Moment Redistributions from base to joints

[wilberz]

from thread

http://www.eng-tips.com/viewthread.cfm?qid=391663

Sort of. If you design yourself a moment frame with pinned column bases and then fix the bases without changing anything else, the following ought to be true which is in line with your thinking I believe:

1) The brace will be stiffer and will attract more seismic load.
2) Some of the seismic moment previously developed in the beam / column joints will redistributed to the fixed column base joints. Whether or not there is a net decrease in moment at the beam / column joint will depend on which effect dominates (#1 or #2). I would expect a net decrease in most scenarios.
3) The plastic hinge moment that needs to be developed at the beam / column joint will remain unchanged because it depends only on the cross section and material properties of the beam which also will remain unchanged.
4) The seismic load at which a full frame mechanism will be formed will be higher because mechanism formation now requires plastic hinge formation at the column bases as well as the beam / column joints.

KootK. Please refer to the figure below.

You mentioned above that in few scenarios, there is no net decrease in the moments of the column-beam joints (even when the column base is fixed).. something about #1 where the frame can be stiffer and attract more seismic load. We know that increase in base shear just needs more tranverse ties in the columns.. so what specific scenerio do you mean where there is no net decrease in the moments at the column-beam joints? The figure above shows the moments decrease in the joint so please show how it can remain the same.. unless you mean the load above beams is increased due to increase member sizes or vertical components of seismic movement.. or what specific scenario are you referring to when you mentioned how the frame being stiffer and attracking more load would make the moments at the column-beam joint with fixed base still similar to the one of the left (pinned and bigger moments at the joint)? Thank you.

 

[KootK]

so what specific scenerio do you mean where there is no net decrease in the moments at the column-beam joints?

I don't have a specific case in mind. However, since fixing the bases stiffens the frame such that it attracts more load, it's conceivable. Fixing the bases spreads the moment around the frame but attracting more load overall will increase those same moments. Give and take. As I said though, I expect that it will be a decrease in most instances.

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 don't have a specific case in mind. However, since fixing the bases stiffens the frame such that it attracts more load, it's conceivable. Fixing the bases spreads the moment around the frame but attracting more load overall will increase those same moments. Give and take. As I said though, I expect that it will be a decrease in most instances.

A good rule of thumb is maybe to fix the base only for slender columns. Recall that k for slender column with fixed base is only one half (0.5k) compared to that of pinned bases with K of 1. This means for short columns. Fixed bases is not necessarily to avoid stiffing the structural more than necessarily for drift and it is only to decrease moment magnification in slender columns that fixing it is important.. what is your thought of this?

 

[KootK]

Recall that k for slender column with fixed base is only one half (0.5k) compared to that of pinned bases with K of 1.

For a column pinned at the top, a fixed base gets you down to K=0.7 (theoretical), K=0.8 (practical). But yeah, in concept, I agree. The return on investment is just a bit less.

Fixed bases is not necessarily to avoid stiffing the structural more than necessarily for drift and it is only to decrease moment magnification in slender columns that fixing it is important.. what is your thought of this?

Providing base fixity will improve column buckling strength for most practically proportioned columns. In my experience that is not why designers choose to fix column bases. We discussed the real reasons for pursuing base fixity quite exhaustively in the previous thread.

A good rule of thumb is maybe to fix the base only for slender columns.

I disagree with this notion for a couple of reasons:

1) It takes relatively little base rotation flexibility before buckling strength revert back to values pretty close to pin-pin conditions. I can't find it now (of course) but I once reviewed an interesting analysis of end fixity for basement walls. Because basement walls are jammed in between soil and slab on grade at the bottom, it's tempting to treat them as fixed based axial members. The article ran through the stability numbers and concluded that your average basement wall footing / soil assembly is nowhere near stiff enough to produce meaningful fixity.

2) Because of #1, most engineers will want to make "improvements" before relying on base fixity in column design. That usually means things like thick base plates, stiffeners, big anchor bolts, enlarged footings, and grade beams connecting columns. These things cost money and usually outweigh the benefit gained from saving a few pounds on column weight.

From time to time, I will consider run of the mill base plate connection to be fixed for buckling analysis in renovation work. The difference is the added risk is accompanied by more substantial reward. In new construction, assuming fixity might save $100 worth of steel tonnage. In renovation, it might save $1500 worth of welded column reinforcement. Axially loaded columns essentially pre-stress the column base connection in compression. I'll often assume that the column base is fixed up until that pre-stress is overcome.

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]

How effective do you think is grade beam say 1.5 meters above the foundation surface? How many percentage can it fix the column versus a larger footing with top rebars? I'm thinking that if the building rotates to the right.. the grade beam can all rotate to the right.. so how effective is this in column fixation? I think grade beams or tie beams are just to prevent settlement and to distribute the moments or rotations.. can it really present column rotations of the foundations (to what degree)?

 

[KootK]

A deep grade beam is one of the most effective ways to achieve fixity in my opinion. You basically get n second, very stiff beam to add to your moment frame at the bottom. I couldn't speculate on an average %fixed as it depends on a number of parameters. Competent base fixity is crucial for special moment frames. In the AISC seismic manual, they specifically recommend founding moment frame columns on deep grade beams.

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]

But the standard meaning of Grade Beam is something you put at grade connecting piles... Is the following what you had in mind about "Grade Beam" that connects the columns at ground? If the rotational inertia of the building is big.. won't the beams bars just pull from the columns?

 

[KootK]

But the standard meaning of Grade Beam is something you put at grade connecting piles

That is the more typical case. Does it really matter what terminology we use? It's a beam. It's at grade. It's a common system. The rest is just semantics.

Is the following what you had in mind about "Grade Beam" that connects the columns at ground?

Very close. I would design the beam much deeper, however, with it's underside at the top of footing elevation normally.

If the rotational inertia of the building is big.. won't the beams bars just pull from the columns?

They would want to but we, being the rock star structural gods that we are, would detail the beams to not do that. It may be prudent to extend the beams a ways past the columns to address this.

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]

Competent base fixity is crucial for special moment frames. In the AISC seismic manual, they specifically recommend founding moment frame columns on deep grade beams.

You generally discourage base fixity but seem to encourage it for special moment frame. I want to be clear what you are thinking. So you are saying that in buildings that totally rely on special moment frames without shear walls and braced frames (due to architectural causes like needing more open spaces in ground floor). Base fixity is crucial and there would be not enough frame stiffness to attract more seismic load that would not decrease the moment demands at the column-beam joints? Or even in special moment frame.. your statement " 1) The brace will be stiffer and will attract more seismic load" and "Whether or not there is a net decrease in moment at the beam / column joint will depend on which effect dominates (#1 or #2) is still valid? Meaning in special moment frames.. #1 can still apply? Or due to no shear walls and brace frames.. it has crossed the threshold where your #1 statement no longer applies?

 

[KootK]

None of that is really what I'm saying Wilber. This document will answer many of your questions: Link. In particular, see figures 3.1 and 6.1 as well as the associated text.

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]

None of that is really what I'm saying Wilber. This document will answer many of your questions: Link. In particular, see figures 3.1 and 6.1 as well as the associated text.

I presume Reinforced Concrete frames and Steel frames have similar concepts? I deal mainly with Reinforced Concrete frames so all my discussions or questions center around them.. and not on steel frames. Do all your comments on steel frames also apply to Reinforced concrete frames?

 

[KootK]

Yesir. Figures 3.1 and 4.1: Link

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 have read that nist file on concrete special moment frames a hundred times.. ok the whole reason I asked all this base fixity from you is because when the RC beams of our building were designed.. it uses Vc + Vs.. Our team is supposed to use Vs only to resist all shear... but included Vc (shear capacity of concrete).

Incidentally. the foundation is oversize 3 times because the geodetic engineer mistaken gave wrong report about it being silty sand when it is rock foundation. And we already ordered all the materials.. so we built almost like mat foundation with top rebars that create full column and foundation base fixity.

Now I'm hoping the base fixity can lessen the moments at the column-beam joints and increase the seismic resistance of the beam (with shear capacity depending on Vc + Vs and not on Vs (stirrup capacity) only).

How about you. Have you designed concrete special moments frames? Do you use Vc + Vs in the shear capacity for plastic hinge or Vs (or stirrup) only?

 

[KootK]

I have. Vs only and no change in plastic hinge moment due to base fixity I'm afraid.

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]

Ok last question. I know no change in probable moment strength and plastic hinge moment because it depends on the material properties and reinforcement (1.25 fy).. but if there is less rotation in the column beam joint.. it would cause higher moments for the plastic hinge to form.

In short and to close. When Vs was not solely used and lets say the structure become merely Magnitude 6.5 (instead of Magnitude 7.0 when Vs was solely used). I was hoping the base fixity can turn it back to Magnitude 7 rating (compensating for VS not solely used). At least this is sound right? Less rotations.. less moment in the joint.. less shear in the beams.. at least before it reaches the probable moment strength.. at least you agree with this before we closed? The essence is that if the joint doesn't rotate at all like when massive braced frames used and massive shear walls installed.. the beams won't reach probable moment strength if no rotations in the joint? This is my last question. Thanks a lot

 

[KootK]

How about this:

1) Base fixity will reduce you design seismic beam moments as you've noted. These are the moments due to "E" in ASCE7.
2) Because your M_E moments are smaller, you might be able to remove some flexural steel from your beam.
3) Because you've removed flexural steel from your beam, your M_pr moments will reduce.
4) Because your M_pr moments will be reduced your associated beam shears should go down as well.

Obviously, I have no idea if this will be enough to make up for your deficiency.

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]

Of course the flexural steel can't be removed because they are already inside the beam. So Mpr stays the same.. but it will take greater seismic moments to reach Mpr.. this is what I'm hoping to justify the 3 times expenses in the foundation.

 

[KootK]

You said that the materials were ordered. You didn't say that the beam was already cast. Garbage in, garbage out.

 

[wilberz]

The building was already fully built.

 

[KootK]

but if there is less rotation in the column beam joint.. it would cause higher moments for the plastic hinge to form.

This is where you're going astray. The beam hinge goes plastic at the same moment (Mpr) and curvature no matter what magnitude of seismic lateral load causes that moment and curvature. It is true that, with base fixity, it will take a larger seismic force to develop the beam plastic hinges. However, unless you're willing to abandon the special moment frame concept altogether and go with an elastic design, your beam is still going to develop M_pr and V_pr.

At least this is sound right? Less rotations.. less moment in the joint.. less shear in the beams.. at least before it reaches the probable moment strength.. at least you agree with this before we closed? The essence is that if the joint doesn't rotate at all like when massive braced frames used and massive shear walls installed.. the beams won't reach probable moment strength if no rotations in the joint?

I do agree with all this. But, again, this would no longer be a special moment frame designed to absorb seismic energy through the development of plastic hinges.

In a special moment frame, what you'll accomplish by fixing the base connection will be to effectively create a design suitable for a lower R value. And, commensurately, you would expect less plastic rotation. If that lower R value kicks you down into, say, an intermediate moment frame, perhaps you can use that to your advantage.

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.