**ACI 318.2M**-14 Building Code Requirements for Concrete Thin Shells (ACI 318.2-19).

Folded plates may be prismatic (Billington 1982; ASCE Task Committee 1963), nonprismatic (ASCE Task Committee 1963), or faceted. The frst two types consist generally of planar thin slabs joined along their longitu- dinal edges to form a beam-like structure spanning between supports. Faceted folded plates are made up of triangular or polygonal planar thin slabs joined along their edges to form three-dimensional spatial structures. Most thin shell structures require ribs or edge beams at their boundaries to resist the shell boundary forces, to assist in transmitting boundary forces to the supporting structure, and to accommodate the increased amount of reinforcement in these areas. Ribbed shells (ACI SP-28; Esquillan 1960) generally have been used for larger spans if the increased thickness of the curved slab alone becomes excessive or uneconom- ical. Ribbed shells are also used because of the construction techniques used and to enhance the aesthetic impact of the completed structure. Thin shells are characterized by their three-dimensional load-resisting behavior, which is determined by the geometry of their forms, by the manner in which they are supported, and by the nature of the applied load. Common types of thin shells are domes (surfaces of revo- lution) (Billington 1982; ASCE Task Committee 1963), cylindrical shells (ASCE Task Committee 1963), barrel vaults (ACI SP-28), conoids (ACI SP-28), elliptical parabo- loids (ACI SP-28), hyperbolic paraboloids (Esquillan 1960), and groined vaults (Esquillan 1960).

R2.4—Stability R2.4.1 Thin shells, like other structures that experi- ence in-plane membrane compressive forces, are subject to buckling when the applied load reaches a critical value. The surface geometry of shells makes calculating buckling loads complex. If one of the principal membrane forces is tensile, the shell is less likely to buckle than if both principal membrane forces are compressive. The membrane forces that develop in a shell depend on its initial shape and the manner in which the shell is supported and loaded. In some types of shells, post-buckling behavior should be considered in determining safety against instability (IASS Working Group No. 5 1979). Investigation of thin shells for stability should consider the efect of: 1) anticipated deviation of the geometry of the shell surface as-built from the idealized geometry; 2) local variations in curvature; 3) large defections; 4) creep and shrinkage of concrete; 5) inelastic properties of materials; 6) cracking of concrete; 7) location, amount, and orientation of reinforcement; and 8) possible deformation of supporting elements. Measures successfully used to improve resistance to buckling include providing two mats of reinforcement, one near each outer surface of the shell; a local increase of shell curvatures; the use of ribbed shells, and the use of concrete with high tensile strength and low creep. A procedure for determining critical buckling loads of shells is given in the IASS recommendations (IASS Working Group No. 5 1979). Some recommendations for buckling design of domes used in industrial applications are given in ACI 372R and ACI SP-67ACI 318.2M pdf download.