Problem $1$: A structural steel bar $($E $=29000$ ksi and g $=0\mathrm{.}284$ lb$/$in$3)$ of rectangular section is made up of a conical part and a prismatic part. The width of the conical part varies linearly from $2$ in at the lower end to $5$ in at the upper end, the length L of the conical part is $100$ in$,$ the bar has a constant thickness of $0\mathrm{.}5$ in$.$ Solve the following sections: a$)$ Determine the total elongation of the bar resulting from the application of a force P $30,000$ lb at its lower end, b$)$ Determine the stress in section B taking into account only the weight of the bar c$)$ Determine the maximum shear stress in the bar taking only the weight of the bar.$\text{'}$