$3.$ A wind generator system is attached to a vertical pole $($pipe$)$ that has an outside diameter of $150$ mm and a wall pipe thickness of $6$ mm $.$ The weight of the generator assembly is $22\mathrm{.}24$ kN and is off from centre by $76$ mm $.$ The engineer is worried that eccentric loading will cause the pole to bend and fail due to added bending stresses.

a$)$ Use an appropriate formula to determine the stress induced in the pole. Take the effective length of pole $\backslash (\backslash$mathrm$\{$Le$\}=2\backslash$mathrm$\{$~L$\}\backslash ).$ Note $\backslash (\backslash$mathrm$\{$L$\}=\backslash )$ Pole Length because pole is fixed at the base and free at the top. $(8$ Marks$)$

b$)$ The pole material has $\backslash (\backslash$sigma y$=250\backslash$mathrm$\{$M$\}\backslash$mathrm$\{$Pa$\}\backslash )$ and allowed a factor of safety of $3,$ determine if the pole is safe under the referred conditions. $(2$ Marks$)$