1) A stepped steel shaft, shown below, is used in a spur gear reducer. The shaft is subjected to aconstant axial stress (A=40 MPa), a constant bending moment that results in a variable stress (M=60MPa) due to loads by bearings and gears, and a steady torque (T-80 MPa). However, these stressvalues do not take into account stress concentration factors. The shaft has a D=45 mm, d=30 mm,and r=6 mm, resulting in kr,bend=1.34, Kr,axial=1.48, and kf,tor 1.2. The shaft is made of steel withS₁=1006 MPa, S,=648 MPa, and H₂=229. The size of the shaft results in a gradient factor of CG=0.9.The shaft has a fine-ground finish. A 90% reliability is required. Verify the stress concentrationfactors are correct for this shaft geometry. Calculate the safety factor relative to infinite life (105cycles). If the safety factor is less than one (i.e., shaft fails), find the number of cycles to failure.(60)M

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 moment that results in a variable stress (M=60 MPa) due to loads by bearings and gears, and a steady torque (T=80 MPa). However, these stress values do not take into account stress concentration factors. The shaft has a D=45 mm, d=30 mm, and r=6 mm, resulting in ki,bend=1.34, Kraxial 1.48, and k₁,tor 1.2. The shaft is made of steel with S,=1006 MPa, S,=648 MPa, and H₂=229. The size of the shaft results in a gradient factor of CG=0.9. The shaft has a fine-ground finish. A 90% reliability is required. Verify the stress concentration factors are correct for this shaft geometry. 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.

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 moment that results in a variable stress (M=60 MPa) due to loads by bearings and gears, and a steady torque (T=80 MPa). However, these stress values do not take into account stress concentration factors. The shaft has a D=45 mm, d=30 mm, and r=6 mm, resulting in ki,bend=1.34, Kraxial 1.48, and k₁,tor 1.2. The shaft is made of steel with S,=1006 MPa, S,=648 MPa, and H₂=229. The size of the shaft results in a gradient factor of CG=0.9. The shaft has a fine-ground finish. A 90% reliability is required. Verify the stress concentration factors are correct for this shaft geometry. 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.

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter3: Torsion

Section: Chapter Questions

Problem 3.3.15P: A hollow steel shaft used in a construction auger has an outer diameter d2= 6.0 in. and inner...

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