Kinetic energy and rotating beams

[Minnie]

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 are inforced 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 steel work could fail causing main or secondary members to fall on toone of the steel containers. I'm trying to determine the kinetic energy that a beam could impact the container with since I know the with stand 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'ma 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 howto 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.

[JAlberts]

This is a bit of a tough one, but I might suggest that since you will have established the rotational velocity of the beam at the point of the second separation, which should theoretically remain constant through and that separation; then, using the height of the center of mass of the beam above the top of the containers you can determine the additional kinetic energy (PE = KE), of the falling beam to add to your original rotational kinetic energy and velocity of the lower contacting end of the beam at impact.