# Structural Analysis Conundrum

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?

• Ax + Dx + Cx = 0 is only true if all forces are 0, since all are pointing in the same direction. I believe you have to analyse the structure as a whole.
– Koo Zhengqun
Jul 27, 2017 at 1:58
• Are you sure that the two members ADC and BEC are supposed to be connected to each other at point C? If they are not connected at point C it is intuitively apparent that this is a well described problem with a unique solution. The reason I'm suspicious about there being a connection at point C is that if you consider members ADC and BEC to be 'real' beams rather than ideal infinitely stiff beams then the force at point C (as well as points D and E) will depend very sensitively on the actual real stiffnesses of the ADC and BEC beams, and that normally isn't the case with these sorts of problems Jul 27, 2017 at 2:03
• Is not Ax=0 due to DE? Imagine AB is a spring, it will neither compress or expand
– Willy Billy Williams
Jul 27, 2017 at 5:06
• This is an example of a statically indeterminate system which can sometimes be solved by considering small displacements. ocw.mit.edu/courses/civil-and-environmental-engineering/… Jul 27, 2017 at 5:48
• @KooZhengqun If the forces are not in the direction indicated by the arrows, they will just be negative. No big deal. Jul 27, 2017 at 17:32