고체역학 (Beer) — Principal Stresses Under a Given Loading: Problem 8.1

8.1 A W10 × 39 rolled-steel beam supports a load P as shown. Knowing that P = 45 kips, a = 10 in., and \(\sigma_{all} = 18\) ksi, determine (a) the maximum value of the normal stress \(\sigma_m\) in the beam, (b) the maximum value of the principal stress \(\sigma_{max}\) at the junction of the flange and web, (c) whether the specified shape is acceptable as far as these two stresses are concerned.