Problem $2,(15\%)$

The bar shown in Figure $1$ can be represented by a series of bar elements. Divide this bar into three equal

lengths of L$/3$ and represent it by four nodes, one bar element for each section. Each section should

be represented by the average width for that section. Then, determine the displacement of each node

$($assume node $1$ starts from the location at the wall$).$

Create a plot of the displacement at each node as a function of the location along the bar $($z$-$direction$).$

Add a column to the table for the normal stress occurring in each bar segment. 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.