Axial Tension in a Post-Tensioned Member 2

[waytsh]

Hi all,

I have a post-tensioned member that has an axial tension load in additon to the bending moment and shear. There is going to be no non-prestressed reinforcing in the member. How do I properly account for the additional stress in the strand and overall reduction in the allowable moment due to this tension? At this point the only thing I can think to do is to calculate the stress in the strand at the moment that I need and then add the additional stress from the tension load and see if it comes out less than or equal to fps. Does this sounds reasonable? Is there a better way?

I would really appreciate some insight into this.

Thanks,

waytsh

 

[hokie66]

You need to draw yourself a picture of this and think about it. When you do, you will see that the externally applied tension force does not increase the force on the strands, but rather relieves the compression force on the concrete.

 

[waytsh]

Thanks hokie66, it was a late night and I was getting caught up in my strand stresses. You're right if I just add the number of strand required to keep the entire section in compression even under combined tension and bending moments then the stress in the strand will not change.

 

[haynewp]

If the axial tension load is applied subsequent to the tightening of the tendons, I think it would increase the force on the tendons.

 

[hokie66]

haynewp,

This is sort of the fundamental of prestressing. If you apply an external tension force, it is true that the strands have to resist that force. But at the same time, the force resisted by the strands is decreased by the same amount due to the compressive force on the concrete being reduced. So the strands don't know the difference.

 

[haynewp]

I disagree. I see this as being the same as a bolt clamping 2 blocks of wood together and someone trying to pull the blocks apart, the force in the bolt would increase would it not?

 

[hokie66]

Well, you are correct in principle. The difference is in the scale of the problem. In the case of the prestressed member, the additional elongation of the strands due to the external tension force will match the elongation of the concrete, so very small in relation to the initial elongation of the strands, and so generally ignored, as it would not exceed the initial losses.

 

[haynewp]

That may be practically correct, I don't know (I would still think it dependent on the amount of subsequent axial force applied in comparison to the initial losses). But I thought it was prudent to point out the correct principle.

 

[hokie66]

Even in your case of someone trying to pull the blocks apart, the bolt force wouldn't increase until the clamping force was overcome. The externally applied force just replaces the internal force.

 

[haynewp]

I know that is normally assumed in pretensioned bolted connections but you are getting into assumptions on the elasticity of the materials connected and functions of contact areas. Again, practically you are probably correct. Theoretically, there is a case where the bolt would take all of the applied tension.

 

[haynewp]

Oh, and even in the case of a typical steel pretensioned connection the bolt does take some amount(albeit small) of an applied axial tensile load prior to it overcoming the pretension.

 

[hokie66]

Yes, I agree. Both the tension and compression part of the assembly act like springs of varying stiffness. But for waytsh's problem, the simplest explanation is the best.

 

[rapt]

Hokie66 and haynewp,

It all depends if it is cracked.

The only way to work out what is happening is to do a strain compatibility cracked section analysis and work out the different strains and related stresses and come up with a tension in the tendons under that load condition.

You cannot just assume that the force will be absorbed by the concrete. Axial tension combined with bending need to be considered together along with cracking if the sectionion goes into tension and the resultying stresss condition determined.

 

[hokie66]

rapt,

Yes, we digressed from the OP, but by waytsh's second post, he is going to keep the entire section in compression.

 

[waytsh]

funny you should mention it because as it turns out I am going to have a member that will be under a net compressive force but will be seeing some tensile stress on the tension face. It is not going to be practical for me to add another strand so it looks like I am going to be forced analyze the stress in the strand somehow. The section will not be cracked since my maximum tensile stress under service loads is -0.186 KSI.

 

[ash060]

If the section is not cracked it is just P/A + M/S for the gross section.

 

[haynewp]

If you design to maintain a minimum amount of precompression given all loads then I think it will be fine. But my 'digression' above was only to point out that the strands do take some tension whether the concrete is cracked or not. This is a fundamental concept which I thought was important for waytsh to understand. This concept is very obvious when looking at the equations for a pretensioned steel bolted connection.

I won't have any more comments in this thread.