Loaded Question on prestress theory

[marc.rogue]

Hello, I am a recent graduate specializing in structural engineering. I didn't take a prestress course while in school but I have learned lots about the subject, I learned soo much that I actually created my own prestress design software. But something always bother me, When applying prestress to a section you are essentially providing extra compression to offset tension (over simplification of course ). I have noticed during my analysis that the neutral axis of the section meaning the concrete never matches with the stress profile, meaning my C distance from the top of the section of concrete isn't the same as the C of the stress profile. My question is, the section must remain in static equilibrium and when looking at the section specially when there are large tensile or compressive stresses the tension or compressive side of the stress profile will go above or below the neutral axis of the section, Does this mean the top or bot of the section is experiencing a net deduction of stress above or below the neutral axis if the stress profile penetrates either way. I know the forces are in balance when interacting together concrete and steel, but if the concrete is experiencing that sort of stress profile does it mean my actual stress above or below is less than the actual result or that the concrete is experiencing compression above the neutral axis. I know at the neutral axis the stress must be zero.

Thanks for any insight into this

 

[Ingenuity]

I know at the neutral axis the stress must be zero.

For pure bending yes, but a section under combined bending and axial loading will not.

The elastic analysis of a section under the actions of prestressing is simply a superposition of stresses, like your diagram indicates. Your resulting stress profile will result in more compression on one face and less compression (possibly tension) on the other face. This is no different to a beam/column section under an external eccentrically applied load.

Post-elastic analysis, when you consider cracking, creep, relaxation etc, then all bets are off.

 

[marc.rogue]

Just to make sure we are on the same page. You are technically saying that the neutral axis moves up or down to maintain static equilibrium under combined loading

. But how come then we use all of the inertial above or below the n/a to calculate stresses? In my head in order to justify the use of the section modulus of the concrete section St or Sb the stress profile must be zero at the neutral axis otherwise it would seem logical new section properties should be acknowledge.

Thanks for your response

 

[dik]

I maybe stand corrected, but I thought the NA was the point of zero stress... may not fall at the centroid, though...

Dik

 

[Celt83]

I just find it weird that we would consider the sections N/A to calculate stresses..

Your not you are using the cross sections centroidal axis to calculate section properties and then stresses. It may just be a terminology mix up, I do this all the time.
The neutral axis is the plane of 0 stress.

Open Source Structural Applications:

https://github.com/buddyd16/Structural-Engineering

 

[marc.rogue]

Hey Celt83 if you look at the images I posted last you will see that the Yt based on section properties isn't the same as the C calculated on the stress profile to calculate force. But the stresses are based on the section properties so its a little bit confusing. I read on a book by Dirk Bondy that the explanation for this is that we are only looking at the concrete diagram while forgetting there is a separate steel diagram that will balance the section out

 

[Retrograde]

I think what they are doing is first checking the stresses on an uncracked section. They then find that the tensile stresses exceed the tensile capacity of the concrete so then they move to a cracked analysis.

 

[rapt]

marc.rogue

You need to understand the difference between a sections centroidal axis and neutral axis.

uncracked section properties including the centroidal axis depth are used to calculate the stress condition.

The stress condition then defines the neutral axis depth which is used to calculate the tension force for crack control. This is all based on the assumption of an uncracked section.

With your current level of understanding, I don't think we should complicate things by going into the effects of cracking.

 

[marc.rogue]

Hey Rapt thanks for your post, I have been using the centroidal axis and neutral axis interchangeably without noticing. It took me no time to understand my mix up, essentially the centroidal axis provides the geometric center making the area above an below the axis equal, once the flexure formula is applied which is based on the centroidal axis as the integral of y dA we obtain the position of the centroid with respect to the top or bot of the section which in a tapered member will be not at H/2 there for our stress will be different and this difference will stablish the bases for our "neutral axis" which in term allow the designer (me) to control tension and compression. Iwill be honest by saying I am embarrassed now for not having thought of this before, thank you