Cross-section Strength Of Columns
Reinforced Concrete Buildings SeriesDesign Booklet RCB-3.1(1)Cross-section Strength of ColumnsPart 1: AS 3600 DesignOneSteel ReinforcingGuide to Reinforced Concrete DesignAugust 2000
ONESTEEL REINFORCINGGUIDE TO REINFORCED CONCRETE DESIGNPublished byOneSteel ReinforcingOneSteel Reinforcing Pty Ltd CAN 004 148 289Produced by theCentre for Construction Technology ResearchUniversity of Western SydneyContributorsProf. Russell BridgeDr. Andrew WheelerCentre for Construction Technology ResearchCopyright 2000 OneSteel Reinforcing and University of Western Sydney.All rights reserved.First published:February 2000Revised:August 2000AcknowledgementSome material in this booklet has been sourced from AustralianStandard AS3600-1994 and permission for its use has been kindlygranted by Standards Australia.DisclaimerWhile every effort has been made and all reasonable care taken toensure the accuracy of the material contained herein, thecontributors, editors and publishers of this booklet shall not be heldto be liable or responsible in any way whatsoever, and expresslydisclaim any liability or responsibility for any loss or damage, costsor expenses, howsoever incurred by any person whether the user ofthis booklet or otherwise including but without in any way limitingany loss or damage, costs or expenses incurred as a result of or inconnection with the reliance, whether whole or partial by any personas aforesaid upon any part of the contents of this booklet. Shouldexpert assistance be required, the services of a competent personshould be sought.RCB3.1(1)-iiCross-section Strength of Columns (Part 1: AS 3600 Design)Reinforced Concrete Buildings: Chapter 3 – ColumnsAugust 2000
ONESTEEL REINFORCINGGUIDE TO REINFORCED CONCRETE DESIGNCONTENTSPREFACE . V1.SCOPE AND GENERAL1.11.2Scope . 1General. 11.2.1 Concrete . 21.2.2 Steel . 22.TERMINOLOGY3.DESIGN CONCEPTS & MODELS3.1General. 33.2Cross-Section Strength . 53.2.1Introduction . 53.2.2Axial Compression . 73.2.3Combined Compression and Bending . 93.2.3.1 Introduction . 93.2.3.2 Load-Moment-Curvature Relationship . 103.2.3.3 Load-Moment Strength. 134.6.Effects of Slenderness . 153.2.5Biaxial Bending . 22DESIGN APPROACH4.1General. 234.2Rectangular Stress Block Method. 234.35.3.2.44.2.1Introduction . 234.2.2The Ultimate Strength Nuo for Pure Bending . 254.2.3The Balanced Condition Mub, Nub for Ultimate Strength . 274.2.4The Limit Condition Mul, Nul for Ultimate Strength . 274.2.5The Ultimate Strength Nuo for Pure Axial Force. 274.2.6Load-Moment Interaction Diagrams . 28Computer Based Analytical Method. 29DESIGN RULES5.1General. 315.1AS3600-1994 Proposed Changes to the Design Rules. 31WORKED EXAMPLES6.1General. 326.2Rectangular Column Reinforced on Four Sides – Analytical Method. 326.3Column Reinforced on Four Sides – Rectangular Stress Block . 33RCB3.1(1)-iii6.3.1Ultimate Strength Muo for Pure Bending . 346.3.2The Balanced Condition Mub, Nub for Ultimate Strength . 376.3.3The Limit Condition Mul, Nul for Ultimate Strength . 39Cross-section Strength of Columns (Part 1: AS 3600 Design)Reinforced Concrete Buildings: Chapter 3 – ColumnsAugust 2000
ONESTEEL REINFORCINGGUIDE TO REINFORCED CONCRETE DESIGN7.The Ultimate Strength Nuo for Pure Axial Force. 416.3.5Load-Moment Strength Interaction Diagrams. 426.4Column Reinforced on Four Sides – Analytical Method . 436.5Eccentrically Loaded Column . 43CASE STUDIES7.1Introduction. 467.2Case 1 – 700mm by 450mm Rectangular Column with 10Y28 bars . 477.37.47.57.68.6.3.47.2.1Major Axis Bending – Change in Steel Grade . 477.2.2Major Axis Bending – Change in Bar Size . 487.2.3Major Axis Bending – Change in Number of Bars . 497.2.4Minor Axis Bending – Change in Steel Grade . 507.2.5Minor Axis Bending – Change in Bar Size. 517.2.6Minor Axis Bending – Change in Number of Bars . 52Case 2 – 700mm by 450mm Rectangular Column with 12Y36 bars . 537.3.1Major Axis Bending – Change in Steel Grade . 537.3.2Major Axis Bending – Change in Bar Size . 547.3.3Major Axis Bending – Change in Number of Bars . 557.3.4Minor Axis Bending – Change in Steel Grade . 567.3.5Minor Axis Bending – Change in Bar Size. 577.3.6Minor Axis Bending – Change in Number of Bars . 58Case 3 – 450mm Square Column with 8Y32 Bars . 597.4.1Change in Steel Grade . 597.4.2Change in Bar Size . 607.4.3Mixed Bar Sizes . 617.4.4Change in Section Size. 62Case 4 – 450mm Circular Column with 8Y28 Bars. 637.5.1Change in Steel Grade . 637.5.2Change in Bar Size . 647.5.3Mixed Bar Sizes . 657.5.4Change in Section Size. 667.5.5Change in Bar Size and Section Size. 67Summary. 68REFERENCES . 69APPENDICESABCRCB3.1(1)-ivReferenced Australian Standards . 70Notation . 71Column Design Charts . 74Cross-section Strength of Columns (Part 1: AS 3600 Design)Reinforced Concrete Buildings: Chapter 3 – ColumnsAugust 2000
ONESTEEL REINFORCINGGUIDE TO REINFORCED CONCRETE DESIGNPREFACEThis design booklet is a part of OneSteel Reinforcing’ Guide to Reinforced Concrete Design that hasbeen produced to promote the superiority of OneSteel Reinforcing’ reinforcing steels, products andtechnical support services. The Guide covers important issues concerning the design and detailingof Reinforced Concrete Buildings, Residential Slabs and Footings, and Concrete Pavements. Theuse of 500PLUS reinforcing steels is featured in the booklets. Special attention is given to showinghow to get the most benefit from these new high-strength steels.The design booklets of the Reinforced Concrete Buildings series have each been written to form twoseparate parts: Part 1- AS 3600 Design which provides insight into major new developments in AS3600; and Part 2 – Advanced Design using OneSteel 500PLUS Rebar which leads to significanteconomic advantages for specifiers of OneSteel steel. These booklets are supported by 500PLUScomputer software that will prove to be indispensable to design engineers who use AS 3600.Columns are an important structural element in reinforced concrete structures. They are usuallyconstructed integrally with framing concrete beams and slabs although precast columns can beenused in appropriate situations. They have to provide resistance to both axial forces and bendingmoments generally resulting from loads applied to the floor beams and slabs. A key aspect in thedesign of columns is the strength of the column cross-section subjected to combined axial force andbending moment. Considering all the possible load and moment combinations for a given crosssection, the manual determination of this strength can be a tedious process [1] , even more so whenall the possible different reinforced cross-sections that might be used are taken into account.Therefore, it has been the practice for designers to use load-moment interaction diagrams that havebeen published [2] for a range of standard cross-section shapes and reinforcement patterns andsteel ratios.A new Australian/New Zealand Standard for reinforcing steels will shortly be introduced with thespecification of 500 MPa reinforcing steels covered for the first time [3]. A revised version ofAS3600-1994 to take account of the use of 500 MPa reinforcing steels has already gone to publicreview as document DR99193CP but no changes were then proposed to the rules for the design ofcolumns. Subsequent research associated with the production of this booklet now recommends thatsome changes be made to the design provisions for columns in AS3600-1994 and these areincluded in this booklet. Revised load-moment interaction diagrams have been developed for typicalcolumn cross-sections used in practice and have been based on considerations of equilibrium,compatibility and appropriate constitutive relationships for the steel and concrete. The method isapplicable to column cross-sections with bonded reinforcement assuming sufficient column ties toprevent buckling of the reinforcement.This design booklet contains both worked examples and important explanatory information about thestrength design method in AS3600-1994 and the recommended changes. It is intended that thisinformation will assist structural design engineers to understand the engineering principles on whichthe design method is based and to better realise the benefits of the increase in yield strength to begained leading to a significant reduction in steel area. Further research is proceeding that will allowthese design provisions to be improved upon when using OneSteel 500PLUS Rebar, and moreadvanced rules will be found in Part 2 of this design booklet.RCB3.1(1)-vCross-section Strength of Columns (Part 1: AS 3600 Design)Reinforced Concrete Buildings: Chapter 3 – ColumnsAugust 2000
ONESTEEL REINFORCINGGUIDE TO REINFORCED CONCRETE DESIGN1. SCOPE AND GENERAL1.1ScopeThis design booklet is concerned with the strength of reinforced concrete cross-sections of concretecolumns subjected to combined axial force and bending moment and designed in accordance withAS 3600-1994 and some proposed changes contained herein. It provides rules essential fordesigners to efficiently detail the main (longitudinal) reinforcement. The need for these rules islargely the result of the introduction of 500 MPa as a standard strength grade. This is a significantincrease on a current grade of 400 MPa for reinforcing bars.The types of reinforced concrete columns that have been considered are shown in Figure 1.1Figure 1.1 Typical Column Cross-sectionsThe reinforcement must consist of deformed bars with a rib geometry that provides adequate bond.This booklet does not directly cover the design of slender columns, the effects of slenderness andreinforcement requirements. Nor does the booklet cover the calculation of the design action effectsresulting from the application of live and dead loads, construction loads, foundation movements,temperature changes and gradients, and creep and shrinkage. Suffice it too say that axial forcesand/or bending moments need to be calculated at critical sections for comparison with the axialforce and bending strengths that are determined using the methods in this booklet. Some of theseaspects will be covered in later booklets. However, the design data in this booklet can be used inconjunction with AS3600-1994 in the consideration of these aspects.1.2GeneralThe design rules presented herein are based on considerations of equilibrium and straincompatibility (plane sections normal to the axis remain plane after bending) to determine the loadand moment strength for reinforced concrete cross-sections subjected to combined bending andaxial force. The column cross-sections are doubly symmetric and are comprised of concrete andfully-bonded longitudinal reinforcement as indicated in Figure 1.1 above.RCB3.1(1)-1Cross-section Strength of Columns (Part 1: AS 3600 Design)Reinforced Concrete Buildings: Chapter 3 – ColumnsAugust 2000
ONESTEEL REINFORCINGGUIDE TO REINFORCED CONCRETE DESIGNTwo design approaches have been used concerning the distribution of stress in the concrete andsteel:(a) the stress-strain curves for both the steel and concrete are assumed to be of a form defined byrecognised simplified equations, or determined from suitable test data; and(b) a simple rectangular stress block of 0.85f′c is used for the concrete at the strength limit statesubject to the limitations of Clause 10.6.2 of AS3600-1994, and the steel is assumed to belinear elastic-plastic in nature with a constant yield stress.1.2.1 ConcreteThe characteristic compressive strengths f′c of the standard concrete grades covered in this bookletare 20 MPa, 25 MPa, 32 MPa, 40 MPa and 50 MPa. The design properties of the concrete arecovered in Section 6.1 of AS3600-1994.It should be noted that if a curvilinear stress-strainrelationship is used for the concrete, the curve is modified for design purposes so that the maximumstress is 0.85f′c . The concrete is assumed to have no tensile strength.1.2.2 ReinforcementThe yield strengths fsy of reinforcement covered in this booklet are: 400 MPa for deformed bar toAS1302-1991 with a designated grade 400Y; and 500 MPa for deformed bar with a proposeddesignated grade of 500N [3]. The other design properties of the reinforcement are covered inSection 6.2 of AS3600-1994. The steel has been assumed to be linear elastic-plastic with an elasticmodulus of 200,000 MPa and with a constant yield plateau at the yield strength fsy .RCB3.1(1)-2Cross-section Strength of Columns (Part 1: AS 3600 Design)Reinforced Concrete Buildings: Chapter 3 – ColumnsAugust 2000
ONESTEEL REINFORCINGGUIDE TO REINFORCED CONCRETE DESIGN2. TERMINOLOGYSome important terminology used in this booklet is summarised in this section.ActionAny agent, such as imposed load, foundation movement or temperature gradient, which may act ona structure.Action effectsThe axial forces and bending moments which are produced in a structure or in its componentelements (column) by an action.Braced columnA column in a structure in which the lateral loads are resisted not by the column but rather bymasonry infill panels, shear walls and bracingBalanced condition for combined bending and compressionThe so-called “balanced” condition is where the ultimate strength in combined bending andcompression is reached when the stress in the outermost layer of the tensile reinforcement has justreached the yield stress.Limit condition for combined bending and compressionThe “limit” condition, as used in this booklet, is where the ultimate strength in combined bending andcompression is reached when the stress in the stress in the outermost layer of the tensilereinforcement is zero, and therefore the rest of the reinforcement is in compression.Rectangular stress blockWhere the neutral axis lies within the cross-section at the strength limit-state, a uniform concretecompressive stress of 0.85f′c can be assumed to act on an area as defined in Section 10.6.2 inAS3600-1994.Short columnA column where the additional bending moments due to slenderness are small and can be taken aszero.Slender columnA column in which slenderness effects cause additional bending moments within the length of thecolumn (and also at the column ends in sway columns)Sway columnA column in which the lateral loads on the structure are resisted by bending of the column.RCB3.1(1)-3Cross-section Strength of Columns (Part 1: AS 3600 Design)Reinforced Concrete Buildings: Chapter 3 – ColumnsAugust 2000
ONESTEEL REINFORCINGGUIDE TO REINFORCED CONCRETE DESIGN3. DESIGN CONCEPTS & MODELS3.1GeneralTypically columns are vertical members with large length to depth (L/D) ratios subject topredominantly compressive loads although some columns may be subjected to significant bending.The strength of a column cross-section can be determined from the geometry of the cross-section,the constitutive relationships of the concrete and steel and a consideration of equilibrium and straincompatibility. This strength is usually expressed in the form a load-moment strength interactiondiagram which plots the locus of φMu and φNu values where Mu is the ultimate strength in bending ata cross-section of an eccentrically loaded compression member, Nu is the corresponding ultimatestrength in compression at the same cross-section of the eccentrically loaded compression member,φ is the strength reduction factor to account for variability in geometric and material properties, ande is the eccentricity of loading at the cross-section where e M*/N* . A typical load-momentinteraction diagram is shown in Figure 3.1.φ NuLocus ofφMu, φNuvaluesφ Nu0N*M*(M*, N*)Load(Unsafe)(M*, N*)(φMub, φNub)(Safe)Momentφ Mu0φ MuFigure 3.1 Typical Load-Moment Strength Interaction for a Column Cross-sectionIn determining the strength of the column, the effects of column slenderness must also beconsidered. Consequently AS 3600 - 1994 classifies columns as either short columns or slendercolumns based on the slenderness ratio Le/r (Clause 10.3 of AS3600). When the design loads(typically 1.25G 1.5Q) are applied to a structure, bending moments M* and axial forces N* aregenerated at every cross-section of each column. For slender columns, M* will include additionalbending moments due to slenderness of the columns (second-order effects) which can be calculateddirectly from a second-order analysis of the loads (Clause 7.7 of AS3600-1994) and/or indirectlyusing moment magnifiers (Clause 10.4 of AS3600-1994). For short columns, the additional bendingmoments are deemed negligible and the design values for combinations of M* and N* are thoseapplied at the cross-sections at the end of the columns (assuming no lateral loading along the lengthRCB3.1(1)-4Cross-section Strength of Columns (Part 1: AS 3600 Design)Reinforced Concrete Buildings: Chapter 3 – ColumnsAugust 2000
ONESTEEL REINFORCINGGUIDE TO REINFORCED CONCRETE DESIGNof the columns). For the design of a column to be considered adequate (safe), the combination ofaction effects (M*, N*) must be less than the combination of design strengths (φMu , φNu) at everycross-section along the l
ONESTEEL REINFORCING GUIDE TO REINFORCED CONCRETE DESIGN RCB3.1(1)-v Cross-section Strength of Columns (Part 1: AS 3600 Design) August 2000 Reinforced Concrete Buildings: Chapter 3 – Columns PREFACE This design booklet is a part of OneSteel Reinforcing’ Guid
Chapter 3 3.1 The Importance of Strength 3.2 Strength Level Required KINDS OF STRENGTH 3.3 Compressive Strength 3.4 Flexural Strength 3.5 Tensile Strength 3.6 Shear, Torsion and Combined Stresses 3.7 Relationship of Test Strength to the Structure MEASUREMENT OF STRENGTH 3.8 Job-Molded Specimens 3.9 Testing of Hardened Concrete FACTORS AFFECTING STRENGTH 3.10 General Comments
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