Amsterdam ArenA, Dynamic Recalculation of Roof Structure
Introduction and History
In 1993-1995, the Amsterdam ArenA was designed and constructed. This multipurpose stadium is located on the southeast of Amsterdam, close to several highways, railways and over a minor highway. The first two floors are parking garage. Above these, the playing field and tribunes rise up to approximately 44 metres above the surrounding fields. A transparent steel structure forms an oval roof over the tribunes. The centre void in this roof can be completely closed by two movable segments. This makes this structure very suitable for sports and other activities, such as concerts. Especially during the activities other than
sports, the roof structure is used frequently to hang tons of audio-visual equipment and components of the set.
The main structure of the roof is formed by a giant H-frame (177x126 metres). This frame spans the field and the tribunes and consists of triangular trusses of several metres in height. On this H-frame, the oval shaped roof-plane is suspended. Also, the movable segments ride on top of this frame. The design of the steel roof structure was carried out using Strucad. By then, it was not possible to model the complete structure. Loads and stability-effects of the oval roof-plane and the movable segments had to be derived separately. All loads, including wind, have been applied statically. Using this model, the structure was optimized
quite extremely.
In the following years, the grandiosity of happenings grew enormously, increasing the temporary loads and bringing the structure closer to its limits. Right now, the city of Amsterdam is developing the area around the stadium. In these plans, two towers of about twice the height of the stadium are posted directly next to the stadium. These towers have a great influence on the wind loads on the roof of the stadium. Wind tunnel tests showed a (local) static increase up to 30%. Feasibility of these towers depended on the strength of the roof structure. |
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Sophisticated Analysis
The total of increasing loads asked for a more sophisticated analysis of the structure. Using the existing design, the whole structure was remodelled in ESA-Prima Win 3.50. Profiles, hinges, supports, offsets of connections, all were copied from the original design. EPW was chosen because of the clarity and easiness of the input, but also because of the great possibilities to (visually) check and modify the complex structure. This was very workable during the process of modelling and validating the H-frame. Not only was the H-frame modeled, also the frame of the oval roof-plane over the tribunes and the frame of the movable segments on top of the H-frame. This made it possible to apply the wind loads directly were they are supposed to act.
In a large area like the roof of a stadium, wind loads will never peak at the same time on the whole surface. Static loads are therefore considered to be too conservative. Using the results of the wind tunnel tests, wind has been incorporated in ESA-Prima Win as dynamic nodal loads. In close consultation with the people of ESA, following steps were taken:
1.Wind tunnel tests produce a continuous pressure parameter for approximately 50 locations on the roof;
2. From these results, for some significant situation (wind directions, 1 or 2 towers) the minute has been derived in which the wind load is maximum;
3. For each of the 50 locations, the continuous pressure has been described by a Fourier-analysis of 10 sinuses;
4. For each cross of main girders of the roof, the area has been calculated. The size of this area, combined with the pressure-
functions which act in this area, result in the (variable) force on that node;
5. Since the roof is a 3-dimensional plane, for each node the normal vector is different. This normal vector of the roof is equal to the direction of the dynamic nodal load;
The steps above have been carried out using Mathcad (wind tunnel results), Autocad (areas/direction nodal loads) and Excel (final parameters of nodal loads and dynamic functions).
6. The dynamic functions were entered in ESAPrima Win manually, using Time History Analysis. Each function in EPW consists out of two functions. In order to enter the Fourierline of 10 sinuses, 5 summarized functions are needed. Each sinus-function has 4 parameters (offset, amplitude, frequency and shift). Therefore, for each situation (wind-direction, number of towers) an amount of 50x5x2x4 = 2000 numbers had to be entered.
7. For each nodal load the direction and magnitude (x,y,z) had to be entered. For each nodal load the 5 applicable functions were assigned.
8. A calculation of Eigen frequencies had to be done to make dynamic analysis possible.
As a result of the dynamic calculations, the continuous signal of each node deflection or each member force could be shown for the one considered minute. The other possibility of output has been used more often to analyse the effects of the wind. For a group of members a list can be produced of the maximum deflection, force or moment which occurred in the considered minute. By combining these output lists, for each member the unity checks for several mechanisms were calculated. From former studies the critical elements were known. For these groups of members (e.g. all column tubes, all end members of a truss), output
lists were produced in ASCII format. This was done for each situation (wind direction, roof open or closed, 1 or 2 towers). For clarity: these values are the maximum values of each member which occurred in the considered minute. In Excel, these ASCII-files were used to combine forces and moments for each critical member or profile (several mechanisms, e.g. N+My+Mz for buckling, Vy+Vz for shear). As a result, the maximum unity check of each member has been derived. These unity checks due to the (dynamic) wind in the new situation (1 or 2 towers) have been compared with the unity checks due to static wind load in the old situation (no towers).
Conclusions
For the steel frame structure of the roof of the Amsterdam ArenA, a comparison has been carried out between a new situation with one or two large towers directly next to the stadium and a situation without large towers. The wind tunnel tests resulted in an increase of the static wind loads on the roof of up to 30% when the tower(s) is(are) added. It is sure that the existing roof structure can not cope with such increased forces. Using the dynamic analysis, the lack of simultaneity of peak loads and the mass inertia of the structure is incorporated. Consequences of this decision are that a complex and extended calculation is necessary. For this model and these calculations, ESA-Prima Win 3.50 was chosen. In close consultation with the people of ESA, the possibilities and optimal methods were elaborated. The input of the loads and the processing of the results required a lot of manual work and spreadsheet calculations. This indicates that the chosen method is really putting ESA to the test. Never before so many loads and variables were used in one model.
We have no doubt that in future versions, the input- and post processing facilities will be adapted to the always shifting boundaries, such as this project. The result of this analysis (dynamic increased loads) is generally that the unity checks are comparable to the ones in the original calculations (with static, lower loads). Since the structure has been designed in a way that left little reserve, only a very small increase of the unity checks is allowable. The final decision whether the increase of loads is acceptable, is still in process at the moment of writing. |
