Suppose we have the following truss-like structure, with a load of 1N on the middle joint and two reactions on the bottom joints.


If I try to analyze this using a Cremona diagram, I run into the problem that I do not know how to handle a load on a joint inside the structure. Is it possible to analyze this with a Cremoda diagram, and if so, how does the naming of the different faces and panels work? Because we can only depict forces on joints between faces, right?

Is there even a solution?


1 Answer 1


The vertical reactions at A and B are clearly 0.5N each, by symmetry.

Since there are reactions at A and B, those points must be connected to something external. If the connections are fixed points, there is no force in member AB because the length of AB can't change.

Interpreting the diagram literally, there are no horizontal components of the reaction at points A and B.

Removing AB makes the truss a statically determinate structure and you can solve for the other member forces in the usual way - for example, start at joint A and find the forces in AC and AD.

If you don't accept the argument that there is no force in AB, there is no unique answer to the problem, because the structure is statically indeterminate.

  • $\begingroup$ Thank you! I came up with this thing (with nonzero force on AB) in high school, and been wondering ever since if there is an acceptable solution. I'll have to settle for statical indeterminism then. The exact solution will depend on the way each of the beams will react to compression or tension, right? $\endgroup$ Commented Oct 3, 2017 at 22:00
  • $\begingroup$ "The exact solution will depend on the way each of the beams will react to compression or tension, right?" - Right! $\endgroup$
    – alephzero
    Commented Oct 3, 2017 at 23:18
  • $\begingroup$ Just for the record: for a given combination of constraints and beam properties, there is a unique answer once deformation compatibility is taken into account. $\endgroup$
    – Wasabi
    Commented Oct 4, 2017 at 15:07

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