Cantilever beam with non-udl on - solution provided, understanding

AI Thread Summary
The discussion revolves around solving a cantilever beam problem with a non-uniform distributed load (UDL). Participants clarify the integration process of moment equations to derive slope and displacement, highlighting confusion over constants and terms in the equations. One user successfully resolves the issue by simplifying the load using singularity functions and confirms their solution aligns with the correct integration method. However, they note that the provided solutions in the attachments are incorrect due to integration errors, leading to frustration over the inaccuracies. The conversation emphasizes the importance of accurate solutions in understanding structural mechanics concepts.
louza8
Messages
58
Reaction score
0
Problem and Solution (albeit to a beam of different length L) provided in attachments.

Hi, I have been able to follow the provided solution to get the moment equations and understand the x1 and x2 positional references etc. I also understand that integrating the moment equations provides the solutions to the slope and further integration the solution to the displacement. I also understand in order to get the constants of integration I have to use known boundary conditions.

My hang up is how the solution has gone from this part:

EI*y''=wL(3x2 - L)/12
EI*y'=wx2^2/8 + C2

Perhaps my calculus is a bit weak these days after a break from studies. Little help?
 

Attachments

  • i1.jpg
    i1.jpg
    10.9 KB · Views: 569
  • i2.jpg
    i2.jpg
    7.1 KB · Views: 541
Physics news on Phys.org
Could someone have a look at this one please? I'm still struggling with the understanding. Much appreciated.
 
So nobody here can help me along with solving this problem or did you run into similar issues?
 
The solution you attached is too small to read. That's could be why you aren't getting any help. (The picture showing the question is just about readable, but not the solution)
 
Hi AlephZero, thanks for the tip.

I have added what I hope are more readable versions for the solution :)

To be specific I know how to get the moment equation here:
EI*y''=wL(3x2 - L)/12
But don't know how they've integrated the above to get here:
EI*y'=wx2^2/8 + C2

I thought there would have been an Lx term in there ?
 

Attachments

  • Screen shot 2012-08-28 at 8.54.28 AM.png
    Screen shot 2012-08-28 at 8.54.28 AM.png
    12.6 KB · Views: 560
  • Screen shot 2012-08-28 at 8.54.41 AM.png
    Screen shot 2012-08-28 at 8.54.41 AM.png
    12.2 KB · Views: 576
  • Screen shot 2012-08-28 at 8.54.46 AM.png
    Screen shot 2012-08-28 at 8.54.46 AM.png
    11.6 KB · Views: 539
Last edited:
louza8 said:
But I don't know how they've integrated the above to get here:
EI*y' = wx2^2/8 + C2

I thought there would have been an Lx term in there?
louza8: Why did you write C2 here, instead of C3? And why did you omit here the L they wrote? And why did you say Lx here? :confused:

Nonetheless, you are correct, in that their second equation currently seems wrong. Feel free to post what you think the second equation instead should be, and we can tell you whether or not it seems correct.
 
Last edited:
hi nvn,

thanks for your reply. both were mistakes. i was trying to be clear but was not, apologies.

anyways...i managed to solve the question by simplifying the load using singularity functions then integrating 4 times. i then went and checked the above method (with the correct integrals for the slope) and got the same answer and was satisfied.
 
louza8: In the last paragraph of post 7, do you mean you got a different answer, or the same final answer, compared to the final answer in the attached files in post 5?
 
Last edited:
Hi nvn. I used the method outlined in the attached file to solve the homework question (with correct integration) but the homework question is for beam length 2L not L as shown in the attached. Hence, the answers differ due to the longer beam under a greater total load deflecting more.

To check my answer I used an alternative method. I simplified the loading using singularity functions into 3 components. (1 big triangle acting down for entire length 2L, 1 rectangle of beam length L acting up between A-B and 1 triangle of length L acting up between A-B). By integrating the functions describing the loading and using known boundary conditions, I arrived at the same answer as I determined using the method outlined in the attached.
 
  • #10
louza8: OK, so you are aware that the answers in the files you attached are wrong, right?
 
  • #11
nvm - yeah I determined (after posting) that it would be incorrect due to the incorrect integration and the resulting on flow effects. It is quite frustrating when solutions are provided that are incorrect, particularly when I'm just trying to wrap my head around concepts/methods.
 
  • #12
louza8 said:
It is quite frustrating when solutions are provided that are incorrect ...
True. And you are correct regarding the resulting on-flow effects. The final answers in the attached files in posts 5 and 1 are completely wrong.
 
Last edited:
Back
Top