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 example, when wire is stretched, its 45° 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° To measure minute strains, the user 45° 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 (Fn); 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 n = E e (Z)/ l = E REGULATED times larger. eB(bh2⁄6)/l B DC Therefore, greater 2) AXIAL STRAIN equals axial – + sensitivity and stress divided by Young’s 2 3 resolution are Modulus. possible when more than one EA = oA /E oA = FA /A strain gage is used. VOUT Where axial stress (oA) equals Fig. B The following the axial load divided by the Wheatstone Bridge equations show the cross-sectional area. The cross- relationships sectional area for rectangles The total strain is represented by a among stress, strain, and force for equals (b x d). Therefore, strain change in V . If each gage had the OUT bending, axial, shear, and torsional gages used in axial same positive strain, the total would strain. configurations can be used to be zero and V would remain OUT determine axial loads (F (axial)). unchanged. Bending, axial, and 1) BENDING STRAIN or moment shear strain are the most common strain is equal to bending stress F (axial) = E e A bh types of strain measured. The actual divided by Young’s Modulus of Elasticity. 3) SHEAR STRAIN equals shear arrangement of your strain gages will stress divided by modulus of determine the type of strain you can eB = oB/E oB = MB/Z = Fn(l )/Z shear stress. measure and the output voltage change. See Figures C through F. Moment stress (oB) equals g = t/G t = Fn x bending moment (Fn x l ) divided Q/bI For example, if a positive (tensile) by sectional modulus. Sectional strain is applied to gages 1 and 3, modulus (Z) is a property of the Where shear stress (t) equals and a negative (compressive) strain cross-sectional configuration of the (Q), the moment of area about to gages 2 and 4, the total strain specimen. For rectangles only, the the neutral axis multiplied by the E-5 compensation of superimposed vertical load (Fn ) divided by the g = 2 x e@ 45° = t/G strains. This table was created using thickness (b) and the moment of t = Mt(d/2)/J a gage factor of 2.0, Poisson’s Ratio inertia ( I ). Both the moment of of 0.3, and it disregards the lead wire area (Q) and the moment of where torsional stress (t) equals resistance. inertia ( I ) are functions of the torque (Mt) multiplied by the specimen’s cross-sectional distance from the center of the This chart is quite useful in geometry. section to the outer fiber (d/2), determining the meter sensitivity divided by (J), the polar moment required to read strain values. For rectangles only of inertia. The polar moment of Q = bh 2⁄8 and I = bh 3⁄12 Temperature compensation is inertia is a function of the cross- achieved in many of the above The shear strain (g ) is sectional area. For solid circular configurations. Temperature determined by measuring the shafts only, J = p (d)4⁄32. The compensation means that the gage’s strain at a 45° angle, as shown in modulus of shear strain (G) has thermal expansion coefficient does Figure E. been defined in the preceding not have to match the specimen’s discussion on shear stress. Strain thermal expansion coefficient; g= 2 X e@ 45° gages can be used to determine therefore, any OMEGA® strain gage, The modulus of shear strain (G) = torsional moments as shown in regardless of its temperature E/2 (1 + m ). Therefore, strain the equation below. This characteristics, can be used with any gages used in a shear strain represents the principle behind specimen material. Quarter bridges configuration can be used to every torque sensor. can have temperature compensation determine vertical loads (Fn ); this if a dummy gage is used. A dummy Mt = t(J) (2/d) gage is a strain gage used in place of is more commonly referred to as a shear beam load cell. = g G (J) (2/d) a fixed resistor. Temperature = g G (p d 3⁄16) compensation is achieved when this Fn = G (g ) bI/Q dummy gage is mounted on a piece Ø = MTL/G(J) of material similar to the specimen = G (g ) b (bh3⁄12)/(bh2⁄8) which undergoes the same = G (g )bh(2/3) temperature changes as does the specimen, but which is not exposed 4) TORSIONAL STRAIN equals to the same strain. Strain torsional stress (t) divided by torsional modulus of elasticity (G). The following table affects output, bridge configuration shows how temperature compensation is not the same as load (stress) temperature See Figure F. temperature compensation, and compensation, because Young's Modulus of Elasticity varies with temperature. STRAIN BRIDGE POSITION SENSITIVITY OUTPUT PER TEMP. SUPERIMPOSED TYPE OF GAGES MV/V @ m e @ 10 V COMP. STRAIN COMPENSATED Figs. C-F 1000 m e EXCITATION 1 ⁄4 1 0.5 5 m V/m e No None BENDING 1 ⁄2 1, 2 1.0 10 m V/m e Yes Axial Full All 2.0 20 m V/m e Yes Axial STRAIN GAGES 1 ⁄4 1 0.5 5 m V/m e No None 1 ⁄2 1, 2 0.65 6.5 m V/m e Yes None AXIAL 1 ⁄2 1, 3 1.0 10 m V/m e No Bending Full All 1.3 13 m V/m e Yes Bending 1 ⁄2 1, 2 1.0 10 m V/m e Yes Axial and Bending SHEAR & @ 45°F E TORSIONAL Full All 2.0 20 m V/m e Yes Axial and Bending @ 45°F Note: Shear and torsional strain = 2 x e @ 45° E-6 One Omega Drive | Stamford, CT 06907 | 1-888-TC-OMEGA (1-888-826-6342) | info@omega.com www.omega.com UNITED KINGDOM www. omega.co.uk Manchester, England 0800-488-488 UNITED STATES FRANCE www.omega.com www.omega.fr 1-800-TC-OMEGA Guyancourt, France Stamford, CT. 088-466-342 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 Amstelveen, NL 0800-8266342 0800-099-33-44 More than 100,000 Products Available! Temperature Data Acquisition Calibrators, Connectors, General Test and Measurement Auto-Dialers and Alarm Monitoring Systems, Instruments, Glass Bulb Thermometers, Handheld Instruments Communication Products and Converters, Data for Temperature Measurement, Ice Point References, Acquisition and Analysis Software, Data Loggers Indicating Labels, Crayons, Cements and Lacquers, Infrared Plug-in Cards, Signal Conditioners, USB, RS232, RS485 Temperature Measurement Instruments, Recorders Relative and Parallel Port Data Acquisition Systems, Wireless Humidity Measurement Instruments, RTD Probes, Elements Transmitters and Receivers and Assemblies, Temperature & Process Meters, Timers and Counters, Temperature and Process Controllers and Power Pressure, Strain and Force Switching Devices, Thermistor Elements, Probes and Displacement Transducers, Dynamic Measurement Assemblies,Thermocouples Thermowells and Head and Well Force Sensors, Instrumentation for Pressure and Strain Assemblies, Transmitters, Wire Measurements, Load Cells, Pressure Gauges, Pressure Flow and Level Reference Section, Pressure Switches, Pressure Transducers, Air Velocity Indicators, Doppler Flowmeters, Level Proximity Transducers, Regulators, Measurement, Magnetic Flowmeters, Mass Flowmeters, Strain Gages, 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 click here to go to the omega.com home page EPG05

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