The shaft shown the figure below, is supported by a bearing on the left end. The shaftalso supports a pulley on the right end, which rotates. The tensions in the belt of thepulley are F =2,739 y and F,=1,362 N. Also, a completely reversed axial load of F =11 N is applied to the right end. The shaft is made of UNS G10450 CD steel, withground surface and 99 % reliability and operates at room temperature. Assume,K =1.35 for torque and formula 6– 34 to calculate KtsK, - 11+ va/VrK, = 1 +(6-34)Bending or axial:Va = 0.246 – 3.08(10~)S, + 1.51(10-)S, – 2.67(10~*)$, 50 s S, S 250 kpsiVa = 1.24 – 2.25(10)S, + 1.60(10-“)S, – 4.11(10-10,s,340 < S S 1700 MPa(6-35)Torsion:Va = 0.190 – 2.51(10)S + 1.35(10~³)s, – 2.67(10**)s, 50 < S., S 220 kpsiVa = 0.958 – 1.83(10~³)S, + 1.43(10-6)S, – 4.11(10-19)S, 340 < S S 1500 MPa(6-36)All fillet radius r=0.1dAll dimensions are in mm-3000-30-25-Fa2个1006001. Identify the critical point(s) on the shaft and show it clearly on the diagram.2. Draw the cartesian coordinate system and identify all the components of stresses at the criticalpoint(s) according to the cartesian coorduinate system.3. Calculate the resultant amplitude of stress.4. Calculate the resultant mean stress.5. Calculate the six Marin factors and endurance limit for the shaft.6. Utlize Gerber theory and estimate the fatigue factor of safety.7. Calculate the maximum stress and estimate the yield factor of safety.8. WIII the shaft fail?9. Calculate the life of the shaft.

The shaft shown the figure below, is supported by a bearing on the left end. The shaft also supports a pulley on the right end, which rotates. The tensions in the belt of the pulley are F =2,739 y and F,= 1,362 N. Also, a completely reversed axial load of F 11 N is applied to the right end. The shaft is made of UNS G10450 CD steel, with %3D ground surface and 99 % reliability and operates at room temperature. Assume, K =1.35 for torque and formula 6– 34 to calculate K .: K, - 1 K, = 1 + 1+ Va/ Vr (6-34) Bending or axial:

The shaft shown the figure below, is supported by a bearing on the left end. The shaft also supports a pulley on the right end, which rotates. The tensions in the belt of the pulley are F =2,739 y and F,= 1,362 N. Also, a completely reversed axial load of F 11 N is applied to the right end. The shaft is made of UNS G10450 CD steel, with %3D ground surface and 99 % reliability and operates at room temperature. Assume, K =1.35 for torque and formula 6– 34 to calculate K .: K, - 1 K, = 1 + 1+ Va/ Vr (6-34) Bending or axial:

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter11: Columns

Section: Chapter Questions

Problem 11.2.4P: Repeat Problem 11.2-3 assuming that R= 10 kN · m/rad and L = 2 m.

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Concept explainers

Combined Loading

Any functioning component, such as machine parts, structural members, pressure vessels, and so on, are all under the influence of more than one force. When anybody is under the influence of more than one force such as shear forces, bending moments, axial forces, torsion, and so on, then such body is said to be under combined loading. A very practical example of combined loading is the crankshaft of an internal combustion engine (IC engine). The crankshaft of the IC engine is under high rpm, which is caused due to the torsional forces. Due to the presence of piston, counterbalances, and internal imbalances, the crankshaft experiences lateral forces and due to the rise in temperature, the crankshaft undergoes thermal expansion, which pulls the crankshaft along the axial direction and lateral direction. The presence of unbalanced loads along the periphery of the crankshaft also induces a bending moment.

Question

The shaft shown the figure below, is supported by a bearing on the left end. The shaft
also supports a pulley on the right end, which rotates. The tensions in the belt of the
pulley are F =2,739 y and F,=1,362 N. Also, a completely reversed axial load of F =
11 N is applied to the right end. The shaft is made of UNS G10450 CD steel, with
ground surface and 99 % reliability and operates at room temperature. Assume,
K =1.35 for torque and formula 6– 34 to calculate K
ts
K, - 1
1+ va/Vr
K, = 1 +
(6-34)
Bending or axial:
Va = 0.246 – 3.08(10~)S, + 1.51(10-)S, – 2.67(10~*)$, 50 s S, S 250 kpsi
Va = 1.24 – 2.25(10)S, + 1.60(10-“)S, – 4.11(10-10,s,
340 < S S 1700 MPa
(6-35)
Torsion:
Va = 0.190 – 2.51(10)S + 1.35(10~³)s, – 2.67(10**)s, 50 < S., S 220 kpsi
Va = 0.958 – 1.83(10~³)S, + 1.43(10-6)S, – 4.11(10-19)S, 340 < S S 1500 MPa
(6-36)
All fillet radius r=0.1d
All dimensions are in mm
-3000
-30
-25-
Fa
2个
100
600
1. Identify the critical point(s) on the shaft and show it clearly on the diagram.
2. Draw the cartesian coordinate system and identify all the components of stresses at the critical
point(s) according to the cartesian coorduinate system.
3. Calculate the resultant amplitude of stress.
4. Calculate the resultant mean stress.
5. Calculate the six Marin factors and endurance limit for the shaft.
6. Utlize Gerber theory and estimate the fatigue factor of safety.
7. Calculate the maximum stress and estimate the yield factor of safety.
8. WIII the shaft fail?
9. Calculate the life of the shaft.

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