- #1

koolraj09

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- 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.

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.