Prestressed column 5

[OAP]

Hi folks,
Let's assume we have a long column (10.0m height ) and cross section of column is 0.3*0.3 m. which we can't have the lateral restraint to reduce the slenderness ratio due to the architectural concept. This column are spacing 6.00 m. and have to support roof truss span of 25.0 m. Do anybody have an idea that if we prestress this column, it's gonna help the slender problem or not?
Thanx
OAP

 

[dlew]

After reading all the messages again I believe that we are all in agreement that prestressing a column does not increase "practically" its buckling load. Is that true?

Let me ask another related question: If we apply an external compressive force P1 to a column prestressed with a prestressing force P2, what would be the compressive stress in the concrete and the tensile stress in the pestressing tendon?

When P1 < P2
fc = (P1+P2)/Ac ?
fs = (P2-P1)/As ?

When P1 > P2
fc = P1/Ac ?
fs = nil ?

Thanks in advance

AEF

 

[Ingenuity]

dlew,

1. Generally and practically, internal prestressing will not increase NOR decrease the buckling load of a PSC column. You can argue that under large external moments is it a little stiffer (less cracking = larger EI = less magnified moments) so you may justify a higher l/r ratio - but this is small effect.

2. Assuming elastic conditions, regardless of the magnitude of the initial prestressing force, P2, under the action of an external axial load, P1, the elastic stress on the concrete will be:

P2/Ac + M2/Ic + P1/At + M1/It

where P1 and M1 are the externally applied axial load and moment, respectively. M2 is P2xE2, where E2 is the eccentricity of the prestress force P2. Ac and Ic are the concrete section properties and At and It are the transformed section properties which account for the now-bonded condition that the column sustains under external load. You can use just gross section properties (Ac and Ic) for all the elastic calcs and the error will be small. Transformed area concept to calculate At and It can be a pain and the extra work is not often worth the small gain - unless there is lots of rebar.

The above is exactly the same as what you would do for a PSC beam - you just have the extra P1/At (external axial load) to deal with. Basically superposition of stresses.

To correctly calculate the change in stress of the prestressing steel you do need to calculate the strain in the concrete then, multiple this by Es to get steel stress. To get the actual stress in the prestressing steel under loads P1,M1, then you need to subtract the above from the initial prestressing stress in the steel: P2/As.

For ultimate strength analysis (not service stresses) you would normally construct the moment-axial(thrust) interaction diagram, and use strain compatibility approach - like any prestress section from first principles. This will provide you with a section ultimate strength curve.

To do the above strain compatibility strength analysis a computer program is best employed - there are not too many that will handle prestressing for axially loaded members that I am aware. I use RAPT that can analyze an irregular shaped section (with voids too) and irregular reinforcing arrangement (including post-tension and pretensioning). The M-N is tabulated and plotted, including the tension part of the M-N interaction curve. Also works for RC too.

HTH

 

[CRP]

After I read all, I'm thinking about big tree which is very high and the stalk is very small when we compare to the height, such as pine. But it can resist high wind load act on its. I think trees also have the prestressed column behaviour, right?
Any idea?

CRP

 

[ishvaaag]

In my view, the consideration of the phenomenon labeled buckling comes to attention as contributor to the ruin of a member or plate.

The example I put, valid as well for post-tensioned beams wich excessive prestress is not customarily labeled a buckling case because we are normally dealing with beam behaviour that we try to favorably modify trough prestress.

Yet in any case and compared with what we have in a doubly pinned buckled column, we have

same kind of curvature (buckled shape)
eccentrical compression (under compression)
failure either in the compressive or tensile side

and stating that this is not buckling may be accepted under the need to agree on some terminology, but not respect the similitude of the kind of failure where it occurs.

This mode of failure of course is normally prevented by mere care in fabrication and prestress transfer, but may develop if unawarely concrete of deficient stress is prestressed or post-tensioned.

Respect gain on buckling load being moderate, well, in about that is in what the question at some moment turned unto, and again I think it would be more proper to re-state the question on if one would be able to meet a higher load than without the prestress, and it is obvious that there are situations where such is the case, out of mere growth of standing inertia of the section or of direct clever counteraction of some otherwise clearly predominating mode of failure.

On the other hand, for very slender elements except great care is exercised in the position of the prestressing elements, even with moderate prestress one can even get accidental tensile action from prestress, and this will be detrimental where the estochastically variable orientation of the buckling under the loads or simply the flexure induced by the end boundaries' forces sums initial tensile stress to such tensile action, and initial compressive stress to the compressive action. In this case the initially locked prestress, even moderate, turns out to be not favorable.

And similar considerations can be made for short-columns if unreasonable tolerances on eccentricity are allowed.

 

[dlew]

Ingenuity,

Thanks for answering my question and explaining it so well.

AEF

 

[beaver12]

Prestressing columns will either help or hinder depending on how and where you place the prestress tendon. If the prestressing strand is located in the center of gravity of the cross section and is held in place (i.e. bonded tendon instead of non-bonded tendon in over size sleve) then when the member undergoes bending, the compressive stress induced by the prestressing will remain normal to the face of the section. This compressive stress will counter the tensile stress induced by the bending. You will have to make sure that the combined compressive stress is less than the crushing stress of the concrete. Hope this helps