Three Moment Equation 2nd Degree Indeterminate Beam Example - Fixed End Continuous

[@AFMathandEngineering]

Note: The equation shown in the top left has had I multiplied throughout it. This is the formula is used when applying the three moment equation at a support in which both adjacent spans have a constant I value (moment of inertia).

[@rubixloverful]

what if there are support settlements, sir?

[@AFMathandEngineering]

We add the term on the end shown at the start of the video to our formula, and plug in the displacements.

[@rubixloverful]

@@AFMathandEngineering thank you for the reply sir, and just a follow-up: if the supports have settled and the same overhanging beam is analyzed, what would be the displacement at the overhanging point, sir? because we need the value of it when we consider the last 3 points on the beam

[@rubixloverful]

@@AFMathandEngineering to make my question a bit more clear sir, if we were to label the last point(overhanging part) of the beam as d, should i take the displacement of c and copy it to d or is there a solution that is evading my brain sir. thank you

[@AFMathandEngineering]

@@rubixloverful settlement displacement is built into the long form of the three.moment equation. You follow exactly the same steps as in this video, but there's simply another term on the end of the formula that we assumed as 0 for this problem. Perhaps we'll make another video with support settlement for clarity. Hope that helps!

[@JakeVoorhees]

Another great video guys, thanks again for all the +++ value you're providing to the engineering community !! :)

[@AFMathandEngineering]

+Jake Voorhees cheers brother! We've been following your content too lately, you've been stepping it up! Great stuff.

[@JakeVoorhees]

Hey Fred / Avi, I'm going to connect you with Adriel, he was asking me about you two last night.. "Who were those Toronto guys you were telling me about?" :) thanks boys! I'm getting a really really strong response from the Brianne Martin interview. We should do an interview / live stream again soon 4 sure. Also, ur right about the custom overlay in OBS. Check out the TubeBuddy live stream overlay, i like theirs !

[@AFMathandEngineering]

Jake Voorhees excellent Jake we love making new connections. Thanks! We loved the interview with Brianne, she's a great personality and the video itself was excellent, interview had a great tone to it. Cheers!

[@AFMathandEngineering]

+Jake Voorhees oh and let's stream again soon! I'll send you a message about that. Glad you got obs sorted.

[@reymondquintos8836]

Hi sir how to solve the misdspan of a cantilever using three moment equation? Thankyouu

[@jstndcsn1850]

What is the direction of Ma? Ccw or Cw?

[@AFMathandEngineering]

The bending moment Ma at the support is - ve, and the sign convention is the beam convention, where the top fibre is in compression for positive and negative for tension. In this case the reaction would be ccw, as in this orientation it would cause a negative moment in portion AB.

[@AxellWietzsche]

I know it's too late but why isn't it 6750 at 4:03

[@MsTanja25]

If I have a moment insted of a force do I use the P or the W in the second part of the formula?

[@AFMathandEngineering]

You can't use a moment in place of a kN or kN/m paramter, the units won't work. You need to convert the moment to an equivalent force or distributed load.

[@MsTanja25]

@@AFMathandEngineering okey, thank you

[@esmatabdualmageedahmedalno8086]

Thank you so

[@jvision6094]

what is the difference between the first degree and second degree

[@AFMathandEngineering]

The difference is that we only have three equations of equilibrium we can use to evaluate the beam, and if we have more reactions than equations we have whats called an indeterminate beam; we have more unknowns than equations and we cant solve it. In order to solve it we need to create additional compatibility equations so the number of unknowns (reactions) = number of equations. In second degree indeterminate we have 5 unknowns and only three equations (sum of forces in x, y = 0 and sum of moments = 0). Therefore we must create two additional equations in order to solve (solving for Mb and Mc), where as for a single degree indeterminacy we only need one additional equation. Hope that clarifies things a bit.

[@govindcharan7827]

What if fixed support is present on both ends of the beam how to solve then. !?

[@AFMathandEngineering]

Is your question if it's one more degree of indeterminacy? You'll need an additional equation as you'll have one more unknown.

[@govindcharan7827]

Thanks for the reply sir , i got it.

[@martrayleigh7988]

Sir, I got -1080 in second equation not -810...

[@AFMathandEngineering]

-810 is correct, double check your work.

[@martrayleigh7988]

Thanks for the quick response sir! I'll try it again. :)

[@martrayleigh7988]

I wrote positive 90 for Mc instead of -90. I answered this without watching your video first, sir and I got tricked by that until I watch that part. Thank you very much sir!

[@AFMathandEngineering]

Glad you learned something thanks for the comment!

[@kashibhojia3797]

Sir i cant understand 90 moment

[@AFMathandEngineering]

kashi Bhojia the 90 kN m moment af support c? It's just the length of the cantilever to the right * the distributed load (1.8 kN/m) * distance to the resultant force (10/2).

[@kashibhojia3797]

AF Math & Engineering thanks sir i got it

[@AFMathandEngineering]

Great thanks for the comments!

[@drandrewsanchez]

Hi there! I found you from a shout-out from Jake Voorhees :) I study chemical engineering and have begun making videos about engineering classes! Feel free to check them out :)

[@AFMathandEngineering]

SanCHEneering hey man thanks for stopping by! Love Jake's channel, he's a great guy. We're always glad to partner up with fellow engineering content creators, we're glad you found us! Well subscribe to your channel and check out your videos! Chem engineering, tough stuff. How are you enjoying it, and where do you go to school?

[@drandrewsanchez]

Greatly appreciated! I go to UC Riverside and am entering my senior year :) I've been quite interested in nanotechnology and materials science so I currently hope to attend grad school in the future. Honestly I love it. I truly struggled with my intro classes but I've really been getting the hang of it lately. I'm passionate about sharing my experiences and started doing engineering videos :)