Design of a shaft subject to torsion/bending/fatigue

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SUMMARY

The discussion revolves around the design of a shaft subjected to torsion, bending, and fatigue. The user, Dan, has successfully created a Free Body Diagram (FBD) and calculated reaction forces at bearings, deducing a torque force 'F' of 1.1 kN and reaction forces at supports A and B. Dan seeks clarification on calculating the equivalent bending moment and torque to determine an appropriate shaft diameter, specifically asking about the maximum bending moment (Mmax) and the torque force (T) to use in his calculations.

PREREQUISITES
  • Understanding of Free Body Diagrams (FBD)
  • Knowledge of shear force and bending moment diagrams
  • Familiarity with torsion and bending stress calculations
  • Basic principles of fatigue analysis in mechanical design
NEXT STEPS
  • Research how to calculate equivalent bending moments using the formula Me= 0.5[ Mmax +[Mmax^2+T^2]^0.5 ]
  • Learn about determining maximum bending moments (Mmax) from bending moment diagrams
  • Study the relationship between torque and bending moments in shaft design
  • Explore methods for calculating shaft diameter based on torsion and bending stress
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This discussion is beneficial for mechanical engineers, students studying mechanical design, and professionals involved in shaft design and analysis under torsional and bending loads.

danz001
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I have attached the design task I have been given and I am unsure as to what to do next! I will explain that which I have done so far and if anyone can point me in the appropriate direction that would be greatly appreciated!
1. I have created a Free body diagram (FBD), and drawn in the unknown two reaction forces at bearings and the torques where known.
2. For the unknown torque force 'F' I have assumed there is no net torque for the system, and stating my positive Z direction and using T=(f2-f1)xr, have deduced that F=1.1KN
3.I have then gone back to my FBD and drawn in the newly calculated force, and by considering moments through the first bearing support A and deduced the reaction force at B is 5.877KN. Using the sum of Y forces = 0, I could then calculate for at A=6.023KN.
4. I then drew my shear force diagram, followed by my bending moment and torque diagrams!

Now I am stuck!
I am lead to believe that I must use the relevant equivalent bending moment and torque diagrams, and tau, sigma and twist rate values calulate a suitable diameter for the shaft.
Where:
Me= 0.5[ Mmax +[Mmax^2+T^2]^0.5 ]
Te=[Mmax^2+T^2]^0.5
Is my Mmax value simply deduced from my highest value on my BM diagram, and what T force do use?
I'm not sure if these questions are rather elementary, apologies if that is the case!
Many thanks
Dan
 
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