Theory and Design for Mechanical Measurements
6th Edition
ISBN: 9781118881279
Author: Richard S. Figliola, Donald E. Beasley
Publisher: WILEY
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Chapter 5, Problem 5.11P
The shear modulus, G, of an alloy can be determined by measuring the angular twist, 0, resulting from a torque applied to a cylindrical rod made from the alloy. For a rod of radius R and a torque applied at a length L from a fixed end, the modulus is found by G = ILT/nR^ft. Examine the effect of the relative uncertainty of each measured variable on the shear modulus. If during test planning all of the uncertainties are estimated to be 1%, what is the uncertainty in G?
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The shear modulus, G, of an alloy can be determined by measuring the angular twist, θ,resulting from a torque applied to a cylindrical rod made from the alloy. For a rod of radius Rand a torque applied at a length L from a fixed end, the modulus is found by G=2LT/pR4θ.Examine the effect of the relative uncertainty of each measured variable on the shearmodulus. If during test planning all of the uncertainties are estimated to be 1%, what is theuncertainty in G?
The shear modulus. G. of a material can be determined by applying a torque. T, on a cylindrical material specimen and measuring the angular twist, 0.
The modulus can then be calculated from: G
each measured variable (L. T.t. 0, R) is 3.4%.
3LT
2 Ree
where R and Lare the specimen radius and length, respectively. The relative uncertainty in
What is the total relative uncertainty in G?
(Provide your amwer as a percentage using two decimal places. Do not include the % symbol.)
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Chapter 5 Solutions
Theory and Design for Mechanical Measurements
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