The Art of Practical and Precise Strain Based ... - Webprofile.info

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