Recently, I designed concrete foundations for several windmills in the NW of Spain using nonlinear finite element analysis.
First of all, I did a simple linear static analysis with nonlinear friction to estimate the amount of steel and the stability. Then, I confirmed the reinforcement using a 3D model with nonlinear materials for concrete and steel. The main problem was the deadline; the job must have been done in three weeks and running a nonlinear simulation took a while.
Square reinforced foundation are inefficient because the wind can blow in all directions and the diagonal load causes high moments. Circular reinforced rings are much more cost effective for wind turbine foundations. The reason why square windmill foundations are still used is because to dig a square hole is simple. An octogonal foundation was my proposal: it is nearly as efficient as a circular one and it is also easy to build. They would probably dig a square hole and backfill the corners. After long and hard talking it was impossible to change the mind of my client and the choice was a square foundation.
Sketch of the two load cases considered. The dimensions of the box are 12.5 x 12.5 x 1.6 m
Nonlinear model for the diagonal load case. (Only a half was modelled)
Nonlinear model for the parallel load case. (Only a half was modelled)
Drawing of the resultant reinforcement
Windmill foundations
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I designed once a link for a tractor-pulled machine I wanted for myself. Main due to my poor skills in maths, I spent about two hours in calculating the angle that an iron must be bent. Went to a workshop and, when asked to do the job, the man there told me:
ReplyDelete"Oh, you speak so well... but my press doesn't measure angles, so you must draw the angle in a paper. I´ll bend the iron a little more and adjust it to the draw opening it back with a hammer."
Of course, the iron got far from the 37 degrees I calculated, but the link worked perfectly anyway.
That was the day I understood that math accuracy was not everything in engineering (fortunatly for me).
In my case, the concrete foundations of the wind turbines were built exactly as I planned but it was a pity to have used a square foundation (an octogonal one requires around 10% less concrete and steel).
ReplyDeleteThe nonlinear computer model was useful. It saved 20% of the steel. If you multiply this amount by forty or fifty foundations whose dimensions are 12.5 x 12.5 x 1.6 m, the client will be satisfied.
Off-topic: our Math teacher in last year of high school told me about an exhibition that may be of interest to you and to some other Galician readers of the blog. Since this information is only relevant to Spanish readers, I'll put it in Spanish. -- La exposición se llama "Estradas e Camiños" y está en el Archivo del Reino de Galicia, en el jardín de San Carlos (A Coruña). Al parecer, incluye proyectos de caminos del Siglo XVIII. (No parece muy difícil hacer apuestas sobre quién debe de ser uno de sus organizadores).
ReplyDeleteCurrently i am on my post graduate studies & was doing some designing on the windmill foundations , i really liked your details , also was wondering if you do happen to have any previous sketches /drawings/non linear modelling analysis which can be useful to me .
ReplyDeleteYour help is appreciated
Many Thanx