- #1
What is the relationship between moment diagrams and the area under the curve?
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Discussion Overview
The discussion revolves around the relationship between moment diagrams and the area under the curve, specifically in the context of calculating deflections in structural analysis. Participants explore the methodology for determining moment areas, including the use of triangular areas and centroids, and the implications of different reference points for calculating moments.
Discussion Character
- Homework-related
- Technical explanation
- Debate/contested
Main Points Raised
- Some participants question why the area of the moment diagram includes a factor of 0.5, suggesting it relates to the triangular shape of the area being calculated.
- Others explain that the area of a triangle is calculated as one half the base times the height, and the centroid's position is also factored into the moment calculation.
- There is confusion regarding the choice of reference points for calculating moments, with some participants asking why moments are taken about different points (A or B) in various solutions.
- Some participants assert that the inclusion or exclusion of certain moments (like 400 Nm) in calculations depends on the reference point chosen and the method used to derive the moment diagram.
- Participants discuss the validity of different solutions, with some suggesting that separate areas for each reaction are considered in one of the methods presented.
Areas of Agreement / Disagreement
Participants express differing views on the methodology for calculating moment areas and the significance of reference points. There is no consensus on the correct approach, and multiple competing explanations are presented.
Contextual Notes
Participants highlight the importance of understanding how to draw moment diagrams and the implications of deriving moments from shear diagrams. There are unresolved questions regarding the assumptions made in the calculations and the definitions of the areas involved.
Who May Find This Useful
This discussion may be useful for students and professionals in structural engineering or mechanics who are looking to understand the relationship between moment diagrams and area calculations in the context of deflection analysis.
- #2
chetzread
- 798
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why there's a need to include 0.5(2) ?
- #3
- 7,201
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I haven't done this in a long long time, but this is part of a method to determine deflections. The method involves computing the moment of the area of the moment diagram about the reactions. The area of the triangle is one half the base (one half of 2) times the height (800). It's centroid is 4/3 from left end. Result is in Nm^3.
- #4
Justus
- 6
- 2
We are looking for the moment area so the formula would be (area of triangle)(centroidal moment of area) and that would be (0.5)(2)(800) as triangle area and (4/3) as the centroid.
- #5
chetzread
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- #6
chetzread
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why the author didnt take the moment about A into consideration ?
- #7
Justus
- 6
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He considered that is why there are two solutions (AreaAB)XA and (AreaAB)XB denoting two moment areas
- #8
chetzread
- 798
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i don't understand , can you explain further?Justus said:
- #9
chetzread
- 798
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why the author want to calculate the area moment by 2 method which is (area AB) x A and (area AB) x B ?
What's the purpose of doing so ?
What's the purpose of doing so ?
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- #10
chetzread
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and I also noticed that the author didnt include the moment 400Nm in the first solution,is it wrong?
- #11
Justus
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You should review how to draw moment diagrams. It is already known that when we derive from shear to moment diagrams , any given moment is considered a straight line thus no area and that is why it isn't included in computing the moment area.
- #12
chetzread
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then, why the author include the moment 400Nm in the second solution ?Justus said:
- #13
Justus
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Again , you should read on how to solve moment areas. The 2nd solution is the separate areas for every reaction or simply it is another way to solve the problem. Also you could see that he took the moment area about A to solve the problem and that is why there is no moment diagram for reaction A.
- #14
chetzread
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what do you mean by separate areas for every reaction?Justus said:
- #15
chetzread
- 798
- 1
the second solution is taking moment about B ? so the 400Nm is included?
While the first solution is taking moment about the point which has 400Nm moment , that's why the moment is not included in the first solution , since dM/ dx = 0 ?
While the first solution is taking moment about the point which has 400Nm moment , that's why the moment is not included in the first solution , since dM/ dx = 0 ?
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