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Strain-Based Measurement Introduction:Beam Stress and Strain Relationships:With reference to Figure 1-39, a beam length of L to the strain gagelocations, having a width of d, thickness of b and where the load W isapplied at distance of L-a inches from the end of the beam, the maximumstress s is given as:s=Mb-------2I(EQ 1-32)Where M = MomentAnd where I = The Polar Moment of Inertia=b 3 d--------12(EQ 1-33)Substituting the Polar Moment of Inertia, I of (1-33) into (1-32) yields:s=6M--------b 2 d(EQ 1-34)And since e = s/E (where E = YoungÕs Modulus)and M = -W(L-a), therefore:6W( L Ð a)e = -------------------------Eb 2 d(EQ 1-35)The above calculations are valid for straight uniform-section beamsshowing small deflections where the width-to-thickness ratio is nominallybetween 8 and 15. The calculations given should be used asapproximations where the actual strains are determined by test 1 .1. Ref: Roarke, Warren Young, P100 case 1a.CHAPTER 1-70 The Art of Practical and Precise Strain Based Measurement 2nd Edition © 1999
Applications Note 1-11:FIGURE 1-39. Cantilevered-Beam Variable Definitions:LW = MaBeam Thickness (b)Acceleration MassLL-aaCenter of SeismicMass[Beam Width (d)]Beam Resonant Frequency Calculations:In the case where the beam mass is insignificant or is a small fraction of the seismicloading mass, the resonant frequency of the beam is given by:1.732F n = ------------2pEb 3 dg-------------------12WL 3(EQ 1-36)Where: F n = Hertzand where L refers to the total beam length from the point of the load applicationto the clamp.Additionally a simple correction for the strain-gage backing and bond-line thickness(t) is made as follows: (Reference Figure 1-40)The Art of Practical and Precise Strain Based Measurement 2nd Edition © 1999 CHAPTER 1-71
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The Art of Practical andPrecise Str
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Special Credits:Mrs. Helen Pierson,
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Table of ContentsBy James G. Pierso
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ContentsApplications Note 4-10:Lead
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ContentsCHAPTER 8Electrical Conside
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CHAPTER 1Strain-BasedMeasurementInt
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Applications Note 1-1: Introduction
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Applications Note 1-1: Introduction
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Applications Note 1-2:The Art of Ap
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Applications Note 1-31. The presenc
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Applications Note 1-3result in a pe
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Applications Note 1-4:The measureme
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Applications Note 1-4:uncertainty i
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Applications Note 1-5:All strain-ba
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