ETABS - Concrete Frame Design Manual

Computers and Structures, Inc.Berkeley, California, USA

Version 8January 2002

ETABS

Integrated Building Design Software

Concrete Frame Design Manual

Copyright Computers and Structures, Inc., 1978-2002.The CSI Logo is a trademark of Computers and Structures, Inc.

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

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The computer program ETABS and all associated documentation are proprietary andcopyrighted products. Worldwide rights of ownership rest with Computers andStructures, Inc. Unlicensed use of the program or reproduction of the documentation inany form, without prior written authorization from Computers and Structures, Inc., isexplicitly prohibited.

Further information and copies of this documentation may be obtained from:

Computers and Structures, Inc.1995 University Avenue

Berkeley, California 94704 USA

Phone: (510) 845-2177FAX: (510) 845-4096

e-mail: [email protected] (for general questions)e-mail: [email protected] (for technical support questions)

web: www.csiberkeley.com

DISCLAIMER

CONSIDERABLE TIME, EFFORT AND EXPENSE HAVE GONE INTO THEDEVELOPMENT AND DOCUMENTATION OF ETABS. THE PROGRAM HASBEEN THOROUGHLY TESTED AND USED. IN USING THE PROGRAM,HOWEVER, THE USER ACCEPTS AND UNDERSTANDS THAT NO WARRANTYIS EXPRESSED OR IMPLIED BY THE DEVELOPERS OR THE DISTRIBUTORSON THE ACCURACY OR THE RELIABILITY OF THE PROGRAM.

THIS PROGRAM IS A VERY PRACTICAL TOOL FOR THE DESIGN/CHECK OFCONCRETE STRUCTURES. HOWEVER, THE USER MUST THOROUGHLY READTHE MANUAL AND CLEARLY RECOGNIZE THE ASPECTS OF CONCRETEDESIGN THAT THE PROGRAM ALGORITHMS DO NOT ADDRESS.

THE USER MUST EXPLICITLY UNDERSTAND THE ASSUMPTIONS OF THEPROGRAM AND MUST INDEPENDENTLY VERIFY THE RESULTS.

iCOMPUTERS AND STRUCTURES, INC., BERKELEY, CALIFORNIA DECEMBER 2001CONCRETE FRAME DESIGN

Contents

General Concrete Frame Design Information

1 General Design InformationDesign Codes 1-1Units 1-1Overwriting the Frame Design Procedure for a Con-

crete Frame1-1

Design Load Combinations 1-2Design of Beams 1-2Design of Columns 1-3Beam/Column Flexural Capacity Ratios 1-4Second Order P-Delta Effects 1-4Element Unsupported Lengths 1-6Analysis Sections and Design Sections 1-7

2 Concrete Frame Design ProcessConcrete Frame Design Procedure 2-1

3 Interactive Concrete Frame DesignGeneral 3-1Concrete Design Information Form 3-1

4 Output Data Plotted Directly on the ModelOverview 4-1Using the Print Design Tables Form 4-1Design Input 4-2Design Output 4-2


ii

Concrete Frame Design Specific to UBC97

5 General and NotationIntroduction to the UBC 97 Series of Technical Notes 5-1Notation 5-2

6 PreferencesGeneral 6-1Using the Preferences Form 6-1Preferences 6-2

7 OverwritesGeneral 7-1Overwrites 7-1Making Changes in the Overwrites Form 7-3Resetting Concrete Frame Overwrites to Default

Values7-4

8 Design Load Combinations

9 Strength Reduction Factors

10 Column DesignOverview 10-1Generation of Biaxial Interaction Surfaces 10-2Calculate Column Capacity Ratio 10-5

Determine Factored Moments and Forces 10-6Determine Moment Magnification Factors 10-6Determine Capacity Ratio 10-8

Required Reinforcing Area 10-10Design Column Shear Reinforcement 10-10

Determine Required Shear Reinforcement 10-14Reference 10-15

11 Beam DesignOverview 11-1Design Beam Flexural Reinforcement 11-1

Determine Factored Moments 11-2Determine Required Flexural Reinforcement 11-2

Contents

iii

Design Beam Shear Reinforcement 11-10

12 Joint DesignOverview 12-1Determine the Panel Zone Shear Force 12-1Determine the Effective Area of Joint 12-5Check Panel Zone Shear Stress 12-5Beam/Column Flexural Capacity Ratios 12-6

13 Input DataInput data 13-1Using the Print Design Tables Form 13-3

14 Output DetailsUsing the Print Design Tables Form 14-3

Concrete Frame Design Specific to ACI-318-99

15 General and NotationIntroduction to the ACI318-99 Series of Technical

Notes15-1

Notation 15-2

16 PreferencesGeneral 16-1Using the Preferences Form 16-1Preferences 16-2

17 OverwritesGeneral 17-1Overwrites 17-1Making Changes in the Overwrites Form 17-3Resetting Concrete Frame Overwrites to Default

Values17-4

18 Design Load Combinations

19 Strength Reduction Factors


iv

20 Column DesignOverview 20-1Generation of Biaxial Interaction Surfaces 20-2Calculate Column Capacity Ratio 20-5

Determine Factored Moments and Forces 20-6Determine Moment Magnification Factors 20-6Determine Capacity Ratio 20-9

Required Reinforcing Area 20-10Design Column Shear Reinforcement 20-10

Determine Section Forces 20-11Determine Concrete Shear Capacity 20-12Determine Required Shear Reinforcement 20-13

References 20-15

21 Beam DesignOverview 21-1Design Beam Flexural Reinforcement 21-1

Determine Factored Moments 21-2Determine Required Flexural Reinforcement 21-2Design for T-Beam 21-5Minimum Tensile Reinforcement 21-8Special Consideration for Seismic Design 21-8

Design Beam Shear Reinforcement 21-9Determine Shear Force and Moment 21-11Determine Concrete Shear Capacity 21-12Determine Required Shear Reinforcement 21-13

22 Joint DesignOverview 22-1Determine the Panel Zone Shear Force 22-1Determine the Effective Area of Joint 22-4

Check Panel Zone Shear Stress 22-4Beam/Column Flexural Capacity Ratios 22-6

23 Input DataInput Data 23-1Using the Print Design Tables Form 23-3

Contents

v

24 Output DetailsUsing the Print Design Tables Form 24-3

Design Codes Technical Note 1 - 1

COMPUTERS AND STRUCTURES, INC., BERKELEY, CALIFORNIA JANUARY 2002CONCRETE FRAME DESIGN

Technical Note 1General Design Information

This Technical Note presents some basic information and concepts helpfulwhen performing concrete frame design using this program.

Design CodesThe design code is set using the Options menu > Preferences > ConcreteFrame Design command. You can choose to design for any one design codein any one design run. You cannot design some elements for one code andothers for a different code in the same design run. You can, however, performdifferent design runs using different design codes without rerunning theanalysis.

UnitsFor concrete frame design in this program, any set of consistent units can beused for input. You can change the system of units at any time. Typically, de-sign codes are based on one specific set of units.

Overwriting the Frame Design Procedure for a ConcreteFrameThe two design procedures possible for concrete beam design are:

Concrete frame design

No design

If a line object is assigned a frame section property that has a concrete ma-terial property, its default design procedure is Concrete Frame Design. A con-crete frame element can be switched between the Concrete Frame Design andthe "None" design procedure. Assign a concrete frame element the "None"design procedure if you do not want it designed by the Concrete Frame De-sign postprocessor.

General Design Information Concrete Frame Design

Technical Note 1 - 2 Design Load Combinations

Change the default design procedure used for concrete frame elements byselecting the element(s) and clicking Design menu > Overwrite FrameDesign Procedure. This change is only successful if the design procedureassigned to an element is valid for that element. For example, if you select aconcrete element and attempt to change the design procedure to Steel FrameDesign, the program will not allow the change because a concrete elementcannot be changed to a steel frame element.

Design Load CombinationsThe program creates a number of default design load combinations for con-crete frame design. You can add in your own design load combinations. Youcan also modify or delete the program default load combinations. An unlim-ited number of design load combinations can be specified.

To define a design load combination, simply specify one or more load cases,each with its own scale factor. For more information see Concrete Frame De-sign UBC97 Technical Note 8 Design Load Combination and Concrete FrameDesign ACI 318-99 Technical Note 18 Design Load Combination.

Design of BeamsThe program designs all concrete frame elements designated as beam sec-tions in their Frame Section Properties as beams (see Define menu >FrameSections command and click the Reinforcement button). In the design ofconcrete beams, in general, the program calculates and reports the requiredareas of steel for flexure and shear based on the beam moments, shears, loadcombination factors, and other criteria, which are described in detail in Con-crete Frame UBC97 Technical Note Beam Design 11 and Concrete Frame ACI318-99 Technical Note 21 Beam Design. The reinforcement requirements arecalculated at each output station along the beam span.

All the beams are designed for major direction flexure and shear only.Effects resulting from any axial forces, minor direction bending, andtorsion that may exist in the beams must be investigated independ-ently by the user.

In designing the flexural reinforcement for the major moment at a particularsection of a particular beam, the steps involve the determination of themaximum factored moments and the determination of the reinforcing steel.

Concrete Frame Design General Design Information

Design of Beams Technical Note 1 - 3

The beam section is designed for the maximum positive and maximum nega-tive factored moment envelopes obtained from all of the load combinations.Negative beam moments produce top steel. In such cases, the beam is al-ways designed as a rectangular section. Positive beam moments producebottom steel. In such cases, the beam may be designed as a rectangular- orT-beam. For the design of flexural reinforcement, the beam is first designedas a singly reinforced beam. If the beam section is not adequate, the requiredcompression reinforcement is calculated.

In designing the shear reinforcement for a particular beam for a particular setof loading combinations at a particular station resulting from the beam majorshear, the steps involve the determination of the factored shear force, thedetermination of the shear force that can be resisted by concrete, and thedetermination of the reinforcement steel required to carry the balance.

Design of ColumnsThe program designs all concrete frame elements designated as column sec-tions in their Frame Section Properties as columns (see Define menu>Frame Sections command and click the Reinforcement button). In thedesign of the columns, the program calculates the required longitudinal steel,or if the longitudinal steel is specified, the column stress condition is reportedin terms of a column capacity ratio. The capacity ratio is a factor that gives anindication of the stress condition of the column with respect to the capacity ofthe column. The design procedure for reinforced concrete columns involvesthe following steps:

Generate axial force-biaxial moment interaction surfaces for all of the dif-ferent concrete section types of the model.

Check the capacity of each column for the factored axial force and bendingmoments obtained from each load combination at each end of the column.This step is also used to calculate the required reinforcement (if none wasspecified) that will produce a capacity ratio of 1.0.

Design the column shear reinforcement.

The shear reinforcement design procedure for columns is very similar to thatfor beams, except that the effect of the axial force on the concrete shear ca-pacity needs to be considered. See Concrete Frame UBC97 Technical Note 10


Technical Note 1 - 4 Second Order P-Delta Effects

Column Design and Concrete Frame ACI 318-99 Technical Note 20 ColumnDesign for more information.

Beam/Column Flexural Capacity RatiosWhen the ACI 318-99 or UBC97 code is selected, the program calculates theratio of the sum of the beam moment capacities to the sum of the columnmoment capacities at a particular joint for a particular column direction, ma-jor or minor. The capacities are calculated with no reinforcing overstrengthfactor, , and including factors. The beam capacities are calculated for re-versed situations and the maximum summation obtained is used.

The moment capacities of beams that frame into the joint in a direction that isnot parallel to the major or minor direction of the column are resolved alongthe direction that is being investigated and the resolved components areadded to the summation.

The column capacity summation includes the column above and the columnbelow the joint. For each load combination, the axial force, Pu, in each of thecolumns is calculated from the program analysis load combinations. For eachload combination, the moment capacity of each column under the influence ofthe corresponding axial load Pu is then determined separately for the majorand minor directions of the column, using the uniaxial column interaction dia-gram. The moment capacities of the two columns are added to give the ca-pacity summation for the corresponding load combination. The maximum ca-pacity summations obtained from all of the load combinations is used for thebeam/column capacity ratio.

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

See Beam/Column Flexural Capacity Ratios in Concrete Frame UBC97 Techni-cal Note 12 Joint Design or in Concrete Frame ACI 318-99 Technical Note 22Joint Design for more information.

Second Order P-Delta EffectsTypically, design codes require that second order P-Delta effects be consid-ered when designing concrete frames. The P-Delta effects come from twosources. They are the global lateral translation of the frame and the local de-formation of elements within the frame.


Second Order P-Delta Effects Technical Note 1 - 5

Consider the frame element shown in Figure 1, which is extracted from astory level of a larger structure. The overall global translation of this frameelement is indicated by . The local deformation of the element is shown as .The total second order P-Delta effects on this frame element are those causedby both and .

The program has an option to consider P-Delta effects in the analysis. Con-trols for considering this effect are found using the Analyze menu > SetAnalysis Options command and then clicking the Set P-Delta Parametersbutton. When you consider P-Delta effects in the analysis, the program does agood job of capturing the effect due to the deformation shown in Figure 1,but it does not typically capture the effect of the deformation (unless, in themodel, the frame element is broken into multiple pieces over its length).

In design codes, consideration of the second order P-Delta effects is generallyachieved by computing the flexural design capacity using a formula similar tothat shown in Equation. 1.

MCAP = aMnt + bMlt Eqn. 1

where,

MCAP = Flexural design capacity

Original position of frameelement shown by verticalline

Position of frame elementas a result of global lateraltranslation, , shown bydashed line

Final deflected position offrame element thatincludes the global lateraltranslation, , and thelocal deformation of theelement,

Figure 1: The Total Second Order P-Delta Effects on a Frame ElementCaused by Both and


Technical Note 1 - 6 Element Unsupported Lengths

Mnt = Required flexural capacity of the member assuming there isno translation of the frame (i.e., associated with the defor-mation in Figure 1)

Mlt = Required flexural capacity of the member as a result of lateraltranslation of the frame only (i.e., associated with the de-formation in Figure 1)

a = Unitless factor multiplying Mnt

b = Unitless factor multiplying Mlt (assumed equal to 1 by theprogram; see below)

When the program performs concrete frame design, it assumes that the factorb is equal to 1 and it uses code-specific formulas to calculate the factor a.That b = 1 assumes that you have considered P-Delta effects in the analysis,as previously described. Thus, in general, if you are performing concreteframe design in this program, you should consider P-Delta effects in theanalysis before running the design.

Element Unsupported LengthsThe column unsupported lengths are required to account for column slender-ness effects. The program automatically determines these unsupportedlengths. They can also be overwritten by the user on an element-by-elementbasis, if desired, using the Design menu > Concrete Frame Design >View/Revise Overwrites command.

There are two unsupported lengths to consider. They are L33 and L22, asshown in Figure 2. These are the lengths between support points of the ele-ment in the corresponding directions. The length L33 corresponds to instabilityabout the 3-3 axis (major axis), and L22 corresponds to instability about the2-2 axis (minor axis). The length L22 is also used for lateral-torsional bucklingcaused by major direction bending (i.e., about the 3-3 axis).

In determining the values for L22 and L33 of the elements, the program recog-nizes various aspects of the structure that have an effect on these lengths,such as member connectivity, diaphragm constraints and support points. Theprogram automatically locates the element support points and evaluates thecorresponding unsupported length.


Analysis Sections and Design Sectio Technical Note 1 - 7

Figure 2: Major and Minor Axes of BendingIt is possible for the unsupported length of a frame element to be evaluatedby the program as greater than the corresponding element length. For exam-ple, assume a column has a beam framing into it in one direction, but not theother, at a floor level. In this case, the column is assumed to be supported inone direction only at that story level, and its unsupported length in the otherdirection will exceed the story height.

Analysis Sections and Design SectionsAnalysis sections are those section properties used to analyze the modelwhen you click the Analyze menu > Run Analysis command. The designsection is whatever section has most currently been designed and thus desig-nated the current design section.

Tip:It is important to understand the difference between analysis sections and design sec-tions.ns


Technical Note 1 - 8 Analysis Sections and Design Sections

It is possible for the last used analysis section and the current design sectionto be different. For example, you may have run your analysis using a W18X35beam and then found in the design that a W16X31 beam worked. In thatcase, the last used analysis section is the W18X35 and the current designsection is the W16X31. Before you complete the design process, verify thatthe last used analysis section and the current design section are the same.The Design menu > Concrete Frame Design > Verify Analysis vs De-sign Section command is useful for this task.

The program keeps track of the analysis section and the design sectionseparately. Note the following about analysis and design sections:

Assigning a beam a frame section property using the Assign menu >Frame/Line > Frame Section command assigns the section as both theanalysis section and the design section.

Running an analysis using the Analyze menu > Run Analysis command(or its associated toolbar button) always sets the analysis section to be thesame as the current design section.

Assigning an auto select list to a frame section using the Assign menu >Frame/Line > Frame Section command initially sets the design sectionto be the beam with the median weight in the auto select list.

Unlocking a model deletes the design results, but it does not delete orchange the design section.

Using the Design menu > Concrete Frame Design > Select DesignCombo command to change a design load combination deletes the designresults, but it does not delete or change the design section.

Using the Define menu > Load Combinations command to change a de-sign load combination deletes the design results, but it does not delete orchange the design section.

Using the Options menu > Preferences > Concrete Frame Designcommand to change any of the composite beam design preferences deletesthe design results, but it does not delete or change the design section.

Deleting the static nonlinear analysis results also deletes the design resultsfor any load combination that includes static nonlinear forces. Typically,


Analysis Sections and Design Sections Technical Note 1 - 9

static nonlinear analysis and design results are deleted when one of thefollowing actions is taken:

9 Use the Define menu > Frame Nonlinear Hinge Properties com-mand to redefine existing or define new hinges.

9 Use the Define menu > Static Nonlinear/Pushover Cases com-mand to redefine existing or define new static nonlinear load cases.

9 Use the Assign menu > Frame/Line > Frame Nonlinear Hingescommand to add or delete hinges.

Again, note that these actions delete only results for load combinations thatinclude static nonlinear forces.

Concrete Frame Design Procedure Technical Note 2 - 1

COMPUTERS AND STRUCTURES, INC., BERKELEY, CALIFORNIA DECEMBER 2001CONCRETE FRAME DESIGN

Technical Note 2Concrete Frame Design Process

This Technical Note describes a basic concrete frame design process usingthis program. Although the exact steps you follow may vary, the basic designprocess should be similar to that described herein. Other Technical Notes inthe Concrete Frame Design series provide additional information, includingthe distinction between analysis sections and design sections (see AnalysisSections and Design Sections in Concrete Frame Design Technical Note 1General Design Information).

The concrete frame design postprocessor can design or check concrete col-umns and can design concrete beams.

Important note: A concrete frame element is designed as a beam or a col-umn, depending on how its frame section property was designated when itwas defined using the Define menu > Frame Sections command. Note thatwhen using this command, after you have specified that a section has a con-crete material property, you can click on the Reinforcement button andspecify whether it is a beam or a column.

Concrete Frame Design ProcedureThe following sequence describes a typical concrete frame design process fora new building. Note that although the sequence of steps you follow mayvary, the basic process probably will be essentially the same.

1. Use the Options menu > Preferences > Concrete Frame Designcommand to choose the concrete frame design code and to review otherconcrete frame design preferences and revise them if necessary. Notethat default values are provided for all concrete frame design prefer-ences, so it is unnecessary to define any preferences unless you want tochange some of the default values. See Concrete Frame Design ACIUBC97 Technical Notes 6 Preferences and Concrete Frame Design ACI318-99 Technical Notes 16 Preferences for more information.

Concrete Frame Design Process Concrete Frame Design

Technical Note 2 - 2 Concrete Frame Design Procedure

2. Create the building model.

3. Run the building analysis using the Analyze menu > Run Analysiscommand.

4. Assign concrete frame overwrites, if needed, using the Design menu >Concrete Frame Design > View/Revise Overwrites command. Notethat you must select frame elements before using this command. Alsonote that default values are provided for all concrete frame design over-writes, so it is unnecessary to define any overwrites unless you want tochange some of the default values. Note that the overwrites can be as-signed before or after the analysis is run. See Concrete Frame DesignUBC97 Technical Note 7 Overwrites and Concrete Frame Design ACI318-99 Technical Note 17 Overwrites for more information.

5. To use any design load combinations other than the defaults created bythe program for your concrete frame design, click the Design menu >Concrete Frame Design > Select Design Combo command. Notethat you must have already created your own design combos by clickingthe Define menu > Load Combinations command. See ConcreteFrame Design UBC97 Technical Note 8 Design Load Combinations andConcrete Frame Design ACI 318-99 Technical Note 18 Design LoadCombinations for more information.

6. Click the Design menu > Concrete Frame Design > Start De-sign/Check of Structure command to run the concrete frame design.

7. Review the concrete frame design results by doing one of the following:

a. Click the Design menu > Concrete Frame Design > Display De-sign Info command to display design input and output information onthe model. See Concrete Frame Design Technical Note 4 Output DataPlotted Directly on the Model for more information.

b. Right click on a frame element while the design results are displayedon it to enter the interactive design mode and interactively design theframe element. Note that while you are in this mode, you can reviseoverwrites and immediately see the results of the new design. SeeConcrete Frame Design Technical Note 3 Interactive Concrete FrameDesign for more information.

Concrete Frame Design Concrete Frame Design Process

Concrete Frame Design Procedure Technical Note 2 - 3

If design results are not currently displayed (and the design has beenrun), click the Design menu > Concrete Frame Design > Interac-tive Concrete Frame Design command and then right click a frameelement to enter the interactive design mode for that element.

8. Use the File menu > Print Tables > Concrete Frame Design com-mand to print concrete frame design data. If you select frame elementsbefore using this command, data is printed only for the selected ele-ments. See Concrete Frame Design UBC97 Technical Note 14 OutputDetails and Concrete Frame Design ACI 318-99 Technical Note 24 Out-put Details for more information.

9. Use the Design menu > Concrete Frame Design > Change DesignSection command to change the design section properties for selectedframe elements.

10. Click the Design menu > Concrete Frame Design > Start De-sign/Check of Structure command to rerun the concrete frame designwith the new section properties. Review the results using the proceduresdescribed in Item 7.

11. Rerun the building analysis using the Analyze menu > Run Analysiscommand. Note that the section properties used for the analysis are thelast specified design section properties.

12. Click the Design menu > Concrete Frame Design > Start De-sign/Check of Structure command to rerun the concrete frame designwith the new analysis results and new section properties. Review the re-sults using the procedures described above.

13. Again use the Design menu > Concrete Frame Design > ChangeDesign Section command to change the design section properties forselected frame elements, if necessary.

14. Repeat the processes in steps 10, 11 and 12 as many times as neces-sary.

15. Rerun the building analysis using the Analyze menu > Run Analysiscommand. Note that the section properties used for the analysis are thelast specified design section properties.

Concrete Frame Design Process Concrete Frame Design

Technical Note 2 - 4 Concrete Frame Design Procedure

Note:Concrete frame design is an iterative process. Typically, the analysis and design will bererun multiple times to complete a design.

16. Click the Design menu > Concrete Frame Design > Start De-sign/Check of Structure command to rerun the concrete frame designwith the new section properties. Review the results using the proceduresdescribed in Item 7.

17. Click the Design menu > Concrete Frame Design > Verify Analysisvs Design Section command to verify that all of the final design sec-tions are the same as the last used analysis sections.

18. Use the File menu > Print Tables > Concrete Frame Design com-mand to print selected concrete frame design results, if desired.

It is important to note that design is an iterative process. The sections used inthe original analysis are not typically the same as those obtained at the endof the design process. Always run the building analysis using the final framesection sizes and then run a design check using the forces obtained from thatanalysis. Use the Design menu > Concrete Frame Design > VerifyAnalysis vs Design Section command to verify that the design sections arethe same as the analysis sections.

General Technical Note 3 - 1


Technical Note 3Interactive Concrete Frame Design

This Technical Note describes interactive concrete frame design and review,which is a powerful mode that allows the user to review the design results forany concrete frame design and interactively revise the design assumptionsand immediately review the revised results.

GeneralNote that a design must have been run for the interactive design mode to beavailable. To run a design, click the Design menu > Concrete Frame De-sign > Start Design/Check of Structure command.

Right click on a frame element while the design results are displayed on it toenter the interactive design mode and interactively design the element in theConcrete Design Information form. If design results are not currently dis-played (and a design has been run), click the Design menu > ConcreteFrame Design > Interactive Concrete Frame Design command and thenright click a frame element to enter the interactive design mode for that ele-ment.

Important note: A concrete frame element is designed as a beam or a col-umn, depending on how its frame section property was designated when itwas defined using the Define menu > Frame Sections command and theReinforcement button, which is only available if it is a concrete section.

Concrete Design Information FormTable 1 describe the features that are included in the Concrete Design Infor-mation form.

Interactive Concrete Frame Design Concrete Frame Design

Technical Note 3 - 2 Table 1 Concrete Design Information Form

Table 1 Concrete Design Information FormItem DESCRIPTIONStory This is the story level ID associated with the frame element.Beam This is the label associated with a frame element that has been

assigned a concrete frame section property that is designatedas a beam. See the important note previously in this TechnicalNote for more information.

Column This is the label associated with a frame element that has beenassigned a concrete frame section property that is designatedas a column. See the important note previously in this Techni-cal Note for more information.

Section Name This is the label associated with a frame element that has beenassigned a concrete frame section property.

Reinforcement InformationThe reinforcement information table on the Concrete Design Information form shows theoutput information obtained for each design load combination at each output stationalong the frame element. For columns that are designed by this program, the item withthe largest required amount of longitudinal reinforcing is initially highlighted. For columnsthat are checked by this program, the item with the largest capacity ratio is initially high-lighted. For beams, the item with the largest required amount of bottom steel is initiallyhighlighted. Following are the possible headings in the table:

Combo ID This is the name of the design load combination considered.Station location This is the location of the station considered, measured from

the i-end of the frame element.Longitudinalreinforcement

This item applies to columns only. It also only applies to col-umns for which the program designs the longitudinal reinforc-ing. It is the total required area of longitudinal reinforcing steel.

Capacity ratio This item applies to columns only. It also only applies to col-umns for which you have specified the location and size of re-inforcing bars and thus the program checks the design. Thisitem is the capacity ratio.

Concrete Frame Design Interactive Concrete Frame Design

Table 1 Concrete Design Information Form Technical Note 3 - 3

Table 1 Concrete Design Information FormItem DESCRIPTION

The capacity ratio is determined by first extending a line fromthe origin of the PMM interaction surface to the point repre-senting the P, M2 and M3 values for the designated load com-bination. Assume the length of this first line is designated L1.Next, a second line is extended from the origin of the PMM in-teraction surface through the point representing the P, M2 andM3 values for the designated load combination until it intersectsthe interaction surface. Assume the length of this line from theorigin to the interaction surface is designated L2. The capacityratio is equal to L1/L2.

Major shearreinforcement

This item applies to columns only. It is the total required area ofshear reinforcing per unit length for shear acting in the columnmajor direction.

Minor shearreinforcement

This item applies to columns only. It is the total required area ofshear reinforcing per unit length for shear acting in the columnminor direction.

Top steel This item applies to beams only. It is the total required area oflongitudinal top steel at the specified station.

Bottom steel This item applies to beams only. It is the total required area oflongitudinal bottom steel at the specified station.

Shear steel This item applies to beams only. It is the total required area ofshear reinforcing per unit length at the specified station forloads acting in the local 2-axis direction of the beam.

Overwrites Button Click this button to access and make revisions to the concreteframe overwrites and then immediately see the new design re-sults. If you modify some overwrites in this mode and you exitboth the Concrete Frame Design Overwrites form and the Con-crete Design Information form by clicking their respective OKbuttons, the changes to the overwrites are saved permanently.When you exit the Concrete Frame Design Overwrites form byclicking the OK button the changes are temporarily saved. Ifyou then exit the Concrete Design Information form by clickingthe Cancel button the changes you made to the concrete frameoverwrites are considered temporary only and are not perma-nently saved. Permanent saving of the overwrites does not ac-tually occur until you click the OK button in the Concrete DesignInformation form as well as the Concrete Frame Design Over-writes form.

Interactive Concrete Frame Design Concrete Frame Design

Technical Note 3 - 4 Table 1 Concrete Design Information Form

Table 1 Concrete Design Information FormItem DESCRIPTIONDetails Button Clicking this button displays design details for the frame ele-

ment. Print this information by selecting Print from the Filemenu that appears at the top of the window displaying the de-sign details.

Interaction Button Clicking this button displays the biaxial interaction curve for theconcrete section at the location in the element that is high-lighted in the table.

Overview Technical Note 4 - 1


Technical Note 4Output Data Plotted Directly on the Model

This Technical Note describes the input and output data that can be plotteddirectly on the model.

OverviewUse the Design menu > Concrete Frame Design > Display Design Infocommand to display on-screen output plotted directly on the program model.If desired, the screen graphics can then be printed using the File menu >Print Graphics command. The on-screen display data presents input andoutput data.

Using the Print Design Tables FormTo print the concrete frame input summary directly to a printer, use the Filemenu > Print Tables > Concrete Frame Design command and click thecheck box on the Print Design Tables form. Click the OK button to send theprint to your printer. Click the Cancel button rather than the OK button tocancel the print. Use the File menu > Print Setup command and theSetup>> button to change printers, if necessary.

To print the concrete frame input summary to a file, click the Print to Filecheck box on the Print Design Tables form. Click the Filename>> button tochange the path or filename. Use the appropriate file extension for the de-sired format (e.g., .txt, .xls, .doc). Click the OK buttons on the Open File forPrinting Tables form and the Print Design Tables form to complete the re-quest.

Note:The File menu > Display Input/Output Text Files command is useful for displaying out-put that is printed to a text file.

The Append check box allows you to add data to an existing file. The path andfilename of the current file is displayed in the box near the bottom of the PrintDesign Tables form. Data will be added to this file. Or use the Filename

Output Data Plotted Directly on the Model Concrete Frame Design

Technical Note 4 - 2 Design Input

button to locate another file, and when the Open File for Printing Tables cau-tion box appears, click Yes to replace the existing file.

If you select a specific concrete frame element(s) before using the File menu> Print Tables > concrete Frame Design command, the Selection Onlycheck box will be checked. The print will be for the selected steel frame ele-ment(s) only.

Design InputThe following types of data can be displayed directly on the model by select-ing the data type (shown in bold type) from the drop-down list on the DisplayDesign Results form. Display this form by selecting he Design menu > Con-crete Frame Design > Display Design Info command.

Design Sections

Design Type

Live Load Red Factors

Unbraced L_Ratios

Eff Length K-Factors

Cm Factors

DNS Factors

DS Factors

Each of these items is described in the code-specific Concrete Frame DesignUBC97 Technical Note 13 Input Data and Concrete Frame Design ACI 318-99Technical Note 23 Input Data.

Design OutputThe following types of data can be displayed directly on the model by select-ing the data type (shown in bold type) from the drop-down list on the DisplayDesign Results form. Display this form by selecting he Design menu > Con-crete Frame Design > Display Design Info command.

Concrete Frame Design Output Data Plotted Directly on the Model

Design Output Technical Note 4 - 3

Longitudinal Reinforcing

Shear Reinforcing

Column Capacity Ratios

Joint Shear Capacity Ratios

Beam/Column Capacity Ratios

Each of these items is described in the code-specific Concrete Frame DesignACI 318-99 Technical Note 24 Output Details and Concrete Frame DesignUBC97 Technical Note 14 Output Details.

General and Notation Technical Note 5 - 1

COMPUTERS AND STRUCTURES, INC., BERKELEY, CALIFORNIA DECEMBER 2001CONCRETE FRAME DESIGN UBC97

Technical Note 5General and Notation

Introduction to the UBC97 Series of Technical NotesThe Concrete Frame Design UBC97 series of Technical Notes describes in de-tail the various aspects of the concrete design procedure that is used by thisprogram when the user selects the UBC97 Design Code (ICBO 1997). Thevarious notations used in this series are listed herein.

The design is based on user-specified loading combinations. The programprovides a set of default load combinations that should satisfy requirementsfor the design of most building type structures. See Concrete Frame DesignUBC97 Technical Note 8 Design Load Combinations for more information.

When using the UBC 97 option, a frame is assigned to one of the followingfive Seismic Zones (UBC 2213, 2214):

Zone 0

Zone 1

Zone 2

Zone 3

Zone 4

By default the Seismic Zone is taken as Zone 4 in the program. However, theSeismic Zone can be overwritten in the Preference form to change the de-fault. See Concrete Frame Design UBC97 Technical Note 6 Preferences formore information.

When using the UBC 97 option, the following Framing Systems are recognizedand designed according to the UBC design provisions (UBC 1627, 1921):

Ordinary Moment-Resisting Frame (OMF)

General and Notation Concrete Frame Design UBC97

Technical Note 5 - 2 General and Notation

Intermediate Moment-Resisting Frame (IMRF)

Special Moment-Resisting Frame (SMRF)

The Ordinary Moment-Resisting Frame (OMF) is appropriate in minimal seis-mic risk areas, especially in Seismic Zones 0 and 1. The Intermediate Mo-ment-Resisting Frame (IMRF) is appropriate in moderate seismic risk areas,specially in Seismic Zone 2. The Special Moment-Resisting Frame (SMRF) isappropriate in high seismic risk areas, specially in Seismic Zones 3 and 4. TheUBC seismic design provisions are considered in the program. The details ofthe design criteria used for the different framing systems are described inConcrete Frame Design UBC97 Technical Note 9 Strength Reduction Factors,Concrete Frame Design UBC97 Technical Note 10 Column Design, ConcreteFrame Design UBC97 Technical Note 11 Beam Design, and Concrete FrameDesign UBC97 Technical Note 12 Joint Design.

By default the frame type is taken in the program as OMRF in Seismic Zone 0and 1, as IMRF in Seismic Zone 2, and as SMRF in Seismic Zone 3 and 4.However, the frame type can be overwritten in the Overwrites form on amember-by-member basis. See Concrete Frame Design UBC97 Technical Note7 Overwrites for more information. If any member is assigned with a frametype, the change of the Seismic Zone in the Preferences will not modify theframe type of an individual member that has been assigned a frame type.

The program also provides input and output data summaries, which are de-scribed in Concrete Frame Design UBC97 Technical Note 13 Input Data andConcrete Frame Design UBC97 Technical Note 14 Output Details.

English as well as SI and MKS metric units can be used for input. The code isbased on Inch-Pound-Second units. For simplicity, all equations and descrip-tions presented in this Technical Note correspond to Inch-Pound-Secondunits unless otherwise noted.

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

Ag Gross area of concrete, sq-in

As Area of tension reinforcement, sq-in

Concrete Frame Design UBC97 General and Notation


'sA Area of compression reinforcement, sq-in

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

Ast Total area of column longitudinal reinforcement, sq-in

Av Area of shear reinforcement, sq-in

Cm Coefficient, dependent upon column curvature, used to calculatemoment magnification factor

D' Diameter of hoop, in

Ec Modulus of elasticity of concrete, psi

Es Modulus of elasticity of reinforcement, assumed as 29,000,000 psi(UBC 1980.5.2)

Ig Moment of inertia of gross concrete section about centroidal axis,neglecting reinforcement, in4

Ise Moment of inertia of reinforcement about centroidal axis of mem-ber cross section, in4

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

Mc Factored moment to be used in design, lb-in

Mns Nonsway component of factored end moment, lb-in

Ms Sway component of factored end moment, lb-in

Mu Factored moment at section, lb-in

Mux Factored moment at section about X-axis, lb-in

Muy Factored moment at section about Y-axis, lb-in

Pb Axial load capacity at balanced strain conditions, lb

General and Notation Concrete Frame Design UBC97

Technical Note 5 - 4 General and Notation

Pc Critical buckling strength of column, lb

Pmax Maximum axial load strength allowed, lb

P0 Acial load capacity at zero eccentricity, lb

Pu Factored axial load at section, lb

Vc Shear resisted by concrete, lb

VE Shear force caused by earthquake loads, lb

VD+L Shear force from span loading, lb

Vu Factored shear force at a section, lb

Vp Shear force computed from probable moment capacity, lb

a Depth of compression block, in

ab Depth of compression block at balanced condition, in

b Width of member, in

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

bw Width of web (T-Beam section), in

c Depth to neutral axis, in

cb 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

ds Thickness of slab (T-Beam section), in

'cf Specified compressive strength of concrete, psi

fy Specified yield strength of flexural reinforcement, psify 80,000 psi (UBC 1909.4)

Concrete Frame Design UBC97 General and Notation


fys Specified yield strength of flexural reinforcement, psi

h Dimension of column, in

k Effective length factor

r Radius of gyration of column section, in

Reinforcing steel overstrength factor

1 Factor for obtaining depth of compression block in concreted Absolute value of ratio of maximum factored axial dead load to

maximum factored axial total load

s Moment magnification factor for sway moments

ns Moment magnification factor for nonsway moments

c Strain in concrete

s Strain in reinforcing steel

Strength reduction factor

General Technical Note 6 - 1


Technical Note 6Preferences

This Technical Note describes the items in the Preferences form.

GeneralThe concrete frame design preferences in this program are basic assignmentsthat apply to all concrete frame elements. Use the Options menu > Prefer-ences > Concrete Frame Design command to access the Preferences formwhere you can view and revise the concrete frame design preferences.

Default values are provided for all concrete frame design preference items.Thus, it is not required that you specify or change any of the preferences. Youshould, however, at least review the default values for the preference itemsto make sure they are acceptable to you.

Using the Preferences FormTo view preferences, select the Options menu > Preferences > ConcreteFrame Design. The Preferences form will display. The preference optionsare displayed in a two-column spreadsheet. The left column of the spread-sheet displays the preference item name. The right column of the spreadsheetdisplays the preference item value.

To change a preference item, left click the desired preference item in eitherthe left or right column of the spreadsheet. This activates a drop-down box orhighlights the current preference value. If the drop-down box appears, selecta new value. If the cell is highlighted, type in the desired value. The prefer-ence value will update accordingly. You cannot overwrite values in the drop-down boxes.

When you have finished making changes to the concrete frame preferences,click the OK button to close the form. You must click the OK button for thechanges to be accepted by the program. If you click the Cancel button to exit

Preferences Concrete Frame Design UBC97

Technical Note 6 - 2 Preferences

the form, any changes made to the preferences are ignored and the form isclosed.

PreferencesFor purposes of explanation in this Technical Note, the preference items arepresented in Table 1. The column headings in the table are described as fol-lows:

Item: The name of the preference item as it appears in the cells at theleft side of the Preferences form.

Possible Values: The possible values that the associated preference itemcan have.

Default Value: The built-in default value that the program assumes forthe associated preference item.

Description: A description of the associated preference item.

Table 1: Concrete Frame Preferences

ItemPossibleValues

DefaultValue Description

Design Code Any code inthe program

UBC97 Design code used for design ofconcrete frame elements.

Phi BendingTension

>0 0.9 Unitless strength reduction factor perUBC 1909.

Phi Compres-sion Tied


Phi Compres-sion Spiral


Phi Shear >0 0.85 Unitless strength reduction factor perUBC 1909.

Number Inter-action Curves

4.0 24 Number of equally spaced interactioncurves used to create a full 360-degreeinteraction surface (this item should bea multiple of four). We recommend thatyou use 24 for this item.

Concrete Frame Design UBC97 Preferences

Preferences Technical Note 6 - 3

Table 1: Concrete Frame Preferences

ItemPossibleValues


Number Inter-action Points

Any odd value1.0

11 Number of points used for defining asingle curve in a concrete frameinteraction surface (this item should beodd).

Time HistoryDesign

Envelopes orStep-by-Step

Envelopes Toggle for design load combinationsthat include a time history designed forthe envelope of the time history, ordesigned step-by-step for the entiretime history. If a single design loadcombination has more than one timehistory case in it, that design loadcombination is designed for theenvelopes of the time histories,regardless of what is specified here.

Overwrites Technical Note 7 - 1


Technical Note 7Overwrites

GeneralThe concrete frame design overwrites are basic assignments that apply onlyto those elements to which they are assigned. This Technical Note describesconcrete frame design overwrites for UBC97. To access the overwrites, selectan element and click the Design menu > Concrete Frame Design >View/Revise Overwrites command.

Default values are provided for all overwrite items. Thus, you do not need tospecify or change any of the overwrites. However, at least review the defaultvalues for the overwrite items to make sure they are acceptable. Whenchanges are made to overwrite items, the program applies the changes onlyto the elements to which they are specifically assigned; that is, to the ele-ments that are selected when the overwrites are changed.

OverwritesFor explanation purposes in this Technical Note, the overwrites are presentedin Table 1. The column headings in the table are described as follows.

Item: The name of the overwrite item as it appears in the program. Tosave space in the formes, these names are generally short.

Possible Values: The possible values that the associated overwrite itemcan have.

Default Value: The default value that the program assumes for the asso-ciated overwrite item.

Description: A description of the associated overwrite item.

An explanation of how to change an overwrite is provided at the end of thisTechnical Note.

Overwrites Concrete Frame Design UBC97

Technical Note 7 - 2 Overwrites

Table 1 Concrete Frame Design Overwrites

ItemPossibleValues


ElementSection

ElementType

Sway Special,Sway Interme-

diate,Sway

OrdinaryNonSway

Sway Special Frame type; see UBC 1910.11 to1910.13.

Live LoadReduction

Factor

>0

1.0

1. Used to reduce the live load contribu-tion to the factored loading.

HorizontalEarthquake

Factor

>0

1.0

1.

UnbracedLength Ratio

(Major)>0

1.0

1.0

UnbracedLength Ratio

(Minor)>0

1.0

1.0

EffectiveLength Factor

(K Major)>0

1.0

1 See UBC 1910.12.1.

EffectiveLength Factor

(K Minor)>0

1.0

1 See UBC 1910.12.1.

MomentCoefficient(Cm Major)

>0

1.0

1 See UBC 1910.12.3.1 relates actualmoment diagram to an equivalent uni-form moment diagram.

MomentCoefficient(Cm Minor)

>0

1.0

1 See UBC 1910.12.3.1 relates actualmoment diagram to an equivalent uni-form moment diagram.

NonSwayMoment Factor

(Dns Major)>0

1.0

1 See UBC 1910.12.

Concrete Frame Design UBC97 Overwrites

Overwrites Technical Note 7 - 3

Table 1 Concrete Frame Design Overwrites

ItemPossibleValues


NonSwayMoment Factor

(Dns Minor)1 See UBC 1910.12.

Sway MomentFactor

(Ds Major)1 See UBC 1910.12.

Sway MomentFactor

(Ds Minor)1 See UBC 1910.12.

Making Changes in the Overwrites FormTo access the concrete frame overwrites, select an element and click the De-sign menu > Concrete Frame Design > View/Revise Overwrites com-mand.

The overwrites are displayed in the form with a column of check boxes and atwo-column spreadsheet. The left column of the spreadsheet contains thename of the overwrite item. The right column of the spreadsheet contains theoverwrites values.

Initially, the check boxes in the Concrete Frame Design Overwrites form areall unchecked and all of the cells in the spreadsheet have a gray backgroundto indicate that they are inactive and the items in the cells cannot bechanged. The names of the overwrite items are displayed in the first columnof the spreadsheet. The values of the overwrite items are visible in the secondcolumn of the spreadsheet if only one element was selected before the over-writes form was accessed. If multiple elements were selected, no values showfor the overwrite items in the second column of the spreadsheet.

After selecting one or multiple elements, check the box to the left of an over-write item to change it. Then left click in either column of the spreadsheet toactivate a drop-down box or highlight the contents in the cell in the right col-umn of the spreadsheet. If the drop-down box appears, select a value from

Overwrites Concrete Frame Design UBC97

Technical Note 7 - 4 Overwrites

the box. If the cell contents is highlighted, type in the desired value. Theoverwrite will reflect the change. You cannot change the values of the drop-down boxes.

When changes to the overwrites have been completed, click the OK button toclose the form. The program then changes all of the overwrite items whoseassociated check boxes are checked for the selected members. You must clickthe OK button for the changes to be accepted by the program. If you click theCancel button to exit the form, any changes made to the overwrites are ig-nored and the form is closed.

Resetting Concrete Frame Overwrites to Default ValuesUse the Design menu > Concrete Frame Design > Reset All Overwritescommand to reset all of the steel frame overwrites. All current design resultswill be deleted when this command is executed.

Important note about resetting overwrites: The program defaults for theoverwrite items are built into the program. The concrete frame overwrite val-ues that were in a .edb file that you used to initialize your model may be dif-ferent from the built-in program default values. When you reset overwrites,the program resets the overwrite values to its built-in values, not to the val-ues that were in the .edb file used to initialize the model.

Design Load Combinations Technical Note 8 - 1


Technical Note 8Design Load Combinations

The design load combinations are the various combinations of the prescribedload cases for which the structure needs to be checked. For the UBC 97 code,if a structure is subjected to dead load (DL) and live load (LL) only, the stresscheck may need only one load combination, namely 1.4 DL + 1.7 LL (UBC1909.2.1). However, in addition to the dead and live loads, if the structure issubjected to wind (WL) and earthquake (EL) loads, and considering that windand earthquake forces are reversible, the following load combinations mayneed to be considered (UBC 1909.2).

1.4 DL (UBC 1909.2.1)1.4 DL + 1.7 LL (UBC 1909.2.1)

0.9 DL 1.3 WL (UBC 1909.2.2)0.75 (1.4 DL + 1.7 LL 1.7 WL) (UBC 1909.2.2)

0.9 DL 1.0 EL (UBC 1909.2.3, 1612.2.1)1.2 DL + 0.5 LL 1.0 EL) (UBC 1909.2.3, 1612.2.1)

These are also the default design load combinations in the program wheneverthe UBC97 code is used.

Live load reduction factors can be applied to the member forces of the liveload condition on an element-by-element basis to reduce the contribution ofthe live load to the factored loading. See Concrete Frame Design UBC97Technical Note 7 Overwrites for more information.

Strength Reduction Factors Technical Note 9 - 1


Technical Note 9Strength Reduction Factors

The strength reduction factors, , are applied on the nominal strength to ob-tain the design strength provided by a member. The factors for flexure, ax-ial force, shear, and torsion are as follows:

= 0.90 for flexure (UBC 1909.3.2.1)

= 0.90 for axial tension (UBC 1909.3.2.2)

= 0.90 for axial tension and flexure (UBC 1909.3.2.2)

= 0.75 for axial compression, and axial compressionand flexure (spirally reinforced column) (UBC 1909.3.2.2)

= 0.70 for axial compression, and axial compressionand flexure (tied column) (UBC 1909.3.2.2)

= 0.85 for shear and torsion (non-seismic design) (UBC 1909.3.2.3)

= 0.60 for shear and torsion (UBC 1909.3.2.3)



Technical Note 10Column Design

This Technical Note describes how the program checks column capacity or de-signs reinforced concrete columns when the UBC97 code is selected.

OverviewThe program can be used to check column capacity or to design columns. Ifyou define the geometry of the reinforcing bar configuration of each concretecolumn section, the program will check the column capacity. Alternatively, theprogram can calculate the amount of reinforcing required to design the col-umn. The design procedure for the reinforced concrete columns of the struc-ture involves the following steps:

Generate axial force/biaxial moment interaction surfaces for all of the dif-ferent concrete section types of the model. A typical biaxial interactionsurface is shown in Figure 1. When the steel is undefined, the programgenerates the interaction surfaces for the range of allowable reinforce-ment1 to 8 percent for Ordinary and Intermediate moment resistingframes (UBC 1910.9.1) and 1 to 6 percent for Special moment resistingframes (UBC 1921.4.3.1).

Calculate the capacity ratio or the required reinforcing area for the fac-tored axial force and biaxial (or uniaxial) bending moments obtained fromeach loading combination at each station of the column. The target capac-ity ratio is taken as 1 when calculating the required reinforcing area.

Design the column shear reinforcement.

The following four subsections describe in detail the algorithms associatedwith this process.

Column Design Concrete Frame Design UBC97

Technical Note 10 - 2 Generation of Biaxial Interaction Surfaces

Figure 1 A Typical Column Interaction Surface

Generation of Biaxial Interaction SurfacesThe column capacity interaction volume is numerically described by a seriesof discrete points that are generated on the three-dimensional interactionfailure surface. In addition to axial compression and biaxial bending, the for-mulation allows for axial tension and biaxial bending considerations. A typicalinteraction diagram is shown in Figure 1.

Concrete Frame Design UBC97 Column Design

Generation of Biaxial Interaction Surfaces Technical Note 10 - 3

The coordinates of these points are determined by rotating a plane of linearstrain in three dimensions on the section of the column. See Figure 2. Thelinear strain diagram limits the maximum concrete strain, c, at the extremityof the section, to 0.003 (UBC 1910.2.3).

The formulation is based consistently upon the general principles of ultimatestrength design (UBC 1910.3), and allows for any doubly symmetric rectan-gular, square, or circular column section.

The stress in the steel is given by the product of the steel strain and the steelmodulus of elasticity, sEs, and is limited to the yield stress of the steel, fy(UBC 1910.2.4). The area associated with each reinforcing bar is assumed tobe placed at the actual location of the center of the bar and the algorithmdoes not assume any further simplifications with respect to distributing thearea of steel over the cross section of the column, such as an equivalent steeltube or cylinder. See Figure 3.

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

stress value of 0.85 'cf (UBC 1910.2.7.1). See Figure 3. The interaction algo-

rithm provides correction to account for the concrete area that is displaced bythe reinforcement in the compression zone.

The effects of the strength reduction factor, , are included in the generationof the interaction surfaces. The maximum compressive axial load is limited toPn(max), where

Pn(max) = 0.85[0.85 'cf (Ag-Ast)+fyAst] (spiral) (UBC 1910.3.5.1)

Pn(max) = 0.85[0.85 'cf (Ag-Ast)+fyAst] (tied) (UBC 1910.3.5.2)

= 0.70 for tied columns (UBC 1909.3.2.2)

= 0.75 for spirally reinforced columns (UBC 1909.3.2.2)

The value of used in the interaction diagram varies from min to 0.9 basedon the axial load. For low values of axial load, is increased linearly from minto 0.9 as the nominal capacity Pn decreases from the smaller of Pb or0.1 'cf Ag to zero, where Pb is the axial force at the balanced condition. In

cases involving axial tension, is always 0.9 (UBC 1909.3.2.2).


Technical Note 10 - 4 Generation of Biaxial Interaction Surfaces

Figure 2 Idealized Strain Distribution for Generation of Interaction Surfaces


Calculate Colum Capacity Ratio Technical Note 10 - 5

Figure 3 Idealization of Stress and Strain Distribution in a Column Section

Calculate Column Capacity RatioThe column capacity ratio is calculated for each loading combination at eachoutput station of each column. The following steps are involved in calculatingthe capacity ratio of a particular column for a particular loading combinationat a particular location:

Determine the factored moments and forces from the analysis load casesand the specified load combination factors to give Pu, Mux, and Muy.

Determine the moment magnification factors for the column moments.

Apply the moment magnification factors to the factored moments. Deter-mine whether the point, defined by the resulting axial load and biaxialmoment 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.n


Technical Note 10 - 6 Calculate Column Capacity Ratio

The following three sections describe in detail the algorithms associated withthis process.

Determine Factored Moments and ForcesThe factored loads for a particular load combination are obtained by applyingthe corresponding load factors to all the load cases, giving Pu, Mux, and Muy.The factored moments are further increased for non-sway columns, if re-quired, to obtain minimum eccentricities of (0.6 + 0.03h) inches, where h isthe dimension of the column in the corresponding direction (UBC1910.12.3.2).

Determine Moment Magnification FactorsThe moment magnification factors are calculated separately for sway (overallstability effect), s, and for non-sway (individual column stability effect), ns.Also the moment magnification factors in the major and minor directions arein general different.

The program assumes that it performs a P-delta analysis and, therefore, mo-ment magnification factors for moments causing sidesway are taken as unity(UBC 1910.10.2). For the P-delta analysis, the load should correspond to aload combination of 0.75 (1.4 dead load + 1.7 live load)/ if wind load gov-erns, or (1.2 dead load + 0.50 live load)/ if seismic load governs, where isthe understrength factor for stability, which is taken as 0.75 (UBC1910.12.3). See also White and Hajjar (1991).

The moment obtained from analysis is separated into two components: thesway (Ms) and the non-sway (Ms) components. The non-sway componentswhich are identified by ns subscripts are predominantly caused by gravityload. The sway components are identified by the s subscripts. The swaymoments are predominantly caused by lateral loads, and are related to thecause 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

M = Mns + sMs. (UBC 1910.13.3)The factor s is the moment magnification factor for moments causing sidesway. The moment magnification factors for sway moments, s, is taken as 1because the component moments Ms and Mns are obtained from a second or-der elastic (P-delta) analysis.


Calculate Column Capacity Ratio Technical Note 10 - 7

The computed moments are further amplified for individual column stabilityeffect (UBC 1910.12.3, 1910.13.5) by the nonsway moment magnificationfactor, ns, as follows:

Mc = nsM2 , where (UBC 1910.12.3)

Mc is the factored moment to be used in design, and

M2 is the larger factored and amplified end moment.

The non-sway moment magnification factor, ns, associated with the major orminor direction of the column is given by (UBC 1910.12.3)

ns =

c

u

m

PP

C

75.01

1.0, where (UBC 1910.12.3)

Pc = 2

2

)( ukl

EI, (UBC 1910.12.3)

k is conservatively taken as 1; however, the program allows the user tooverride this value.

EI is associated with a particular column direction given by:

EI =d

gc IE

+14.0

, (UBC 1910.12.3)

maximum factored axial dead loadd = maximum factored axial total load and (UBC 1910.12.3)

Cm = 0.6 + 0.4b

a

MM

0.4. (UBC 1910.12.3.1)

Ma and Mb are the moments at the ends of the column, and Mb is numericallylarger than Ma. Ma / Mb is positive for single curvature bending and negativefor double curvature bending. The above expression of Cm is valid if there isno transverse load applied between the supports. If transverse load is presenton the span, or the length is overwritten, Cm = 1. Cm can be overwritten bythe user on an element-by-element basis.


Technical Note 10 - 8

The magnification factor, ns, must be a positive number and greater than 1.Therefore, Pu must be less than 0.75Pc. If Pu is found to be greater than orequal to 0.75Pc, a failure condition is declared.

The above calculations use the unsupported length of the column. The twounsupported lengths are l22 and l33, corresponding to instability in the minorand major directions of the element, respectively. See Figure 4. These are thelengths between the support points of the element in the corresponding di-rections.

Figure 4 Axes of Bending and Unsupported Length

If the program as umptions are not satisfactory for a particular member, theuser can explicitly specify values of and .

Determine CapacityThe program calcof the column. Ths Calculate Column Capacity Ratio

s ns

Ratioulates a capacity ratio as a measure of the stress conditione capacity ratio is basically a factor that gives an indication


Calculate Column Capacity Ra

of the stress condition of the column with respect to the capacity of the col-umn.

Before entering the interaction diagram to check the column capacity, themoment magnification factors are applied to the factored loads to obtain Pu,Mux, and Muy. The point (Pu, Mux, Muy.) is then placed in the interaction spaceshown as point L in Figure 5. If the point lies within the interaction volume,the column capacity is adequate; however, if the point lies outside the inter-action volume, the column is overstressed.

Figure 5 Geometric R presentation of Column Capacity Ratios

This capacity ratio is acation of point C. Thextended outwards) wby three-dimensional etio Technical Note 10 - 9

chieved by plotting the point L and determining the lo-e point C is defined as the point where the line OL (ifill intersect the failure surface. This point is determinedlinear interpolation between the points that define the


Technical Note 10 - 10 Required Reinforcing Area

failure surface. See Figure 5. The capacity ratio, CR, is given by the ratio

OCOL

.

If OL = OC (or CR=1), the point lies on the interaction surface and thecolumn is stressed to capacity.

If OL < OC (or CR OC (or CR>1), the point lies outside the interaction volume and thecolumn is overstressed.

The maximum of all the values of CR calculated from each load combination isreported for each check station of the column, along with the controlling Pu,Mux, and Muy set and associated load combination number.

Required Reinforcing AreaIf the reinforcing area is not defined, the program computes the reinforce-ment that will give a column capacity ratio of one, calculated as described inthe previous section entitled "Calculate Column Capacity Ratio."

Design Column Shear ReinforcementThe shear reinforcement is designed for each loading combination in the ma-jor and minor directions of the column. The following steps are involved indesigning the shear reinforcing for a particular column for a particular loadcombination caused by shear forces in a particular direction:

Determine the factored forces acting on the section, Pu and Vu. Note thatPu is needed for the calculation of Vc.

Determine the shear force, Vc, that can be resisted by concrete alone.

Calculate the reinforcement steel required to carry the balance.

For Special and Intermediate moment resisting frames (Ductile frames), theshear design of the columns is also based on the probable and nominal mo-ment capacities of the members, respectively, in addition to the factored


Design Column Shear Reinforcement Technical Note 10 - 11

moments. Effects of the axial forces on the column moment capacities areincluded in the formulation.

The following three sections describe in detail the algorithms associated withthis process.

Determine Section Forces In the design of the column shear reinforcement of an Ordinary moment

resisting concrete frame, the forces for a particular load combination,namely, the column axial force, Pu, and the column shear force, Vu, in aparticular direction are obtained by factoring the program analysis loadcases with the corresponding load combination factors.

In the shear design of Special moment resisting frames (i.e., seismicdesign) the column is checked for capacity-shear in addition to the re-quirement for the Ordinary moment resisting frames. The capacity-shearforce in a column, Vp, in a particular direction is calculated from the prob-able moment capacities of the column associated with the factored axialforce acting on the column.

For each load combination, the factored axial load, Pu, is calculated. Then,

the positive and negative moment capacities, +uM and

uM , of the column

in a particular direction under the influence of the axial force Pu is calcu-lated using the uniaxial interaction diagram in the corresponding direction.The design shear force, Vu, is then given by (UBC 1921.4.5.1)

Vu = Vp + VD+L (UBC 1921.4.5.1)

where, Vp is the capacity-shear force obtained by applying the calculatedprobable ultimate moment capacities at the two ends of the column actingin two opposite directions. Therefore, Vp is the maximum of 1PV and 2PV ,

where

1PV = LMM JI

+ + , and

2PV = LMM JI

+ +, where


Technical Note 10 - 12 Design Column Shear Reinforcement

+II MM , , = Positive and negative moment capacities at end I of the

column using a steel yield stress value of fy and no factors ( = 1.0),

+JJ MM , , = Positive and negative moment capacities at end J of the

column using a steel yield stress value of fy and no factors ( = 1.0), and

L = Clear span of column.

For Special moment resisting frames, is taken as 1.25 (UBC 1921.0).VD+L is the contribution of shear force from the in-span distribution ofgravity loads. For most of the columns, it is zero.

For Intermediate moment resisting frames, the shear capacity of thecolumn is also checked for the capacity-shear based on the nominal mo-ment capacities at the ends and the factored gravity loads, in addition tothe check required for Ordinary moment resisting frames. The designshear force is taken to be the minimum of that based on the nominal ( =1.0) moment capacity and factored shear force. The procedure for calcu-lating nominal moment capacity is the same as that for computing theprobable moment capacity for special moment resisting frames, exceptthat is taken equal to 1 rather than 1.25 (UBC 1921.0, 1921.8.3). Thefactored shear forces are based on the specified load factors, except theearthquake load factors are doubled (UBC 1921.8.3).

Determine Concrete Shear CapacityGiven the design force set Pu and Vu, the shear force carried by the concrete,Vc, is calculated as follows:

If the column is subjected to axial compression, i.e., Pu is positive,

Vc = 2 cvg

uc AA

Pf

+000,2

1' , (UBC 1911.3.1.2)

where,

'cf 100 psi, and (UBC 1911.1.2)


Design Column Shear Reinforcement

Vc 3.5 'cf cvg

u AA

P

+500

1 . (UBC 1911.3.2.2)

The term g

u

AP

must have psi units. Acv is the effective shear area which is

shown shaded in Figure 6. For circular columns, Acv is not taken to begreater than 0.8 times the gross area (UBC 1911.5.6.2).

Figure 6 Shear Stress Area, AcTechnical Note 10 - 13

v


Technical Note 10 - 14 Design Column Shear Reinforcement

If the column is subjected to axial tension, Pu is negative, (UBC1911.3.2.3)

Vc = 2'cf

+g

u

AP

5001 Acv 0 (UBC 1911.3.2.3)

For Special moment resisting concrete frame design, Vc is set to zeroif the factored axial compressive force, Pu, including the earthquake effect

is small (Pu < 'cf Ag / 20) and if the shear force contribution from earth-

quake, VE, is more than half of the total factored maximum shear forceover the length of the member Vu(VE 0.5Vu) (UBC 1921.4.5.2).

Determine Required Shear ReinforcementGiven Vu and Vc, the required shear reinforcement in the form of stirrups orties within a spacing, s, is given for rectangular and circular columns by thefollowing:

Av = df

sVV

ys

cu )/( , for rectangular columns (UBC 1911.5.6.1, 1911.5.6.2)

Av = '

)/(2Df

sVV

ys

cu

, for circular columns (UBC 1911.5.6.1, 1911.5.6.2)

Vu is limited by the following relationship.

(Vu / -Vc) 8 'cf Acv (UBC 1911.5.6.8)

Otherwise redimensioning of the concrete section is required. Here , thestrength reduction factor, is 0.85 for nonseismic design or for seismic designin Seismic Zones 0, 1, and 2 (UBC 1909.3.2.3) and is 0.60 for seismic designin Seismic Zones 3 and 4 (UBC 1909.3.4.1). The maximum of all the calcu-lated values obtained from each load combination are reported for the majorand minor directions of the column, along with the controlling shear force andassociated load combination label.

The column shear reinforcement requirements reported by the program arebased purely on shear strength consideration. Any minimum stirrup require-ments to satisfy spacing considerations or transverse reinforcement volumet-


Reference Technical Note 10 - 15

ric considerations must be investigated independently of the program by theuser.

ReferenceWhite. D. W., and J.F., Hajjar. 1991. Application of Second-Order Elastic

Analysis in LRFD: Research in Practice. Engineering Journal. AmericanInstitute of Steel Construction, Inc. Vol. 28, No. 4.



Technical Note 11Beam Design

This Technical Note describes how this program completes beam design whenthe UBC97 code is selected. The program calculates and reports the requiredareas of steel for flexure and shear based on the beam moments, shears, loadcombination factors and other criteria described herein.

OverviewIn the design of concrete beams, the program calculates and reports the re-quired areas of steel for flexure and shear based upon the beam moments,shears, load combination factors, and other criteria described below. The re-inforcement requirements are calculated at a user-defined number ofcheck/design stations along the beam span.

All beams are designed for major direction flexure and shear only.Effects caused by axial forces, minor direction bending, and torsionthat may exist in the beams must be investigated independently bythe user.

The beam design procedure involves the following steps:

Design beam flexural reinforcement

Design beam shear reinforcement

Design Beam Flexural ReinforcementThe beam top and bottom flexural steel is designed at check/design stationsalong the beam span. The following steps are involved in designing the flex-ural reinforcement for the major moment for a particular beam for a particu-lar section:

Determine the maximum factored moments

Determine the reinforcing steel

Beam Design Concrete Frame Design UBC97

Technical Note 11 - 2 Design Beam Flexural Reinforcement

Determine Factored MomentsIn the design of flexural reinforcement of Special, Intermediate, or Ordinarymoment resisting concrete frame beams, the factored moments for each loadcombination at a particular beam section are obtained by factoring the corre-sponding moments for different load cases with the corresponding load fac-tors.

The beam section is then designed for the maximum positive +uM and maxi-

mum negative uM factored moments obtained from all of the load combina-

tions.

Negative beam moments produce top steel. In such cases, the beam is al-ways designed as a rectangular section. Positive beam moments producebottom steel. In such cases, the beam may be designed as a Rectangular- ora T-beam.

Determine Required Flexural ReinforcementIn the flexural reinforcement design process, the program calculates both thetension and compression reinforcement. Compression reinforcement is addedwhen the applied design moment exceeds the maximum moment capacity ofa singly reinforced section. The user has the option of avoiding the compres-sion reinforcement by increasing the effective depth, the width, or the gradeof concrete.

The design procedure is based on the simplified rectangular stress block asshown in Figure 1 (UBC 1910.2). It is assumed that the compression carriedby concrete is less than 0.75 times that which can be carried at the balancedcondition (UBC 1910.3.3). When the applied moment exceeds the momentcapacity at this designed balanced condition, the area of compression rein-forcement is calculated assuming that the additional moment will be carriedby compression and additional tension reinforcement.

The design procedure used by the program for both rectangular and flangedsections (L- and T-beams) is summarized below. It is assumed that the de-

sign ultimate axial force does not exceed 0.1 'cf Ag (UBC 1910.3.3); hence, all

the beams are designed for major direction flexure and shear only.

Concrete Frame Design UBC97 Beam Design

Design Beam Flex al Reinforcement Technical Note 11 - 3

Figure 1 Design of a Rectangular Beam Section

Design for Rectangular BeamIn designing for a factored negative or positive moment, Mu (i.e., designingtop or bottom steel), the depth of the compression block is given by a (seeFigure 1), where,

a = d - bf

Md

c

u

'2

85.0

2,

where the value of is 0.90 (UBC 1909.3.2.1) in the above and the followingequations. Also 1 and cb are calculated as follows:

1 = 0.85 - 0.05

000,1000,4'cf , 0.65 1 0.85, (UBC 1910.2.7.3)

cb = dfE

E

ysc

sc

+

=

yf+000,87000,87

d. (UBC 1910.2.3, 1910.2.4)ur



The maximum allowed depth of the compression block is given by

amax = 0.751cb. (UBC 1910.2.7.1, 1910.3.3) If a amax, the area of tensile steel reinforcement is given by

As =

2a

df

M

y

u .

This steel is to be placed at the bottom if Mu is positive, or at the top if Muis negative.

If a > amax, compression reinforcement is required (UBC 1910.3.3) and iscalculated as follows:

The compressive force developed in concrete alone is given by

C = 0.85 'cf bamax, and (UBC 1910.2.7.1)

the moment resisted by concrete compression and tensile steel is

Muc = C

2maxad .

Therefore the moment resisted by compression steel and tensile steel is

Mus = Mu - Muc.

So the required compression steel is given by

'sA = )'(' ddf

M

s

us , where

'sf = 0.003Es

cdc '

. (UBC 1910.2.4)

The required tensile steel for balancing the compression in concrete is


Design Beam Flexural Reinforcement Technical Note 11 - 5

As1 =

2maxadf

M

y

uc , and

the tensile steel for balancing the compression in steel is given by

As2 = )'( ddfM

y

us .

Therefore, the total tensile reinforcement, As = As1 + As2, and total com-

pression reinforcement is 'sA . As is to be placed at bottom and 'sA is to

be placed at top if Mu is positive, and vice versa if Mu is negative.

Design for T-BeamIn designing for a factored negative moment, Mu (i.e., designing top steel),the calculation of the steel area is exactly the same as above, i.e., no T-Beamdata is to be used. See Figure 2. If Mu > 0, the depth of the compressionblock is given by

a = d -fc

u

bf

Md

'2

85.0

2 .

The maximum allowed depth of the compression block is given by

amax = 0.751cb. (UBC 1910.2.7.1)If a ds, the subsequent calculations for As are exactly the same as previouslydefined for the rectangular section design. However, in this case, the width ofthe compression flange is taken as the width of the beam for analysis. Com-pression reinforcement is required if a > amax.

If a > ds, calculation for As is performed in two parts. The first part is for bal-ancing the compressive force from the flange, Cf, and the second part is forbalancing the compressive force from the web, Cw, as shown in Figure 2. Cf isgiven by

Cf = 0.85'cf (bf - bw) ds.



Figure 2 Design of a T-Beam Section

Therefore, As1 = y

f

fC

and the portion of Mu that is resisted by the flange is

given by

Muf = Cf

2sdd .

Again, the value for is 0.90. Therefore, the balance of the moment, Mu to becarried by the web is given by

Muw = Mu - Muf.

The web is a rectangular section of dimensions bw and d, for which the designdepth of the compression block is recalculated as

a1 = d - wc

uw

bf

Md

'2

85.0

2.

If a1 amax, the area of tensile steel reinforcement is then given by



As2 =

21adf

M

y

uw , and

As = As1 + As2.

This steel is to be placed at the bottom of the T-beam.

If a1 > amax, compression reinforcement is required (UBC 1910.3.3) and iscalculated as follows:

The compressive force in web concrete alone is given by

C = 0.85 'cf bamax. (UBC 1910.2.7.1)

Therefore the moment resisted by concrete web and tensile steel is

Muc = C

2maxad , and

the moment resisted by compression steel and tensile steel is

Mus = Muw - Muc.

Therefore, the compression steel is computed as

'sA = )'(' ddf

M

s

us , where

'sf = 0.003Es

cdc '

. (UBC 1910.2.4)

The tensile steel for balancing compression in web concrete is

As2 =

2maxadf

M

y

uc , and

the tensile steel for balancing compression in steel is



As3 = ( ) 'ddfM

y

us .

The total tensile reinforcement, As = As1 + As2 + As3, and total compres-

sion reinforcement is 'sA . As is to be placed at bottom and 'sA is to be

placed at top.

Minimum Tensile ReinforcementThe minimum flexural tensile steel provided in a rectangular section in an Or-dinary moment resisting frame is given by the minimum of the two followinglimits:

As max

dbf

dbf

fw

yw

y

c 200 and 3 '

or (UBC 1910.5.1)

As 34

As(required) (UBC 1910.5.3)

Special Consideration for Seismic DesignFor Special moment resisting concrete frames (seismic design), the beam de-sign satisfies the following additional conditions (see also Table 1 for compre-hensive listing):

The minimum longitudinal reinforcement shall be provided at both the topand bottom. Any of the top and bottom reinforcement shall not be lessthan As(min) (UBC 1921.3.2.1).

As(min) max

dbf

dbf

fw

yw

y

c 200 and 3 '

or (UBC 1910.5.1, 1921.3.2.1)

As(min) 34

As(required). (UBC 1910.5.3, 1921.3.2.1)

The beam flexural steel is limited to a maximum given by

As 0.25 bwd. (UBC 1921.3.2.1)



Table 1 Design Criteria Table

Type ofCheck/Design

Ordinary MomentResisting F

Documents

ETABS - Concrete Frame Design Manual