PRACTICAL STRAIN GAGE MEASUREMENTS - OMEGA

1 E-94 ESTRAIN GAGESPRACTICAL STRAIN GAGE MEASUREMENTSINTRODUCTIONWith today s emphasis onproduct liability andenergy efficiency, designs must notonly be lighter and stronger, butalso more thoroughly tested thanever before. This places newimportance on the subject ofexperimental stress analysis andthe techniques for measuring STRAIN . The main theme of thisapplication note is aimed at strainAppendix B contains schematics ofmany of the ways STRAIN gages areused in bridge circuits and theequations which apply to wishing a more thoroughdiscussion of bridge circuit theory are invited to read Item 7 referenced in the using bondedresistance STRAIN gages.

2 We willintroduce considerations that affectthe accuracy of this measurementand suggest procedures forimproving will also emphasize thepractical considerations of straingage measurement, with anemphasis on computer STRAIN GAGE MEASUREMENTSSTRESS & STRAINThe relationship betweenstress and STRAIN is one of themost fundamental concepts fromthe study of the mechanics ofmaterials and is of paramountimportance to the stress analyst. Inexperimental stress analysis, weapply a given load and thenmeasure the STRAIN on individualmembers of a structure or we use the stress -strainrelationships to compute thestresses in those members to verifythat these stresses remain withinthe allowable limits for the particularmaterials a force is applied to a body,the body deforms.

3 In the generalcase, this deformation is calledstrain. In this application note, wewill be more specific and define theterm STRAIN to mean deformationper unit length or fractional changein length and give it the symbol, .See Figure 1. This is the STRAIN thatwe typically measure with a bondedresistance STRAIN gage. STRAIN maybe either tensile (positive) orcompressive (negative). See Figure 2. When this is written inequation form, = L/L, we cansee that STRAIN is a ratio and,therefore, maintain the physicalsignificance of STRAIN , it is oftenwritten in units of inches/inch. Formost metals, the strains measuredin experimental work are typicallyless than inch/inch.

4 Sincepractical STRAIN values are so are often expressed as micro- STRAIN , which is x 106(note this isequivalent to parts per million orppm) with the symbol . StillSYMBOLS normal stress shear stress STRAIN (normal) micro- STRAIN ( x 106) shear strainEmodulus of elasticityor Young s modulus Poisson RatioGFgage factorRggage resistance in ohmsKttransverse sensitivity ratioLlength Lchange in length Rgchange in gage resistance(due to STRAIN )% GF% change in gage factor(due to temperature)Rllead wire resistanceTtemperature in CVIN bridge excitation voltageVOUT bridge output voltageVr[(VOUT/VIN)[strained] (VOUT/VIN)[unstrained]]Figure 1: Uniaxial Force AppliedFigure 2.

5 Cantilever in BendingE-96 ESTRAIN GAGES another way to express STRAIN is aspercent STRAIN , which is x 100. Forexample: inch/inch = 5000 = described to this point, STRAIN isfractional change in length and isdirectly measurable. STRAIN of thistype is also often referred to asnormal STRAINA nother type of STRAIN , calledSHEARING STRAIN , is a measureof angular distortion. Shearing strainis also directly measurable, but notas easily as normal STRAIN . If we hada thick book sitting on a table topand we applied a force parallel tothe covers, we could see the shearstrain by observing the edges of Figure 3.

6 Shearing STRAIN , , isdefined as the angular change inradians between two line segmentsthat were orthogonal in theundeformed state. Since this angleis very small for most metals,shearing STRAIN is approximated bythe tangent of the STRAINIn Figure 4 is a bar with a uniaxialtensile force applied, like the bar inFigure 1. The dashed lines show theshape of the bar after deformation,pointing out another phenomenon,that of Poisson STRAIN . The dashedlines indicate that the bar not onlyelongates but that its girth contraction is a STRAIN in thetransverse direction due to aproperty of the material known asPoisson s Ratio.

7 Poisson s ratio, ,is defined as the negative ratio ofthe STRAIN in the transverse directionto the STRAIN in the longitudinaldirection. It is interesting to note thatno stress is associated with thePoisson STRAIN . Referring to Figure4, the equation for Poisson s ratio is = t/ 1. Note that STRESSW hile forces and strains aremeasurable quantities used by thedesigner and stress analyst, stressis the term used to compare theloading applied to a material with itsability to carry the load. Since it isFigure 4: Poisson Strainusually desirable to keep machinesand structures as small and light aspossible, component parts shouldbe stressed, in service, to thehighest permissible level.

8 stress refers to force per unit area on agiven plane within a bar in Figure 5 has a uniaxialtensile force, F, applied along the x-axis. If we assume the force to beuniformly distributed over the cross-sectional area, A, the average stress on the plane of the section isF/A. This stress is perpendicular tothe plane and is called NORMALSTRESS, . Expressed in equationform, = F/A, and is denoted inunits of force per unit area. Sincethe normal stress is in the xdirection and there is no componentof force in the y direction, there isno normal stress in that normal stress is in the positivex direction and is 5: Normal StressPRACTICAL STRAIN GAGE MEASUREMENTSF igure 3: Visualizing Shearing StrainE-97 SHEAR STRESSJust as there are two types of STRAIN ,there is also a second type of stresscalled SHEAR stress .

9 Wherenormal stress is normal to thedesignated plane, shear stress isparallel to the plane and has thesymbol . In the example shown inFigure 5, there is no y component offorce, therefore no force parallel tothe plane of the section, so there isno shear stress on that plane. Sincethe orientation of the plane isarbitrary, what happens if the planeis oriented other than normal to theline of action of the applied force? Figure 6 demonstrates this conceptwith a section taken on the n-tcoordinate system at some arbitraryangle, , to the direction of actionof the force. We see that the force vector, F, canbe broken into two components, FnandFt, that are normal and parallelto the plane of the section.

10 Thisplane has a cross-sectional area ofA' and has both normal and shearstresses applied. The averagenormal stress , ,is in the ndirection and the average shearstress, , is in the t direction. Theirequations are: = Fn/A' and = Ft/A'. Note that it was the forcevector that was broken intocomponents, not the stresses, andthat the resulting stresses are afunction of the orientation of thesection. This means that stresses(and strains), while having bothmagnitude and direction, are notvectors and do not follow the laws ofvector addition, except in certainspecial cases, and they should notbe treated as such.