- #1
What is the relationship between moment diagrams and the area under the curve?
In summary, the author is looking to calculate the area moment of a reaction. He uses two methods, one which is taking the moment about the point which has a moment of 400Nm from the reaction, and the second which is taking the moment about B. The first solution does not include the moment of 400Nm, and the second solution includes it.
- #2
chetzread
- 801
- 1
why there's a need to include 0.5(2) ?
- #3
PhanthomJay
Science Advisor
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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
- 801
- 1
- #6
chetzread
- 801
- 1
why the author didnt take the moment about A into consideration ?
- #7
Justus
- 6
- 2
He considered that is why there are two solutions (AreaAB)XA and (AreaAB)XB denoting two moment areas
- #8
chetzread
- 801
- 1
i don't understand , can you explain further?Justus said:
- #9
chetzread
- 801
- 1
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
- 801
- 1
and I also noticed that the author didnt include the moment 400Nm in the first solution,is it wrong?
- #11
Justus
- 6
- 2
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
- 801
- 1
then, why the author include the moment 400Nm in the second solution ?Justus said:
- #13
Justus
- 6
- 2
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
- 801
- 1
what do you mean by separate areas for every reaction?Justus said:
- #15
chetzread
- 801
- 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 ?
FAQ: What is the relationship between moment diagrams and the area under the curve?
What is an area of moment diagram?
An area of moment diagram is a graphical representation of the distribution of moments along the length of a beam or structure. It shows the magnitude and direction of the bending moments at various points along the beam.
How is an area of moment diagram calculated?
An area of moment diagram is calculated by dividing the beam into small sections and calculating the moment at each section using the equations for bending moments. These moments are then plotted on a graph to create the diagram.
What information can be obtained from an area of moment diagram?
An area of moment diagram provides information about the bending moments at different points along the beam. This can be used to determine the maximum bending moment, the location of points of zero bending moment, and the points of maximum deflection.
How is an area of moment diagram used in structural analysis?
An area of moment diagram is an important tool in structural analysis as it helps engineers determine the structural integrity of a beam or structure. It can be used to identify areas of high stress and design for maximum strength and stability.
What factors can affect the shape of an area of moment diagram?
The shape of an area of moment diagram can be affected by factors such as the type of loading (point load, distributed load, etc.), the type of support (fixed, pinned, etc.), and the properties of the beam (material, cross-sectional shape, etc.). Changes in any of these factors can result in a different shape of the moment diagram.