exam2 - The members have the elastic moduli given above...

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ME 246 In-term exam 2, 2.11.2009, 110 minutes Notes: a) Draw figures (free-body diagrams and other helpful diagrams) as necessary and indicate quantities clearly. b) Show your axes . c) Indicate units . d) Write neatly. Make sure what you write is readable . ------------------------------------------------------------------------------------------------------------------------------------------ 1) (20 pts.) The two circular rod segments of different materials are fixed to the rigid walls such that there is a gap of 0.1 mm between them when T 1 =15 ° C. Each rod has a DIAMETER of 30 mm, α al =23x10 -6 m/m/ ° C, α cu =17x10 -6 m/m/ ° C, E al =70 GPa, E cu =126 GPa. a) Determine the average normal stress in each rod if T 2 =135 ° C. b) Calculate the new length of the aluminum segment. 2) (20 pts.) The two pipes of different materials are connected as shown. Member BC is aluminum and CD is copper. The cross- sectional area of BC is A and that of CD is 2A.
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Unformatted text preview: The members have the elastic moduli given above. Determine the reactions at B and D when a force P is applied at the junction C. 3) (20 pts.) Knowing that a force P of magnitude 50 kN is required to punch a hole of diameter d=20 mm in an aluminum sheet of thickness t=5 mm, determine the average shearing stress in the aluminum at failure. 4) (20 pts.) Rotation is prevented at the lower end (at B and D) of each shaft. A torque of T=75 N.m is applied to end A of shaft AB. G= 80 GPa for both shafts. The upper plate does not pose any resistance to rotation of the shafts at A and C. Determine a) the maximum stress in shaft CD, b) the angle of twist at C. 5) (20 pts.) The stepped shaft shown must transmit 40 kW at a speed of 720 rpm. Determine the minimum radius of the fillet if an allowable stress of 50 MPa is not to be exceeded....
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