Suspension structures are those with horizontal planes (road decks, roofs, and even floors) supported by cables (hangers) hung from the parabolic sag of large, high-strength steel cables.
2. STRUCTURAL CHARACTERISTICS
The strength of a suspended structure is derived from the parabolic form of the sagging high-strength cable. This parabolic form is designed so that its shape closely follows the exact form of the moment diagram(s). This creates a highly eff icient structure. The sagging cable performs best under symmetric loading conditions because the cable may deform significantly as it attempts to adjust to an eccentric loading . As the cable adjusts to this load it shifts the rest of the structure. Th is adjustment causes secondary stresses in the horizontal surface and additional deformation. The parabolic curve of the cable is also susceptible to developing harmonics from eccentric or lateral loads such as wind. These increased harmonics can create great movement in a structure, sometimes enough to cause dramatic failure, as in the case of the Tacoma Narrows bridge. Rather extensive calculations must be made to determine the natural frequency of a suspension structure and to test the stiffness of it's horizontal surface in order to prevent the structure from developing destructive harmonics.
3. CONSTRUCTION CHARACTERISTICS
The horizontal surface (bridge deck, etc.) is usually a simple or continuous beam, most commonly configured as a truss or box beam. The box beam is advantageous because it resists torsional forces well, although it provides a greater surface area subject to wind loading. The large curving cable consists of many, many smaller cables which are tightly spun together. As the cables are being spun together they are also stretched over the span and attached to the supports. After being attached the appropriate curve is cre ated by tensioning the cable. This curve is formed without the real dead load of the structure, therefore the completed curve has a different shape than the one created during construction. Finally, the horizontal surface supported by the cable is hung piece by piece from the sagging cable.
4. TYPICAL MATERIALS
The horizontal surface is most commonly a steel structure because of its relative lightness, or a steel and concrete composite. the towers may be of either stone, concrete, or steel. The cables are steel.
5. RULES OF THUMB DESIGN
The shape of the cable can be found quite simply with graphic statics methods. Once the moment diagrams of various loading conditions have been drawn, simply make the shape of the sagging cable approximate the worst case scenario or a composite approxima tion of the different loading cases.
The tower height is usually about 1/9 of the span. Longest Spans:
- Golden Gate Bridge: 4200 feet = 1280 meters (built in San Francisco in 1937 by O.H. Ammann)
- Humber Estuary Bridge: 1410 meters (Germany)
6. CASE STUDY EXAMPLES
CALATRAVA, SANTIAGO Alamillo Bridge, Seville, Spain, 1987-1992, Maximum Span: 200m Tower Height: 142m Materials: Steel tower with concrete infill where needed, steel bridge deck structure, concrete abuttments.
The mass of the bent tower plays the role of the back stays of traditional cable-stayed bridges. The mass and the bend of the tower exerts a backward downward force while the cable stays and roadbed mass exert a forward downward force. The mass of the t ower had to be carefully calculated so that its backward and downward force wouldn't lift the bridge off the ground. Therefore, where additional mass was needed to counter vertical forces the steel box girder of the tower and the steel deck structure we re filled with concrete.
The meeting of the tower, deck and abutment near the ground necesitated a continuous moment connection so this joint was cast out of concrete. The connection of the various individual pieces happened places with fewer concerns about moments.
The horizontal force component in the bent tower and the horizontal force of the roadway counteract each other so that the abuttment only needs to resist vertical forces, unlike traditional cable-stayed bridges with towers at 90 degrees to the roadbed wit hout any horizontal force component of their own to counteract the horizontal force from the road bed.
Bach de Roda Bridge, Barcelona Spain, 1985-7 Maximum Span: 46m Materials: steel arches and cables, steel deck structure, and concrete foundation abutments
Dual steel arches with hung suspension cables have a distinct problem, a tendency to buckle. Usually a truss is located between the arches to solve this lateral bracing problem. In the Bach de Roda Bridge, secondary, angled arches lean on the outsides of the two primary arches and are tied to the primary arch with fins. The angled arch provides the lateral support and the primary arches no longer need to be tied together. The span of an arch system is considerably less than that of a suspended system.
- Frampton, Kenneth, Tishchhauser, Anthony, and Webster, Anthony C., Calatrava Bridges, Artemis, Zurich, 1993.
- Bach de Roda: Calatrava 1: p. 28
- Bach de Roda: Calatrava 1b: p. 17
- Bach de Roda: Calatrava 1c: p. 24
- Alamillo Bridge: Calatrava 2a: p. 69
- Alamillo Bridge: Calatrava 2b: p. 63
- Alamillo Bridge: Calatrava 2c: p. 56
- Constantinopoulos, ed., Foster Associates; Recent Works, St. Martins Press, New York City, 1992
- Viaduct, Rennes (project) Foster.2: p. 98-99
- Russell, James S., "Cable Staying a Convention Center," Architectural Record, March 1994, v. 182, no. 3, p. 27
- Bartle Convention Center, Kansas City , Mo. Convention.center: p. 27
- Golden Gate bridge: golden.gate.1a (and 1b): Jen's photos
Matt Rumbaugh, University of Oregon. 1995
9. Adapted from