Bending Moment Diagram for Trapezoidal Distributed Load: Homework Help

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Discussion Overview

The discussion revolves around the challenge of drawing a bending moment diagram for a trapezoidal distributed load on a beam. Participants explore various methods to approach the problem, including comparisons to uniform and triangular distributions, and seek clarification on how to represent the trapezoidal load accurately in their diagrams.

Discussion Character

  • Homework-related
  • Technical explanation
  • Exploratory
  • Debate/contested

Main Points Raised

  • One participant expresses difficulty in linking the bending moment diagrams for uniform and triangular distributions to create one for a trapezoidal distribution.
  • Another participant requests clarification on the support conditions of the beam and emphasizes the relationship between shear and moment diagrams.
  • Some participants suggest breaking down the trapezoidal load into simpler components, such as a uniformly distributed load and a triangular load, to facilitate calculations.
  • A later reply mentions the possibility of rotating an angled beam to horizontal for easier diagram drawing, noting that the geometry must remain consistent.
  • One participant asks for assistance in determining shear and moment diagrams using both the Equation Method and the Area Method.

Areas of Agreement / Disagreement

Participants generally agree on the complexity of the problem and the usefulness of breaking down the trapezoidal load into simpler components. However, there is no consensus on the best method to draw the bending moment diagram, as various approaches and interpretations are discussed.

Contextual Notes

Some participants mention unresolved mathematical steps and the need for clarity on support conditions, which may affect the calculations and diagram representations.

TheCamBee
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Homework Statement


I have a problem which involves me drawing the bending moment diagram for a trapezoidal distributed load. I understand the bending moment diagrams for a uniform distribution, and partially for a triangular distribution, however i am struggling to link the two for a trapezoid shape distribution. How would i go about knowing what sort of shape will be required and how to draw this?

Homework Equations


The beam is 2.35m in total length, with a 0.1 segment at each end, and the distribution in the centre at a length of 2.15m. The 'small' side of the trapezoid is 20N/m and the longer side is 40N/m. This distribution is seen to be 'hanging' downwards from the beam, and a reaction load from another beam is situated at the far right of the beam, in the upwards direction.

The Attempt at a Solution


I think i have calculated the max moment to be 15.4084N. How would i draw this on my diagram.
 
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Firstly, I'd like to welcome you to PF!

TheCamBee said:

Homework Statement


I have a problem which involves me drawing the bending moment diagram for a trapezoidal distributed load. I understand the bending moment diagrams for a uniform distribution, and partially for a triangular distribution, however i am struggling to link the two for a trapezoid shape distribution. How would i go about knowing what sort of shape will be required and how to draw this?

Homework Equations


The beam is 2.35m in total length, with a 0.1 segment at each end, and the distribution in the centre at a length of 2.15m. The 'small' side of the trapezoid is 20N/m and the longer side is 40N/m. This distribution is seen to be 'hanging' downwards from the beam, and a reaction load from another beam is situated at the far right of the beam, in the upwards direction.

The Attempt at a Solution


I think i have calculated the max moment to be 15.4084N. How would i draw this on my diagram.
Please show how you arrived at your number, which should have the units of N-m, if that's a moment you are trying to calculate. This problem looks very similar to this one:
https://www.physicsforums.com/showthread.php?t=385188

Is it? If not, what are the end support conditions...is this a cantilever with a fixed support at one end? Remember, the slope of the shear diagram curve at a given point is equal to the value of the load intensity at that point; and the slope of the moment diagram curve at a given point is equal to the value of the shear at that point. Is this a homework problem, or a take-home exam?
 
Indeed this is the same question as the problem in 'mikex24' post. Turns out to be a bit of a challenge!
Anyway after abit more work i managed to complete my horizontal beam calculations, however thankyou for getting back to me!
The angled beam seemed quite simple compared to the horizontal beam, most likely because of the lack of distributed loads. Just to clarify, it is possible to rotate the angled beam so it is horizontal, providing the geometry is the same to draw the bending moment and shear force diagrams?
Once again thanks for getting back to me so quick, i will go and have a quick look at the induced stresses!
 
TheCamBee said:
Indeed this is the same question as the problem in 'mikex24' post. Turns out to be a bit of a challenge!
Anyway after abit more work i managed to complete my horizontal beam calculations, however thankyou for getting back to me!
The angled beam seemed quite simple compared to the horizontal beam, most likely because of the lack of distributed loads. Just to clarify, it is possible to rotate the angled beam so it is horizontal, providing the geometry is the same to draw the bending moment and shear force diagrams?
Once again thanks for getting back to me so quick, i will go and have a quick look at the induced stresses!
Yes, you are quite correct that the shear and moment diagrams for the angled member is a lot easier to develop than the horizontal member, primarily because there is no distributed load on the angled member. And yes, once you determine the forces and moments acting on the angled member at its ends, rotate the member (and the forces and moments with it) so it's horizontal, and draw the shear and moment diagrams. It's easier than tilting your head :wink:
 
hi to all, i jst want to share my problem. it is a simple beam with trapezoidal loading on it. i resolve the trapezoid by making it into a uniformly distributed load and a triangular loading.. but still i can't determing how to solve or to draw the share and moment diagram.. using both the Equation Method and the Area Method.. can anybody share your genius idea? thanks here's the image of the problem
 

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Let x be the distance from the left hand end.
Then Vx = ... and Mx=...? That is, what are the values of shear force and bending moment at section X, as functions of x. That is how to start.
 

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