Simple analysis of post-tension

[postTensionBeginner]

I am trying to understand the basic physics of post-tensioning. Consider the following:

Concrete hollow cylinder, say 5cm in diameter has a hole of diameter 1cm. Put a steel bolt of dia 0.75cm, put a nut at the bottom and top; post-tension it to 10Newtons. I stick this in the ground. Assume the bolt sticks out of the ground, all the concrete cylinder is in the ground.

Force balance:
a) Concrete will have 5N of force on the top from the top nut, 5N of force from the bottom nut.
b) The bolt is being pulled 5N from top and 5N from bottom. All forces match.

Now I apply a vertical force of 2N to the bolt that is sticking out of the ground.

Force balance on the cylinder:
a) on the vertical surface of the cylinder, the soil will exert a downward force of 2N (negative)
b) on the bottom surface the nut will still exert 5N (positive)
c) on the top surface the nut will exert 3N of force (negative). this force gets reduced due to the 2N force that was applied

Force balance on the bolt:
a) on the bottom the cylinder pushes by 5N (negative)
b) on the top the cylinder pushes by 3N (positive)
c) the external force is 2N (positive)

So the force on the bolt does not change, it stays tensioned at 10N (I am not sure if it is called 5N of tension or 10N of tension).

Please let me know if this is correct.
thanks

 

[asixth]

It is post-tensioning the tendon which means it will exert a compression force of 10N of the concrete tube. These are internal stresses. If you then turn it on it's side like a pre-tensioned column (only post-tensioned), then the external compression forces developed will be in addition to the pre-tensioning forces (which are compressive). So the total internal compression force of the cylinder will be 12N.

Post-tensioning is used to counterbalance tensile stresses which are developed in concrete structures. They are best used for columns subject to uplift and flexural members (to balance the flexural tensile stresses).

 

[postTensionBeginner]

Want to clarify my post. Suppose the cylinder is 50cm long and 5cm in diameter and it is put into the ground (like a foundation) vertically. So one end of the bolt is at the 50cm below the ground and other end of the bolt is sticking out. Bolt is post-tensioned with 10N.

In this scenario, when a vertical force of +2N is applied on the bolt (attempting to pull out of ground), the compression on the concrete cylinder has to reduce. Assuming the expansion of concrete is almost zero, will the stress on the bolt stay the same even after +2N force is applied?

 

[Zambo]

I think it would be better to consider a real example, the 5cm diam. 50 cm long cylinder doesn't seem to have any practical purpose.

Is this an anchor bolt? In which case you are trying to use post tensioning to prestress the concrete which the bolt is cast into. You will need a way of anchoring the bolt in the concrete,this could be a nut and washer at the end and/or partially grouting the threaded length. You will also have to have a way for the bolt to increase in length as the force is applied, so part of the length needs to be debonded from the concrete.

Once you have the arrangement above you can post tension the bolt. This will cause lengthening of the bolt and a tensile stress (steel is a material which can accommodate significant tensile stress). The concrete at the same time will be compressed causing a shortening, thus it is prestressed. Now as a tensile load is applied to the concrete the prestressing of the concrete will increase the tensile capacity of the system.

Remember if the concrete does not shorten as tension is applied to cause pre or post-tensioning the concrete is not prestressed.