Problem 1: 25 points A gear train is driven by a motor at A (See Figure...

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Problem 1: 25 points A gear train is driven by a motor at A (See Figure 1.1) that generates a power of 8 kW. This power is transmitted using a steel shaft AD and consumed by two gears at B and C, which produce resisting torques T and T with the senses shown in the figure. Note that the steel shaft AD has a uniform diameter (dAD) from A to D and rotates at a constant angular velocity (@AD). The shaft AD must satisfy two design requirements: 1) AD 1.8 (AD is the angle of twist between A and D) and 2) Tallow = 62 MPa (TAllow is the allowable shear stress for the steel shaft AD). Take 2LAB = LBC = 3LCD = 0.6 m, TB = 300 N-m, Tc = 500 N-m, and Gst = 77 GPa (Gst is the shear modulus of steel). a) Find the angular velocity (@AD) of the shaft AD. b) Draw the torsion moment diagram of the shaft AD from A to D. c) Determine the minimum d that satisfies the two design requirements stated above. d) Using the minimum dD from c), determine the maximum shear stress in each segment of the shaft AD (i.e., find Tmax in segments AB, BC, and CD). TB Tc LAB LBC LCD+ Problem 1: 25 points A gear train is driven by a motor at A (See Figure 1.1) that generates a power of 8 kW. This power is transmitted using a steel shaft AD and consumed by two gears at B and C, which produce resisting torques T and T with the senses shown in the figure. Note that the steel shaft AD has a uniform diameter (dAD) from A to D and rotates at a constant angular velocity (@AD). The shaft AD must satisfy two design requirements: 1) AD 1.8 (AD is the angle of twist between A and D) and 2) Tallow = 62 MPa (TAllow is the allowable shear stress for the steel shaft AD). Take 2LAB = LBC = 3LCD = 0.6 m, TB = 300 N-m, Tc = 500 N-m, and Gst = 77 GPa (Gst is the shear modulus of steel). a) Find the angular velocity (@AD) of the shaft AD. b) Draw the torsion moment diagram of the shaft AD from A to D. c) Determine the minimum d that satisfies the two design requirements stated above. d) Using the minimum dD from c), determine the maximum shear stress in each segment of the shaft AD (i.e., find Tmax in segments AB, BC, and CD). TB Tc LAB LBC LCD+