Shells can be defined as curved structures capable of transmitting loads in more than two directions to supports. Loads applied to shell surfaces are carried to the ground by the development of compressive, tensile, and shear stresses acting in the in-plane direction of the surface. Thin shell structures are uniquely suited to carrying distributed loads and find wide application as roof structures in building. They are, however, unsuitable for carrying concentrated loads.(Shodeck)
STRUCTURAL CHARACTERISTICS
The behavior of any shell surface under the action of a load is analogous to a membrane, a surface element so thin that only tension forces can be developed (e.g. a soap bubble). Of primary importance is the existence of two sets of internal forces in the surface of a membrane that act in perpendicular directions. Also in existence is a type of tangential shearing stress which is developed within the membrane surface which helps carry the applied load. The shell tends to act in a fashion sim ilar to a two-way plate structure. (Schodeck)
Support Conditions
Support conditions in both shells of revolution (spherical) and shells of translation (cylindrical) are a major design consideration. Some device must be employed to gather forces at the lower edges of the shell. In domes, common methods include circular buttressing systems or a tension ring. Cylindrical shells are usually supported by edge beams.
CONSTRUCTION CHARACTERISTICS
A consequence of carrying loads by in-plane forces (primarily tension and compression) is that shell structures can be very thin in comparison to their spans. Span to thickness ratios of 400 or 500 are not uncommon. (e.g. A 3 in. thickness is possible for domes spanning 100-125 ft.) Reinforced concrete has become the ideal material used for these types of three dimensional surfaces, however, they may also be made of assemblies of short, rigid bars. In concrete structures, the careful laying and specification of reinforcement is key to the success of the structure. (Shodeck)
TYPICAL MATERIALS
Shells can be made of almost any material -- cold formed steel, wood, reinforced concrete, plastics. Structures made of short, rigid bars of wood or steel are technically not shell structures since they are not surface elements, however, thei r structural behavior can still be conceptualized in this fashion. (Fig. 4 - Tacoma Dome)
BARREL SHELLS
DEFINITION
A curved slab which as been cut from a full cylinder. The slab is bounded by two straight "longitudinal" edges parallel to the axis of the cylinder and by two curved "transverse" edges in planes perpendicular to that axis. The longitudinal e dge beams stiffen the shell edges and act together with the shell in carrying loads to the transverse frames. (Fig. 5 - Basic Barrel) When the edge beams are fully supported by continuous foundations, the curved slab carries loads like a barrel arch. (Bi llington) (Fig. 6 - Barrel Arch)
STRUCTURAL CHARACTERISTICS
Transverse frames, which fully support the shell, provide complete rigidity in their vertical planes, and complete flexibility in planes parallel to the shell middle surface. Ideally, the shell is assumed to be supported by a wall both so dee p that no in-plane displacement can occur and so thin that no out-of-plane shear or bending can be developed.
Edge Beams
Edge beams serve to stiffen the shell edge and to act together with the shell in carrying flexural stresses, usually tension. Normally there are two types of edge beams: vertical and horizontal. Vertical beams are usually employed for long shells, where the principal structural action is longitudinal bending. Horizontal beams are commonly used with short shells, where the principal structural action is transverse arching. (Fig. 7 - Beam Types)
Without adequate edge beams or comparable support, large tension stresses due to transverse bending moments occur at the crown of the shell.
CONSTRUCTION CHARACTERISTICS
Transverse frames fully support the shell and edge beams and are usually composed of ribs, columns and footings. The ribs are normally arches built monolithically with the shell. In general it is not desirable to design shell slopes greater than 45 degrees because of the difficulty in casting. Shells with slopes less than 45 degrees will be easier to build, but the stresses will be higher. As a guideline, the slope should be neither too steep (for construction economy) nor too shallow (for material economy). (Billington)
TYPICAL MATERIALS
Although barrel shells of materials such as wood, steel and plastics are often found, reinforced concrete is by far the most common material employed in the construction of these shells.
Statics DIAGRAMS
((Figure 8. - Force Diagrams))
Billington p. 238 - moment diagram of loaded arch, p. 301 - formulas with Beam diagrams, Shodeck Fig. 12-5
RULES OF THUMB DESIGN
As noted earlier, vertical edge beams would be employed for a long shell while short shells would use horizontal beams.
- Long shells: where r/l < .4
- Intermediate shells: where .4 < r/l < 2.0
- Short shells: where r/l > 2.0
TYPICAL CONSTRUCTION DETAILS
Fig. 9 - Typical Detail) A minimum of three layers of reinforcement is normally used: top and bottom wire fabric with the main bars in between. The cover over the fabric should be at least 3/8 in., preferably 1/2 in. The main bars may be as large as 3/4 in. in diameter and the fabric will probably be about 1/4 in. thick. This requires a minimum of 2 in. Decreasing the amount of concrete usually means one must use more careful field labor; 3 in. of concrete will give ample cover and permit reasonably rapid construction. (Billin gton) (Fig. 10 - Loading Affects)
CASE STUDY EXAMPLES
- Warehouse Complex, PA, USA - (Billington)
- Covered Market in Rheims, France. Freyssinet
- Mechanische Werkstatt der Fabrik, Yugoslavia - (Born)
- Lufthansa Hanger. Germany.
- Kimball Art Museum - (Komendant)
Author
Jennifer Marsicek, University of Oregon. 1995
