Compressive axial force across section resulting in increased flexural rigidity
Compressive axial force across section resulting in increased flexural rigidity
(OP)
Hello
If you evenly post tension or pre tension (ignoring all losses to simplify) say a concrete column resulting in no net bending across the section do you increase the flexural rigidity of the member in some way? Will it lead to less deflection? At the most fundamental level solving for the uncracked (gross) and cracked stiffness does not rely on any forces across the section - only the mathematical first moment of area. The force in pre/post tensioning elements has nothing to do with that calculation. If anything it will help the section remain in an uncracked state under higher service load due to the additional compressive stress across the section and thus yield a greater flexural rigidity where we would otherwise be forced to switch to either an uncracked or effective (via tension stiffening) flexural rigidity.
Is there anything else to this line of thinking other than a yielding a larger cracking moment under pre/post tension? I'd be interested to hear all your thoughts on this.
If you evenly post tension or pre tension (ignoring all losses to simplify) say a concrete column resulting in no net bending across the section do you increase the flexural rigidity of the member in some way? Will it lead to less deflection? At the most fundamental level solving for the uncracked (gross) and cracked stiffness does not rely on any forces across the section - only the mathematical first moment of area. The force in pre/post tensioning elements has nothing to do with that calculation. If anything it will help the section remain in an uncracked state under higher service load due to the additional compressive stress across the section and thus yield a greater flexural rigidity where we would otherwise be forced to switch to either an uncracked or effective (via tension stiffening) flexural rigidity.
Is there anything else to this line of thinking other than a yielding a larger cracking moment under pre/post tension? I'd be interested to hear all your thoughts on this.






RE: Compressive axial force across section resulting in increased flexural rigidity
RE: Compressive axial force across section resulting in increased flexural rigidity
With time dependent effects included, things would change a bit. Creep will result in a disproportionate amount of your prestress being carried in your conventional reinforcing at the expense of the precompression in the concrete. That would mess with the cracking moment yet again.
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: Compressive axial force across section resulting in increased flexural rigidity
Deflections were pretty big (large selfweight and all) using cracked sections
I reasoned if I use smaller collumns and prestress them, they could remain uncracked under SLS seismic load.
In the end I couldnt find examples of it being done (aside from few curiosity pics in some textbooks) and local contractors never done it before so I scratched it and just thickened the columns (thereby also increasing selfweight -> more seismic force...)
Anyone here done something similar?
RE: Compressive axial force across section resulting in increased flexural rigidity
Yes. Concrete rupture will not occur until the tension stress from outside forces exceeds the pre-compression stress [Pe / Ag * (1 + e c / r^2)] + concrete rupture (root 3 f'c +/-). Pe = tensioning force, e = eccentricity (0 for your example)
Ignoring long term effects, yes in most cases.
Long term creep will be greater. If you need to increase deflection performance for a given concrete section, the PCA has an article on using higher f'c concrete (increases E - http://www.cement.org/cement-concrete-basics/produ... ). You can get about 12 ksi max here on the east coast and 19 ksi on the west coast (North America).
Until rupture is exceeded, the element can be treated as totally elastic.
RE: Compressive axial force across section resulting in increased flexural rigidity
This is not correct (in my opinion). The effect of creep and shrinkage can be modelled as a negative (i.e. compressive) prestress applied to the reinforcement. Since prestressed reinforcement starts of with a tensile strain the total flexural deflection will always be less than for a section with no initial stress, and a virtual negative prestress due to the effect of creep and shrinkage.
Axial strains (both short term and long term) will obviously be greater for the prestressed section.
The only proviso to the statement above is that if a flexural member is restrained against axial strain then the combined effects of flexure, creep and shrinkage may well result in greater cracking and deflection than in a reinforced section.
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: Compressive axial force across section resulting in increased flexural rigidity
I certainly did not intend to imply this. My stance is that a prestressed column would be flexurally stiffer but, as a result of long term effects, not as stiff as would be predicted when long term effects are ignored.
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: Compressive axial force across section resulting in increased flexural rigidity
Beams usually come up to 10-15% max (Ive seen some engineers just take 20% and dont bother calculating)...
RE: Compressive axial force across section resulting in increased flexural rigidity
But in my opinion, Tension increase geometric rigidity and compression lower geometric rigidity !
For example, considering P-Delta / p-delta effect in analysis will increase the period of a building because all column and walls are in compression !
RE: Compressive axial force across section resulting in increased flexural rigidity
I don't believe that this will be the case here. Prestressing generally introduces no additional, net compression on the concrete cross section. As such, it should not impact P-delta 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.