The Finite Element Method | Part 15: 3D Frame Example

[@donaldkhanye9011]

Hello Dr. CEE, I see you are simply reading off the element Lambda unit vectors directly from the figure (that’s nice). Before I watched this video, I had actually went all-full-out and assigned each node its corresponding global coordinates (x,y,z) and used those coordinates to calculate the unit vectors for lambda as it was explained in the previous lecture. For element #2 (the one you read off at 05:05 ^_^), I ran into the “special case problem” because the local x axis of element #2 is parallel to the structure GLOBAL Z axis. I simply cross-product the “Local x” with the “GLOBAL Y” to find the “Local z” of element #2….. I them continued with the other cross products to find the other unit vectors. Yes, the end results are the same as the values that you are reading off, but seeing you effortlessly reading them off as you are doing, I am second guessing the need for my calculations (cross products and vector length checks) in this regard? Is it correct that the reading off of the unit vectors is only working in this case because the elements (members) are “horizontal / vertical” relative to the referenced structure global axis? Would the reading off still work if the members were inclined? or would it then become necessary to carry out the calculations that I did? I like the foreshadowing (04:33, 6:10) It does help to sharpen and to highlight a better mindset to approaching things in general. 08:10 thank you for mentioning this, for a moment, I thought it was just me who is struggling to see how that moment is going (luckily indeed it is written on the figure). Ooh, I did not realise there was challenge at the end (Axial, SF, and BM diagrams). I will definitely try this out. Thank you Doctor CEE; for me this is quite a milestone and it is indeed very very satisfying. You are simply the best and I am grateful to have an opportunity to learn from you. What you have already achieved through this series is nothing short of miraculous for many people like me who had very little to no experience in the FEM. Respect to the CEE channel and more specifically to your dedication MJ. I have enjoyed this video and I am looking forward to future videos from the CEE channel. Regards, DK

[@CivilEngineeringEssentials]

Hi there Engr. DK, The only reason why I seem to "effortlessly read them off" is because all of the nightmarish bugs I had to eliminate while programming STRADO. I somehow got battle hardened and can spot transformation matrices from miles (1.6 km) away. Yes, reading the vectors off is because they are of special cases. You still can get a good "idea" as of what the signs of the unit vector components should be by looking at the coordinates of the points. It is kind of a sp(a)cial imagination. If it is inclined, then I lose all ability to read those things off, and get back to my calculation bench. It is really challenging and hard to see those moments in 3D. Back in my day, I once opened Autocad and drew this stuff in 3D just to be able to "orbit it around" and appreciate the complexity. Most welcome, I am happy you find those vids beneficial and helpful, it is a joy to me to see people improving their talents based on those vids. Stay tuned for more content, Regards, CEE

[@towhidurrahman8961]

Now how can i calculate the member strain and stresses?

[@CivilEngineeringEssentials]

Once you determine the internal moments of each member, you can use principles of Mechanics of Materials for that: sigma = P(x)/A + My(x) cz / Iy + Mz(x) cy / Iz; So, with that regard, to FEM principles are needed there. For strains, you can use the moments (once again) to predict them. Check out the "beam curvature" in R.C. Hibbeler's Mechanics of Material book. Regards, CEE