고체역학 (Gere) — Applications of Plane Stress: Problem 8.4-10

8.4-10 An overhanging beam \(ABC\) has a guided support at \(A\), a rectangular cross section, and supports an upward uniform load \(q = P/L\) over \(AB\) and a downward concentrated load \(P\) at the free end \(C\) (see figure). The span length from \(A\) to \(B\) is \(L\), and the length of the overhang is \(L/2\). The cross section has a width of \(b\) and a height \(h\). Point \(D\) is located midway between the supports at a distance \(d\) from the top face of the beam. Knowing that the maximum tensile stress (principal stress) at point \(D\) is \(\sigma_1 = 38\text{ MPa}\), determine the magnitude of the load \(P\). Data for the beam are \(L = 1.75\text{ m}\), \(b = 50\text{ mm}\), \(h = 220\text{ mm}\), and \(d = 55\text{ mm}\).