Post tensioned strength with no P/A 1

[chillerz69]

I am currently setting up a spreadsheet to calculate strengths, stresses etc of prestressed beams ans slabs. I have been instructed to have the option of whether or not to include the P/A component, as sometimes axial deformation cannot occur when the slab is say tied into stiff walls or frames. How should I modify my limit state strength equations and stress equations to allow for this? Anyone know where I can look this up?
Cheers

 

[haynewp]

This sounds really strange, I would not design PT in this way.

 

[slickdeals]

Actually P/A will very detrimental if you are restrained from axial deformations, you will need to worry about restraint cracking.

When you are applying a post-tensioning force, you will have an axial force induced in the slab. What do you mean by include or not include P/A?

 

[hokie66]

Restraint which prevents the prestress from being effective in areas of the structure mostly affects deflections and cracking, not ultimate capacity. Ultimate capacity is still based on all the steel, both bars and strands, being at yield.

 

[haynewp]

Yes, but that part is already accounted for in the strength equations. It sounds like he is trying to base the design stresses as if the PT never gets into the concrete?

 

[chillerz69]

Yeah I assumed the strength equations didnt need to be modified, except in places where axial deformation cannot occur the losses may slightly change.

"Yes, but that part is already accounted for in the strength equations. It sounds like he is trying to base the design stresses as if the PT never gets into the concrete? "

I Dont necessarily want to base the design stresses as if the PT never gets into the concrete, but I want to include the option of whether or not to include the P/A component in calculating the stresses at transfer etc. In my understanding if the structure cannot physically shorten axially then there is no P/A component, but still uplift due to the tendon drape. So far I have set up a solver in excel that solves for the neutral axis of the section depending on whether its cracked etc, based on a triangular stress distribution and strains in the steel etc. Is it at simple as simply misusing P/A from my found stresses at the end or am I missing something? I have a few more questions but I think thats enough for now haha
Cheers

 

[kslee1000]

I couldn't clearly see the benefits of postensioning slab with restraind edges, instead, I sense some problems need to be looked into/discussed farther, such as pre-load on the support/restrained edges (could be a positive thing to do), cracks (depending on stiffness of the restraind and prestressing force). Also, it requires higher prestress force in order to achieve the same result as for an un-restrained slab, wouldn't it? Sounds an interesting topic though.

 

[haynewp]

It sounds like you are wanting to treat the PT like a suspension cable only. I guess you could look at the catenary cable formulas to get uplift without compression and apply this load to the concrete as uplift. But I think I would try to avoid the PT loss into restraint elements or use mild steel if it is an extremely stiff frame you are looking at. I might look at what you are talking about if I am checking an existing problem.

 

[rapt]

chillerz69,

Include the prestress force and apply an equal direct tension force (equal to the prestress force) at the centroid of the concrete (cracked centroid) to represent the restraint force

 

[chillerz69]

rapt,

Could you have a look at the attachments I sent and tell me if that is correct for the limit state at transfer? Your help is much appreciated. For the elastic stress analysis should I find the geometrical centroid or the neutral axis assuming a triangular stress distribution in the compression zone? Also does the fact that a tendon may be unbonded affect both the limit state transfer equations and the elastic stress equations besides the fact that if its bonded there will be more area of transformed concrete etc?
Any help is much appreciated

 

[haynewp]

Why don't you just set the P/A to zero? If you use the restraint as a separately applied load wouldn't
that change the results as you go along a multiple span beam with varying widths and section modulus?

 

[chillerz69]

I cant just set P/A to zero, because there is no direct P/A component in my model for elastic stresses. I have set excel to initially choose a strain in the compressive fibre of the concrete, solve for the neutral axis based on equilibrium and then determine the resultant moment of the section. This repeats until the resultant moment of the section equals the applied moment.

 

[rapt]

When you are dealing with cracked section/strain compatibility analysis, P/A does not come into it. P does but the P is still there in the steel independant of the restraint and gives you the capacity of the section based on P * lever arm. It is just not getting into the A!!

So to model this you put the P into the steel but you put a tension force into the concrete to counteract this.

(looks like too many people have been relying on computer programs and idiots guides to PT design rather than doing the real calculations and understanding what they are doing)

chillerz69

The tension force should be applied at the neutral axis of the cracked section.

Don't forget that there is no Pe term added to the applied moments, only Msec for the prestress component.

 

[haynewp]

rapt, you must be a joy to work with everyday. Can I come visit?

 

[rapt]

Haynewp
Yes, it is a laugh a minute here. Anyone is welcome as long as they take me out for a good lunch!

 

[haynewp]

Ok, we can eat shrimp on the barbie. I will bring my "Idiot's Guide to PT Design" and we will have a picnic.