Isolated Footings - Fixed or Pinned 1

[rushitbvm]

In structural analysis on CASAD software, there are two types of working systems, we keep column end node either fixed or pinned with the footing.
1) What are the site conditions or any detailing privileges to consider them (column footing joints) as fixed or pinned.
2) are there any benefit in economy on either side
3) which type of commencement is more realistic and safe as well

 

[Stenbrook]

This depends on how you are designing your column/building, not necessarily the footing. If you are required to fix the column at the base to transfer the lateral load down to the foundation or to stiffen your structure, then you can design the footing to resist that moment, however if it is not required and you can get away with pinned bases, then you can design the footing for a pinned base with no moment on it (theoretically this works however in practicality there is no such thing as a truly fixed or truly pinned connection). This is entirely dependent on what you have decided for your structure. Obviously, if you are fixing the base, the base plate and footing will be larger than if you were just pinning the base so it will be more expensive in that department. As for safeness, if you follow the loads and design everything appropriately both options are equally safe in my opinion.

 

[wilberz]

Stenbrook.. let's say the column is not only rotationally restrained to the foundation but the column is designed such that it won't deflect even during lateral loads (say the foundation and column is solid steel that is large (1 meter solid steel column). If a beam is connected to it.. would the beam rotate? The way I understand it.. it is the moment or the drift of the column that produced rotation and probable moment strength in the beam.. with fixed column.. the beam wouldn't reach Mpr and shear from that Mpr. Am I correct?

 

[Stenbrook]

There are a few ways of looking at this (assuming I understand the question). I am assuming we are looking at a simple three member frame (2 columns and a beam). There are a few options you have to restrain the frame laterally. The first would be to fix the rotation of the beam at the ends (thus designing a moment connection of the beam to the column). The base will still be pinned at the foundation. This is usually a very flexible design from what I have experienced with large amounts of drift (depending on the size of your members) but can get the job done. The beam will experience some moment at the ends of the beam and will see rotation. The moment in the column at the top I would expect to be the same as the moment at the end of the column. The next option is to fix the base of the column at the foundation and keep the beam as a simple beam connected to the columns. In this case, the beam will see minimal moment from the lateral force and thus minimal rotation. The last option is to to design a moment connection for the beam to column and then the column to the foundation. This will be the stiffest option other than adding a brace. In this option the beam and the column will experience some moment, flexure and rotation at each end.
If that wasn't clear, you can always run some calculations using the matrix method of analysis to determine the exact rotation at each node as well. Or input a simple frame into a program like RISA or STAAD which will determine your beam deflections and what not for you.

 

[wilberz]

Once I designed a foundation where two separate footings were made to combined into one large footing (for rotational restrained).. then I made the column twice bigger (to prevent moment).. I guess the beam would be more resistant to rotations with this design.. isn't it hence it wouldn't reach Mpr and no shear failure would develop. Is this correct?

 

[Stenbrook]

I'm not going to say that I know if your particular beam is failing underneath the loads due to the plastic moment and shear or not as I do not know specifically what beam and column size you have, what loading conditions you have, as well as how the connections are detailed. All of these will play a factor into how the structure behaves.... Saying you doubled the size of the columns with no context as to where you began tells me nothing. Also, the size of the column only gets you so far. It also depends how you are designing and detailing the connection of your column to the foundation.

 

[KootK]

Some of what follows will duplicate Stenbrook's comments.

1) What are the site conditions or any detailing privileges to consider them (column footing joints) as fixed or pinned.

There are all kinds of arcane exceptions but, in general, you need:

1) A footing reinforced on both top and bottom (top rebar adds cost).
2) A footing sized to resist column base moment (extra width adds cost).
3) Soil that is stiff enough that the footing doesn't rotate appreciably when moments are applied.
4) Anchor bolts that won't pop out of the concrete under tension (longer, bigger bolts add cost).
5) A base plate thick enough that it won't yield or rotate excessively under the applied column moments (with large moments, the extra detailing can add lots of cost).

2) are there any benefit in economy on either side

As you've surely gathered from my previous comments, I feel that fixed base columns are very expensive. In practice, they are only used when they are required. This includes columns that cantilever from the foundations and sometimes moment frame columns. You might be able to use smaller columns assuming them to be fixed at the foundation but that benefit is likely to be offset in spades by the other issues.

3) which type of commencement is more realistic and safe as well

In my opinion, a building with a bunch of fixed based columns is safer. It provides a multitude of redundant load paths for lateral loads and stability. However, I don't recommend this approach. As structural engineers, our job is not to design the safest possible building. Our job is to design the cheapest possible building that is safe enough.

I agree with Stenbrook that, in reality, all column bases are fixed to some extent. Even without the extra detailing measures, you will get some fixity from the fact the the joint is somewhat prestressed by the column axial loads. In renovation work, I will sometimes take advantage of this fixity to avoid reinforcing overloaded columns.

I think that your real question here is "what is standard modelling practice for column/footing joints". The answer to that question is that they should always be pinned unless you have a very good reason for fixing them.

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]

There are all kinds of arcane exceptions but, in general, you need:

1) A footing reinforced on both top and bottom (top rebar adds cost).
2) A footing sized to resist column base moment (extra width adds cost).
3) Soil that is stiff enough that the footing doesn't rotate appreciably when moments are applied.
4) Anchor bolts that won't pop out of the concrete under tension (longer, bigger bolts add cost).
5) A base plate thick enough that it won't yield or rotate excessively under the applied column moments (with large moments, the extra detailing can add lots of cost).

If costs is not a factor.. mat foundation reinforced top and bottom would produced the rotation restrained of the columns.. isn't it? Also this means large building with mat foundation is naturally more earthquake resistant? I guess the columns need to be oversized too to avoid larger moments (you didn't mention oversizing columns)?

 

[RPMG]

By default, the column ends should be pinned.

For moment frames, some fixity at the base can be added with a rotational spring. But I would not count on only the footing connection for stability unless it's not subject to any serious lateral loads.

 

[Okiryu]

Interesting topic. Although almost all my work is related to geotechnical engineering, I am always curious to see how structural engineers design foundations. @ KootK, what could be the good reasons for having fixed columns in footings? another related related question: do you use factored loads to size your footings or you just use unfactored D + L loads? Also for lateral loads, do you apply factors to them? I have heard different opinions about this, so would like to know your approach. Thanks!

 

[Stenbrook]

For footings, I usually use ASD load combinations to size the footing but use LRFD when it comes to specifying the reinforcing steel. This is the easiest way in my opinion due to the fact that our bearing pressures are always given to us as allowable values.

I have used fixed columns on footings only when I am limited in what I can do for the bracing. For instance, if I were to be designing a carport , I can't throw a brace at the end because the client wants it to be an open frame. Sometimes a moment connection at the top with pinned bases is not enough to resist the lateral movement. In that case, fixing the base is the best option for the client to maintain the look they want.

As for designing a footing for a moment, there are several programs out there that will do this, but the calculation is not too terribly difficult to do by hand. P/A+M/S and P/A-M/S will be the pressures on either side of the footing. There is a little more to it involving the eccentricity of the footing with a minimum length based on the M/P ratio. There is a good example in the Structural Engineering Reference Manual by Alan Williams.

 

[KootK]

@ KootK, what could be the good reasons for having fixed columns footings?

Similar to Stenbrook:

- flag pole colums
- moment frames if I need it.
- renovation if I'm desperate.

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.

 

[KootK]

If costs is not a factor.. mat foundation reinforced top and bottom would produced the rotation restrained of the columns.. isn't it? Also this means large building with mat foundation is naturally more earthquake resistant? I guess the columns need to be oversized too to avoid larger moments (you didn't mention oversizing columns)?

A mat/raft footing would probably improve column base restraint and, in very general terms, also improve seismic redundancy. If one intentionally used the generic building columns for seismic resistance then, without question, they would need to be sized to accommodate the anticipated moments.


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... I read that fixed foundation can attract more seismic forces.. higher base shear.. like this thread detailed :

http://www.eng-tips.com/viewthread.cfm?qid=256630

In special moment frames.. there is an R or Reduction of 8 of the base shear because of the flexibility of the structure.. if you make the foundation on rock stiff and the column totally fixed to the foundation with all longitudinal bars at full development and bent at bottom.. in your experience.. how much bigger you need to make the columns to resist the base shear? But at least the beams won't reach probable moments at the ends as when it's flexible structure.. what can you say about this?

Why does one need (in your observation) to go for fixed foundation in moments frame.. maybe because of the lack of bracing or shear wall (when the ground need no walls such as parking)?

 

[KootK]

in your experience.. how much bigger you need to make the columns to resist the base shear?

I would expect the columns to be smaller with fixed bases. There would be more base shear but, probably, lower maximum moment. Shear in columns is usually pretty easy to handle.

But at least the beams won't reach probable moments at the ends as when it's flexible structure.. what can you say about this?

Fixed bases don't eliminate plastic hinging in beams. Special moment frames must form mechanisms which means eventual hinging at column bases and beam/column connections.

Why does one need (in your observation) to go for fixed foundation in moments frame

1) Drift control
2) Inability to create a convincing pin connection.

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 would expect the columns to be smaller with fixed bases. There would be more base shear but, probably, lower maximum moment. Shear in columns is usually pretty easy to handle.

You were referring to the Vc and Vs of the column concrete shear capacity and stirrup rebar capacity in resisting base shear? And it uses the same formulas as beam shear capacity of Vc and Vs?

Fixed bases don't eliminate plastic hinging in beams. Special moment frames must form mechanisms which means eventual hinging at column bases and beam/column connections.

Since there is very big reserve of shear capacity in columns. If you have certain fixed column base and fixed big foundation on stiff soil/rock. Then why not increase the moment resistance of the columns by making it bigger and putting more rebars.. this would make it stronger in moment hence causing less rotations in the beam-column joint.

In other words. In your experience.. how big have you made the columns and foundations to create seismic resistance totally on the elastic limit (without yielding and plastic hinges forming)?

1) Drift control
2) Inability to create a convincing pin connection.

Since it is easy to create shear resistance in columns (by enlarging the concrete Vc shear capacity and putting more transverse ties (increase Vs).. what is the reason why you need to go for longer period and lesser base shear and making the frames more flexible. Why not make fixed foundation and fixed column bases and creating bigger columns that would resist bigger base shear and cause lesser rotations by increasing moment rebar capacity? (in other words, causing less period, more base shear and making frames more rigid) What is the cons in this method?

 

[KootK]

You were referring to the Vc and Vs of the column concrete shear capacity and stirrup rebar capacity in resisting base shear? And it uses the same formulas as beam shear capacity of Vc and Vs?

Precisely.


Clients tend to frown upon unnecessarily ginormous columns. Besides, making your column huge still wouldn't eliminate the need for plastic hinging at the beam ends. The only way to get around the plastic hinging would be to accept a greatly reduced R value consistent with essentially elastic level earthquake forces.

In your experience.. how big have you made the columns and foundations to create seismic resistance totally on the elastic limit (without yielding and plastic hinges forming)?

I can't comment as I've never done this on a building located in a seismically active jurisdiction. Such a solution would be economically irresponsible, in my opinion, for any structures other than perhaps essential service facilities which are sometimes required to remain undamaged post-earthquake.

Since it is easy to create shear resistance in columns (by enlarging the concrete Vc shear capacity and putting more transverse ties (increase Vs).. what is the reason why you need to go for longer period and lesser base shear and making the frames more flexible.

You don't need to go for a longer period, lesser base shear, and making the frames more flexible. Those are just a subset of the many parameters that a designer can play with to optimize cost while preserving safety and architectural intent. Consider that:

1) For very short buildings, it's pretty hard to get beyond the constant velocity plateau of the response spectrum whether you fix the column bases or not (i.e. little change in base shear) and;

2) For very tall buildings, the effect of base fixity on stiffness and period will be negligible (i.e. little change in base shear).

So it's really only intermediate buildings that might have their base shears appreciably affected by column base fixity. And even then, the impact is unlikely to be very great.

Why not make fixed foundation and fixed column bases and creating bigger columns that would resist bigger base shear and cause lesser rotations by increasing moment rebar capacity? (in other words, causing less period, more base shear and making frames more rigid) What is the cons in this method?

Why not cast buildings out of solid blocks of concrete and just core out little tunnels for folks to move around in? Again, the answer is economy. Imagine a parabolic curve pointing downwards that represents overall cost plotted as the ordinate and frame rigidity plotted as the abscissa. At one end, you've gone out of your way to make your structure super flexible... and it's very expensive. At the other end, you've gone out of your way to make your structure super rigid... and it's very expensive. Somewhere in between, cost is minimized. That's where we want to be.

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]

1) For very short buildings, it's pretty hard to get beyond the constant velocity plateau of the response spectrum whether you fix the column bases or not (i.e. little change in base shear) and;

How many storeys do you consider "very short buildings"? Does 3 storey fall under it?

But even if there is little change in base shear by fixing the column and foundation bases.. it still is helpful.. are you saying it is not helpful? I'm saying helpful because if there is less rotation in the column base.. there is less rotation in the column-beam joint.. hence lower moment and lower shear in the beams? Do you agree with this?

 

[KootK]

How many storeys do you consider "very short buildings"? Does 3 storey fall under it?

It's tough to say. Like the response spectrum, it depends on the location, soil conditions, and occupancy. and a bunch of other factors too such as seismic mass. Also remember that moment frames are often sized for drift. Consequently, frame stiffness may well be the same regardless of whether or not the column bases are fixed.

. are you saying it is not helpful?

I'm saying a) that it is helpful is some regards and not others and b) that it is just one of many factors that goes into optimizing a design.

hence lower moment and lower shear in the beams? Do you agree with this?

In a seismic, plastic design context, I definitely do not agree with this. As I mentioned a couple of times above, your beams will develop plastic hinge level moments and shears no matter what you do with column/base/footing stiffness.

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]

In a seismic, plastic design context, I definitely do not agree with this. As I mentioned a couple of times above, your beams will develop plastic hinge level moments and shears no matter what you do with column/base/footing stiffness.

We know the reason the beams will develop plastic hinge moments is due to the energy of the seismic force being dissipated in the ductility of the frames (yielding for example) which is beyond the mere elastic capacity of the frames. But in braced frames, the plastic hinge will develop at much greater seismic energy because it's first absorbed by the braced frames.. so Im thinking if you can similarly make the frames stiff by fixing the column/base footing, it can have greater resistance. And plastic hinge can develop at greater seismic force (so instead of your structure failing at magnitude 6.. it fails at magnitude 7) by fixing the base (just like braced frames making the frames rigid). Do you agree with this now?