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Consider the case of shafts subjected to bending moment only. Figure Q2 shows a pair of wheels of a railway wagon that carries a load of 50kN on each axle box, acting at a distance of 100 mm outside the wheel base. The gauge of the rails is 1.4m.

Consider the case of shafts subjected to bending moment only. Figure Q2 shows a pair of wheels of a railway wagon that carries a load of 50kN on each axle box, acting at a distance of 100 mm outside the wheel base. The gauge of the rails is 1.4m.

Mechanics of Materials (MindTap Course List)
Mechanics of Materials (MindTap Course List)
9th Edition
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Barry J. Goodno, James M. Gere
Chapter7: Analysis Of Stress And Strain
Section: Chapter Questions
Problem 7.2.17P: A simply supported beam is subjected to point load P at mid-span. The normal stress on an element at...
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Consider the case of shafts subjected to bending moment only.

Figure Q2 shows a pair of wheels of a railway wagon that carries a load of 50kN on each axle box, acting at a distance of 100 mm outside the wheel base. The gauge of the rails is 1.4m.

Figure Q2

If the stress is not to exceed 100MPa, find,

  1. the diameter of the axle between the wheels, and
  2. if a hollow circular shaft is to be used in place of the solid shaft, find the inside and outside diameter when the ratio of inside to outside diameter is 0.5.
Attachment Q2 Shafts Subjected to Bending Moment Only When the shaft is subjected to a bending moment only, then the maximum stress (tensile or compressive) is given by the bending equation. We know that м ..(i) ...(1) I y where M = Bending moment, I = Moment of inertia of cross-sectional area of the shaft about the axis of rotation, O, = Bending stress, and y = Distance from neutral axis to the outer-most fibre. We know that for a round solid shaft, moment of inertia, d I = 64 -× d* and y = 2 Substituting these values in equation (î), we have M M= 32 d or 64 From this equation, diameter of the solid shaft (d) may be obtained. We also know that for a hollow shaft, moment of inertia, [d.)* - (4,)*] = (d." (1 – k*) ..(where k= d;/ d,) %3D 64 and y = d/2 Again substituting these values in equation (i), we have м X Og (d,)³ (1 – k*) M= d. (d)* (1 – k*) or 32 64 2 From this equation, the outside diameter of the shaft (d) may be obtained.
Transcribed Image Text:Attachment Q2 Shafts Subjected to Bending Moment Only When the shaft is subjected to a bending moment only, then the maximum stress (tensile or compressive) is given by the bending equation. We know that м ..(i) ...(1) I y where M = Bending moment, I = Moment of inertia of cross-sectional area of the shaft about the axis of rotation, O, = Bending stress, and y = Distance from neutral axis to the outer-most fibre. We know that for a round solid shaft, moment of inertia, d I = 64 -× d* and y = 2 Substituting these values in equation (î), we have M M= 32 d or 64 From this equation, diameter of the solid shaft (d) may be obtained. We also know that for a hollow shaft, moment of inertia, [d.)* - (4,)*] = (d." (1 – k*) ..(where k= d;/ d,) %3D 64 and y = d/2 Again substituting these values in equation (i), we have м X Og (d,)³ (1 – k*) M= d. (d)* (1 – k*) or 32 64 2 From this equation, the outside diameter of the shaft (d) may be obtained.
Question.02 Attachment Q2 refers. Consider the case of shafts subjected to bending moment only. Figure Q2 shows a pair of wheels of a railway wagon that carries a load of 50kN on each axle box, acting at a distance of 100 mm outside the wheel base. The gauge of the rails is 1.4m. 50 kN 50 kN 100 mm- 1.4 m 100 mm A B Rc Rp Figure Q2 If the stress is not to exceed 100MP,, find, a) the diameter of the axle between the wheels, and b) if a hollow circular shaft is to be used in place of the solid shaft, find the inside and outside diameter when the ratio of inside to outside diameter is 0.5.
Transcribed Image Text:Question.02 Attachment Q2 refers. Consider the case of shafts subjected to bending moment only. Figure Q2 shows a pair of wheels of a railway wagon that carries a load of 50kN on each axle box, acting at a distance of 100 mm outside the wheel base. The gauge of the rails is 1.4m. 50 kN 50 kN 100 mm- 1.4 m 100 mm A B Rc Rp Figure Q2 If the stress is not to exceed 100MP,, find, a) the diameter of the axle between the wheels, and b) if a hollow circular shaft is to be used in place of the solid shaft, find the inside and outside diameter when the ratio of inside to outside diameter is 0.5.
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