Question $1$

$($a$)$ An initially straight beam of height $20$ mm is subjected to a moment such that the radius of curvature of the beam is $5$ m $.$ For the plots discussed below: clearly label all curves and axes; graph paper is not necessary; use a ruler or straight edge for the axes or straight lines; the plot does not have to be perfectly to scale.

Note that Y is the coordinate as shown in Figure Q$1$a

$($i$)$ Create a plot of strain vs $\backslash ($ Y $\backslash )$

$($ii$)$ For a linearly elastic material with $\backslash (\backslash$mathrm$\{$E$\}=77\backslash$mathrm$\{$GPa$\}\backslash ),$ create a plot of stress vs Y

$($iii$)$ For a linearly elastic, perfectly plastic material with $\backslash (\backslash$mathrm$\{$E$\}=77\backslash$mathrm$\{$GPa$\}\backslash )$ and $\backslash (\backslash$varepsilon$\_\{\backslash$text $\{$yield $\}\}=0\mathrm{.}1\backslash \%\backslash ),$ create a plot of stress vs Y

Figure Q$1$a

Please draw out the plots and label axes and important values on the axes.