Kinetic energy in container from falling beam

[nkclarke]

I need some help.

I'm carrying out a debris scenario analysis for a structure subject to seismic loading. To expand, there is a steel-framed loading bay that temporarily stores steel containers containing hazardous material before the containers are moved to a more permanent home inside a reinforced concrete structure. The RC structure is seismically qualified but the steel framed loading bay is not so in an earthquake, it is likely that some connections between structural steelwork could fail causing main or secondary members to fall onto one of the steel containers. I'm trying to determine the kinetic energy that a beam could impact the container with since I know the withstand of the container from FE analysis.

I've been asked to consider the following scenario and to provide hand-calcs to demonstrate:
A horizontal steel beam spans the width of the loading bay (LB) and is connected at each end to columns at each side of the LB. Assume that the connection at one end fails first. The beam will then rotate until the ductility of the remaining connection is reached - assume about 15 degrees, after which the remaining connection also fails. The problem then becomes a dynamics one but it seems beyond me. The beam will have an initial rotation after the first connection fails but after the second connection fails, the beam will then start to fall but it will also rotate as it falls due to the initial rotation about the remaining connection.

I'm a bit confused about how to go about trying to solve it. I can calculate the rotational velocity at the end that fails first but after the second connection fails, I lose the plot and am unsure how to continue. Will the angular velocity remain constant? Will it rotate about its centre of mass? I know it all boils down to a conservation of energy/conservation of momentum problem but I'd greatly appreciate some guidance from anyone who feels that they can discuss the problem with a bit more confidence than me. It's been quite a while since I studied dynamics.

Ultimately, I want to determine the kinetic energy that will be transferred into the steel container when it is impacted by the beam. I can provide more info as needed if anything is unclear or incomplete.

Thanks in advance.

 

[Ron]

You have enough variables here I'm not sure that a plausible solution exists.
If the first connection fails completely, it is likely that the second connection will fail by deformation in a different manner than the first and at a slower rate, thus reducing the dynamic effect of the beam falling. The chance of both connections failing simultaneously is low. The first failure would likely be a fastener failure while the second would likely fail by deforming the attachment clips.

In any case, only one side would fall at a time, thus producing an angular impact with the containers. The impact velocity would not likely be high; however, depending on the mass of the beam, the resulting "glancing" blow to the top of the container could produce a high point load that would damage the container or kick it to the side or both. I don't see a plausible modeling of this. You might need to model a dozen different scenarios, with a remaining likelihood that none of them would be an accurate depiction of the failure and collision.

Good luck!

 

[IDS]

Since you are concerned with kinetic energy, rather than the exact dynamics of the fall, I'd suggest calculating the maximum possible drop in the level of the centre of gravity of the beam, then calculate the loss of potential energy and deduct the energy required to deform the second connection through 15 degrees (or whatever failure deformation you end up with). The remaining energy will go into kinetic energy of the beam.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[grogannc]

One could solve this with a good explicit fea software; LS-DYNA would be a good one. But if you don't don't use it regularly, don't count on picking it up in a week or two. Outside of that; the only energy in the system sounds like potential energy at the beam height at rest. Since this potential energy is the only energy in the system it is equal to the kinetic energy. You could start with kinetic energy in the system and take it out as you go (i.e. some for the rotation, etc.) If you are trying to predict time and location with hand calcs I think you will dead end. My experience with several projects is the energy balance hand calcs are going to be off by 50-100% especially if you credit plasticity. Bottom line- do something conservative you are comfortable with. I've spent 3 years in a program at a former company studying similar problems and you won't get there with closed form hand calcs. Numerical methods are your best bet.

Good Luck-sounds like a fun problem.

 

[rb1957]

as i understand it, the connections are assumed to due due to external siesmic forces, and the beam is falling onto stuff below it. isn't it just a weight (the beam) falling, from a height ?

Quando Omni Flunkus Moritati

 

[grogannc]

Yes-that's how I would approach it if I just wanted a quick answer. Otherwise you will quickly have too many variables and time dependent impacts/loadings which is probably more than is required in this situation.

 

[BAretired]

The second connection may not fail at all. After one connection fails, the other could act as a hinge until the beam end strikes the ground or whatever is in its path.

BA

 

[nkclarke]

Thanks to all of you who have replied to my thread; I really appreciated your thoughts and ideas on how to approach this problem. There were a lot of good suggestions there. I think the bottom line is that it's not an easy problem. I'm trying to solve the problem by taking a dynamics approach using conservation of energy and making a few assumptions. It's a work in progress.

BTW, I accidentally re-posted this as another thread.