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MECHANICS OF SOLIDS (EM 319) FINAL EXAM Spring 1996 Monday, May 13th, 2:00 p.m. - 5:00 p.m., GEA 105 Closed Book 8.5" x 11" equation sheet [--I indicates maximum possible score for each question NAME: Section: (circle one) W: 5-7 W: 7-9 1 [15]. The conical tank shown below holds a fluid of density, p (mass/unit volume). The apex angle of the tank is 2a and the fluid depth is h. The wall thickness of the tank is t and is such that the tank can be considered to be a thin-walled structure. Find expressions for the hoop stress and longitudinal stress in the wall of the structure as a function of y, the distance from the apex. Neglect the weight of the structure. -. 2 [15]. A bimaterial beam subjected to a uniform bending moment M deforms to a circular arc of curvature K. The axial normal strain is continuous throughout the thickness and is given by E, = - KY. (a) Use an equilibrium argument to show that the neutral axis is given by (b) Similarly, show that the curvature (c) The wood beam (El = 1.5 x lo6 psi, hl = 7.5 in) shown below has an allowable tensile and compressive stress of 1 ksi. By itself, the wood cannot withstand the uniform moment, Mo, that must be carried by the structure. A steel reinforcement is being considered that has a thickness of 0.25 in. The steel modulus Ez = 30 x 106 psi and its allowable tensile and compressive strength is 12 ksi. Determine how wide the steel should be so that the allowable stresses in the steel and wood are reached simultaneously. 3 [20]. A radio antenna protrudes 540mm above an airplane fuselage. In addition to being built-in to the fuselage, it is supported by a guy wire. The loading on the antenna is the drag force which acts opposite to the flight direction. The drag force D is uniformly distributed as qo (N/m) along the antenna. (a) Determine the tension in the guy wire that minimizes the magnitude of the bending moment in the antenna. [Hint: Sketch the bending moment diagram for various wire tensions, paying particular attention to the bending moment at the built-in end and the minimum bending moment]. (b) Determine the locations and magnitude of the highest normal stress (tensile or compressive) in the antenna under the same conditions as in (a). The antenna is a solid rod with a 25mm diameter. (c) Determine the maximum deflection of the antenna under the conditions established in (a). iuy wire Fly this way, please 4 [lo]. The structure shown below has a gap, 6, at B prior to loading. The distributed load, go, is sufficient to cause contact at B. Find the reactions, axial force in CB and the deflection at C in terms of go, L and E1ll. Take E l l l = 5E212= 2 ~ 4 6=7qoL l(80 EII1) You may make use of the following solutions: 4 ~