Etabs concrete frame design manual

Etabs concrete frame design manual Etabs concrete frame design manual Etabs concrete frame design manual Etabs concrete frame design manual Etabs concrete frame design manual Etabs concrete frame design manual Etabs concrete frame design manual Etabs concrete frame design manual Etabs concrete frame design manual Etabs concrete frame design manual Etabs concrete frame design manual Etabs concrete frame design manual Etabs concrete frame design manual Etabs concrete frame design manual Etabs concrete frame design manual Etabs concrete frame design manual Etabs concrete frame design manual

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Concrete Frame Design Manual

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ETABS ®

Integrated Three-Dimensional Static and Dynamic Analysis and Design

of Building Systems

CONCRETE FRAME DESIGN MANUAL

COMPUTERS &

STRUCTURES INC.

R

Computers and Structures, Inc.

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The computer program ETABS and all associated documentation areproprietary and copyrighted products Worldwide rights of ownershiprest with Computers and Structures, Inc Unlicensed use of the program

or reproduction of the documentation in any form, without prior writtenauthorization from Computers and Structures, Inc., is explicitly prohib-ited

Further information and copies of this documentation may be obtainedfrom:

Computers and Structures, Inc

1995 University AvenueBerkeley, California 94704 USATel: (510) 845-2177Fax: (510) 845-4096

E-mail: info@csiberkeley.com Web: www.csiberkeley.com

The CSI Logo is a registered trademark of Computers and Structures, Inc.

ETABS is a registered trademark of Computers and Structures, Inc.

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CONSIDERABLE TIME, EFFORT AND EXPENSE HAVE GONEINTO THE DEVELOPMENT AND DOCUMENTATION OF ETABS.THE PROGRAM HAS BEEN THOROUGHLY TESTED AND USED

IN USING THE PROGRAM, HOWEVER, THE USER ACCEPTSAND UNDERSTANDS THAT NO WARRANTY IS EXPRESSED ORIMPLIED BY THE DEVELOPERS OR THE DISTRIBUTORS ONTHE ACCURACY OR THE RELIABILITY OF THE PROGRAM.THIS PROGRAM IS A VERY PRACTICAL TOOL FOR THE DE-SIGN OF REINFORCED CONCRETE STRUCTURES HOWEVER,THE USER MUST THOROUGHLY READ THE MANUAL ANDCLEARLY RECOGNIZE THE ASPECTS OF REINFORCED CON-CRETE DESIGN THAT THE PROGRAM ALGORITHMS DO NOTADDRESS

THE USER MUST EXPLICITLY UNDERSTAND THE TIONS OF THE PROGRAM AND MUST INDEPENDENTLY VER-IFY THE RESULTS

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ASSUMP-CHAPTER I Introduction 1

Overview 1

Organization 2

Recommended Reading 3

CHAPTER II Design Algorithms 5 Design Load Combinations 6

Design and Check Stations 7

Identifying Beams and Columns 8

Design of Beams 8

Design of Columns 9

Design of Joints 14

Beam/Column Flexural Capacity Ratios 18

P-DEffects 18

Element Unsupported Lengths 19

Special Considerations for Seismic Loads 20

Choice of Input Units 21

CHAPTER III Design for ACI 318-99 23 Design Load Combinations 23

Strength Reduction Factors 26

Column Design 27

Generation of Biaxial Interaction Surfaces 27

Check Column Capacity 29

Determine Factored Moments and Forces 29

Determine Moment Magnification Factors 29

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Determine Capacity Ratio 31

Design Column Shear Reinforcement 32

Determine Section Forces 33

Determine Concrete Shear Capacity 34

Determine Required Shear Reinforcement 36

Beam Design 36

Design Beam Flexural Reinforcement 37

Determine Factored Moments 37

Determine Required Flexural Reinforcement 37

Design Beam Shear Reinforcement 44

Determine Shear Force and Moment 44

Design of Joints 46

Determine the Panel Zone Shear Force 47

Determine the Effective Area of Joint 48

Check Panel Zone Shear Stress 48

CHAPTER IV Design for UBC 97 51 Design Load Combinations 54

Column Design 56

Beam Design 66

Design of Joints 76

Determine the Panel Zone Shear Force 77

Determine the Effective Area of Joint 78

Check Panel Zone Shear Stress 78

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ETABS Concrete Design Manual

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CHAPTER V Design for CSA-A23.3-94 81 Design Load Combinations 84

Column Design 85

Beam Design 97

CHAPTER VI Design for BS 8110-85 R1989 111 Design Load Combinations 111

Design Strength 114

Column Design 114

Determine Additional Moments 117

Beam Design 121

CHAPTER VII Design for Eurocode 2 129 Design Load Combinations 129

Design Strength 132

Column Design 133

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Determine Code Total Moments 135

Beam Design 142

CHAPTER VIII Design for NZS 3101-95 153 Design Load Combinations 156

Column Design 157

Dynamic Moment Magnification 162

Beam Design 170

CHAPTER IX Design Output 185 Overview 185

Graphical Display of Design Input and Output 186

Tabular Display of Design Input and Output 187

Member Specific Information 190

iv

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Overview

ETABS features powerful and completely integrated modules for design of bothsteel and reinforced concrete structures (CSI 1999, 2000) The program providesthe user with options to create, modify, analyze and design structural models, allfrom within the same user interface

The program provides an interactive environment in which the user can study thestress conditions, make appropriate changes, such as revising member properties,and re-examine the results without the need to re-run the analysis A single mouseclick on an element brings up detailed design information Members can begrouped together for design purposes The output in both graphical and tabulatedformats can be readily printed

The program is structured to support a wide variety of the latest national and national building design codes for the automated design and check of concrete andsteel frame members The program currently supports the following concrete framedesign codes:

inter-• U.S ACI (ACI 1999),

• U.S UBC (UBC 1997),

• Canadian (CSA 1994),

Overview 1

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In the design of the columns, the program calculates the required longitudinal andshear reinforcement However the user may specify the longitudinal steel, in whichcase a column capacity ratio is reported The column capacity ratio gives an indica-tion of the stress condition with respect to the capacity of the column.

Every beam member is designed for flexure and shear at a user defined number ofstations along the beam span

The presentation of the output is clear and concise The information is in a form thatallows the engineer to take appropriate remedial measures in the event of memberoverstress Backup design information produced by the program is also providedfor convenient verification of the results

English as well as SI and MKS metric units can be used to define the model try and to specify design parameters

geome-Organization

This manual is organized in the following way:

Chapter II outlines various aspects of the concrete design procedures of the ETABSprogram This chapter describes the common terminology of concrete design as im-plemented in ETABS

Each of six subsequent chapters gives a detailed description of a specific code ofpractice as interpreted by and implemented in ETABS Each chapter describes thedesign loading combination, column and beam design procedures, and other spe-cial consideration required by the code In addition Chapter IV describes the jointdesign according to the UBC code

• Chapter III gives a detailed description of the ACI code (ACI 1999) as mented in ETABS

imple-2 Organization

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• Chapter IV gives a detailed description of the UBC concrete code (UBC 1997)

Recommended Reading 3

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C h a p t e r II

Design Algorithms

This chapter outlines various aspects of the concrete design and design-check cedures that are used by the ETABS program The concrete design and check may

pro-be performed in ETABS according to one of the following design codes:

• The 1995 American Concrete Institute Building Code Requirements for

Struc-tural Concrete, ACI 318-99 (ACI 1999).

• International Conference of Building Officials’ 1997 Uniform Building Code:

Volume 2: Structural Engineering Design Provisions, Chapter 19 “Concrete”,

UBC 1997 (ICBO 1997).

• The 1994 Canadian Standards Association Design of Concrete Structures for

Buildings, CSA-A23.3-94 (CSA 1994).

• The 1989 British Standards Institution Structural Use of Concrete, BS 8110-85 R1989 (BSI 1989).

• The 1992 European Committee for Standardization, Design of Concrete

Struc-tures, EUROCODE 2 (CEN 1992).

• The 1995 Standards New Zealand Concrete Structures Standard, NZS 3101-95

(NZS 1995)

Details of the algorithms associated with each of these codes as implemented inETABS are described in the subsequent chapters However, this chapter provides abackground which is common to all the design codes

5

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For referring to pertinent sections of the corresponding code, a unique prefix is signed for each code.

as-– References to the ACI 318-99 code has the prefix of “ACI”

– References to the UBC 1997 code has the prefix of “UBC”

– References to the Canadian code carry the prefix of “CSA”

– References to the British code carry the prefix of “BS”

– References to the Eurocode 2 carry the prefix of “EC2”

– References to the New Zealand code carry the prefix of “NZS”

In writing this manual it has been assumed that the user has an engineering ground in the general area of structural reinforced concrete design and familiaritywith at least one of the above mentioned design codes

back-Design Load Combinations

The design load combinations are used for determining the various combinations ofthe load cases for which the structure needs to be designed/checked The load com-bination factors to be used vary with the selected design code The load combina-tion factors are applied to the forces and moments obtained from the associated loadcases and the results are then summed to obtain the factored design forces and mo-ments for the load combination

For multi-valued load combinations involving response spectrum, time history, andmulti-valued combinations (of type enveloping, square-root of the sum of thesquares or absolute) where any correspondence between interacting quantities islost, the program automatically produces multiple sub combinations using max-ima/minima permutations of interacting quantities Separate combinations withnegative factors for response spectrum cases are not required because the programautomatically takes the minima to be the negative of the maxima for response spec-trum cases and the above described permutations generate the required sub combi-nations

When a design combination involves only a single multi-valued case of time tory or moving load, further options are available The program has an option to re-quest that time history combinations produce sub combinations for each time step

his-of the time history

For normal loading conditions involving static dead load, live load, wind load, andearthquake load, and/or dynamic response spectrum earthquake load, the programhas built-in default loading combinations for each design code These are based on

6 Design Load Combinations

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the code recommendations and are documented for each code in the correspondingchapters.

For other loading conditions involving time history, pattern live loads, separateconsideration of roof live load, snow load, etc., the user must define design loadingcombinations either in lieu of or in addition to the default design loading combina-tions

The default load combinations assume all static load cases declared as dead load to

be additive Similarly, all cases declared as live load are assumed additive ever, each static load case declared as wind or earthquake, or response spectrumcases, is assumed to be non additive with each other and produces multiple lateralload combinations Also wind and static earthquake cases produce separate loadingcombinations with the sense (positive or negative) reversed If these conditions arenot correct, the user must provide the appropriate design combinations

How-The default load combinations are included in design if the user requests them to beincluded or if no other user defined combination is available for concrete design Ifany default combination is included in design, then all default combinations willautomatically be updated by the program any time the user changes to a differentdesign code or if static or response spectrum load cases are modified

Live load reduction factors can be applied to the member forces of the live load case

on an element-by-element basis to reduce the contribution of the live load to thefactored loading

The user is cautioned that if time history results are not requested to be recovered inthe analysis for some or all the frame members, then the effects of these loads will

be assumed to be zero in any combination that includes them

Design and Check Stations

For each load combination, each beam, column, or brace element is designed orchecked at a number of locations along the length of the element The locations arebased on equally spaced segments along the clear length of the element By defaultthere will be at least 3 stations in a column or brace element and the stations in abeam will be at most 2 feet (0.5m if model is created in SI unit) apart The number

of segments in an element can be overwritten by the user before the analysis ismade The user can refine the design along the length of an element by requestingmore segments See the section “Frame Output Stations Assigned to Line Objects”

in the ETABS User’s Manual Volume 1 (CSI 1999) for details.

Design and Check Stations 7

Chapter II Design Algorithms

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When using 1997 UBC design codes, requirements for joint design at the beam tocolumn connections are evaluated at the topmost station of each column The pro-gram also performs a joint shear analysis at the same station to determine if specialconsiderations are required in any of the joint panel zones The ratio of the beamflexural capacities with respect to the column flexural capacities considering axialforce effect associated with the weak beam-strong column aspect of any beam/col-umn intersection are reported.

Identifying Beams and Columns

In ETABS all beams and columns are represented as frame elements But design ofbeams and columns requires separate treatment Identification for a concrete ele-ment is done by specifying the frame section assigned to the element to be of typebeam or column If there is any brace element in the frame, the brace element wouldalso be identified as either a beam or a column element based on the assigned sec-tion to the brace element

Design of Beams

In the design of concrete beams, in general, ETABS calculates and reports the quired areas of steel for flexure and shear based upon the beam moments, shears,load combination factors, and other criteria which are described in detail in the codespecific chapters The reinforcement requirements are calculated at a user-definednumber of stations along the beam span

re-All the beams are only designed for major direction flexure and shear Effects due

to any axial forces, minor direction bending, and torsion that may exist in the beamsmust be investigated independently by the user

In designing the flexural reinforcement for the major moment at a particular section

of a particular beam, the steps involve the determination of the maximum factoredmoments and the determination of the reinforcing steel The beam section is de-

signed for the maximum positive M u + and maximum negative M u - factored momentenvelopes obtained from all of the load combinations Negative beam momentsproduce top steel In such cases the beam is always designed as a rectangular sec-tion Positive beam moments produce bottom steel In such cases the beam may bedesigned as a rectangular- or a T-beam For the design of flexural reinforcement,the beam is first designed as a singly reinforced beam If the beam section is notadequate, then the required compression reinforcement is calculated

8 Identifying Beams and Columns

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In designing the shear reinforcement for a particular beam for a particular set ofloading combinations at a particular station due to the beam major shear, the stepsinvolve the determination of the factored shear force, the determination of the shearforce that can be resisted by concrete, and the determination of the reinforcementsteel required to carry the balance.

Special considerations for seismic design are incorporated in ETABS for ACI,UBC, Canadian, and New Zealand codes

Design of Columns

In the design of the columns, the program calculates the required longitudinal steel,

or if the longitudinal steel is specified, the column stress condition is reported interms of a column capacity ratio, which is a factor that gives an indication of thestress condition of the column with respect to the capacity of the column The de-sign procedure for the reinforced concrete columns of the structure involves the fol-lowing steps:

• Generate axial force-biaxial moment interaction surfaces for all of the differentconcrete section types of the model A typical interaction surface is shown inFigure II-2

• Check the capacity of each column for the factored axial force and bending ments obtained from each loading combination at each end of the column Thisstep is also used to calculate the required reinforcement (if none was specified)that will produce a capacity ratio of 1.0

mo-• Design the column shear reinforcement

The generation of the interaction surface is based on the assumed strain and stressdistributions and some other simplifying assumptions These stress and strain dis-tributions and the assumptions vary from code to code A typical assumed straindistribution is described in Figure II-1

Here maximum compression strain is limited toec For most of the design codes,this assumed distribution remains valid However, the value ofec varies from code

to code For example,ec= 0.003 for ACI, UBC and New Zealand codes, and

ec= 0.0035for Canadian, British and European codes The details of the generation

of interaction surfaces differ from code to code These are described in the chaptersspecific to the code

Design of Columns 9

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A typical interaction surface is shown in Figure II-2 The column capacity tion volume is numerically described by a series of discrete points that are gener-ated on the three-dimensional interaction failure surface The coordinates of thesepoints are determined by rotating a plane of linear strain in three dimensions on thesection of the column as described in Figure II-1.

interac-The area associated with each rebar is placed at the actual location of the center ofthe bar and the algorithm does not assume any simplifications in the manner inwhich the area of steel is distributed over the cross section of the column The inter-action algorithm provides corrections to account for the concrete area that is dis-placed by the reinforcing in the compression zone

Neutral Axis Direction

c c

Reinforcement Bars

Varying Linear Strain Plane

Figure II-1

Idealized Strain Distribution for Generation of Interaction Surfaces

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The effects of code specified strength reduction factors and maximum limit on theaxial capacity are incorporated in the interaction surfaces The formulation is basedconsistently upon the general principles of ultimate strength design, and allows forrectangular, square or circular, doubly symmetric column sections In addition toaxial compression and biaxial bending, the formulation allows for axial tension andbiaxial bending considerations as shown in Figure II-2.

1 23

Pby

-P0+P 0

Figure II-2

A Typical Column Interaction Surface

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The capacity check is based on whether the design load points lie inside the tion volume in a force space, as shown in Figure II-3 If the point lies inside the vol-ume, the column capacity is adequate, and vice versa The point in the interaction

interac-volume (P, M x , and M y) which is represented by point L is placed in the tion space as shown in Figure II-3 If the point lies within the interaction volume,the column capacity is adequate; however, if the point lies outside the interactionvolume, the column is overstressed As a measure of the stress condition of the col-umn, a capacity ratio is calculated This ratio is achieved by plotting the point L, de-fined by P, Mxand My, and determining the location of point C The point C is de-fined as the point where the line OL (if extended outwards) will intersect the failuresurface This point is determined by three-dimensional linear interpolation betweenthe points that define the failure surface The capacity ratio, CR, is given by the ra-tio OL OC

Lines Defining Failure Surface

Figure II-3

Geometric Representation of Column Capacity Ratio

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• If OL = OC (or CR=1) the point lies on the interaction surface and the column isstressed to capacity.

• If OL < OC (or CR<1) the point lies within the interaction volume and the umn capacity is adequate

• If OL > OC (or CR>1) the point lies outside the interaction volume and the umn is overstressed

col-The capacity ratio is basically a factor that gives an indication of the stress tion of the column with respect to the capacity of the column In other words, if theaxial force and biaxial moment set for which the column is being checked is ampli-fied by dividing it by the reported capacity ratio, the point defined by the resultingaxial force and biaxial moment set will lie on the failure (or interaction volume) sur-face

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The shear reinforcement design procedure for columns is very similar to that forbeams, except that the effect of the axial force on the concrete shear capacity needs

to be considered

For certain special seismic cases, the design of column for shear is based on the pacity-shear The capacity-shear force in a particular direction is calculated fromthe moment capacities of the column associated with the factored axial force acting

ca-on the column For each load combinatica-on, the factored axial load is calculated, ing the ETABS analysis load cases and the corresponding load combination factors.Then, the moment capacity of the column in a particular direction under the influ-ence of the axial force is calculated, using the uniaxial interaction diagram in thecorresponding direction as shown in Figure II-4

us-Design of Joints

To ensure that the beam-column joint of special moment resisting frames possessesadequate shear strength, the program performs a rational analysis of the beam-column panel zone to determine the shear forces that are generated in the joint Theprogram then checks this against design shear strength

Only joints having a column below the joint are designed The material properties

of the joint are assumed to be the same as those of the column below the joint.The joint analysis is done in the major and the minor directions of the column Thejoint design procedure involves the following steps:

• Determine the panel zone design shear force, V u

h

• Determine the effective area of the joint

• Check panel zone shear stress

The following three sections describe in detail the algorithms associated with theabove mentioned steps

Determine the Panel Zone Shear Force

For a particular column direction, major or minor, the free body stress condition of

a typical beam-column intersection is shown in Figure II-5

The force V u h is the horizontal panel zone shear force that is to be calculated The

forces that act on the joint are P u , V u , M u L and M u R The forces P u and V uare axialforce and shear force, respectively, from the column framing into the top of the

joint The moments M u L and M u R are obtained from the beams framing into the

14 Design of Joints

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joint The joint shear forceV u h is calculated by resolving the moments into C and T

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The moments and the C and T forces from beams that frame into the joint in a

direc-tion that is not parallel to the major or minor direcdirec-tions of the column are resolvedalong the direction that is being investigated, thereby contributing force compo-nents to the analysis

In the design of special moment resisting concrete frames, the evaluation of the sign shear force is based upon the moment capacities (with reinforcing steeloverstrength factor, , and no factors) of the beams framing into the joint,

de-(ACI 21.5.1.1, UBC 1921.5.1.1) The C and T force are based upon these moment capacities The column shear forceV u is calculated from the beam moment capaci-ties as follows:

V = M + M

H

u u L u R

See Figure II-6 It should be noted that the points of inflection shown on Figure II-6are taken as midway between actual lateral support points for the columns.The effects of load reversals, as illustrated in Case 1 and Case 2 of Figure II-5 areinvestigated and the design is based upon the maximum of the joint shears obtainedfrom the two cases

Determine the Effective Area of Joint

The joint area that resists the shear forces is assumed always to be rectangular inplan view The dimensions of the rectangle correspond to the major and minor di-mensions of the column below the joint, except if the beam framing into the joint isvery narrow The effective width of the joint area to be used in the calculation islimited to the width of the beam plus the depth of the column The area of the joint isassumed not to exceed the area of the column below The joint area for joint shearalong the major and minor directions is calculated separately (ACI R21.5.3)

It should be noted that if the beam frames into the joint eccentrically, the above sumptions may be unconservative and the user should investigate the acceptability

as-of the particular joint

Check Panel Zone Shear Stress

The panel zone shear stress is evaluated by dividing the shear forceV u hby the tive area of the joint and comparing it with the following design shear strengths(ACI 21.5.3, UBC 1921.5.3) :

effec-16 Design of Joints

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f c¢ , for joints confined on three faces or on two opposite faces,

12j f c for all other joints,

ELEVATION

POINT OF INFLECTION

Figure II-6

Column Shear Force, V u

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Beam/Column Flexural Capacity Ratios

At a particular joint for a particular column direction, major or minor, the programwill calculate the ratio of the sum of the beam moment capacities to the sum of thecolumn moment capacities, (ACI 21.4.2.2, UBC 1921.4.2.2)

The column capacity summation includes the column above and the column below

the joint For each load combination the axial force, P u, in each of the columns iscalculated from the ETABS analysis load conditions and the corresponding loadcombination factors For each load combination, the moment capacity of each col-

umn under the influence of the corresponding axial load P uis then determined rately for the major and minor directions of the column, using the uniaxial columninteraction diagram, see Figure II-4 The moment capacities of the two columns areadded to give the capacity summation for the corresponding load combination Themaximum capacity summations obtained from all of the load combinations is usedfor the beam/column capacity ratio

sepa-The beam/column flexural capacity ratios are only reported for Special ment-Resisting Frames involving seismic design load combinations

Mo-P- D Effects

The ETABS design algorithms require that the analysis results include the P-D

ef-fects The P-D effects are considered differently for “braced” or “nonsway” and

“unbraced” or “sway” components of moments in frames For the braced moments

in frames, the effect of P-D is limited to “individual member stability” For

un-braced components, “lateral drift effects” should be considered in addition to vidual member stability” effect In ETABS, it is assumed that “braced” or

“indi-“nonsway” moments are contributed from the “dead” or “live” loads Whereas,

“unbraced” or “sway” moments are contributed from all other types of loads

18 Beam/Column Flexural Capacity Ratios

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For the individual member stability effects, the moments are magnified with ment magnification factors as in the ACI, UBC, Canadian, and New Zealand codes

mo-or with additional moments as in the British and European codes

For lateral drift effects, ETABS assumes that the P-D analysis is performed and

that the amplification is already included in the results The moments and forces tained from P-D analysis are further amplified for individual column stability effect

ob-if required by the governing code as in the ACI, UBC, Canadian, and New Zealandcodes

The users of ETABS should be aware that the default analysis option in ETABS forP-D effect is turned OFF The default number of iterations for P-D analysis is 1

itera-tions for the analysis For further reference, the user is referred to ETABS User’s

Manual Volume 2 (CSI 1999).

The user is also cautioned that ETABS currently considers P-D effects due to axial

loads in frame members only Forces in other types of elements do not contribute tothis effect If significant forces are present in other types of elements, for example,large axial loads in shear walls modeled as shell elements, then the additional forcescomputed for P-D will be inaccurate

Element Unsupported Lengths

To account for column slenderness effects the column unsupported lengths are

re-quired The two unsupported lengths are l33and l22 These are the lengths between

support points of the element in the corresponding directions The length l33

corre-sponds to instability about the 3-3 axis (major axis), and l22corresponds to ity about the 2-2 axis (minor axis)

instabil-Normally, the unsupported element length is equal to the length of the element, i.e.,the distance between END-I and END-J of the element See Figure II-7 The pro-gram, however, allows users to assign several elements to be treated as a singlemember for design This can be done differently for major and minor bending.Therefore, extraneous joints, as shown in Figure II-8, that affect the unsupportedlength of an element are automatically taken into consideration

In determining the values for l22and l33of the elements, the program recognizesvarious aspects of the structure that have an effect on these lengths, such as memberconnectivity, diaphragm constraints and support points The program automati-cally locates the element support points and evaluates the corresponding unsup-ported element length

Element Unsupported Lengths 19

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Therefore, the unsupported length of a column may actually be evaluated as beinggreater than the corresponding element length If the beam frames into only one di-rection of the column, the beam is assumed to give lateral support only in that direc-tion.

The user has options to specify the unsupported lengths of the elements on an ment-by-element basis

ele-Special Considerations for Seismic Loads

The ACI code imposes a special ductility requirement for frames in seismic regions

by specifying frames either as Ordinary, Intermediate, or Special moment resistingframes The Special moment resisting frame can provide the required ductility andenergy dissipation in the nonlinear range of cyclic deformation The UBC code re-quires that the concrete frame must be designed for a specific Seismic Zone which

is either Zone 0, Zone 1, Zone 2, Zone 3, or Zone 4, where Zone 4 is designated asthe zone of severe earthquake The Canadian code requires that the concrete framemust be designed as either an Ordinary, Nominal, or Ductile moment resisting

20 Special Considerations for Seismic Loads

l 33

l 22

Element Axis

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frame The New Zealand code also requires that the concrete frame must be signed as either an Ordinary, Elastically responding, frames with Limited ductility,

de-or Ductile moment resisting frame

Unlike the ACI, UBC, Canadian, and New Zealand codes, the current tion of the British code and the Eurocode 2 in ETABS does not account for any spe-cial requirements for seismic design

implementa-Choice of Input Units

English as well as SI and MKS metric units can be used for input But the codes arebased on a specific system of units All equations and descriptions presented in thesubsequent chapters correspond to that specific system of units unless otherwisenoted For example, the ACI code is published in inch-pound-second units By de-fault, all equations and descriptions presented in the chapter “Design for ACI318-99” correspond to inch-pound-second units However, any system of units can

be used to define and design the structure in ETABS

Choice of Input Units 21

Figure II-8

Unsupported Lengths and Interior Nodes

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Design for ACI 318-99

This chapter describes in detail the various aspects of the concrete design procedurethat is used by ETABS when the user selects the ACI 318-99 Design Code (ACI1999) Various notations used in this chapter are listed in Table III-1

The design is based on user-specified loading combinations But the program vides a set of default load combinations that should satisfy requirements for the de-sign of most building type structures

pro-ETABS provides options to design or check Ordinary, Intermediate (moderate mic risk areas), and Special (high seismic risk areas) moment resisting frames as re-quired for seismic design provisions The details of the design criteria used for thedifferent framing systems are described in the following sections

seis-English as well as SI and MKS metric units can be used for input But the code isbased on Inch-Pound-Second units For simplicity, all equations and descriptions

presented in this chapter correspond to Inch-Pound-Second units unless otherwise

noted

Design Load Combinations

The design load combinations are the various combinations of the prescribed loadcases for which the structure needs to be checked For the ACI 318-99 code, if a

Design Load Combinations 23

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24 Design Load Combinations

A cv Area of concrete used to determine shear stress, sq-in

A g Gross area of concrete, sq-in

A s Area of tension reinforcement, sq-in

A s¢ Area of compression reinforcement, sq-in

A s required( ) Area of steel required for tension reinforcement, sq-in

A st Total area of column longitudinal reinforcement, sq-in

A v Area of shear reinforcement, sq-in

a Depth of compression block, in

a b Depth of compression block at balanced condition, in

b Width of member, in

b f Effective width of flange (T-Beam section), in

b w Width of web (T-Beam section), in

C m Coefficient, dependent upon column curvature, used to calculate

mo-ment magnification factor

c Depth to neutral axis, in

c b Depth to neutral axis at balanced conditions, in

d Distance from compression face to tension reinforcement, in

d¢ Concrete cover to center of reinforcing, in

d s Thickness of slab (T-Beam section), in

E c Modulus of elasticity of concrete, psi

E s Modulus of elasticity of reinforcement, assumed as 29,000,000 psi

(ACI 8.5.2)

f c¢ Specified compressive strength of concrete, psi

f y Specified yield strength of flexural reinforcement, psi

I se Moment of inertia of reinforcement about centroidal axis of

member cross section, in4

Table III-1

List of Symbols Used in the ACI code

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Design Load Combinations 25

k Effective length factor

L Clear unsupported length, in

M1 Smaller factored end moment in a column, lb-in

M2 Larger factored end moment in a column, lb-in

M c Factored moment to be used in design, lb-in

M ns Nonsway component of factored end moment, lb-in

M s Sway component of factored end moment, lb-in

M u Factored moment at section, lb-in

M ux Factored moment at section about X-axis, lb-in

M uy Factored moment at section about Y-axis, lb-in

P b Axial load capacity at balanced strain conditions, lb

P c Critical buckling strength of column, lb

P max Maximum axial load strength allowed, lb

P0 Axial load capacity at zero eccentricity, lb

P u Factored axial load at section, lb

r Radius of gyration of column section, in

V c Shear resisted by concrete, lb

V E Shear force caused by earthquake loads, lb

V D+L Shear force from span loading, lb

V u Factored shear force at a section, lb

V p Shear force computed from probable moment capacity, lb

a Reinforcing steel overstrength factor

b1 Factor for obtaining depth of compression block in concrete

bd Absolute value of ratio of maximum factored axial dead load to

maxi-mum factored axial total load

ds Moment magnification factor for sway moments

dns Moment magnification factor for nonsway moments

ec Strain in concrete

es Strain in reinforcing steel

j Strength reduction factor

Table III-1

List of Symbols Used in the ACI code (continued)

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structure is subjected to dead load (DL) and live load (LL) only, the stress checkmay need only one load combination, namely 1.4 DL + 1.7 LL (ACI 9.2.1) How-ever, in addition to the dead and live loads, if the structure is subjected to wind(WL) and earthquake (EL) loads, and considering that wind and earthquake forcesare reversible, then the following load combinations have to be considered (ACI9.2).

Live load reduction factors can be applied to the member forces of the live loadcondition on an element-by-element basis to reduce the contribution of the live load

to the factored loading

Strength Reduction Factors

The strength reduction factors,j, are applied on the nominal strength to obtain the

design strength provided by a member Thej factors for flexure, axial force, shear,

and torsion are as follows:

j = 0.75 for axial compression, and axial compression

and flexure (spirally reinforced column), (ACI 9.3.2.2)

j = 0.70 for axial compression, and axial compression

and flexure (tied column), and (ACI 9.3.2.2)

26 Strength Reduction Factors

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Column Design

The user may define the geometry of the reinforcing bar configuration of each crete column section If the area of reinforcing is provided by the user, the programchecks the column capacity However, if the area of reinforcing is not provided bythe user, the program calculates the amount of reinforcing required for the column.The design procedure for the reinforced concrete columns of the structure involvesthe following steps:

con-• Generate axial force/biaxial moment interaction surfaces for all of the differentconcrete section types of the model A typical biaxial interaction surface isshown in Figure II-2 When the steel is undefined, the program generates theinteraction surfaces for the range of allowable reinforcement 1 to 8 percentfor Ordinary and Intermediate moment resisting frames (ACI 10.9.1) and 1 to 6percent for Special moment resisting frames (ACI 21.4.3.1)

• Calculate the capacity ratio or the required reinforcing area for the factored ial force and biaxial (or uniaxial) bending moments obtained from each loadingcombination at each station of the column The target capacity ratio is taken asone when calculating the required reinforcing area

ax-• Design the column shear reinforcement

The following three subsections describe in detail the algorithms associated withthe above-mentioned steps

Generation of Biaxial Interaction Surfaces

The column capacity interaction volume is numerically described by a series of crete points that are generated on the three-dimensional interaction failure surface

dis-In addition to axial compression and biaxial bending, the formulation allows for ial tension and biaxial bending considerations A typical interaction diagram isshown in Figure II-2

ax-The coordinates of these points are determined by rotating a plane of linear strain inthree dimensions on the section of the column See Figure II-1 The linear straindiagram limits the maximum concrete strain,ec, at the extremity of the section

to 0.003 (ACI 10.2.3)

The formulation is based consistently upon the general principles of ultimatestrength design (ACI 10.3), and allows for any doubly symmetric rectangular,square, or circular column section

Column Design 27

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The stress in the steel is given by the product of the steel strain and the steel lus of elasticity,es E , and is limited to the yield stress of the steel, f s y (ACI 10.2.4).The area associated with each reinforcing bar is assumed to be placed at the actuallocation of the center of the bar and the algorithm does not assume any further sim-plifications in the manner in which the area of steel is distributed over the cross sec-tion of the column, such as an equivalent steel tube or cylinder See Figure III-1.

modu-The concrete compression stress block is assumed to be rectangular, with a stress

value of 0.85 f c¢ (ACI 10.2.7.1) See Figure III-1 The interaction algorithm vides correction to account for the concrete area that is displaced by the reinforce-ment in the compression zone

pro-The effects of the strength reduction factor,j, are included in the generation of the

interaction surfaces The maximum compressive axial load is limited tojP n(max),where

jP n(max) =0.85j[ 0.85f c¢(A - A g st)+ f y A st] spiral column, (ACI 10.3.5.1)

jP n(max) =0.80j[ 0.85f c¢(A - A g st) + f y A st] tied column, (ACI 10.3.5.2)

1 s C

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The value of j used in the interaction diagram varies from j(compression) toj(flexure) based on the axial load For low values of axial load, j is increased lin-

early fromj(compression) to j(flexure) as the jP n decreases from the smaller of

jP b or 0.1 f A c¢ g to zero, wherejP bis the axial force at the balanced condition The

j factor used in calculating jP n andjP bis thej(compression) In cases involving

axial tension,j is always j(flexure) which is 0.9 by default (ACI 9.3.2.2)

Check Column Capacity

The column capacity is checked for each loading combination at each check station

of each column In checking a particular column for a particular loading tion at a particular station, the following steps are involved:

combina-• Determine the factored moments and forces from the analysis load cases and

the specified load combination factors to give P M u, ux,andM uy

• Determine the moment magnification factors for the column moments

• Apply the moment magnification factors to the factored moments Determinewhether the point, defined by the resulting axial load and biaxial moment set,lies within the interaction volume

The factored moments and corresponding magnification factors depend on theidentification of the individual column as either “sway” or “non-sway”

The following three sections describe in detail the algorithms associated with theabove-mentioned steps

Determine Factored Moments and Forces

The factored loads for a particular load combination are obtained by applying the

corresponding load factors to all the load cases, giving P M u, ux,andM uy The tored moments are further increased for non-sway columns, if required, to obtainminimum eccentricities of (0.6 0.03+ h) inches, where h is the dimension of the

fac-column in the corresponding direction (ACI 10.12.3.2)

Determine Moment Magnification Factors

The moment magnification factors are calculated separately for sway (overall bility effect),dsand for non-sway (individual column stability effect),dns Also themoment magnification factors in the major and minor directions are in general dif-ferent (ACI 10.0, R10.13)

sta-Column Design 29

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The moment obtained from analysis is separated into two components: the sway(M s)and the non-sway (M ns) components The non-sway components which are

identified by “ns” subscripts are predominantly caused by gravity load The sway components are identified by the “s” subscripts The sway moments are predomi-

nantly caused by lateral loads, and are related to the cause of side sway

For individual columns or column-members in a floor, the magnified momentsabout two axes at any station of a column can be obtained as

The program assumes that a P-D analysis has been performed in ETABS and,

there-fore, moment magnification factor ds for moments causing sidesway is taken asunity (ACI 10.10.2) For the P-D analysis the load should correspond to a load com-

bination of 1.4 dead load + 1.7 live load (ACI 10.13.6) See also White and Hajjar(1991) The user should use reduction factors for the moment of inertias in ETABS

as specified in ACI 10.11 The moment of intertia reduction for sustained lateralload involves a factorbd (ACI 10.11) Thisbdfor sway frame in second-order anal-ysis is different from the one that is defined later for non-sway moment magnifica-tion (ACI 10.0, R10.12.3, R10.13.4.1) The default moment of inertia factor inETABS is 1

The computed moments are further amplified for individual column stability effect(ACI 10.12.3, 10.13.5) by the nonsway moment magnification factor,dns, as fol-lows:

M c is the factored moment to be used in design

The non-sway moment magnification factor,dns, associated with the major or nor direction of the column is given by (ACI 10.12.3)

mi-dns

m u c

C P P

=0.75

30 Column Design

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M a and M b are the moments at the ends of the column, and M bis numerically

larger than M a M a M bis positive for single curvature bending and negative

for double curvature bending The above expression of C mis valid if there is notransverse load applied between the supports If transverse load is present on

the span, or the length is overwritten, C m =1 C mcan be overwritten by the user

on an element by element basis

k is conservatively taken as 1, however ETABS allows the user to

over-ride this value (ACI 10.12.1),

l u is the unsupported length of the column for the direction of bending

considered The two unsupported lengths are l22 and l33 corresponding toinstability in the minor and major directions of the element, respectively.See Figure II-7 These are the lengths between the support points of theelement in the corresponding directions

EI is associated with a particular column direction:

EI = E I

+

c g d

0.4

bd =maximum factored axial sustained (dead) load

maximum factored axial total load .(ACI 10.0,R10.12.3)The magnification factor,dns, must be a positive number and greater than one

Therefore P u must be less than 0.75P c If P uis found to be greater than or equal to

0.75P c, a failure condition is declared

The above calculations are done for major and minor directions separately Thatmeans thatds,dns , C m , k, l u , EI, and P c assume different values for major and minordirections of bending

If the program assumptions are not satisfactory for a particular member, the usercan explicitly specify values ofdsanddns

Determine Capacity Ratio

As a measure of the stress condition of the column, a capacity ratio is calculated.The capacity ratio is basically a factor that gives an indication of the stress condi-tion of the column with respect to the capacity of the column

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Before entering the interaction diagram to check the column capacity, the moment

magnification factors are applied to the factored loads to obtain P M u, ux, andM uy

The point (P M u, ux,M uy) is then placed in the interaction space shown as point L inFigure II-3 If the point lies within the interaction volume, the column capacity isadequate; however, if the point lies outside the interaction volume, the column isoverstressed

This capacity ratio is achieved by plotting the point L and determining the location

of point C The point C is defined as the point where the line OL (if extended wards) will intersect the failure surface This point is determined by three-dimensional linear interpolation between the points that define the failure surface.See Figure II-3 The capacity ratio, CR, is given by the ratioOL

re-P M u, ux, andM uy set and associated load combination number

If the reinforcing area is not defined, ETABS computes the reinforcement that willgive an interaction ratio of unity

Design Column Shear Reinforcement

The shear reinforcement is designed for each loading combination in the major andminor directions of the column In designing the shear reinforcing for a particularcolumn for a particular loading combination due to shear forces in a particular di-rection, the following steps are involved:

• Determine the factored forces acting on the section, P u and V u Note that P u is

needed for the calculation of V c

• Determine the shear force, V c, that can be resisted by concrete alone

• Calculate the reinforcement steel required to carry the balance

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For Special and Intermediate moment resisting frames (ductile frames), the sheardesign of the columns is also based upon the probable and nominal moment capaci-ties of the members, respectively, in addition to the factored moments Effects ofthe axial forces on the column moment capacities are included in the formulation.The following three sections describe in detail the algorithms associated with theabove-mentioned steps.

Determine Section Forces

• In the design of the column shear reinforcement of an Ordinary moment sisting concrete frame, the forces for a particular load combination, namely,

re-the column axial force, P u , and the column shear force,V u, in a particular tion are obtained by factoring the ETABS analysis load cases with the corre-sponding load combination factors

direc-• In the shear design of Special moment resisting frames (seismic design) the

column is checked for capacity-shear in addition to the requirement for the

Or-dinary moment resisting frames The capacity-shear force in a column, V p, in aparticular direction is calculated from the probable moment capacities of thecolumn associated with the factored axial force acting on the column

For each load combination, the factored axial load, P u, is calculated Then, the

positive and negative moment capacities, M u+ and M u-, of the column in a

par-ticular direction under the influence of the axial force P uis calculated using theuniaxial interaction diagram in the corresponding direction The design shear

force, V u, is then given by (ACI 21.4.5.1)

M I+, M I- = Positive and negative moment capacities at end I of

the column using a steel yield stress value ofaf y

and noj factors (j =1.0),

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M J+, M J- = Positive and negative moment capacities at end J of

the column using a steel yield stress value ofaf y

and noj factors (j =1.0),and

For Special moment resisting framesa is taken as 1.25 (ACI 10.0, R21.4.5.1)

V D+L is the contribution of shear force from the in-span distribution of gravityloads For most of the columns, it is zero

• For Intermediate moment resisting frames, the shear capacity of the column

is also checked for the capacity-shear based on the nominal moment capacities

at the ends and the factored gravity loads, in addition to the check required forOrdinary moment resisting frames The design shear force is taken to be theminimum of that based on the nominal (j =1.0) moment capacity and modified

factored shear force The procedure for calculating nominal moment capacity

is the same as that for computing the probable moment capacity for special ment resisting frames, except thata is taken equal to 1 rather than 1.25 (ACI

mo-21.10.3.a, R21.10) The modified factored shear forces are based on the fied load factors except the earthquake load factors are doubled (ACI21.10.3.b)

speci-Determine Concrete Shear Capacity

Given the design force set P u and V u , the shear force carried by the concrete, V c, iscalculated as follows:

• If the column is subjected to axial compression, i.e P u is positive,

A A

c c

u g cv

2000

¢æè

The term P A u g must have psi units A cv is the effective shear area which is shown

shaded in Figure III-2 For circular columns A cv is taken to be equal to the grossarea of the section (ACI 11.3.3, R11.3.3)

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