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How can I calculate the deflection of a Cantilever beam if there is a load at different points on the beam? My current scenario is the following → I have a ruler that I have modelled to be cantilever and I am moving a piece of blu-tac down the ruler to calculate different resonance frequencies. Is there a formula relating the position of blu tac and deflection? Or any relationship between this and its centre of gravity

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  • $\begingroup$ You have used the tag for resonance but your question is asking about deflection of the beam. $\endgroup$ – sammy gerbil Mar 15 at 20:47
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The theoretical method is

  • Draw the shear force and bending moment diagram for the beam with the point load
  • Calculate the curvature at any point from the bending moment
  • Integrate the curvature twice to get the deflection

You should find this in any textbook on "strength of materials" with a section on beam bending.

The practical method is find a beam calculator program on the internet that does the calculations for you!

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  • $\begingroup$ Is there a given formula I can work out using this method? $\endgroup$ – Rohan Mar 15 at 15:05
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Based on structx.com formula here:

https://structx.com/Beam_Formulas_017.html

This is the formula:

Fixed Both Ends Beam - Point Load at Any Point

There is fomula for other types (like cantilever etc as well):

https://structx.com/beams.html

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