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## Strain Gage Theory

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**Strain Gage Theory**UAA School of Engineering CE 334 - Properties of Materials Lecture # 18 Strain Gage Theory**What are Strain Gages?**• One of several devices that can be used to obtain strains directly. • A small device that can be attached directly to the item for which strain data is required. • The device measures strain at the surface of an structural element. • A strain gage is a small wire grid whose electrical resistance changes as it strains. Strain Gage Theory**Basic Principle**• Professor William Thomson (Lord Kelvin) was the first to discover the relationship between electrical resistance of wires and induced strains. • Strains imposed by tensile stresses cause an increase in electrical resistance. • Strains imposed by compressive stresses cause a decrease in electrical resistance. Strain Gage Theory**Uses of Strain Gages**• Valuable tool for use by stress analysts. • Analyze new designs (prototypes) • Trouble shooting and correcting old designs. • Service load analysis • Theoretical investigations • Control systems. Strain Gage Theory**Wheatstone Bridge**• Wheatstone bridge (an electrical circuit devised by Sir Charles Wheatstone) is most commonly used to determine the change of electric resistant. • R1 is the active gage and is placed at the location where strain is to be measured. • R2 is a dummy gage. • R4 is a precision variable resistor. • Galvanometer is calibrated to read in strain units. Strain Gage Theory**Measurement of Change in Resistance**• Resistance changes are small. On the order of thousandths of an ohm. • Bridge is balance when Ig=0: I1R1 = I2R2 and I1= I4,I2=I3, I1R4 = I2R3 or I1/I2=R2/R1, I1/I2=R3/R4, R2/R1 =R3/R4 R1 = (R2/R3)R4 Strain Gage Theory**Gage Factor**• Thegage factor, K, of a strain gage relates the change in resistance(R) to the change in length(L). This is constant for a given strain gage. • K = (R/R)/(L/L) = (R/R)/. • Rearrange the terms to get: = (R/R)/K • Once installed, we read the change in resistance (R) and use the above equation to determine the strain (). Strain Gage Theory**Points to be considered in selecting a resistance alloy**• Gage Factor (The higher the better) • Resistance (The higher the better) • The effect of temperature • Relationship between the change in resistance and strain (should be linear) • Wire size (small so as to be weaker than adhesive) Strain Gage Theory**Temperature Compensation:**Temperature Compensation • Reasons: • The resistance of the wires changes with temperature. • If the temperature coefficient of the strain gage differs from that of the specimen, there are some temperature effects in the readings. • Temperature effects are compensated for by attaching the dummy gage R2to the specimen in such a way that it is not strained. R1/R4 = R2/R3 at the balance condition. if R1 ~= R2 and R1 = R2 then (R1+R1)/R4 = (R2+R2)/R3 Strain Gage Theory**Temperature Compensation:**Temperature Compensation and Doubling output on aBendingMember • Attach the two active gages onopposite sides. • The circuit not only compensates for temperature but also doubles the sensitivity. • Because with R1 in compression and R2 in tension,the resistant changes of opposite signs in effect add together. R1 R2 R4 R3 Strain Gage Theory**Temperature Compensation:**Poisson Arrangement • Temperature compensation only. • Attach both gages to same side but at one perpendicular to the direction of stress. • Need to know Poisson’s Ratio to compensate for strain in the dummy gage. R1 R2 R4 R3 Strain Gage Theory**FilteringBendingForces**P e • R1’ and R1 are used as the active gages on opposite sides. • The strain in R1>Raxial,in R’1<Raxial. • The circuit adds their results and divides by two. Errors are canceled out. • It gives the true axial strain irrespective of any bending. R1’ R2’ R1 R2 R4 R3 Strain Gage Theory**Placement on Shaft inTorsion**• All four gages used. • Output is quadrupled. • Temperature is compensated. • Gages are measuring the principle strains. R1 R2 R4 R3 Strain Gage Theory**Multi-element Strain Gages**• Multi-element strain gages have 2 or more strain gages built into them. • The orientation of the gages relative to each other is fixed. • Using Mohr’s Circle for strain, the magnitude and direction of the principle stresses can be computed. Strain Gage Theory**45E Rosette**For the 45 deg rosette, the magnitudes of principle stresses can be determined from basic strain relationships: a b c Strain Gage Theory**60E Rosette**• The principle stresses and strains can be determine from basic relationships. • Advantage of the Rosettes is that they make it possible to determinethe magnitude and directionof principle stresses when the direction is not obvious or changes with loading. Strain Gage Theory**Specialty Gages**• There are a myriad of specialty gages that have been developed for special applications. • Gages may vary in types of materials used or in configuration to meet the demands of special situations. • High heat, moist environments, and large strains are examples of situations that require special gages. Strain Gage Theory**Advantages of Strain Gages**• Ease of Installation • Relatively high accuracy • Adjustable sensitivity • Remote indication • Very short gage length • Response to dynamic strain. Strain Gage Theory**Strain Gage Testing of a Cantilever**Strain Gage Theory**Strain Gage Testing of a Cantilever**Objectives: 1. Assist in acquiring strain gage measurements from a cantilever beam. 2. Determine the stresses in a cantilever from the strain gage measurements. 3. Compare the results with the theoretical predictions based on ES-331, the Mechanics of Materials course. Strain Gage Theory**Strain Gage Testing**Have fun! Strain Gage Theory