Determinate vs Indeterminate Structures - Intro to Structural Analysis
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- Опубликовано: 12 июл 2024
- This video defines determinate and indeterminate structural systems, and how to tell the difference.
The unknown reaction forces and internal forces of determinate systems can be solved using only the equations of equilibrium (i.e., statics). Indeterminate systems have more unknowns than can be solved using statics alone, and therefore new structural analysis techniques are required.
The number of unknowns can be counted and compared to the number of equilibrium equations. Examples are shown for how to do this with trusses and frames (or beams, which work the same as frames). 
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Glad I could help, and welcome aboard!
I greatly thank you for these videos. They are extremely helpful!
You are welcome!
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Really great 👍
Your teaching style is amazing, very clear, straightforward which confuses me less. Cheers :)
Thank you! I'm glad this was helpful!
Great video. You explained it well and I’m happy to have learned something.
Glad it was helpful!
thank you! You made this so easy.
extremely helpful sir. very well explained. Thanks you sir
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Thank you!
Great and straightforward revision before my structural analysis final exam
Yep, that is the goal here. Glad you liked it!
Thank you. It was really helpful.
THANK YOU FOR HELPING ME WITH THESE VIDEOS
Glad this was helpful!
Beautifully explained
Thank you!
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Thanks for sharing, it really helps. May I ask a question for the last frame, if there is only one hinge in the middle on the top how could I make the cut?
Great question, because this can get a little weird. Two cases to clarify here.
(1) If the middle column only has a hinge on one side (instead of hinges on both sides, as shown in the video), then you would only need to make a single cut on the side with the hinge. The degree of indeterminacy would then be: 7 reactions + 6 internal forces - 3*(4 FBDs) = 1... meaning the frame is now indeterminate.
(2) However, if both beams and the middle column all come together at a single hinged point, that's a bit different. This moment release is now applied to all three members, unlike in Case 1 described above where the hinge-to-the-side only affects a single beam and the column. To "cut" this, you'll separate all three members that connect into this hinge from each other. Once you've done that, you will have identical free body diagrams as in the video, so the DOI is still 0.
@@StructuresProfH It makes perfect sense and thank you for the explaination.
How do you know at what points equilibrium can be considered for the trusses example?
Very Nice explanation ...
Thank you! I'm glad I could be of service.
Thank you🙏🏼🌺
You are welcome!
Hello, what about those systems where DoI=0, but you can't solve the reactions? (the critical ones)
This is my question as well
@@luziya7486 These systems are very dangerous (they allow some displacements nearby the position of equilibrium and the magnitudes of some reactions are tending to infinite) so you have to avoid them. The problem of recognizing the critical forms is a serious problem.
Nice🎉
Thank you
You're welcome!
for the last example if there were no hinges in the frame then would it be indeterminate to the fourth degree?
That is correct!
Does it mean that when ever your calculations gives you zero as an answer, it shows that the trusses is determinate?
Yep, zero means determinate (unless there is some other issue that causes instability).
I don't understand the frames.. Is there any other simple way..?
There is an equation too. For two-dimensional frames, the Degree of indeterminacy (DOI) can be computed as:
DOI = Reactions + 3*Members - 3*Connections - Releases
... where ...
Reactions is the total number of reaction forces or moments
Members is the total number of members (beams, columns, whatever) in the structure
Connections is the total number of connections between members (including connections to the ground)
Releases in the total number of hinges, expansion joints, etc. in the structure
how do you find r?
"r" is the number of releases, where a release counts as a single known internal force. So for example, a hinge in a beam forces the bending moment to be zero at that location - that counts as one release, because we know that M = 0 at that point. You can also have releases for shear and axial forces as well. These can even be combined. For example, a roller-like expansion joint in a bridge might count as two releases if both the axial force N = 0 and the bending moment M = 0 at that location.
@@StructuresProfH thank you!