maximum positive moment on a continuous beam

[jonad]

[URL unfurl="true"]https://res.cloudinary.com/engineering-com/image/upload/v1643675638/tips/Pos_Moment_zukhqn.pdf[/url]

If given the following known variables, M1, M2, V1, V2, anyone know an equation for finding maximum positive moment in a continuous beam model? See image for details.


thank you,

jonad

edit: Thank you everyone for the responses. Realizing the error in my analysis from your responses. Will have to go at this from a different angle. Thank You!

 

[rb1957]

this looks like moment distribution method ...

another day in paradise, or is paradise one day closer ?

 

[jonad]

Sorry for the confusion rb1957. Should have specified how I got to this point. Modeled it as a fixed end model. Then used the FEM's using the theorem of three moments to get the negative moments. Now I can't figure out how to get the maximum positive moment.

 

[dik]

Something like ql^2/8 -(M1+M2)/2 for a uniform load?

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

 

[KootK]

To do what you're proposing, it seems that you would need to somehow work backwards from the FEM's to get the disposition of the actual applied loads. I don't know that's possible without making some assumptions. For example, the same FEM's might be produced by either a uniform or a concentrated load.

 

[271828]

Like KootK mentioned, you're going to have to tell us what the member load is. Uniform, point load, series of point loads, some combination?

I don't think I understand where you're coming from. You've already done the hard part. With the end moments and member loads, this is a basic Statics shear and bending moment diagram problem.

 

[jonad]

Thanks everyone for the responses. Just realized my question had a huge error. I edited the original post to not include FEM's.

 

[KootK]

If there is actually no load on the span being considered, the end moments should be the peak moments, both positive and negative as applicable. Your moment diagram would be a straight line, right?

 

[Celt83]

Check out the 2-cycle moment distribution method for an approximation on the positive moment: Link

If the span is unloaded then peak moments are at the ends. If the span is loaded then you can either do a numerical root finding algorithm on the shear or determine the actual shear formulas and solve for the roots exactly. My own thread on a similar topic: Link

My Personal Open Source Structural Applications:

https://github.com/buddyd16/Structural-Engineering

Open Source Structural GitHub Group:

https://github.com/open-struct-engineer

 

[JoshPlumSE]

We would need to know the loading to get the max moments.

For example we know the difference in shear between point 1 and point 2, which tells us the total load difference. But, that could be a point load applied near 1, at mid-span, near 2. It could be a distributed load, or a combination.

 

[le99]

If I remember correctly, for a simply supported beam, the maximum span moment is the sum of the shear areas from the support to where the shear change signs (where V = 0). For a continuous beam, it is the above less the area under the negative moment.

 

[rb1957]

what you are showing is a span from the moment distribution method ... research that topic .... you learning something is better than us giving you an answer (that you may not appreciate/understand). As many have said already, if there is no loading on the span, then the max moment is at one end (but telling you that doesn't teach you much).

another day in paradise, or is paradise one day closer ?

 

[BAretired]

See below:

BA

 

[WARose]

Pattern loading sometimes controls for continuous beams. IIRC, it can wind up being (the equivalent of) a simple span moment if the pattern is right. (I.e. M=wl²/8)

 

[dik]

Time for a 'plug'... that's one of the nice things about plastic design.

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik