Interaction diagrams for columns

[drasticxxxx]

I have a question that I need to understand to let me know the answer of another question.

While we are creating the interaction diagram, we always sum moment around the centroid of the section which in most cases will be the h/2,, I thinks this true if the section under complete compression, but under some cases it will be under tension and the moment should be sum around neutral axis (similar to beam design), why this is not followed!!!!

My second question which I may answer if I get the first question answered, is while in column, the steel is not focused only at the two edges, because under pure axial load all the steel will contribute the same regardless of steel distribution, while under moment and lateral load the steel far away from N.A will have the most significant contribution, so why to distribute steel in all section, is it to count for the other moment direction!!!

 

[IDS]

In a beam it doesn't matter where you take moments about, because there is no axial load.

In a column the moments are normally calculated assuming the column is a line located at the centroid of the section, so that is the line we should also use for calculating the moment capacity.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[drasticxxxx]

But it should be calculated around N.A not centroid in column case, I found that ACI 2002 Used to calculate it on N.A, but now it changed,so do you have any clue,it doesn't make since to me?

 

[sponton]

You can calculate the moment at any point in the section as long as you're consistent with it. In any case if you're doing an interaction diagram what you do is shift the N.A. from bottom to top [from pure compression to tension] and do the sum of the moments at the neutral axis. Then you add the Tension and Compression forces, and what you have is the axial load at that point in the diagram, so you get your two points.

I don't understand your second question. So here's my attempt to respond. We distribute the steel in one direction because we get to choose how we use the steel section, we make assumptions. When we have moment frames we orient the column to act in the strong direction, not in the weak direction. It's about choice, why would we standardize sections to be completely efficient in both directions if we are given the choice of how the structural system will work. Plus, sections are not perfect, when you hot roll the sections you end up introducing residual stresses in the flange-web connection, so your section is not exactly uniformly distributing stresses, since part of your sections have already reached Fy/3, so you can only allocate 2fy/3, and the more difficult shapes get and the more welding you have to do the more residual stresses you introduce [of course these depend on the procedure and other variants]

 

[IDS]

But it should be calculated around N.A not centroid in column case

Just saying it doesn't make it true. Why do you think the moment resistance should be calculated about the NA? Look at the applied load as an eccentric vertical load. Where do you measure the eccentricity from?

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[KootK]

I'm with sponton on this one. Moments can be calculated about any point: centroid, neutral axis, Memphis... The only reason to prefer one location over another is computational convenience.

Biaxial concrete column design is horrendous which is why computers have been doing it for a long time. Taking moments about the centroid is straight forward in code which is probably why it's often shown to be done that way. If I had to do it by hand, I probably would take moments about the neutral axis. This is because you'd already have all the perpendicular distances to the bars handy because those distances would have been required to work out the strain and stress in the rebar.

so why to distribute steel in all section, is it to count for the other moment direction!!!

That is the main reason. The other is that columns are usually intentionally compact elements for architectural reasons. Often a smaller column with some bars utilized sub-optimally is the best decision for the project.

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.

 

[drasticxxxx]

Thank you guys.

Your help is appreciated.

But if you calculate around N.A or Centroid ,does it give the same result!!!

 

[KootK]

But if you calculate around N.A or Centroid ,does it give the same result!!!

Sponton and I think so. Why not fire up your calculator and run one both ways to settle the debate?

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.

 

[IDS]

But if you calculate around N.A or Centroid ,does it give the same result!!!

Sponton and I think so. Why not fire up your calculator and run one both ways to settle the debate?

It depends how you do it.

If you add all the moments of the steel and concrete about the NA you will get a different answer to adding the moments about the centroid.

If you add the moments about the NA then add the moment due to the resultant axial force x eccentricity of NA from the centroid, you will get the same result.

If the resultant axial force is zero, then it makes no difference.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[mes7a]

Just want to ask something related to this. Supposed at bar strain of 0.0021, the bars at compression side has capacity of 1,000kN.. and supposed there is no concrete at compression side (say it has a void where there is only reinforcement).. any quick way to get estimate for moment capacity when the column is bending towards and compressing that side without solving for the interaction diagram (where you solve for moment and axial load to get eccentricity plots in the diagrams)?

 

[IDS]

mes7a - If there is no concrete around the bars they will buckle so the capacity will be much less than if the bars are embedded in concrete.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[mes7a]

mes7a - If there is no concrete around the bars they will buckle so the capacity will be much less than if the bars are embedded in concrete.

Let's say there is epoxy that hold the bars (preventing buckling) but epoxy being soft can't take compression.. so the bars are what simply take the compression (for sake of discussion). Do you just make zero all the compression block and still solve for the interaction diagram.. but I'm asking if there is a faster way to estimate the moment capacity from a given axial load capacity in the compression side with no concrete but with epoxy that bind the bar and prevent buckling (in say 4 inches portion of a column)?

 

[IDS]

You don't need to do an interaction diagram to find the moment capacity whether there is any concrete there or not, but if you have some magical way of preventing buckling, and there is no concrete in the compression zone then only the steel will be active in both tension and compression, so you could analyse it like a steel beam.

Is this just hypothetical, or do you have some real structure you are asking about?

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[mes7a]

You don't need to do an interaction diagram to find the moment capacity whether there is any concrete there or not, but if you have some magical way of preventing buckling, and there is no concrete in the compression zone then only the steel will be active in both tension and compression, so you could analyse it like a steel beam.

Is this just hypothetical, or do you have some real structure you are asking about?

It's real. 2 years ago the structure was built. But there was problem with one column with a hole because of bad formworks. See picture:

The designer told us to inject it with epoxy to cover the hole:

Pure epoxy has low modulus of elasticity so it acts like very soft plug. For pure gravity load, the column can make it. But I'm thinking how it performs when it is moving back and forth from seismic activity. At unit strain of 0.0021.. the bars alone at the hole have axial capacity of about 1000kN. Is there a way to quickly convert it to moment capacity? The rebar details are:

The one shown in red is the one with hole.

 

[sponton]

Well, the shear resistance is provided by the concrete that is confined by the ties rather than the one that the one in the edges. So I wouldn't really worry about it. I have seen loads of provided solutions where epoxy is used [not by itself, normally it's mixed with grout] and is merely an aesthetic/water intrusion prevention kind of thing, the times used we have known the column in questions is conservatively designed [so no need to really assess the structural damage numerically], besides in most of the situations the column 'core' has remained protected. The addition of the epoxy/grout mixed in any case, shouldn't decrease the strength of the column if properly done.

by the way buckling is prevented by ties and other conditions not just because it has epoxy. Epoxy is used [in conjunction with grout] because of good adherence to existing concrete and it seals the whole thing [we have used it successfully in concrete channels that were horridly constructed]

 

[mes7a]

stonpon.. please look at this in closer view.. it's not damaged?

 

[Angre]

The moment(s) in column are calculated about COG of concrete cross section.
This is so because the line of action of P(axial force) is through the COG of concrete cross section.
There is nothing special about it though.
To illustrate through an example, assume a column with P=1000KN(downwards) alone and no moments.Say the Column size is 1m x 1m.
If I were to write force system ABOUT the COG it would be P=1000KN Mx=0KN-m My=0KN-m.
But if I were write force system ABOUT top-right corner, the force system would be written as P=1000KN Mx= - 1000KN*0.5m My=-1000KN*0.5m .

I have confronted this problem while writing a spreadsheet for designing a concrete column subject to axial load and biaxial moment,
so Iam aware of the conundrum.By the way the spreadsheet works even if the axial force were to be tensile.

 

[sponton]

1) spalling of the concrete it's not necessarily as detrimental as it looks, specially because we give a protective cover against weathering of the reinforcement. Of course, the effect depends on the loadimg conditions and the type and direction of load that the column is subjected to.
2) it is necessary to know where the column is located, is it an edge column, is it a inner column, how many stories is the column supporting, are the dimensions of the column similar to inner columns if this is an edge column?
If the former is true then it is quite likely that the column is a bit conservstive in its design. Like someone commented further up, spalling of the concrete wouldnt necessarily matter, since you have reinforcement that can take the load and it seems that it 'properly' constrained laterally so it won't buckle with the extra load (this is assuming that it was actually designed to the limit which quite likely isnt the case since seeing the reinforcement, concrete columns properly designed and detailed should always anticipate stuff like this (at least we did where i work because supervision was shite)
3) are you in a highly seismic or hurricane prone region?
4) just a thought in design, there should be a joint between those two little walls (parapets) and the column, in high seismic areas these ram against the columns and create concentrated shears ( there are a couple of videos of life size buildings being tested im japan, you can find them in youtube). These are rather small and i guess its ground level so it wouldnt be as detrimental but its still some food for thought.
5) is the structural engineer that provided the solution the designer that designed the bdg? If so he knows best. I have seem similar solutions before and its not uncommon. Typically here we mix the epoxy with cement. I've seen engineers add another rebar and anchoring it with epoxy and spaling the concrete around the column to add new ties (they knew this was unnecessry but client was scared becuase of bad contractor) also repairing of walls that have spalled off with epoxy and grout and welded wire mesh.

 

[mes7a]

1) spalling of the concrete it's not necessarily as detrimental as it looks, specially because we give a protective cover against weathering of the reinforcement. Of course, the effect depends on the loadimg conditions and the type and direction of load that the column is subjected to.
2) it is necessary to know where the column is located, is it an edge column, is it a inner column, how many stories is the column supporting, are the dimensions of the column similar to inner columns if this is an edge column?
If the former is true then it is quite likely that the column is a bit conservstive in its design. Like someone commented further up, spalling of the concrete wouldnt necessarily matter, since you have reinforcement that can take the load and it seems that it 'properly' constrained laterally so it won't buckle with the extra load (this is assuming that it was actually designed to the limit which quite likely isnt the case since seeing the reinforcement, concrete columns properly designed and detailed should always anticipate stuff like this (at least we did where i work because supervision was shite)
3) are you in a highly seismic or hurricane prone region?
4) just a thought in design, there should be a joint between those two little walls (parapets) and the column, in high seismic areas these ram against the columns and create concentrated shears ( there are a couple of videos of life size buildings being tested im japan, you can find them in youtube). These are rather small and i guess its ground level so it wouldnt be as detrimental but its still some food for thought.
5) is the structural engineer that provided the solution the designer that designed the bdg? If so he knows best. I have seem similar solutions before and its not uncommon. Typically here we mix the epoxy with cement. I've seen engineers add another rebar and anchoring it with epoxy and spaling the concrete around the column to add new ties (they knew this was unnecessry but client was scared becuase of bad contractor) also repairing of walls that have spalled off with epoxy and grout and welded wire mesh.

I'm deeply analyzing the derivation of the interaction diagram (also solving for it). I noticed something. My interaction diagram for that column is:

The deadload they computed for the column is 357 kN. SD load = 214 kN, Live load is 166 kN. Total load is 737 kN. (I'm just verifying stuff manually)

The nominal axial load capacity of the column (as the above diagram) shows 6927 kN (it was designed for 4-storey but only 2-storey with roofdeck built)
The Mn (nomimal moment capacity) is 726 kN.m

You will notice that the actual load of 737 kN is much below the balanced P and M of the interaction diagram (shown in x in the illustration). Now my question is this.

I'm analyzing the derivations of the formula. They say axial load can press on the tension side making the moments capacity larger. But below the balanced point.. there is no axial load anymore pressing on the tension side. The formula for Moment in the interaction diagram is

Pn = 0.85fc' ab + As' fs' - As fs

Mn = Pn e = 0.85 fc' ab (h/2 - a/2) + As' fs' (h/2 - d') + As fs (d-h/2)
note 0.85fc' ab is just the role of concrete in the compression side.. but where is the role of concrete in the tension side?

Also for eccentricity larger than balanced point.. I noticed the tensile strength (85 ksi when the bars would break) would be reached for eccentricity of 324mm (compared to balanced e of 284mm). The P computed is 2150 kN and M is 698kN (below the balanced point in the tension failure part). But my total load is only 737kN. Does it mean the bars would break (reach tensile strength) when the moment is 698kN? But it corresponds to axial load of 2150kN. Does it mean I must make the load heavier at 2150kN to avail of the moment capacity? But where is the role of concrete in the tension side at the interaction diagram formula at large eccentricity?