Gere & Goodno — Applications of Plane Stress: Problem 8.4-11

8.4-11 Solve the preceding problem if the stress and dimensions are \(\sigma_1 = 18 \text{ MPa}\), \(L = 2 \text{ m}\), \(b = 60 \text{ mm}\), \(h = 250 \text{ mm}\), and \(d = 65 \text{ mm}\). [Reference Problem 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 \(\sigma_1\), determine the magnitude of the load \(P\).