Question

A metal alloy has poisson's ratio of 0.8. If a strain gauge is made of that metal alloy, the length L is 2cm, the cross-section area is 1 mm^2. With stretch, the length change to 2.0001cm. what is the cross-section area after the stretch in unit of m^2.

Answer 1

Poisson's ratio = change in diameter / change in length = 0.8

= (dD / D) / (dL / L)

where, L = 2 cm

dL = 2.0001 - 2 = 0.0001 cm

Cross section area, A = pi*D^2 / 4

1 mm^2 = 3.14*D^2 / 4

D = 1.128*10^(-3) m

Put the values in formula,

0.8 = (dD / 1.128*10^(-3)) / (0.0001*10^(-2) / 2*10^(-2))

dD = 4.52*10^(-8) m

Changed diameter, D' = 1.128*10^(-3) + 4.52*10^(-8)

D' 1.128*10^(-3) m

change in diameter is ver less. so cross section area is approx same.

A' = 0.999*10^(-6) m^2