How Do You Derive the Bending Moment Distribution for a Beam?

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Discussion Overview

The discussion focuses on deriving the bending moment distribution for a beam, addressing both theoretical and practical aspects of the problem. Participants explore the necessary steps and considerations involved in this derivation.

Discussion Character

  • Homework-related
  • Technical explanation
  • Exploratory

Main Points Raised

  • One participant expresses concern about whether the bending moment profile should taper to zero.
  • Another participant suggests that drawing a free body diagram and constructing a shear force curve are essential steps to arrive at the correct bending moment curve.
  • A participant states that the moment should be zero at the free end of the beam.
  • One participant confirms they made a cut in the beam and plans to share their equations.
  • A later reply indicates that a participant forgot to subtract certain terms in their expression, which may have affected their results.

Areas of Agreement / Disagreement

Participants have not reached a consensus on the bending moment distribution, and multiple viewpoints and approaches remain in the discussion.

Contextual Notes

There may be limitations related to the assumptions made in the derivation process, as well as dependencies on the definitions of terms used in the equations. Some mathematical steps remain unresolved.

Sahdev
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Homework Statement



Derive the bending moment distribution of the beam:
AL_zps46bd4df3.png


Homework Equations





The Attempt at a Solution


I end up with something like this:
BM1_zps5c818fe9.png


Im abit concerned with the profile, should it taper to zero? Any thoughts?

Thanks
 
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Did you draw a free body diagram of this beam? Did you construct a proper shear force curve? Do these things and you will arrive at the correct bending moment curve.
 
Moment should be zero at free end.
 
Yes I did by making a cut in the beam. I'll post up my equations
 
working_zps5831d800.png
 
If anyone's interested, I simply forgot to subtract q2 from the q1 terms in the expression
 

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