Continuous beam on girder instead of column 2

[wilberz]

The reactions for continuous beam on column at middle with 2 point loads at midspan at either side has the following formula:

reactions at column or middle = 11P/16 where P is the point load at either side
reactions at either end = 5P/16

how about if a girder instead of column intersects the middle of the continuous beam (imagine forming a cross).. would the reactions be the same?

 

[KootK]

The reactions would be different. The girder would deflect and some of the center reaction would redistribute to the outer supports. We ignore this pretty routinely in typical design situations, however, unless an FEM model of the floor plate is run that accounts for it.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[wilberz]

So what is the formula for this continuous beam on girder? can anyone share some references on the calculations of this?

 

[msquared48]

You would have to equate the deflections at the contact point and solve for the shared load if I understand the problem correctly.

Mike McCann, PE, SE (WA)

 

[wilberz]

The reactions would be different. The girder would deflect and some of the center reaction would redistribute to the outer supports. We ignore this pretty routinely in typical design situations, however, unless an FEM model of the floor plate is run that accounts for it.

by the way.. were you referring to the outer supports of the girder or outer supports of the continuous beam crossing it? i'm interested in the end reactions of the continuous beam (not the girder) compare to the middle reaction and wondering if it would still be 11P/16 and 5P/16.. can you imagine what I was asking?

 

[Lomarandil]

There's not going to be a convenient formula (at least not that I'm aware of) for this situation. However, you could solve for it by hand or 2D computer methods replacing the girder support with an equivalent spring based on its stiffness to support the beam.

 

[wilberz]

Ok, the following is the sketch, the middle is the girder where the continuous beam from either side carrying the slabs cross it on top of the steel bars. Irregardless of the deflections of the girder.. would the reactions at either side still be 5P/16?

 

[KootK]

@wilberz: I was refering to the continuous crossing beam as well.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[wilberz]

Kootk.. so the formula is only valid for a fixed center like a column (which of course still has strain).. and if your use a flexible center (like girder).. the moments of the continuous beam would redistribute such that the end of it would not be 5P/16 but even 7P/16.. is this what you were saying?

 

[SlideRuleEra]

reactions at column or middle = 11P/16 where P is the point load at either side

No, it would be twice that value, there are two point loads (2P) carried by the 3 supports:

Reactions at column or middle = 22P/16 where P is the point load at either side

regardless of the deflections of the girder.. would the reactions at either side still be 5P/16?

If girder deflection at point of contact = 0, then reaction at either side = 5P/16

If girder deflection at point of contact is greater than 0, then reaction at either side is greater than 5P/16, up to a maximum value of P (when the girder is so "weak" that it would deflect with "zero" load). The "continuous beam" just became a simple span.

http://www.SlideRuleEra.net

http://www.VacuumTubeEra.net

 

[IDS]

Replace the girder with a spring. It is obvious that if the spring is very soft the reaction will be close to zero. If it is very stiff the reaction will be close to what it would be for an unyielding point support. Clearly the actual reaction will be somewhere between these two extremes.

A procedure for calculating the reaction has been outlined in previous posts. It would be easy to set up on a spreadsheet.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[MacGruber22]

You could have solved this numerically 20 times in the time it is taking you to ask for an analytical solution.

If not, open your Hibbeler structural analysis book and pound away at an energy method.



"It is imperative Cunth doesn't get his hands on those codes."

 

[KootK]

Kootk.. so the formula is only valid for a fixed center like a column (which of course still has strain).. and if your use a flexible center (like girder).. the moments of the continuous beam would redistribute such that the end of it would not be 5P/16 but even 7P/16.. is this what you were saying?

Yessir. If the girder is properly designed to support the continuous beam, I suspect that the impact of its flexibility will be relatively small.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[wilberz]

So if your girder is big.. it would attract more weight to it than if it is less big.. so is it logical to design it not big so that the other beams at the ends of the continuous beams would share some load?

 

[wilberz]

No, it would be twice that value, there are two point loads (2P) carried by the 3 supports:

Reactions at column or middle = 22P/16 where P is the point load at either side

That's wrong Slideruleera. Look at the following from

http://www.awc.org/pdf/DA6-BeamFormulas.pdf

 

[SlideRuleEra]

Depends on what you want to do:

Want a certain size continuous beam to support maximum load? Design a "strong" girder.

Want to distribute the 2P load equally at four supports (at both ends of the continuous beam and at both ends of the girder)?
Design an optimal sized girder to do exactly that.

There are many possibilities, no "correct" answer for all cases.

http://www.SlideRuleEra.net

http://www.VacuumTubeEra.net

 

[KootK]

You could do it that way depending on your goals but it isn't the usual process.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[SlideRuleEra]

R2 = 11P/8 = 22P/16
Exactly what I said.

http://www.SlideRuleEra.net

http://www.VacuumTubeEra.net

 

[BUGGAR]

Sometimes I just figure a system like this considering the through girder as having no cross beam support and the cross beams as having no girder support. Crude, but if it works, just call it redundant and take the rest of the day off.

Seriously, this is how we are designing Navy stuff now.

 

[wilberz]

Did you notice that when your make the flexure of the girder stronger, it can attract more load and hence more shear in the girder?? What is this design principle called where you have to adjust between flexure and shear counterbalance.. because the less flexural capability, the less load and less shear at the support.. do designers think of this?