Question

What is the change in volume of a circular bar 1m in length with a radius of 5cm loaded axially by a 50kN tensile load (E = 206GPa and v = 0.3).

Answer 1

Answer on Question #52118-Engineering-Other

What is the change in volume of a circular bar 1m in length with a radius of 5cm loaded axially by a 50kN tensile load (E = 206GPa and v = 0.3).

Solution

The strain is

e = \frac {F}{\frac {A}{E}} = \frac {\frac {50 \mathrm{kN}}{\frac {\pi \cdot (0.05 \, m)^2}{206 \mathrm{GPa}}} = 0.0309.

The new length is

$$l' = (1 + e)l = (1 + 0.0309)1 \, m = 1.0309 \, m.$$

The new radius is

$$r' = r(1 - ev) = 0.05 \, m(1 - 0.0309 \cdot 0.3) = 0.0495365 \, m.$$

The change in volume of a circular bar is

$$V' - V = \pi(r'^2 l' - r^2 l) = 9.33 \cdot 10^{-5} \, m^3.$$

Answer: $9.33 \cdot 10^{-5} \, m^3$.

https://www.AssignmentExpert.com