Compound Bar Stress and Strain Analysis

[FDhint]

Question

The compound bar is composed of Aluminium surrounded by High Density Polyethylene

Al= E = 69x10^9 Pa
Al= r = 0.035 m

HDPE= E = 0.8x10^9 Pa
HDPE= r = 0.055 m


The compound bar has a load of 75000N applied evenly to each of its ends.

Part 1.

Find the change in length of the bar due to the direct stress produced by the applied load.

Part 2.

Given that the Poisson's Ratios for Aluminium and HDPE are 0.33 and 0.38 respectively, comment on the realism of the calculations and any problems that may occur if this experiment were performed.


Question 1 attempt-

I was wondering if the way you work out the change in length is to work it out for both materials or for the whole bar. If it is for the whole bar I am unsure on how to work out this question.

Equations I believe should be used-

σ=F/A

then

E=σ/ε → ε=σ/E

so

ΔL= ε*L

Are these the right equation and process to work out the answer?

Any working outs or answer would much appreciated

 

[LawrenceC]

Hint: Think about two springs, one inside the other, supporting a load.