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Structural mechanics question - Force deflection relationship

Structural mechanics question - Force deflection relationship

Structural mechanics question - Force deflection relationship

(OP)
Hello everyone, I need some advice. I am working with impact response and got a little stuck.
For my simply supported RC beam with load at midspan I have a moment-curvature relationship. Now i need to use it to construct force-deflection diagram, taking into account formation of a plastic hinge at the midspan. Length of the plastic hinge is already estimated. I found information, that I need to integrate moment-curvature relationship over one half of the beam's length and also account for plastic hinge region that will have a constant curvature. However I don't understand how to connect it to my impact load, because bending moment from it is much larger than the moments of the moment-curvature relationship.
I wasn't able to find this case anywhere in the literature, although it seems quite simple, because articles usually omit the calculation procedure for it. Could someone recommend me, where I can find an example of such task's solution? Thank you all in advance.

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