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

MIn summary, the conversation is discussing the derivation of the bending moment distribution for a beam. The person is concerned about the profile and whether it should taper to zero. Another person suggests drawing a free body diagram and constructing a proper shear force curve to arrive at the correct bending moment curve. It is also mentioned that the moment should be zero at the free end. The person confirms that they have included all necessary terms in their equations.
  • #1
Sahdev
5
0

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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  • #2
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.
 
  • #3
Moment should be zero at free end.
 
  • #4
Yes I did by making a cut in the beam. I'll post up my equations
 
  • #5
working_zps5831d800.png
 
  • #6
If anyone's interested, I simply forgot to subtract q2 from the q1 terms in the expression
 

What is "Bending Moment Distribution"?

"Bending Moment Distribution" is a method used in structural engineering to determine the internal forces, specifically bending moments, in a beam or structural element. It is used to analyze the strength and stability of a structure.

How is "Bending Moment Distribution" calculated?

The calculation of "Bending Moment Distribution" involves breaking down a beam into smaller segments and determining the bending moment at each segment using equations and principles of statics. The results are then used to create a graphical representation of the bending moment along the entire length of the beam.

What factors affect "Bending Moment Distribution"?

The factors that affect "Bending Moment Distribution" include the type of load applied to the beam, the type of support at each end of the beam, and the properties of the beam itself, such as its length, cross-sectional shape, and material. These factors can also affect the shape of the bending moment diagram.

Why is "Bending Moment Distribution" important in structural engineering?

"Bending Moment Distribution" is important in structural engineering as it allows engineers to accurately determine the internal forces acting on a beam, which are crucial in designing and analyzing structures. It also helps to identify areas of high stress and potential failure, allowing engineers to make necessary design changes or reinforcements.

What are the limitations of "Bending Moment Distribution"?

One limitation of "Bending Moment Distribution" is that it assumes the beam is linearly elastic, which may not always be the case in real-world situations. It also does not take into account any deformations or stresses caused by shear forces. Additionally, "Bending Moment Distribution" is most accurate for simple, straight beams and may be less accurate for more complex or irregularly shaped beams.

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