Bending moment Diagram for fixed-fixed beam

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Discussion Overview

The discussion revolves around the challenge of drawing a bending moment diagram for a fixed-fixed beam subjected to specific forces and moments. Participants explore different methods for solving the problem, including the method of cuts and the concept of superposition.

Discussion Character

  • Homework-related
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant describes a beam with a force and moment applied at each end and expresses uncertainty about the method of sections for obtaining the bending moment diagram.
  • Another participant suggests breaking the problem into two separate problems: one focusing on forces and the other on moments, and then combining the results to form the bending moment diagram.
  • A follow-up question is raised regarding the rationale for using the suggested method over the section method, highlighting a discrepancy in results when approaching the problem from different ends of the beam.
  • A participant indicates that they cannot comment on the initial approach without seeing the work done, reinforcing the idea of simplifying the problem through superposition.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the best method to use for this problem. There are competing views on the effectiveness of the method of sections versus the proposed superposition approach.

Contextual Notes

There is an indication that the method of sections may not be universally applicable in this scenario, but the specific limitations or assumptions are not fully explored.

Who May Find This Useful

Students and practitioners dealing with structural analysis, particularly those interested in bending moment diagrams and methods for analyzing fixed beams.

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Homework Statement



There is a beam, say length L, with a force F UP on the left built-in support and a CLOCKWISE moment. The right side has a force, F, DOWN and a COUNTERCLOCKWISE moment

i.e F up, cw moment -------------------------------------------------------------F down, ccw moment

I am required to draw a bending moment diagram for this. The only way I've ever been shown is the method of cuts/sections which I hope you are familiar with this. If I work from the right hand end, the equation I get is different from working from the left hand end. [/B]

Homework Equations


[/B]

The Attempt at a Solution


As stated above, I'm not sure if the method of sections works here although I was never made aware that it had occasions where it was useless. How can I get a BM diagram here?Thanks
 
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Try breaking this problem up into two separate problems: the first one with only forces, and the second one with only moments.

For the first problem, what would the shear force diagram look like? What would the BM diagram look like?

For the second problem, what would the BM diagram look like?

Combine the two BM diagrams et voila.
 
SteamKing said:
Try breaking this problem up into two separate problems: the first one with only forces, and the second one with only moments.

For the first problem, what would the shear force diagram look like? What would the BM diagram look like?

For the second problem, what would the BM diagram look like?

Combine the two BM diagrams et voila.
Hi - thanks for that. I understand this. Just one Question; how did you know to do this c.f. other methods e.g. section method? W.r.t the sectioning method - If I work from right to left (call right 0, and left L) then I get the correct diagram. Working from left to right gives me the wrong answer!
 
I can't comment on what you did without seeing your work.

What I recommended was just splitting one problem into two (simpler) ones, and then using superposition to combine the results.

You have studied superposition, haven't you?
 

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