(40 pts) Analyze the main wing of a Cessna 172 aircraft. Approximate it as a uniform...

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(40 pts) Analyze the main wing of a Cessna 172 aircraft. Approximate it as a uniform beam of length L that is clamped at the wing root (x =0) and supported by a pinned support at x = 2L/5. In steady level flight, approximate the lift on the wing by a vertical distributed load p(x) with known magnitude po (force/unit length) at the wing root, tapering linearly to the wing tip as shown below. (Neglect the weight of the wing itself.) (a) Find the deflection curve, w(x), in terms of the given parameters. (b) Plot w = w/L versus = x/L for po = EI/L. (c) Plot the shear force V(x) and bending moment M(x) diagrams, labeling all significant points. (d) Find the maximum tensile stress (max) and indicate where it occurs (x, y, z). Z,W Po mmm X 2L/5 3L/5 5 t 2t N-> b. Wingbox cross-section (magnified) -y (40 pts) Analyze the main wing of a Cessna 172 aircraft. Approximate it as a uniform beam of length L that is clamped at the wing root (x =0) and supported by a pinned support at x = 2L/5. In steady level flight, approximate the lift on the wing by a vertical distributed load p(x) with known magnitude po (force/unit length) at the wing root, tapering linearly to the wing tip as shown below. (Neglect the weight of the wing itself.) (a) Find the deflection curve, w(x), in terms of the given parameters. (b) Plot w = w/L versus = x/L for po = EI/L. (c) Plot the shear force V(x) and bending moment M(x) diagrams, labeling all significant points. (d) Find the maximum tensile stress (max) and indicate where it occurs (x, y, z). Z,W Po mmm X 2L/5 3L/5 5 t 2t N-> b. Wingbox cross-section (magnified) -y