\section*{Rotating Discs}
\item \textbf{Briefly state the assumptions made in the stress analysis of thin rotating discs. (4)}
\begin{itemize}
\item The component is rotating with a constant angular speed.
\item The disc is thin with a constant thickness
\item The disc material is homogeneous.
\item Their is no stress in the z-direction.
\end{itemize}
\item \textbf{Give the boundary conditions for a thin rotating disc with a central hole if the inner and outer boundaries are both unloaded. (3)}
\begin{center}
$\sigma_{radial}=0$ at $r=r_{internal}$\\
$\sigma_{radial}=0$ at $r=r_{external}$\\
$\sigma_{radial-max}$ at $r=\sqrt{r_{internal}r_{external}}$\\
$\sigma_{Hoop}=\sigma_{Max}$ at $r=r_{internal}$

\end{center}\pagebreak

\section*{Thin Circular Plates}
\item \textbf{Briefly state the assumptions made in the stress and deflection analysis of small deflections in thin plates. (5)}
\begin{itemize}
\item The plate is initially flat before loading.
\item The plate is thin, 10\% of the diameter.
\item The deflection is in the order of the plate thickness.
\item External loads are applied normal to the plate and are axisymmetric.
\item There is no deformation in the mid-plane of the plate.
\item A line normal to the mid-plane remains normal after deformation.
\item The material is homogeneous, isotropic and linear elastic.
\end{itemize}


\item \textbf{The deflection, W, of a thin circular plate at radius r, subjected to a uniform pressure, p, on one surface is given by: $$ W = \frac{P r^{4}}{64D} + \frac{C_{1}r^{2}}{4} + C_{2}\ln(r) + C_{3} $$ are constants, D is flexural rigidity).
(Symbols have their usual meanings).
For a thin circular plate of radius ‘a’. Give the appropriate boundary conditions if it is:}
\begin{enumerate}
\item \textbf{clamped around its edge. (3)}
	$$\frac{dw}{dr}=0\ \text{at}\ r=0$$
	$$\frac{dw}{dr}=0\ \text{at}\ r=a$$
	$$\text{w}=0\ \text{at}\ r=a$$


\item \textbf{simply supported around its edge. (3)}
	$$\frac{dw}{dr}=0\ \text{at}\ r=0$$
	$$\text{w}=0\ \text{at}\ r=a$$
	$$M_{r}=0\ \text{at}\ r=a$$

\end{enumerate}