Timeline for How is this basic equation of a Timoshenko beam derived?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| May 17, 2021 at 17:14 | comment | added | Michael Seifert | Yes, $q(x,t)$ is the external load per unit length as a function of position and time. It's meant to be something that you know, i.e., I apply such-and-such amount of force distributed in such-and-such a way over such-and-such a time period and see how the beam responds. If the beam has no external forces on it (other than at the ends, where the boundary conditions are enforced), then $q(x,t) = 0$. | |
| May 16, 2021 at 0:00 | history | edited | Chemomechanics | CC BY-SA 4.0 |
Minor polishing
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| May 15, 2021 at 22:31 | comment | added | mike | Or is $q$ just meant to be "any externally added force"? I see they use a $q(x)$ here with that intention as well for the similar Euler beam: en.wikipedia.org/wiki/Euler%E2%80%93Bernoulli_beam_theory | |
| May 15, 2021 at 22:21 | vote | accept | mike | ||
| May 15, 2021 at 22:19 | comment | added | mike | Thanks Mike. That makes sense in the context of seeing the derivation wiki box. They have eliminated $ϕ$ because then everything can easily be solved based on displacements/derivatives (eg. in a finite difference model). Then the only remaining question I have is: If you were solving this in a finite difference model per time sample & x-increment, what would you put in for "$q$" and it's derivatives? They give $EI\frac{d^4w}{dx^4}=q-\frac{EI}{kAG}\frac{d^2q}{dx^2}$ so maybe use that to solve $q$ and it's derivatives backwards/recursively from the prior few samples' data? Thanks. | |
| May 15, 2021 at 21:15 | history | answered | Michael Seifert | CC BY-SA 4.0 |