Moment Redistributions from base to joints
Moment Redistributions from base to joints
(OP)
from thread http://www.eng-tips.com/viewthread.cfm?qid=391663
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.
Quote:
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.






RE: Moment Redistributions from base to 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.
RE: Moment Redistributions from base to joints
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?
RE: Moment Redistributions from base to joints
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.
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.
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.
RE: Moment Redistributions from base to joints
RE: Moment Redistributions from base to joints
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: Moment Redistributions from base to joints
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?
RE: Moment Redistributions from base to joints
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.
Very close. I would design the beam much deeper, however, with it's underside at the top of footing elevation normally.
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.
RE: Moment Redistributions from base to joints
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?
RE: Moment Redistributions from base to joints
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: Moment Redistributions from base to joints
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?
RE: Moment Redistributions from base to joints
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: Moment Redistributions from base to joints
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?
RE: Moment Redistributions from base to joints
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: Moment Redistributions from base to joints
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 :)
RE: Moment Redistributions from base to joints
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.
RE: Moment Redistributions from base to joints
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.
RE: Moment Redistributions from base to joints
RE: Moment Redistributions from base to joints
RE: Moment Redistributions from base to joints
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.
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.
RE: Moment Redistributions from base to joints
By the way. I have the beams wrapped with very expensive carbon fiber to make the shear capacity Vc + Vs + Vf (to compensate for not using solely Vs). But I read strain synchronization between carbon fiber and stirrups may not go together and it may not be Vs + Vf(shear capacity of carbon fiber). So I don't rely on it.
Oh. Just a clarification. In ACI 421 it is mentioned on beams:
"Transverse reinforcement over the length L, identified in Section 421.6.4.1 shall be proportioned to resist shear assuming Vc=0 when both of the following conditions occur:
1. The earthquake-induced shear force, calculated in accordance with Section 421.6.5.1 represent one-half or more of the maximum required shear strength within L
2. The factored axial compression force, Pu, including earthquake effects is less than Agfc/20."
Our analysis shows the earthquake induced shear force is much less than one half so #1 doesn't satisfy.
But our analysis team doesn't understand #2. How can there be axial compression force in the beam? where does it come from? This is the reason we assume Vc=0 and existing Vs become inadequate a bit to resist all shear forces so we added carbon fiber that is not sure to compensate (and prayed our 3 times more expensive foundation with fixed base can lower the seismic moments).
Oh. How is AgFc/20 in #2 derived?
RE: Moment Redistributions from base to joints
Is it that the carbon fiber is stiffer than the stirrups and would rupture before the stirrups reach fy?
Yes. The earthquake-induced shear force is V_pr + V_gravity though, right?
Generally, the shear load is not coming in from the portions of the building on either side of the frame in equal amounts. But it is assumed to be resisted equally by each moment frame column assuming that the moment frame itself is symmetrical. If you do the statics on that, you'll find that there's usually an axial load in the moment frame beams. I usually find that it's hard to justify an axial beam load that I'm confident will be there all of the time and in both directions though so I often ignore that provision.
I'm afraid I've no idea. I would assume it to be a number verified by testing. Under some amount of compression, I would presume that cracks wouldn't widen progressively with each displacement cycle and Vc would be preserved.
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: Moment Redistributions from base to joints
In the column interaction diagram. There must be certain Pu for cerain optimal Mu (balance failure). Without Pu, the tension side would yield earlier because no compression force.
In the beams. I guess similar concept, but then it is the flexural capacity that is affected (akin to the interaction diagram in columns). What is the effect on axial force of beams on shear like #2 stated (again):
"2. The factored axial compression force, Pu, including earthquake effects is less than Agfc/20."
RE: Moment Redistributions from base to joints
With no axial load, flexural shear cracks open up and get progressively wider under cyclic reversals. This results in a loss of aggregate interlock and anything really resembling Vc. With some axial prestress, that doesn't happen I guess.
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: Moment Redistributions from base to joints
RE: Moment Redistributions from base to joints
Your above quote can't be reconciled with the following quote. Or the part where fixing the base would make you expect less rotations. But in the following you said it's possible the rotation would stay same because "fixing the bases spreads the moment around the frame but attracting more load overall will increase those same moments".
Can you think of a specific case where the rotations would remain the same because more moments occur increasing those same moments as you put it.. maybe it has to do with structure with many columns versus few.. what is the threshold or the situations.. please meditate and think of one :)
how do you compute for this? Or any reference how to tell what structure will experience what.. or what scenarios can create this difference where the rotations/moments remain the same in the column-beam joints even if you fix the base or worse even increase the rotations because by attracting more seismic load.. you add more base shear and more moments in the column bases?
RE: Moment Redistributions from base to joints
I think that they reconcile if you consider that the first quote refers to post-hinging plastic rotations and the second quote refers to pre-hinging elastic moments (M_E). Those are very different things.
Nope.
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: Moment Redistributions from base to joints
I know.. you said "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". This plastic rotation being related to Mpr. Or are you just referring to ordinary frames where column-beam joints are damaged or cracked (plastic rotations).
But pre-hinging elastic moments is related to post-hinging plastic rotations. How. The more pre-hinging elastic moments there are in a frame, the faster (or more possible) post-hinging plastic rotations can form. And the less pre-hinging elastic moments, the slower post-hinging plastic rotations can form.
My concern is for a certain frame.. how do you know whether there will be an increase or decrease of the elastic moments by fixing (and stiffing the frame)? Particularly, I'd like to analyze if my building will have increase or decrease of the elastic moments in the columns and column-beam joint compared to when the bases are pinned. I'd like to see example how one analyze it. Thanks.
RE: Moment Redistributions from base to joints
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: Moment Redistributions from base to joints
That's a great idea. Many Thanks. (One of these days if you encounter references or studies that compares pinned and fixed bases on the same structure and how moments of each members increase or decrease.. please let me know (post the link at this thread) so I can see bird eye view of them). The building was designed years ago and the original designers already resigned so can't reach them anymore.
RE: Moment Redistributions from base to joints
I entered all structural members sizes, Live load, SD load, etc. into ETABs.. and ran exhaustive comparisons between fixed and pinned column base. And here is my finding.
1. In the 2nd storey floor, there is 5-7% reduction in shear (at EQ loading).
2. Above 2nd storey, there is almost no changes in shear (all tested at EQ loading).
3. Looking at the shear and diagram of the columns. I noticed only the ground floor has more than normal effect overall because there is base moments (bec fixed) instead of just moment at the top column-beam joint (pinned condition). However in the 2nd floor and above. I noticed that even if the column base in foundation is pinned.. the columns in the 2nd floor and above automatically fixed (so you have an S shaped moments). This is the reason no changes in the shear above 2nd storey. Did you expect this?
4. The reason there is only 5-7% reductive in shear at 2nd storey floor is because the moments in the column of the ground floor is 1/4 that of the moment of the beams. This means with pinned vs fixed base, the bigger moments of the beam seem to dominate. In Etabs.. I set the column "Reinforcement to be Checked". It produced 1/4 less moments than the beam positive moments at midspan. Is Etabs is it displaying the full moment of the columns without reinforcement or moments taking account of the reinforcement when has certain loading conditions like EQ?
5. The big effect is the deflection.. there is better deflection control overall when the based is fixed.. even when I duplicate the storey in etabs and add higher floors.
The building is 3 years old. I'm just trying to understand it (not intend to do anything because it's already built). Thanks.
RE: Moment Redistributions from base to joints
I did. That's partly why I excluded taller buildings from the range of buildings that would be meaningfully affected at the beginning of the discussion. Even the effect on drift should become minor for the upper floors of high rise buildings. I don't play with ETABS much these days so I'm not the best person to be commenting on it's algorithms.
Thanks for posting the results of your study. Interesting stuff.
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.