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?

 

[wilberz]

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.

 

[Enhineyero]

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.

 

[wilberz]

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..

 

[KootK]

@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.

 

[wilberz]

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

 

[KootK]

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.

 

[dcarr82775]

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.

 

[wilberz]

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..

 

[KootK]

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.

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.

 

[wilberz]

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??

 

[IDS]

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:
[link ]

https://newtonexcelbach.wordpress.com/2015/04/03/conbeamu-update-defined-support-deflections/

[/url]



Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[KootK]

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.

 

[MacGruber22]

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."

 

[wilberz]

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?

 

[Ingenuity]

How accurate in Etabs in this thing?

Only as good as the input!

 

[wilberz]

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?

 

[wilberz]

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?

 

[mike20793]

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.

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

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

 

[wilberz]

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_Analyze_Structures_Using_ETABS

 

[mike20793]

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.