1、Design Guide for Twisting Moments in Slabs Reported by Joint ACI-ASCE Committee 447 ACI 447R-18First Printing April 2018 ISBN: 978-1-64195-010-7 Design Guide for Twisting Moments in Slabs Copyright by the American Concrete Institute, Farmington Hills, MI. All rights reserved. This material may not b
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11、crete Codes, Specifications, and Practices. American Concrete Institute 38800 Country Club Drive Farmington Hills, MI 48331 Phone: +1.248.848.3700 Fax: +1.248.848.3701 www.concrete.orgThis guide assists practitioners in understanding: 1) twisting moments in two-way slabs, when twisting moments are a
12、n essential consideration; 2) methods that can be used to account for twisting moments in design; and 3) the options available for each method of the various system geometries. Descriptions of twisting moments are provided theoretically and visually in the guide, and six methods of accounting for tw
13、isting moments in design are discussed. Appli- cability of the various methods is evaluated through a comparison of designs resulting from each method for a variety of two-way slab types and geometries. The theories described in the guide also apply to the design of two-way wall and two-way dome sys
14、tems. Keywords: finite element analysis; shell design; slab design; torsion; twist; twisting moments; wall design. CONTENTS CHAPTER 1INTRODUCTION AND SCOPE, p. 2 1.1Introduction, p. 2 1.2Scope, p. 2 CHAPTER 2NOTATION AND DEFINITIONS, p. 2 2.1Notation, p. 2 2.2Defintions, p. 3 CHAPTER 3BACKGROUND, p.
15、 3 3.1Qualitative introduction to twisting moments in slabs, p. 3 3.2Behavior of linear-elastic isotropic slabs, p. 4 3.3Equilibrium in slabs, p. 4 3.4Principal axes, p. 4 3.5Orthogonal reinforcement and equilibrium for twisting moments, p. 5 3.6Effects of slab geometry on twisting moments, p. 5 3.7
16、Traditional slab design methods, p. 6 3.8Finite element analysis (FEA)-based slab design resultants, p. 6 Ganesh Thiagarajan, Chair Jian Zhao, Secretary ACI 447R-18 Design Guide for Twisting Moments in Slabs Reported by Joint ACI-ASCE Committee 447 Riadh S. Al-Mahaidi Gangolu Appa Rao Ashraf S. Ayou
17、b Zdenk P. Baant Allan P. Bommer Mi-Geum Chorzepa Carlos Arturo Coronado Gianluca Cusatis Mukti L. Das James B. Deaton Jason L. Draper Serhan Guner Trevor D. Hrynyk John F. Jakovich Song F. Jan Ioannis Koutromanos Laura N. Lowes Yong Lu Yi-Lung Mo Abbas Mokhtar Zadeh Wassim I. Naguib Dan Palermo Gui
18、llermo Alberto Riveros Mohammad Sharafbayani Hazim Sharhan Sri Sritharan Consulting Members Ahmet Emin Aktan Sarah L. Billington Johan Blaauwendraad Oral Buyukozturk Ignacio Carol Luigi Cedolin Wai F. Chen Christopher H. Conley Robert A. Dameron Filip C. Filippou Kurt H. Gerstle Walter H. Gerstle Ro
19、bert Iding Anthony R. Ingraffea Feng-Bao Lin Christian Meyer Hiroshi Noguchi Gilles Pijaudier-Cabot Syed Mizanur Rahman Victor E. Saouma Frank J. Vecchio Kaspar J. Willam ACI Committee Reports, Guides, and Commentaries are intended for guidance in planning, designing, executing, and inspecting const
20、ruction. This document is intended for the use of individuals who are competent to evaluate the significance and limitations of its content and recommendations and who will accept responsibility for the application of the material it contains. The American Concrete Institute disclaims any and all re
21、sponsibility for the stated principles. The Institute shall not be liable for any loss or damage arising therefrom. Reference to this document shall not be made in contract documents. If items found in this document are desired by the Architect/Engineer to be a part of the contract documents, they s
22、hall be restated in mandatory language for incorporation by the Architect/Engineer. ACI 447R-18 was adopted and published April 2018. Copyright 2018, American Concrete Institute. All rights reserved including rights of reproduction and use in any form or by any means, including the making of copies
23、by any photo process, or by electronic or mechanical device, printed, written, or oral, 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. 1CHAPTER 4AVAILABLE DESIGN METHODS
24、, p. 7 4.1Finite element analysis (FEA)-based design ignoring twist, p. 7 4.2Design using the Wood and Armer method, p. 7 4.3Design using the sandwich model, p. 7 4.4Design using element nodal forces, p. 8 4.5Design using twist-free analysis, p. 9 CHAPTER 5COMPARISON OF DESIGN METHODS, p. 10 5.1Sens
25、itivity to angle of principal axes, p. 10 5.2Typical design conditions, p. 11 CHAPTER 6TWO-WAY WALLS, p. 21 6.1General considerations, p. 21 6.2Impact of twisting moment on walls exhibiting two adjacent fixed edges, p. 21 CHAPTER 7SHELL STRUCTURES, p. 24 7.1General considerations, p. 24 7.2Typical b
26、ulk material storage hemisphere, p. 24 7.3Typical loading conditions, p. 25 7.4Typical design regions, p. 25 CHAPTER 8REFERENCES, p. 29 Authored documents, p. 29 CHAPTER 1INTRODUCTION AND SCOPE 1.1Introduction Section 8.2.1 of ACI 318-14 allows slabs to be designed by any procedure that satisfies eq
27、uilibrium and geometric compatibility, and requires that, at each section, the design strength exceeds the required strength and serviceability requirements are fulfilled. Traditional strip design methods for slabs are based on approximate analysis and provide neither a complete equilibrium load pat
28、h or satisfy geometric compatibility. Nonetheless, these methods have been used successfully for many years to design slabs with supports arranged in a rectangular grid. From 1995 to 2015, design engineers transitioned from predominantly using traditional slab analysis methods to using finite elemen
29、t analysis (FEA). More recently, engi- neers use FEA to assist in the structural design of two-way concrete members. Twisting moments in two-way slabs can require additional reinforcement from those proportioned for bending moments, yet they are often misunderstood and sometimes ignored, neglected,
30、or both, by practitio- ners in design. This is most likely due to their lack of being discussed comprehensively in design codes and frequent exclusion from college concrete design course curricula. Although FEA solutions provide a full equilibrium load path and satisfy geometric compatibility, they
31、determine load paths that require twisting moments for equilib- rium (Shin et al. 2009). Many designers using FEA have ignored these twisting momentsa possible unconserva- tive assumption where twisting moments are high (Park and Gamble 2000). To provide designers with guidance related to this issue
32、, methods for explicitly incorporating twisting moments determined from FEA in the design of slabs are discussed in this guide. The purpose of this design guide is to provide advice to design engineers who analyze slab systems with finite element methods and who need to ensure their designs are sati
33、sfactory for the twisting moments predicted by the anal- ysis. This guide provides background information regarding twisting moments and describes multiple approaches for consideration of twisting moments in design. It also provides advice for designers of walls and shells with twisting moment condi
34、tions similar to those in slabs. 1.2Scope This design guide applies to slabs of both uniform and nonuniform thicknesses, including drop caps and drop panels, except where noted in the text. This guide does not apply to waffle slabs, or the beams of beam-and-slab floor systems. Chapters 3 through 6 a
35、ddress slabs and walls in which the response is determined purely by bending. Chapter 7 addresses shells for which the response is determined by bending and membrane action. Chapter 6 and the theory sections of this guide are applicable to walls. Chapter 7 and the theory sections of this guide are a
36、pplicable to shells, with the caveat that equations presented in Chapter 3 are not valid for curved shells. CHAPTER 2NOTATION AND DEFINITIONS 2.1Notation c i,j= fraction for consideration of sections partially crossing element to apply to forces in local node j in element i D = flexural rigidity of
37、plate, in.-lb (Nmm) E = Youngs modulus, psi (MPa) F = force vector, lb (N) f i,j= nodal force vector for local node j in element i h = thickness of slab or plate, in. (mm) L = width of design section, in. (mm) M = bending moment, or moment vector, in.-lb (Nmm) M d= design bending moment, in.-lb (Nmm
38、) M i= bending moment from isotropic analysis, in.-lb (Nmm) M tf= bending moment from twist-free analysis, in.-lb (Nmm) M u= design moment for slab cross section, in.-lb (Nmm) m i,j= nodal moment vector for local node j in element i, in.-lb/in. (Nmm/mm) m r= bending moment causing stresses parallel
39、to r-axis, per unit length of slab or plate, in.-lb/in. (Nmm/ mm) m rs= twisting moment relative to r-s-axes per unit length of slab or plate, in.-lb/in. (Nmm/mm) m s= bending moment causing stresses parallel to s-axis, per unit length of slab or plate, in.-lb/in. (Nmm/mm) American Concrete Institut
40、e Copyrighted Material www.concrete.org 2 DESIGN GUIDE FOR TWISTING MOMENTS IN SLABS (ACI 447R-18)m ux= design moment causing stresses parallel to x-axis, per unit length of slab or plate, in.-lb/in. (Nmm/ mm) m ux += positive design moment causing stresses parallel to x-axis, per unit length of sla
41、b or plate, in.-lb/in. (Nmm/mm) m ux = negative design moment causing stresses parallel to x-axis, per unit length of slab or plate, in.-lb/in. (Nmm/mm) m uy= design moment causing stresses parallel to y-axis, per unit length of slab or plate, in.-lb/in. (Nmm/mm) m uy += positive design moment causi
42、ng stresses parallel to y-axis, per unit length of slab or plate, in.-lb/in. (Nmm/mm) m uy = negative design moment causing stresses parallel to y-axis, per unit length of slab or plate, in.-lb/in. (Nmm/mm) m x= bending moment causing stresses parallel to x-axis, per unit length of slab or plate, in
43、.-lb/in. (Nmm/mm) m xy= twisting moment relative to x-y-axes per unit length of slab or plate, in.-lb/in. (Nmm/mm) m y= bending moment causing stresses parallel to y-axis, per unit length of slab or plate, in.-lb/in. (Nmm/mm) n x= membrane tension in x-axis direction per unit length, lb/in. (N/mm) n
44、 xy= membrane in plane-shear in x-y-axes direction per unit length, lb/in. (N/mm) n y= membrane tension in y-axis direction per unit length, lb/in. (N/mm) q = transverse load per unit area, lb/in. 2(N/mm 2 ) T = torsional moment, in.-lb (Nmm) V = shear force, lb (N) V d= design shear force, lb (N) v
45、 x= transverse shear on x-face per unit length, lb/in. (N/mm) v y= transverse shear on y-face per unit length, lb/in. (N/mm) w = transverse deflection, in. (mm) x i,j= distance vector from section centroid to local node j in element i, in. (mm) = Poissons ratio 2.2Defintions ACI provides a comprehen
46、sive list of definitions through an online resource, ACI Concrete Terminology. Definitions provided herein complement that source. anticlastic bendingcurvature caused by the Poisson effect and curvature about a perpendicular axis. strip design methoda method of designing slabs by dividing them into
47、two sets of approximately perpendicular strips, with each strip analyzed and designed independently from each other. CHAPTER 3BACKGROUND 3.1Qualitative introduction to twisting moments in slabs Twist exists in most every slab, except those theoretical- case-only slabs whose moments at any point are
48、identical about any axis. Figure 3.1 illustrates an extreme case of twist; a square slab with supports at three corners and a load at the fourth corner. From equilibrium, it can be shown that the bending moment about the A-A and B-B axes in the figure is zero, although this slab is clearly supportin
49、g a load and needs to be reinforced. Looking at the C-C axis, whose bending moment is nonzero, gives us insight to the load-carrying Fig. 3.1Twisting moment example free body diagram. American Concrete Institute Copyrighted Material www.concrete.orgDESIGN GUIDE FOR TWISTING MOMENTS IN SLABS (ACI 447R-18) 3mechanism of the slab. What appears as twist about A-A and B-B is bending about C-C and D-D, as shown in the deflected shapes along C-C and D-D. 3.2Behavior of linear-elastic isotropic slabs Like other co
