Problem $1,(15\%)$ Introduction

For the tapered bar depicted in Figure $1,$ assume that for the material being modelled, $E=68$GPa.

Assume $b_2=0\mathrm{.}04m,b_1=0\mathrm{.}02m$ and $t=0\mathrm{.}02m.$ For this case, $L=0\mathrm{.}2m.$ Assume a load $P=10,500N$

the last $3$ digits of your student number.

Figure $1$: Schematic of the axial loaded tapered bar.

For the problem in Figure $1,$ create a plot of the displacement of the bar using a simple analytical analysis

$($i$.$e$.,$ you can find the cross$-$section of it as a function of $z,$ so you can determine displacement along the

length$).$ It is known that for some location z $,$ elongation $$ is given by:

$=\frac{Pz}{Et(b_2-b)}ln(\frac{b_2}{b})$

Note that for the entire bar, the total elongation is:

$=\frac{PL}{Et(b_2-b_1)}ln(\frac{b_2}{b_1})$