Two-Hinge Moment-Resisting Frame with Lateral Load

Hi @coachlizschneider, clipped here is a question from a practice exam. I didn’t know how to approach this because of the hinges. Going through the answer makes sense, but honestly I still don’t get it. B and C will have the same moment value (I think). But what about the moment value for A and D? How does the load distribute from B to A, and similarly from C to D? Why doesn’t the length of the beam matter but the height of the column does?

Thank you!

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Hi @coachlizschneider can you answer this question for @ctan ?

@ctan
Ok so first thing to know is that the frame is acting as a unit. The connections between the beams and columns are fixed, so the forces are moving through the frame differently than if there was a pinned connection between the beam and column. Because the frame has fixed connections your reactions are going to occur at the base of each column and the load will be divided equally between the two columns.
The second thing to keep in mind is that moment forces are a combination of force and distance. The distance that you use is the one perpendicular to the force. In this case that is the height of the column. If we were looking at a beam with a gravity load, then you would use the length of the beam .
So ultimately yes B and C have the same moment. Again because this is a frame the moments will be highest at B and C and tapper off to 0 towards A and D.

For more information on frames check out Chapter 15 of Form and Forces by Edward Allen.
Additionally, there is a helpful diagram at this website: https://theconstructor.org/structural-engg/analysis/analysis-of-moment-resisting-frame-lateral-load-distribution/1720/

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