PROBLEM $2(33$ MARKS$)$

A simply supported steel beam is $60$ inches long and has a rectangular cross section $1\mathrm{.}0$ inches wide by $3\mathrm{.}0$ inches deep. A Weight of $78$ lb is dropped from a height h at mid$-$span.

a$)$ If the yield strength of the material is $40000$ psi $,$ and if the beam mass is neglected, what drop height would be required to produce first cvidence of yielding in the beam?

b$)$ What is the impact factor under these circumstances?