# Exam Winter 2013

The task is to explore alternative load-bearing structure types for an existing building: an arch structure, a hanging cable structure and a cable-stayed structure. The different structure types in the three parts of the exercise are required to span 30 m. The existing building is the B&B Italia administration building in Novedrate, Italy. It was designed and constructed by Renzo Piano in the years 1971 â€“ 1973.

## Design of alternative structure types

The task is to explore alternative load-bearing structure types for an existing building: an arch structure, a hanging cable structure and a cable-stayed structure. The different structure types in the three parts of the exercise are required to span 30 m. The existing building is the B&B Italia administration building in Novedrate, Italy. It was designed and constructed by Renzo Piano in the years 1971 – 1973.

The design was mainly driven by the client's need for a high degree of flexibility and the possibility to expand the building to meet future demands. In response to these requirements, Renzo Piano designed the column-free space of 1200 m2 as a steel space frame structure with a span of 30 m. The roof is a so-called cold roof, i.e. it consists of two roof layers. The outer layer is used as a rain screen and is made of corrugated metal sheeting; the inner layer, which is the ceiling of the office space, is insulated. In the void between the two layers, all the technical installations are inserted, in particular the ventilation ducts of the building.

### Arch structure

Design an arch structure to span the 30m wide column-free space. This arch spans between supports 1 and 2 and passes through point 3. The form of the arch is determined by the loads acting on it. The arch is loaded with 10 equal point loads Pd1 = 84kN spaced at horizontally equal intervals of 3m.

• Draw the form and the force diagram of the arch for the given loading case (Steps 1-4).
• Indicate the maximum force of the arch in kN (Steps 5-6).
• Construct a support structure for the arch at the left and right support that transfers the forces to the foundations as efficiently as possible (Step 7).
• Assume an asymmetric loading case. In addition to the 10 equal point loads Pd1, a single load Pd2 = 2 x Pd1 is placed at a horizontal distance of 7,5m to the left of support 2. Construct the new arch form and compare it to the previously found symmetric arch form (Steps 8-10).

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.

### Hanging cable structure

Design a cable structure to span the 30m wide column-free space. Each cable spans between the supports 4 and 5 and passes through point 6. The form of the cable is determined by the loads acting on it. The cable is loaded with a uniformly distributed line load wd = 28 kN/m.

• Draw the form and the force diagram of the cable for the given loads and give the maximum force in the cable in kN (Steps 1-5).
• Use the maximum force in the cable structure to dimension the steel cable (S500). Indicate the diameter in mm (Step 6).
• Indicate the magnitude and the direction of the reaction forces of the cable at the support point 4 (Steps 7-8).
• Indicate the character of the reaction forces using red for tension and blue for compression (Step 9).
• Use these forces to dimension the support structures of the cable structure (elements 4-7 and 4-8) made of steel tubes (S355). A ROR-profile with a diameter D = 355.6mm is given. Find the necessary thickness t in mm and choose the corresponding profile with the given diameter (Steps 10-11).

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.

### Cable-stayed structure

Design the roof as a cable-stayed structure. The primary structure consists of pairs of symmetrical but independent cable-stayed structures at intervals of 7m. The secondary structure consists of 7m long beams supported by the anchor points of the cables. The structure has to carry a snow load wsk = 3.0 kN/m2 and a dead load wgk = 1.85 kN/m2. Consider the left hand side of a cable-stayed structure in the center of the building.

• Determine the line load wd to be applied as the design load for the beams of the secondary structure (Step 1).
• Determine the point load Pd to be applied as the design load on each of the cables’ anchor points (Step 2).
• Draw the form and the force diagram and indicate the magnitude and direction (tension or compression) of all member forces in the structure (cables, backstays, pylon, roof beams). Find the magnitude and direction of the reaction forces (Steps 3-10).
• How does the geometry of the backstays have to be changed such that a steel cable S500 with a diameter of D = 76 mm could be used? Which members of the structure are affected by this solution? Compare the magnitude of these forces to the original solution (Steps 11-12).

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.