1. The rocket below consists of two thin-walled cylinders stacked on top of each other. The...

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1. The rocket below consists of two thin-walled cylinders stacked on top of each other. The top and bottom of the rocket is initially fixed. For the entire rocket, E = 70 GPa, v = 0.3, and a = 26 10-6/C. (For a thin-walled cylinder, the cross-sectional area is approximately Dt, where D is the mean diameter and t is the thickness.) 1 D = 200 mm (mean diameter) t = 3 mm (thickness) L = 500 mm 2 D = 200 mm (mean diameter) t = 2 mm (thickness) L = 500 mm (i) The rocket experiences a 10C internal temperature increase. Calculate the resulting reactions at the two supports. (Note: The cylinders are not pressurized at this point.) (ii) The top tank now is pressurized. Determine the gauge pressure that results in zero axial stress in the top tank, assuming that the reactions are kept the same as in part (i). If you did not get an answer for part (i), assume compressive reaction forces of 15 kN applied by both the top and bottom supports. (Note: This is not the correct answer.) (iii) The bottom tank is now pressurized to the same gauge pressure as the top tank, and the top and bottom constraints are removed. If the hoop stress in either tank should not exceed 200 MPa, what is the safety factor for this system? If you did not get an answer for part (ii), use a pressure of 1 MPa. (Note: This is not the correct answer.) (iv) Assume a Cartesian coordinate system such that y points to the left, x points out of the page, z is aligned with the long centroidal axis of the structure, and the origin is placed at the top of the structure. What is the stress state, in Cartesian coordinates, at x = 100, y = -100, z = 750 mm? (v) The entire rocket also now experiences a sudden internal torque of -10 N-m. What is the new stress state, in Cartesian coordinates, at x = 100, y 100, z = 750 mm? 1. The rocket below consists of two thin-walled cylinders stacked on top of each other. The top and bottom of the rocket is initially fixed. For the entire rocket, E = 70 GPa, v = 0.3, and a = 26 10-6/C. (For a thin-walled cylinder, the cross-sectional area is approximately Dt, where D is the mean diameter and t is the thickness.) 1 D = 200 mm (mean diameter) t = 3 mm (thickness) L = 500 mm 2 D = 200 mm (mean diameter) t = 2 mm (thickness) L = 500 mm (i) The rocket experiences a 10C internal temperature increase. Calculate the resulting reactions at the two supports. (Note: The cylinders are not pressurized at this point.) (ii) The top tank now is pressurized. Determine the gauge pressure that results in zero axial stress in the top tank, assuming that the reactions are kept the same as in part (i). If you did not get an answer for part (i), assume compressive reaction forces of 15 kN applied by both the top and bottom supports. (Note: This is not the correct answer.) (iii) The bottom tank is now pressurized to the same gauge pressure as the top tank, and the top and bottom constraints are removed. If the hoop stress in either tank should not exceed 200 MPa, what is the safety factor for this system? If you did not get an answer for part (ii), use a pressure of 1 MPa. (Note: This is not the correct answer.) (iv) Assume a Cartesian coordinate system such that y points to the left, x points out of the page, z is aligned with the long centroidal axis of the structure, and the origin is placed at the top of the structure. What is the stress state, in Cartesian coordinates, at x = 100, y = -100, z = 750 mm? (v) The entire rocket also now experiences a sudden internal torque of -10 N-m. What is the new stress state, in Cartesian coordinates, at x = 100, y 100, z = 750 mm?