Need assistance with Moment diagram

[uber_beetle]

I am familiar with what the shear and moment diagrams should look like for a simply supported beam with one moment couple located somewhere between the supports. However, I'm working with one that has multiple couples applied to it and I'm having trouble wrapping my head around how it should work out.

Please consider the following:

...>...>...>
-------(--------(--------(--------

The moments are all the same size, and distance apart.

The Extent of what I know about this:
I know that if you only have one moment, the diagrams should look something like

F:
...<
------)--------

V:
0____________

M:
0_____
..._______


My Theory:
Am I right in thinking that each one of those consecutive moments would not add any shear, but would jump the line of the moment graph up by it's magnitude repeatedly leaving me with a diagram that looks like a set of steps?

Thank you!

 

[PhanthomJay]

I am familiar with what the shear and moment diagrams should look like for a simply supported beam with one moment couple located somewhere between the supports. However, I'm working with one that has multiple couples applied to it and I'm having trouble wrapping my head around how it should work out.

Please consider the following:

...>...>...>
-------(--------(--------(--------

The moments are all the same size, and distance apart.

The Extent of what I know about this:
I know that if you only have one moment, the diagrams should look something like

F:
...<
------)--------

V:
0____________

M:
0_____
..._______


My Theory:
Am I right in thinking that each one of those consecutive moments would not add any shear, but would jump the line of the moment graph up by it's magnitude repeatedly leaving me with a diagram that looks like a set of steps?

Thank you!

You are not quite on track, but close. The shear stays constant along the length of the beam(determine end reactions first). The moment along the beam jumps at each applied couple, but is not constant in between couples...it varies linearly with a slope equal to the shear at any given point.

 

[kataya]

I am familiar with what the shear and moment diagrams should look like for a simply supported beam with one moment couple located somewhere between the supports. However, I'm working with one that has multiple couples applied to it and I'm having trouble wrapping my head around how it should work out.

Please consider the following:

...>...>...>
-------(--------(--------(--------

The moments are all the same size, and distance apart.

The Extent of what I know about this:
I know that if you only have one moment, the diagrams should look something like

F:
...<
------)--------

V:
0____________

M:
0_____
..._______

You should also realize that your original diagrams were not correct. As phanthomjay pointed out, the moment is the integral of the shear force along the beam. If v is zero, then the moment is a constant.

 

[uber_beetle]

Ok... an update.. I'm pretty sure i got it straightened out.. but can you confirm that this thing's moment diagram would look sort of like a saw blade?

The reactions work out in my homework version as a large fraction of M... basically, if you sum them across the beam... the moment creeps up above the x-axis and finally ends with a 0 at the far right support.

 

[PhanthomJay]

Ok... an update.. I'm pretty sure i got it straightened out.. but can you confirm that this thing's moment diagram would look sort of like a saw blade?

The reactions work out in my homework version as a large fraction of M... basically, if you sum them across the beam... the moment creeps up above the x-axis and finally ends with a 0 at the far right support.

Yes, looks like a rip saw blade; the reactions are 3M/L and -3M/L at each end, respectively; shear is constant at -3M/L; the moments are zero at each end and zig-zag below and above the x-axis in between.