Post-tensioned pier cap 1

[broekie]

I have a design question with a post-tensioned pier cap that I was hoping to get some help with. We are designing a post-tensioned pier cap that has two supports. My colleague and I have designed it two different ways as a matter of QA/QC and I wanted some other opinions on the methodology.

In the first option, we are going to make the supports as a pinned condition. He did the design by using the "load balancing" method - the loads that he had on the cap were the dead loads, live loads, and the upward acting distributed force due to the post-tensioned force w=8*F*h/L^2. (h is the drape of the tendon) With these loads on the cap, he then computed stresses in the concrete cross section.

I did the design by just putting the dead and live loads on the cap. I computed the stresses in the extreme fiber of the cross section due to these forces. I then took the post-tensioning force and computed the stresses due to this force as:

stress = P/a +- P*e*y/I

I then added these stresses to the stresses from the external loads to get the final stresses in the cap. For the simple support design, we got the same results, which made us feel pretty good.

However, if we fix one of the columns, the results that we got were quite different. Is one of the two methods described above no longer valid for a fixed support? He did not change his "load balancing" equation for the post-tensioned force. He still is using w = 8*F*h/L^2. It seems to me that this might no longer be valid.

My method of looking at the external loads and internal loads separately and using superposition should still be valid.

Any thoughts that anyone could give me would be most appreciated.

 

[rapt]

Broekie,

In determinant prestress members there are no secondary prestress reactions and moments induced. This was the first case. Both approaches are correct for this.

In indeterminant prestressed members, there are secondary prestress reactions and moments induced. Your method is ignoring this. The other method will be more correct if it is done properly. Unfortunately, load balancing cannot allow for any variation in prestress forces along the tendon so there will be some inaccuracy from that.

This is explained in the most basic prestressed concrete design texts.

 

[broekie]

Thanks for the reminder, rapt. I forgot that when I fix one of the supports I am bascially making a "continuous" member and need to include those secondary moments.