# Exam Summer 2013

The grandstand roof of the Paavo Nurmen stadium in Turku, Finland, was designed by the Finnish architecture office NRT in 1981 as part of an architectural competition and completed in 1989. The stadium can accommodate 13000 spectators and is mainly used for football matches and athletics competitions. The covered grandstand with a total of 4000 seats and a roof overhang of 17.5 m had to appear as light and transparent as possible to not disrupt the continuity of the surrounding park. The task is to calculate two different structure types for the existing structure: a truss and a cable-stayed structure.

## Design of a grandstand roof

The grandstand roof of the Paavo Nurmen stadium in Turku, Finland, was designed by the Finnish architecture office NRT in 1981 as part of an architectural competition and completed in 1989. The stadium can accommodate 13000 spectators and is mainly used for football matches and athletics competitions. The covered grandstand with a total of 4000 seats and a roof overhang of 17.5 m had to appear as light and transparent as possible to not disrupt the continuity of the surrounding park.
The task is to calculate two different structure types for the existing structure: a truss and a cable-stayed structure. The different structure types in the two parts of this exercise are required to cantilever 17.5 m to cover the grandstand.

### A truss for the grandstand roof

In the first part of the exercise, assume that the grandstand roof is supported by a truss. At each of the nodes of the truss, different point loads are acting on the structure: Pd1 = 30 kN, Pd2 = 55 kN and Pd3 = 50 kN. The truss is supported in point 2 and held back in point 3 by a backstay. Determine the forces in the truss and backstay graphically.

• Confirm that the truss is statically determinate (Step 1).
• Determine the magnitude and direction of the reaction forces of the truss graphically, using a substitute system (Steps 2-5).
• Complete the force diagram of the truss to determine all the member forces. (Steps 6-7).
• Indicate the character of the truss member forces using red for tension and blue for compression (Steps 8-10).
• Based on the form and force diagram, indicate the truss members with the maximum tension and compression force (Step 11).
• Label the most critical truss member and dimension it as a steel HEA-profile (S355) (Step 12).
• Change the geometry of the truss such that the force in the critical truss member is reduced by 30%. Sketch the solution in the existing form and force diagram and explain your approach (Steps 13-14). Note: The location of the supports 2 and 5 and the line of action of the applied loads should remain the same.

Click here to open the interactive drawing that shows the graphical solution. Use the slider in the bottom right corner to browse through the different steps.

### A cable-stayed structure for the grandstand roof

In the second part of the exercise, assume that the grandstand roof is designed as a cable-stayed structure. At each of the cable anchor points a point load Pd = 44 kN is acting on the structure. The reaction forces at the supports 2 and 5 are given: F2V = 420.52 kN, F2H = 0 and F5V = 200.52 kN.

• Draw the form and the force diagram of the cable-stayed structure (Steps 1-3).
• Indicate the character of the truss member forces using red for tension and blue for compression (Steps 4-6).
• Verify the given reaction forces at the supports based on the force diagram and explain briefly (Step 7).
• Identify the most critical steel cable and dimension it using steel S500. Determine the required diameter D rounded to mm (Step 8).
• Verify if the given ROR-Profile (S355) with diameter D = 168.3 mm and material thickness t = 16 mm can be used for the pylon (Step 9).
• Incline the pylon 30° to the rear. Investigate the resulting changes in the geometry (form diagram) and the impact on the distribution of forces (force diagram). Indicate advantages and disadvantages (Step 10).

Click here to open the interactive drawing that shows the graphical solution. Use the slider in the bottom right corner to browse through the different steps.