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POSITIONING STRAIN GAGES TO MONITOR BENDING, AXIAL, SHEAR, AND TORSIONAL LOADS In the glossary to the Pressure Reference Section, “strain” is defined Fv as the ratio of the change in length to 1 the initial unstressed reference 3 length. A strain gage is the element L h that senses this change and converts it into an electrical signal. This can be 4 2 3 4 Fv b accomplished because a strain gage changes resistance as it is stretched, 1 h or compressed, similar to wire. For Figure C - Bending Strain 45 example, when wire is stretched, its cross-sectional area decreases; b therefore, its resistance increases. 2 The important factors that must be 3 4 Figure E - Shear Strain considered before selecting a strain gage are the direction, type, and Y resolution of the strain you wish to 4 b 3 measure. FA 45 45 To measure minute strains, the user Z must be able to measure minute h 45 Z resistance changes. The Wheatstone 1 2 45 Bridge configuration, shown in Figure Figure D - Axial Strain MT 2 1 B, is capable of measuring these Y small resistance changes. Note the L signs associated with each gage Figure F - Torsional Strain numbered 1 through 4. The total strain is always the sum of the four strains. would be 4 times the strain on one sectional modulus is (bh2/6). gage. See Figure C. Strain gages used in the bending strain configuration can be used If total strain is four to determine vertical load (F ); times the strain on this is more commonly referred to 4 one gage, this as a bending beam load cell. 1 + – means that the VIN output will be four F = E B (Z)/ l = E B (bh 2⁄6)/ l REGULATED times larger. DC Therefore, greater 2) AXIAL STRAIN equals axial sensitivity and stress divided by Young’s – + 2 3 resolution are Modulus. possible when EA = oA /E oA = FA /A more than one strain gage is used. Where axial stress (oA) equals VOUT the axial load divided by the Fig. B The following cross-sectional area. The cross- Wheatstone Bridge equations show the sectional area for rectangles relationships equals (b x d). Therefore, strain The total strain is represented by a among stress, strain, and force for gages used in axial change in V . If each gage had the OUT bending, axial, shear, and torsional configurations can be used to same positive strain, the total would strain. determine axial loads (F (axial)). be zero and V would remain OUT 1) BENDING STRAIN or moment unchanged. Bending, axial, and F (axial) = E A bh strain is equal to bending stress shear strain are the most common divided by Young’s Modulus of 3) SHEAR STRAIN equals shear types of strain measured. The actual Elasticity. stress divided by modulus of arrangement of your strain gages will shear stress. determine the type of strain you can B = oB/E oB = MB/Z = F (l )/Z measure and the output voltage = /G = F x Q/bI change. See Figures C through F. Moment stress (oB) equals bending moment (F x l ) divided Where shear stress ( ) equals For example, if a positive (tensile) by sectional modulus. Sectional (Q), the moment of area about strain is applied to gages 1 and 3, modulus (Z) is a property of the the neutral axis multiplied by the and a negative (compressive) strain cross-sectional configuration of the vertical load (F ) divided by the to gages 2 and 4, the total strain specimen. For rectangles only, the thickness (b) and the moment of E-5 POSITIONING STRAIN GAGES TO MONITOR BENDING, AXIAL, SHEAR, AND TORSIONAL LOADS inertia ( I ). Both the moment of where torsional stress ( ) equals a gage factor of 2.0, Poisson’s Ratio area (Q) and the moment of torque (Mt) multiplied by the of 0.3, and it disregards the lead wire inertia ( I ) are functions of the distance from the center of the resistance. specimen’s cross-sectional section to the outer fiber (d/2), geometry. This chart is quite useful in divided by (J), the polar moment determining the meter sensitivity For rectangles only of inertia. The polar moment of required to read strain values. Q = bh 2⁄8 and I = bh 3⁄12 inertia is a function of the cross- sectional area. For solid circular Temperature compensation is The shear strain ( ) is shafts only, J = (d)4⁄32. The achieved in many of the above determined by measuring the modulus of shear strain (G) has configurations. Temperature strain at a 45° angle, as shown in been defined in the preceding compensation means that the gage’s Figure E. discussion on shear stress. Strain thermal expansion coefficient does gages can be used to determine not have to match the specimen’s = 2 X @ 45° torsional moments as shown in thermal expansion coefficient; The modulus of shear strain (G) = the equation below. This therefore, any OMEGA® strain gage, E/2 (1 + ). Therefore, strain represents the principle behind regardless of its temperature gages used in a shear strain every torque sensor. characteristics, can be used with any configuration can be used to specimen material. Quarter bridges determine vertical loads (F ); this Mt = (J) (2/d) can have temperature compensation is more commonly referred to as = G (J) (2/d) if a dummy gage is used. A dummy a shear beam load cell. = G ( d 3⁄16) gage is a strain gage used in place of a fixed resistor. Temperature F = G ( ) bI/Q Ø = MTL/G(J) compensation is achieved when this = G ( ) b (bh ⁄12)/(bh ⁄8) 3 2 dummy gage is mounted on a piece of material similar to the specimen = G ( )bh(2/3) which undergoes the same temperature changes as does the 4) TORSIONAL STRAIN equals specimen, but which is not exposed torsional stress ( ) divided by torsional modulus of elasticity (G). See Figure F. T he following table shows how bridge configuration affects output, to the same strain. Strain temperature compensation is not the same as load (stress) temperature = 2 x @ 45° = /G temperature compensation, and compensation, because Young's compensation of superimposed Modulus of Elasticity varies with = Mt(d/2)/J strains. This table was created using temperature. POSITION SENSITIVITY OUTPUT PER STRAIN GAGES BRIDGE OF GAGES mV/V @ @ 10 V TEMP. SUPERIMPOSED STRAIN TYPE FIG. C-F 1000 EXCITATION COMP. STRAIN COMPENSATED 1 ⁄4 1 0.5 5 V/ No None BENDING 1 ⁄2 1, 2 1.0 10 V/ Yes Axial Full All 2.0 20 V/ Yes Axial 1 ⁄4 1 0.5 5 V/ No None E 1 ⁄2 1, 2 0.65 6.5 V/ Yes None AXIAL 1 ⁄2 1, 3 1.0 10 V/ No Bending Full All 1.3 13 V/ Yes Bending 1 ⁄2 1, 2 1.0 10 V/ Yes Axial and Bending SHEAR @ 45°F AND TORSIONAL Full All 2.0 20 V/ Yes Axial and Bending @ 45°F Note: Shear and torsional strain = 2 x @ 45°. E-6 Freephone 0800 488 488 | International +44(0) 161 777 6622 | Fax +44(0) 161 777 6622 | Sales@omega.co.uk www.omega.co.uk UNITED KINGDOM www. omega.co.uk Manchester, England 0800-488-488 UNITED STATES FRANCE www.omega.com www.omega.fr 1-800-TC-OMEGA 088-466-342 Stamford, CT. CANADA CZECH REPUBLIC www.omega.ca www.omegaeng.cz Laval(Quebec) Karviná, Czech Republic 1-800-TC-OMEGA 596-311-899 GERMANY BENELUX www.omega.de www.omega.nl Deckenpfronn, Germany 0800-099-33-44 0800-8266342 More than 100,000 Products Available! Temperature Data Acquisition Calibrators, Connectors, General Test and Measurement Auto-Dialers and Alarm Monitoring Systems, Instruments, Handheld Instruments for Temperature Communication Products and Converters, Data Measurement, Ice Point References, Indicating Labels, Acquisition and Analysis Software, Data Loggers Crayons, Cements and Lacquers, Infrared Temperature Plug-in Cards, Signal Conditioners, USB, RS232, RS485 Measurement Instruments, Recorders, Relative Humidity and Parallel Port Data Acquisition Systems, Wireless Measurement Instruments, PT100 Probes, PT100 Elements, Transmitters and Receivers Temperature & Process Meters, Timers and Counters, Temperature and Process Controllers and Power Switching Pressure, Strain and Force Devices, Thermistor Elements, Probes and Assemblies, Displacement Transducers, Dynamic Measurement Force Thermocouples, Thermowells and Head and Well Sensors, Instrumentation for Pressure and Strain Assemblies, Transmitters, Thermocouple Wire, RTD Probes Measurements, Load Cells, Pressure Gauges, Pressure Flow and Level Reference Section, Pressure Switches, Pressure Transducers, Air Velocity Indicators, Doppler Flowmeters, Level Proximity Transducers, Regulators, Pressure Transmitters, Measurement, Magnetic Flowmeters, Mass Flowmeters, Strain Gauges, Torque Transducers, Valves Pitot Tubes, Pumps, Rotameters, Turbine and Paddle Wheel Flowmeters, Ultrasonic Flowmeters, Valves, Variable Area Heaters Flowmeters, Vortex Shedding Flowmeters Band Heaters, Cartridge Heaters, Circulation Heaters, Comfort Heaters, Controllers, Meters and Switching pH and Conductivity Devices, Flexible Heaters, General Test and Measurement Conductivity Instrumentation, Dissolved Oxygen Instruments, Heater Hook-up Wire, Heating Cable Instrumentation, Environmental Instrumentation, pH Systems, Immersion Heaters, Process Air and Duct, Electrodes and Instruments, Water and Soil Analysis Heaters, Radiant Heaters, Strip Heaters, Tubular Heaters Instrumentation

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