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Hello, I have a small question about moments and bending moments.

So, if I have a beam with a loading given by q (N/m) which is given as a function of x then what do these calculations get me?

[tex]\int xq(x) dx[/tex]

[tex]\int (\int q(x) dx) dx[/tex]

The first integral gives me the moment about a point because I am taking a differential distance and multiplying it with the value of Force there given by q(x) and adding up all these differential moments.

The second integral gives me the bending moment about a point..

And here is what has been troubling me.

Isn't the bending moment the resultant moment on one side of the beam? I mean:

So, isn't the bending moment at a point simply the first equation where you integrate from the point you are interested in to the end and then subtract the moment due to the reaction?

So, bending moment = [tex](\int_{x}^L xq(x) dx ) - R2x[/tex]

But that that doesn't seem right. Since the bending moment is [tex]\int (\int q(x) dx) dx[/tex]

and you fill in the boundary conditions and plug in the value of where you want it...

In short, what is the fundamental difference between the bending moment and the resultnt moment on one side of the beam. To me it seems they are the same, the bending moment is the moment the beam is having to apply at that point to counteract the resultant moment on the other side of the beam, but mathematically they seem different.

So, if I have a beam with a loading given by q (N/m) which is given as a function of x then what do these calculations get me?

[tex]\int xq(x) dx[/tex]

[tex]\int (\int q(x) dx) dx[/tex]

The first integral gives me the moment about a point because I am taking a differential distance and multiplying it with the value of Force there given by q(x) and adding up all these differential moments.

The second integral gives me the bending moment about a point..

And here is what has been troubling me.

Isn't the bending moment the resultant moment on one side of the beam? I mean:

So, isn't the bending moment at a point simply the first equation where you integrate from the point you are interested in to the end and then subtract the moment due to the reaction?

So, bending moment = [tex](\int_{x}^L xq(x) dx ) - R2x[/tex]

But that that doesn't seem right. Since the bending moment is [tex]\int (\int q(x) dx) dx[/tex]

and you fill in the boundary conditions and plug in the value of where you want it...

In short, what is the fundamental difference between the bending moment and the resultnt moment on one side of the beam. To me it seems they are the same, the bending moment is the moment the beam is having to apply at that point to counteract the resultant moment on the other side of the beam, but mathematically they seem different.

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