Kinetic energy and rorating beams

[nkclarke]

Hi,
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. 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.

 

[JAE]

I've had this type of problem presented to me before as well - (a roof that needed to be capable of withstanding an airliner impact from above).

The problem with all these types of impact calculations is that the energy transferred into your containers depends an awful lot on the "crunch stiffness" of the containers - i.e. you need to know the deceleration of the beam over time, which involves multiple variables, parameters, assumptions, etc. So you almost have to test the container to know how it responds to impact (think of all the highway bollards and guide rails that are field tested vs. calculated/designed).

I'm sure there might be info out there on this using differential equations, etc. but it would still be based on lots of assumptions.

For my roof, I ended up telling them that I couldn't design for an airliner impact - but I could guarantee that the roof would withstand three teenagers in a small Ford with a 12 pack of beer impacting the roof at a max. 37.5 degree angle at a speed not more than 45 mph.

 

[nkclarke]

Thanks JAE,

It's definitely not a closed-form solution.

To others who thinks this thread looks familiar. Sorry, I accidentally copied and pasted this from a thread I submitted last week. Sorry about that; I didn't mean to duplicate it. Your suggestions on how to approach it over on the original thread were very useful and much appreciated.