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Strain-Based Measurement Introduction:be infinitely rigid and side-wall bending will occur especially in the case ofhigh-pressure sensor designs. For this reason, the calculations given are bestused as an initial estimation of the strains that will result for a given diaphragmthickness, diameter, and pressure loading.DeÞnitions: With reference to Figure 1-55.W = Total load in pounds forcew = Pounds per square inch (psi) where: W = wpa 2m = 1/n where n is PoissonÕs ratiot = Diaphragm thicknessE = YoungÕs Modulusa = Diaphragm radiusr = The distance from the diaphragm centere = s/E (strain)y c = Center of diaphragm deflection at maximum loadFIGURE 1-55. Variable Definitions for the Circular Flat Plate UnderUniform Pressure Loading:(W = total load in lbf)w psitrRadius aCLCHAPTER 1-88 The Art of Practical and Precise Strain Based Measurement 2nd Edition © 1999
Applications Note 1-13:Radial Stress:s r=3W æ--------------- ( 3m + 1) r2 ö---- Ð ( m + 1)8pmt 2 ç ÷èøa 2(EQ 1-38)Tangential Stress:s t=3W æ--------------- ( m + 3) r2 ö---- Ð ( m + 1)8pmt 2 çè a 2 ÷ø(EQ 1-39)At the center of the diaphragm: r = 0 and therefore:3W( m+1)s r = s t = Ð --------------------------èæ 8pmt 2 øö(EQ 1-40)The maximum deflection at the center of the diaphragm is given by:3wa 4 ( 1 Ð u 2 )y c = Ð--------------------------------( 16t 3 E)(EQ 1-41)The radial stress at the clamp occurs when r = a and is given by:3wa 2s ra = ------------4t 2(EQ 1-42)The tangential stress at the clamp also occurs when r = a and is given by:s t=3wa 2 uÐ----------------4t 2(EQ 1-43)By setting equation (1-38) to equal zero, the equation may be solved to find thevalue of r at which the radial stress is equal to zero with the result being:r = 0.63aWhen PoissonÔs Ratio = .3(EQ 1-44)The Art of Practical and Precise Strain Based Measurement 2nd Edition © 1999 CHAPTER 1-89
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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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Applications Note 1-6:Applications
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Applications Note 1-6:ical size of
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Applications Note 1-6:and where:j i
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Applications Note 1-6:5. millivolts
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Applications Note 1-6:.Electrodynam
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Strain-Based Measurement Introducti
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