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

• koolraj09
In summary, the conversation discusses the impact of adding a point mass at the end of a cantilever beam with a point load at the same location. The discussion concludes that neglecting gravity, the point mass will have no impact on the deflection. However, in dynamic analyses, the added mass plays a more important role in the system's response to load. The conversation also touches on the relevance of the beam's mass and the center of mass in relation to vibration problems. Overall, the participants agree that the point mass at the end of the beam would contribute to inertia and potentially affect the natural frequencies.
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.

#### Attachments

• IMG_20200524_131045.jpg
75.1 KB · Views: 327
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.

koolraj09 and 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

Lnewqban

## 1. What is a cantilever beam?

A cantilever beam is a type of structural element that is supported at only one end, with the other end projecting into space. It is commonly used in construction and engineering to support loads and resist bending forces.

## 2. How does a point mass affect the deflection of a cantilever beam?

A point mass, also known as a concentrated load, is a single force applied at a specific point on a beam. The presence of a point mass at a certain location on a cantilever beam will cause the beam to bend and deflect at that point, depending on the magnitude and direction of the force.

## 3. What is the equation for calculating deflection in a cantilever beam with a point mass?

The equation for calculating deflection in a cantilever beam with a point mass is:
δ = (PL^3)/(3EI) + (Mx^2)/(2EI)
where δ is the deflection at a given point, P is the point load, L is the length of the beam, E is the modulus of elasticity, I is the moment of inertia, M is the point moment, and x is the distance from the fixed end.

## 4. How does a point load at the end of a cantilever beam affect its deflection?

A point load at the end of a cantilever beam will cause the beam to deflect downwards at the point of the load. The magnitude and direction of the deflection will depend on the magnitude and direction of the load, as well as the properties of the beam.

## 5. What are some practical applications of analyzing cantilever beam deflection with point mass and point load at the end?

This type of analysis is commonly used in engineering and construction to design and optimize structures such as bridges, buildings, and cranes. It can also be applied in other fields such as biomechanics to study the behavior of bones and joints under different loads.

• Mechanical Engineering
Replies
6
Views
943
• Mechanical Engineering
Replies
9
Views
2K
• Mechanical Engineering
Replies
15
Views
1K
• Engineering and Comp Sci Homework Help
Replies
3
Views
453
• Mechanical Engineering
Replies
8
Views
1K
• Mechanical Engineering
Replies
8
Views
3K
• Mechanical Engineering
Replies
5
Views
4K
• Mechanical Engineering
Replies
5
Views
7K
• Mechanical Engineering
Replies
10
Views
1K
• General Engineering
Replies
8
Views
1K