Question

A square steel bar has a length of 6.2 ft and a 2.4 in by 2.4 in cross section and is subjected to axial tension. The final length is 6.20379 ft . The final side length is 2.39943 in . What is Poisson's ratio for the material

Answer 1

The Poisson's ratio for the material is 0.389

Step-by-step explanation:

Poisson's ratio is given as
`-(Lateral \ strain)/(Longitudinal \ strain) = -(\epsilon_r)/(\epsilon_l)`

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

`Longitudinal \ strain, \epsilon_l = (\delta L)/(L_1) = (0.00379)/(6.2) = 6.113 *10^(-4)`

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

`Lateral \ strain, \epsilon_r = (\delta r)/(r_1) = (-0.00057)/(2.4) = -2.375 *10^(-4)`

Thus, Poisson's ratio
`= -(\epsilon _r)/(\epsilon _l) = -((-2.375*10^(-4))/(6.113*10^(-4)) ) =0.389`

Therefore, the Poisson's ratio for the material is 0.389