Hi, @TM'sChannel: I found a confirm mistake for the value of a2 which should be: a2=-3/L3(v1-v2) - 1/L(2 Θ1+Θ2) [Not "...-1/L( 1/L(Θ1+Θ2)" as per your slides]. I checked the after derivation part with matrix and also the algebra so I have confirmed this by all means. You also check and confirm. [P.S: Just checked you already mentioned that in description and also uploaded corrected video. Thanks for that. ] updated.
hi, one doubt, at 6:47, i am not getting the expansion of m1 as mentioned in the video, i get it as EI/l3 * (6LV1+fi1L^2-6LV2+fi2L^2) instead of EI/l3 * (6LV1+4fi1L^2-6LV2+2fi2L^2)...could you please upload a screenshot of the derivation .. thanks
Hi, thanks for pointing it out :). I went back to my derivation and I discovered a typing error on the slide when calculating the displacement function v(x) at 4:44. The expression for the second term i.e. a2 should be: a2 = -3 (v1-v2) /L^2-( 2fi1 + fi2 )/L . Using this adjustment you can obtain the correct expression for v(x) and from there calculate the correct coefficients as in the video. Sorry for the inconvenience, I will upload a revision of this video with the typing error corrected. Please let me know if you encounter any more errors/doubts.
Hi, I came across this document: people.duke.edu/~hpgavin/cee421/frame-finite-def.pdf Which has a version of the derivation. I will add it to my list for future videos. :)
Hi, thanks for the comment. Honestly I don't really know. But the theory used to derive the matrix models the center line displacement of the (straight) beam. If that line is curved, I presume the theory also changes. Unfortunately I cannot say how. Another thing that also changes is the inertia (I), this becomes a function of position due to the change in height (h). Sorry if this is not very helpful, I have not yet dealt with the analysis of haunch beams.
Hi, I actually have no idea. I haven't worked with such beams yet. Maybe you can find a paper or a book which deals with this topic and post it here? I would love to read it.
+TM'sChannel I realise you left it out since there is no load in the axial direction :) I am trying to solve a problem with three degrees of freedom at each node and looking for a way to deal with the stifness matrices.
+Chris10B I see :). It sounds like you are describing a frame element. It is the combination of a beam and a bar element and thus have three degrees of freedom at each note. You can have a look at my derivation video of this element at ruclips.net/video/wq7Os0hdYtk/видео.html . The stiffness matrix is shown there. I also have a video showing an example on how to approach a problem with frame elements. I hope this comment was helpful :)
Hi, I have a video on the derivation of a frame element (which has 6 degrees of freedom, 3 at each node). You are welcome to view it here: ruclips.net/video/wq7Os0hdYtk/видео.html
I see, I shall try to make a video for such an element, although it may take me a while. For torsion the basis is similar to that of the truss element, only with AE/L replaced by GJ/L. For the time being you may look at the book "a first course in the finite element method" by D.L. Logan which does provide a derivation of a 3D frame element. Hope this helps
It took forever to find this video, but this was the concept I was stuck on. Thank you so much for making this video.
Hi, @TM'sChannel: I found a confirm mistake for the value of a2 which should be: a2=-3/L3(v1-v2) - 1/L(2 Θ1+Θ2) [Not "...-1/L( 1/L(Θ1+Θ2)" as per your slides]. I checked the after derivation part with matrix and also the algebra so I have confirmed this by all means. You also check and confirm.
[P.S: Just checked you already mentioned that in description and also uploaded corrected video. Thanks for that. ] updated.
a2=-3/L2(v1-v2) - 1/L(2 Θ1+Θ2)
I agree, a factor 2 is missing
Thank you for pointing this out
@Yong-Min Jeong I have noticed this and posted the corrected video at ruclips.net/video/RNIZ8Ju3_CI/видео.html
Thank you for noticing... :)
Thanks. FYI, I think thet the General displacement equation(4:42) needs some revision on the fourth term.
a2 = -3/L^2(v1-v2) - 1/L(2phi1+ phi2)
Haha I can relate
@@MaltaLumpie Yes, there is this mistake in your calculation.
@@igorbarcelos9531 this mistake destroyed my day
TM's channel, can you show the derivation of stiffness matrix of 2 noded beam element
Thank you so very much. That was very helpful.
can you tell me how to find out the missing element in the matrix using shape function
hi, one doubt, at 6:47, i am not getting the expansion of m1 as mentioned in the video, i get it as EI/l3 * (6LV1+fi1L^2-6LV2+fi2L^2) instead of EI/l3 * (6LV1+4fi1L^2-6LV2+2fi2L^2)...could you please upload a screenshot of the derivation .. thanks
Hi, thanks for pointing it out :). I went back to my derivation and I discovered a typing error on the slide when calculating the displacement function v(x) at 4:44. The expression for the second term i.e. a2 should be: a2 = -3 (v1-v2) /L^2-( 2fi1 + fi2 )/L . Using this adjustment you can obtain the correct expression for v(x) and from there calculate the correct coefficients as in the video. Sorry for the inconvenience, I will upload a revision of this video with the typing error corrected. Please let me know if you encounter any more errors/doubts.
Can you elaborate more on how the geometric stiffness matrix for a beam element is derived? thx
Hi, I came across this document: people.duke.edu/~hpgavin/cee421/frame-finite-def.pdf Which has a version of the derivation. I will add it to my list for future videos. :)
How v(x) changes when beam is parabolic haunch beam ? Or what changes?
Hi, thanks for the comment. Honestly I don't really know. But the theory used to derive the matrix models the center line displacement of the (straight) beam. If that line is curved, I presume the theory also changes. Unfortunately I cannot say how. Another thing that also changes is the inertia (I), this becomes a function of position due to the change in height (h). Sorry if this is not very helpful, I have not yet dealt with the analysis of haunch beams.
Hi, thanks for reply. Video is a very helpful. Haunch beam is not a easy topic. Thanks again.
hi,how can i derive the stiffness matrix for authotropic beam?
Hi, I actually have no idea. I haven't worked with such beams yet. Maybe you can find a paper or a book which deals with this topic and post it here? I would love to read it.
a beam element has 3 dofs at each node
+Chris10B Thanks for your comment. Are you referring to the degree of freedom associated with axial force and displacement as the one I left out?
+TM'sChannel I realise you left it out since there is no load in the axial direction :) I am trying to solve a problem with three degrees of freedom at each node and looking for a way to deal with the stifness matrices.
+Chris10B I see :). It sounds like you are describing a frame element. It is the combination of a beam and a bar element and thus have three degrees of freedom at each note. You can have a look at my derivation video of this element at ruclips.net/video/wq7Os0hdYtk/видео.html . The stiffness matrix is shown there. I also have a video showing an example on how to approach a problem with frame elements. I hope this comment was helpful :)
If you have a cantilever does the stiffness matrix change ?
Hi, no it does not. Only the boundary conditions are different i.e. the end degrees of freedom are not prescribed.
TM'sChannel can you add a video of 6 degree of freedom derivation ?
Hi, I have a video on the derivation of a frame element (which has 6 degrees of freedom, 3 at each node). You are welcome to view it here: ruclips.net/video/wq7Os0hdYtk/видео.html
TM'sChannel sorry I meant 12, 6 at each node. I am interested in twist
I see, I shall try to make a video for such an element, although it may take me a while. For torsion the basis is similar to that of the truss element, only with AE/L replaced by GJ/L. For the time being you may look at the book "a first course in the finite element method" by D.L. Logan which does provide a derivation of a 3D frame element. Hope this helps
You teach me how to obtain stiffness coefficients, I teach you how to record on something other than a potato
Hahaha, As long as you supply the computer :)
😂
Can you prove it with cojugate method or virutual work
I can't find a1 and a2 at 04:15. Has anyone done this?
+Salman Khan Hi, I have made a mistake in the video. Please see ruclips.net/video/RNIZ8Ju3_CI/видео.html for the corrected version.
+TM'sChannel thanks for the fast response.
thanks