Impact loading on a massed beam

[tjbr]

Hey guys, I've got a problem that I have been puzzling over for a long time now.

If I have a beam, which has no mass, and a weight is dropped onto the centre of the beam, then the deflection is easy to work out, we let the strain energy of the beam equal the potential energy of the mass:

1/2 P*delta = mg(h + delta)

and delta = PL^3/(48 EI)

However, if we say that the beam did have a mass, how would this effect the deflection? I was reasoning that the potential energy would be turned into kinetic energy when it hits the mass, however, when the beam is at its greatest deflection, the kinetic energy = 0.

So does this mean that the weight of a beam plays no part in the deflection caused by dropping a mass onto it? It seems backwards to think so, so I'm a bit puzzled here.

 

[eljose79]

Hi there,

First of all, it's great that you've been thinking about this problem and trying to understand it better. I can tell you that curiosity and questioning are important traits to have.

To answer your question, the weight of the beam does play a role in the deflection caused by dropping a mass onto it. The concept you are referring to is called "dynamic loading," where the sudden impact of the mass onto the beam causes a temporary increase in the load on the beam. This can result in a larger deflection than what would occur with just the weight of the mass.

To fully understand the effect of dynamic loading, we need to take into account the mass of the beam and its stiffness, or ability to resist deformation. This is where the concept of "natural frequency" comes into play. Every object has a natural frequency, which is the frequency at which it will vibrate most easily. In the case of a beam, this frequency is affected by its mass and stiffness.

When a mass is dropped onto the beam, it causes the beam to vibrate at its natural frequency. This vibration can result in a larger deflection than what would occur with just the weight of the mass. This is because the beam is now experiencing both the weight of the mass and the added force of the dynamic load.

To calculate the deflection in this scenario, we would need to use a different equation that takes into account the mass and stiffness of the beam, as well as the natural frequency. This equation would be more complex than the one you mentioned in your post.

I hope this helps to clarify things for you. Keep asking questions and exploring new ideas – that's how we make progress in science!

 

[astrokreng]

I can provide some insights into the impact loading on a massed beam. First, it is important to note that the deflection of a beam under impact loading is a complex phenomenon and cannot be accurately predicted using simple equations. This is because the behavior of the beam is affected by various factors such as the material properties, geometry, and boundary conditions.

In the case of a massed beam, the weight of the beam does play a role in the deflection caused by dropping a mass onto it. This is because the weight of the beam adds to the total load on the beam, which affects its deflection. Additionally, the mass of the beam also affects its stiffness, which in turn affects the deflection.

Furthermore, when a mass is dropped onto the beam, the kinetic energy is not completely converted into potential energy. Some of the energy is dissipated as heat due to internal stresses and deformations in the beam. This dissipation of energy also affects the deflection of the beam.

To accurately predict the deflection of a massed beam under impact loading, advanced techniques such as finite element analysis or experimental testing may be required. These methods take into account the complex behavior of the beam and provide more accurate results.

In conclusion, the weight of a beam does play a role in its deflection under impact loading. It is important to consider all factors, including the mass and material properties of the beam, to accurately predict its behavior.