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5. During the assembly of an aircraft wing, oversized fasteners are pressed into holes to fasten the skin and spars together. The stress field that develops in the skin takes on the form (in polar coordinates) = 0 = 0 = 0 = 0, where A = 0.001" is the amount of interference, Ore θz -AaE ΔαΕ ee = 4r² 472, ZZ rz Orr = a = 0.5" is the hole diameter, E = 10,000 ksi is the Young's modulus and r is the distance from the center of the hole. Take the Poisson's ratio of the material to be v = 0.33 and the yield strength to be Oy = 45 ksi. During operation, the wing bends and there is an additional far field axial stress in the skin of ax = 20 ksi. Note: when a press fit fastener is inserted, the stress concentration in a hole is greatly reduced. Take the fastener stress concentration factor to be K = 1 here. a. What and where are the greatest principal stresses around the hole without a fastener? (5 points) b. What and where are the greatest principal stresses around the hole with a fastener? (10 points) c. Does the material yield under a von Mises yield criterion in either case. (10 points) d. Why might it be advantageous to include press fit rivets (vs loose fasteners)? (10 points) Upper surface of sleeve Clearance-fit A2aA Lower surface of bolt head 6 Interference-fit Bolt Sleeve 6 a 6 ax

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