Cantilever beam deflection with point mass and point load at the end

[koolraj09]

TL;DR Summary

Hi all,
I was looking for help with obtaining deflection at end of a cantilever beam with point load at end as well as point mass at the same location. I believe it would be exactly same. Pardon me for the not so great handwriting and sketches :)

Hi all,
I was looking for help with obtaining deflection at end of a cantilever beam with point load at end as well as point mass at the same location. I believe it would be exactly same. Is this correct? That is, I think just adding point mass at the cantilever's end wouldn't change the deflection (=PL^3/3EI). Since we're just considering a point mass at the end and neglecting the effect of gravity (ex: consider the beam is bending is happening in a horizontal plane with loading mentioned). The reason is the just adding point mass wouldn't affect the flexural stiffness theoretically. Hence all the contribution to the deflection will only be from the point load at the end. I simulated the same in Ansys with Beam 188 element and ran for both cases 1. Beam with only point load (deflection (=PL^3/3EI) and 2. Beam with same point load at the end but added a mass of say 50lb. The results say that the deflection at the end of the beam is exactly the same. I believe this does make sense. Any help to derive/prove the same from first principles would also be great.

 

[FEAnalyst]

If you neglect gravity then of course the point mass will have no impact on the deflection. In FEA software you have to enable gravity to make point masses work. Static analyses (with gravity) account for point masses by simply turning them into concentrated forces. In case of dynamic (modal) analyses, added mass plays more important role, impacting the dynamic response of the system. For example natural frequencies of cantilever beam won't be different with point load (ignoring preload effects) but they will be different with point mass at the end.

 

[Lnewqban]

I fully agree with FEAnalyst's post above.
For static load, neither the mass of the beam nor the one at the extreme would be relevant.
If vibration is expected, the location and magnitude of the center of mass of the system would change; therefore, its response to load would change respect to no-end-mass condition.

 

[koolraj09]

Thanks FEAnalslyst and Lnewqban for your responses confirming my understanding.
I agree if it were a vibration problem then the point mass at end would contribute to inertia and lead to different natural frequencies. Thanks again