Analyzing Support Conditions for Tables/Tripods

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When analyzing support conditions for tables or tripods under vertical forces, it is crucial to avoid assuming a "fixed" base, as this misrepresents the actual system. A more accurate approach is to fix one leg completely while allowing the other legs to move vertically but remain free in other directions. This method prevents the model from becoming a mechanism, which could lead to a singular global stiffness matrix. The analogy of a table on ice illustrates this concept, where friction is absent for three legs, yet a solution can still be achieved. Properly defining these support conditions is essential for accurate static analysis.
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If I am doing a simple, static analysis on something like a table, or tripod with a vertical force acting on it, what support condition do I assign to the base at which the legs contact the ground? I feel like it is incorrect to specify this as "fixed," since that would be like saying the legs are bolted/welded to the ground and not truly representative of the system. All of the simulation tutorials with tables that I can find just assume the base is fixed.
 
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Try this: one leg is completely "fixed" (presumably you are dealing with a plate-and-rods model, so each node has six degrees of freedom), the other legs are not allowed to move in the vertical direction, but free to move otherwise. That's the simplest approach that would ensure that the model is not a mechanism (the latter case would lead to the global stiffness matrix becoming singular). Well, it would be something like the table standing on ice (no friction between the remaining three legs and the floor), but still, that would deliver a solution.
 
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