1. Consider two solid circular shafts connected by 5-cm and 25-cm-pitch- ø gears as shown in the figure. Find the angular rotation of D, the right end of one shaft, with respect to A, the left end of the other, caused by the torque of 280 N-m applied at D. The left shaft is steel for which G = 80 GPa and the right is brass for which G = 33 GPa. (all answers should be in rad)

The two solid shafts are connected by the gears shown. The motor constantly supplies 20 kW of power at 15 Hz to system at A. The yield shear stress is 140 MPa for shaft (1) and 220 MPa for the shaft (2), and over all factor of safety is 2. a) Find the diameter of both shafts. b) If the modulus of rigidity of shaft (2) G is 77.2 GPa, calculate the relative angle of twist D with respect to C. 30 teeth B (1) 48 teeth Tp 0.8 m

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A solid 0.64-in.-diameter shaft is subjected to the torques shown. The bearings shown allow the shaft to turn freely. Determine the shear stress magnitude in shaft (1). 10 lb-ft 50 lb-ft 70 Ib-ft | (1) 30 lb-ft A (3) B D 3150 psi O 2524 psi 1876 psi O 2331 psi O 2932 psi

Problem 3

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600 Nm An aluminum shaft with a constant diameter of 50 mm is loaded by torques applied to gears attached to it as shown in Figure. Using G = 28 GPa, determine the relative angle of twist of gear D relative to 900 Nm 1100 Nm 2 m 800 N-m gear A. 3m 2 m

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The two solid steel shafts shown in the figure are connected together using gear wheels. The length of the CD shaft is Lcd=2 m and the length of the AB shaft is LAB= 1.5 m. The radius of gear C is rc=45 mm and the radius of gear B is rB= 90 mm. The CD and AB shafts rotate freely in the bearings on which they are supported. Also, shaft AB is fixed at point A. Each shaft has a diameter of 20 mm and a shear modulus of G=65 GPa. When a torque of T= 450 N.m is applied to the CD shaft from the D end;a) Calculate the torsion angle on shaft AB. (Write your result in radians.)b) Calculate the total rotation (torsion angle) of the D end of the CD shaft. (Write your result in radians.)

Problem 2: Consider the two gears mounted on the shaft, as shown. Distances are L1 = 100 mm, L2 = 250 mm, and L3 = 175 mm. Diameter of shaft AB is 15 mm, diameter of shaft BC is 20 mm, and diameter of shaft CD is 17.5 mm. Young's modulus for each portion is 200 GPa. Determine the displacement of point D with reference to point A. Also, determine the displacement of point A relative to C. b. Determine the axial strain at any point in shaft segments AB, BC and CD, respectively. If Poisson's ratio for the material of the shafts is v = 0.2, determine the lateral strain in each of the shaft segments. Based on your answers to part (a), do the gears move towards each other, or do they separate from each other? Note that in real gearboxes, movement of gears towards or away from each other is prevented by using thrust bearings. 10 kN 4 kN 5 kN 7 kN 4 kN NY 0I 17.