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1、Anton Tedesko Chairman Frank Baron David P. Billington Richard R. Bradshaw Felix Candela John V. Christiansen ACI 334.1R-92 (Reapproved 2002) Concrete Shell Structures Practice and Commentary Reported by ACI Committee 334 Committee mebers voting on the 1992 revisions: Phillip L. Gould Chairman Jack
2、Christiansen John F. Abel David P. Billington Arthur J. Boyt, Jr. Eli W. Cohen Morris N. Fialkow Ajaya K. Gupta Robert B. Haber Alfred L. Parme Secretary Wilhelm Flugge Richard M. Gensert Otto Gruenwald Milo S. Ketchum, Jr. James A. McCarthy Kye J. Han Harry G. Harris Mark A. Ketchum Milo S. Ketchum
3、 Stefan J. Medwadowski Luis F. Meyer Eldon F. Mockry John K. Parsons A report on the practical aspects of shell design including recommen- dations and a commentary for designers of thin concrete shells. General guidance based on current practice is given on analysis, proportioning, reinforcing, and
4、construction. A selected bibliography on analytical methods featuring design tables and aids is included to assist the engineer. Keywords: ACI committee report; aggregate size; buckling; construction; design; double-curvature shell; edge beam; folded plate; formwork; model; prestressing; reinforceme
5、nt; shell; single-curvature shell; splice; stiffening member; supporting member, thickness; thin shell. CONTENTS Preface, pg. 334.1R-2 CRITERIA Chapter l-General, pg. 334.1R-2 1.l-Definitions 1.2-Scope ACI Committee Reports, Guides, Standard Practices and Commentaries are intended for guidance in de
6、signing, planning, executing, or inspecting construction and in preparing specifications. References to these documents shall not be made in the Project Documents. If items found in these documents are desired to be a part of the Project Documents, they should be phrased in mandatory language and in
7、corporated into the project documents. Eric C. Molke Vice Chairman Stefan J. Medwadowski Mario G. Salvadori John B. Skilling Bruno Thurlimann Robert Zaborowski Stuart E. Swartz Secretary William C. Schnobrich Alexander Scordelis David B. South Anton Tedesko Bing-Yuan Ting Daniel F. Tully Arnold Wils
8、on Chapter 2-Analysis, pg. 334.1R-2 2.1-Assumptions 2.2-Analysis of thin shells 2.3-Analysis of supporting members 2.4-Model analysis Chapter 3-Stability analysis, pg. 334.1R-3 3.1-Buckling Chapter 4-Proportioning, pg. 334.1R-3 4.1-Allowable stresses and load factors 4.2-Shell thickness 4.3-Shell re
9、inforcement 4.4-Prestressing 4.5-Concrete cover over reinforcement Chapter 5-Construction, pg. 334.1R-4 ACI 334.1R-92 replaces ACI 334.1R-64 (Revised 1982) (Reapproved 1956) effective Mar. 1.1992. The 1992 revision included minor editorial corrections and the deletion of the year designation for ACI
10、 318 to make the current code the applicable reference. Copyright 0 2002 American Concrete Institute. All rights reserved including rights of reproduction and use in any form or by any means, including the making of copies by any photo process, or by any elec- tronic or mechanical device, printed or
11、 written or oraI, or recording for sound or visual reproduction or for use in any knowledge or retrieval system or device, unless permission in writing is obtained from the copyright proprietors. 334.1R-l 334.1R-2 ACI COMMlTTEE REPORT 5.1-Aggregate size 5.2-Forms PART II-COMMENTARY Chapter I-General
12、, pg. 334.1R-4 Chapter 2-Analysis of shell, pg. 334.1R-4 2.1-Thin shells of single curvature 2.2-Folded plates 2.3-Thin shells of double curvature Chapter 3-Analysis of supporting members, pg. 334.1R-6 Chapter 4-Prestressing, pg. 334.1R-6 Chapter 5-Stability, pg. 334.1R-6 Chapter 6-Proportioning, pg
13、. 334.1R-7 Chapter 7-Construction, pg. 334.1R-8 7.1-Forms and decentering 7.2-Concrete placing 7.3-Curing of concrete Chapter 8-Models, pg. 334.1R-8 Chapter 9-Standards and ACI documents cited in this report, pg. 334.1R-9 PART III-SELECTED BIBLIOGRAPHY PREFACE With the increased use of thin shells h
14、as come an increased understanding of their behavior through field observations, laboratory tests, and mathematical refine- ment of analytic procedures. However, because of the wide range of geometry possible with thin shells, the ac- cumulated understanding is still limited. For some thin shell sys
15、tems, such as cylindrical barrel shells, the design can be made with the same degree of accuracy as for conventional reinforced concrete construction. For other thin shell systems, such as those of double curvature, the design must be at times based on less refined analyses in the same sense as the
16、empirical design of flat plate floors. Therefore, it was felt desirable to divide this report into two parts. The first part, entitled “Criteria,” covers general design recommendations. The second part, entitled “Commentary,” contains data of general interest to the designers of thin shells and refl
17、ects current practice. A “Selected Bibliography” is included as reference material on current methods of analysis. The analysis, design, and construction of thin shell structures requires a thorough knowledge in this field. Therefore, the recommendations contained herein are not sufficient in themse
18、lves for the satisfactory execution of thin shell structures. Designers are referred to the many texts and technical papers that are readily available. PART I-CRITERIA CHAPTER l-GENERAL 1.1-Definitions 1.1.1 Thin shells-Curved or folded slabs whose thick- nesses are small compared to their other dim
19、ensions. They are characterized by their three dimensional load carrying behavior which is determined by their geomet- rical shape, their boundary conditions and the nature of the applied load. Thin shells are usually bounded by sup- porting members and edge members. 1.1.2 Auxiliary members-In a bro
20、ad sense any mem- ber located along the boundary of a shell or shell seg- ment, with a capacity to stiffen the shell and distribute or carry load in composite action with the shell. They are classified as follows in accordance with established usage, although for certain shells a member may serve in
21、 a com- bination of capacities: a) Supporting members-Beams, arches, trusses, dia- phragms, etc., along the edges of thin shells which serve both to support and to stiffen the thin shell b) Edge members-Beams, trusses, etc., along the edges of thin shells which do not form part of the main supportin
22、g structure, but serve to stiffen and act integrally, i.e., in composite action with the thin shell to carry loads to the supporting members c)Stiffening members-Ribs which serve only to stiff- en the thin shell or to control local deformations 1.1.3 Elastic analysis-Any structural analysis based on
23、 elastic behavior and involving assumptions which are suit- able to approximations of three dimensional elastic be- havior. Analyses based on the results of elastic model tests, when conducted properly, are considered as valid elastic analyses. 1.2-Scope 1.2.1 These recommendations cover the design
24、of thin shell concrete structures and only apply to the thin shell portions of such structures unless otherwise stated. 1.2.2 All applicable sections of the ACI Building Code (ACI 318), including the precast and prestressed concrete sections of the Code, should be followed in the design of shell str
25、uctures except where they conflict with the fol- lowing provisions. CHAPTER 2-ANALYSIS 2.l-Assumptions 2.1.1 For an elastic analysis, concrete may be assumed CONCRETE SHELL STRUCTURES 334.1R-3 uncracked, homogeneous, and isotropic. 2.1.2 Poissons ratio may be assumed equal to zero. 2.2-Analysis of t
26、hin shells 2.2.1 Elastic behavior is the commonly accepted basis for determining stresses, displacements, and stability of thin shells. 2.2.2 The rigor and the necessary degree of accuracy required in the analysis of any specific thin shell structure depend on certain critical factors. These include
27、: the configuration of the surface and the degree of curvature (geometry), the size of the structure, the type of boun- dary conditions and the nature of the loading. Because of the complex interrelationship between these factors, spe- cific recommendations regarding rigor and accuracy of analysis a
28、re not given. 2.2.3 Approximate methods of analysis which do not satisfy compatibility of strains or stresses in the shell may be used in cases where authoritative sources and experi- ence have shown them to be applicable within the range employed. 2.2.4 Equilibrium checks of internal stresses and e
29、xternal loads are to be made to insure consistency of results. 2.2.5 An ultimate strength analysis may be used only as a check on the adequacy of the design. It is not to be used as a sole criterion for design, except where it can be proven to be applicable. 2.3-Analysis of supporting members 2.3.1
30、Supporting members shall be designed in accor- dance with a recognized elastic analysis. 2.3.2 A portion of the thin shell shall be assumed to act with the supporting member. 2.4-Model analysis 2.4.1 Models may be used as the basis for a design and/or to check the validity of assumptions involved in
31、 a mathematical analysis. When models are used, only those portions which significantly affect the items under study need be simulated. Every attempt must be made to en- sure that these tests reveal the quantitative behavior of the prototype structure. CHAPTER 3-STABILITY ANALYSIS 3.1-Buckling 3.1.1
32、 When investigating shells for stability, consid- eration shall be given to the possible reduction in the value of the buckling load caused by large deflections, creep effects, and the deviation between the actual and theoretical shell surface. CHAPTER 4-PROPORTIONING 4.1-Allowable stresses and load
33、 factors 4.1.1 Unless otherwise stated, concrete and steel stresses and load factors will be as specified in the Building Code (ACI 318). 4.1.2 Minimum standard cylinder strength,f, shall be 3000 psi. 4.2-Shell thickness 4.2.1 Shell thickness is not always dictated by strength requirements but often
34、 by deformation of edge members, stability, and cover over reinforcing steel. 4.2.2 Stress concentrations due to abrupt changes in section shall be considered and, where necessary, the thin shell shall be gradually thickened. 4.3-Shell reinforcement 4.3.1 The stress in the reinforcement may be assum
35、ed at the allowable value independently of the strain in the concrete. 4.3.2 Where the tensile stresses vary greatly in mag- nitude over the shell, as in the case of cylindrical shells, the reinforcement capable of resisting the total tension may be concentrated in the region of maximum tensile stre
36、ss. Where this is done, the percentage of crack con- trol reinforcing in any 12 in. width of shell shall be not less than 0.35 percent throughout the tensile zone. 4.3.3 The principal tensile stresses shall be resisted entirely by reinforcement. 4.3.4 Reinforcement to resist the principal tensile st
37、resses, assumed to act at the middle surface of the shell, may be placed either in the general direction of the lines of principal tensile stress (also referred to as par- allel to the lines of principal tensile stress), or in two or three directions. In the regions of high tension it is advis- able
38、, based on experience, to place the reinforcing in the general direction of the principal stress. 4.3.5 The reinforcement may be considered parallel to the line of principal stress when its direction does not deviate from the direction of the principal stress more than 15 deg. Variations in the dire
39、ction of the principal stress over the cross section of a shell due to moments need not be considered for the determination of the max- imum deviation. In areas where the stress in the rein- forcing is less than the allowable stress a deviation greater than 15 deg can still be considered parallel pl
40、acing; a stress decrease of 5 percent shall be considered to compensate for each additional degree of deviation above 15 deg. Wherever possible, such reinforcing may run along lines considered most practical for construc- tion, such as straight lines. 4.3.6 Where placed in more than one direction, t
41、he reinforcement shall resist the components of the principal tension force in each direction. 4.3.7 In those areas where the computed principal tensile stress in the concrete exceeds 300 psi, placement of at least one layer of the reinforcing shall be parallel to the principal tensile stress, unles
42、s it can be proven that a deviation of the reinforcing from the direction parallel to the lines of principal tensile stress is permissible because 334.1R-4 ACI COMMlTTEE REPORT of the geometrical characteristics of a particular shell and because for reasons of geometry only insignificant and local c
43、racking could develop. 4.3.8 Where the computed principal tensile stress (psi) in the concrete exceeds the value 2fl (where such cases include: 1. Cylindrical shells under torsional loading 2. Cylindrical shells under radial inward pressure As stated, poor correlation between the results of theory a
44、nd experiment exists when both principal mem- brane forces are compressive, as in the case of: 1. Cylindrical shells under axial compressive load 2. Cylindrical shells under distributed load normal to the surface which causes bending 3. Domes under inward radial pressure In extreme cases the bucklin
45、g load obtained experi- mentally has been found to be as little as 10 percent of that predicted by the small deflection theory. The effect of creep of concrete is similar to lowering E, the modulus of elasticity. The effect may be estimated as follows: Assume a reduced value of E or, knowing the pri
46、nci- pal membrane forces at any point of a given shell, de- termine the tangent modulus of elasticity. Divide the tangent modulus of elasticity by a multiplier for long- term deflections. The multiplier shall not be less than 2. The use of a reduced E accomplishes the same purpose as a buckling load
47、 reduction factor. A deviation of the shell dimensions from the geo- metry used in stress analysis is associated with a change in the principal radii of curvature of the shell surface. Elastic and creep deformations may also lead to a change of curvature. If the actual radii are larger, (i.e., the s
48、hell is flatter), the membrane forces are generally greater. Hence the value of the buckling load will be lower, pos- sibly substantially lower. In general, the value of the buckling load depends on shell geometry, type of restraint at boundary, material properties of shell, the location of reinforc
49、ing steel, and the type of load. With respect to shell geometry, the dominant factor is whether the surface is synclastic or anticlastic. For a) Synclastic surfaces, such as most shells of revo- lution, cylinders and cones, the buckling resistance usually lies somewhere between a sphere and a cyl- inder, the two shell forms which have been exten- sively studied. Hence an estimate of the critical stress may be sometimes obtained by comparing the given shell to a cylinder or a sphere b) Anticlastic surfaces, such as hyperbolic para- boloids, the buckling resistance is much greater than that o