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[tex]\textbf{F} = -\textit{K}\vartheta[/tex]

with theta representing the angular deflection from its equilibrium position and K the spring constant. Using the diagram below I can work out the forces and deflection if I applied a force at the green dots but I can't find a formula anywhere for calculating the force transferred along the beam that I would apply at the red dots. The top part of the digram represents one torsional spring, and the bottom is what I'm trying to do. I assume the formula would be something like

[tex]\textbf{F} = [/tex] Force applied / [tex]\textit{K}[/tex] / Distance (length of the beam)

Any help would be much appreciated