(Solved): A uniformly loaded steel wide-flange beam is simply-supported at its ends. The W12x58, A992 Gr. 50 ...

A uniformly loaded steel wide-flange beam is simply-supported at its ends. The W12x58, A992 Gr. 50 beam is bent about is major axis. The span length is $10?\mathrm{ft}$. 1. Derive the formula for the deflection curve $(v)$ for a simply-supported beam of length $L$, uniform downwards load $(q)$, and a constant bending rigidity of (EI); your answer should be entirely in terms of these variables. 2. Derive the formula for the maximum transverse deflection $(d)$ of the beam. 3. The building code permits a maximum displacement of L/360 due to live load. Find the maximum allowable live load that the beam can support. 4. The building code permits a maximum normal stress due to bending that is $(2/3)$ of the yield stress, i.e., a factor of safety of 1.5. Find the maximum allowable load due to with respect to yielding. 5. Draw the deflected shape of the beam superimposed on a drawing of the beam and its loading.