1、Report on Equivalent Rectangular Concrete Stress Block and Transverse Reinforcement for High- Strength Concrete Columns Reported by Joint ACI-ASCE Committee 441 ACI 441.1R-18First Printing July 2018 ISBN: 978-1-64195-018-3 Report on Equivalent Rectangular Concrete Stress Block and Transverse Reinfor
2、cement for High-Strength Concrete Columns Copyright by the American Concrete Institute, Farmington Hills, MI. All rights reserved. This material may not be reproduced or copied, in whole or part, in any printed, mechanical, electronic, film, or other distribution and storage media, without the writt
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11、nt and may be obtained by contacting ACI. Most ACI standards and committee reports are gathered together in the annually revised the ACI Collection of Concrete Codes, Specifications, and Practices. American Concrete Institute 38800 Country Club Drive Farmington Hills, MI 48331 Phone: +1.248.848.3700
12、 Fax: +1.248.848.3701 www.concrete.orgThis report provides a research summary of equivalent rectangular concrete compressive stress blocks and transverse reinforcement design requirements for high-strength concrete (HSC) columns. Because ACI 318 code provisions for column design are mostly based on
13、concrete strengths less than 10,000 psi (70 MPa), the use of equivalent rectangular concrete stress block factors given in the code has been questioned. As a result, many alternative expressions have been developed. This report provides a summary of various suggestions of equivalent rectangular conc
14、rete stress block and design guidelines for HSC columns. The report also provides highlights of the research on the perfor- mance of HSC columns under various loading conditions, including monotonically increasing concentric or eccentric compression, and load reversals with increasing deformation an
15、d constant axial compression. The behavior of HSC columns subjected to combined axial load and bending moment is discussed. Various proposals for determining the amount and details of transverse reinforcement for seismic design are also reviewed. Keywords: axial load; bending moment; columns; concre
16、te stress block; ductility; flexural strength; high-strength concrete; longitudinal reinforce- ment; seismic design; transverse reinforcement. CONTENTS CHAPTER 1INTRODUCTION, p. 2 CHAPTER 2NOTATION AND DEFINITIONS, p. 2 2.1Notation, p. 2 2.2Definitions, p. 3 CHAPTER 3EQUIVALENT RECTANGULAR CONCRETE
17、STRESS BLOCK, p. 3 3.1ACI 318-14 concrete stress block, p. 3 3.2Other concrete stress blocks, p. 4 3.3Performance of ACI concrete stress block, p. 6 CHAPTER 4TRANSVERSE REINFORCEMENT, p. 7 4.1Constitutive models for confined concrete, p. 7 4.2Previous research and general observations, p. 8 4.3Equat
18、ions for determining transverse reinforcement required in columns, p. 9 4.4Definition of limiting drift ratio on basis of expected drift demand, p. 10 Sungjin Bae, Chair Aly Said, Secretary ACI 441.1R-18 Report on Equivalent Rectangular Concrete Stress Block and Transverse Reinforcement for High- St
19、rength Concrete Columns Reported by Joint ACI-ASCE Committee 441 Ahmed Abd El Fattah Perry Adebar Shahria Alam Bassem Andrawes Oguzhan Bayrak Muhammad A. Cheema Rami Eid Asad Esmaeily Richard W. Furlong Wael Mohammed Hassan Riyadh A. Hindi Mahmoud E. Kamara Tony C. Liu Mustafa A. Mahamid S. Ali Mirz
20、a Ronald L. OKane Patrick Paultre Hayder A. Rasheed Murat Saatcioglu Ayman E. Salama Halil Sezen Shamim A. Sheikh Nadim I. Wehbe Consulting Members Alaa E. Elwi Esko Hyttinen Said Iravani Chien-Hung Lin Santiago Pujol L. N. Ramamurthy ACI Committee Reports, Guides, and Commentaries are intended for
21、guidance in planning, designing, executing, and inspecting construction. 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 co
22、ntains. The American Concrete Institute disclaims any and all responsibility 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 A
23、rchitect/Engineer to be a part of the contract documents, they shall be restated in mandatory language for incorporation by the Architect/Engineer. ACI 441.1R-18 was adopted and published July 2018. Copyright 2018, American Concrete Institute. All rights reserved including rights of reproduction and
24、 use in any form or by any means, including the making of copies 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 f
25、rom the copyright proprietors. 14.5Use of high-strength reinforcement for transverse reinforcement, p. 11 4.6Maximum hoop spacing requirements for columns, p. 12 CHAPTER 5SUMMARY AND RECOMMENDATIONS, p. 13 CHAPTER 6REFERENCES, p. 13 Authored documents, p. 13 CHAPTER 1INTRODUCTION High-strength concr
26、ete (HSC) has advantages over normal-strength concrete (NSC), especially for columns of high-rise buildings, as it reduces column sizes and increases the durability of concrete (Smith and Rad 1989). Moreover, HSC can be advantageous with regard to lateral stiffness and axial shortening (Colaco 1985)
27、. Another advantage cited by Colaco in the use of HSC columns is the cost reduction of formwork stemming from reduced cross-sectional dimen- sions. This economic advantage is achieved by using HSC in lower-story columns and reducing concrete strength over the height of the building while keeping the
28、 same column size over the building height. Increased use of HSC has caused concerns over the appli- cability of the current building code requirements (ACI 318) for the design and detailing of HSC columns. Those concerns are mainly related to: 1) equivalent rectangular concrete stress distribution;
29、 and 2) transverse reinforcement requirements for seismic design. Chapter 22 of ACI 318-14 provides a concept of equivalent rectangular concrete stress distribution (ACI concrete stress block) for design of reinforced concrete columns. In the equivalent rectangular concrete stress block, an average
30、stress of 0.85f c is used with a rectangle of depth a = 1 c. The 1976 supplement to the 1971 code adopted a lower limit of 1equal to 0.65 based on research data from tests with concrete strengths exceeding 8000 psi (55 MPa). Several research studies reported that the use of current rectangular concr
31、ete stress block expressions of ACI 318 could produce overestimated flexural and axial strengths of HSC columns (Wahidi 1995; Ibrahim and MacGregor 1996; Lloyd and Rangan 1996). As a result, alternative concrete stress block expressions have been proposed (Ibrahim and MacGregor 1997; Bae and Bayrak
32、2003; Ozbakkaloglu and Saatcioglu 2004; Azizinamini et al. 1994). Numerous research studies (Sakai and Sheikh 1989; Elwood et al. 2009a,b; Paultre and Lgeron 2008) have been conducted in several countries to investigate the behavior of HSC columns, to evaluate similarities or differences between HSC
33、 and NSC columns, and to identify important param- eters affecting performance of HSC columns designed for seismic, as well as nonseismic, areas. As a result, Chapter 18 of ACI 318-14 has updated the transverse reinforce- ment requirement to address the concern on the use of HSC columns for seismic
34、design. This document reports the results of recent studies on the equivalent rectangular concrete stress distribution, or concrete stress block, and transverse reinforcement require- ments of HSC columns for seismic design. CHAPTER 2NOTATION AND DEFINITIONS 2.1Notation A b= area of an individual lo
35、ngitudinal reinforcing bar, in. 2(mm 2 ) A c= area of core concrete measured out-to-out of trans- verse reinforcement, in. 2(mm 2 ) A ch= cross-sectional area of a member measured to the outside edges of transverse reinforcement, in. 2(mm 2 ) A g= gross area of concrete section, in. 2(mm 2 ). For a
36、hollow section, A gis the area of concrete only and does not include the area of void(s) A sh= total cross-sectional area of transverse reinforce- ment, including crossties, within spacing s (or s h ) and perpendicular to dimension b c , in. 2(mm 2 ) A st= total area of nonprestressed longitudinal r
37、einforce- ment including bars or steel shapes, and excluding prestressing reinforcement, in. 2(mm 2 ) A te= sum of the areas of tie legs used to provide lateral support against buckling for longitudinal reinforce- ment of column, in. 2(mm 2 ) b = width of compression face of member, in. (mm) b c= cr
38、oss-sectional dimension of member core measured to the outside edges of the transverse reinforcement composing area A sh , in. (mm) c = distance from extreme compression fiber to neutral axis, in. (mm) d = distance from extreme compression fiber to centroid of longitudinal tension reinforcement, in.
39、 (mm) d = depth of concrete core of column measured from center-to-center of peripheral rectangular hoop, circular hoop, or spiral in. (mm) d b= nominal diameter of bar, wire, or prestressing strand, in. (mm) E s= modulus of elasticity of reinforcement and struc- tural steel, excluding prestressing
40、reinforcement, psi (MPa) f c = specified compressive strength of concrete, psi (MPa) f cm= measured compressive strength of concrete, psi (MPa) f s= transverse steel stress at or shortly after the attain- ment of maximum strength under concentric compression, psi (Eq. (4.5) f y= specified yield stre
41、ngth for nonprestressed rein- forcement, psi (MPa) f yh(or f yt )= specified yield strength of transverse reinforce- ment, psi (MPa) h = overall height or depth of member, in. (mm) h = dimension of concrete core of rectangular section, measured perpendicular to the direction of the hoop legs, measur
42、ed to the outside of the peripheral hoop, in. (mm) h c= cross-sectional dimension of member core measured to outside edges of transverse reinforce- ment composing area A sh , in. (mm), parallel to shear force in the member American Concrete Institute Copyrighted Material www.concrete.org 2 CONCRETE
43、STRESS BLOCK AND TRANSVERSE REINFORCEMENT FOR HSC COLUMNS (ACI 441.1R-18)h x= maximum center-to-center spacing of longitudinal bars laterally supported by corners of crossties or hoop legs around the perimeter of the column, in. (mm) k f= concrete strength factor, which is calculated as f c /25,000
44、+ 0.6 1.0, where f c is in psi k n= confinement effectiveness factor, which is calcu- lated as n /(n 2), where n is the number of longi- tudinal bars or bar bundles around the perimeter of a column core with rectilinear hoops that are later- ally supported by the corner of hoops or by seismic hooks
45、M = maximum moment, in.-lb (N-mm) (Fig. 3.3) M n= nominal flexural strength of the section, in.-lb (N-mm) N* = design axial load at ultimate limit state; to be taken as positive for compression and negative for tension, lb (N) P = maximum axial load; to be taken as positive for compression and negat
46、ive for tension, lb (N) (Fig. 3.3) P n= nominal axial strength of member, lb (N) P n,max= maximum nominal axial compressive strength of member, lb (N) P o= nominal axial strength at zero eccentricity, lb (N) P u= factored axial load; to be taken as positive for compression and negative for tension,
47、lb (N) s (or s h ) = center-to-center spacing of items, such as longi- tudinal reinforcement, transverse reinforcement, tendons, or anchors, in. (mm) s o= center-to-center spacing of transverse reinforce- ment within potential plastic hinge length, in. (mm) 1= factor relating magnitude of uniform st
48、ress in equivalent rectangular concrete stress block to specified compressive strength of concrete 1= factor relating depth of equivalent rectangular concrete stress block to depth of neutral axis = relative lateral deflection between the top and bottom of a column, in. (mm) A b= sum of areas of lon
49、gitudinal reinforcing bars reliant on the tie, in. 2(mm 2 ) s= ratio of the volume of spiral reinforcement to the total volume of core confined by spiral (measured out-to-out of spirals) t= ratio of the area of nonprestressed longitudinal reinforcement to gross concrete area (= A st /A g ) tc= ratio of the area of transverse reinforcement, A sh , to the area of core perpendicular to that transverse reinforcement = strength reduction factor 2.2Definitions ACI provides a comprehensive list of definitions through an online resou
