Many shell structures, Fig. 12-1, have shapes other than cylindrical or spherical. These include hyperbolic paraboloids, Fig. 12-2a, elliptic paraboloids, Fig. 12-2b, barrel structures, Fig. 12-3a, and folded plates, Fig. 12-3b. These structures are characterized by having a small depth to length ratio. They are referred to as shallow shells and the derivation of their pertinent equations is based on the following assumptions
1. The depth to length ratio is less than about 0.20.
2. Forces are mainly due to uniformly distributed dead and live loads.
3. Forces are projected on a rectangular coordinate system for ease of calculations.
4. Thickness of the shell is small compared to depth or length.
In this chapter a brief discussion is presented for the analysis of each of the roof shapes mentioned above. A more complete treatment of the design and detail of these roof structures is discussed in the references cited in this chapter.