A beam with a rectangular cross section, as in Figure, is made of 2219-T851 aluminum and must withstand a bending moment of M = 150N m. The thickness is b = 20 mm, and a quarter-circular corner crack as large as a = 1mm may be present. (a) What beam depth t is required for a safety factor 3.0 against brittle fracture? (b) For the beam depth t as calculated in (a), is the design adequate with respect to possible fully plastic failure? (Suggestion: Make a conservative estimate of M, by assuming that the crack extends across the full thickness b.) (c) What beam depth t is required for a safety factor 3.0 against brittle fracture if an axial load P of 5 kN is added to the moment?