EXPERIMENT A2

Strain Gage Measurements

Summary:

Welcome to the ME-242 laboratory! In this laboratory you will perform hands-on experiments with strain gages. Strain gages are a key tool in the testing of materials. This includes everything from simple test coupons to advanced and very complex structures. This experiment will provide you with an understanding 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 Strain Gage Technology booklet that is supplied by the Department of Mechanical Engineering. This experiment should give you the tools necessary to instrument and conduct your own strain gage experiments if called upon in future projects.

In this experiment you will be examining the stress state in cantilever beams. You will also use a strain gage rosette that has already been mounted for you to calculate principal strains in the cantilevered beam 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 Poisson's 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 Poisson's ratio, etc.).

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Suggestions and reminders on report content are offered in the Report Notes sections.

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What’s a Strain Gage Used For?The Birdman Contest is an annual event held on Lake Biwa near Kyoto, Japan. In this contest cleverly designed human-powered airplanes and gliders fly several hundred meters across the lake. Aside from the great spectacle of this event, it is a wonderful view of engineering experimentation and competition. Despite the careful designs and well-balanced airframes occasionally the wings of these vehicles fail and crash into the lake. There have been some spectacular crashes but few, if any, injuries to the contestants.

Increasingly, each time a new airplane, automobile, or other vehicle is introduced, the structure of such vehicles is designed to be lighter to attain faster running speeds and less fuel consumption. It is possible to design a lighter and more efficient product by selecting light-weight materials. However, as with all technology, there are plusses and minuses to be balanced. If a structural material is made lighter or thinner the safety of the vehicle is compromised unless the required strength is maintained. By the same token, if only the strength is taken into consideration, the vehicle’s weight will increase and its economic feasibility is compromised.

In engineering design the balance between safety and economics is one variable in the equation of creating a successful product. While attempting to design a component or vehicle that provides the appropriate strength it is important to understand the stress borne by the various parts under different conditions. However, there is no technology or test tool that allows direct measurement of stress. Thus, strain on the surface is frequently measured in order to determine internal stress. Strain gages are the most common instrument to measure surface strain.

Structural Element of Benicia-Martinez Bridge in Southern California

Undergoing a Load Test

Picture of A Strain Gage Attached to Bridge

Element

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.

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Strain Gages:

There are many types of strain gages. The fundamental structure of a strain gage consists of a grid-shaped sensing element of thin metallic resistive foil (3 to 6 microns thick) that is sandwiched between a base of thin plastic film (12-16 micron thick) and a covering or lamination of thin film.

Strain 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”) may elongate or contract in the same manner as the strain experienced by the test article. Typically the sensing 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 that applies the principle of resistance change as a means to effectively sense strain.

Strain MeasurementIt should be noted that there are various types of strain measuring methods available. These may be roughly classified into mechanical, electrical, and even optical techniques.

From a geometric perspective, strain recorded during any test may be regarded as a distance change between two points on a test article. Thus all techniques are simply a way of measuring this change in distance.

If the elastic modulus of the test article’s constituent material is known, strain measurement will allow calculation of stress. As you have learned from your studies and prior labs strain measurement is often performed to determine the stress created in a test article by some external force, rather than to simply gain knowledge of the strain value itself.

This LVDT, attached to a tensile specimen, is also a

common tool for measuring strain.

A resistance strain gage consists of a thin strain-sensitive wire mounted on a backing that insulates the wire from the test structure. Strain gages are calibrated with a gage factor F, which relates strain to the resistance change in the wire by

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Thin Film Laminate

Plastic Base

Resistive Foil

Figure 1: Strain Gage

Construction

F = R/RL/L

F = R/RL/L

where R is the resistance and L is the length of the wire. The change in resistance corresponding to 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?

The gage factor, F, differs depending on the material used for the resistive foil. Typically, the gage factors of the strain gages you will use in this experiment are between 2 and 3. It should be noted that the resistance change caused by strain is extremely small. For example, assume a structural element in a bridge is instrumented with a strain gage. The structural element experiences a strain of 1000 x 10-6. If the strain gage used to measure this has a resistance of 120Ω and a gage factor of 2 the following relationship 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 resistance changes are typically measured with a dedicated strain amplifier that uses an electric circuit called a Wheatstone Bridge.

The Wheatstone Bridge A Wheatstone bridge is a measuring instrument that, despite popular myth, was not invented by Sir Charles Wheatstone, but by Samuel H. Christie in 1833. The device was later improved upon and popularized by Wheatstone. The bridge is used to measure an unknown electrical resistance by balancing two legs of a circuit, one leg of which includes the unknown component that is to be measured. The Wheatstone bridge illustrates the concept of a difference measurement, which can be extremely accurate. Variations on the Wheatstone bridge can be used to measure capacitance, inductance, and impedence.

In a typical Wheatstone configuration, Rx is the unknown resistance to be measured; R1, R2 and R3 are resistors of known resistance and the resistance of R2 is adjustable. If the ratio of the two resistances in the known leg (R2/R1) is equal to the ratio of the two in the unknown leg (Rx/R3), then the voltage between the two midpoints will be zero and no current will flow between the midpoints. R2 is varied until this condition is reached. The current direction indicates if R2 is too high or too low.

Typical Wheatstone Bridge diagram with strain gage at

Rx

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Detecting zero current can be done to extremely high accuracy. Therefore, if R1, R2 and R3 are known to high precision, then Rx can be measured to high precision. Very small changes in Rx disrupt the balance and are readily detected.

Alternatively, if R1, R2, and R3 are known, but R2 is not adjustable, the voltage or current flow through the meter can be used to calculate the value of Rx. This setup is what you will use in strain gage measurements, as it is usually faster to read a voltage level off a meter than to adjust a resistance to zero the voltage.

Because conventional ohmmeters are not capable of measuring these small changes in resistance accurately, a Wheatstone bridge is usually employed. It can be operated in either a balanced or unbalanced configuration. The configuration for an unbalanced bridge is shown in Figure 2. For an unbalanced bridge, a change in resistance is measured as a non-zero voltage Vo which, can be calibrated in standard strain units (∆L/L x 10-6) or micro strain. A balanced bridge is rebalanced after each load increment so that the output voltage Vo is zero. The appropriate changes in resistance are then noted and strain calculated using the gage factor.

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 gage elements vs. the number of fixed resistors. The various common configurations and their relationship to Figure 1 are described in Table 1, below:

Table 1: Wheatstone Bridge Summary

Type of Bridge

Typical Designation

Active Resistance

Elements

Precision Fixed

Resistances

Usual Application

Quarter Bridge R1 R2, R3, R4 Easiest to use, requires

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Digital Strain Indicator

2.065

P2 S1 D1-120

BLH

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.

These include 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 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 are compensating 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 expansion coefficients), 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 temperature changes.

To achieve temperature compensation with two active gages, where should 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 interacting factors must be considered together if accurate measurements are to be obtained. The following define the 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.)

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(5) What is the expression for the axial strain gradient along a cantilevered beam’s upper

surface? From observing this expression, explain why the strain gage length is not an

important factor here.

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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

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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 the

second you will be using a pre-mounted strain gage rosette on another beam to make

measurements.

PART I - MOUNTING AND USE OF A STRAIN GAGE

I.a) Mounting

Surface 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 the

Student 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 bonding

procedure 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 (and

align them on) the beam. After aligning the gage, carefully lift one side of the tape so the gage is off

the surface of the beam. Apply M-Bond 200 catalyst onto the gage and along the tape-beam junction

and press the gage onto the beam as described in the manual. Remove the tape.

Figure 4: Strain Gage and Tabs under tape on beam

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Strain Gage

Connector Tabs

(6) List the properties of the mounting surface that are important for accurate strain gage

measurement.

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 and the

percent difference in your report.

(8) Check the resistance between the strain gage and the beam. A thoroughly dried gage

should show a resistance of 1,000 megaohms or more. Lower resistances can be tolerated,

but a minimum of 50 megaohms is necessary for accurate stable functioning of the gage.

Include the measured value in your report and explain/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 Cantilever

Flexure 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 series

entitled “E-101 Modulus of Elasticity - Flexure".)

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Lt

P,

b

Fixed end

L = length between gage an applied displacement

= length between clamp and applied displacement

= applied displacement

P = load corresponding to the applied displacement

b = beam width

t = beam thickness

Figure 3: Beam with Strain Gage in Flexure Fixture

To prepare the experiment, back the micrometer out of the way and insert the beam into the Flexor, with

the gage on the top surface and the gage end in the clamp. Center the free end of the beam between the

sides 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 a function

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 a

cantilever beam. The location of the displacement should be at the point of application of the

load.

Connect the lead wires from the strain gage to the binding posts on the Flexor and the

appropriate wires from the Flexor to the BLH Digital Strain Indicator so that the strain gage is

connected to the BLH Indicator as shown in Figure 5.

(11) Write down the equation which relates axial stress to axial strain.

Figure 5: Schematic of BLH Digital Strain Indicator

Measure the distance from the centerline of the strain gage grid to the point of load

application at the free end of the beam, using an accurate scale. Also, measure the distance from the

clamp to the point of load application. Measure the width and thickness of the beam. Record, not

only the measured value, but also the resolution (estimated error) for each value.

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OK BETTER

short jumperlong jumper, connecting at gage

With the beam unloaded (except for its own weight), set the gage factor on the strain indicator

to the value given on the strain gage package data form. Balance the bridge using the coarse and

fine bridge balance controls.

To prevent plastic deformation, the maximum deflection for the thick beam should be 0.1

inches and for the thin beam should be 0.3 inches. To prevent damage (permanent bending) of the

beam do not exceed these limits.

Apply the maximum displacement in ten equal increments. At each displacement increment

record the micrometer reading and strain. (The display will be in micro inches/inch if the X1 switch is

depressed.) Unload the beam in 10 equal decrements and again record the micrometer reading and

strain 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?

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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 rectangular

rosette, consisting of 3 strain gages mounted at 45 degree angles, to measure the strain on the upper

surface of a cantilever beam. The principal strains and stresses will then be calculated and compared

with simple beam theory. (Note: Portions of this procedure are taken directly from the Experiments in

Mechanics 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 of

the 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 the

top surface and the gage end in the clamp. Connect the lead wires from the rosette to the binding

posts 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 from

the gages must be connected to the G terminal. Use jumper wires between the W and W’ terminals

and between P1 and D1 as shown in Figure 6. Set the gage resistance to the HB position and the

digital strain indicator to 1/4 bridge operation.

Figure 6: Wiring schematic for the BLH Switching and Balancing Unit

Hook up the Switching and Balancing Unit to the Strain Indicator as shown in Figure 7. Additional

information can be obtained from the manuals provided.

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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 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 the

readings 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. Unload

the beam in 10 equal decrements and again record the micrometer reading and strain in the three

gages 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?

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EXPERIMENT A2 STRAIN GAGES

PRELIMINARY QUESTIONS

Group 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 be

attached. Also indicate the direction of "transverse sensitivity". Should the transverse sensitivity be high or

low? What is the difference between a strain gage and a rosette?

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3. Using the variables defined for the cantilevered beam in Figure 2, write down an equation fora) displacement 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 x 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 (i.e., eliminate P from the equation.). Use this equation during

the 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?

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4. Using the results of question 3, derive an expression for the axial strain gradient along the

beam’s upper surface. (Note that the strain gradient is dex/dx.)

5. Using the results of question 3, calculate the displacement to be applied at the free end of the

cantilever beam in order to produce an axial stress of approximately 5,000 psi at the fixed end of the

beam. 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 maximum

displacement before plastic deformation of the beam will occur. Avoid plastic deformation of the

beams.

6. Write down the equations for the principal strains in terms of the strains e0, e45, and e90 measured

using a strain gage rosette. Also give the equation for the angle between the rosette and the principal

axes. Make sure you include a sketch defined the angle.

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APPENDIX 1: Model 1225 Specifications…

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APPENDIX 2: Model 1200B Specifications…

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