# Moment-area diagram

1. Jul 15, 2016

### foo9008

in this question , can i redraw the -1000Nm moment area triangle ? (red line part) is it wrong to do so ?

Last edited: Jul 15, 2016
2. Jul 15, 2016

### foo9008

If I do so, then my answer would be the same as the author's working, but is my concept correct?

3. Jul 16, 2016

### foo9008

can i do the same thing for the moment -4800Nm??

4. Jul 17, 2016

### David Lewis

The middle diagram with the red line, what is it? A shear diagram? A moment diagram? What does the horizontal black line represent?

5. Jul 17, 2016

### foo9008

I am not sure what does the horizontal line represent
I think it's distance , and I rhink it's a moment -area diagram , where the vertical axis represent value of different moment , am i right ?

6. Jul 17, 2016

### David Lewis

Good question. The horizontal line might be the beam itself? You always want the load, shear & moment curves to be a different line weight, line type, or color than the structural member in your drawing. And each diagram needs to be labelled (SFD = shear force diagram, BMD = bending moment diagram) so you know what you're looking at.

7. Jul 17, 2016

### foo9008

Sorry, this is from my notes, the author didnt indicate whether the graph is bending moment diagram or shear force diagram, so you th ink what the graph represent? I think it represent the bending moment graph, am I right?

8. Jul 17, 2016

### David Lewis

It's not a shear diagram. The SFD would look like this:
(x,V)
0, 1000 N
1, 600 N
2, 200 N
2, -300 N
3, -700 N
4, -700 N

9. Jul 17, 2016

### foo9008

Then, do u have any idea what the graph is? It's not moment diagram?

10. Jul 17, 2016

### PhanthomJay

11. Jul 17, 2016

### foo9008

so , the three moment area diagram are drawn using A as reference point ?

12. Jul 18, 2016

### foo9008

if i take the reference point at B , the moment diagram will look like this ?

Ans , i also couldnt understand what does (Area AB) x A bar and (Area AB) x B bar mean ...it's not bending moment , am i right ?
in the notes , the author has chosen to draw the moment diagram by taking A as refrence point , so , he should only calculate it using (Area AB) x A bar , am i right ?

Last edited: Jul 18, 2016
13. Jul 18, 2016

### PhanthomJay

Example uses A as ref point. Using B as ref point, your moment diagrams are generally correct except the last one will be part quadratic and part linear. Deflection analysis requires summing moments of the areas under the moment diagram, using the centroid of each area to determine moment arm. Since it was 50 years ago when I last did one of these tedious calcs, I can't comment much further.

14. Jul 18, 2016

### foo9008

OK, can you explain what does (area AB x A bar) and (area AB x B bar mean)??

15. Jul 19, 2016

### PhanthomJay

These are the 'moments' of the bending moment areas about a given point and are equal to the areas of the moment graph times the distance of centroid of those areas to that point. For example, where the moment graph is a right triangle, it's area is 1/2 the base (b) times the height and the centroid is located at 1/3 (b) from fat end, as shown. This area of the moment graph part times the distance from Centroid to the given point A or B is called the Moment area .

16. Jul 19, 2016

### foo9008

why the moment area doesnt mean area under the graph only? why we must multiply the area of the diagram with position of centroid measured from a specific point?

17. Jul 19, 2016

### foo9008

moments' of the bending moment areas about a given point mean taking moment about different point in a beam,right? why there's a need to multiply the area under graph with position of centroid measured from a specific point?
http://www.mathalino.com/reviewer/m...ution-to-problem-624-moment-diagrams-by-parts
in this example, the author taking moment about different points , so he used 3 different solutions to solve the problem...
in the first solution,he take the moment about 2m from A,
in the second solution, he took the moment about B,
in the third solution, he took the moment about A....

18. Jul 20, 2016

### PhanthomJay

Don't lose sight of the fact that the ultimate goal of these examples is to determine deflections. Determining moments using moment diagrams by parts is only the first step. If all you were concerned with was bending moments, you would stop there, and probably not use moment diagrams by parts, but rather, conventional shear and moment diagrams and free body diagrams which I discussed earlier.. The author gives 3 examples of determining moments by parts, by summing moments about different points. They all lead to the same result. The moments are in units of N-m. But now since you are looking for deflections, you must continue to the next step , which is to determine the areas of the moment diagram graphs (in N-m^2, which, when divided by EI, gives slopes), and then determining the centroids of those areas, and then determining the moments of those moment areas from tje centroid about a chosen point (in N-m^3, which, when divided by EI, gives deflections) in order to go on to determine deflections. This all stems from the calculus of beam theory. Determining deflections by hand calcs is often a tedious task (except for the simpler cases), no matter what method you use.

19. Jul 20, 2016

### foo9008

But the author want us to compute the area moment diagram only, no deflection is mentioned in question....

20. Jul 20, 2016

### PhanthomJay

I don't know why you would want to compute area moment diagrams if you were not ultimately interested in deflections. Maybe just for practice.