A B C D E F G H I J K L M N O P Q R S
SAFETY ASSESSMENT SAFFMAN LENGTH SALINE WATER RECLAMATION SALT SALT DILUTION METHOD FOR FILM FLOW RATE MEASUREMENT SALTATION SALTING OUT SAMPLING SAMPLING METHODS, FOR DROPSIZE MEASUREMENT SAND BLASTING SANDIA NATIONAL LABORATORY, SNL Satellite remote sensing SATELLITES SATURATED FLUID PROPERTIES SATURATED SURFACES SATURATED VOLUME SATURATION PRESSURE SATURATION TEMPERATURE SAUTER MEAN DIAMETER SCALE-UP OF PERFORATION PROCESS SCALES OF TURBULENCE SCALING SCATTERING SCATTERING AMPLITUDE SCATTERING EFFICIENCY SCATTERING INDICATRIX SCATTERING OF RADIATION Scattering problem for cylindrical particles SCHEIBEL EQUATION FOR DIFFUSION IN LIQUIDS SCHLIEREN INTERFEROMETRY SCHLIEREN TECHNIQUE SCHMIDT NUMBER SCHMIDT, ERNST (1892-1975) SCHUSTER-HAMAKER MODEL SCHUSTER-SCHWARZCHILD APPROXIMATION, FOR COMBINED RADIATION AND CONDUCTION SCRAPED SURFACE HEAT EXCHANGERS SCREEN SEPARATORS SCREENS SCREW ROTARY COMPRESSOR SCREWS, PLASTICATING SCROLL DISCHARGE CENTRIFUGE SCRUBBERS SEA WATER COMPOSITION SECOND LAW OF THERMODYNAMICS SECOND NORMAL STRESS DIFFERENCE COEFFICIENT Secondary Flows Secondary quantity SECONDARY RECOVERY PROCESSES SEDIMENTATION SEDIMENTING CENTRIFUGES SEEPAGE SEGMENTAL BAFFLES SEGREGATION SEIDER-TATE CORRELATION SELECTIVE FROTH FLOTATION SELF ORGANIZATION SELF-SIMILAR HARDENING BEHAVIOR SELF-SIMILARITY SEMI-CONDUCTOR THERMOMETERS SEMI-SLUG FLOWS Semi-transparent media containing bubbles SEMIANNULAR FLOW SEMICONDUCTOR DIODE LASERS SEMICONDUCTORS SEMITRANSPARENT MEDIA SENSIBLE HEAT STORAGE SEPARATED FLOW MODELS SEPARATED LIQUID FLOWS SEPARATION OF BOUNDARY LAYERS SEPARATION OF EMULSIONS SEPARATION OF FLUID MIXTURES SEPARATION OF GAS AND SOLIDS SEPARATION OF LIQUIDS SEPARATION OF LIQUIDS AND SOLIDS SEPARATION OF PHASES IN GAS-LIQUID FLOWS SEPARATION PROCESSES SEPARATION, LIQUID/LIQUID SEPARATION, PARTICLES/LIQUID SERIES EXPANSIONS SESSILE DROPS AND BUBBLES SETTLING SLURRIES SEVERE ACCIDENTS, IN NUCLEAR REACTORS, CONTAINMENT OF SHADOWGRAPH TECHNIQUE SHAPE MEMORY SHAPE OF VAPOR FORMATIONS IN EXPLOSIVE BOILING SHAPE SELECTIVE CATALYSIS SHEAR FLOW Shear Layer SHEAR MODULUS Shear Stress SHEAR STRESS MEASUREMENT SHEAR STRESS VELOCITY SHEAR THICKENING SHEAR THICKENING FLUIDS SHEAR THINNING FLUIDS SHEAR VISCOSITY SHEARING INTERFEROGRAM SHEATH CHARACTERISTICS SHEET SPLITTING, IN DROP FORMATION SHELL AND TUBE CONDENSERS SHELL AND TUBE HEAT EXCHANGERS SHELL BOILER SHELL PROGRESSIVE MODEL SHELL-SIDE REFRIGERATION CHILLERS SHELLS SHERWOOD NUMBER SHERWOOD, THOMAS KILGORE (1903-1976) SHOCK TUBES SHOCK WAVE PROPAGATION SHOCK WAVES SHOCK WAVES, CONICAL SHORT ROUGHNESS STRIP SHORT TIME LAPSE PHOTOGRAPHY SHORT-TUBE VERTICAL EVAPORATOR SHOT TOWERS SHRINKING CORE MODEL SI UNITS SIDERITES SIEVE, TRAY COLUMN Silica based nanoporous composite materials SILICA GEL SILICON SILICON CARBIDE SILICON SOLAR CELLS SILOS, GRANULAR FLOW FROM SILVER SILVER METHOD SIMILARITY CONDITIONS SIMILARITY, THEORY OF SIMILITUDE Simplest approximations of double spherical harmonics SIMPLEX ATOMIZER SIMPLIFIED BOILING WATER REACTOR, SBWR SIMULATING SUBSURFACE TEMPERATURE SINCLAIR-LA MER AEROSOL GENERATOR Single-phase medium SINGLET STATE SINGLET STATE LIFETIME Singularities SINGULARITIES, HYDRAULIC RESISTANCE IN SINTERING SINUOUS JETS SIPHON CENTRIFUGE SKIMMER PIPE AND KNIFE CENTRIFUGES SKIN EFFECT SKIN FRICTION SLAG FORMATION SLIGHTLY DEFORMED POROUS CIRCULAR CYLINDER SLIGHTLY INCLINED SURFACE-MOUNTED PRISMS Slip ratio SLIT FLOW METERS SLIT FLOWS SLOT-PERFORATED FLAT FINS SLOW MOTION PHOTOGRAPHY Slug flow SLUG FLOW, SOLID SUSPENSIONS SLUG FREQUENCY SLUG LENGTH SLURRIES SMALL ANCLE SCATTERING METHOD, FOR DROPSIZE MEASUREMENT SMELTING SMOKE, AS AN AIR POLLUTANT SMOKES SNELL REFRACTION LAW SNL SOAVE EQUATION SODA ASH SODIUM SODIUM CARBONATE SODIUM CHLORIDE SODIUM COOLED NUCLEAR REACTOR SODIUM HYDROXIDE SOFTENING OF WATER SOFTWARE ENGINEERING SOIL, THERMAL PROPERTIES SOL SOLAR AIR HEATERS SOLAR CELLS SOLAR COOKERS SOLAR DRYING SOLAR ENERGY SOLAR ENERGY THERMAL CONVERSION SOLAR PONDS SOLAR RADIATION SOLAR RADIATION SPECTRUM SOLAR REFRIGERATION SOLAR SELECTIVE SURFACES SOLAR SODIUM EVAPORATOR SOLAR STILLS SOLAR WATER HEATERS SOLENOIDAL FLOW SOLID FUELS SOLID HOLDUP SOLID PROPELLANT SOLID STATE LASERS SOLID-LIQUID-LIQUID FLOWS SOLIDIFICATION SOLIDIFICATION CONSTANT SOLIDOSITY SOLIDS CONCENTRATION SOLIDS IN LIQUIDS, BOILING HEAT TRANSFER SOLIDS SEPARATION SOLIDS, THERMAL CONDUCTIVITY OF SOLITARY WAVE SOLITON SOLUBILITY SOLUBILITY OF GASES IN LIQUIDS SOLUBILITY OF SOLIDS IN LIQUIDS SOLUTE SOLUTE DIFFUSION SOLUTE FUNCTIONALITY Solution algorithm SOLUTIONS Solutions for one-dimensional problems Solutions for One-Dimensional Radiative Transfer Problems SOLVENT SOLVENT EXTRACTION Some applications: electrical arcs and atmospheric re-entry Some applied problems of combined heat transfer Some methods for detailed numerical simulation of radiative transfer Some validity studies SONIC OSCILLATOR SONIC VELOCITY SONOCAPILLARY EFFECT SOOT SORET AND DUFOUR EFFECTS ON FREE CONVECTION SORET EFFECT SORPTION HEAT PUMPS SOUND ABSORPTION SOUND GENERATION SOUND PROPAGATION SOUR GASES SOUTTER-ION PUMP SPACE HEATING SPACERS SPACERS, EFFECT ON CHF SPARK-IGNITION ENGINES SPARSELY PACKED POROUS MEDIUM Spatial discretization schemes SPATIAL-TEMPORAL CORRELATION SPECIFIC HEAT CAPACITY SPECIFIC WORK, IN TURBINES SPECKLE METHOD SPECKLE PHOTOGRAPHY SPECTRA, EMISSION AND ABSORPTION SPECTRAL ANALYSIS SPECTRAL DENSITY FUNCTION SPECTRAL EMISSIVITY SPECTRAL EXTINCTION METHOD Spectral radiative properties of diesel fuel droplets Spectral radiative properties of disperse systems: theoretical modeling and experimental characterization Spectral radiative properties of gases and plasma: theoretical models and experimental data Spectral radiative properties of some important materials: experimental data and theoretical models SPECTROFLUORIMETRY Spectroscopic databases SPECTROSCOPY SPECULAR REFLECTION SPEED OF LIGHT SPEED OF SOUND SPENT FUEL SPHERE, DRAG COEFFICIENT FOR SPHERES, CONVECTIVE HEAT AND MASS TRANSFER SPHERES, DRAG AND LIFT SPHERES, SOLID, DRAG ON Spherical particles SPHERICITY SPIRAL CLASSIFIER SPIRAL HEAT EXCHANGERS SPIRAL TUBES, USE IN BENSON BOILERS SPIROPYRAN SPLATTERING, EFFECT ON JET IMPINGEMENT SPONTANEOUS CONDENSATION SPRAY CHARACTERISTICS SPRAY COLUMNS SPRAY CONDENSERS SPRAY COOLING SPRAY DRYER SPRAY DRYING SPRAY EQUATION SPRAY EVAPORATORS SPRAY FLOWS SPRAY FORMATION SPRAY NOZZLES SPRAY TOWERS SPRAYERS SPRAYING SPRAYS SPREADING OF LIQUIDS ON LIQUIDS SPUTTERING STABILITY STABILITY CRITERIA STABILITY OF EMULSIONS STABILITY OF FLOATING BODIES STACKS, POLLUTION FROM STAGGERED TUBE BANKS STAGNANT FILM MODEL STAGNATION POINT STAGNATION PRESSURE STAGNATION TEMPERATURE STANDARD CONDITIONS STANTON GAUGE STANTON NUMBER STANTON, SIR THOMAS EDWARD (1865-1931) STARK BROADENING STARK NUMBER STARS, FUSION REACTIONS IN Static Head STATIC INSTABILITIES IN TWO-PHASE SYSTEMS STATIC MIXERS STATIC REGENERATORS STATIONARY PHASE, SP, CHROMATOGRAPHY Statistical band models STATISTICAL MECHANICS STATISTICAL THEORY, OF TURBULENT FLOW STATISTICAL THERMODYNAMICS STEAM ENGINES STEAM GAS TURBINE UNITS STEAM GENERATORS, NUCLEAR STEAM JET EJECTORS STEAM JET REFRIGERATION STEAM TABLES STEAM TURBINE STEAM-WATER SEPARATION STEEL AND TUBE CONDENSERS STEELS STEFAN'S LAW STEFAN, JOSEF (1835-1893) STEFAN-BOLTZMANN CONSTANT STEFAN-BOLTZMANN LAW STEFAN-MAXWELL EQUATIONS STEPWISE HEAT RELEASE STEREOSCOPIC IMAGING Stewart number Stewart number STEWARTSON TYPE FLOW STIELTJES' INTEGRAL STIRRED TANK REACTOR STIRRED TANKS STIRRED VESSEL PHASE INVERSION STOCHASTIC DIFFERENTIAL EQUATIONS STOCHASTIC PROCESS STOICHIOMETRIC COMBUSTION STOKES EQUATION STOKES FLOW STOKES LENGTH STOKES PARADOX STOKES PROBLEM STOKES SHIFT STOKES STREAM FUNCTION STOKES' LAW FOR SOLID SPHERES AND SPHERICAL BUBBLES STOKES-EINSTEIN EQUATION STOKES-EINSTEIN EQUATION, FOR DIFFERENTIAL COEFFICIENTS IN LIQUIDS STOMATAL CONTROL OF WATER LOSS FROM PLANTS STOPPING DISTANCE STORE'S FORMULA STRAIN STRAIN GAUGES STRAIN RATE STRANGE ATTRACTORS STRATIFICATION, UNSTABLE AND STABLE Stratified Gas-Liquid Flow STRATIFIED WAVY FLOW STRATOSPHERE STREAM ANALYSIS METHOD STREAM AVAILABILITY Stream Function Streamline Streamline Flow STREAMLINED BODIES, FLOW OVER STREAMLINES STREAMLINES, VISUALIZATION STREAMTUBE STRESS Stress in Fluids STRESS IN SOLID MATERIALS STRESS TENSOR STRESS VECTOR STRESS, NORMAL STRESS, SHEAR STRETCHING SHEET STRETCHING SURFACE STRETCHING/STABILIZING EFFLUX FLUID FILMS STROUHAL NUMBER Structure of plasma spectra STRUCTURED SURFACE STUART NUMBER SUBCHANNEL ANALYSIS SUBCHANNEL MIXING SUBCOOLED TWISTED FLOW SUBCOOLING SUBCOOLING EFFECTS ON POOL BOILING SUBLAYER FENCE SUBLIMATION SUBMERGED COMBUSTION SUBMERGED COMBUSTION EVAPORATORS SUBMERGED JETS SUBROUTINES SUBSTITUTE NATURAL GAS (SNG) SUBSURFACE BARRIER SUBUNDAL FLOW SUCTION SUCTION EFFECTS SULFUR SULFUR DIOXIDE SULFUR HEXAFLUORIDE SULFUR POLLUTION SULFURIC ACID SUN, HEAT TRANSFER IN SUPER-PHENIX SUPERCAVITATION SUPERCOMPUTING SUPERCONDUCTING MAGNETS SUPERCONDUCTORS SUPERCRITICAL HEAT TRANSFER SUPERFICIAL VELOCITY SUPERHEATING SUPERSATURATION SUPERSONIC EXTERNAL FLOW SUPERSONIC FLOW SUPERSONIC FLOW, IN NOZZLES SUPERSONIC HETEROGENEOUS FLOW SUPERSONIC JET SUPERUNDAL FLOW SUPPRESSION OF NUCLEATE BOILING SURFACE ACTIVE SUBSTANCES SURFACE ALLOYING OF METALS Surface and interfacial tension SURFACE CONDENSERS SURFACE DIFFUSION SURFACE DIMPLES SURFACE EFFECTS ON BOILING SURFACE EFFICIENCY SURFACE ENERGY SURFACE EXTENSIONS SURFACE FLOW VISUALIZATION SURFACE ROUGHNESS SURFACE TENSION SURFACE TENSION DEVICES SURFACE TREATMENT SURFACE, CIRCULAR SURFACE, PERMEABLE SURFACTANT COLLECTORS SURFACTANTS SURGE TANKS SUSPENSION OF PARTICLES IN LIQUID SUTHERLAND COEFFICIENT SWEATING SWEETENING OF GASES SWIRL BURNERS SWIRL FLOW DEVICES SWIRLING FLOW SWIRLING TAPES, FOR INCREASING BURNOUT FLUX SYMMETRIC TENSOR SYMMETRY ANALYSIS OF SECOND-GRADE FLOW SYNCHROTON RADIATION SYNOPTIC SCALE CIRCULATION, OF ATMOSPHERE SYNTHETIC ZEOLITES System of units
T U V W X Y Z

STRAIN GAUGES

Interlinking between Articles
Visual Navigation

A number of devices are used to measure strain. Among them, the electrical resistance strain gauges are, by far, the most commonly used. The electrical resistance of a wire increases when the wire is stretched. The ratio between the change in resistance and the corresponding percent increase in length is called the gauge factor, k,

(1)

For the metals in common use, k varies between 0-0.5 and 5. Semiconductor gauges of silicon or germanium have gauge factors as high as 150.

A resistance strain gauge consists of a conductor, bonded to a carrier which is, in turn, fixed on to the structure or machine (base). The carrier may be in the form of a foil, a sheath or a frame and it may be cemented or welded to the base (Figure 1). The sheath and frame types are usually referred to as unbonded gauges.

Resistance strain gauges of the bonded type (a), and unbonded type (b).

Figure 1. Resistance strain gauges of the bonded type (a), and unbonded type (b).

When the temperature of gauge and base change by ΔT, the gauge grid stretches by αΔT while the carrier and base stretch by βΔT, α and β being respectively the thermal expansion coefficients of the grid and of the base metal. At the same time, the change in temperature results in a change in resistivity of γΔT (ohm/ohm). Assuming that the base is far more rigid than the gauge itself, the strain to which the gauge grid is subjected is (B − α) ΔT and the total change in resistance is,

(2)

In some commercially available gauges, the parameters α and γ are chosen in such a way that the term in brackets in the previous expression is zero, for a given base material. Such gauges are called self-compensated.

The change in resistance is measured by either a Wheatstone bridge or a potentiometer circuit. The former is used for static measurements (null balance method in general) and dynamic measurements (deflection method). The latter is only used for dynamic measurements (with temperature compensated gauges usually).

In the bridge shown in Figure 2, the terminals are connected to input source (V), BD to output (E). Arms' resistance AB = R1, BC = R2, CD = R3, DA = R4. Output is given by

(3)

When the bridge is initially balanced, R1R3 = R2R4. In the null balance method the bridge is continuously balanced in such a way that

(4)

For small changes,

(5)

If R4 is the measuring resistor, such as a precision decade box, potentiometer or slide wire, for a quarter bridge configuration in which R1 is the strain gauge, the strain is

(6)

In a half bridge with two strain gauges R1, R2 normally used to measured bending, the tensile strain measured by R1 is equal in magnitude to the compressive strain measured by R2,

(7)

In the deflection method the output E is measured by means of a millivoltmeter or resistance RL. In general, R1, R2, R3, and R4 are approximately equal and much smaller than RL. It can then be shown that for a quarter bridge,

(8)

and for the half bridge

(9)

In the potentiometer circuit (Figure 3) the gauge is in series with a ballast resistor. Input terminals A, C, output B, C. Resistance AB = R2, BC = R1 (gauge). Open circuit output is

(10)

The circuit cannot be balanced, so that the initial reading of the measuring instrument (large impedance) is E. Upon application of strain,

(11)

hence

(12)

Since V is of the order of 10 V, ΔR of the order of a few mV, the measuring instrument must have high resolution plus extended full-scale range. For this reason, only dynamic measurements are possible with DC current and filter to block the steady state output, letting only ΔE through (ΔE cyclic).

Wheatson bridge circuit for the measurement of resistance changes in strain gauges.

Figure 2. Wheatson bridge circuit for the measurement of resistance changes in strain gauges.

Potentiometer circuit for strain gauges.

Figure 3. Potentiometer circuit for strain gauges.

The nominal resistance of most strain gauges is 120 Ω. For a strain sensitivity of 10−5 (10 microstrain) and a maximum strain of 10−2 (1%) with a voltage input of 10 V, the output of a Wheatstone bridge will only be about 100 mV full scale deflection with 0.1 mV sensitivity.

The material used for the strain gauges is Cu/Ni alloy up to temperatures of 300°C. For higher temperatures, Pt may be used. The base may be epoxy, polyester or, in wire strain gauges, resin impregnated paper. A variety of cements, ranging from epoxies to cyanocrylates are available. There is a large variety of gauge materials, base materials and cements and for the selection of a commercially available system it is necessary to consult suppliers' catalogues.

Protection of the strain gauge against the environment is also an important issue.

REFERENCES

Dally, J. W. and Riley, W. F. (1965) Experimental Stress Analysis, McGraw-Hill.

Kobayashi, A. S. (1991) Handbook of Experimental Mechanics, Soc.Exp. Mech.

References

  1. Dally, J. W. and Riley, W. F. (1965) Experimental Stress Analysis, McGraw-Hill.
  2. Kobayashi, A. S. (1991) Handbook of Experimental Mechanics, Soc.Exp. Mech.

This article belongs to the following areas:

S in A-Z Index
Number of views: 4222 Article added: 2 February 2011 Article last modified: 9 February 2011 © Copyright 2010-2014 Back to top