P-M Interaction diagram

[RFreund]

It seems like explanations of most interaction diagrams leave out the portion where you have sufficient compression to overcome any tension in the section, i.e. c/d > 1 (distance from extreme fiber to neutral axis is beyond the edge of the section). How should these situations be handled? I'm looking for masonry and concrete references. Maybe it is just left out because it is a small piece of the diagram, but I can't seem to get passed it...

EIT

http://www.HowToEngineer.com

 

[JedClampett]

If I'm understanding you, doesn't it top out at the column capacity without a moment? I don't think you can take advantage of the increase of axial capacity due to the moment.

 

[IDS]

It's normally taken as linear between the point where the stress block extends to the base of the section, and the point where the strain across the section is uniform (i.e. Neutral Axis at infinity), but it's straightforward to calculate M and P for any given NA position, if you want to.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[PicoStruc]

P-M diagra always consider case where c>=d but bound maximum allowed response to PrMax (cutout at P=PrMax)

Don't forget that everything above balanced condition line (yielding occur in same time as concrete crushing) is, in theory, a fragile rupture / Not ductile.
We accept it because we have more reserve in that zone due to safety factor in concrete being more important as the compression increase.

 

[RFreund]

Thanks for the input.
I suppose I have a series of questions I'm trying to understand. See attached for questions.

1. Applying the code, ACI (for concrete) and MSJC (for masonry) to determine the correct maximum nominal axial capacity and moment capacity when c/d is greater than 1 but less than infinite.

2. The best way to 'code' this into some sort of algorithm. Problem being is that I need to switch between 2 different ways to determine the moment when c/d > 1 and when it is less than 1. But I suppose that is OK.

Attached are my thoughts and I think I am having a hard time transitioning between strain vs stress and generic vs code.

Questions:

1. Concrete - when the equivalent stress block is greater than the depth of the section. In this case how do you determine moment capacity? The stress block is uniform and covers the entire section. Therefore how do you determine moment strength? There is no eccentricity. Even if the stress was not rectangular, what is the best way to handle this?

Any suggestions are appreciated.

EIT
www.HowToEngineer.com

 

[IDS]

For a rectangular stress block the concrete has zero moment about the centroid of the section, but the reinforcement closer to the NA will normally be at less than yield, so will have a smaller force than steel close to the compression face, which normally will be past the yield strain, so the moment is entirely due to the steel.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[RFreund]

IDS -> I see, that makes sense. However, what if it were unreinforced?

EIT

http://www.HowToEngineer.com

 

[IDS]

Then there will be zero moment when the stress block reaches the face with least compressive strain.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[RFreund]

But then if plotting the interaction diagram you would have a case with axial resistance and no moment resistance? So you could have a case where you have an axial load with moment and it is outside of the interaction diagram, no?
I missing something here.

EIT

http://www.HowToEngineer.com

 

[jayrod12]

If the stress on the extreme fibre never reaches a tension state then the column (or wall) doesn't know it is in bending. At least that's how I've always interpreted it.

 

[IDS]

Rfreund - I'm not sure if I follow your question, but for a symmetrical section the maximum axial load capacity has zero moment capacity, so yes if you apply a moment it will be outside the capacity line.

Codes require a minimum load eccentricity (or equivalent procedure) so the axial load capacity to the code will be less than the theoretical maximum with no moment.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/