Multi-Section Beam Bending Calculations

[MaxOtis]

Hello all,

I have a shaft supported on both sides with a charge on each bearing, as shown on the following link: http://www.engineersedge.com/beam_bending/beam_bending4.htm

I need to calculate the shaft deflection with the formula provided on the website, but my shaft often have different section (ie Ø23 mm machined to Ø20 mm for the bearings). I am not too sure how to calculate a deflection since the Moment of Intertia will depend on the position.

Thank you very much for any help.

Max Otis

 

[Achy47]

Hello Max,

Thank you for sharing your question with the forum. I am happy to help you with your calculation for the shaft deflection.

Firstly, it is important to understand that the moment of inertia is a measure of an object's resistance to changes in rotation. In this case, it is related to the deflection of the shaft due to the applied forces. When the shaft has different sections, the moment of inertia will vary along the length of the shaft.

To calculate the deflection of the shaft, you will need to use the equation for deflection due to bending moment:

δ = (PL^3)/(3EI)

Where:
δ = deflection
P = applied load
L = length of the shaft
E = Young's modulus of the material
I = moment of inertia

To account for the varying moment of inertia, you will need to break the shaft into smaller sections and calculate the moment of inertia for each section. Then, you can use the equation above to calculate the deflection for each section and add them together to get the total deflection of the shaft.

Alternatively, you can use a finite element analysis software to accurately calculate the deflection of the shaft with varying sections. This method will take into account all the different variables and provide a more precise result.

I hope this helps you with your calculation. If you have any further questions, please feel free to ask. Good luck with your project!