Shells and Folded Plates*

APPENDIX A ACI Building Code Requirements for Thin Shells and Folded Plates* Since concrete is the basic, most common material for the construction of thin shells, the requirements of such specific codes as those of the American Concrete Institute must be followed. Unfortunately, for many years these codes did not address in specific terms the unique problems related to thin shells, so that in the absence of special provisions only the common rules on concrete structures could in general be followed. One major result has been a great thickness for shells being imposed by minimum cover requirements for steel reinforcement. Naturally, code requirements vary from country to country, so that although ACI restrictions were enforced in the United States, shells only three-quarters of an inch thick were legally possible in Mexico, as demonstrated by the numerous thin shells there by Felix Candela. The ACI's design provisions for shells and folded plates are covered in Chapter 19 of its code. These include such major topics as definitions, criteria for structural and model analysis, reinforcement, prestressing, and construction. In separating the supporting members of a thin shell structure from its whole, the code explicitly specifies that Chapter 19's provisions apply only on the thin shell portion of the structure. The edge beams, columns, footings, and other supporting members are covered by other chapters in the code. Naturally, thin shell designs should also be controlled by the rest of the code, except for provisions that may conflict with those in Chapter 19. *From Building Code Requirements for Reinforced Concrete (ACI 318-89). The full text of Chapter 19 and its Commentary are reprinted with the permission of the American Concrete Institute, Detroit. 343 ACI Buildina Code Requirements [Code] [Commentary] 19.0-NOTATION Ec = modulus of elasticity of concrete, psi (see 8.5.1) Fe = specified compressive strength of concrete, psi = square root of specified compressive strength of concrete, psi = specified yield strength of nonprestressed reinforcement, psi = thickness of shell or folded plate, in. = develop length, in. = strength reduction factor (see 9.3) 19.1 Scope and Definitions This code and commentary provides building code information on the design, analysis, and construction of concrete thin shells and folded plates. The process began in 1964 with the pub lication of a practice and commentary by ACI Committee 334,19.1 and continued with the in clusion of Chapter 19 in ACI Building Code ACI 318-71 and in later editions. The current revision reflects additional experience in de sign, analysis, and construction gained since the earlier publications, and was influenced by the publication of the "Recommendations for Concrete Shells and Folded Plates" of the In ternational Association for Shell and Spatial Structures (lASS) in 1979.19.2 Since Chapter 19 applies to concrete thin shells and folded plates of all shapes, extensive discussion of their design, analysis, and con struction in the commentary is not possible. Ad ditional information can be obtained from the references listed at the end of this chapter, which are provided for the assistance of the designer. They are not an official part of the code. The designer is responsible for their in terpretation and use. Particular emphasis on de velopments and practice in the United States is given in "Concrete Thin Shells," ACI SP_28. 19-3 19.1.1 Provisions of Chapter 19 shall apply to R 19 .1.1 Chapter 19 is intended to apply to thin shell and folded plate concrete structures, thin shells and folded plate concrete structures including ribs and edge members. in building construction. Discussion of the ap plication of thin shells in special structures such as cooling towers and circular prestressed con crete tanks may be found in the reports of ACI ASCE Committee 33419.4 and ACI Committee 344. 19.5 344 Thin Shells and Folded Plates [Code] [Commentary] 19.1.2 All provisions of this code not specifi cally excluded, and not in conflict with provi sions of Chapter 19 shall apply to thin-shell structures. 19.1.3 Thin shells: three-dimensional spatial R 19.1. 3 Common types of thin shells are structures made up of one or more curved slabs domes (surfaces of revolution), 19.3. 19.6-19.9 cy or folded plates whose thicknesses are small lindrical shells, 19.3. 19.6. 19.8. 19.10-19.15 conoids, compared to their other dimensions. Thin shells 19.6. 19.16-19.18 elliptical paraboloids, 19.6. 19.19 hy are characterized by their three-dimensional perbolic paraboloids, 19.3. 19.6. 19.8. 19.19-19.28 and load-carrying behavior which is determined by groin vauIts.19.3. 19.19. 19.29. 19.30 Considerable in the geometry of their forms, by the manner in formation on the experience gained in the de which they are supported, and by the nature of sign, analysis and construction of these shells the applied load. may be found in the cited references. Less experience is available regarding other shell types or shapes, including free-form shells. However, a number of these have been success fully built. Thin shell elements are slabs or plates with thicknesses less than one-fifth the transverse width and less than one-twentieth the radius of curvature on span lengths. 19.1.4 Folded plates: a special class of shell R19.1.4 Folded plates may be prismatic,19.3. structures formed by joining flat, thin slabs 19.6. 19.31-33 nonprismatic,19.34 or faceted. The along their edges so as to create a three-dimen first two types, which are the most common, sional spatial structure. consist generally of planar thin slabs joined along their longitudinal edges to form a beam like structure spanning between supports. Fac eted folded plates, which are much less com mon, are made up of triangular and/or poly gonal planar thin slabs joined along their edges to form three-dimensional spatial structures similar to continuously curved thin shells such as domes or other shell forms. Only limited ex perience is available on the design, analysis, and construction of faceted folded plates. 19.1.5 Ribbed shells: spatial structures with R19.1.5 Ribbed shells I9.3. 19.35. 19.36 generally material placed primarily along certain pre have been used for larger spans where the in ferred rib lines, with the area between the ribs creased thickness of the curved slab alone be filled with thin slabs or left open. comes excessive or uneconomical. Ribbed shells also have been used because of the construction techniques employed and to enhance the aes thetic impact of the completed structure. 19.1.6 Auxiliary members: ribs or edge beams R 19.1.6 Most thin shell structures require ribs which serve to strengthen, stiffen, and/or sup or edge beams at their boundaries to carry the port the shell; usually, auxiliary members act shell boundary forces, to assist in transmitting jointly with the shell. them to the supporting structure, and to accom modate the increased amount of reinforcement in these areas. 345 ACI BUilding Code Requirements [Code] [Commentary] 19.1.7 Elastic analysis: an analysis of defor R 19.1. 7 Elastic analysis of thin shells and mations and internal forces based on equilib folded plates means any method of structural rium, compatibility of strains, and assumed elas analysis which is based on assumptions which tic behavior, and representing to suitable provide suitable approximations to the three approximation the three-dimensional action of dimensional behavior of the structure. The the shell together with its auxiliary members. method must provide the internal forces and displacements needed in the design of the shell proper, the rib or edge members, and the sup porting structure. Equilibrium of internal forces and external loads and compatibility of deformations must be satisfied. Methods of elastic analysis based on classical shell theory, simplified mathematical or analyti cal models, or numerical solutions using finite e1ement,19.37 finite differences, or numerical in tegration techniques, are described in the cited references. The choice of the method of analysis and the degree of accuracy required depend on certain critical factors. These include: the size of the structure, the geometry of the thin shell or folded plate, the manner in which the structure is supported, the nature of the applied load and, finally, the extent of personal or documented experience regarding the reliability of the given method of analysis in predicting the behavior of the specific type of shell or folded plate. 19.1.8 Inelastic analysis: an analysis of defor R19.1.8 Inelastic analysis of thin shells and mations and internal forces based on equilib folded plates means a refined method of analy rium, nonlinear stress-strain relations for con sis based on the specific nonlinear material crete and reinforcement, consideration of properties, nonlinear behavior due to the crack cracking and time dependent effects, and com ing of concrete, and time dependent effects patibility of strains. The analysis shall represent such as creep, shrinkage, temperature, and load to suitable approximation the three-dimen history. These effects are incorporated in order sional action of the shell together with its auxil to trace the response and crack propagation of a iary members. reinforced concrete shell through the elastic, inelastic and ultimate ranges. Such analyses usu ally require incremental loading and iterative procedures to converge on solutions which sat isfy both equilibrium and strain compatibil ity.19.38 Analysis of this type generally requires extensive computer time. 19.1.9 Experimental analysis: an analysis pro cedure based on the measurement of deforma tions and/or strains of the structure or its model; experimental analysis is based on either elastic or inelastic behavior.

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