Problem $1$ : $(10$ marks$)$

A radio tower experiences heavy winds during a storm, approximated as a distributed load, w $,$ as shown below. The structure must be designed such that a single guy wire can support the entire load when the wind acts in a plane parallel to the wire.

Draw the free body diagram for the structure, replace the tower with a slender rod and the distributed and guy wire with their respective, equivalent point forces. $(2$ points$)$

HINT: For simplicity, assume that the base of the tower acts as a pin support that CANNOT support moments.

Relate the tensile force in the wire, $T,$ to the unknown slope of the distributed load, $w.(3$ points$)$

Given that the diameter of the guy wire is $9\mathrm{.}5$ mm and its equivalent yield strength is $750$ MPa $,$ determine the maximum allowable value for the slope of the distributed load, w $,$ to ensure points