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(A) A cylindrical specimen of an alloy 8 mm (0.31 in.) in diameter is stressed elastically in...

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(A) A cylindrical specimen of an alloy 8 mm (0.31 in.) in diameter is stressed elastically in tension. A force of 15,700 N (3530 lbf) produces a reduction in specimen diameter of 5 * 10^-3 mm (2 * 10^-4 in.). Compute Poisson's ratio for this material if its modulus of elasticity is 140 GPa (20.3 * 10^6 psi).

(B) Consider a cylindrical specimen of some hypothetical metal alloy that has a diameter of 8.0 mm (0.31 in.). A tensile force of 1000 N (225 lbf) produces an elastic reduction in diameter of 2.8 * 10^-4 mm (1.10 * 10^-5 in.). Compute the modulus of elasticity for this alloy, given that Poisson's ratio is 0.30

Poisson's Ratio:

When a body is subjected to uni axial tension, the length of the body increases creating a longitudinal strain. Simultaneously, the width of the body decreases creating a lateral strain in the body. The ratio of the lateral strain to the longitudinal strain is called Poisson's ratio.

Answer and Explanation:

(A) Calculation of Poisson's Ratio (v)

Given,

Elastic modulus, E=140 GPa={eq}\displaystyle 140810^{9} {/eq} N/m2

Force, F= 15700 N

Initial...

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Poisson's Ratio: Definition & Equation

from Introduction to Engineering

Chapter 1 / Lesson 17
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