In this assignment you are to evaluate and comment on the torsional rigidities of three different cell configurations shown below. You will perform calculations of the torsional rigidities and make observations concerning the benefits of each configuration as it relates to torsional rigidity. You will determine the torsion constant of each configuration using three designs.

Note: You only need to calculate the torsional rigidity of configuration $1$ one time, as its dimensions do not change. The other two configurations have three different designs; hence you need to calculate the torsion constant for each of those configurations three times.

The thickness, t $,$ is constant in all walls of all the cell configurations.

You should report your individual calculations as well as how each calculation compares to the baseline of configuration $1.$ This value should be a percentage.

$\backslash$begin$\{$tabular$\}\{|$c$|$c$|$c$|$c$|\}$

$\backslash$hline & Design $1$ & Design $2$ & Design $3\backslash \backslash$

$\backslash$hline Length Parameter & $\backslash$begin$\{$tabular$\}\{$c$\}$

Value in $\backslash \backslash$

centimeters

$\backslash$end$\{$tabular$\}$ & $\backslash$begin$\{$tabular$\}\{$c$\}$

Value in $\backslash \backslash$

centimeters

$\backslash$end$\{$tabular$\}$ & $\backslash$begin$\{$tabular$\}\{$c$\}$

Value in $\backslash \backslash$

centimeters

$\backslash$end$\{$tabular$\}\backslash \backslash$

$\backslash$hline L$1$ & $20$ & $20$ & $20\backslash \backslash$

$\backslash$hline L$2$ & $30$ & $30$ & $30\backslash \backslash$

$\backslash$hline L$3$ & $15$ & $5$ & $1\backslash \backslash$

$\backslash$hline L$4$ & $15$ & $25$ & $29\backslash \backslash$

$\backslash$hline t & $0\mathrm{.}3$ & $0\mathrm{.}3$ & $0\mathrm{.}3\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$