고체역학 (Beer) — Analysis and Design of Beams for Bending: Problem 5.142

5.142 Two cover plates, each $\frac{1}{2}$ in. thick, are welded to a W27 $\times$ 84 beam as shown. Knowing that $\sigma_{all} = 24 \text{ ksi}$ for both the beam and the plates, determine the required value of (a) the length of the plates, (b) the width of the plates.