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Poisson's Ratio question?
A bar with a 2.375 inch x 0.188 inch cross section that is 11.25 inches long is known to have a Poisson ratio of 0.3. If the bar is loaded so that it becomes 11.31 inches long, what will the final cross sectional area of the bar be?
1 Answer
- civil_av8rLv 79 years agoFavorite Answer
Small change assumption
Change in Volume / Original Volue = (1 - 2*v)*Change in Length / Original Length
(Vf - Vi) / Vi = (1-2*v) * (Lf - Li) / Li
Solve for Vf
Vf = ((1-2*v) * (Lf - Li) / Li)*Vi + Vi
Vi = Li*Ai with Ai = 2.375" * 0.188"
Vf = Lf*Af ==> Af = Vf/Lf
Af = (((1-2*v) * (Lf - Li))*Ai + Li*Vi) / Lf
Plug and chug
