Answer:
The Poisson's ratio for the material is 0.389
Explanation:
Poisson's ratio is given as [tex]-\frac{Lateral \ strain}{Longitudinal \ strain} = -\frac{\epsilon_r}{\epsilon_l}[/tex]
Given data for Longitudinal Strain;
Initial length of the square steel bar, L₁ = 6.2 ft
Final length of the square steel bar, L₂ = 6.20379 ft
Change in length of the square steel bar, ΔL = 6.20379 ft - 6.2 ft = 0.00379 ft
[tex]Longitudinal \ strain, \epsilon_l = \frac{\delta L}{L_1} = \frac{0.00379}{6.2} = 6.113 *10^{-4}[/tex]
Given data for Contraction or lateral Strain
Initial radius or cross section, r₁ = 2.4 in
Final radius or cross section, r₂ = 2.39943 in
Change in radius, Δr = r₂ - r₁ = 2.39943 in - 2.4 in = -0.00057 in
[tex]Lateral \ strain, \epsilon_r = \frac{\delta r}{r_1} = \frac{-0.00057}{2.4} = -2.375 *10^{-4}[/tex]
Thus, Poisson's ratio [tex]= -\frac{\epsilon _r}{\epsilon _l} = -(\frac{-2.375*10^{-4}}{6.113*10^{-4}} ) =0.389[/tex]
Therefore, the Poisson's ratio for the material is 0.389
