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![]() This is an additional equation that solves the indeterminacy. the fact that the slope at the fixed end is zero. the problem is solved by bringing another equation into play. The fact that solutions exist in texts is beside the point. since it has more reactions than the statically determinate simply supported beam. ![]() We'll probably get into an argument over how statically indeterminate is defined.Ī propped cantilever is a redundant structure. RE: Statics Problem with 3 supports but only 2 Unknowns (because 2 reactions are known to be equal) rb1957 (Aerospace) 5 Sep 23 19:12 That's the result I consistently end up with for all values of P and S that I've tried. I ran it for multiple different values of P (which is equal to Q, remember) and multiple different values of S. After realizing the above, I went ahead and just plugged the system into a structural analysis program. Please definitely let me know if you disagree though. So in conclusion I think the problem is statically indeterminate and that's why I've had so much trouble solving it the normal/basic way using sum of forces in Y and sum of moments in Z. The fact that the two equal reactions (A and C) occur at separate supports is more important than the fact that they are equal to one another (for the purpose of determining if statically determinate, that is). So it seems to me that since the number of support reactions is 3, then the number "3" is the number relevant for determining statical-determinancy (if that's a word), and not the number 2, even though I know that there are truly only 2 variables I don't know the value of. " A system is externally statically indeterminate, if the number of support reactions exceeds the number of possible movement directions." The black dot at B is just there to show that I'm approximating B as a pinned support (just as a formality so that the system isn't technically under- or over-constrained).Īfter posting, I found this definition for "statically indeterminate" that I hadn't seen before and seems more helpful/specific than other definitions I had seen before and gotten used to. (it actually represents a shaft freely rotating inside 3 plates, which are the 3 "supports") The structure is symmetrical and the beam is continuous. RE: Statics Problem with 3 supports but only 2 Unknowns (because 2 reactions are known to be equal) IRstuff (Aerospace) 5 Sep 23 17:06 Or maybe one of you guys will just solve this in five minutes and I'll realize I've just missed something obvious.Ĭurious to hear your thoughts/commentary. I definitely insist it should be pointing downward with the others, though) (There was also a time I tried to solve a less-simplified version of this problem, and the solution told me that B was actually pointing upward. Or maybe it's statically indeterminate, despite there only being 2 unknowns? Normally, these equations absolutely should be independent however, so I suspect there is some other kind of issue going on here-OR maybe they really are not independent, in which case I would like to know what makes them non-independent, and how I can make sure to avoid constructing such problems in the future. But this problem has kind of humbled me-maybe it's just a brain fart, or maybe I've constructed a problem that isn't actually possible to solve for reasons not currently apparent to me.Įvery time I try to solve this problem, attempting to solve the moment-sum equation combined with the force-sum equation eventually results in a trivial 0 = 0 identity, which means (by my understanding) that the equations were not truly independent. I feel that my statics foundation is pretty solid. I make free-body diagrams all the time and solve statics problems on a regular basis. I've actually been a practicing engineer for a few years now. But this has actually been giving me a lot of trouble, and I suspect it might be because I'm forgetting some sort of basic principle that I've perhaps been taking for granted up til now, which maybe happens to uniquely cause issues with this problem. A and C are known to be equal however, so there are really only 2 unknowns.Ī, B, and C are known to all be pointing downward.Īt first glance this looks like a pretty easy/standard statics problem.
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