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.

 

[wilberz]

KootK. Thanks so much for all the information and sharing.

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?

 

[KootK]

You're most welcome Wilberz.

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.

Is it that the carbon fiber is stiffer than the stirrups and would rupture before the stirrups reach fy?

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

Yes. The earthquake-induced shear force is V_pr + V_gravity though, right?

How can there be axial compression force in the beam? where does it come from?

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.

How is AgFc/20 in #2 derived?

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.

 

[wilberz]

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."

 

[KootK]

What is the effect on axial force of beams on shear like #2 stated (again):

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.

 

[wilberz]

Many thanks for all the insights Kootk!

 

[wilberz]

Oh, just one thing more. Being one of the structural structure gods that you are I can't find this in any reference anywhere.

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.

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".

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.

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?

 

[KootK]

Structural structure god indeed.

Your above quote can't be reconciled with the following quote.

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.

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..

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.

 

[wilberz]

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.

 

[KootK]

It seems to me that what you need to do to answer all of your latest questions is simply rerun your seismic and structural analysis with the fixed bases and find out what actually happens. The only difference from the analysis that you did originally for the building would be updated frame stiffness. Yes, pretty much everything effects pretty much everything else in some way great or small. That's why we have structural analysis techniques and computers to execute them. It's time to stop playing what if and get on with the business of determining what is.

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]

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.

 

[wilberz]

It seems to me that what you need to do to answer all of your latest questions is simply rerun your seismic and structural analysis with the fixed bases and find out what actually happens. The only difference from the analysis that you did originally for the building would be updated frame stiffness. Yes, pretty much everything effects pretty much everything else in some way great or small. That's why we have structural analysis techniques and computers to execute them. It's time to stop playing what if and get on with the business of determining what is.

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.

 

[KootK]

Did you expect this?

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.