A pulley is keyed to a shaft midway between two bearings. The shaft is made of cold drawn steel for which the ultimate strength is 500 MPa and the yield strength is 450 MPa. The bending moment at the pulley varies from – 150 N-m to + 400 N-m as the torque on the shaft varies from – 50 N-m to + 150 N-m. Obtain the diameter of the shaft for an indefinite life. The stress concentration factors for the keyway at the pulley in bending and in torsion are 1.6 and 1.3 respectively. Take the following values: Factor of safety = 1.5; Load correction factors = 1.0 in bending and 0.6 in torsion Size effect factor = 0.85; Surface effect factor = 0.88

4) A stepped steel shaft, shown below, is used in a spur gear reducer. The shaft is subjected to a constant axial stress (A=40 MPa), a constant bending stress due to loads by bearings and gears (M=60 MPa), and a steady torque (T=80 MPa) during shaft rotation. Neglect the stress concentration factors (we will cover this next week) that result from the stepped shaft geometry. The shaft is made of steel with Su=1006 MPa, Sy=648 MPa, and HB-229. The size of the shaft results in a gradient factor of CG=0.9. The shaft has a fine-ground finish. A 95% reliability is required. Calculate the safety factor relative to infinite life (106 cycles). If the safety factor is less than one (i.e., shaft fails), find the number of cycles to failure. (60) M d M

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A section of a rotating shaft is under an alternating bending moment of 70Nm and a torque of 35Nm. The yield strength of the material is 560 MPa and the ultimate tensile strength of the material is 700 MPa. The estimated actual endurance strength is assumed to be 210 MPa and the stress concentration factor is 1.5 for well rounded fillet. (Design Factor = 2) Determine the minimum diameter of the section of the shaft: D =  mm

Design a suitable wire rope to lift a load of 13 kN of debris from a well 70 m deep. The rope should have a factor of safety equal to 6. The weight of the bucket is 7.5 kN. The load is lifted with a maximum speed of 150 m/min which is attained in 1 second. Find also the stress induced in the rope due to starting with an initial slack of 250 mm. The average tensile strength of the rope may be taken as 590 d2 Newtons (where d is the rope diameter in mm) for 6 x 19 wire rope. The weight of the rope is 18.5 N/m. Take the diameter of the wire (dw) = 0.063d and area of rope A = 0.38 d2.

You are designing a driveshaft for a motor from a material with G = 15,000 ksi. The specifications for the project require a solid shaft to be used. Based on the location of the motor, the driveshaft has a length L = 9.55 ft. The motor provides 67 hp at a rotation rate of 2475 rpm.Your design requires φ ≤ 0.905° over the length of the shaft. Additionally, the maximum shear stress in the material τmax ≤ 4.0 ksi.Determine rmin, the minimum radius