Aegon would in return participate in the renewing of the square. The landscape architects "West 8" from Rotterdam were asked to make a design for the town square. A part of their plan was to build six so-called "follies". These follies are large sails made out of gauze, stretched between steel cables and steel tubes. The gauze will be overgrown with vegetation in time. The follies vary from a simple single mast with several stays to real tensegrity structures. A tensegrity can be described as an island of compression in a sea of tension. The element under compression (the tube) is held in place by cables. Each end of the tube must be secured by at least three cables under tension. The last word is very important: tension is needed to give the structure stiffness. Therefore the structure will have to be prestressed. If in a certain loadcase tension lacks in one of the cables, the tube end becomes instable. Some of the cables will lose there tension in some loadcases, but as long as three tensed cables on each tube end remain this is no problem for the structure. (The three tensed cables must also go in different directions: if one sees the tube from above, the cables must cover more than 180°). Use of ESA-Prima Win Technical questions in ESA-Prima Win: The design process took quit some time. In this time several versions of ESA-Prima Win were used. The last version was 3.40. The gauze was not calculated, only the cables, the tubes and the foundation. Some of the specific problems of calculating the follies are described below. The structure needs tension to function. This is not only valid for the real structure, but also for the calculation itself. If a structure is not stiff, the stiffness matrix will have a zero on the main diagonal. This means the equations cannot be solved. By introducing prestressing the zero on the main diagonal will be replaced by a value representing the initial strain in. This means the equations can be solved. The structure behaves non linear. With each (large) deformation the stiffness of the structure changes. With the Newton Rhapson procedure the stiffness matrix is recalculated after every iteration. This means that several iterations are necessary, each time with a slightly different stiffness matrix. The calculation is stopped when the structure reaches equilibrium. With some follies the load had to be applied in steps (increments), otherwise the deformations per iteration would become to great. The use of increments can help to keep the calculation stable. In some follies certain cables would lose there prestressing. As long as enough cables under tension per tube end remain this is no problem. The cable element is removed from the calculation when the element comes under compression.. If the cable is necessary for the stability of the structure, the calculation will stop. The structure is no longer stiff. This means that the level of prestressing has to be raised or that extra cables have to be added. With non-linear calculations superposing different load cases in post processing is not possible. The load is necessary to find the right equilibrium with the right structural stiffness. This means that non-linear load cases have to be made. The following loads were used: wind in three directions (x, y and z direction: +, 0 and -), permanent loads (+) en temperature loads (+, 0 and -). These loads can be combined in 3x3x3x1x3=81 load cases. To reduce the calculation time the number of load cases has to be minimized. This is done by first looking at load cases with the permanent load and only one variable load (load cases 1 to 10). The effect of this particular variable load on the maximum and minimum stress in the cables and on the foundation was studied. Then the worst variable loads for the structures were combined in some extra load cases. Experience with ESA-Prima Win when realising the project: The program makes it possible to calculate a tensegrity structure. It was not necessary to model the gauze sails. I'm not sure if the sails could have been modelled using plate elements with the Newton Rhapson procedure for large deformations. It is possible to model the sails by replacing them by numerous parallel cables. This will however greatly increase the calculation time. Removing the sails made the calculation faster, it sadly means that the loads on the cables had to be inputted by hand. I have simplified this by only looking at the projections of the sails in the three directions, not by calculating the proper direction perpendicular to the sail for each element. In the first models in ESA-Prima Win I encountered some problems with the elements used. For example the output showed large shear forces in the cables, which could not be real. In a later model I found out that the rotations at the cable ends could no be correct. All these problems were solved in later patches or new releases after having consulted SCIA. The models are very sensitive to changes. I found that the outcome of the calculations could vary when using different versions of ESAPrima Win. In version 3.40 I suddenly had to use more increments to keep the calculation stable. The calculation engine of ESA-Prima Win had changes a bit, which was noticeable in the results. Conclusion: With these kinds of complicated and delicate structures one has to be very careful using a powerful tool such as ESAPrima Win. You have to know what you want to find and what you expect to find. Calculation by hand is hardly possible, so when in doubt it is best to try to simplify the model to a level where you can understand and approve the results. Off course this is valid for all models in ESA-Prima Win, but it is specially important for the models were checking the results by hand is not possible. The work on the follies has been completed in April this year. During erection the stresses in the structure have been measured to check the validity of the calculations. The measurements confirmed the calculations. Now we only have to wait for the vegetation to grow on the gauze. Modules used: 3d frame Dynamic document 2nd order frame Physical non linear conditions 13 SCIA User Contest Catalog
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