고체역학 (Beer) — Analysis and Design of Beams for Bending: Problem 5.147

5.147 Two cover plates, each \(\frac{5}{8}\) in. thick, are welded to a W30 × 99 beam as shown. Knowing that \(\sigma_{\text{all}} = 22 \text{ ksi}\) for both the beam and the plates, determine the required value of (a) the length of the plates, (b) the width of the plates.