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Continuous beam on girder instead of column
2

Continuous beam on girder instead of column

Continuous beam on girder instead of column

(OP)

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?

RE: Continuous beam on girder instead of column

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.

RE: Continuous beam on girder instead of column

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

RE: Continuous beam on girder instead of column

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)


RE: Continuous beam on girder instead of column

(OP)

Quote:

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?

RE: Continuous beam on girder instead of column

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.

RE: Continuous beam on girder instead of column

(OP)
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?

RE: Continuous beam on girder instead of column

@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.

RE: Continuous beam on girder instead of column

(OP)
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?

RE: Continuous beam on girder instead of column

Quote (wilberz)

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



Quote (wilberz)

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.

www.SlideRuleEra.net idea
www.VacuumTubeEra.net r2d2

RE: Continuous beam on girder instead of column

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/

RE: Continuous beam on girder instead of column

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."

RE: Continuous beam on girder instead of column

Quote (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?

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.

RE: Continuous beam on girder instead of column

(OP)

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?

RE: Continuous beam on girder instead of column

(OP)

Quote:

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

RE: Continuous beam on girder instead of column

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.

www.SlideRuleEra.net idea
www.VacuumTubeEra.net r2d2

RE: Continuous beam on girder instead of column

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.

RE: Continuous beam on girder instead of column

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.

RE: Continuous beam on girder instead of column

(OP)

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?

RE: Continuous beam on girder instead of column

(OP)

Quote:

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

Yes.. I usually solve for 11P/16 for one side first and multiply by 2 since there are 2 sides.

RE: Continuous beam on girder instead of column

Quote (wilbers)

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?

Hi wilbers, I think what you are pertaning to is the effects of stiffness/rigity of members to the load distribution in a system. This phenomenon is largely expalined to civil engineering students in the theory of structures courses.

However, a good analogy is when you have a piece of log carried by 3 people, the strongest of the group will carry the largest load but it is still dependent on where he is in the system and how "weak" the others are. The closer he is to the center of mass the more loads he will be carrying.

A well experienced structural engineer will always be aware of this and take this into consideration when setting out the framing system.

RE: Continuous beam on girder instead of column

(OP)

This all assumes the continuous beams end are at same level as the girder.. but during construction if the girder is higher by let's say 10mm.. then the ends of the continuous beam will always be 5P/16.. is this agreed by all here?

Note also that you usually put the top bars of the continuous beam over the girder bars.. this means the continuous beams are always higher than the girder..

RE: Continuous beam on girder instead of column

@wilberz: the elevation effects that you mentioned would have no effect on the load distribution within the system.

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.

RE: Continuous beam on girder instead of column

(OP)
If the girder is say one foot higher than the continuous beam ends.. still no effect? how come?

RE: Continuous beam on girder instead of column

All that matters is that the deflection of the two beams is constrained to match where they cross. They could be separated by seven miles if they were connected by an axially rigid column.

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.

RE: Continuous beam on girder instead of column

Is this a homework problem? Just plug into RISA (maybe Josh will give me a free license for the plug) and get the answer. You can solve it by hand, but whomever made the project budget will not be too happy about it.

RE: Continuous beam on girder instead of column

(OP)

Kootk.. is it like during concrete pouring.. the initial formula 5P/16 at the ends of the continuous beam got reset. And upon removal of the formwork even if the girder is one meter higher, the deflections from formworks removal would redistribute the moments and make the ends contribution higher. Is this what you meant? I can imagine the spring analogy of girder flexibility but can't see how it could still work even if the girder or spring is one meter higher... do you have other ways to explain it? thanks..

RE: Continuous beam on girder instead of column

Quote (wilberz)

Is this what you meant?

The formwork business complicates the important features of this unnecessarily. I'd recommend just envisioning a pair of steel beams.

Quote (wilberz)

do you have other ways to explain it?

Try looking at it through the lens of superposition:

1) Take the interior support away from the continuous beam altogether. Your end reactions would each be P.

2) Add an upwards force (R_c) at the center of the continuous beam of any magnitude. For statics to be satisfied, the end reactions must become P - R_c/2. This is valid for any center support reaction that might be rigid or flexible, such as the support provided by a girder.

3) For the particular case where the interior support is rigid, R_c would be the force that would return the center of the beam to an elevation level with its ends. End reaction = P - R_c/2 = 5/16P.

If you apply this logic to any of the cases that we've been considering, you will find that it holds true.

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.

RE: Continuous beam on girder instead of column

(OP)

I got the above.. but there is something else. remember the ends of the continuous beams are on other beams and the beam can deflect too. I tried to imagine this scenario while sleeping and it keeps me awake half of time. So let me ask about this to be certain.. what is the effect if the ends of the continuous beams deflect too via the beams carrying the ends??

RE: Continuous beam on girder instead of column

If the central support is stiffer than the ends then it will attract a greater load. In the extreme case the central support would take all the load, and the beam would act as two cantilevers. The same applies if the beam is continuous when it is placed, and the central support is higher than the ends.

Why not have a play with some computer analysis, and you can check the results tie in with your intuition, or if they don't you can investigate why not.

I have a free continuous beam analysis spreadsheet which allows spring supports or defined deflections at the support, and can be set up very quickly:
https://newtonexcelbach.wordpress.com/2015/04/03/conbeamu-update-defined-support-deflections/

Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/

RE: Continuous beam on girder instead of column

1) if an end deflects downwards, it will decrease the reaction at that end, increase the reaction in the middle, and decrease the reaction at the opposite end.

2) if an end deflects upwards, it will increase the reaction at that end, decrease the reaction in the middle, and increase the reaction at the opposite end.

3) if both ends and the middle support deflect the same amount, you're back to 5P/16 & 11P/8.

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.

RE: Continuous beam on girder instead of column

Agree with IDS - it is a good idea to play with computer analysis so you can quickly change variables and see results. All else equal, you will find fairly quickly that axial stiffness often dominates flexural stiffness.

Also, what you can do is dust off your physics textbook and play around with the basic equations for springs in series and in parallel. Then you can relate that back to your "real" system of flexural and axial "springs".

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

RE: Continuous beam on girder instead of column

(OP)

When I model it in Etabs.. the girder (either side) is coming out with 0.54P and continuous beam end at 0.454P. While the formula is 0.68P for girder and 0.3125P for ends. How accurate in Etabs in this thing?

RE: Continuous beam on girder instead of column

Quote (wilberz)

How accurate in Etabs in this thing?

Only as good as the input!

RE: Continuous beam on girder instead of column

(OP)

Did anyone notice that in continuous beams.. if the girder near the face of column got cut off suddenly (say from shear failure), the continuous beam ends from both sides can still carry the entire loads even temporarily enough for the occupants to run outside. Has anyone thought of this in the design? Me and my colleagues don't think usually of this.. like if one member fails.. how others would take over.. do you usually consider this in your design?

RE: Continuous beam on girder instead of column

(OP)

Quote:

Only as good as the input!

You are right Ingenuity. Anyway just this one question about etabs and continuous beams.. when modelling the continuous beam ends.. must you initiate Moment Release there or not?

RE: Continuous beam on girder instead of column

Quote (willberz)

Did anyone notice that in continuous beams.. if the girder near the face of column got cut off suddenly (say from shear failure), the continuous beam ends from both sides can still carry the entire loads even temporarily enough for the occupants to run outside. Has anyone thought of this in the design? Me and my colleagues don't think usually of this.. like if one member fails.. how others would take over.. do you usually consider this in your design?

This type of analysis is called progressive collapse and it used quite frequently, especially in highly sensitive buildings.

Quote (willberz)

when modelling the continuous beam ends.. must you initiate Moment Release there or not?

If you release the moments, the beam is not continuous.

RE: Continuous beam on girder instead of column

(OP)

Quote:

If you release the moments, the beam is not continuous.

No. If you don't release the moments in etabs in columns based continuous beams the following results (it's not clear if you need to release the continuous beams when it is BEAMS crossing BEAMS, well?)

from http://www.academia.edu/10032492/How_to_Model_and_...

RE: Continuous beam on girder instead of column

I misread your previous post. I was thinking about the actual connections of a continuous beam, not at the theoretical continuous beam ends. Yes, the edge can be released, depending on what type of connection is at the edges. I disagree with the statement about wrong design when those moments ends are kept rigid. It can lead to incorrect design, but definitely not always.

Releasing the moment at the interior supports will make the beam non-continuous. The definition of a moment release is exactly as it sounds, it releases the moment. This is why people should not blindly follow design guides without knowing what the guide itself is doing. By the looks of it, it's not even a good design guide. Beam fixity is a basic concept of structural engineering.

RE: Continuous beam on girder instead of column

(OP)

If the edge is moment connected to the column with many bars.. or in other words.. not pinned but fixed connection.. can this affect the formula of 11P/16 and 5P/16?

RE: Continuous beam on girder instead of column

(OP)

This is what is puzzling.. in Etabs why do you have to release the moments at the edge when in actual contruction, the edge can even be fixed and 5P/16 still satisfies as the earlier messages by Kootk and company shows?

RE: Continuous beam on girder instead of column

This thread is killing my soul... wink

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

RE: Continuous beam on girder instead of column

Quote:

This is what is puzzling.. in Etabs why do you have to release the moments at the edge when in actual contruction, the edge can even be fixed and 5P/16 still satisfies as the earlier messages by Kootk and company shows?

Which message are you talking about?

The 5P/16 factor only applies for pinned supports with no deflection at any of the supports, and no moment restraint. Any change from those conditions will change the reaction distribution.

Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/

RE: Continuous beam on girder instead of column

(OP)

Quote:

Which message are you talking about?

The 5P/16 factor only applies for pinned supports with no deflection at any of the supports, and no moment restraint. Any change from those conditions will change the reaction distribution.

Thanks for this important information. Before some structural engineers told me in continuous beams where the middle and ends support are columns.. they just assume it's pinned (since it's so difficult to tell how many percentage is the column-beam connections fixed or pinned). So what they did is put few moment bars in the ends assuming the middle column will take the major loads (close to 22P/16). Anyway. In your designs guys.. how many percentage do you think is your column-beam pinned or fixed? Do you design it as pinned or fixed?

RE: Continuous beam on girder instead of column

Quote (wilberz)

If the edge is moment connected to the column with many bars.. or in other words.. not pinned but fixed connection.. can this affect the formula of 11P/16 and 5P/16?

You bet. Fixed end connections will draw more load to those ends.

Quote (wilberz)

in Etabs why do you have to release the moments at the edge when in actual contruction, the edge can even be fixed and 5P/16 still satisfies as the earlier messages by Kootk and company shows?

You don't have to release the ends of continuous beams. In fact, for most monolithic beam/column/girder framing systems, I'recommend against doing so. And, as I mentioned above, fixity will affect the reactions.

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.

RE: Continuous beam on girder instead of column

(OP)
In monolithic beam/column/girder framing systems, would putting less moment bars in the connection makes it more pinned than fixed? instead of using deflection to control the loads, can you use moment bars to design it such that there is no (or very few) load at the end of continuous beams because you put it all in the center? How many do this here?

RE: Continuous beam on girder instead of column

Yes, to some degree, reinforcing is a self fulfilling prophecy. If you reinforce it, the loads will come! The degree of "control" is not great, however, and designs should generally not deviate too far from anticipated elastic analysis results in my opinion. For example, even when faking a pin connection, any SE worthy of the title will provide significant negative moment capacity at the ends. The rule of thumb that I apply is that the negative moment capacity should be at least 1/3 the positive moment capacity.

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.

RE: Continuous beam on girder instead of column

(OP)
Kootk, others



Please refer to the above. I'm learning how to design 2 interconnecting continuous beams. If the beam column connections at the top and bottom were made more pinned.. there would be more moments in the midspan where the beams holding the slab frame into.. this would cause more deflection that would distribute the slabs loads to the ends girder (rather than focusing all at the center). If I made the top and bottom column-beam more fixed.. there are less moments and less deflection at midspan.. this would attract more load from the slabs. In your design which do you prefer?

RE: Continuous beam on girder instead of column

(OP)
About the above, isn't it always a good design to distribute the loads to different or more columns. So it's better to make the top and bottom columns connection to the girder beams as fixed as possible.. this involves extending the moment rebars one meter below the end column-beam joint? But then as I understand this (and wanted confirmation). When the top and bottom column and beams are more fixed, the moments in midspan would get lesser.. this would create lesser deflection and producing more load in the middle girder.. or is it like what Kootk said that during concrete pouring and hardness, the initial boundary conditions are set even if the secondary continuous ends are one meter higher as we originally discussed? So the deflections in the primary girder beam would have no effect on the load distribution of the secondary continuous beams?

RE: Continuous beam on girder instead of column

(OP)

I guess you will say that depending on the tension bars at positive moments.. there is no problem with deflection if you choose either the pinned or fixed ends of the primary girder. Ok. And depending on the tension bars at negative moments at the continuous ends, you can control approximately the pinned and fixed condition. And these two is what can make the design different.

Well. I let 2 fellow structural engineers design the above. They come out with totally different designs. One guy modelled the ends as pinned while the other guy modelled it as fixed. Since there is no way to totally predict if it will be pinned or fixed and by how much amount, then you should design the center column to be stronger and the girder to avoid unexpected loads. Is this correct? If it is, the it summarizes this thread. Thank Koots for the very enlightening thoughts.

RE: Continuous beam on girder instead of column

Go back up to your nice little shear diagram from AWS.....

You will note that V2 shading above and to the right of R2 is equal to the V2 shading that goes to the left and below R2. That line running thru R2 (the reaction at R2) is the sum of V2+V2.....exactly what SlideRuleEra told you long ago.....you seem to be arguing with a lot of people who have tremendously more experience than you.....why is that?





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