I am analysing the forces within a certain frame, and for some reason there do not seem to be sufficient equations of equilibrium to solve for all the internal forces. Is there something about this structure than makes it unsolvable without more information?
There is a frame, ABCDE, shown below. Two equal forces are applied to it (both shown as F). Assume we know F, w, and h (and from the illustration, l = w/2). Let's try to find the forces within member ADC.
First, we can analyse the frame as a whole. It is straightforward to show that Ay = By = F.
Next, we should be able to analyse member ADC by itself.
If we sum forces in the y-direction, we get:
Ay + Cy - F = 0
Since we already found that Ay = F when we analysed the whole frame, we know that Cy = 0
If we sum forces in the x-direction, we get:
Ax + Dx + Cx = 0
And if we sum moments around A, we get:
F*w/4 + Dx*h + Cx*w/2 = 0
Without going any further, we can see that we have two equations with three unknowns (Ax, Dx, and Cx).
If we look at the other members in the frame, we don't get any new information, I don't think... So what's missing? How can this simple frame be an unsolvable physical conundrum?