you will mount a strain gage on a beam and make measurements with it. In thesecond you will be using a pre-mounted strain gage rosette on another beam to make measurements.PART I - MOUNTING AND USE OF A STRAIN GAGEI.a) MountingSurface preparation has five component steps: 1) solvent degreasing 2) surface abrasion 3) application of layout lines for gage 4) surface conditioning 5) neutralizing Procedures for preparing the surface and mounting the strain gage are described in theStudent Instruction Manual, Strain Gage Installations with M-Bond 200 and AE-10 Adhesive Systems.Prepare the surface as described in sections 2 and 3. Then immediately begin the bondingprocedure described in section 4. Soldering of leads onto the gage is described in section 5. Note: the gage and terminal is first transferred to a clear glass plate using the tweezers.Figure 4 shows the strain gage and tabs under the tape that is then used to transfer them to (andalign them on) the beam. After aligning the gage, carefully lift one side of the tape so the gage is offthe surface of the beam. Apply M-Bond 200 catalyst onto the gage and along the tape-beam junctionand press the gage onto the beam as described in the manual. Remove the tape. Strain Gage Connector Tabs Figure 4: Strain Gage and Tabs under tape on beam(6) List the properties of the mounting surface that are important for accurate straingage measurement. A2-8
  9. 9. I.b) Testing of Strain Gage Before proceeding perform the following tests to verify the gage and mounting procedure.(7) Check gage resistance with the manufacturer’s value. Include both values andthe percent difference in your report.(8) Check the resistance between the strain gage and the beam. A thoroughly driedgage should show a resistance of 1,000 megaohms or more. Lower resistances canbe tolerated, but a minimum of 50 megaohms is necessary for accurate stablefunctioning of the gage. Include the measured value in your report andexplain/discuss why a large resistance is necessary.I.c) Making Measurements with the Strain Gage The beam with the strain gage you have just attached will be placed in the Flexor CantileverFlexure Frame to take strain measurements. The arrangement is schematically shown in Figure 2.(Note: Portions of this procedure are taken directly from the Experiments in Mechanics strain Gage seriesentitled “E-101 Modulus of Elasticity - Flexure".) P, δ Fixed end t L b  L = length between gage an applied displacement  = length between clamp and applied displacement δ = applied displacement P = load corresponding to the applied displacement b = beam width t = beam thickness Figure 3: Beam with Strain Gage in Flexure Fixture A2-9
  10. 10. To prepare the experiment, back the micrometer out of the way and insert the beam into the Flexor, withthe gage on the top surface and the gage end in the clamp. Center the free end of the beam between thesides of the Flexor and firmly clamp the beam in place with the knurled clamping screw.(9) Write down the equation which relates the axial stress on the upper surface (as afunction of position along the beam) to the applied load for a cantilever beam.(10) Write down the equation which relates end displacement and applied load for acantilever beam. The location of the displacement should be at the point ofapplication of the load. Connect the lead wires from the strain gage to the binding posts on the Flexor and theappropriate wires from the Flexor to the BLH Digital Strain Indicator so that the strain gage isconnected to the BLH Indicator as shown in Figure 5.(11) Write down the equation which relates axial stress to axial strain. long jumper, short jumper connecting at gage OK BETTER Figure 5: Schematic of BLH Digital Strain Indicator Measure the distance from the centerline of the strain gage grid to the point of loadapplication at the free end of the beam, using an accurate scale. Also, measure the distance from theclamp to the point of load application. Measure the width and thickness of the beam. Record, not onlythe measured value, but also the resolution (estimated error) for each value. A2-10
  11. 11. With the beam unloaded (except for its own weight), set the gage factor on the strain indicatorto the value given on the strain gage package data form. Balance the bridge using the coarse andfine bridge balance controls. To prevent plastic deformation, the maximum deflection for the thick beam should be 0.1inches and for the thin beam should be 0.3 inches. To prevent damage (permanent bending) of thebeam do not exceed these limits. Apply the maximum displacement in ten equal increments. At each displacement incrementrecord the micrometer reading and strain. (The display will be in micro inches/inch if the X1 switch isdepressed.) Unload the beam in 10 equal decrements and again record the micrometer reading andstrain at each decrement. Report Note: • Be sure to include a graph of strain versus displacement in your report. • Compare your measurements (quantitatively) to theoretical predictions. • Discuss the sources of error in the experimental data. • Were any problems encountered in your experiment? • Did they cause errors in the measurement? • Did you observed any hysteresis - and if so, what % and what was the source? A2-11
  12. 12. PART II - PRINCIPAL STRESSES AND STRAINS ON A CANTILEVER BEAM In this part of the experiment you will use a beam which has already had a rectangularrosette, consisting of 3 strain gages mounted at 45 degree angles, to measure the strain on the uppersurface of a cantilever beam. The principal strains and stresses will then be calculated and comparedwith simple beam theory. (Note: Portions of this procedure are taken directly from the Experiments inMechanics strain Gage series entitled “E-101 Modulus of Elasticity - Flexure".) Measure the distance from the centerline of the rosette to the loading point on the free end ofthe beam, using an accurate scale. Measure the width and thickness of the beam with a micrometer.Record, not only the measured value, but also the resolution (estimated error) for each value. Back the micrometer out of the way and insert the beam into the Flexor with the gage on thetop surface and the gage end in the clamp. Connect the lead wires from the rosette to the bindingposts of the Flexor. Connect the strain gages between the G and W terminals as shown in Figure 6.Note that the G (or GN) terminals are connected in series so therefore the common ground wire fromthe gages must be connected to the G terminal. Use jumper wires between the W and W’ terminalsand between P1 and D1 as shown in Figure 6. Set the gage resistance to the HB position and thedigital strain indicator to 1/4 bridge operation. NOTES: All “GN” posts are interconnected inside unit. Strain gages 1, 2, 3, etc. Jumper all W to W´ posts externally. Use channel selector knob. Figure 6: Wiring schematic for the BLH Switching and Balancing UnitHook up the Switching and Balancing Unit to the Strain Indicator as shown in Figure 7. Additionalinformation can be obtained from the manuals provided. A2-12
  13. 13. Figure 7 - Wire diagram for the connection between the BLH Switching and Balancing Unit and the Digital Strain Indicator With the beam unloaded, set the gage factor and zero the strain reading, recording thereadings for all three gages. Apply the maximum displacement of 0.3 in. in ten equal increments.At each displacement increment record the micrometer reading and strain in the three gages. Unloadthe beam in 10 equal decrements and again record the micrometer reading and strain in the threegages at each decrement Report Note: Be sure to address the following in your report…. • Be sure to include a graph of strain versus displacement in your report for each of the gages (in one figure). • Calculate the principal strains using the equation requested in question 6 of your prelab. Compare (quantitatively) the theoretical predicted axial strain (question 3 of prelab) to the appropriate principal strain. • Use Hooke’s law for plane stress to calculate the principal stresses from the experimentally determined principal strains. • Also calculate Poisson’s ratio. Assume E = 71,700 MPa. • Calculate the angle the rosette makes with the beam axis (be sure to define the angle using a diagram) and quantitatively compare the measured angle to the calculated angle. • Be sure to organize the analysis section so that it is easy to read and not excessively long. Discuss any differences between theory and experiment. Discuss the sources of error in the experimental data. Were any problems encountered in your experiment? Did they cause errors in the measurement? • Did you observed any hysteresis - and if so, what % and what was the source? A2-13
  14. 14. EXPERIMENT A2 STRAIN GAGES PRELIMINARY QUESTIONSGroup number (names):_____________________________ Date:______________1. What are potential safety concerns for this experiment?2. Sketch a simple (metal wire) strain gage. On this drawing indicate where the leads should beattached. Also indicate the direction of "transverse sensitivity". Should the transverse sensitivity be high orlow? What is the difference between a strain gage and a rosette? A2-14
  15. 15. 3. Using the variables defined for the cantilevered beam in Figure 2, write down an equation for a) displacement δ at the loading point for an applied end load P. (Use tables in ME226 text.) b) moment as a function of position x, M(x) for an applied end load P. (Apply static equilibrium to a free-body diagram of a portion of the beam.) c) axial stress σx in terms of moment (Consult your ME226 text.) d) axial strain ex as a function axial stress (Reduce Hooke’s law.)Combine these equations to obtain axial strain ex(x) on the upper surface of the beam as a function of x,in terms of the applied displacement δ (i.e., eliminate P from the equation.). Use this equation duringthe lab, to check whether your measured strains are accurate.Use these equations to answer the following questions: i) Where along the length of the beam will the maximum deflection occur? ii)Where along the length of the beam will the maximum linear strain occur? iii) Does this strain occur perpendicular or parallel to the axis of the beam? A2-15
  16. 16. 4. Using the results of question 3, derive an expression for the axial strain gradient along thebeam’s upper surface. (Note that the strain gradient is de x/dx.)5. Using the results of question 3, calculate the displacement to be applied at the free end of thecantilever beam in order to produce an axial stress of approximately 5,000 psi at the fixed end of thebeam. Assume E = 71,700 MPa, L= 10 in, and t = 0.125 in. Compare to the value for t=0.25 in. Note that,if the yield strength of the aluminum bar S=5000 psi, then this calculated displacement is the maximumdisplacement before plastic deformation of the beam will occur. Avoid plastic deformation of thebeams.6. Write down the equations for the principal strains in terms of the strains e 0, e45, and e90 measuredusing a strain gage rosette. Also give the equation for the angle between the rosette and the principalaxes. Make sure you include a sketch defined the angle. A2-16
  17. 17. APPENDIX 1: Model 1225 Specifications… A2-17
  18. 18. APPENDIX 2: Model 1200B Specifications… A2-18
  19. 19. APPENDIX 2: Model 1200B Specifications… A2-18
  20. 20. APPENDIX 2: Model 1200B Specifications… A2-18
  21. 21. APPENDIX 2: Model 1200B Specifications… A2-18

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