Redistribution of forces

[slickdeals]

Pardon me if this comes across as a naive question.

Assume I have a 3 span continuous beam (each span say 40') in which the sequence of construction is such that the two end spans are built first and then cantilever towards each other in the mid span. Assume the final piece that gets put is rather short (say 4') so as to maximize cantilever moment. The final piece is a full moment connection.

What happens to the negative moment (and stresses) at the supports after this piece is put in? The cantilevered moment is more than the continuous beam moment. Does the system compensate for the addition of the middle member? I presume it will if the system is elastic. Are there any locked-in stresses?

Thoughts?

 

[Lion06]

Here are my thoughts. I think the stresses are what they are based on the construction sequence. If they are built as cants, then the stresses will reflect that (assuming unshored construction). That being said, that is only true of the self weight, and will likely have little impact on the intended end result.

Regarding the "locked in" stresses - if you have a fixed end beam that is installed unshored with the shear connection first it's going to behave pinned-pinned for self weight, but that doesn't impact the final design.

 

[rscassar]

I am assuming that the beam is steel?

If the beam is adequately propped during construction than it will behave as a continuous beam.

If it is built as a cantilevered system before a moment splice is installed, the selfweight moment distribution (two cantilevers) will be built-in and any additional loading after the installation of the moment-splice will be based on a continuous beam moment distribution.

 

[Ron]

Agree with kikflip that this is the way the system will react. In sequencing this way, you are maximizing the self-weight load deflection at the center span, and increasing the self weight moment over the supports. A more common method would be to do a shear splice at the moment inflection points of a continuous beam.

Will the residual stresses go away with redistribution? Only if you jack up the cantilevers to remove the deflection prior to installing the last section with moment connections.

 

[slickdeals]

What if the cantilevered segment is built with enough camber such that after the last piece is dropped in, there is still some camber left?

How does that affect behavior?

 

[Ron]

The appearance of deflection is lessened, but the residual stresses remain, as well as the stresses necessary to produce the camber.

 

[haynewp]

I agree. Without any shoring; you superimpose the moment diagrams and stresses from the first case to that of the second case with all remaining elastic. If it is cambered I would still approach it the same way.

 

[Ron]

Further, there could be an argument made that "prestressing" to produce the camber would negate the induced self-weight stresses...theoretically true; however, cambering stresses might have to occur in different locations along the beam to produce the desired effect and wouldn't necessarily coincide with the concentration of self-weight stress.

 

[abusementpark]

I agree with Ron and kikflip.

 

[rb1957]

am i missing something ? (wouldn't be the 1st time, won't be the last) ... but to me a 4' central sapn on a 40' span doesn't sound "optimal" ? what's the advantage of a short central span, over say 3 equal spans ?

 

[paddingtongreen]

The camber has no effect on the moments, kikflip still rules the day.
Deflections will be the same amounts from the installed position of the steel.

Michael.
Timing has a lot to do with the outcome of a rain dance.

 

[slickdeals]

@rb1957,
No, you are not missing anything. This was a hypothetical question. I was trying to maximize the negative moment due to the cantilever and compare it to a monolithic continuous beam.

 

[rb1957]

wouldn't a single support at the mid-span cause the largest reaction, then largest -ve moment ?