ETABS. Integrated Building Design Software. Concrete Frame Design Manual. Computers and Structures, Inc. Berkeley, California, USA

Transcription

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2 ETABS Integrated Building Design Software Concrete Frame Design Manual Computers and Structures, Inc. Berkeley, California, USA Version 8 January 2002

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4 Copyright The computer program ETABS and all associated documentation are proprietary and copyrighted products. Worldwide rights of ownership rest with Computers and Structures, Inc. Unlicensed use of the program or reproduction of the documentation in any form, without prior written authorization from Computers and Structures, Inc., is explicitly prohibited. Further information and copies of this documentation may be obtained from: Computers and Structures, Inc University Avenue Berkeley, California USA Phone: (510) FAX: (510) (for general questions) (for technical support questions) web: Copyright Computers and Structures, Inc., 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. Adobe and Acrobat are registered trademarks of Adobe Systems Incorporated

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6 DISCLAIMER CONSIDERABLE TIME, EFFORT AND EXPENSE HAVE GONE INTO THE DEVELOPMENT AND DOCUMENTATION OF ETABS. THE PROGRAM HAS BEEN THOROUGHLY TESTED AND USED. IN USING THE PROGRAM, HOWEVER, THE USER ACCEPTS AND UNDERSTANDS THAT NO WARRANTY IS EXPRESSED OR IMPLIED BY THE DEVELOPERS OR THE DISTRIBUTORS ON THE ACCURACY OR THE RELIABILITY OF THE PROGRAM. THIS PROGRAM IS A VERY PRACTICAL TOOL FOR THE DESIGN/CHECK OF CONCRETE STRUCTURES. HOWEVER, THE USER MUST THOROUGHLY READ THE MANUAL AND CLEARLY RECOGNIZE THE ASPECTS OF CONCRETE DESIGN THAT THE PROGRAM ALGORITHMS DO NOT ADDRESS. THE USER MUST EXPLICITLY UNDERSTAND THE ASSUMPTIONS OF THE PROGRAM AND MUST INDEPENDENTLY VERIFY THE RESULTS.

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8 COMPUTERS AND STRUCTURES, INC., BERKELEY, CALIFORNIA DECEMBER 2001 CONCRETE FRAME DESIGN Contents General Concrete Frame Design Information 1 General Design Information Design Codes 1-1 Units 1-1 Overwriting the Frame Design Procedure for a Concrete 1-1 Frame Design Load Combinations 1-2 Design of Beams 1-2 Design of Columns 1-3 Beam/Column Flexural Capacity Ratios 1-4 Second Order P-Delta Effects 1-4 Element Unsupported Lengths 1-6 Analysis Sections and Design Sections Concrete Frame Design Process Concrete Frame Design Procedure Interactive Concrete Frame Design General 3-1 Concrete Design Information Form Output Data Plotted Directly on the Model Overview 4-1 Using the Print Design Tables Form 4-1 Design Input 4-2 Design Output 4-2 i

9 Concrete Frame Design Manual Concrete Frame Design Specific to UBC97 5 General and Notation Introduction to the UBC 97 Series of Technical Notes 5-1 Notation Preferences General 6-1 Using the Preferences Form 6-1 Preferences Overwrites General 7-1 Overwrites 7-1 Making Changes in the Overwrites Form 7-3 Resetting Concrete Frame Overwrites to Default 7-4 Values 8 Design Load Combinations 9 Strength Reduction Factors 10 Column Design Overview 10-1 Generation of Biaxial Interaction Surfaces 10-2 Calculate Column Capacity Ratio 10-5 Determine Factored Moments and Forces 10-6 Determine Moment Magnification Factors 10-6 Determine Capacity Ratio 10-8 Required Reinforcing Area Design Column Shear Reinforcement Determine Required Shear Reinforcement Reference Beam Design Overview 11-1 Design Beam Flexural Reinforcement 11-1 Determine Factored Moments 11-2 Determine Required Flexural Reinforcement 11-2 ii

10 Contents Design Beam Shear Reinforcement Joint Design Overview 12-1 Determine the Panel Zone Shear Force 12-1 Determine the Effective Area of Joint 12-5 Check Panel Zone Shear Stress 12-5 Beam/Column Flexural Capacity Ratios Input Data Input data 13-1 Using the Print Design Tables Form Output Details Using the Print Design Tables Form 14-3 Concrete Frame Design Specific to ACI General and Notation Introduction to the ACI Series of Technical 15-1 Notes Notation Preferences General 16-1 Using the Preferences Form 16-1 Preferences Overwrites General 17-1 Overwrites 17-1 Making Changes in the Overwrites Form 17-3 Resetting Concrete Frame Overwrites to Default 17-4 Values 18 Design Load Combinations 19 Strength Reduction Factors iii

11 Concrete Frame Design Manual 20 Column Design Overview 20-1 Generation of Biaxial Interaction Surfaces 20-2 Calculate Column Capacity Ratio 20-5 Determine Factored Moments and Forces 20-6 Determine Moment Magnification Factors 20-6 Determine Capacity Ratio 20-9 Required Reinforcing Area Design Column Shear Reinforcement Determine Section Forces Determine Concrete Shear Capacity Determine Required Shear Reinforcement References Beam Design Overview 21-1 Design Beam Flexural Reinforcement 21-1 Determine Factored Moments 21-2 Determine Required Flexural Reinforcement 21-2 Design for T-Beam 21-5 Minimum Tensile Reinforcement 21-8 Special Consideration for Seismic Design 21-8 Design Beam Shear Reinforcement 21-9 Determine Shear Force and Moment Determine Concrete Shear Capacity Determine Required Shear Reinforcement Joint Design Overview 22-1 Determine the Panel Zone Shear Force 22-1 Determine the Effective Area of Joint 22-4 Check Panel Zone Shear Stress 22-4 Beam/Column Flexural Capacity Ratios Input Data Input Data 23-1 Using the Print Design Tables Form 23-3 iv

12 Contents 24 Output Details Using the Print Design Tables Form 24-3 v

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14 COMPUTERS AND STRUCTURES, INC., BERKELEY, CALIFORNIA JANUARY 2002 CONCRETE FRAME DESIGN Technical Note 1 General Design Information This Technical Note presents some basic information and concepts helpful when performing concrete frame design using this program. Design Codes The design code is set using the Options menu > Preferences > Concrete Frame Design command. You can choose to design for any one design code in any one design run. You cannot design some elements for one code and others for a different code in the same design run. You can, however, perform different design runs using different design codes without rerunning the analysis. Units For concrete frame design in this program, any set of consistent units can be used for input. You can change the system of units at any time. Typically, design codes are based on one specific set of units. Overwriting the Frame Design Procedure for a Concrete Frame The 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 material property, its default design procedure is Concrete Frame Design. A concrete frame element can be switched between the Concrete Frame Design and the "None" design procedure. Assign a concrete frame element the "None" design procedure if you do not want it designed by the Concrete Frame Design postprocessor. Design Codes Technical Note 1-1

15 General Design Information Concrete Frame Design Change the default design procedure used for concrete frame elements by selecting the element(s) and clicking Design menu > Overwrite Frame Design Procedure. This change is only successful if the design procedure assigned to an element is valid for that element. For example, if you select a concrete element and attempt to change the design procedure to Steel Frame Design, the program will not allow the change because a concrete element cannot be changed to a steel frame element. Design Load Combinations The program creates a number of default design load combinations for concrete frame design. You can add in your own design load combinations. You can also modify or delete the program default load combinations. An unlimited 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 Design UBC97 Technical Note 8 Design Load Combination and Concrete Frame Design ACI Technical Note 18 Design Load Combination. Design of Beams The program designs all concrete frame elements designated as beam sections in their Frame Section Properties as beams (see Define menu >Frame Sections command and click the Reinforcement button). In the design of concrete beams, in general, the program calculates and reports the required areas of steel for flexure and shear based on the beam moments, shears, load combination factors, and other criteria, which are described in detail in Concrete Frame UBC97 Technical Note Beam Design 11 and Concrete Frame ACI Technical Note 21 Beam Design. The reinforcement requirements are calculated 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, and torsion that may exist in the beams must 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 factored moments and the determination of the reinforcing steel. Technical Note 1-2 Design Load Combinations

16 Concrete Frame Design General Design Information The beam section is designed for the maximum positive and maximum negative factored moment envelopes obtained from all of the load combinations. Negative beam moments produce top steel. In such cases, the beam is always designed as a rectangular section. Positive beam moments produce bottom steel. In such cases, the beam may be designed as a rectangular- or T-beam. For the design of flexural reinforcement, the beam is first designed as a singly reinforced beam. If the beam section is not adequate, the required compression reinforcement is calculated. In designing the shear reinforcement for a particular beam for a particular set of loading combinations at a particular station resulting from the beam major shear, the steps involve the determination of the factored shear force, the determination of the shear force that can be resisted by concrete, and the determination of the reinforcement steel required to carry the balance. Design of Columns The program designs all concrete frame elements designated as column sections in their Frame Section Properties as columns (see Define menu >Frame Sections command and click the Reinforcement button). 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 in terms of a column capacity ratio. The capacity ratio is a factor that gives an indication of the stress condition of the column with respect to the capacity of the column. The design procedure for reinforced concrete columns involves the following steps: Generate axial force-biaxial moment interaction surfaces for all of the different concrete section types of the model. Check the capacity of each column for the factored axial force and bending moments obtained from each load combination at each end of the column. This step is also used to calculate the required reinforcement (if none was specified) 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 that for beams, except that the effect of the axial force on the concrete shear capacity needs to be considered. See Concrete Frame UBC97 Technical Note 10 Design of Beams Technical Note 1-3

17 General Design Information Concrete Frame Design Column Design and Concrete Frame ACI Technical Note 20 Column Design for more information. Beam/Column Flexural Capacity Ratios When the ACI or UBC97 code is selected, the program calculates the ratio of the sum of the beam moment capacities to the sum of the column moment capacities at a particular joint for a particular column direction, major or minor. The capacities are calculated with no reinforcing overstrength factor, α, and including ϕ factors. The beam capacities are calculated for reversed situations and the maximum summation obtained is used. The moment capacities of beams that frame into the joint in a direction that is not parallel to the major or minor direction of the column are resolved along the direction that is being investigated and the resolved components are added to the summation. 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 is calculated from the program analysis load combinations. For each load combination, the moment capacity of each column under the influence of the corresponding axial load P u is then determined separately for the major and minor directions of the column, using the uniaxial column interaction diagram. The moment capacities of the two columns are added to give the capacity summation for the corresponding load combination. The maximum capacity summations obtained from all of the load combinations is used for the beam/column capacity ratio. The beam/column flexural capacity ratios are only reported for Special Moment-Resisting Frames involving seismic design load combinations. See Beam/Column Flexural Capacity Ratios in Concrete Frame UBC97 Technical Note 12 Joint Design or in Concrete Frame ACI Technical Note 22 Joint Design for more information. Second Order P-Delta Effects Typically, design codes require that second order P-Delta effects be considered when designing concrete frames. The P-Delta effects come from two sources. They are the global lateral translation of the frame and the local deformation of elements within the frame. Technical Note 1-4 Second Order P-Delta Effects

18 Concrete Frame Design General Design Information Original position of frame element shown by vertical line Position of frame element as a result of global lateral translation,, shown by dashed line δ Final deflected position of frame element that includes the global lateral translation,, and the local deformation of the element, δ Figure 1: The Total Second Order P-Delta Effects on a Frame Element Caused by Both and δ Consider the frame element shown in Figure 1, which is extracted from a story level of a larger structure. The overall global translation of this frame element is indicated by. The local deformation of the element is shown as δ. The total second order P-Delta effects on this frame element are those caused by both and δ. The program has an option to consider P-Delta effects in the analysis. Controls for considering this effect are found using the Analyze menu > Set Analysis Options command and then clicking the Set P-Delta Parameters button. When you consider P-Delta effects in the analysis, the program does a good job of capturing the effect due to the deformation shown in Figure 1, but it does not typically capture the effect of the δ deformation (unless, in the model, the frame element is broken into multiple pieces over its length). In design codes, consideration of the second order P-Delta effects is generally achieved by computing the flexural design capacity using a formula similar to that shown in Equation. 1. where, M CAP = am nt + bm lt Eqn. 1 M CAP = Flexural design capacity Second Order P-Delta Effects Technical Note 1-5

19 General Design Information Concrete Frame Design M nt = Required flexural capacity of the member assuming there is no translation of the frame (i.e., associated with the δ deformation in Figure 1) M lt = Required flexural capacity of the member as a result of lateral translation of the frame only (i.e., associated with the deformation in Figure 1) a = Unitless factor multiplying M nt b = Unitless factor multiplying M lt (assumed equal to 1 by the program; see below) When the program performs concrete frame design, it assumes that the factor b 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 concrete frame design in this program, you should consider P-Delta effects in the analysis before running the design. Element Unsupported Lengths The column unsupported lengths are required to account for column slenderness effects. The program automatically determines these unsupported lengths. They can also be overwritten by the user on an element-by-element basis, if desired, using the Design menu > Concrete Frame Design > View/Revise Overwrites command. There are two unsupported lengths to consider. They are L 33 and L 22, as shown in Figure 2. These are the lengths between support points of the element in the corresponding directions. The length L 33 corresponds to instability about the 3-3 axis (major axis), and L 22 corresponds to instability about the 2-2 axis (minor axis). The length L 22 is also used for lateral-torsional buckling caused by major direction bending (i.e., about the 3-3 axis). In determining the values for L 22 and L 33 of the elements, the program recognizes various aspects of the structure that have an effect on these lengths, such as member connectivity, diaphragm constraints and support points. The program automatically locates the element support points and evaluates the corresponding unsupported length. Technical Note 1-6 Element Unsupported Lengths

20 Concrete Frame Design General Design Information Figure 2: Major and Minor Axes of Bending It is possible for the unsupported length of a frame element to be evaluated by the program as greater than the corresponding element length. For example, assume a column has a beam framing into it in one direction, but not the other, at a floor level. In this case, the column is assumed to be supported in one direction only at that story level, and its unsupported length in the other direction will exceed the story height. Analysis Sections and Design Sections Analysis sections are those section properties used to analyze the model when you click the Analyze menu > Run Analysis command. The design section is whatever section has most currently been designed and thus designated the current design section. Tip: It is important to understand the difference between analysis sections and design sections. Analysis Sections and Design Sections Technical Note 1-7

21 General Design Information Concrete Frame Design It is possible for the last used analysis section and the current design section to be different. For example, you may have run your analysis using a W18X35 beam and then found in the design that a W16X31 beam worked. In that case, the last used analysis section is the W18X35 and the current design section is the W16X31. Before you complete the design process, verify that the last used analysis section and the current design section are the same. The Design menu > Concrete Frame Design > Verify Analysis vs Design Section command is useful for this task. The program keeps track of the analysis section and the design section separately. 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 the analysis 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 the same 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 section to be the beam with the median weight in the auto select list. Unlocking a model deletes the design results, but it does not delete or change the design section. Using the Design menu > Concrete Frame Design > Select Design Combo command to change a design load combination deletes the design results, but it does not delete or change the design section. Using the Define menu > Load Combinations command to change a design load combination deletes the design results, but it does not delete or change the design section. Using the Options menu > Preferences > Concrete Frame Design command to change any of the composite beam design preferences deletes the design results, but it does not delete or change the design section. Deleting the static nonlinear analysis results also deletes the design results for any load combination that includes static nonlinear forces. Typically, Technical Note 1-8 Analysis Sections and Design Sections

22 Concrete Frame Design General Design Information static nonlinear analysis and design results are deleted when one of the following actions is taken: Use the Define menu > Frame Nonlinear Hinge Properties command to redefine existing or define new hinges. Use the Define menu > Static Nonlinear/Pushover Cases command to redefine existing or define new static nonlinear load cases. Use the Assign menu > Frame/Line > Frame Nonlinear Hinges command to add or delete hinges. Again, note that these actions delete only results for load combinations that include static nonlinear forces. Analysis Sections and Design Sections Technical Note 1-9

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24 COMPUTERS AND STRUCTURES, INC., BERKELEY, CALIFORNIA DECEMBER 2001 CONCRETE FRAME DESIGN Technical Note 2 Concrete Frame Design Process This Technical Note describes a basic concrete frame design process using this program. Although the exact steps you follow may vary, the basic design process should be similar to that described herein. Other Technical Notes in the Concrete Frame Design series provide additional information, including the distinction between analysis sections and design sections (see Analysis Sections and Design Sections in Concrete Frame Design Technical Note 1 General Design Information). The concrete frame design postprocessor can design or check concrete columns and can design concrete beams. Important note: A concrete frame element is designed as a beam or a column, depending on how its frame section property was designated when it was defined using the Define menu > Frame Sections command. Note that when using this command, after you have specified that a section has a concrete material property, you can click on the Reinforcement button and specify whether it is a beam or a column. Concrete Frame Design Procedure The following sequence describes a typical concrete frame design process for a new building. Note that although the sequence of steps you follow may vary, the basic process probably will be essentially the same. 1. Use the Options menu > Preferences > Concrete Frame Design command to choose the concrete frame design code and to review other concrete frame design preferences and revise them if necessary. Note that default values are provided for all concrete frame design preferences, so it is unnecessary to define any preferences unless you want to change some of the default values. See Concrete Frame Design ACI UBC97 Technical Notes 6 Preferences and Concrete Frame Design ACI Technical Notes 16 Preferences for more information. Concrete Frame Design Procedure Technical Note 2-1

25 Concrete Frame Design Process Concrete Frame Design 2. Create the building model. 3. Run the building analysis using the Analyze menu > Run Analysis command. 4. Assign concrete frame overwrites, if needed, using the Design menu > Concrete Frame Design > View/Revise Overwrites command. Note that you must select frame elements before using this command. Also note that default values are provided for all concrete frame design overwrites, so it is unnecessary to define any overwrites unless you want to change some of the default values. Note that the overwrites can be assigned before or after the analysis is run. See Concrete Frame Design UBC97 Technical Note 7 Overwrites and Concrete Frame Design ACI Technical Note 17 Overwrites for more information. 5. To use any design load combinations other than the defaults created by the program for your concrete frame design, click the Design menu > Concrete Frame Design > Select Design Combo command. Note that you must have already created your own design combos by clicking the Define menu > Load Combinations command. See Concrete Frame Design UBC97 Technical Note 8 Design Load Combinations and Concrete Frame Design ACI Technical Note 18 Design Load Combinations for more information. 6. Click the Design menu > Concrete Frame Design > Start Design/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 Design Info command to display design input and output information on the model. See Concrete Frame Design Technical Note 4 Output Data Plotted Directly on the Model for more information. b. Right click on a frame element while the design results are displayed on it to enter the interactive design mode and interactively design the frame element. Note that while you are in this mode, you can revise overwrites and immediately see the results of the new design. See Concrete Frame Design Technical Note 3 Interactive Concrete Frame Design for more information. Technical Note 2-2 Concrete Frame Design Procedure

26 Concrete Frame Design Concrete Frame Design Process If design results are not currently displayed (and the design has been run), click the Design menu > Concrete Frame Design > Interactive Concrete Frame Design command and then right click a frame element to enter the interactive design mode for that element. 8. Use the File menu > Print Tables > Concrete Frame Design command to print concrete frame design data. If you select frame elements before using this command, data is printed only for the selected elements. See Concrete Frame Design UBC97 Technical Note 14 Output Details and Concrete Frame Design ACI Technical Note 24 Output Details for more information. 9. Use the Design menu > Concrete Frame Design > Change Design Section command to change the design section properties for selected frame elements. 10. Click the Design menu > Concrete Frame Design > Start Design/Check of Structure command to rerun the concrete frame design with the new section properties. Review the results using the procedures described in Item Rerun the building analysis using the Analyze menu > Run Analysis command. Note that the section properties used for the analysis are the last specified design section properties. 12. Click the Design menu > Concrete Frame Design > Start Design/Check of Structure command to rerun the concrete frame design with the new analysis results and new section properties. Review the results using the procedures described above. 13. Again use the Design menu > Concrete Frame Design > Change Design Section command to change the design section properties for selected frame elements, if necessary. 14. Repeat the processes in steps 10, 11 and 12 as many times as necessary. 15. Rerun the building analysis using the Analyze menu > Run Analysis command. Note that the section properties used for the analysis are the last specified design section properties. Concrete Frame Design Procedure Technical Note 2-3

27 Concrete Frame Design Process Concrete Frame Design Note: Concrete frame design is an iterative process. Typically, the analysis and design will be rerun multiple times to complete a design. 16. Click the Design menu > Concrete Frame Design > Start Design/Check of Structure command to rerun the concrete frame design with the new section properties. Review the results using the procedures described in Item Click the Design menu > Concrete Frame Design > Verify Analysis vs Design Section command to verify that all of the final design sections are the same as the last used analysis sections. 18. Use the File menu > Print Tables > Concrete Frame Design command to print selected concrete frame design results, if desired. It is important to note that design is an iterative process. The sections used in the original analysis are not typically the same as those obtained at the end of the design process. Always run the building analysis using the final frame section sizes and then run a design check using the forces obtained from that analysis. Use the Design menu > Concrete Frame Design > Verify Analysis vs Design Section command to verify that the design sections are the same as the analysis sections. Technical Note 2-4 Concrete Frame Design Procedure

28 COMPUTERS AND STRUCTURES, INC., BERKELEY, CALIFORNIA DECEMBER 2001 CONCRETE FRAME DESIGN Technical Note 3 Interactive 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 for any concrete frame design and interactively revise the design assumptions and immediately review the revised results. General Note that a design must have been run for the interactive design mode to be available. To run a design, click the Design menu > Concrete Frame Design > Start Design/Check of Structure command. Right click on a frame element while the design results are displayed on it to enter the interactive design mode and interactively design the element in the Concrete Design Information form. If design results are not currently displayed (and a design has been run), click the Design menu > Concrete Frame Design > Interactive Concrete Frame Design command and then right click a frame element to enter the interactive design mode for that element. Important note: A concrete frame element is designed as a beam or a column, depending on how its frame section property was designated when it was defined using the Define menu > Frame Sections command and the Reinforcement button, which is only available if it is a concrete section. Concrete Design Information Form Table 1 describe the features that are included in the Concrete Design Information form. General Technical Note 3-1

29 Interactive Concrete Frame Design Concrete Frame Design Table 1 Concrete Design Information Form Item Story Beam Column Section Name DESCRIPTION This is the story level ID associated with the frame element. This is the label associated with a frame element that has been assigned a concrete frame section property that is designated as a beam. See the important note previously in this Technical Note for more information. This is the label associated with a frame element that has been assigned a concrete frame section property that is designated as a column. See the important note previously in this Technical Note for more information. This is the label associated with a frame element that has been assigned a concrete frame section property. Reinforcement Information The reinforcement information table on the Concrete Design Information form shows the output information obtained for each design load combination at each output station along the frame element. For columns that are designed by this program, the item with the largest required amount of longitudinal reinforcing is initially highlighted. For columns that are checked by this program, the item with the largest capacity ratio is initially highlighted. For beams, the item with the largest required amount of bottom steel is initially highlighted. Following are the possible headings in the table: Combo ID Station location Longitudinal reinforcement Capacity ratio This is the name of the design load combination considered. This is the location of the station considered, measured from the i-end of the frame element. This item applies to columns only. It also only applies to columns for which the program designs the longitudinal reinforcing. It is the total required area of longitudinal reinforcing steel. This item applies to columns only. It also only applies to columns for which you have specified the location and size of reinforcing bars and thus the program checks the design. This item is the capacity ratio. Technical Note 3-2 Table 1 Concrete Design Information Form

30 Concrete Frame Design Interactive Concrete Frame Design Table 1 Concrete Design Information Form Item Major shear reinforcement Minor shear reinforcement Top steel Bottom steel Shear steel Overwrites Button DESCRIPTION The capacity ratio is determined by first extending a line from the origin of the PMM interaction surface to the point representing the P, M2 and M3 values for the designated load combination. Assume the length of this first line is designated L1. Next, a second line is extended from the origin of the PMM interaction surface through the point representing the P, M2 and M3 values for the designated load combination until it intersects the interaction surface. Assume the length of this line from the origin to the interaction surface is designated L2. The capacity ratio is equal to L1/L2. This item applies to columns only. It is the total required area of shear reinforcing per unit length for shear acting in the column major direction. This item applies to columns only. It is the total required area of shear reinforcing per unit length for shear acting in the column minor direction. This item applies to beams only. It is the total required area of longitudinal top steel at the specified station. This item applies to beams only. It is the total required area of longitudinal bottom steel at the specified station. This item applies to beams only. It is the total required area of shear reinforcing per unit length at the specified station for loads acting in the local 2-axis direction of the beam. Click this button to access and make revisions to the concrete frame overwrites and then immediately see the new design results. If you modify some overwrites in this mode and you exit both the Concrete Frame Design Overwrites form and the Concrete Design Information form by clicking their respective OK buttons, the changes to the overwrites are saved permanently. When you exit the Concrete Frame Design Overwrites form by clicking the OK button the changes are temporarily saved. If you then exit the Concrete Design Information form by clicking the Cancel button the changes you made to the concrete frame overwrites are considered temporary only and are not permanently saved. Permanent saving of the overwrites does not actually occur until you click the OK button in the Concrete Design Information form as well as the Concrete Frame Design Overwrites form. Table 1 Concrete Design Information Form Technical Note 3-3

31 Interactive Concrete Frame Design Concrete Frame Design Table 1 Concrete Design Information Form Item Details Button Interaction Button DESCRIPTION Clicking this button displays design details for the frame element. Print this information by selecting Print from the File menu that appears at the top of the window displaying the design details. Clicking this button displays the biaxial interaction curve for the concrete section at the location in the element that is highlighted in the table. Technical Note 3-4 Table 1 Concrete Design Information Form

32 COMPUTERS AND STRUCTURES, INC., BERKELEY, CALIFORNIA DECEMBER 2001 CONCRETE FRAME DESIGN Technical Note 4 Output Data Plotted Directly on the Model This Technical Note describes the input and output data that can be plotted directly on the model. Overview Use the Design menu > Concrete Frame Design > Display Design Info command 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 and output data. Using the Print Design Tables Form To print the concrete frame input summary directly to a printer, use the File menu > Print Tables > Concrete Frame Design command and click the check box on the Print Design Tables form. Click the OK button to send the print to your printer. Click the Cancel button rather than the OK button to cancel the print. Use the File menu > Print Setup command and the Setup>> button to change printers, if necessary. To print the concrete frame input summary to a file, click the Print to File check box on the Print Design Tables form. Click the Filename>> button to change the path or filename. Use the appropriate file extension for the desired format (e.g.,.txt,.xls,.doc). Click the OK buttons on the Open File for Printing Tables form and the Print Design Tables form to complete the request. Note: The File menu > Display Input/Output Text Files command is useful for displaying output that is printed to a text file. The Append check box allows you to add data to an existing file. The path and filename of the current file is displayed in the box near the bottom of the Print Design Tables form. Data will be added to this file. Or use the Filename Overview Technical Note 4-1

33 Output Data Plotted Directly on the Model Concrete Frame Design button to locate another file, and when the Open File for Printing Tables caution 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 Only check box will be checked. The print will be for the selected steel frame element(s) only. Design Input The following types of data can be displayed directly on the model by selecting the data type (shown in bold type) from the drop-down list on the Display Design Results form. Display this form by selecting he Design menu > Concrete 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 Design UBC97 Technical Note 13 Input Data and Concrete Frame Design ACI Technical Note 23 Input Data. Design Output The following types of data can be displayed directly on the model by selecting the data type (shown in bold type) from the drop-down list on the Display Design Results form. Display this form by selecting he Design menu > Concrete Frame Design > Display Design Info command. Technical Note 4-2 Design Input

34 Concrete Frame Design Output Data Plotted Directly on the Model 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 Design ACI Technical Note 24 Output Details and Concrete Frame Design UBC97 Technical Note 14 Output Details. Design Output Technical Note 4-3

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36 COMPUTERS AND STRUCTURES, INC., BERKELEY, CALIFORNIA DECEMBER 2001 CONCRETE FRAME DESIGN UBC97 Technical Note 5 General and Notation Introduction to the UBC97 Series of Technical Notes The Concrete Frame Design UBC97 series of Technical Notes describes in detail the various aspects of the concrete design procedure that is used by this program when the user selects the UBC97 Design Code (ICBO 1997). The various notations used in this series are listed herein. The design is based on user-specified loading combinations. The program provides a set of default load combinations that should satisfy requirements for the design of most building type structures. See Concrete Frame Design UBC97 Technical Note 8 Design Load Combinations for more information. When using the UBC 97 option, a frame is assigned to one of the following five 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, the Seismic Zone can be overwritten in the Preference form to change the default. See Concrete Frame Design UBC97 Technical Note 6 Preferences for more information. When using the UBC 97 option, the following Framing Systems are recognized and designed according to the UBC design provisions (UBC 1627, 1921): Ordinary Moment-Resisting Frame (OMF) General and Notation Technical Note 5-1

37 General and Notation Concrete Frame Design UBC97 Intermediate Moment-Resisting Frame (IMRF) Special Moment-Resisting Frame (SMRF) The Ordinary Moment-Resisting Frame (OMF) is appropriate in minimal seismic risk areas, especially in Seismic Zones 0 and 1. The Intermediate Moment-Resisting Frame (IMRF) is appropriate in moderate seismic risk areas, specially in Seismic Zone 2. The Special Moment-Resisting Frame (SMRF) is appropriate in high seismic risk areas, specially in Seismic Zones 3 and 4. The UBC seismic design provisions are considered in the program. The details of the design criteria used for the different framing systems are described in Concrete Frame Design UBC97 Technical Note 9 Strength Reduction Factors, Concrete Frame Design UBC97 Technical Note 10 Column Design, Concrete Frame Design UBC97 Technical Note 11 Beam Design, and Concrete Frame Design UBC97 Technical Note 12 Joint Design. By default the frame type is taken in the program as OMRF in Seismic Zone 0 and 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 a member-by-member basis. See Concrete Frame Design UBC97 Technical Note 7 Overwrites for more information. If any member is assigned with a frame type, the change of the Seismic Zone in the Preferences will not modify the frame type of an individual member that has been assigned a frame type. The program also provides input and output data summaries, which are described in Concrete Frame Design UBC97 Technical Note 13 Input Data and Concrete Frame Design UBC97 Technical Note 14 Output Details. English as well as SI and MKS metric units can be used for input. The code is based on Inch-Pound-Second units. For simplicity, all equations and descriptions presented in this Technical Note correspond to Inch-Pound-Second units unless otherwise noted. Notation A cv Area of concrete used to determine shear stress, sq-in A g A s Gross area of concrete, sq-in Area of tension reinforcement, sq-in Technical Note 5-2 General and Notation

38 Concrete Frame Design UBC97 General and Notation ' As Area of compression reinforcement, sq-in A s(required) A st A v C m D' E c E s I g I se L M 1 M 2 M c M ns M s M u M ux M uy P b Area of steel required for tension reinforcement, sq-in Total area of column longitudinal reinforcement, sq-in Area of shear reinforcement, sq-in Coefficient, dependent upon column curvature, used to calculate moment magnification factor Diameter of hoop, in Modulus of elasticity of concrete, psi Modulus of elasticity of reinforcement, assumed as 29,000,000 psi (UBC ) Moment of inertia of gross concrete section about centroidal axis, neglecting reinforcement, in 4 Moment of inertia of reinforcement about centroidal axis of member cross section, in 4 Clear unsupported length, in Smaller factored end moment in a column, lb-in Larger factored end moment in a column, lb-in Factored moment to be used in design, lb-in Nonsway component of factored end moment, lb-in Sway component of factored end moment, lb-in Factored moment at section, lb-in Factored moment at section about X-axis, lb-in Factored moment at section about Y-axis, lb-in Axial load capacity at balanced strain conditions, lb General and Notation Technical Note 5-3

39 General and Notation Concrete Frame Design UBC97 P c P max P 0 P u V c V E V D+L V u V p a a b b b f b w c c b d d' d s ' fc Critical buckling strength of column, lb Maximum axial load strength allowed, lb Acial load capacity at zero eccentricity, lb Factored axial load at section, lb Shear resisted by concrete, lb Shear force caused by earthquake loads, lb Shear force from span loading, lb Factored shear force at a section, lb Shear force computed from probable moment capacity, lb Depth of compression block, in Depth of compression block at balanced condition, in Width of member, in Effective width of flange (T-Beam section), in Width of web (T-Beam section), in Depth to neutral axis, in Depth to neutral axis at balanced conditions, in Distance from compression face to tension reinforcement, in Concrete cover to center of reinforcing, in Thickness of slab (T-Beam section), in Specified compressive strength of concrete, psi f y Specified yield strength of flexural reinforcement, psi f y 80,000 psi (UBC ) Technical Note 5-4 General and Notation

40 Concrete Frame Design UBC97 General and Notation f ys h k r α β 1 β d δ s δ ns ε c ε s ϕ Specified yield strength of flexural reinforcement, psi Dimension of column, in Effective length factor Radius of gyration of column section, in Reinforcing steel overstrength factor Factor for obtaining depth of compression block in concrete Absolute value of ratio of maximum factored axial dead load to maximum factored axial total load Moment magnification factor for sway moments Moment magnification factor for nonsway moments Strain in concrete Strain in reinforcing steel Strength reduction factor General and Notation Technical Note 5-5

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42 COMPUTERS AND STRUCTURES, INC., BERKELEY, CALIFORNIA DECEMBER 2001 CONCRETE FRAME DESIGN UBC97 Technical Note 6 Preferences This Technical Note describes the items in the Preferences form. General The concrete frame design preferences in this program are basic assignments that apply to all concrete frame elements. Use the Options menu > Preferences > Concrete Frame Design command to access the Preferences form where 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. You should, however, at least review the default values for the preference items to make sure they are acceptable to you. Using the Preferences Form To view preferences, select the Options menu > Preferences > Concrete Frame Design. The Preferences form will display. The preference options are displayed in a two-column spreadsheet. The left column of the spreadsheet displays the preference item name. The right column of the spreadsheet displays the preference item value. To change a preference item, left click the desired preference item in either the left or right column of the spreadsheet. This activates a drop-down box or highlights the current preference value. If the drop-down box appears, select a new value. If the cell is highlighted, type in the desired value. The preference value will update accordingly. You cannot overwrite values in the dropdown 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 the changes to be accepted by the program. If you click the Cancel button to exit General Technical Note 6-1

43 Preferences Concrete Frame Design UBC97 the form, any changes made to the preferences are ignored and the form is closed. Preferences For purposes of explanation in this Technical Note, the preference items are presented in Table 1. The column headings in the table are described as follows: Item: The name of the preference item as it appears in the cells at the left side of the Preferences form. Possible Values: The possible values that the associated preference item can have. Default Value: The built-in default value that the program assumes for the associated preference item. Description: A description of the associated preference item. Table 1: Concrete Frame Preferences Item Possible Values Default Value Description Design Code Any code in the program UBC97 Design code used for design of concrete frame elements. Phi Bending Tension Phi Compression Tied Phi Compression Spiral >0 0.9 Unitless strength reduction factor per UBC >0 0.7 Unitless strength reduction factor per UBC > Unitless strength reduction factor per UBC Phi Shear > Unitless strength reduction factor per UBC Number Interaction Curves Number of equally spaced interaction curves used to create a full 360-degree interaction surface (this item should be a multiple of four). We recommend that you use 24 for this item. Technical Note 6-2 Preferences

44 Concrete Frame Design UBC97 Preferences Table 1: Concrete Frame Preferences Item Number Interaction Points Time History Design Possible Values Any odd value 1.0 Envelopes or Step-by-Step Default Value Description 11 Number of points used for defining a single curve in a concrete frame interaction surface (this item should be odd). Envelopes Toggle for design load combinations that include a time history designed for the envelope of the time history, or designed step-by-step for the entire time history. If a single design load combination has more than one time history case in it, that design load combination is designed for the envelopes of the time histories, regardless of what is specified here. Preferences Technical Note 6-3

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46 COMPUTERS AND STRUCTURES, INC., BERKELEY, CALIFORNIA DECEMBER 2001 CONCRETE FRAME DESIGN UBC97 Technical Note 7 Overwrites General The concrete frame design overwrites are basic assignments that apply only to those elements to which they are assigned. This Technical Note describes concrete frame design overwrites for UBC97. To access the overwrites, select an 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 to specify or change any of the overwrites. However, at least review the default values for the overwrite items to make sure they are acceptable. When changes are made to overwrite items, the program applies the changes only to the elements to which they are specifically assigned; that is, to the elements that are selected when the overwrites are changed. Overwrites For explanation purposes in this Technical Note, the overwrites are presented in 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. To save space in the formes, these names are generally short. Possible Values: The possible values that the associated overwrite item can have. Default Value: The default value that the program assumes for the associated overwrite item. Description: A description of the associated overwrite item. An explanation of how to change an overwrite is provided at the end of this Technical Note. Overwrites Technical Note 7-1

47 Overwrites Concrete Frame Design UBC97 Table 1 Concrete Frame Design Overwrites Item Possible Values Default Value Description Element Section Element Type Live Load Reduction Factor Horizontal Earthquake Factor Unbraced Length Ratio (Major) Unbraced Length Ratio (Minor) Effective Length Factor (K Major) Effective Length Factor (K Minor) Moment Coefficient (Cm Major) Moment Coefficient (Cm Minor) NonSway Moment Factor (Dns Major) Sway Special, Sway Intermediate, Sway Ordinary NonSway >0 1.0 >0 1.0 >0 1.0 >0 1.0 >0 1.0 >0 1.0 >0 1.0 >0 1.0 >0 1.0 Sway Special Frame type; see UBC to Used to reduce the live load contribution to the factored loading See UBC See UBC See UBC relates actual moment diagram to an equivalent uniform moment diagram. 1 See UBC relates actual moment diagram to an equivalent uniform moment diagram. 1 See UBC Technical Note 7-2 Overwrites

48 Concrete Frame Design UBC97 Overwrites Table 1 Concrete Frame Design Overwrites Item Possible Values Default Value Description NonSway Moment Factor (Dns Minor) Sway Moment Factor (Ds Major) Sway Moment Factor (Ds Minor) 1 See UBC See UBC See UBC Making Changes in the Overwrites Form To access the concrete frame overwrites, select an element and click the Design menu > Concrete Frame Design > View/Revise Overwrites command. The overwrites are displayed in the form with a column of check boxes and a two-column spreadsheet. The left column of the spreadsheet contains the name of the overwrite item. The right column of the spreadsheet contains the overwrites values. Initially, the check boxes in the Concrete Frame Design Overwrites form are all unchecked and all of the cells in the spreadsheet have a gray background to indicate that they are inactive and the items in the cells cannot be changed. The names of the overwrite items are displayed in the first column of the spreadsheet. The values of the overwrite items are visible in the second column of the spreadsheet if only one element was selected before the overwrites form was accessed. If multiple elements were selected, no values show for the overwrite items in the second column of the spreadsheet. After selecting one or multiple elements, check the box to the left of an overwrite item to change it. Then left click in either column of the spreadsheet to activate a drop-down box or highlight the contents in the cell in the right column of the spreadsheet. If the drop-down box appears, select a value from Overwrites Technical Note 7-3

49 Overwrites Concrete Frame Design UBC97 the box. If the cell contents is highlighted, type in the desired value. The overwrite will reflect the change. You cannot change the values of the dropdown boxes. When changes to the overwrites have been completed, click the OK button to close the form. The program then changes all of the overwrite items whose associated check boxes are checked for the selected members. You must click the OK button for the changes to be accepted by the program. If you click the Cancel button to exit the form, any changes made to the overwrites are ignored and the form is closed. Resetting Concrete Frame Overwrites to Default Values Use the Design menu > Concrete Frame Design > Reset All Overwrites command to reset all of the steel frame overwrites. All current design results will be deleted when this command is executed. Important note about resetting overwrites: The program defaults for the overwrite items are built into the program. The concrete frame overwrite values that were in a.edb file that you used to initialize your model may be different 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 values that were in the.edb file used to initialize the model. Technical Note 7-4 Overwrites

50 COMPUTERS AND STRUCTURES, INC., BERKELEY, CALIFORNIA DECEMBER 2001 CONCRETE FRAME DESIGN UBC97 Technical Note 8 Design Load Combinations The design load combinations are the various combinations of the prescribed load 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 stress check may need only one load combination, namely 1.4 DL LL (UBC ). However, 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 forces are reversible, the following load combinations may need to be considered (UBC ). 1.4 DL (UBC ) 1.4 DL LL (UBC ) 0.9 DL ± 1.3 WL (UBC ) 0.75 (1.4 DL LL ± 1.7 WL) (UBC ) 0.9 DL ± 1.0 EL (UBC , ) 1.2 DL LL ± 1.0 EL) (UBC , ) These are also the default design load combinations in the program whenever the UBC97 code is used. Live load reduction factors can be applied to the member forces of the live load condition on an element-by-element basis to reduce the contribution of the live load to the factored loading. See Concrete Frame Design UBC97 Technical Note 7 Overwrites for more information. Design Load Combinations Technical Note 8-1

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52 COMPUTERS AND STRUCTURES, INC., BERKELEY, CALIFORNIA DECEMBER 2001 CONCRETE FRAME DESIGN UBC97 Technical Note 9 Strength Reduction Factors The strength reduction factors, ϕ, are applied on the nominal strength to obtain the design strength provided by a member. The ϕ factors for flexure, axial force, shear, and torsion are as follows: ϕ = 0.90 for flexure (UBC ) ϕ = 0.90 for axial tension (UBC ) ϕ = 0.90 for axial tension and flexure (UBC ) ϕ = 0.75 for axial compression, and axial compression and flexure (spirally reinforced column) (UBC ) ϕ = 0.70 for axial compression, and axial compression and flexure (tied column) (UBC ) ϕ = 0.85 for shear and torsion (non-seismic design) (UBC ) ϕ = 0.60 for shear and torsion (UBC ) Strength Reduction Factors Technical Note 9-1

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54 COMPUTERS AND STRUCTURES, INC., BERKELEY, CALIFORNIA DECEMBER 2001 CONCRETE FRAME DESIGN UBC97 Technical Note 10 Column Design This Technical Note describes how the program checks column capacity or designs reinforced concrete columns when the UBC97 code is selected. Overview The program can be used to check column capacity or to design columns. If you define the geometry of the reinforcing bar configuration of each concrete column section, the program will check the column capacity. Alternatively, the program can calculate the amount of reinforcing required to design the column. The design procedure for the reinforced concrete columns of the structure involves the following steps: Generate axial force/biaxial moment interaction surfaces for all of the different concrete section types of the model. A typical biaxial interaction surface is shown in Figure 1. When the steel is undefined, the program generates the interaction surfaces for the range of allowable reinforcement 1 to 8 percent for Ordinary and Intermediate moment resisting frames (UBC ) and 1 to 6 percent for Special moment resisting frames (UBC ). Calculate the capacity ratio or the required reinforcing area for the factored axial force and biaxial (or uniaxial) bending moments obtained from each loading combination at each station of the column. The target capacity 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 associated with this process. Overview Technical Note 10-1

55 Column Design Concrete Frame Design UBC97 Figure 1 A Typical Column Interaction Surface Generation of Biaxial Interaction Surfaces The column capacity interaction volume is numerically described by a series of discrete points that are generated on the three-dimensional interaction failure surface. In addition to axial compression and biaxial bending, the formulation allows for axial tension and biaxial bending considerations. A typical interaction diagram is shown in Figure 1. Technical Note 10-2 Generation of Biaxial Interaction Surfaces

56 Concrete Frame Design UBC97 Column Design The coordinates of these points are determined by rotating a plane of linear strain in three dimensions on the section of the column. See Figure 2. The linear strain diagram limits the maximum concrete strain, ε c, at the extremity of the section, to (UBC ). The formulation is based consistently upon the general principles of ultimate strength design (UBC ), and allows for any doubly symmetric rectangular, square, or circular column section. The stress in the steel is given by the product of the steel strain and the steel modulus of elasticity, ε s E s, and is limited to the yield stress of the steel, f y (UBC ). The area associated with each reinforcing bar is assumed to be placed at the actual location of the center of the bar and the algorithm does not assume any further simplifications with respect to distributing the area of steel over the cross section of the column, such as an equivalent steel tube or cylinder. See Figure 3. ' c The concrete compression stress block is assumed to be rectangular, with a stress value of 0.85 f (UBC ). See Figure 3. The interaction algorithm provides correction to account for the concrete area that is displaced by the reinforcement in the compression zone. The effects of the strength reduction factor, ϕ, are included in the generation of the interaction surfaces. The maximum compressive axial load is limited to ϕp n(max), where ϕp n(max) = 0.85ϕ[0.85 f c ' (A g -A st )+f y A st ] (spiral) (UBC ) ϕp n(max) = 0.85ϕ[0.85 f c ' (A g -A st )+f y A st ] (tied) (UBC ) ϕ = 0.70 for tied columns (UBC ) ϕ = 0.75 for spirally reinforced columns (UBC ) The value of ϕ used in the interaction diagram varies from ϕ min to 0.9 based on the axial load. For low values of axial load, ϕ is increased linearly from ϕ min to 0.9 as the nominal capacity ϕp n decreases from the smaller of ϕp b or 0.1 f ' c A g to zero, where P b is the axial force at the balanced condition. In cases involving axial tension, ϕ is always 0.9 (UBC ). Generation of Biaxial Interaction Surfaces Technical Note 10-3

57 Column Design Concrete Frame Design UBC97 Figure 2 Idealized Strain Distribution for Generation of Interaction Surfaces Technical Note 10-4 Generation of Biaxial Interaction Surfaces

58 Concrete Frame Design UBC97 Column Design Figure 3 Idealization of Stress and Strain Distribution in a Column Section Calculate Column Capacity Ratio The column capacity ratio is calculated for each loading combination at each output station of each column. The following steps are involved in calculating the capacity ratio of a particular column for a particular loading combination at a particular location: Determine the factored moments and forces from the analysis load cases and the specified load combination factors to give P u, M ux, and M uy. Determine the moment magnification factors for the column moments. Apply the moment magnification factors to the factored moments. Determine whether 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 the identification of the individual column as either sway or non-sway. Calculate Column Capacity Ratio Technical Note 10-5

59 Column Design Concrete Frame Design UBC97 The following three sections describe in detail the algorithms associated with this process. 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 u, M ux, and M uy. The factored moments are further increased for non-sway columns, if required, to obtain minimum eccentricities of ( h) inches, where h is the dimension of the column in the corresponding direction (UBC ). Determine Moment Magnification Factors The moment magnification factors are calculated separately for sway (overall stability effect), δ s, and for non-sway (individual column stability effect), δ ns. Also the moment magnification factors in the major and minor directions are in general different. The program assumes that it performs a P-delta analysis and, therefore, moment magnification factors for moments causing sidesway are taken as unity (UBC ). For the P-delta analysis, the load should correspond to a load combination of 0.75 (1.4 dead load live load)/ϕ if wind load governs, or (1.2 dead load live load)/ϕ if seismic load governs, where ϕ is the understrength factor for stability, which is taken as 0.75 (UBC ). See also White and Hajjar (1991). The moment obtained from analysis is separated into two components: the sway (M s ) and the non-sway (M s ) 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 predominantly caused by lateral loads, and are related to the cause of side-sway. For individual columns or column-members in a floor, the magnified moments about two axes at any station of a column can be obtained as M = M ns + δ s M s. (UBC ) The factor δ s is the moment magnification factor for moments causing side sway. The moment magnification factors for sway moments, δ s, is taken as 1 because the component moments M s and M ns are obtained from a second order elastic (P-delta) analysis. Technical Note 10-6 Calculate Column Capacity Ratio

60 Concrete Frame Design UBC97 Column Design The computed moments are further amplified for individual column stability effect (UBC , ) by the nonsway moment magnification factor, δ ns, as follows: M c = δ ns M 2, where (UBC ) M c is the factored moment to be used in design, and M 2 is the larger factored and amplified end moment. The non-sway moment magnification factor, δ ns, associated with the major or minor direction of the column is given by (UBC ) δ ns = Cm Pu P c 1.0, where (UBC ) P c = π 2 EI ( kl u ) 2, (UBC ) k is conservatively taken as 1; however, the program allows the user to override this value. EI is associated with a particular column direction given by: EI = 0.4E c I g 1 + β d, (UBC ) maximum factored axial dead load β d = maximum factored axial total load and (UBC ) Ma C m = (UBC ) M b M a and M b are the moments at the ends of the column, and M b is numerically larger than M a. M a / M b is positive for single curvature bending and negative for double curvature bending. The above expression of C m is valid if there is no transverse load applied between the supports. If transverse load is present on the span, or the length is overwritten, C m = 1. C m can be overwritten by the user on an element-by-element basis. Calculate Column Capacity Ratio Technical Note 10-7

61 Column Design Concrete Frame Design UBC97 The magnification factor, δ ns, must be a positive number and greater than 1. Therefore, P u must be less than 0.75P c. If P u is found to be greater than or equal to 0.75P c, a failure condition is declared. The above calculations use the unsupported length of the column. The two unsupported lengths are l 22 and l 33, corresponding to instability in the minor and major directions of the element, respectively. See Figure 4. These are the lengths between the support points of the element in the corresponding directions. Figure 4 Axes of Bending and Unsupported Length If the program assumptions are not satisfactory for a particular member, the user can explicitly specify values of δ s and δ ns. Determine Capacity Ratio The program calculates a capacity ratio as a measure of the stress condition of the column. The capacity ratio is basically a factor that gives an indication Technical Note 10-8 Calculate Column Capacity Ratio

62 Concrete Frame Design UBC97 Column Design of the stress condition of the column with respect to the capacity of the column. Before entering the interaction diagram to check the column capacity, the moment magnification factors are applied to the factored loads to obtain P u, M ux, and M uy. The point (P u, M ux, M uy.) is then placed in the interaction space shown 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 interaction volume, the column is overstressed. Figure 5 Geometric Representation of Column Capacity Ratios 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 outwards) will intersect the failure surface. This point is determined by three-dimensional linear interpolation between the points that define the Calculate Column Capacity Ratio Technical Note 10-9

63 Column Design Concrete Frame Design UBC97 failure surface. See Figure 5. The capacity ratio, CR, is given by the ratio OL. OC If OL = OC (or CR=1), the point lies on the interaction surface and the column is stressed to capacity. If OL < OC (or CR<1), the point lies within the interaction volume and the column capacity is adequate. If OL > OC (or CR>1), the point lies outside the interaction volume and the column is overstressed. The maximum of all the values of CR calculated from each load combination is reported for each check station of the column, along with the controlling P u, M ux, and M uy set and associated load combination number. Required Reinforcing Area If the reinforcing area is not defined, the program computes the reinforcement that will give a column capacity ratio of one, calculated as described in the previous section entitled "Calculate Column Capacity Ratio." Design Column Shear Reinforcement The shear reinforcement is designed for each loading combination in the major and minor directions of the column. The following steps are involved in designing the shear reinforcing for a particular column for a particular load combination caused by shear forces in a particular direction: 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. For Special and Intermediate moment resisting frames (Ductile frames), the shear design of the columns is also based on the probable and nominal moment capacities of the members, respectively, in addition to the factored Technical Note Required Reinforcing Area

64 Concrete Frame Design UBC97 Column Design moments. Effects of the axial forces on the column moment capacities are included in the formulation. The following three sections describe in detail the algorithms associated with this 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, P u, and the column shear force, V u, in a particular direction are obtained by factoring the program analysis load cases with the corresponding load combination factors. In the shear design of Special moment resisting frames (i.e., seismic design) the column is checked for capacity-shear in addition to the requirement for the Ordinary moment resisting frames. The capacity-shear force in a column, V p, in a particular direction is calculated from the probable moment capacities of the column 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 particular direction under the influence of the axial force P u is calculated using the uniaxial interaction diagram in the corresponding direction. The design shear force, V u, is then given by (UBC ) V u = V p + V D+L (UBC ) where, V p is the capacity-shear force obtained by applying the calculated probable ultimate moment capacities at the two ends of the column acting in two opposite directions. Therefore, V p is the maximum of V and V, where P 1 P 2 V P 1 = M I + L M + J, and V P 2 = M + I + L M J, where Design Column Shear Reinforcement Technical Note 10-11

65 Column Design Concrete Frame Design UBC97 + I M I M, + J M J M,, = Positive and negative moment capacities at end I of the column using a steel yield stress value of αf y and no ϕ factors (ϕ = 1.0),, = Positive and negative moment capacities at end J of the column using a steel yield stress value of αf y and no ϕ factors (ϕ = 1.0), and L = Clear span of column. For Special moment resisting frames, α is taken as 1.25 (UBC ). V D+L is the contribution of shear force from the in-span distribution of gravity loads. 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 for Ordinary moment resisting frames. The design shear force is taken to be the minimum of that based on the nominal (ϕ = 1.0) moment capacity and factored shear force. The procedure for calculating nominal moment capacity is the same as that for computing the probable moment capacity for special moment resisting frames, except that α is taken equal to 1 rather than 1.25 (UBC , ). The factored shear forces are based on the specified load factors, except the earthquake load factors are doubled (UBC ). Determine Concrete Shear Capacity Given the design force set P u and V u, the shear force carried by the concrete, V c, is calculated as follows: If the column is subjected to axial compression, i.e., P u is positive, V c = 2 f ' c Pu 1 + 2,000A g A cv, (UBC ) where, ' fc 100 psi, and (UBC ) Technical Note Design Column Shear Reinforcement

66 Concrete Frame Design UBC97 Column Design V c 3.5 ' fc P u 1 + A cv. (UBC ) A 500 g Pu The term must have psi units. A cv is the effective shear area which is Ag shown shaded in Figure 6. For circular columns, A cv is not taken to be greater than 0.8 times the gross area (UBC ). Figure 6 Shear Stress Area, A cv Design Column Shear Reinforcement Technical Note 10-13

67 Column Design Concrete Frame Design UBC97 If the column is subjected to axial tension, P u is negative, (UBC ) V c = 2 ' f c Pu 1 + A cv 0 (UBC ) 500Ag For Special moment resisting concrete frame design, V c is set to zero if the factored axial compressive force, P u, including the earthquake effect is small (Pu < f ' c A g / 20) and if the shear force contribution from earthquake, V E, is more than half of the total factored maximum shear force over the length of the member V u (V E 0.5V u ) (UBC ). Determine Required Shear Reinforcement Given V u and V c, the required shear reinforcement in the form of stirrups or ties within a spacing, s, is given for rectangular and circular columns by the following: A v = ( V / ϕ V u c ) f ys d s, for rectangular columns (UBC , ) A v = 2 ( V π u / ϕ V f ys D' c ) s, for circular columns (UBC , ) V u is limited by the following relationship. (V u / ϕ-v c ) 8 ' fc A cv (UBC ) Otherwise redimensioning of the concrete section is required. Here ϕ, the strength reduction factor, is 0.85 for nonseismic design or for seismic design in Seismic Zones 0, 1, and 2 (UBC ) and is 0.60 for seismic design in Seismic Zones 3 and 4 (UBC ). The maximum of all the calculated values obtained from each load combination are reported for the major and minor directions of the column, along with the controlling shear force and associated load combination label. The column shear reinforcement requirements reported by the program are based purely on shear strength consideration. Any minimum stirrup requirements to satisfy spacing considerations or transverse reinforcement volumet- Technical Note Design Column Shear Reinforcement

68 Concrete Frame Design UBC97 Column Design ric considerations must be investigated independently of the program by the user. Reference White. D. W., and J.F., Hajjar Application of Second-Order Elastic Analysis in LRFD: Research in Practice. Engineering Journal. American Institute of Steel Construction, Inc. Vol. 28, No. 4. Reference Technical Note 10-15

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70 COMPUTERS AND STRUCTURES, INC., BERKELEY, CALIFORNIA DECEMBER 2001 CONCRETE FRAME DESIGN UBC97 Technical Note 11 Beam Design This Technical Note describes how this program completes beam design when the UBC97 code is selected. The program calculates and reports the required areas of steel for flexure and shear based on the beam moments, shears, load combination factors and other criteria described herein. Overview In the design of concrete beams, the program calculates and reports the required areas of steel for flexure and shear based upon the beam moments, shears, load combination factors, and other criteria described below. The reinforcement requirements are calculated at a user-defined number of check/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 torsion that may exist in the beams must be investigated independently by the user. The beam design procedure involves the following steps: Design beam flexural reinforcement Design beam shear reinforcement Design Beam Flexural Reinforcement The beam top and bottom flexural steel is designed at check/design stations along the beam span. The following steps are involved in designing the flexural reinforcement for the major moment for a particular beam for a particular section: Determine the maximum factored moments Determine the reinforcing steel Overview Technical Note 11-1

71 Beam Design Concrete Frame Design UBC97 Determine Factored Moments In the design of flexural reinforcement of Special, Intermediate, or Ordinary moment resisting concrete frame beams, the factored moments for each load combination at a particular beam section are obtained by factoring the corresponding moments for different load cases with the corresponding load factors. + M u and maxi- The beam section is then designed for the maximum positive mum negative tions. M u factored moments obtained from all of the load combina- Negative beam moments produce top steel. In such cases, the beam is always designed as a rectangular section. Positive beam moments produce bottom steel. In such cases, the beam may be designed as a Rectangular- or a T-beam. Determine Required Flexural Reinforcement In the flexural reinforcement design process, the program calculates both the tension and compression reinforcement. Compression reinforcement is added when the applied design moment exceeds the maximum moment capacity of a singly reinforced section. The user has the option of avoiding the compression reinforcement by increasing the effective depth, the width, or the grade of concrete. The design procedure is based on the simplified rectangular stress block as shown in Figure 1 (UBC ). It is assumed that the compression carried by concrete is less than 0.75 times that which can be carried at the balanced condition (UBC ). When the applied moment exceeds the moment capacity at this designed balanced condition, the area of compression reinforcement is calculated assuming that the additional moment will be carried by compression and additional tension reinforcement. The design procedure used by the program for both rectangular and flanged sections (L- and T-beams) is summarized below. It is assumed that the design ultimate axial force does not exceed 0.1 f ' c A g (UBC ); hence, all the beams are designed for major direction flexure and shear only. Technical Note 11-2 Design Beam Flexural Reinforcement

72 Concrete Frame Design UBC97 Beam Design Figure 1 Design of a Rectangular Beam Section Design for Rectangular Beam In designing for a factored negative or positive moment, M u (i.e., designing top or bottom steel), the depth of the compression block is given by a (see Figure 1), where, a = d - d 2 2 Mu ' 0.85f ϕb c, where the value of ϕ is 0.90 (UBC ) in the above and the following equations. Also β 1 and c b are calculated as follows: β 1 = ' f c 4,000, 0.65 β 1, , (UBC ) c b = ε c ε E c s E s + f y d = 87,000 87,000 + f y d. (UBC , ) Design Beam Flexural Reinforcement Technical Note 11-3

73 Beam Design Concrete Frame Design UBC97 The maximum allowed depth of the compression block is given by a max = 0.75β 1 c b. (UBC , ) If a a max, the area of tensile steel reinforcement is given by A s = ϕf y Mu. a d 2 This steel is to be placed at the bottom if M u is positive, or at the top if M u is negative. If a > a max, compression reinforcement is required (UBC ) and is calculated as follows: The compressive force developed in concrete alone is given by ' c C = 0.85 f ba max, and (UBC ) the moment resisted by concrete compression and tensile steel is a M uc = C d max ϕ. 2 Therefore the moment resisted by compression steel and tensile steel is M us = M u - M uc. So the required compression steel is given by ' A s = Mus, where f ( d d' )ϕ ' s ' c f s = 0.003E s c d'. (UBC ) The required tensile steel for balancing the compression in concrete is Technical Note 11-4 Design Beam Flexural Reinforcement

74 Concrete Frame Design UBC97 Beam Design A s1 = f y M d uc a max 2 ϕ, and the tensile steel for balancing the compression in steel is given by A s2 = Mus. f ( d d' )ϕ y Therefore, the total tensile reinforcement, A s = A s1 + A s2, and total compression reinforcement is A s. A s is to be placed at bottom and A s is to ' ' be placed at top if M u is positive, and vice versa if M u is negative. Design for T-Beam In designing for a factored negative moment, M u (i.e., designing top steel), the calculation of the steel area is exactly the same as above, i.e., no T-Beam data is to be used. See Figure 2. If M u > 0, the depth of the compression block is given by a = d - d 2 2M 0.85f ϕb u ' c f. The maximum allowed depth of the compression block is given by a max = 0.75β 1 c b. (UBC ) If a d s, the subsequent calculations for A s are exactly the same as previously defined for the rectangular section design. However, in this case, the width of the compression flange is taken as the width of the beam for analysis. Compression reinforcement is required if a > a max. If a > d s, calculation for A s is performed in two parts. The first part is for balancing the compressive force from the flange, C f, and the second part is for balancing the compressive force from the web, C w, as shown in Figure 2. C f is given by ' c C f = 0.85 f (bf - b w ) d s. Design Beam Flexural Reinforcement Technical Note 11-5

75 Beam Design Concrete Frame Design UBC97 Figure 2 Design of a T-Beam Section Therefore, A s1 = given by C f f y and the portion of M u that is resisted by the flange is M uf = C f ds d ϕ. 2 Again, the value for ϕ is Therefore, the balance of the moment, M u to be carried by the web is given by M uw = M u - M uf. The web is a rectangular section of dimensions b w and d, for which the design depth of the compression block is recalculated as a 1 = d - d 2 2M 0.85f uw ' c ϕ b w. If a 1 a max, the area of tensile steel reinforcement is then given by Technical Note 11-6 Design Beam Flexural Reinforcement

76 Concrete Frame Design UBC97 Beam Design A s2 = ϕf y M uw d a 1 2, and A s = A s1 + A s2. This steel is to be placed at the bottom of the T-beam. If a 1 > a max, compression reinforcement is required (UBC ) and is calculated as follows: The compressive force in web concrete alone is given by ' c C = 0.85 f ba max. (UBC ) Therefore the moment resisted by concrete web and tensile steel is M uc = C d a max 2 ϕ, and the moment resisted by compression steel and tensile steel is M us = M uw - M uc. Therefore, the compression steel is computed as ' A s = Mus, where f ( d d' )ϕ ' s ' c f s = 0.003E s c d'. (UBC ) The tensile steel for balancing compression in web concrete is A s2 = f y M d uc a max 2, and ϕ the tensile steel for balancing compression in steel is Design Beam Flexural Reinforcement Technical Note 11-7

77 Beam Design Concrete Frame Design UBC97 A s3 = f y Mus. ( d d' )ϕ The total tensile reinforcement, A s = A s1 + A s2 + A s3, and total compression reinforcement is A s. A s is to be placed at bottom and A s is to be ' ' placed at top. Minimum Tensile Reinforcement The minimum flexural tensile steel provided in a rectangular section in an Ordinary moment resisting frame is given by the minimum of the two following limits: 3 f ' c 200 A s max bw d and bw d or (UBC ) fy fy A s 3 4 As(required) (UBC ) Special Consideration for Seismic Design For Special moment resisting concrete frames (seismic design), the beam design satisfies the following additional conditions (see also Table 1 for comprehensive listing): The minimum longitudinal reinforcement shall be provided at both the top and bottom. Any of the top and bottom reinforcement shall not be less than A s(min) (UBC ). 3 f ' c 200 A s(min) max bw d and bw d or (UBC , ) fy fy A s(min) 3 4 As(required). (UBC , ) The beam flexural steel is limited to a maximum given by A s 0.25 b w d. (UBC ) Technical Note 11-8 Design Beam Flexural Reinforcement

78 Concrete Frame Design UBC97 Beam Design Table 1 Design Criteria Table Type of Check/ Design Column Check (interaction) Column Design (interaction) Column Shears Beam Design Flexure Ordinary Moment Resisting Frames (Seismic Zones 0&1) Intermediate Moment Resisting Frames (Seismic Zone 2) Special Moment Resisting Frames (Seismic Zones 3 & 4) NLD a Combinations NLD a Combinations NLD a Combinations NLD a Combinations 1% < ρ < 8% NLD a Combinations NLD a Combinations NLD a Combinations 1% < ρ < 8% Modified NLD a Combinations (earthquake loads doubled) Column Capacity ϕ = 1.0 and α = 1.0 NLD a Combinations NLD a Combinations α = 1.0 1% < ρ < 6% NLD a Combinations and Column shear capacity ϕ = 1.0 and α = 1.25 NLD a Combinations ρ f ' c 200 ρ, ρ f f y y Beam Min. Moment Override Check Beam Design Shear Joint Design Beam/ Column Capacity Ratio No Requirement NLD a Combinations + 1 M uend MuEND M uspan max M u, M M uspan max M u, M 5 { u } END { u } END Modified NLD a Combinations (earthquake loads doubled) Beam Capacity Shear (Vp) with α = 1.0 and ϕ = 1.0 plus VD+L + 1 M uend MuEND M uspan max M u, M 4 1 M uspan max M u, M 4 { u } END { u } END NLD a Combinations Beam Capacity Shear (Vp) with α = 1.25 and ϕ = 1.0 plus VD+L Vc = 0 No Requirement No Requirement Checked for shear No Requirement No Requirement Reported in output file NLD a = Number of specified loading Design Beam Flexural Reinforcement Technical Note 11-9

79 Beam Design Concrete Frame Design UBC97 At any end (support) of the beam, the beam positive moment capacity (i.e., associated with the bottom steel) would not be less than 1/2 of the beam negative moment capacity (i.e., associated with the top steel) at that end (UBC ). Neither the negative moment capacity nor the positive moment capacity at any of the sections within the beam would be less than 1/4 of the maximum of positive or negative moment capacities of any of the beam end (support) stations (UBC ). For Intermediate moment resisting concrete frames (i.e., seismic design), the beam design would satisfy the following conditions: At any support of the beam, the beam positive moment capacity would not be less than 1/3 of the beam negative moment capacity at that end (UBC ). Neither the negative moment capacity nor the positive moment capacity at any of the sections within the beam would be less than 1/5 of the maximum of positive or negative moment capacities of any of the beam end (support) stations (UBC ). Design Beam Shear Reinforcement The shear reinforcement is designed for each load combination at a userdefined number of stations along the beam span. The following steps are involved in designing the shear reinforcement for a particular beam for a particular load combination at a particular station resulting from the beam major shear: Determine the factored shear force, V u. Determine the shear force, V c, that can be resisted by the concrete. Determine the reinforcement steel required to carry the balance. For Special and Intermediate moment resisting frames (Ductile frames), the shear design of the beams is also based on the probable and nominal moment capacities of the members, respectively, in addition to the factored load design. Technical Note Design Beam Shear Reinforcement

80 Concrete Frame Design UBC97 Beam Design The following three sections describe in detail the algorithms associated with this process. Determine Shear Force and Moment In the design of the beam shear reinforcement of an Ordinary moment resisting concrete frame, the shear forces and moments for a particular load combination at a particular beam section are obtained by factoring the associated shear forces and moments with the corresponding load combination factors. In the design of Special moment resisting concrete frames (i.e., seismic design), the shear capacity of the beam is also checked for the capacity-shear associated with the probable moment capacities at the ends and the factored gravity load. This check is performed in addition to the design check required for Ordinary moment resisting frames. The capacity-shear force, V p, is calculated from the probable moment capacities of each end of the beam and the gravity shear forces. The procedure for calculating the design shear force in a beam from probable moment capacity is the same as that described for a column in section Design Column Shear Reinforcement in Concrete Frame Design UBC97 Technical Note 10 Column Design. See also Table 1 for details. The design shear force V u is then given by (UBC ) V u = V p + V D+L (UBC ) where V p is the capacity shear force obtained by applying the calculated probable ultimate moment capacities at the two ends of the beams acting in opposite directions. Therefore, V p is the maximum of V P 1 and V P 2, where V P 1 = V P 2 = M M I + L + I + L M M + J J, and, where M I = Moment capacity at end I, with top steel in tension, using a steel yield stress value of αf y and no ϕ factors (ϕ = 1.0), Design Beam Shear Reinforcement Technical Note 11-11

81 Beam Design Concrete Frame Design UBC97 + M J = Moment capacity at end J, with bottom steel in tension, using a steel yield stress value of αf y and no ϕ factors (ϕ = 1.0), + M I = Moment capacity at end I, with bottom steel in tension, using a steel yield stress value of αf y and no ϕ factors (ϕ = 1.0), M J = Moment capacity at end J, with top steel in tension, using a steel yield stress value of αf y and no ϕ factors (ϕ = 1.0), and L = Clear span of beam. For Special moment resisting frames, α is taken as 1.25 (UBC ). V D+L is the contribution of shear force from the in-span distribution of gravity loads. For Intermediate moment resisting frames, the shear capacity of the beam 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 for Ordinary moment resisting frames. The design shear force in beams is taken to be the minimum of that based on the nominal moment capacity and factored shear force. The procedure for calculating nominal (ϕ = 1.0) moment capacity is the same as that for computing the probable moment capacity for Special moment resisting frames, except that α is taken equal to 1 rather than 1.25 (UBC , ). The factored shear forces are based on the specified load factors, except the earthquake load factors are doubled (UBC ). The computation of the design shear force in a beam of an Intermediate moment resisting frame is also the same as that for columns, which is described in Concrete Frame Design UBC97 Technical Note 10 Column Design. Also see Table 1 for details. Determine Concrete Shear Capacity The allowable concrete shear capacity is given by V c = 2 ' fc b w d. (UBC ) For Special moment resisting frame concrete design, V c is set to zero if both the factored axial compressive force, including the earthquake effect P u, is less than f ' c A g /20 and the shear force contribution from earthquake V E is Technical Note Design Beam Shear Reinforcement

82 Concrete Frame Design UBC97 Beam Design more than half of the total maximum shear force over the length of the member V u (i.e., V E 0.5V u ) (UBC ). Determine Required Shear Reinforcement Given V u and V c, the required shear reinforcement in area/unit length is calculated as A v = ( Vu / ϕ Vc ) s. (UBC , ) f d ys The shear force resisted by steel is limited by (V u /ϕ - V c ) 8 ' fc bd. (UBC ) Otherwise, redimensioning of the concrete section is required. Here ϕ, the strength reduction factor, is 0.85 for nonseismic design or for seismic design in Seismic Zones 0, 1, and 2 (UBC ) and is 0.60 for seismic design in Seismic Zones 3 and 4 (UBC ). The maximum of all the calculated A v values, obtained from each load combination, is reported along with the controlling shear force and associated load combination number. The beam shear reinforcement requirements displayed by the program are based purely on shear strength considerations. Any minimum stirrup requirements to satisfy spacing and volumetric considerations must be investigated independently of the program by the user. Design Beam Shear Reinforcement Technical Note 11-13

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84 COMPUTERS AND STRUCTURES, INC., BERKELEY, CALIFORNIA DECEMBER 2001 CONCRETE FRAME DESIGN UBC97 Technical Note 12 Joint Design This Technical Note explains how the program performs a rational analysis of the beam-column panel zone to determine the shear forces that are generated in a joint. The program then checks this against design shear strength. Overview To ensure that the beam-column joint of special moment resisting frames possesses adequate 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. The program 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 completed in the major and the minor directions of the column. The joint 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 algorithms associated with these three steps are described in detail in the following three sections. Determine the Panel Zone Shear Force Figure 1 illustrates the free body stress condition of a typical beam-column intersection for a column direction, major or minor. Overview Technical Note 12-1

85 Joint Design Concrete Frame Design UBC97 Figure1 Beam-Column Joint Analysis Technical Note 12-2 Determine the Panel Zone Shear Force

86 Concrete Frame Design UBC97 Joint Design The force V h u 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 L u and M R u. The forces P u and V u are axial force and shear force, respectively, from the column framing into the L top of the joint. The moments M u and M R u are obtained from the beams h framing into the joint. The program calculates the joint shear force V u by resolving the moments into C and T forces. Noting that T L = C L and T R = C R, V u h = T L + T R - V u The location of C or T forces is determined by the direction of the moment. The magnitude of C or T forces is conservatively determined using basic principles of ultimate strength theory, ignoring compression reinforcement as follows. The program first calculates the maximum compression, C max, and the maximum moment, M max, that can be carried by the beam. C max = 0. 85fc ' bd M = C max max d 2 Then the program conservatively determines C and T forces as follows: C = T = C max 1 abs( M ) 1 M max The program resolves the moments and the C and T forces from beams that frame into the joint in a direction that is not parallel to the major or minor directions of the column along the direction that is being investigated, thereby contributing force components to the analysis. Also, the program calculates the C and T for the positive and negative moments, considering the fact that the concrete cover may be different for the direction of moment. In the design of special moment resisting concrete frames, the evaluation of the design shear force is based on the moment capacities (with reinforcing steel overstrength factor, α, and no ϕ factors) of the beams framing into the joint (UBC ). The C and T forces are based on these moment capacities. The program calculates the column shear force V u from the beam moment capacities, as follows: Determine the Panel Zone Shear Force Technical Note 12-3

87 Joint Design Concrete Frame Design UBC97 V u = M L u + M H R u See Figure 2. It should be noted that the points of inflection shown on Figure 2 are taken as midway between actual lateral support points for the columns. If there is no column at the top of the joint, the shear force from the top of the column is taken as zero. Figure 2 Column Shear Force V u Technical Note 12-4 Determine the Panel Zone Shear Force

88 Concrete Frame Design UBC97 Joint Design The effects of load reversals, as illustrated in Case 1 and Case 2 of Figure 1, are investigated and the design is based on the maximum of the joint shears obtained from the two cases. Determine the Effective Area of Joint The joint area that resists the shear forces is assumed always to be rectangular in plan view. The dimensions of the rectangle correspond to the major and minor dimensions of the column below the joint, except if the beam framing into the joint is very narrow. The effective width of the joint area to be used in the calculation is limited to the width of the beam plus the depth of the column. The area of the joint is assumed not to exceed the area of the column below. The joint area for joint shear along 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 assumptions may be unconservative and the user should investigate the acceptability of the particular joint. Check Panel Zone Shear Stress The panel zone shear stress is evaluated by dividing the shear force V h u by the effective area of the joint and comparing it with the following design shear strengths (UBC ): { 20ϕ f ' for joints confined on all four sides c v = 15ϕ f ' for joints confined on three faces or on two c opposite faces 12ϕ f ' for all other joints c where ϕ = 0.85 (by default). (UBC , ) A beam that frames into a face of a column at the joint is considered in this program to provide confinement to the joint if at least three-quarters of the face of the joint is covered by the framing member (UBC ). Determine the Effective Area of Joint Technical Note 12-5

89 Joint Design Concrete Frame Design UBC97 For light-weight aggregate concrete, the design shear strength of the joint is reduced in the program to at least three-quarters of that of the normal weight concrete by replacing the ' fc with min f cs, factor f ' c,3 / 4 f ' c (UBC ) For joint design, the program reports the joint shear, the joint shear stress, the allowable joint shear stress and a capacity ratio. Beam/Column Flexural Capacity Ratios At a particular joint for a particular column direction, major or minor, the program will calculate the ratio of the sum of the beam moment capacities to the sum of the column moment capacities. For Special Moment-Resisting Frames, the following UBC provision needs to be satisfied (UBC ). M e 5 6 Mg (UBC ) The capacities are calculated with no reinforcing overstrength factor, α, and including ϕ factors. The beam capacities are calculated for reversed situations (Cases 1 and 2) as illustrated in Figure 1 and the maximum summation obtained is used. The moment capacities of beams that frame into the joint in a direction that is not parallel to the major or minor direction of the column are resolved along the direction that is being investigated and the resolved components are added to the summation. 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 is calculated from the program analysis load combinations. For each load combination, the moment capacity of each column under the influence of the corresponding axial load P u is then determined separately for the major and minor directions of the column, using the uniaxial column interaction diagram, see Figure 3. The moment capacities of the two columns are added to give the capacity summation for the corresponding load combination. The maximum capacity summations obtained from all of the load combinations is used for the beam/column capacity ratio. Technical Note 12-6 Beam/Column Flexural Capacity Ratios

90 Concrete Frame Design UBC97 Joint Design The beam/column flexural capacity ratios are only reported for Special Moment-Resisting Frames involving seismic design load combinations. If this ratio is greater than 5/6, a warning message is printed in the output file. Figure 3 Moment Capacity M u at a Given Axial Load P u Beam/Column Flexural Capacity Ratios Technical Note 12-7

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92 COMPUTERS AND STRUCTURES, INC., BERKELEY, CALIFORNIA DECEMBER 2001 CONCRETE FRAME DESIGN UBC97 Technical Note 13 Input Data This Technical Note describes the concrete frame design input data for UBC97. The input can be printed to a printer or to a text file when you click the File menu > Print Tables > Concrete Frame Design command. A printout of the input data provides the user with the opportunity to carefully review the parameters that have been input into the program and upon which program design is based. Further information about using the Print Design Tables form is presented at the end of this Technical Note. Input Data The program provides the printout of the input data in a series of tables. The column headings for input data and a description of what is included in the columns of the tables are provided in Table 1 of this Technical Note. Table 1 Concrete Frame Design Input Data COLUMN HEADING Load Combination Multipliers DESCRIPTION Combo Design load combination. See Technical Note 8. Type Case Factor Code Preferences Phi_bending Phi_tension Phi_compression (Tied) Phi_compression (Spiral) Phi_shear Load type: dead, live, superimposed dead, earthquake, wind, snow, reduced live load, other. Name of load case. Load combination scale factor. Bending strength reduction factor. Tensile strength reduction factor. Compressive strength reduction factor for tied columns. Compressive strength reduction factor for reinforced columns. Shear strength reduction factor. Input Data Technical Note 13-1

93 Input Data Concrete Frame Design UBC97 Table 1 Concrete Frame Design Input Data COLUMN HEADING Material Property Data Material Name Material Type Design Type Modulus of Elasticity Poisson's Ratio Thermal Coeff DESCRIPTION Concrete, steel, other. Isotropic or orthotropic. Shear Modulus Material Property Mass and Weight Material Name Mass Per Unit Vol Weight Per Unit Vol Coefficient of thermal expansion. Concrete, steel, other. Used to calculate self-mass of structure. Material Design Data for Concrete Materials Material Name Lightweight Concrete Concrete FC Rebar FY Rebar FYS Lightwt Reduc Fact Concrete Column Property Data Section Label Mat Label Column Depth Column Width Rebar Pattern Concrete Cover Bar Area Used to calculate self-weight of structure. Concrete, steel, other. Concrete compressive strength. Bending reinforcing steel yield strength. Shear reinforcing steel yield strength. Shear strength reduction factor for light weight concrete; default = 1.0. Label applied to section. Material label. Layout of main flexural reinforcing steel. Minimum clear concrete cover. Area of individual reinforcing bar to be used. Technical Note 13-2 Table 1 Concrete Frame Design Input Data

94 Concrete Frame Design UBC97 Input Data Table 1 Concrete Frame Design Input Data COLUMN HEADING DESCRIPTION Concrete Column Design Element Information Story ID Column Line Section ID Framing Type RLLF Factor L_Ratio Major L_Ratio Minor Column assigned to story level at top of column. Grid line. Name of section assigned to column. Lateral or gravity. Unbraced length about major axis. Unbraced length about minor axis. K Major Effective length factor; default = 1.0. K Minor Effective length factor; default = 1.0. Concrete Beam Design Element Information Story ID Bay ID Section ID Framing type RLLF Factor L_Ratio Major L_Ratio Minor Story level at which beam occurs. Grid lines locating beam. Section number assigned to beam. Lateral or gravity. Unbraced length about major axis. Unbraced length about minor axis. Using the Print Design Tables Form To print steel frame design input data directly to a printer, use the File menu > Print Tables > Concrete Frame Design command and click the check box on the Print Design Tables form. Click the OK button to send the print to your printer. Click the Cancel button rather than the OK button to cancel the print. Use the File menu > Print Setup command and the Setup>> button to change printers, if necessary. To print steel frame design input data to a file, click the Print to File check box on the Print Design Tables form. Click the Filename>> button to change the Using the Print Design Tables Form Technical Note 13-3

95 Input Data Concrete Frame Design UBC97 path or filename. Use the appropriate file extension for the desired format (e.g.,.txt,.xls,.doc). Click the OK buttons on the Open File for Printing Tables form and the Print Design Tables form to complete the request. Note: The File menu > Display Input/Output Text Files command is useful for displaying output that is printed to a text file. The Append check box allows you to add data to an existing file. The path and filename of the current file is displayed in the box near the bottom of the Print Design Tables form. Data will be added to this file. Or use the Filename>> button to locate another file, and when the Open File for Printing Tables caution box appears, click Yes to replace the existing file. If you select a specific frame element(s) before using the File menu > Print Tables > Concrete Frame Design command, the Selection Only check box will be checked. The print will be for the selected beam(s) only. Technical Note 13-4 Using the Print Design Tables Form

96 COMPUTERS AND STRUCTURES, INC., BERKELEY, CALIFORNIA DECEMBER 2001 CONCRETE FRAME DESIGN UBC97 Technical Note 14 Output Details This Technical Note describes the concrete frame design output for UBC97 that can be printed to a printer or to a text file. The design output is printed when you click the File menu > Print Tables > Concrete Frame Design command and select Output Summary of the Print Design Tables dialog box. Further information about using the Print Design Tables dialog box is presented at the end of this Technical Note. The program provides the output data in a series of tables. The column headings for output data and a description of what is included in the columns of the tables are provided in Table 1 of this Technical Note. Table 1 Concrete Column Design Output COLUMN HEADING DESCRIPTION Biaxial P-M Interaction and Shear Design of Column-Type Elements Story ID Column assigned to story level at top of column. Column Line Section ID Station ID Required Reinforcing Longitudinal Combo Shear22 Combo Shear33 Grid lines. Name of section assigned to column. Area of longitudinal reinforcing required. Load combination for which the reinforcing is designed. Shear reinforcing required. Load combination for which the reinforcing is designed. Shear reinforcing required. Table 1 Concrete Column Design Output Technical Note 14-1

97 Output Details Concrete Frame Design UBC97 Table 1 Concrete Column Design Output COLUMN HEADING Combo DESCRIPTION Load combination for which the reinforcing is designed. Table 2 Concrete Column Joint Output COLUMN HEADING DESCRIPTION Beam to Column Capacity Ratios and Joint Shear Capacity Check Story ID Column Line Section ID Story level at which joint occurs. Grid line. Assigned section name. Beam-Column Capacity Ratios Major Combo Minor Combo Ratio of beam moment capacity to column capacity. Load combination upon which the ratio of beam moment capacity to column capacity is based. Ratio of beam moment capacity to column capacity. Load combination upon which the ratio of beam moment capacity to column capacity is based. Joint Shear Capacity Ratios Major Combo Minor Combo Ratio of factored load versus allowed capacity. Load combination upon which the ratio of factored load versus allowed capacity is based. Ratio of factored load versus allowed capacity. Load combination upon which the ratio of factored load versus allowed capacity is based. Technical Note 14-2 Table 2 Concrete Column Joint Output

98 Concrete Frame Design UBC97 Output Details Using the Print Design Tables Form To print concrete frame design input data directly to a printer, use the File menu > Print Tables > Concrete Frame Design command and click the check box on the Print Design Tables dialog box. Click the OK button to send the print to your printer. Click the Cancel button rather than the OK button to cancel the print. Use the File menu > Print Setup command and the Setup>> button to change printers, if necessary. To print concrete frame design input data to a file, click the Print to File check box on the Print Design Tables dialog box. Click the Filename>> button to change the path or filename. Use the appropriate file extension for the desired format (e.g.,.txt,.xls,.doc). Click the OK buttons on the Open File for Printing Tables dialog box and the Print Design Tables dialog box to complete the request. Note: The File menu > Display Input/Output Text Files command is useful for displaying output that is printed to a text file. The Append check box allows you to add data to an existing file. The path and filename of the current file is displayed in the box near the bottom of the Print Design Tables dialog box. Data will be added to this file. Or use the Filename>> button to locate another file, and when the Open File for Printing Tables caution box appears, click Yes to replace the existing file. If you select a specific frame element(s) before using the File menu > Print Tables > Concrete Frame Design command, the Selection Only check box will be checked. The print will be for the selected beam(s) only. Using the Print Design Tables Form Technical Note 14-3

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100 COMPUTERS AND STRUCTURES, INC., BERKELEY, CALIFORNIA DECEMBER 2001 CONCRETE FRAME DESIGN ACI Technical Note 15 General and Notation Introduction to the ACI Series of Technical Notes The ACI Concrete Frame Design series of Technical Notes describes in detail the various aspects of the concrete design procedure that is used by this program when the user selects the ACI Design Code (ACI 1999). The various notations used in this series are listed herein. The design is based on user-specified loading combinations. The program provides a set of default load combinations that should satisfy requirements for the design of most building type structures. See Concrete Frame Design ACI Technical Note 18 Design Load Combination for more information. The program provides options to design or check Earthquake resisting frames; Ordinary, Earthquake resisting frames; Intermediate (moderate seismic risk areas), and Earthquake resisting frames; Special (high seismic risk areas) moment resisting frames as required for seismic design provisions. The details of the design criteria used for the different framing systems are described in Concrete Frame Design ACI Technical Note 19 Strength Reduction Factors, Concrete Frame Design ACI Technical Note 20 Column Design, Concrete Frame Design ACI Technical Note 21 Beam Design, and Concrete Frame Design ACI Technical Note 22 Joint Design. The program uses preferences and overwrites, which are described in Concrete Frame Design ACI Technical Note 16 Preferences and Concrete Frame Design ACI Technical Note 17 Overwrites. It also provides input and output data summaries, which are described in Concrete Frame Design ACI Technical Note 23 Input Data and Concrete Frame Design ACI Technical Note 24 Output Details. English as well as SI and MKS metric units can be used for input. But the code is based on Inch-Pound-Second units. For simplicity, all equations and descriptions presented in this chapter correspond to Inch-Pound-Second units unless otherwise noted. Introduction to the ACI Series of Technical Notes Technical Note 15-1

101 General and Notation Concrete Frame Design ACI Notation A cv A g A s ' As Area of concrete used to determine shear stress, sq-in Gross area of concrete, sq-in Area of tension reinforcement, sq-in Area of compression reinforcement, sq-in A s(required) A st A v C m E c Area of steel required for tension reinforcement, sq-in Total area of column longitudinal reinforcement, sq-in Area of shear reinforcement, sq-in Coefficient, dependent upon column curvature, used to calculate moment magnification factor Modulus of elasticity of concrete, psi E s Modulus of elasticity of reinforcement, assumed as 29,000,000 psi (ACI 8.5.2) I g I se L M 1 M 2 M c M ns M s Moment of inertia of gross concrete section about centroidal axis, neglecting reinforcement, in 4 Moment of inertia of reinforcement about centroidal axis of member cross section, in 4 Clear unsupported length, in Smaller factored end moment in a column, lb-in Larger factored end moment in a column, lb-in Factored moment to be used in design, lb-in Nonsway component of factored end moment, lb-in Sway component of factored end moment, lb-in Technical Note 15-2 Notation

102 Concrete Frame Design ACI General and Notation M u M ux M uy P b P c P max P 0 P u V c V E V D+L V u V p a a b b b f b w c c b d d' Factored moment at section, lb-in Factored moment at section about X-axis, lb-in Factored moment at section about Y-axis, lb-in Axial load capacity at balanced strain conditions, lb Critical buckling strength of column, lb Maximum axial load strength allowed, lb Axial load capacity at zero eccentricity, lb Factored axial load at section, lb Shear resisted by concrete, lb Shear force caused by earthquake loads, lb Shear force from span loading, lb Factored shear force at a section, lb Shear force computed from probable moment capacity, lb Depth of compression block, in Depth of compression block at balanced condition, in Width of member, in Effective width of flange (T-Beam section), in Width of web (T-Beam section), in Depth to neutral axis, in Depth to neutral axis at balanced conditions, in Distance from compression face to tension reinforcement, in Concrete cover to center of reinforcing, in Notation Technical Note 15-3

103 General and Notation Concrete Frame Design ACI d s ' fc Thickness of slab (T-Beam section), in Specified compressive strength of concrete, psi f y f ys h k r α β 1 β d δ s δ ns ε c ε s ϕ Specified yield strength of flexural reinforcement, psi f y 80,000 psi (ACI 9.4) Specified yield strength of shear reinforcement, psi Dimension of column, in Effective length factor Radius of gyration of column section, in Reinforcing steel overstrength factor Absolute value of ratio of maximum factored axial dead load to maximum factored axial total load Absolute value of ratio or maximum factored axial dead load to maximum factored axial total load Moment magnification factor for sway moments Moment magnification factor for nonsway moments Strain in concrete Strain in reinforcing steel Strength reduction factor Technical Note 15-4 Notation

104 COMPUTERS AND STRUCTURES, INC., BERKELEY, CALIFORNIA DECEMBER 2001 CONCRETE FRAME DESIGN ACI Technical Note 16 Preferences This Technical Note describes the items in the Preferences form. General The concrete frame design preferences in this program are basic assignments that apply to all concrete frame elements. Use the Options menu > Preferences > Concrete Frame Design command to access the Preferences form where 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. You should, however, at least review the default values for the preference items to make sure they are acceptable to you. Using the Preferences Form To view preferences, select the Options menu > Preferences > Concrete Frame Design. The Preferences form will display. The preference options are displayed in a two-column spreadsheet. The left column of the spreadsheet displays the preference item name. The right column of the spreadsheet displays the preference item value. To change a preference item, left click the desired preference item in either the left or right column of the spreadsheet. This activates a drop-down box or highlights the current preference value. If the drop-down box appears, select a new value. If the cell is highlighted, type in the desired value. The preference value will update accordingly. You cannot overwrite values in the dropdown boxes. When you have finished making changes to the composite beam preferences, click the OK button to close the form. You must click the OK button for the changes to be accepted by the program. If you click the Cancel button to exit General Technical Note 16-1

105 Preferences Concrete Frame Design ACI the form, any changes made to the preferences are ignored and the form is closed. Preferences For purposes of explanation in this Technical Note, the preference items are presented in Table. The column headings in the table are described as follows: Item: The name of the preference item as it appears in the cells at the left side of the Preferences form. Possible Values: The possible values that the associated preference item can have. Default Value: The built-in default value that the program assumes for the associated preference item. Description: A description of the associated preference item. Table 1: Concrete Frame Preferences Item Possible Values Default Value Description Design Code Any code in the program ACI Design code used for design of concrete frame elements. Phi Bending Tension Phi Compression Tied Phi Compression Spiral >0 0.9 Unitless strength reduction factor per ACI 9.3. >0 0.7 Unitless strength reduction factor per ACI 9.3. > Unitless strength reduction factor per ACI 9.3. Phi Shear > Unitless strength reduction factor per ACI 9.3. Number Interaction Curves Number of equally spaced interaction curves used to create a full 360-degree interaction surface (this item should be a multiple of four). We recommend that you use 24 for this item. Technical Note 16-2 Preferences

106 Concrete Frame Design ACI Preferences Table 1: Concrete Frame Preferences Item Number Interaction Points Time History Design Possible Values Any odd value 4.0 Envelopes or Step-by-Step Default Value Description 11 Number of points used for defining a single curve in a concrete frame interaction surface (this item should be odd). Envelopes Toggle for design load combinations that include a time history designed for the envelope of the time history, or designed step-by-step for the entire time history. If a single design load combination has more than one time history case in it, that design load combination is designed for the envelopes of the time histories, regardless of what is specified here. Preferences Technical Note 16-3

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108 COMPUTERS AND STRUCTURES, INC., BERKELEY, CALIFORNIA DECEMBER 2001 CONCRETE FRAME DESIGN ACI Technical Note 17 Overwrites General The concrete frame design overwrites are basic assignments that apply only to those elements to which they are assigned. This Technical Note describes concrete frame design overwrites for ACI To access the overwrites, select an 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 to specify or change any of the overwrites. However, at least review the default values for the overwrite items to make sure they are acceptable. When changes are made to overwrite items, the program applies the changes only to the elements to which they are specifically assigned; that is, to the elements that are selected when the overwrites are changed. Overwrites For explanation purposes in this Technical Note, the overwrites are presented in 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. To save space in the formes, these names are generally short. Possible Values: The possible values that the associated overwrite item can have. Default Value: The default value that the program assumes for the associated overwrite item. Description: A description of the associated overwrite item. An explanation of how to change an overwrite is provided at the end of this Technical Note. Overwrites Technical Note 17-1

109 Overwrites Concrete Frame Design ACI Table 1 Concrete Frame Design Overwrites Item Possible Values Default Value Description Element Section Element Type Live Load Reduction Factor Horizontal Earthquake Factor Unbraced Length Ratio (Major) Unbraced Length Ratio (Minor) Effective Length Factor (K Major) Effective Length Factor (K Minor) Moment Coefficient (Cm Major) Moment Coefficient (Cm Minor) NonSway Moment Factor (Dns Major) Sway Special, Sway Intermediate, Sway Ordinary NonSway >0 1.0 >0 1.0 >0 1.0 >0 1.0 >0 1.0 >0 1.0 >0 1.0 >0 1.0 >0 1.0 Sway Special Frame type per moment frame definition given in ACI Used to reduce the live load contribution to the factored loading See ACI 10.12, and Figure R See ACI 10.12, and Figure R Factor relating actual moment diagram to an equivalent uniform moment diagram. See ACI Factor relating actual moment diagram to an equivalent uniform moment diagram. See ACI See ACI Technical Note 17-2 Overwrites

110 Concrete Frame Design ACI Overwrites Table 1 Concrete Frame Design Overwrites Item Possible Values Default Value Description NonSway Moment Factor (Dns Minor) Sway Moment Factor (Ds Major) Sway Moment Factor (Ds Minor) 1 See ACI See ACI See ACI Making Changes in the Overwrites Form To access the concrete frame overwrites, select an element and click the Design menu > Concrete Frame Design > View/Revise Overwrites command. The overwrites are displayed in the form with a column of check boxes and a two-column spreadsheet. The left column of the spreadsheet contains the name of the overwrite item. The right column of the spreadsheet contains the overwrites values. Initially, the check boxes in the Concrete Frame Design Overwrites form are all unchecked and all of the cells in the spreadsheet have a gray background to indicate that they are inactive and the items in the cells cannot be changed. The names of the overwrite items are displayed in the first column of the spreadsheet. The values of the overwrite items are visible in the second column of the spreadsheet if only one element was selected before the overwrites form was accessed. If multiple elements were selected, no values show for the overwrite items in the second column of the spreadsheet. After selecting one or multiple elements, check the box to the left of an overwrite item to change it. Then left click in either column of the spreadsheet to activate a drop-down box or highlight the contents in the cell in the right column of the spreadsheet. If the drop-down box appears, select a value from Overwrites Technical Note 17-3

111 Overwrites Concrete Frame Design ACI the box. If the cell contents is highlighted, type in the desired value. The overwrite will reflect the change. You cannot change the values of the dropdown boxes. When changes to the overwrites have been completed, click the OK button to close the form. The program then changes all of the overwrite items whose associated check boxes are checked for the selected members. You must click the OK button for the changes to be accepted by the program. If you click the Cancel button to exit the form, any changes made to the overwrites are ignored and the form is closed. Resetting Concrete Frame Overwrites to Default Values Use the Design menu > Concrete Frame Design > Reset All Overwrites command to reset all of the steel frame overwrites. All current design results will be deleted when this command is executed. Important note about resetting overwrites: The program defaults for the overwrite items are built into the program. The concrete frame overwrite values that were in a.edb file that you used to initialize your model may be different 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 values that were in the.edb file used to initialize the model. Technical Note 17-4 Overwrites

112 COMPUTERS AND STRUCTURES, INC., BERKELEY, CALIFORNIA DECEMBER 2001 CONCRETE FRAME DESIGN ACI Technical Note 18 Design Load Combinations The design load combinations are the various combinations of the prescribed load cases for which the structure needs to be checked. For the ACI code, if a structure is subjected to dead load (DL) and live load (LL) only, the stress check may need only one load combination, namely 1.4 DL LL (ACI 9.2.1). However, 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 forces are reversible, the following load combinations should be considered (ACI 9.2). 1.4 DL 1.4 DL LL (ACI 9.2.1) 0.9 DL ± 1.3 WL 0.75 (1.4 DL LL ± 1.7 WL) (ACI 9.2.2) 0.9 DL ± 1.3 * 1.1 EL 0.75 (1.4 DL LL ± 1.7 * 1.1 EL) (ACI 9.2.3) These are also the default design load combinations in the program whenever the ACI code is used. The user is warned that the above load combinations involving seismic loads consider service-level seismic forces. Different load factors may apply with strength-level seismic forces (ACI R9.2.3). Live load reduction factors can be applied to the member forces of the live load condition on an element-by-element basis to reduce the contribution of the live load to the factored loading. See Concrete Frame Design ACI Technical Note 17 Overwrites for more information. Design Load Combinations Technical Note 18-1

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114 COMPUTERS AND STRUCTURES, INC., BERKELEY, CALIFORNIA DECEMBER 2001 CONCRETE FRAME DESIGN ACI Technical Note 19 Strength Reduction Factors The strength reduction factors, ϕ, are applied on the nominal strength to obtain the design strength provided by a member. The ϕ factors for flexure, axial force, shear, and torsion are as follows: ϕ = 0.90 for flexure (ACI ) ϕ = 0.90 for axial tension (ACI ) ϕ = 0.90 for axial tension and flexure (ACI ) ϕ = 0.75 for axial compression, and axial compression and flexure (spirally reinforced column) (ACI ) ϕ = 0.70 for axial compression, and axial compression and flexure (tied column) (ACI ) ϕ = 0.85 for shear and torsion (ACI ) Strength Reduction Factors Technical Note 19-1

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116 COMPUTERS AND STRUCTURES, INC., BERKELEY, CALIFORNIA DECEMBER 2001 CONCRETE FRAME DESIGN ACI Technical Note 20 Column Design This Technical Note describes how the program checks column capacity or designs reinforced concrete columns when the ACI code is selected. Overview The program can be used to check column capacity or to design columns. If you define the geometry of the reinforcing bar configuration of each concrete column section, the program will check the column capacity. Alternatively, the program can calculate the amount of reinforcing required to design the column. The design procedure for the reinforced concrete columns of the structure involves the following steps: Generate axial force/biaxial moment interaction surfaces for all of the different concrete section types of the model. A typical biaxial interaction surface is shown in Figure 1. When the steel is undefined, the program generates the interaction surfaces for the range of allowable reinforcement 1 to 8 percent for Ordinary and Intermediate moment resisting frames (ACI ) and 1 to 6 percent for Special moment resisting frames (ACI ). Calculate the capacity ratio or the required reinforcing area for the factored axial force and biaxial (or uniaxial) bending moments obtained from each loading combination at each station of the column. The target capacity ratio is taken as one when calculating the required reinforcing area. Design the column shear reinforcement. The following four sections describe in detail the algorithms associated with this process. Overview Technical Note 20-1

117 Column Design Concrete Frame Design ACI Figure 1 A Typical Column Interaction Surface Generation of Biaxial Interaction Surfaces The column capacity interaction volume is numerically described by a series of discrete points that are generated on the three-dimensional interaction failure surface. In addition to axial compression and biaxial bending, the formulation allows for axial tension and biaxial bending considerations. A typical interaction diagram is shown in Figure 1. The coordinates of these points are determined by rotating a plane of linear strain in three dimensions on the section of the column. See Figure 2. The Technical Note 20-2 Generation of Biaxial Interaction Surfaces

118 Concrete Frame Design ACI Column Design linear strain diagram limits the maximum concrete strain, ε c, at the extremity of the section, to (ACI ). The formulation is based consistently upon the general principles of ultimate strength design (ACI 10.3), and allows for any doubly symmetric rectangular, square, or circular column section. The stress in the steel is given by the product of the steel strain and the steel modulus of elasticity, ε s E s, and is limited to the yield stress of the steel, f y (ACI ). The area associated with each reinforcing bar is assumed to be placed at the actual location of the center of the bar and the algorithm does not assume any further simplifications with respect to distributing the area of steel over the cross section of the column, such as an equivalent steel tube or cylinder. See Figure 3. The concrete compression stress block is assumed to be rectangular, with a stress value of 0.85 f (ACI ). See Figure 3. The interaction algorithm ' c provides correction to account for the concrete area that is displaced by the reinforcement in the compression zone. The effects of the strength reduction factor, ϕ, are included in the generation of the interaction surfaces. The maximum compressive axial load is limited to ϕp n(max), where ϕp n(max) = 0.85ϕ[0.85 f c ' (A g -A st )+f y A st ] spiral column, (ACI ) ϕp n(max) = 0.80ϕ[0.85 f c ' (A g -A st )+f y A st ] tied column, (ACI ) ϕ = 0.70 for tied columns, and (ACI ) ϕ = 0.75 for spirally reinforced columns. (ACI ) The value of ϕ used in the interaction diagram varies from ϕ(compression) to ϕ(flexure) based on the axial load. For low values of axial load, ϕ is increased linearly from ϕ(compression) to ϕ(flexure) as the ϕp n decreases from the ' c smaller of ϕp b or 0.1 f A g to zero, where ϕp b is the axial force at the balanced condition. The ϕ factor used in calculating ϕp n and ϕp b is the ϕ(compression). In cases involving axial tension, ϕ is always ϕ(flexure), which is 0.9 by default (ACI ). Generation of Biaxial Interaction Surfaces Technical Note 20-3

119 Column Design Concrete Frame Design ACI Figure 2 Idealized Strain Distribution for Generation of Interaction Source Technical Note 20-4 Generation of Biaxial Interaction Surfaces

120 Concrete Frame Design ACI Column Design Figure 3 Idealization of Stress and Strain Distribution in a Column Section Calculate Column Capacity Ratio The column capacity ratio is calculated for each load combination at each output station of each column. The following steps are involved in calculating the capacity ratio of a particular column for a particular load combination at a particular location: Determine the factored moments and forces from the analysis load cases and the specified load combination factors to give P u, M ux, and M uy. Determine the moment magnification factors for the column moments. Apply the moment magnification factors to the factored moments. Determine whether 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 the identification of the individual column as either sway or non-sway. The following three sections describe in detail the algorithms associated with this process. Calculate Column Capacity Ratio Technical Note 20-5

121 Column Design Concrete Frame Design ACI 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 u, M ux, and M uy. The factored moments are further increased for non-sway columns, if required, to obtain minimum eccentricities of ( h) inches, where h is the dimension of the column in the corresponding direction (ACI ). Determine Moment Magnification Factors The moment magnification factors are calculated separately for sway (overall stability effect), δ s and for non-sway (individual column stability effect), δ ns. Also, the moment magnification factors in the major and minor directions are in general different (ACI 10.0, R10.13). 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 predominantly caused by lateral loads, and are related to the cause of side sway. For individual columns or column-members in a floor, the magnified moments about two axes at any station of a column can be obtained as M = M ns + δ s M s. (ACI ) The factor δ s is the moment magnification factor for moments causing side sway. The moment magnification factors for sway moments, δ s, is taken as 1 because the component moments M s and M ns are obtained from a second order elastic (P-delta) analysis (ACI R10.10, , R10.13, ). The program assumes that it performs a P-delta analysis and, therefore, moment magnification factor δ s for moments causing side-sway is taken as unity (ACI ). For the P-delta analysis, the load should correspond to a load combination of 1.4 dead load live load (ACI ). See also White and Hajjar (1991). The user should use reduction factors for the moment of inertias in the program as specified in ACI The moment of inertia reduction for sustained lateral load involves a factor β d (ACI 10.11). This β d for sway frame in second-order analysis is different from the one that is defined later for non-sway moment magnification (ACI 10.0, R , R ). The default moment of inertia factor in this program is 1. Technical Note 20-6 Calculate Column Capacity Ratio

122 Concrete Frame Design ACI Column Design The computed moments are further amplified for individual column stability effect (ACI , ) by the nonsway moment magnification factor, δ ns, as follows: M c = δ ns M, where (ACI ) M c is the factored moment to be used in design. The non-sway moment magnification factor, δ ns, associated with the major or minor direction of the column is given by (ACI ) δ ns = Cm Pu P c 1.0, where (ACI ) Ma C m = , (ACI ) M b M a and M b are the moments at the ends of the column, and M b is numerically larger than M a. M a / M b is positive for single curvature bending and negative for double curvature bending. The above expression of C m is valid if there is no transverse load applied between the supports. If transverse load is present on the span, or the length is overwritten, C m =1. The user can overwrite C m on an element-byelement basis. P c = π 2 EI ( kl u ) 2, where (ACI ) k is conservatively taken as 1; however, the program allows the user to override this value (ACI ). l u is the unsupported length of the column for the direction of bending considered. The two unsupported lengths are l 22 and l 33, corresponding to instability in the minor and major directions of the element, respectively. See Figure 4. These are the lengths Calculate Column Capacity Ratio Technical Note 20-7

123 Column Design Concrete Frame Design ACI Figure 4 Axes of Bending and Unsupported Length between the support points of the element in the corresponding directions. EI is associated with a particular column direction: EI = 0.4E c I g 1 + β d, where (ACI ) β d = maximum factored axial sustained (dead) load maximum factored axial total load (ACI 10.0,R ) The magnification factor, δ ns, must be a positive number and greater than one. Therefore, P u must be less than 0.75P c. If P u is found to be greater than or equal to 0.75P c, a failure condition is declared. Technical Note 20-8 Calculate Column Capacity Ratio

124 Concrete Frame Design ACI Column Design The above calculations are performed for major and minor directions separately. That means that δ s, δ ns, C m, k, l u, EI, and P c assume different values for major and minor directions of bending. If the program assumptions are not satisfactory for a particular member, the user can explicitly specify values of δ s and δ ns. 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 condition of the column with respect to the capacity of the column. Before entering the interaction diagram to check the column capacity, the moment magnification factors are applied to the factored loads to obtain P u, M ux, and M uy. The point (P u, M ux, M uy ) is then placed in the interaction space shown 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 interaction volume, the column is overstressed. 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 outwards) will intersect the failure surface. This point is determined by three-dimensional linear interpolation between the points that define the failure surface. See Figure 5. The capacity ratio, CR, is given by the ratio. OL OC If OL = OC (or CR=1), the point lies on the interaction surface and the column is stressed to capacity. If OL < OC (or CR<1), the point lies within the interaction volume and the column capacity is adequate. If OL > OC (or CR>1), the point lies outside the interaction volume and the column is overstressed. The maximum of all the values of CR calculated from each load combination is reported for each check station of the column along with the controlling P u, M ux, and M uy set and associated load combination number. Calculate Column Capacity Ratio Technical Note 20-9

125 Column Design Concrete Frame Design ACI Figure 5 Geometric Representation of Column Capacity Ratio Required Reinforcing Area If the reinforcing area is not defined, the program computes the reinforcement that will give a column capacity ratio of one, calculated as described in the previous section entitled "Calculate Column Capacity Ratio." Design Column Shear Reinforcement The shear reinforcement is designed for each load combination in the major and minor directions of the column. The following steps are involved in designing the shear reinforcing for a particular column for a particular load combination resulting from shear forces in a particular direction: Technical Note Required Reinforcing Area

126 Concrete Frame Design ACI Column Design 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. For Special and Intermediate moment resisting frames (Ductile frames), the shear design of the columns is also based on the Probable moment and nominal moment capacities of the members, respectively, in addition to the factored moments. Effects of the axial forces on the column moment capacities are included in the formulation. The following three sections describe in detail the algorithms associated with this 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, P u, and the column shear force, V u, in a particular direction are obtained by factoring the program analysis load cases with the corresponding load combination factors. In the shear design of Special moment resisting frames (i.e., seismic design), the column is checked for capacity shear in addition to the requirement for the Ordinary moment resisting frames. The capacity shear force in a column, V p, in a particular direction is calculated from the probable moment capacities of the column 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 particular direction under the influence of the axial force P u is calculated using the uniaxial interaction diagram in the corresponding direction. The design shear force, V u, is then given by (ACI ) V u = V p + V D+L (ACI ) where, V p is the capacity shear force obtained by applying the calculated probable ultimate moment capacities at the two ends of the column acting Design Column Shear Reinforcement Technical Note 20-11

127 Column Design Concrete Frame Design ACI in two opposite directions. Therefore, V p is the maximum of where VP 1 and V P 2, V P 1 = V P 2 = M M I + L + I + L M M + J J, and, where + I M I M,, = Positive and negative moment capacities at end I of the + J M J column using a steel yield stress value of αf y and no ϕ factors (ϕ = 1.0), M,, = Positive and negative moment capacities at end J of the column using a steel yield stress value of αf y and no ϕ factors (ϕ = 1.0), and L = Clear span of column. For Special moment resisting frames α is taken as 1.25 (ACI 10.0, R ). V D+L is the contribution of shear force from the in-span distribution of gravity loads. 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 for Ordinary moment resisting frames. The design shear force is taken to be the minimum of that based on the nominal (ϕ = 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 moment resisting frames, except that α is taken equal to 1 rather than 1.25 (ACI a, R21.10). The modified factored shear forces are based on the specified load factors, except the earthquake load factors are doubled (ACI b). Determine Concrete Shear Capacity Given the design force set P u and V u, the shear force carried by the concrete, V c, is calculated as follows: Technical Note Design Column Shear Reinforcement

128 Concrete Frame Design ACI Column Design If the column is subjected to axial compression, i.e., P u is positive, V c = 2 f ' c Pu 1 + 2,000A g A cv, where (ACI ) ' fc 100 psi, and (ACI ) V c 3.5 ' f c Pu 1 + A cv. (ACI ) 500Ag The term P u / A g must have psi units. A cv is the effective shear area, which is shown shaded in Figure 6. For circular columns, A cv is taken to be equal to the gross area of the section (ACI , R11.3.3). If the column is subjected to axial tension, P u is negative V c = 2 ' f c Pu 1 + A cv 0 (ACI ) 500Ag For Special moment resisting concrete frame design, V c is set to zero if the factored axial compressive force, P u, including the earthquake effect, is small (P u < fc ' A g / 20) and if the shear force contribution from earthquake, V E, is more than half of the total factored maximum shear force over the length of the member V u (V E 0.5V u ) (ACI ). Determine Required Shear Reinforcement Given V u and V c, the required shear reinforcement in the form of stirrups or ties within a spacing, s, is given for rectangular and circular columns by A v = A v = ( V / ϕ V u c ) f ys d s, for rectangular columns and (ACI , ) ( Vu / ϕ Vc ) s, for circular columns. (ACI , ) f (0.8D) ys V u is limited by the following relationship. (V u / ϕ-v c ) 8 ' fc A cv (ACI ) Design Column Shear Reinforcement Technical Note 20-13

129 Column Design Concrete Frame Design ACI Figure 6 Shear Stress Area, A cv Otherwise, redimensioning of the concrete section is required. Here ϕ, the strength reduction factor, is 0.85 (ACI ). The maximum of all the calculated A v values obtained from each load combination are reported for the major and minor directions of the column, along with the controlling shear force and associated load combination label. The column shear reinforcement requirements reported by the program are based purely on shear strength consideration. Any minimum stirrup requirements to satisfy spacing considerations or transverse reinforcement volumetric considerations must be investigated independently of the program by the user. Technical Note Design Column Shear Reinforcement

130 Concrete Frame Design ACI Column Design Reference White, D.W. and J.F. Hajjar Application of Second-Order Elastic Analysis in LRFD: Research to Practice. Engineering Journal. American Institute of Steel Construction, Inc. Vol. 28. No. 4. Reference Technical Note 20-15

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132 COMPUTERS AND STRUCTURES, INC., BERKELEY, CALIFORNIA DECEMBER 2001 CONCRETE FRAME DESIGN ACI Technical Note 21 Beam Design This Technical Note describes how this program completes beam design when the ACI code is selected. The program calculates and reports the required areas of steel for flexure and shear based on the beam moments, shears, load combination factors and other criteria described herein. Overview In the design of concrete beams, the program calculates and reports the required areas of steel for flexure and shear based on the beam moments, shears, load combination factors, and other criteria described below. The reinforcement requirements are calculated at a user-defined number of check/design stations along the beam span. All beams are designed for major direction flexure and shear only. Effects resulting from any axial forces, minor direction bending, and torsion that may exist in the beams must be investigated independently by the user. The beam design procedure involves the following steps: Design beam flexural reinforcement Design beam shear reinforcement Design Beam Flexural Reinforcement The beam top and bottom flexural steel is designed at check/design stations along the beam span. The following steps are involved in designing the flexural reinforcement for the major moment for a particular beam for a particular section: Determine the maximum factored moments Determine the reinforcing steel Overview Technical Note 21-1

133 Beam Design Concrete Frame Design ACI Determine Factored Moments In the design of flexural reinforcement of Special, Intermediate, or Ordinary moment resisting concrete frame beams, the factored moments for each load combination at a particular beam section are obtained by factoring the corresponding moments for different load cases with the corresponding load factors. + M u and maxi- The beam section is then designed for the maximum positive mum negative tions. M u factored moments obtained from all of the load combina- Negative beam moments produce top steel. In such cases, the beam is always designed as a rectangular section. Positive beam moments produce bottom steel. In such cases, the beam may be designed as a Rectangular- or a T-beam. Determine Required Flexural Reinforcement In the flexural reinforcement design process, the program calculates both the tension and compression reinforcement. Compression reinforcement is added when the applied design moment exceeds the maximum moment capacity of a singly reinforced section. The user has the option of avoiding the compression reinforcement by increasing the effective depth, the width, or the grade of concrete. The design procedure is based on the simplified rectangular stress block as shown in Figure 1 (ACI 10.2). It is assumed that the compression carried by concrete is less than 0.75 times that which can be carried at the balanced condition (ACI ). When the applied moment exceeds the moment capacity at this designed balanced condition, the area of compression reinforcement is calculated assuming that the additional moment will be carried by compression and additional tension reinforcement. The design procedure used by this program for both rectangular and flanged sections (L- and T-beams) is summarized below. It is assumed that the design ultimate axial force does not exceed 0.1 f ' c A g (ACI ); hence, all the beams are designed for major direction flexure and shear only. Technical Note 21-2 Design Beam Flexural Reinforcement

134 Concrete Frame Design ACI Beam Design Figure 1 Design of Rectangular Beam Section Design for Rectangular Beam In designing for a factored negative or positive moment, M u (i.e., designing top or bottom steel), the depth of the compression block is given by a (see Figure 1), where, a = d - d 2 2 M 0.85f u 1 c, (ACI ) ϕb where, the value of ϕ is 0.90 (ACI ) in the above and the following equations. Also β 1 and c b are calculated as follows: β 1 = ' f c 4,000, 0.65 β 1, , (ACI ) c b = ε c ε E c s E s + f y d = 87,000 87,000 + f y d. (ACI , ) Design Beam Flexural Reinforcement Technical Note 21-3

135 Beam Design Concrete Frame Design ACI The maximum allowed depth of the compression block is given by a max = 0.75β 1 c b. (ACI , ) If a a max, the area of tensile steel reinforcement is then given by A s = ϕf y Mu. a d 2 This steel is to be placed at the bottom if M u is positive, or at the top if M u is negative. If a > a max, compression reinforcement is required (ACI ) and is calculated as follows: The compressive force developed in concrete alone is given by ' c C = 0.85 f ba max, and (ACI ) the moment resisted by concrete compression and tensile steel is a M uc = C d max ϕ. 2 Therefore the moment resisted by compression steel and tensile steel is M us = M u - M uc. So the required compression steel is given by ' A s = Mus, where f ( d d' )ϕ ' s ' c f s = 0.003E s c d'. (ACI ) The required tensile steel for balancing the compression in concrete is Technical Note 21-4 Design Beam Flexural Reinforcement

136 Concrete Frame Design ACI Beam Design A s1 = f y M d uc a max 2 ϕ, and the tensile steel for balancing the compression in steel is given by A s2 = Mus. f ( d d' )ϕ y Therefore, the total tensile reinforcement, A s = A s1 + A s2, and total compression reinforcement is ' ' A s. A s is to be placed at bottom and A s is to be placed at top if M u is positive, and vice versa if M u is negative. Design for T-Beam In designing for a factored negative moment, M u (i.e., designing top steel), the calculation of the steel area is exactly the same as above, i.e., no T-Beam data is to be used. See Figure 2. If M u > 0, the depth of the compression block is given by 2 2Mu a = d - d. ' 0.85fc ϕbf The maximum allowed depth of compression block is given by a max = 0.75β 1 c b. (ACI , ) If a d s, the subsequent calculations for A s are exactly the same as previously defined for the rectangular section design. However, in this case the width of the compression flange is taken as the width of the beam for analysis. Compression reinforcement is required if a > a max. If a > d s, calculation for A s is performed in two parts. The first part is for balancing the compressive force from the flange, C f, and the second part is for balancing the compressive force from the web, C w, as shown in Figure 2. C f is given by C f = 0.85 ' f c (b f - b w )d s. Design Beam Flexural Reinforcement Technical Note 21-5

137 Beam Design Concrete Frame Design ACI Figure 2 Design of a T-Beam Section Therefore, A s1 = given by C f f y and the portion of Mu that is resisted by the flange is M uf = C f ds d ϕ. 2 Again, the value for ϕ is ϕ(flexure), which is 0.90 by default. Therefore, the balance of the moment, M u to be carried by the web is given by M uw = M u - M uf. The web is a rectangular section of dimensions b w and d, for which the design depth of the compression block is recalculated as a 1 = d - d 2 2M 0.85f uw i c ϕ b w. If a 1 a max, the area of tensile steel reinforcement is then given by A s2 = ϕf y Muw, and a d 1 2 Technical Note 21-6 Design Beam Flexural Reinforcement

138 Concrete Frame Design ACI Beam Design A s = A s1 + A s2. This steel is to be placed at the bottom of the T-beam. If a 1 > a max, compression reinforcement is required (ACI ) and is calculated as follows: The compressive force in web concrete alone is given by C = 0.85 ' fc ba max. (ACI ) Therefore, the moment resisted by concrete web and tensile steel is a M uc = C d max ϕ, and 2 the moment resisted by compression steel and tensile steel is M us = M uw - M uc. Therefore, the compression steel is computed as ' A s = ' s M us f ( d d' )ϕ, where ' c f s = 0.003E s c d'. (ACI ) The tensile steel for balancing compression in web concrete is A s2 = f ( d y M uc a max )ϕ 2, and the tensile steel for balancing compression in steel is A s3 = Mus. f ( d d' )ϕ y Design Beam Flexural Reinforcement Technical Note 21-7

139 Beam Design Concrete Frame Design ACI The total tensile reinforcement, A s = A s1 + A s2 + A s3, and total ' compression reinforcement is A s. A s is to be placed at bottom and ' A s is to be placed at top. Minimum Tensile Reinforcement The minimum flexural tensile steel provided in a rectangular section in an Ordinary moment resisting frame is given by the minimum of the two following limits: 3 f c 200 A s max bw d and bw d fy fy or (ACI ) A s (4/3)A s(required). (ACI ) Special Consideration for Seismic Design For Special moment resisting concrete frames (seismic design), the beam design satisfies the following additional conditions (see also Table 1): The minimum longitudinal reinforcement shall be provided at both the top and bottom. Any of the top and bottom reinforcement shall not be less than A s(min) (ACI ). A s(min) max 3 f ' c 200 bw d and bw d or (ACI ) fy fy A s(min) 3 4 As(required). (ACI ) The beam flexural steel is limited to a maximum given by A s b w d. (ACI ) At any end (support) of the beam, the beam positive moment capacity (i.e., associated with the bottom steel) would not be less than 1/2 of the beam negative moment capacity (i.e., associated with the top steel) at that end (ACI ). Neither the negative moment capacity nor the positive moment capacity at any of the sections within the beam would be less than 1/4 of the Technical Note 21-8 Design Beam Flexural Reinforcement

140 Concrete Frame Design ACI Beam Design maximum of positive or negative moment capacities of any of the beam end (support) stations (ACI ). For Intermediate moment resisting concrete frames (i.e., seismic design), the beam design would satisfy the following conditions: At any support of the beam, the beam positive moment capacity would not be less than 1/3 of the beam negative moment capacity at that end (ACI ). Neither the negative moment capacity nor the positive moment capacity at any of the sections within the beam would be less than 1/5 of the maximum of positive or negative moment capacities of any of the beam end (support) stations (ACI ). Design Beam Shear Reinforcement The shear reinforcement is designed for each load combination at a user defined number of stations along the beam span. The following steps are involved in designing the shear reinforcement for a particular beam for a particular load combination at a particular station due to the beam major shear: Determine the factored shear force, V u. Determine the shear force, V c, that can be resisted by the concrete. Determine the reinforcement steel required to carry the balance. For Special and Intermediate moment resisting frames (ductile frames), the shear design of the beams is also based upon the probable and nominal moment capacities of the members, respectively, in addition to the factored load design. The following three sections describe in detail the algorithms associated with this process. Design Beam Shear Reinforcement Technical Note 21-9

141 Beam Design Concrete Frame Design ACI Table 1 Design Criteria Table Type of Check/ Design Column Check (interaction) Ordinary Moment Resisting Frames (non-seismic) Intermediate Moment Resisting Frames (Seismic) Special Moment Resisting Frames (Seismic) NLD a Combinations NLD a Combinations NLD a Combinations Column Design (interaction) NLD a Combinations 1% < ρ < 8% NLD a Combinations 1% < ρ < 8% NLD a Combinations α = 1.0 1% < ρ < 6% Column Shears NLD a Combinations Modified NLD a Combinations (earthquake loads doubled) Column capacity ϕ = 1.0 and α = 1.0 NLD a Combinations Column shear capacity ϕ = 1.0 and α = 1.25 Beam Design Flexure NLD a Combinations NLD a Combinations NLD a Combinations ρ ρ f f c ' y, ρ 200 f y Beam Min. Moment Override Check No Requirement + 1 M uend M u 3 END M M + uspan uspan + { M u M u } END 1 max, max M u, M 5 { u } END + 1 M uend M u 2 END M M + uspan uspan 1 max 4, 1 max 4, + { M u M u } END { M u M u } END Beam Design Shear NLD a Combinations Modified NLD a Combinations (earthquake loads doubled) Beam Capacity Shear (Vp) with α = 1.0 and ϕ = 1.0 plus VD+L NLD a Combinations Beam Capacity Shear (Vp) with α = 1.25 and ϕ = 1.0 plus VD+L Vc = 0 Joint Design No Requirement No Requirement Checked for shear Beam/Column Capacity Ratio No Requirement No Requirement Reported in output file NLD a = Number of specified loading Technical Note Design Beam Shear Reinforcement

142 Concrete Frame Design ACI Beam Design Determine Shear Force and Moment In the design of the beam shear reinforcement of an Ordinary moment resisting concrete frame, the shear forces and moments for a particular load combination at a particular beam section are obtained by factoring the associated shear forces and moments with the corresponding load combination factors. In the design of Special moment resisting concrete frames (i.e., seismic design), the shear capacity of the beam is also checked for the capacity shear resulting from the probable moment capacities at the ends and the factored gravity load. This check is performed in addition to the design check required for Ordinary moment resisting frames. The capacity shear force, V p, is calculated from the probable moment capacities of each end of the beam and the gravity shear forces. The procedure for calculating the design shear force in a beam from probable moment capacity is the same as that described for a column in section Design Column Shear Reinforcement of Concrete Frame Design ACI Technical Note 20 Column Design. See also Table 1 for details. The design shear force V u is then given by (ACI ) V u = V p + V D+L (ACI ) where V p is the capacity shear force obtained by applying the calculated probable ultimate moment capacities at the two ends of the beams acting in two opposite directions. Therefore, V p is the maximum of V and V, where P 1 P 2 V P 1 = V P 2 = M M I + L L I + + M M + J J, and, where M I = Moment capacity at end I, with top steel in tension, using a steel yield stress value of αf y and no ϕ factors (ϕ = 1.0), + M J = Moment capacity at end J, with bottom steel in tension, using a steel yield stress value of αf y and no ϕ factors (ϕ = 1.0), Design Beam Shear Reinforcement Technical Note 21-11

143 Beam Design Concrete Frame Design ACI M I = Moment capacity at end I, with bottom steel in tension, using a steel yield stress value of αf y and no ϕ factors (ϕ = 1.0), M J = Moment capacity at end J, with top steel in tension, using a steel yield stress value of αf y and no ϕ factors (ϕ = 1.0), and L = Clear span of beam. For Special moment resisting frames α is taken as 1.25 (ACI 21.0, R ). V D+L is the contribution of shear force from the in-span distribution of gravity loads. For Intermediate moment resisting frames, the shear capacity of the beam 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 for Ordinary moment resisting frames. The design shear force in beams is taken to be the minimum of that based on the nominal moment capacity and modified factored shear force. The procedure for calculating nominal (ϕ = 1.0) moment capacity is the same as that for computing the probable moment capacity for Special moment resisting frames, except that α is taken equal to 1 rather than 1.25 (ACI a, R21.10). The modified factored shear forces are based on the specified load factors, except the earthquake load factors are doubled (ACI b). The computation of the design shear force in a beam of an Intermediate moment resisting frame is the same as described for columns in section Determine Section Forces of Concrete Frame Design ACI Technical Note 20 Column Design. See also Table 1 for details. Determine Concrete Shear Capacity The allowable concrete shear capacity is given by V c = 2 ' fc b w d. (ACI ) For Special moment resisting frame concrete design, V c is set to zero if both the factored axial compressive force, including the earthquake effect P u, is less than f ' c A g /20 and the shear force contribution from earthquake V E is more than half of the total maximum shear force over the length of the member V u (i.e., V E 0.5V u ) (ACI ). Technical Note Design Beam Shear Reinforcement

144 Concrete Frame Design ACI Beam Design Determine Required Shear Reinforcement Given V u and V c, the required shear reinforcement in area/unit length is calculated as A v = ( Vu / ϕ Vc ) s. (ACI , ) f d ys The shear force resisted by steel is limited by (V u / ϕ - V c ) 8 ' fc bd. (ACI ) Otherwise, redimensioning of the concrete section is required. Here, ϕ, the strength reduction factor for shear, is 0.85 by default (ACI ). The maximum of all the calculated A v values, obtained from each load combination, is reported along with the controlling shear force and associated load combination number. The beam shear reinforcement requirements displayed by the program are based purely on shear strength considerations. Any minimum stirrup requirements to satisfy spacing and volumetric considerations must be investigated independently of the program by the user. Design Beam Shear Reinforcement Technical Note 21-13

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146 COMPUTERS AND STRUCTURES, INC., BERKELEY, CALIFORNIA DECEMBER 2001 CONCRETE FRAME DESIGN ACI Technical Note 22 Joint Design This Technical Note explains how the program performs a rational analysis of the beam-column panel zone to determine the shear forces that are generated in a joint. The program then checks this against design shear strength. Overview To ensure that the beam-column joint of special moment resisting frames possesses adequate 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. The program 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 completed in the major and the minor directions of the column. The joint 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 algorithms associated with these three steps are described in detail in the following three sections. Determine the Panel Zone Shear Force Figure 1 illustrates the free body stress condition of a typical beam-column intersection for a column direction, major or minor. Overview Technical Note 22-1

147 Joint Design Concrete Frame Design ACI Figure 1 Beam-Column Joint Analysis Technical Note 22-2 Determine the Panel Zone Shear Force

148 Concrete Frame Design ACI Joint Design The force V h u 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 L u and M R u. The forces P u and V u are axial force and shear force, respectively, from the column framing into the L top of the joint. The moments M u and M R u are obtained from the beams h framing into the joint. The program calculates the joint shear force V u by resolving the moments into C and T forces. Noting that T L = C L and T R = C R, V u h = T L + T R - V u The location of C or T forces is determined by the direction of the moment. The magnitude of C or T forces is conservatively determined using basic principles of ultimate strength theory, ignoring compression reinforcement as follows. The program first calculates the maximum compression, C max, and the maximum moment, M max, that can be carried by the beam. C max = 0. 85f ' c bd M = C max max d 2 Then the program conservatively determines C and T forces as follows: C = T = C max 1 abs( M ) 1 M max The program resolves the moments and the C and T forces from beams that frame into the joint in a direction that is not parallel to the major or minor directions of the column along the direction that is being investigated, thereby contributing force components to the analysis. Also, the program calculates the C and T for the positive and negative moments, considering the fact that the concrete cover may be different for the direction of moment. In the design of special moment resisting concrete frames, the evaluation of the design shear force is based on the moment capacities (with reinforcing steel overstrength factor, α, and no ϕ factors) of the beams framing into the joint (ACI , UBC ). The C and T force are based on these moment capacities. The program calculates the column shear force V u from the beam moment capacities, as follows: Determine the Panel Zone Shear Force Technical Note 22-3

149 Joint Design Concrete Frame Design ACI V u = M L u + M H R u See Figure 2. It should be noted that the points of inflection shown on Figure 2 are taken as midway between actual lateral support points for the columns. If there is no column at the top of the joint, the shear force from the top of the column is taken as zero. The effects of load reversals, as illustrated in Case 1 and Case 2 of Figure 1, are investigated and the design is based on the maximum of the joint shears obtained from the two cases. Determine the Effective Area of Joint The joint area that resists the shear forces is assumed always to be rectangular in plan view. The dimensions of the rectangle correspond to the major and minor dimensions of the column below the joint, except if the beam framing into the joint is very narrow. The effective width of the joint area to be used in the calculation is limited to the width of the beam plus the depth of the column. The area of the joint is assumed not to exceed the area of the column below. The joint area for joint shear along 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 assumptions may be unconservative and the user should investigate the acceptability of the particular joint. Check Panel Zone Shear Stress The panel zone shear stress is evaluated by dividing the shear force V u h by the effective area of the joint and comparing it with the following design shear strengths (ACI , UBC ): { 20ϕ f ' for joints confirmed on all four sides c v = 15ϕ f ' for joints confirmed on three faces or on two c opposite faces 12ϕ f ' for all other joints c Technical Note 22-4 Determine the Effective Area of Joint

150 Concrete Frame Design ACI Joint Design Figure 2 Column Shear Force V u where ϕ = 0.85 (by default). (ACI , UBC , ) A beam that frames into a face of a column at the joint is considered in this program to provide confinement to the joint if at least three-quarters of the face of the joint is covered by the framing member (ACI , UBC ). Determine the Effective Area of Joint Technical Note 22-5

151 Joint Design Concrete Frame Design ACI For light-weight aggregate concrete, the design shear strength of the joint is reduced in the program to at least three-quarters of that of the normal weight ' concrete by replacing the f c with ' ' min f cs, factor fc,3 / 4 fc (ACI , UBC ) For joint design, the program reports the joint shear, the joint shear stress, the allowable joint shear stress and a capacity ratio. Beam/Column Flexural Capacity Ratios At a particular joint for a particular column direction, major or minor, the program will calculate the ratio of the sum of the beam moment capacities to the sum of the column moment capacities (ACI ). M e 5 6 Mg (ACI ) The capacities are calculated with no reinforcing overstrength factor, α, and including ϕ factors. The beam capacities are calculated for reversed situations (Cases 1 and 2) as illustrated in Figure 1 and the maximum summation obtained is used. The moment capacities of beams that frame into the joint in a direction that is not parallel to the major or minor direction of the column are resolved along the direction that is being investigated and the resolved components are added to the summation. 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 is calculated from the program analysis load combinations. For each load combination, the moment capacity of each column under the influence of the corresponding axial load P u is then determined separately for the major and minor directions of the column, using the uniaxial column interaction diagram; see Figure 3. The moment capacities of the two columns are added to give the capacity summation for the corresponding load combination. The maximum capacity summations obtained from all of the load combinations is used for the beam/column capacity ratio. Technical Note 22-6 Beam/Column Flexural Capacity Ratios

152 Concrete Frame Design ACI Joint Design The beam/column flexural capacity ratios are only reported for Special Moment-Resisting Frames involving seismic design load combinations. If this ratio is greater than 5/6, a warning message is printed in the output file. Figure 3 Moment Capacity M u at a Given Axial Load P u Beam/Column Flexural Capacity Ratios Technical Note 22-7

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154 COMPUTERS AND STRUCTURES, INC., BERKELEY, CALIFORNIA DECEMBER 2001 CONCRETE FRAME DESIGN ACI Technical Note 23 Input Data This Technical Note describes the concrete frame design input data for ACI The input can be printed to a printer or to a text file when you click the File menu > Print Tables > Concrete Frame Design command. A printout of the input data provides the user with the opportunity to carefully review the parameters that have been input into the program and upon which program design is based. Further information about using the Print Design Tables form is presented at the end of this Technical Note. Input Data The program provides the printout of the input data in a series of tables. The column headings for input data and a description of what is included in the columns of the tables are provided in Table 1 of this Technical Note. Table 1 Concrete Frame Design Input Data COLUMN HEADING Load Combination Multipliers DESCRIPTION Combo Design load combination. See Technical Note 8. Type Case Factor Code Preferences Phi_bending Phi_tension Phi_compression (Tied) Phi_compression (Spiral) Phi_shear Load type: dead, live, superimposed dead, earthquake, wind, snow, reduced live load, other. Name of load case. Load combination scale factor. Bending strength reduction factor. Tensile strength reduction factor. Compressive strength reduction factor for tied columns. Compressive strength reduction factor for reinforced columns. Shear strength reduction factor. Input Data Technical Note 23-1

155 Input Data Concrete Frame Design ACI Table 1 Concrete Frame Design Input Data COLUMN HEADING Material Property Data Material Name Material Type Design Type Modulus of Elasticity Poisson's Ratio Thermal Coeff DESCRIPTION Concrete, steel, other. Isotropic or orthotropic. Shear Modulus Material Property Mass and Weight Material Name Mass Per Unit Vol Weight Per Unit Vol Coefficient of thermal expansion. Concrete, steel, other. Used to calculate self-mass of structure. Material Design Data for Concrete Materials Material Name Lightweight Concrete Concrete FC Rebar FY Rebar FYS Lightwt Reduc Fact Concrete Column Property Data Section Label Mat Label Column Depth Column Width Rebar Pattern Concrete Cover Bar Area Used to calculate self-weight of structure. Concrete, steel, other. Concrete compressive strength. Bending reinforcing steel yield strength. Shear reinforcing steel yield strength. Shear strength reduction factor for light weight concrete; default = 1.0. Label applied to section. Material label. Layout of main flexural reinforcing steel. Minimum clear concrete cover. Area of individual reinforcing bar to be used. Technical Note 23-2 Table 1 Concrete Frame Design Input Data

156 Concrete Frame Design ACI Input Data Table 1 Concrete Frame Design Input Data COLUMN HEADING DESCRIPTION Concrete Column Design Element Information Story ID Column Line Section ID Framing Type RLLF Factor L_Ratio Major L_Ratio Minor Column assigned to story level at top of column. Grid line. Name of section assigned to column. Lateral or gravity. Unbraced length about major axis. Unbraced length about minor axis. K Major Effective length factor; default = 1.0. K Minor Effective length factor; default = 1.0. Concrete Beam Design Element Information Story ID Bay ID Section ID Framing type RLLF Factor L_Ratio Major L_Ratio Minor Story level at which beam occurs. Grid lines locating beam. Section number assigned to beam. Lateral or gravity. Unbraced length about major axis. Unbraced length about minor axis. Using the Print Design Tables Form To print concrete frame design input data directly to a printer, use the File menu > Print Tables > Concrete Frame Design command and click the check box on the Print Design Tables form. Click the OK button to send the print to your printer. Click the Cancel button rather than the OK button to cancel the print. Use the File menu > Print Setup command and the Setup>> button to change printers, if necessary. To print concrete frame design input data to a file, click the Print to File check box on the Print Design Tables form. Click the Filename>> button to change Using the Print Design Tables Form Technical Note 23-3

157 Input Data Concrete Frame Design ACI the path or filename. Use the appropriate file extension for the desired format (e.g.,.txt,.xls,.doc). Click the OK buttons on the Open File for Printing Tables form and the Print Design Tables form to complete the request. Note: The File menu > Display Input/Output Text Files command is useful for displaying output that is printed to a text file. The Append check box allows you to add data to an existing file. The path and filename of the current file is displayed in the box near the bottom of the Print Design Tables form. Data will be added to this file. Or use the Filename>> button to locate another file, and when the Open File for Printing Tables caution box appears, click Yes to replace the existing file. If you select a specific frame element(s) before using the File menu > Print Tables > Concrete Frame Design command, the Selection Only check box will be checked. The print will be for the selected beam(s) only. Technical Note 23-4 Using the Print Design Tables Form

158 COMPUTERS AND STRUCTURES, INC., BERKELEY, CALIFORNIA DECEMBER 2001 CONCRETE FRAME DESIGN ACI Technical Note 24 Output Details This Technical Note describes the concrete frame design output for ACI that can be printed to a printer or to a text file. The design output is printed when you click the File menu > Print Tables > Concrete Frame Design command and select Output Summary on the Print Design Tables form. Further information about using the Print Design Tables form is presented at the end of this Technical Note. The program provides the output data in a series of tables. The column headings for output data and a description of what is included in the columns of the tables are provided in Table 1 of this Technical Note. Table 1 Concrete Column Design Output COLUMN HEADING DESCRIPTION Biaxial P-M Interaction and Shear Design of Column-Type Elements Story ID Column assigned to story level at top of column. Column Line Section ID Station ID Required Reinforcing Longitudinal Combo Shear22 Combo Shear33 Grid lines. Name of section assigned to column. Area of longitudinal reinforcing required. Load combination for which the reinforcing is designed. Shear reinforcing required. Load combination for which the reinforcing is designed. Shear reinforcing required. Table 1 Concrete Column Design Output Technical Note 24-1

159 Output Details Concrete Frame Design ACI Table 1 Concrete Column Design Output COLUMN HEADING Combo DESCRIPTION Load combination for which the reinforcing is designed. Table 2 Concrete Column Joint Output COLUMN HEADING DESCRIPTION Beam to Column Capacity Ratios and Joint Shear Capacity Check Story ID Column Line Section ID Story level at which joint occurs. Grid line. Assigned section name. Beam-Column Capacity Ratios Major Combo Minor Combo Ratio of beam moment capacity to column capacity. Load combination upon which the ratio of beam moment capacity to column capacity is based. Ratio of beam moment capacity to column capacity. Load combination upon which the ratio of beam moment capacity to column capacity is based. Joint Shear Capacity Ratios Major Combo Minor Combo Ratio of factored load versus allowed capacity. Load combination upon which the ratio of factored load versus allowed capacity is based. Ratio of factored load versus allowed capacity. Load combination upon which the ratio of factored load versus allowed capacity is based. Technical Note 24-2 Table 2 Concrete Column Joint Output

160 Concrete Frame Design ACI Output Details Using the Print Design Tables Form To print concrete frame design input data directly to a printer, use the File menu > Print Tables > Concrete Frame Design command and click the check box on the Print Design Tables form. Click the OK button to send the print to your printer. Click the Cancel button rather than the OK button to cancel the print. Use the File menu > Print Setup command and the Setup>> button to change printers, if necessary. To print concrete frame design input data to a file, click the Print to File check box on the Print Design Tables form. Click the Filename>> button to change the path or filename. Use the appropriate file extension for the desired format (e.g.,.txt,.xls,.doc). Click the OK buttons on the Open File for Printing Tables form and the Print Design Tables form to complete the request. Note: The File menu > Display Input/Output Text Files command is useful for displaying output that is printed to a text file. The Append check box allows you to add data to an existing file. The path and filename of the current file is displayed in the box near the bottom of the Print Design Tables form. Data will be added to this file. Or use the Filename>> button to locate another file, and when the Open File for Printing Tables caution box appears, click Yes to replace the existing file. If you select a specific frame element(s) before using the File menu > Print Tables > Concrete Frame Design command, the Selection Only check box will be checked. The print will be for the selected beam(s) only. Using the Print Design Tables Form Technical Note 24-3

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