Airplane fuselages are subject to a variety of complex loads during flight. Consider a Boeing 777 modeled as a cylinder with 1/4 in wall thickness of 2024 aluminum, 209 ft length and 20.3 ft outer diameter. Assume the cylinder is loaded uniformly along the length with total weight (self-weight, passengers, all that luggage, cargo) of 600,000 lb. The load is supported by a lift from the wings, which can be simply modeled as a uniformly distributed load along the 31 ft length of the wingbox as shown. The fuselage is also pressurized for passenger safety and comfort, so that at a cruising altitude of 32,000 ft the internal pressure is atmospheric pressure at 7200 ft, resulting in an internal pressure 7.3 psi higher than the outside air. Aerodynamic loads that cause several modes of bending and twisting are not considered in this problem.
a. Find the position (x) along the length of the fuselage that experiences the maximum bending moment. At this section, find the normal stress in the fuselage due to the weight and lift loads, as a function of vertical position in the section (z).
b. Find the stresses due to pressure.
c. Considering only the stresses determined in parts (a) and (b), that is, neglecting shear due to bending and dynamic loads, what is the factor of safety with respect to yielding in the fuselage? Hint: consider points with extreme values of the stress components.
