Since some years ago almost all wind turbine manufacturers (“OEM” - I hate acronyms) have modified their tower to foundation interface.

The previous technical solution to connect tower and foundation was based on an embedded steel section (like a “ring” inside the foundation).

It did not work properly and the issues caused by this element might be easily subject of several articles, about the problems caused by the ring and on the solutions developed to fix those problems (i.e. retrofitting and repairs works necessary to ensure the necessary lifetime of the turbine foundations).

In the last years (I would say since around 2010) the embedded ring has been replaced with a pre-stressed anchor cage, as shown in the following picture:

The design methodology for this element is usually based on simplified hypothesis:

The **first assumption **is that the tensile/compression strength on each element is calculated assuming a uniform load distribution, usually using formulas such as:

**T = 4Md / (n*D) + N/n**

Being

T = Maximum tension force on the more loaded bolt

Md = Bending moment from the tower

n = Number of anchors

D = Average diameter of the anchor cage

N = Axial force

This is usually known as the “Petersen approach”.

Petersen is a German engineer who wrote a book about steel structure design appropriately titled “Stahlbau” (“steel construction” in German) where this calculation method is presented.

The **second assumption** is that the tensile force is distributed between concrete and steel if there is no decompression.

If decompression happens (something that will always happen under ultimate limit state factored loads) all the tensile force will be taken by the steel.

The only problem with this approach is that the first assumption is only true in case there is no decompression.

This approach leads to conservative results, as it does not account for the force re-distribution due to the stiffness change when decompression occurs.

However, it is very easy to obtain the maximum tension the more loaded bolt or to calculate the needed number bolts or their dimensions for a given tension.

When decompression occurs the stiffness in the “compressed” side and in the “tensioned” side stops having the same value, as the concrete stops providing its stiffness (this is the magic of pre-stressing, before de-compression the concrete is somehow taking some tension, a thing that concrete rarely does).

In the compressed side we will have an area of concrete under compression and bolts in tension (due to the prestressing), that take the compression by de-tensioning.

In the tensioned side we will only have the bolts in tension.

Similarly to a hyper static structure the stiffer side (in this case the one under compression) is able to take more load.

This works like a beam supported by springs:

In the picture on the left all the springs have the same stiffness. This would be the current design model, as in the formula shown above.

In the picture on the right the tension springs (right side of the beam) have only half the stiffness.

This is just to show how stiffness affects the force distribution, in a real anchor cage the loss of stiffness when decompression occurs might be over 80% as the concrete area contribution it is much bigger than the bolts area (total stiffness would be Es*As+Ec*Ac, being Es and As the area and elastic modulus of steel, and Ec, Ac the ones from concrete).

The “softer springs” on the right take less load, that is redistributed to the more rigid area on the left.

Please note that this would not happen in an isostatic structure (with only two supports)

As the neutral axis moves, the redistribution of forces changes. This lead to a non-linear calculation.

To perform this analysis we can implement a model with a homogenized concrete-steel section, and with variable parameters depending of the location of the neutral axis. Using this type model, we would be able to obtain the maximum stress on concrete and the tensile force on the pre-stressing element.

This way the anchors size may be adjusted, and we will get a more accurate value for the concrete compression which is slightly underestimated with the current models.

I am not going more deep into this boring details about calculations but I think that it is interesting to know that there is still room for optimization in anchor cage design.

Hi Jose,

Interesting, I have started design of this anchor cages and I follow a method of the stiffness ratio between bolt and concrete, that is usually between 7 and 12 % meaning that I give, lets round in 10% of stiffnes ratio, of loads to the bolts and the rest to concrete in the compression side. What called my attention is that in tension side they say that were there is no uplift the force in the bolt will be (Stress in bolts due to pretension + (+M/W-P/A)*Stiffnes factor) that make sense because 90% of the load is working to de-compress the concrete previously compressed but for ULS moment there is always uplift and the max tension stress in bolts is M/W-P/A, without any pretension stress previosly applied to bolts. That is something that I cannot figure it out yet, do you think it the same way?. Great content by the way

Dear Alejo

First of all, thanks for your feedback.

What you mention in your email is basically what the article is about. As under ULS (extreme factored loads) there is always uplift, Petersen approach assumes that all the load goes to the bolt, as you said, M/W-P/A, without any pretension stress previously applied to bolts. This assumption is a simplification and is not physically correct, the problem as I explain in the article is that to calculate the real tension force in the bolts when the uplift occurs you need to consider the overall equilibrium of the section and the variable stiffness of the system, something that is not so simple....

Best regards.

Jose