®
ETABS
Integrated Building Design Software
Concrete Frame Design Manual
Computers and Structures, Inc.
Berkeley, California, USA
Version 8
January 2002
Copyright
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Structures, Inc. Unlicensed use of the program or reproduction of the documentation in
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explicitly prohibited.
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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.
©COMPUTERS AND STRUCTURES, INC., BERKELEY, CALIFORNIA DECEMBER 2001
CONCRETE FRAME DESIGN
Contents
General Concrete Frame Design Information
1
2
3
4
General Design Information
Design Codes
Units
Overwriting the Frame Design Procedure for a Concrete Frame
Design Load Combinations
Design of Beams
Design of Columns
Beam/Column Flexural Capacity Ratios
Second Order P-Delta Effects
Element Unsupported Lengths
Analysis Sections and Design Sections
1-2
1-2
1-3
1-4
1-4
1-6
1-7
Concrete Frame Design Process
Concrete Frame Design Procedure
2-1
Interactive Concrete Frame Design
General
Concrete Design Information Form
3-1
3-1
Output Data Plotted Directly on the Model
Overview
Using the Print Design Tables Form
Design Input
Design Output
4-1
4-1
4-2
4-2
1-1
1-1
1-1
i
Concrete Frame Design Manual
Concrete Frame Design Specific to UBC97
5
6
7
5-1
5-2
Preferences
General
Using the Preferences Form
Preferences
6-1
6-1
6-2
Overwrites
General
Overwrites
Making Changes in the Overwrites Form
Resetting Concrete Frame Overwrites to Default
Values
8
Design Load Combinations
9
Strength Reduction Factors
10
11
ii
General and Notation
Introduction to the UBC 97 Series of Technical Notes
Notation
Column Design
Overview
Generation of Biaxial Interaction Surfaces
Calculate Column Capacity Ratio
Determine Factored Moments and Forces
Determine Moment Magnification Factors
Determine Capacity Ratio
Required Reinforcing Area
Design Column Shear Reinforcement
Determine Required Shear Reinforcement
Reference
Beam Design
Overview
Design Beam Flexural Reinforcement
Determine Factored Moments
Determine Required Flexural Reinforcement
7-1
7-1
7-3
7-4
10-1
10-2
10-5
10-6
10-6
10-8
10-10
10-10
10-14
10-15
11-1
11-1
11-2
11-2
Contents
Design Beam Shear Reinforcement
12
13
14
11-10
Joint Design
Overview
Determine the Panel Zone Shear Force
Determine the Effective Area of Joint
Check Panel Zone Shear Stress
Beam/Column Flexural Capacity Ratios
12-1
12-1
12-5
12-5
12-6
Input Data
Input data
Using the Print Design Tables Form
13-1
13-3
Output Details
Using the Print Design Tables Form
14-3
Concrete Frame Design Specific to ACI-318-99
15
16
17
General and Notation
Introduction to the ACI318-99 Series of Technical
Notes
Notation
Preferences
General
Using the Preferences Form
Preferences
Overwrites
General
Overwrites
Making Changes in the Overwrites Form
Resetting Concrete Frame Overwrites to Default
Values
18
Design Load Combinations
19
Strength Reduction Factors
15-1
15-2
16-1
16-1
16-2
17-1
17-1
17-3
17-4
iii
Concrete Frame Design Manual
20
21
22
23
iv
Column Design
Overview
Generation of Biaxial Interaction Surfaces
Calculate Column Capacity Ratio
Determine Factored Moments and Forces
Determine Moment Magnification Factors
Determine Capacity Ratio
Required Reinforcing Area
Design Column Shear Reinforcement
Determine Section Forces
Determine Concrete Shear Capacity
Determine Required Shear Reinforcement
References
20-1
20-2
20-5
20-6
20-6
20-9
20-10
20-10
20-11
20-12
20-13
20-15
Beam Design
Overview
Design Beam Flexural Reinforcement
Determine Factored Moments
Determine Required Flexural Reinforcement
Design for T-Beam
Minimum Tensile Reinforcement
Special Consideration for Seismic Design
Design Beam Shear Reinforcement
Determine Shear Force and Moment
Determine Concrete Shear Capacity
Determine Required Shear Reinforcement
21-1
21-1
21-2
21-2
21-5
21-8
21-8
21-9
21-11
21-12
21-13
Joint Design
Overview
Determine the Panel Zone Shear Force
Determine the Effective Area of Joint
Check Panel Zone Shear Stress
Beam/Column Flexural Capacity Ratios
22-1
22-1
22-4
22-4
22-6
Input Data
Input Data
Using the Print Design Tables Form
23-1
23-3
Contents
24
Output Details
Using the Print Design Tables Form
24-3
v
©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:
ƒ
Concrete frame design
ƒ
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
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 318-99 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
318-99 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
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:
ƒ
Generate axial force-biaxial moment interaction surfaces for all of the different concrete section types of the model.
ƒ
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.
ƒ
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
General Design Information
Concrete Frame Design
Column Design and Concrete Frame ACI 318-99 Technical Note 20 Column
Design for more information.
Beam/Column Flexural Capacity Ratios
When the ACI 318-99 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, Pu, 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 Pu 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 318-99 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
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.
MCAP
=
aMnt + bMlt
=
Flexural design capacity
Eqn. 1
where,
MCAP
Second Order P-Delta Effects
Technical Note 1 - 5
General Design Information
Concrete Frame Design
Mnt
=
Required flexural capacity of the member assuming there is
no translation of the frame (i.e., associated with the δ deformation in Figure 1)
Mlt
=
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 Mnt
b
=
Unitless factor multiplying Mlt (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 L33 and L22, as
shown in Figure 2. These are the lengths between support points of the element in the corresponding directions. The length L33 corresponds to instability
about the 3-3 axis (major axis), and L22 corresponds to instability about the
2-2 axis (minor axis). The length L22 is also used for lateral-torsional buckling
caused by major direction bending (i.e., about the 3-3 axis).
In determining the values for L22 and L33 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
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
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:
ƒ
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.
ƒ
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.
ƒ
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.
ƒ
Unlocking a model deletes the design results, but it does not delete or
change the design section.
ƒ
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.
ƒ
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.
ƒ
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.
ƒ
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
Concrete Frame Design
General Design Information
static nonlinear analysis and design results are deleted when one of the
following actions is taken:
9
Use the Define menu > Frame Nonlinear Hinge Properties command to redefine existing or define new hinges.
9
Use the Define menu > Static Nonlinear/Pushover Cases command to redefine existing or define new static nonlinear load cases.
9
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
©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
318-99 Technical Notes 16 Preferences for more information.
Concrete Frame Design Procedure
Technical Note 2 - 1
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
318-99 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 318-99 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
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 318-99 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 7.
11.
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
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 7.
17.
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
©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
Interactive Concrete Frame Design
Concrete Frame Design
Table 1 Concrete Design Information Form
Item
DESCRIPTION
Story
This is the story level ID associated with the frame element.
Beam
This is the label associated with a frame element that has been
assigned a concrete frame section property that is designated
as a beam. See the important note previously in this Technical
Note for more information.
Column
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.
Section Name
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
This is the name of the design load combination considered.
Station location
This is the location of the station considered, measured from
the i-end of the frame element.
Longitudinal
reinforcement
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.
Capacity ratio
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
Concrete Frame Design
Interactive Concrete Frame Design
Table 1 Concrete Design Information Form
Item
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.
Major shear
reinforcement
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.
Minor shear
reinforcement
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.
Top steel
This item applies to beams only. It is the total required area of
longitudinal top steel at the specified station.
Bottom steel
This item applies to beams only. It is the total required area of
longitudinal bottom steel at the specified station.
Shear steel
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.
Overwrites Button
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
Interactive Concrete Frame Design
Concrete Frame Design
Table 1 Concrete Design Information Form
Item
DESCRIPTION
Details Button
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.
Interaction Button
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
©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
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.
ƒ
Design Sections
ƒ
Design Type
ƒ
Live Load Red Factors
ƒ
Unbraced L_Ratios
ƒ
Eff Length K-Factors
ƒ
Cm Factors
ƒ
DNS Factors
ƒ
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 318-99
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
Concrete Frame Design
ƒ
Longitudinal Reinforcing
ƒ
Shear Reinforcing
ƒ
Column Capacity Ratios
ƒ
Joint Shear Capacity Ratios
ƒ
Beam/Column Capacity Ratios
Output Data Plotted Directly on the Model
Each of these items is described in the code-specific Concrete Frame Design
ACI 318-99 Technical Note 24 Output Details and Concrete Frame Design
UBC97 Technical Note 14 Output Details.
Design Output
Technical Note 4 - 3
©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):
ƒ
Zone 0
ƒ
Zone 1
ƒ
Zone 2
ƒ
Zone 3
ƒ
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):
ƒ
Ordinary Moment-Resisting Frame (OMF)
General and Notation
Technical Note 5 - 1
General and Notation
ƒ
Intermediate Moment-Resisting Frame (IMRF)
ƒ
Special Moment-Resisting Frame (SMRF)
Concrete Frame Design UBC97
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
Acv
Area of concrete used to determine shear stress, sq-in
Ag
Gross area of concrete, sq-in
As
Area of tension reinforcement, sq-in
Technical Note 5 - 2
General and Notation
Concrete Frame Design UBC97
General and Notation
As'
Area of compression reinforcement, sq-in
As(required)
Area of steel required for tension reinforcement, sq-in
Ast
Total area of column longitudinal reinforcement, sq-in
Av
Area of shear reinforcement, sq-in
Cm
Coefficient, dependent upon column curvature, used to calculate
moment magnification factor
D'
Diameter of hoop, in
Ec
Modulus of elasticity of concrete, psi
Es
Modulus of elasticity of reinforcement, assumed as 29,000,000 psi
(UBC 1980.5.2)
Ig
Moment of inertia of gross concrete section about centroidal axis,
neglecting reinforcement, in4
Ise
Moment of inertia of reinforcement about centroidal axis of member cross section, in4
L
Clear unsupported length, in
M1
Smaller factored end moment in a column, lb-in
M2
Larger factored end moment in a column, lb-in
Mc
Factored moment to be used in design, lb-in
Mns
Nonsway component of factored end moment, lb-in
Ms
Sway component of factored end moment, lb-in
Mu
Factored moment at section, lb-in
Mux
Factored moment at section about X-axis, lb-in
Muy
Factored moment at section about Y-axis, lb-in
Pb
Axial load capacity at balanced strain conditions, lb
General and Notation
Technical Note 5 - 3
General and Notation
Concrete Frame Design UBC97
Pc
Critical buckling strength of column, lb
Pmax
Maximum axial load strength allowed, lb
P0
Acial load capacity at zero eccentricity, lb
Pu
Factored axial load at section, lb
Vc
Shear resisted by concrete, lb
VE
Shear force caused by earthquake loads, lb
VD+L
Shear force from span loading, lb
Vu
Factored shear force at a section, lb
Vp
Shear force computed from probable moment capacity, lb
a
Depth of compression block, in
ab
Depth of compression block at balanced condition, in
b
Width of member, in
bf
Effective width of flange (T-Beam section), in
bw
Width of web (T-Beam section), in
c
Depth to neutral axis, in
cb
Depth to neutral axis at balanced conditions, in
d
Distance from compression face to tension reinforcement, in
d'
Concrete cover to center of reinforcing, in
ds
Thickness of slab (T-Beam section), in
f c'
Specified compressive strength of concrete, psi
fy
Specified yield strength of flexural reinforcement, psi
fy ≤ 80,000 psi (UBC 1909.4)
Technical Note 5 - 4
General and Notation
Concrete Frame Design UBC97
General and Notation
fys
Specified yield strength of flexural reinforcement, psi
h
Dimension of column, in
k
Effective length factor
r
Radius of gyration of column section, in
α
Reinforcing steel overstrength factor
β1
Factor for obtaining depth of compression block in concrete
βd
Absolute value of ratio of maximum factored axial dead load to
maximum factored axial total load
δs
Moment magnification factor for sway moments
δns
Moment magnification factor for nonsway moments
εc
Strain in concrete
εs
Strain in reinforcing steel
ϕ
Strength reduction factor
General and Notation
Technical Note 5 - 5
©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
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:
ƒ
Item: The name of the preference item as it appears in the cells at the
left side of the Preferences form.
ƒ
Possible Values: The possible values that the associated preference item
can have.
ƒ
Default Value: The built-in default value that the program assumes for
the associated preference item.
ƒ
Description: A description of the associated preference item.
Table 1: Concrete Frame Preferences
Possible
Values
Default
Value
Design Code
Any code in
the program
UBC97
Phi Bending
Tension
>0
0.9
Unitless strength reduction factor per
UBC 1909.
Phi Compression Tied
>0
0.7
Unitless strength reduction factor per
UBC 1909.
Phi Compression Spiral
>0
0.75
Unitless strength reduction factor per
UBC 1909.
Phi Shear
>0
0.85
Unitless strength reduction factor per
UBC 1909.
Number Interaction Curves
≥4.0
24
Item
Technical Note 6 - 2
Description
Design code used for design of
concrete frame elements.
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.
Preferences
Concrete Frame Design UBC97
Preferences
Table 1: Concrete Frame Preferences
Item
Possible
Values
Number Inter- Any odd value
action Points
≥1.0
Time History
Design
Preferences
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.
Technical Note 6 - 3
©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.
ƒ
Item: The name of the overwrite item as it appears in the program. To
save space in the formes, these names are generally short.
ƒ
Possible Values: The possible values that the associated overwrite item
can have.
ƒ
Default Value: The default value that the program assumes for the associated overwrite item.
ƒ
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
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)
Technical Note 7 - 2
Sway Special, Sway Special Frame type; see UBC 1910.11 to
1910.13.
Sway Intermediate,
Sway
Ordinary
NonSway
>0
1.
≤1.0
>0
Used to reduce the live load contribution to the factored loading.
1.
≤1.0
>0
1.0
≤1.0
>0
1.0
≤1.0
>0
1
See UBC 1910.12.1.
1
See UBC 1910.12.1.
1
See UBC 1910.12.3.1 relates actual
moment diagram to an equivalent uniform moment diagram.
1
See UBC 1910.12.3.1 relates actual
moment diagram to an equivalent uniform moment diagram.
1
See UBC 1910.12.
≤1.0
>0
≤1.0
>0
≤1.0
>0
≤1.0
>0
≤1.0
Overwrites
Concrete Frame Design UBC97
Overwrites
Table 1 Concrete Frame Design Overwrites
Item
Possible
Values
Default
Value
Description
NonSway
Moment Factor
(Dns Minor)
1
See UBC 1910.12.
Sway Moment
Factor
(Ds Major)
1
See UBC 1910.12.
Sway Moment
Factor
(Ds Minor)
1
See UBC 1910.12.
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
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
©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 + 1.7 LL (UBC
1909.2.1). 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 may
need to be considered (UBC 1909.2).
1.4 DL
1.4 DL + 1.7 LL
(UBC 1909.2.1)
(UBC 1909.2.1)
0.9 DL ± 1.3 WL
0.75 (1.4 DL + 1.7 LL ± 1.7 WL)
(UBC 1909.2.2)
(UBC 1909.2.2)
0.9 DL ± 1.0 EL
1.2 DL + 0.5 LL ± 1.0 EL)
(UBC 1909.2.3, 1612.2.1)
(UBC 1909.2.3, 1612.2.1)
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
©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 1909.3.2.1)
ϕ
= 0.90 for axial tension
(UBC 1909.3.2.2)
ϕ
= 0.90 for axial tension and flexure
(UBC 1909.3.2.2)
ϕ
= 0.75 for axial compression, and axial compression
and flexure (spirally reinforced column)
(UBC 1909.3.2.2)
ϕ
= 0.70 for axial compression, and axial compression
and flexure (tied column)
(UBC 1909.3.2.2)
ϕ
= 0.85 for shear and torsion (non-seismic design)
(UBC 1909.3.2.3)
ϕ
= 0.60 for shear and torsion
(UBC 1909.3.2.3)
Strength Reduction Factors
Technical Note 9 - 1
©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:
ƒ
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 1910.9.1) and 1 to 6 percent for Special moment resisting
frames (UBC 1921.4.3.1).
ƒ
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.
ƒ
Design the column shear reinforcement.
The following four subsections describe in detail the algorithms associated
with this process.
Overview
Technical Note 10 - 1
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
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, εc, at the extremity
of the section, to 0.003 (UBC 1910.2.3).
The formulation is based consistently upon the general principles of ultimate
strength design (UBC 1910.3), 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, εsEs, and is limited to the yield stress of the steel, fy
(UBC 1910.2.4). 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 c' (UBC 1910.2.7.1). 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
ϕPn(max), where
ϕPn(max) = 0.85ϕ[0.85 f c' (Ag-Ast)+fyAst] (spiral)
(UBC 1910.3.5.1)
ϕPn(max) = 0.85ϕ[0.85 f c' (Ag-Ast)+fyAst] (tied)
(UBC 1910.3.5.2)
ϕ
= 0.70 for tied columns
(UBC 1909.3.2.2)
ϕ
= 0.75 for spirally reinforced columns
(UBC 1909.3.2.2)
The value of ϕ used in the interaction diagram varies from ϕmin to 0.9 based
on the axial load. For low values of axial load, ϕ is increased linearly from ϕmin
to 0.9 as the nominal capacity ϕPn decreases from the smaller of ϕPb or
0.1 f c' Ag to zero, where Pb is the axial force at the balanced condition. In
cases involving axial tension, ϕ is always 0.9 (UBC 1909.3.2.2).
Generation of Biaxial Interaction Surfaces
Technical Note 10 - 3
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
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:
ƒ
Determine the factored moments and forces from the analysis load cases
and the specified load combination factors to give Pu, Mux, and Muy.
ƒ
Determine the moment magnification factors for the column moments.
ƒ
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
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 Pu, Mux, and Muy.
The factored moments are further increased for non-sway columns, if required, to obtain minimum eccentricities of (0.6 + 0.03h) inches, where h is
the dimension of the column in the corresponding direction (UBC
1910.12.3.2).
Determine Moment Magnification Factors
The moment magnification factors are calculated separately for sway (overall
stability effect), δs, and for non-sway (individual column stability effect), δns.
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 1910.10.2). For the P-delta analysis, the load should correspond to a
load combination of 0.75 (1.4 dead load + 1.7 live load)/ϕ if wind load governs, or (1.2 dead load + 0.50 live load)/ϕ if seismic load governs, where ϕ is
the understrength factor for stability, which is taken as 0.75 (UBC
1910.12.3). See also White and Hajjar (1991).
The moment obtained from analysis is separated into two components: the
sway (Ms) and the non-sway (Ms) 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 = Mns + δsMs.
(UBC 1910.13.3)
The factor δs is the moment magnification factor for moments causing side
sway. The moment magnification factors for sway moments, δs, is taken as 1
because the component moments Ms and Mns are obtained from a “second order elastic (P-delta) analysis.”
Technical Note 10 - 6
Calculate Column Capacity Ratio
Concrete Frame Design UBC97
Column Design
The computed moments are further amplified for individual column stability
effect (UBC 1910.12.3, 1910.13.5) by the nonsway moment magnification
factor, δns, as follows:
Mc = δnsM2 , where
(UBC 1910.12.3)
Mc is the factored moment to be used in design, and
M2 is the larger factored and amplified end moment.
The non-sway moment magnification factor, δns, associated with the major or
minor direction of the column is given by (UBC 1910.12.3)
δns =
Pc =
Cm
≥ 1.0,
Pu
1−
0.75Pc
π 2 EI
(kl u )2
where
(UBC 1910.12.3)
,
(UBC 1910.12.3)
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 + βd
,
maximum factored axial dead load
βd = maximum factored axial total load
Cm = 0.6 + 0.4
Ma
≥ 0.4.
Mb
(UBC 1910.12.3)
and
(UBC 1910.12.3)
(UBC 1910.12.3.1)
Ma and Mb are the moments at the ends of the column, and Mb is numerically
larger than Ma. Ma / Mb is positive for single curvature bending and negative
for double curvature bending. The above expression of Cm 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, Cm = 1. Cm can be overwritten by
the user on an element-by-element basis.
Calculate Column Capacity Ratio
Technical Note 10 - 7
Column Design
Concrete Frame Design UBC97
The magnification factor, δns, must be a positive number and greater than 1.
Therefore, Pu must be less than 0.75Pc. If Pu is found to be greater than or
equal to 0.75Pc, a failure condition is declared.
The above calculations use the unsupported length of the column. The two
unsupported lengths are l22 and l33, 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 δs and δns.
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
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 Pu,
Mux, and Muy. The point (Pu, Mux, Muy.) 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
Column Design
Concrete Frame Design UBC97
failure surface. See Figure 5. The capacity ratio, CR, is given by the ratio
OL
.
OC
ƒ
If OL = OC (or CR=1), the point lies on the interaction surface and the
column is stressed to capacity.
ƒ
If OL < OC (or CR<1), the point lies within the interaction volume and the
column capacity is adequate.
ƒ
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 Pu,
Mux, and Muy 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:
ƒ
Determine the factored forces acting on the section, Pu and Vu. Note that
Pu is needed for the calculation of Vc.
ƒ
Determine the shear force, Vc, that can be resisted by concrete alone.
ƒ
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 10 - 10
Required Reinforcing Area
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
ƒ
In the design of the column shear reinforcement of an Ordinary moment
resisting concrete frame, the forces for a particular load combination,
namely, the column axial force, Pu, and the column shear force, Vu, in a
particular direction are obtained by factoring the program analysis load
cases with the corresponding load combination factors.
ƒ
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, Vp, 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, Pu, is calculated. Then,
the positive and negative moment capacities, Mu+ and Mu− , of the column
in a particular direction under the influence of the axial force Pu is calculated using the uniaxial interaction diagram in the corresponding direction.
The design shear force, Vu, is then given by (UBC 1921.4.5.1)
Vu = Vp + VD+L
(UBC 1921.4.5.1)
where, Vp is the capacity-shear force obtained by applying the calculated
probable ultimate moment capacities at the two ends of the column acting
in two opposite directions. Therefore, Vp is the maximum of VP1 and VP2 ,
where
VP1 =
M I− + M J+
, and
L
VP2 =
M I+ + M J−
, where
L
Design Column Shear Reinforcement
Technical Note 10 - 11
Column Design
Concrete Frame Design UBC97
M I+ , M I− , = Positive and negative moment capacities at end I of the
column using a steel yield stress value of αfy and no ϕ
factors (ϕ = 1.0),
M J+ , M J− , = Positive and negative moment capacities at end J of the
column using a steel yield stress value of αfy 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 1921.0).
VD+L is the contribution of shear force from the in-span distribution of
gravity loads. For most of the columns, it is zero.
ƒ
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 1921.0, 1921.8.3). The
factored shear forces are based on the specified load factors, except the
earthquake load factors are doubled (UBC 1921.8.3).
Determine Concrete Shear Capacity
Given the design force set Pu and Vu, the shear force carried by the concrete,
Vc, is calculated as follows:
ƒ
If the column is subjected to axial compression, i.e., Pu is positive,

Pu
Vc = 2 f c' 1 +

2,000 Ag


 Acv ,


(UBC 1911.3.1.2)
where,
f c' ≤ 100 psi, and
Technical Note 10 - 12
(UBC 1911.1.2)
Design Column Shear Reinforcement
Concrete Frame Design UBC97
Vc ≤ 3.5 f c'
The term

1 + Pu

500 Ag

Column Design

 Acv .


(UBC 1911.3.2.2)
Pu
must have psi units. Acv is the effective shear area which is
Ag
shown shaded in Figure 6. For circular columns, Acv is not taken to be
greater than 0.8 times the gross area (UBC 1911.5.6.2).
Figure 6 Shear Stress Area, Acv
Design Column Shear Reinforcement
Technical Note 10 - 13
Column Design
ƒ
Concrete Frame Design UBC97
If the column is subjected to axial tension, Pu is negative, (UBC
1911.3.2.3)

Pu
Vc = 2 f c' 1 +

500
Ag

ƒ

 Acv ≥ 0


(UBC 1911.3.2.3)
For Special moment resisting concrete frame design, Vc is set to zero
if the factored axial compressive force, Pu, including the earthquake effect
is small (Pu < f c' Ag / 20) and if the shear force contribution from earthquake, VE, is more than half of the total factored maximum shear force
over the length of the member Vu(VE ≥ 0.5Vu) (UBC 1921.4.5.2).
Determine Required Shear Reinforcement
Given Vu and Vc, 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:
Av =
Av =
(Vu / ϕ − Vc )s
, for rectangular columns
f ys d
2 (Vu / ϕ − Vc )s
, for circular columns
f ys D'
π
(UBC 1911.5.6.1, 1911.5.6.2)
(UBC 1911.5.6.1, 1911.5.6.2)
Vu is limited by the following relationship.
(Vu / ϕ-Vc) ≤ 8
f c' Acv
(UBC 1911.5.6.8)
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 1909.3.2.3) and is 0.60 for seismic design
in Seismic Zones 3 and 4 (UBC 1909.3.4.1). 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 10 - 14
Design Column Shear Reinforcement
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. 1991. 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
©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:
ƒ
Design beam flexural reinforcement
ƒ
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:
ƒ
Determine the maximum factored moments
ƒ
Determine the reinforcing steel
Overview
Technical Note 11 - 1
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.
The beam section is then designed for the maximum positive M u+ and maximum negative M u− factored moments 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
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 1910.2). It is assumed that the compression carried
by concrete is less than 0.75 times that which can be carried at the balanced
condition (UBC 1910.3.3). 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' Ag (UBC 1910.3.3); hence, all
the beams are designed for major direction flexure and shear only.
Technical Note 11 - 2
Design Beam Flexural Reinforcement
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, Mu (i.e., designing
top or bottom steel), the depth of the compression block is given by a (see
Figure 1), where,
a=d-
d2 −
2 Mu
0.85f c' ϕb
,
where the value of ϕ is 0.90 (UBC 1909.3.2.1) in the above and the following
equations. Also β1 and cb are calculated as follows:
 f ' − 4,000 
,
β1 = 0.85 - 0.05  c
 1,000 


cb =
εc E s
87,000
d.
d =
ε c E s + fy
87,000 + f y
Design Beam Flexural Reinforcement
0.65 ≤ β1 ≤ 0.85,
(UBC 1910.2.7.3)
(UBC 1910.2.3, 1910.2.4)
Technical Note 11 - 3
Beam Design
Concrete Frame Design UBC97
The maximum allowed depth of the compression block is given by
amax = 0.75β1cb.
ƒ
(UBC 1910.2.7.1, 1910.3.3)
If a ≤ amax, the area of tensile steel reinforcement is given by
As =
Mu
a

ϕf y  d − 
2

.
This steel is to be placed at the bottom if Mu is positive, or at the top if Mu
is negative.
ƒ
If a > amax, compression reinforcement is required (UBC 1910.3.3) and is
calculated as follows:
−
The compressive force developed in concrete alone is given by
C = 0.85 f c' bamax, and
(UBC 1910.2.7.1)
the moment resisted by concrete compression and tensile steel is
a

Muc = C  d − max
2

−

 ϕ.

Therefore the moment resisted by compression steel and tensile steel is
Mus = Mu - Muc.
−
So the required compression steel is given by
As' =
M us
f s' (d
− d' )ϕ
, where
 c − d' 
f s' = 0.003Es 
 .
 c 
−
(UBC 1910.2.4)
The required tensile steel for balancing the compression in concrete is
Technical Note 11 - 4
Design Beam Flexural Reinforcement
Concrete Frame Design UBC97
As1 =
Muc
a


f y d − max  ϕ
2 

Beam Design
, and
the tensile steel for balancing the compression in steel is given by
As2 =
−
M us
.
f y (d − d' )ϕ
Therefore, the total tensile reinforcement, As = As1 + As2, and total compression reinforcement is As' . As is to be placed at bottom and As' is to
be placed at top if Mu is positive, and vice versa if Mu is negative.
Design for T-Beam
In designing for a factored negative moment, Mu (i.e., designing top steel),
the calculation of the steel area is exactly the same as above, i.e., no T-Beam
data is to be used. See Figure 2. If Mu > 0, the depth of the compression
block is given by
a = d - d2 −
2M u
0.85f c' ϕbf
.
The maximum allowed depth of the compression block is given by
amax = 0.75β1cb.
(UBC 1910.2.7.1)
If a ≤ ds, the subsequent calculations for As 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 > amax.
If a > ds, calculation for As is performed in two parts. The first part is for balancing the compressive force from the flange, Cf, and the second part is for
balancing the compressive force from the web, Cw, as shown in Figure 2. Cf is
given by
Cf = 0.85 f c' (bf - bw) ds.
Design Beam Flexural Reinforcement
Technical Note 11 - 5
Beam Design
Concrete Frame Design UBC97
Figure 2 Design of a T-Beam Section
Therefore, As1 =
Cf
fy
and the portion of Mu that is resisted by the flange is
given by
d

Muf = Cf  d − s
2


 ϕ .

Again, the value for ϕ is 0.90. Therefore, the balance of the moment, Mu to be
carried by the web is given by
Muw = Mu - Muf.
The web is a rectangular section of dimensions bw and d, for which the design
depth of the compression block is recalculated as
a1 = d -
ƒ
d2 −
2M uw
0.85f c' ϕbw
.
If a1 ≤ amax, the area of tensile steel reinforcement is then given by
Technical Note 11 - 6
Design Beam Flexural Reinforcement
Concrete Frame Design UBC97
As2 =
Beam Design
M uw
a 

ϕf y  d − 1 
2 

, and
As = As1 + As2.
This steel is to be placed at the bottom of the T-beam.
ƒ
If a1 > amax, compression reinforcement is required (UBC 1910.3.3) and is
calculated as follows:
−
The compressive force in web concrete alone is given by
C = 0.85 f c' bamax.
−
(UBC 1910.2.7.1)
Therefore the moment resisted by concrete web and tensile steel is
a

Muc = C  d − max
2


 ϕ, and

the moment resisted by compression steel and tensile steel is
Mus = Muw - Muc.
−
Therefore, the compression steel is computed as
As' =
M us
f s' (d
− d' )ϕ
, where
 c − d' 
f s' = 0.003Es 
.
 c 
−
(UBC 1910.2.4)
The tensile steel for balancing compression in web concrete is
As2 =
M uc
a

f y  d − max
2


ϕ

, and
the tensile steel for balancing compression in steel is
Design Beam Flexural Reinforcement
Technical Note 11 - 7
Beam Design
Concrete Frame Design UBC97
As3 =
−
Mus
.
f y (d − d')ϕ
The total tensile reinforcement, As = As1 + As2 + As3, and total compression reinforcement is As' . As is to be placed at bottom and As' 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 '

200


c
As ≥ max 
bw d and
bw d  or
fy
 f y

As ≥
(UBC 1910.5.1)
4
As(required)
3
(UBC 1910.5.3)
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):
ƒ
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 As(min) (UBC 1921.3.2.1).
3 f '

200


c
As(min) ≥ max 
bw d and
bw d  or
fy
 f y

As(min) ≥
ƒ
4
As(required).
3
(UBC 1910.5.1, 1921.3.2.1)
(UBC 1910.5.3, 1921.3.2.1)
The beam flexural steel is limited to a maximum given by
As ≤ 0.25 bwd.
Technical Note 11 - 8
(UBC 1921.3.2.1)
Design Beam Flexural Reinforcement
Concrete Frame Design UBC97
Beam Design
Table 1 Design Criteria Table
Type of
Check/
Design
Ordinary Moment
Resisting Frames
(Seismic Zones 0&1)
Column
Check
(interaction)
NLDa Combinations
NLDa Combinations
NLDa Combinations
NLDa Combinations
NLDa Combinations
1% < ρ < 8%
NLDa Combinations
α = 1.0
1% < ρ < 6%
Modified NLDa Combinations
(earthquake loads doubled)
Column Capacity
ϕ = 1.0 and α = 1.0
NLDa Combinations and
Column shear capacity
ϕ = 1.0 and α = 1.25
Column
Design
(interaction)
Column
Shears
Beam
Design
Flexure
Beam Min.
Moment
Override
Check
1% < ρ < 8%
NLDa
Combinations
NLDa Combinations
Intermediate Moment
Resisting Frames
(Seismic Zone 2)
NLDa Combinations
ρ ≤ 0.025
NLDa Combinations
1 −
M uEND
3
1
≥ max M u+ , M u−
5
ρ≥
+
≥
M uEND
No Requirement
+
M uSPAN
−
M uSPAN
≥
Special Moment
Resisting Frames
(Seismic Zones 3 & 4)
3 f c'
fy
{
}
END
+
≥
MuSPAN
{
}
−
MuSPAN
END
200
fy
1 −
MuEND
2
+
≥
MuEND
1
max M u+ , M u−
5
,ρ ≥
{
{
1
max Mu+ , Mu−
4
1
≥ max Mu− , Mu−
4
Beam
Design
Shear
NLDa Combinations
Modified NLDa Combinations
(earthquake loads doubled)
Beam Capacity Shear (Vp)
with α = 1.0 and ϕ = 1.0
plus VD+L
Joint
Design
No Requirement
No Requirement
Checked for shear
Beam/
Column
Capacity
Ratio
No Requirement
No Requirement
Reported in output file
}
}
END
END
NLDa Combinations
Beam Capacity Shear (Vp)
with α = 1.25 and ϕ = 1.0
plus VD+L
Vc = 0
NLDa = Number of specified loading
Design Beam Flexural Reinforcement
Technical Note 11 - 9
Beam Design
Concrete Frame Design UBC97
ƒ
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 1921.3.2.2).
ƒ
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 1921.3.2.2).
For Intermediate moment resisting concrete frames (i.e., seismic design), the
beam design would satisfy the following conditions:
ƒ
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 1921.8.4.1).
ƒ
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 1921.8.4.1).
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:
ƒ
Determine the factored shear force, Vu.
ƒ
Determine the shear force, Vc, that can be resisted by the concrete.
ƒ
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 11 - 10
Design Beam Shear Reinforcement
Concrete Frame Design UBC97
Beam Design
The following three sections describe in detail the algorithms associated with
this process.
Determine Shear Force and Moment
ƒ
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.
ƒ
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, Vp, 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 Vu is then given by (UBC 1921.3.4.1)
Vu = Vp + VD+L
(UBC 1921.3.4.1)
where Vp 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, Vp is the maximum of VP1 and VP2 ,
where
VP1 =
M I− + M J+
, and
L
VP2 =
M I+ + M J−
, where
L
M I−
= Moment capacity at end I, with top steel in tension, using a
steel yield stress value of αfy and no ϕ factors (ϕ = 1.0),
Design Beam Shear Reinforcement
Technical Note 11 - 11
Beam Design
M J+
Concrete Frame Design UBC97
= Moment capacity at end J, with bottom steel in tension, using a
steel yield stress value of αfy 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 αfy 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 αfy 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 1921.0).
VD+L is the contribution of shear force from the in-span distribution of
gravity loads.
ƒ
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 1921.0, 1921.8.3). The
factored shear forces are based on the specified load factors, except the
earthquake load factors are doubled (UBC 1921.8.3). 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
Vc = 2 f c' bwd.
(UBC 1911.3.1.1)
For Special moment resisting frame concrete design, Vc is set to zero if both
the factored axial compressive force, including the earthquake effect Pu, is
less than f c' Ag/20 and the shear force contribution from earthquake VE is
Technical Note 11 - 12
Design Beam Shear Reinforcement
Concrete Frame Design UBC97
Beam Design
more than half of the total maximum shear force over the length of the member Vu (i.e., VE ≥ 0.5Vu) (UBC 1921.3.4.2).
Determine Required Shear Reinforcement
Given Vu and Vc, the required shear reinforcement in area/unit length is calculated as
Av =
(Vu / ϕ − Vc )s
.
f ys d
(UBC 1911.5.6.1, 1911.5.6.2)
The shear force resisted by steel is limited by
(Vu/ϕ - Vc) ≤ 8 f c' bd.
(UBC 1911.5.6.8)
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 1909.3.2.3) and is 0.60 for seismic design
in Seismic Zones 3 and 4 (UBC 1909.3.4.1). The maximum of all the calculated Av 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
©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,Vuh
•
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
Joint Design
Concrete Frame Design UBC97
Figure1 Beam-Column Joint Analysis
Technical Note 12 - 2
Determine the Panel Zone Shear Force
Concrete Frame Design UBC97
Joint Design
The force Vuh is the horizontal panel zone shear force that is to be calculated.
The forces that act on the joint are Pu, Vu, MuL and MuR. The forces Pu and Vu
are axial force and shear force, respectively, from the column framing into the
top of the joint. The moments MuL and MuR are obtained from the beams
framing into the joint. The program calculates the joint shear force Vuh by resolving the moments into C and T forces. Noting that TL = CL and TR = CR,
Vuh = TL + TR - Vu
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, Cmax, and the
maximum moment, Mmax, that can be carried by the beam.
C max = 0.85f c' bd
Mmax = C max
d
2
Then the program conservatively determines C and T forces as follows:

abs( M ) 
C = T = C max 1 − 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 1921.5.1.1). The C and T forces are based on these moment capacities. The program calculates the column shear force Vu from the beam
moment capacities, as follows:
Determine the Panel Zone Shear Force
Technical Note 12 - 3
Joint Design
Concrete Frame Design UBC97
L
Vu =
Mu + Mu
H
R
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 Vu
Technical Note 12 - 4
Determine the Panel Zone Shear Force
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 Vuh by
the effective area of the joint and comparing it with the following design shear
strengths (UBC 1921.5.3):
v =
{
20ϕ
f 'c
for joints confined on all four sides
15ϕ
f 'c
for joints confined on three faces or on two
opposite faces
12ϕ
f 'c
for all other joints
where ϕ = 0.85 (by default).
(UBC 1909.3.2.3,1909.3.4.1)
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 1921.5.3.1).
Determine the Effective Area of Joint
Technical Note 12 - 5
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
f c' with
minf cs, factor f ' c ,3 / 4 f c' 


(UBC 1921.5.3.2)
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 1921.4.2.2).
∑Me ≥
6
∑Mg
5
(UBC 1921.4.2.2)
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, Pu, 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 Pu 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
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 Mu at a Given Axial Load Pu
Beam/Column Flexural Capacity Ratios
Technical Note 12 - 7
©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
DESCRIPTION
Load Combination Multipliers
Combo
Design load combination. See Technical Note 8.
Type
Load type: dead, live, superimposed dead, earthquake, wind,
snow, reduced live load, other.
Case
Name of load case.
Factor
Load combination scale factor.
Code Preferences
Phi_bending
Bending strength reduction factor.
Phi_tension
Tensile strength reduction factor.
Phi_compression
(Tied)
Compressive strength reduction factor for tied columns.
Phi_compression (Spiral)
Compressive strength reduction factor for reinforced columns.
Phi_shear
Shear strength reduction factor.
Input Data
Technical Note 13 - 1
Input Data
Concrete Frame Design UBC97
Table 1 Concrete Frame Design Input Data
COLUMN HEADING
DESCRIPTION
Material Property Data
Material Name
Concrete, steel, other.
Material Type
Isotropic or orthotropic.
Design Type
Modulus of Elasticity
Poisson's Ratio
Thermal Coeff
Coefficient of thermal expansion.
Shear Modulus
Material Property Mass and Weight
Material Name
Concrete, steel, other.
Mass Per Unit Vol
Used to calculate self-mass of structure.
Weight Per Unit Vol
Used to calculate self-weight of structure.
Material Design Data for Concrete Materials
Material Name
Concrete, steel, other.
Lightweight Concrete
Concrete FC
Concrete compressive strength.
Rebar FY
Bending reinforcing steel yield strength.
Rebar FYS
Shear reinforcing steel yield strength.
Lightwt Reduc Fact
Shear strength reduction factor for light weight concrete; default
= 1.0.
Concrete Column Property Data
Section Label
Label applied to section.
Mat Label
Material label.
Column Depth
Column Width
Rebar Pattern
Layout of main flexural reinforcing steel.
Concrete Cover
Minimum clear concrete cover.
Bar Area
Area of individual reinforcing bar to be used.
Technical Note 13 - 2
Table 1 Concrete Frame Design Input Data
Concrete Frame Design UBC97
Input Data
Table 1 Concrete Frame Design Input Data
COLUMN HEADING
DESCRIPTION
Concrete Column Design Element Information
Story ID
Column assigned to story level at top of column.
Column Line
Grid line.
Section ID
Name of section assigned to column.
Framing Type
Lateral or gravity.
RLLF Factor
L_Ratio Major
Unbraced length about major axis.
L_Ratio Minor
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
Story level at which beam occurs.
Bay ID
Grid lines locating beam.
Section ID
Section number assigned to beam.
Framing type
Lateral or gravity.
RLLF Factor
L_Ratio Major
Unbraced length about major axis.
L_Ratio Minor
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
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
©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
Grid lines.
Section ID
Name of section assigned to column.
Station ID
Required Reinforcing
Longitudinal
Area of longitudinal reinforcing required.
Combo
Load combination for which the reinforcing is designed.
Shear22
Shear reinforcing required.
Combo
Load combination for which the reinforcing is designed.
Shear33
Shear reinforcing required.
Table 1 Concrete Column Design Output
Technical Note 14 - 1
Output Details
Concrete Frame Design UBC97
Table 1 Concrete Column Design Output
COLUMN HEADING
DESCRIPTION
Combo
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
Story level at which joint occurs.
Column Line
Grid line.
Section ID
Assigned section name.
Beam-Column Capacity Ratios
Major
Ratio of beam moment capacity to column capacity.
Combo
Load combination upon which the ratio of beam moment capacity to column capacity is based.
Minor
Ratio of beam moment capacity to column capacity.
Combo
Load combination upon which the ratio of beam moment capacity to column capacity is based.
Joint Shear Capacity Ratios
Major
Ratio of factored load versus allowed capacity.
Combo
Load combination upon which the ratio of factored load versus
allowed capacity is based.
Minor
Ratio of factored load versus allowed capacity.
Combo
Load combination upon which the ratio of factored load versus
allowed capacity is based.
Technical Note 14 - 2
Table 2 Concrete Column Joint Output
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
©COMPUTERS AND STRUCTURES, INC., BERKELEY, CALIFORNIA DECEMBER 2001
CONCRETE FRAME DESIGN ACI-318-99
Technical Note 15
General and Notation
Introduction to the ACI318-99 Series of Technical Notes
The ACI-318-99 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-318-99 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-318-99 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-318-99 Technical Note 19 Strength
Reduction Factors, Concrete Frame Design ACI-318-99 Technical Note 20 Column Design, Concrete Frame Design ACI-318-99 Technical Note 21 Beam Design, and Concrete Frame Design ACI-318-99 Technical Note 22 Joint Design.
The program uses preferences and overwrites, which are described in Concrete Frame Design ACI-318-99 Technical Note 16 Preferences and Concrete
Frame Design ACI-318-99 Technical Note 17 Overwrites. It also provides input and output data summaries, which are described in Concrete Frame Design ACI-318-99 Technical Note 23 Input Data and Concrete Frame Design
ACI-318-99 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 ACI318-99 Series of Technical Notes
Technical Note 15 - 1
General and Notation
Concrete Frame Design ACI-318-99
Notation
Acv
Area of concrete used to determine shear stress, sq-in
Ag
Gross area of concrete, sq-in
As
Area of tension reinforcement, sq-in
As'
Area of compression reinforcement, sq-in
As(required)
Area of steel required for tension reinforcement, sq-in
Ast
Total area of column longitudinal reinforcement, sq-in
Av
Area of shear reinforcement, sq-in
Cm
Coefficient, dependent upon column curvature, used to calculate
moment magnification factor
Ec
Modulus of elasticity of concrete, psi
Es
Modulus of elasticity of reinforcement, assumed as 29,000,000
psi (ACI 8.5.2)
Ig
Moment of inertia of gross concrete section about centroidal axis,
neglecting reinforcement, in4
Ise
Moment of inertia of reinforcement about centroidal axis of
member cross section, in4
L
Clear unsupported length, in
M1
Smaller factored end moment in a column, lb-in
M2
Larger factored end moment in a column, lb-in
Mc
Factored moment to be used in design, lb-in
Mns
Nonsway component of factored end moment, lb-in
Ms
Sway component of factored end moment, lb-in
Technical Note 15 - 2
Notation
Concrete Frame Design ACI-318-99
General and Notation
Mu
Factored moment at section, lb-in
Mux
Factored moment at section about X-axis, lb-in
Muy
Factored moment at section about Y-axis, lb-in
Pb
Axial load capacity at balanced strain conditions, lb
Pc
Critical buckling strength of column, lb
Pmax
Maximum axial load strength allowed, lb
P0
Axial load capacity at zero eccentricity, lb
Pu
Factored axial load at section, lb
Vc
Shear resisted by concrete, lb
VE
Shear force caused by earthquake loads, lb
VD+L
Shear force from span loading, lb
Vu
Factored shear force at a section, lb
Vp
Shear force computed from probable moment capacity, lb
a
Depth of compression block, in
ab
Depth of compression block at balanced condition, in
b
Width of member, in
bf
Effective width of flange (T-Beam section), in
bw
Width of web (T-Beam section), in
c
Depth to neutral axis, in
cb
Depth to neutral axis at balanced conditions, in
d
Distance from compression face to tension reinforcement, in
d'
Concrete cover to center of reinforcing, in
Notation
Technical Note 15 - 3
General and Notation
Concrete Frame Design ACI-318-99
ds
Thickness of slab (T-Beam section), in
f c'
Specified compressive strength of concrete, psi
fy
Specified yield strength of flexural reinforcement, psi
fy ≤ 80,000 psi (ACI 9.4)
fys
Specified yield strength of shear reinforcement, psi
h
Dimension of column, in
k
Effective length factor
r
Radius of gyration of column section, in
α
Reinforcing steel overstrength factor
β1
Absolute value of ratio of maximum factored axial dead load to
maximum factored axial total load
βd
Absolute value of ratio or maximum factored axial dead load to
maximum factored axial total load
δs
Moment magnification factor for sway moments
δns
Moment magnification factor for nonsway moments
εc
Strain in concrete
εs
Strain in reinforcing steel
ϕ
Strength reduction factor
Technical Note 15 - 4
Notation
©COMPUTERS AND STRUCTURES, INC., BERKELEY, CALIFORNIA DECEMBER 2001
CONCRETE FRAME DESIGN ACI318-99
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
Preferences
Concrete Frame Design ACI318-99
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:
ƒ
Item: The name of the preference item as it appears in the cells at the
left side of the Preferences form.
ƒ
Possible Values: The possible values that the associated preference item
can have.
ƒ
Default Value: The built-in default value that the program assumes for
the associated preference item.
ƒ
Description: A description of the associated preference item.
Table 1: Concrete Frame Preferences
Possible
Values
Default
Value
Design Code
Any code in
the program
ACI 318-99
Phi Bending
Tension
>0
0.9
Unitless strength reduction factor per
ACI 9.3.
Phi Compression Tied
>0
0.7
Unitless strength reduction factor per
ACI 9.3.
Phi Compression Spiral
>0
0.75
Unitless strength reduction factor per
ACI 9.3.
Phi Shear
>0
0.85
Unitless strength reduction factor per
ACI 9.3.
Number Interaction Curves
≥4.0
24
Item
Technical Note 16 - 2
Description
Design code used for design of
concrete frame elements.
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.
Preferences
Concrete Frame Design ACI318-99
Preferences
Table 1: Concrete Frame Preferences
Item
Possible
Values
Number Inter- Any odd value
action Points
≥4.0
Time History
Design
Preferences
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.
Technical Note 16 - 3
©COMPUTERS AND STRUCTURES, INC., BERKELEY, CALIFORNIA DECEMBER 2001
CONCRETE FRAME DESIGN ACI318-99
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 ACI318-99. 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.
ƒ
Item: The name of the overwrite item as it appears in the program. To
save space in the formes, these names are generally short.
ƒ
Possible Values: The possible values that the associated overwrite item
can have.
ƒ
Default Value: The default value that the program assumes for the associated overwrite item.
ƒ
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
Overwrites
Concrete Frame Design ACI318-99
Table 1 Concrete Frame Design Overwrites
Possible
Values
Item
Default
Value
Description
Element
Section
Element
Type
Sway Special, Sway Special Frame type per moment frame definition given in ACI 21.1.
Sway Intermediate,
Sway
Ordinary
NonSway
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)
Technical Note 17 - 2
>0
1.
≤1.0
>0
Used to reduce the live load contribution to the factored loading.
1
≤1.0
>0
1.0
≤1.0
>0
1.0
≤1.0
>0
1
See ACI 10.12, 10.13 and Figure
R10.12.1.
1
See ACI 10.12, 10.13 and Figure
R10.12.1.
1
Factor relating actual moment diagram
to an equivalent uniform moment diagram. See ACI 10.12.3.
1
Factor relating actual moment diagram
to an equivalent uniform moment diagram. See ACI 10.12.3.
1
See ACI 10.12.
≤1.0
>0
≤1.0
>0
≤1.0
>0
≤1.0
>0
≤1.0
Overwrites
Concrete Frame Design ACI318-99
Overwrites
Table 1 Concrete Frame Design Overwrites
Item
Possible
Values
Default
Value
Description
NonSway
Moment Factor
(Dns Minor)
1
See ACI 10.13.
Sway Moment
Factor
(Ds Major)
1
See ACI 10.13.
Sway Moment
Factor
(Ds Minor)
1
See ACI 10.13.
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
Overwrites
Concrete Frame Design ACI318-99
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
©COMPUTERS AND STRUCTURES, INC., BERKELEY, CALIFORNIA DECEMBER 2001
CONCRETE FRAME DESIGN ACI-318-99
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 318-99
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 + 1.7 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 + 1.7 LL
(ACI 9.2.1)
0.9 DL ± 1.3 WL
0.75 (1.4 DL + 1.7 LL ± 1.7 WL)
(ACI 9.2.2)
0.9 DL ± 1.3 * 1.1 EL
0.75 (1.4 DL + 1.7 LL ± 1.7 * 1.1 EL)
(ACI 9.2.3)
These are also the default design load combinations in the program whenever
the ACI 318-99 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 318-99
Technical Note 17 Overwrites for more information.
Design Load Combinations
Technical Note 18 - 1
©COMPUTERS AND STRUCTURES, INC., BERKELEY, CALIFORNIA DECEMBER 2001
CONCRETE FRAME DESIGN ACI-318-99
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 9.3.2.1)
ϕ
= 0.90 for axial tension
(ACI 9.3.2.2)
ϕ
= 0.90 for axial tension and flexure
(ACI 9.3.2.2)
ϕ
= 0.75 for axial compression, and axial compression
and flexure (spirally reinforced column)
(ACI 9.3.2.2)
ϕ
= 0.70 for axial compression, and axial compression
and flexure (tied column)
(ACI 9.3.2.2)
ϕ
= 0.85 for shear and torsion
Strength Reduction Factors
(ACI 9.3.2.3)
Technical Note 19 - 1
©COMPUTERS AND STRUCTURES, INC., BERKELEY, CALIFORNIA DECEMBER 2001
CONCRETE FRAME DESIGN ACI-318-99
Technical Note 20
Column Design
This Technical Note describes how the program checks column capacity or designs reinforced concrete columns when the ACI-318-99 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:
ƒ
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 10.9.1) and 1 to 6 percent for Special moment resisting
frames (ACI 21.4.3.1).
ƒ
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.
ƒ
Design the column shear reinforcement.
The following four sections describe in detail the algorithms associated with
this process.
Overview
Technical Note 20 - 1
Column Design
Concrete Frame Design ACI-318-99
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
Concrete Frame Design ACI-318-99
Column Design
linear strain diagram limits the maximum concrete strain, εc, at the extremity
of the section, to 0.003 (ACI 10.2.3).
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, εsEs, and is limited to the yield stress of the steel, fy
(ACI 10.2.4). 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 c' (ACI 10.2.7.1). 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
ϕPn(max), where
ϕPn(max) = 0.85ϕ[0.85 f c' (Ag-Ast)+fyAst] spiral column,
(ACI 10.3.5.1)
ϕPn(max) = 0.80ϕ[0.85 f c' (Ag-Ast)+fyAst] tied column,
(ACI 10.3.5.2)
ϕ
=
0.70 for tied columns, and
(ACI 9.3.2.2)
ϕ
=
0.75 for spirally reinforced columns.
(ACI 9.3.2.2)
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 ϕPn decreases from the
smaller of ϕPb or 0.1 f c' Ag to zero, where ϕPb is the axial force at the balanced
condition. The ϕ factor used in calculating ϕPn and ϕPb is the ϕ(compression).
In cases involving axial tension, ϕ is always ϕ(flexure), which is 0.9 by default
(ACI 9.3.2.2).
Generation of Biaxial Interaction Surfaces
Technical Note 20 - 3
Column Design
Concrete Frame Design ACI-318-99
Figure 2 Idealized Strain Distribution for Generation of Interaction Source
Technical Note 20 - 4
Generation of Biaxial Interaction Surfaces
Concrete Frame Design ACI-318-99
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:
ƒ
Determine the factored moments and forces from the analysis load cases
and the specified load combination factors to give Pu, Mux, and Muy.
ƒ
Determine the moment magnification factors for the column moments.
ƒ
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
Column Design
Concrete Frame Design ACI-318-99
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 Pu, Mux, and Muy.
The factored moments are further increased for non-sway columns, if required, to obtain minimum eccentricities of (0.6+0.03h) inches, where h is
the dimension of the column in the corresponding direction (ACI 10.12.3.2).
Determine Moment Magnification Factors
The moment magnification factors are calculated separately for sway (overall
stability effect), δs and for non-sway (individual column stability effect), δns.
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 (Ms) and the non-sway (Mns) 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 = Mns + δsMs.
(ACI 10.13.3)
The factor δs is the moment magnification factor for moments causing side
sway. The moment magnification factors for sway moments, δs, is taken as 1
because the component moments Ms and Mns are obtained from a “second order elastic (P-delta) analysis” (ACI R10.10, 10.10.1, R10.13, 10.13.4.1).
The program assumes that it performs a P-delta analysis and, therefore, moment magnification factor δs for moments causing side-sway is taken as unity
(ACI 10.10.2). For the P-delta analysis, the load should correspond to a load
combination of 1.4 dead load + 1.7 live load (ACI 10.13.6). See also White
and Hajjar (1991). The user should use reduction factors for the moment of
inertias in the program as specified in ACI 10.11. The moment of inertia reduction for sustained lateral load involves a factor βd (ACI 10.11). This βd for
sway frame in second-order analysis is different from the one that is defined
later for non-sway moment magnification (ACI 10.0, R10.12.3, R10.13.4.1).
The default moment of inertia factor in this program is 1.
Technical Note 20 - 6
Calculate Column Capacity Ratio
Concrete Frame Design ACI-318-99
Column Design
The computed moments are further amplified for individual column stability
effect (ACI 10.12.3, 10.13.5) by the nonsway moment magnification factor,
δns, as follows:
Mc
= δnsM, where
(ACI 10.12.3)
Mc is the factored moment to be used in design.
The non-sway moment magnification factor, δns, associated with the major or
minor direction of the column is given by (ACI 10.12.3)
δns
Cm
Cm
≤ 1.0, where
Pu
1−
0.75Pc
=
= 0.6 +0.4
Ma
≥ 0.4,
Mb
(ACI 10.12.3)
(ACI 10.12.3.1)
Ma and Mb are the moments at the ends of the column, and Mb is
numerically larger than Ma. Ma / Mb is positive for single curvature
bending and negative for double curvature bending. The above expression of Cm 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, Cm=1. The user can overwrite Cm on an element-byelement basis.
Pc =
π 2 EI
(kl u )2
, where
(ACI 10.12.3)
k is conservatively taken as 1; however, the program allows the
user to override this value (ACI 10.12.1).
lu is the unsupported length of the column for the direction of
bending considered. The two unsupported lengths are l22 and l33,
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
Column Design
Concrete Frame Design ACI-318-99
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 + βd
, where
βd = maximum factored axial sustained (dead) load
maximum factored axial total load
(ACI 10.12.3)
(ACI 10.0,R10.12.3)
The magnification factor, δns, must be a positive number and greater than
one. Therefore, Pu must be less than 0.75Pc. If Pu is found to be greater than
or equal to 0.75Pc, a failure condition is declared.
Technical Note 20 - 8
Calculate Column Capacity Ratio
Concrete Frame Design ACI-318-99
Column Design
The above calculations are performed for major and minor directions separately. That means that δs, δns, Cm, k, lu, EI, and Pc 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 δs and δns.
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 Pu,
Mux, and Muy. The point (Pu, Mux, Muy) 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 failOL
ure surface. See Figure 5. The capacity ratio, CR, is given by the ratio
.
OC
ƒ
If OL = OC (or CR=1), the point lies on the interaction surface and the
column is stressed to capacity.
ƒ
If OL < OC (or CR<1), the point lies within the interaction volume and the
column capacity is adequate.
ƒ
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 Pu,
Mux, and Muy set and associated load combination number.
Calculate Column Capacity Ratio
Technical Note 20 - 9
Column Design
Concrete Frame Design ACI-318-99
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 20 - 10
Required Reinforcing Area
Concrete Frame Design ACI-318-99
Column Design
ƒ
Determine the factored forces acting on the section, Pu and Vu. Note that
Pu is needed for the calculation of Vc.
ƒ
Determine the shear force, Vc, that can be resisted by concrete alone.
ƒ
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
ƒ
In the design of the column shear reinforcement of an Ordinary moment
resisting concrete frame, the forces for a particular load combination,
namely, the column axial force, Pu, and the column shear force, Vu, in a
particular direction are obtained by factoring the program analysis load
cases with the corresponding load combination factors.
ƒ
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, Vp, 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, Pu, is calculated. Then,
the positive and negative moment capacities, Mu+ and Mu− , of the column
in a particular direction under the influence of the axial force Pu is calculated using the uniaxial interaction diagram in the corresponding direction.
The design shear force, Vu, is then given by (ACI 21.4.5.1)
Vu = Vp + VD+L
(ACI 21.4.5.1)
where, Vp 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
Column Design
Concrete Frame Design ACI-318-99
in two opposite directions. Therefore, Vp is the maximum of VP1 and VP2 ,
where
VP1 =
M I− + M J+
, and
L
VP2 =
M I+ + M J−
, where
L
M I+ , M I− ,
= Positive and negative moment capacities at end I of the
column using a steel yield stress value of αfy and no ϕ
factors (ϕ = 1.0),
M J+ , M J− ,
= Positive and negative moment capacities at end J of the
column using a steel yield stress value of αfy 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,
R21.4.5.1). VD+L is the contribution of shear force from the in-span distribution of gravity loads. For most of the columns, it is zero.
ƒ
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 21.10.3.a,
R21.10). The modified factored shear forces are based on the specified
load factors, except the earthquake load factors are doubled (ACI
21.10.3.b).
Determine Concrete Shear Capacity
Given the design force set Pu and Vu, the shear force carried by the concrete,
Vc, is calculated as follows:
Technical Note 20 - 12
Design Column Shear Reinforcement
Concrete Frame Design ACI-318-99
ƒ
Column Design
If the column is subjected to axial compression, i.e., Pu is positive,

Pu
Vc = 2 f c' 1 +

2,000 Ag


 Acv, where


(ACI 11.3.1.2)
f c' ≤ 100 psi, and
Vc ≤ 3.5 f c'
(ACI 11.1.2)

1 + Pu

500 Ag


 Acv.


(ACI 11.3.2.2)
The term Pu / Ag must have psi units. Acv is the effective shear area, which
is shown shaded in Figure 6. For circular columns, Acv is taken to be equal
to the gross area of the section (ACI 11.3.3, R11.3.3).
ƒ
If the column is subjected to axial tension, Pu is negative
Vc = 2 f c'
ƒ

1 + Pu

500 Ag


 Acv ≥ 0


(ACI 11.3.2.3)
For Special moment resisting concrete frame design, Vc is set to zero
if the factored axial compressive force, Pu, including the earthquake effect,
is small (Pu < f c' Ag / 20) and if the shear force contribution from earthquake, VE, is more than half of the total factored maximum shear force
over the length of the member Vu (VE ≥ 0.5Vu) (ACI 21.4.5.2).
Determine Required Shear Reinforcement
Given Vu and Vc, the required shear reinforcement in the form of stirrups or
ties within a spacing, s, is given for rectangular and circular columns by
Av =
(Vu / ϕ − Vc )s
, for rectangular columns and
f ys d
Av =
(Vu / ϕ − Vc )s
, for circular columns.
f ys (0.8D)
(ACI 11.5.6.1, 11.5.6.2)
(ACI 11.5.6.3, 11.3.3)
Vu is limited by the following relationship.
(Vu / ϕ-Vc) ≤ 8
f c' Acv
Design Column Shear Reinforcement
(ACI 11.5.6.9)
Technical Note 20 - 13
Column Design
Concrete Frame Design ACI-318-99
Figure 6 Shear Stress Area, Acv
Otherwise, redimensioning of the concrete section is required. Here ϕ, the
strength reduction factor, is 0.85 (ACI 9.3.2.3). The maximum of all the calculated Av 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 20 - 14
Design Column Shear Reinforcement
Concrete Frame Design ACI-318-99
Column Design
Reference
White, D.W. and J.F. Hajjar. 1991. 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
©COMPUTERS AND STRUCTURES, INC., BERKELEY, CALIFORNIA DECEMBER 2001
CONCRETE FRAME DESIGN ACI-318-99
Technical Note 21
Beam Design
This Technical Note describes how this program completes beam design when
the ACI 318-99 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:
ƒ
Design beam flexural reinforcement
ƒ
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:
ƒ
Determine the maximum factored moments
ƒ
Determine the reinforcing steel
Overview
Technical Note 21 - 1
Beam Design
Concrete Frame Design ACI-318-99
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.
The beam section is then designed for the maximum positive M u+ and maximum negative M u− factored moments 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
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 10.3.3). 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' Ag (ACI 10.3.3); hence, all the
beams are designed for major direction flexure and shear only.
Technical Note 21 - 2
Design Beam Flexural Reinforcement
Concrete Frame Design ACI-318-99
Beam Design
Figure 1 Design of Rectangular Beam Section
Design for Rectangular Beam
In designing for a factored negative or positive moment, Mu (i.e., designing
top or bottom steel), the depth of the compression block is given by a (see
Figure 1), where,
a=d-
d2 −
2 Mu
0.85f c1 ϕb
,
(ACI 10.2.7.1)
where, the value of ϕ is 0.90 (ACI 9.3.2.1) in the above and the following
equations. Also β1 and cb are calculated as follows:
 f ' − 4,000 
 , 0.65 ≤ β1 ≤ 0.85,
β1 = 0.85-0.05  c
 1,000 


cb =
εc Es
87,000
d =
d.
87,000 + f y
ε c E s + fy
Design Beam Flexural Reinforcement
(ACI 10.2.7.3)
(ACI 10.2.3, 10.2.4)
Technical Note 21 - 3
Beam Design
Concrete Frame Design ACI-318-99
The maximum allowed depth of the compression block is given by
amax = 0.75β1cb.
ƒ
(ACI 10.2.7.1, 10.3.3)
If a ≤ amax, the area of tensile steel reinforcement is then given by
As =
Mu
a

ϕf y  d − 
2

.
This steel is to be placed at the bottom if Mu is positive, or at the top if Mu
is negative.
ƒ
If a > amax, compression reinforcement is required (ACI 10.3.3) and is calculated as follows:
−
The compressive force developed in concrete alone is given by
C = 0.85 f c' bamax, and
(ACI 10.2.7.1)
the moment resisted by concrete compression and tensile steel is
a

Muc = C  d − max
2

−

 ϕ.

Therefore the moment resisted by compression steel and tensile steel
is
Mus = Mu - Muc.
−
So the required compression steel is given by
As' =
M us
f s' (d
− d' )ϕ
, where
 c − d' 
f s' = 0.003Es 
.
 c 
−
(ACI 10.2.4)
The required tensile steel for balancing the compression in concrete is
Technical Note 21 - 4
Design Beam Flexural Reinforcement
Concrete Frame Design ACI-318-99
As1 =
M uc
a


f y d − max  ϕ
2 

Beam Design
, and
the tensile steel for balancing the compression in steel is given by
As2 =
−
M us
.
f y (d − d' )ϕ
Therefore, the total tensile reinforcement, As = As1 + As2, and total
compression reinforcement is As' . As is to be placed at bottom and As'
is to be placed at top if Mu is positive, and vice versa if Mu is negative.
Design for T-Beam
In designing for a factored negative moment, Mu (i.e., designing top steel),
the calculation of the steel area is exactly the same as above, i.e., no T-Beam
data is to be used. See Figure 2. If Mu > 0, the depth of the compression
block is given by
a=d-
d2 −
2Mu
0.85f c' ϕbf
.
The maximum allowed depth of compression block is given by
amax = 0.75β1cb.
(ACI 10.2.7.1, 10.3.3)
•
If a ≤ ds, the subsequent calculations for As 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 > amax.
•
If a > ds, calculation for As is performed in two parts. The first part is for
balancing the compressive force from the flange, Cf, and the second part
is for balancing the compressive force from the web, Cw, as shown in Figure 2. Cf is given by
Cf = 0.85 f c' (bf - bw)ds.
Design Beam Flexural Reinforcement
Technical Note 21 - 5
Beam Design
Concrete Frame Design ACI-318-99
Figure 2 Design of a T-Beam Section
Therefore, As1 =
Cf
fy
and the portion of Mu that is resisted by the flange is
given by
d 

Muf = Cf  d − s  ϕ.
2 

Again, the value for ϕ is ϕ(flexure), which is 0.90 by default. Therefore,
the balance of the moment, Mu to be carried by the web is given by
Muw = Mu - Muf.
The web is a rectangular section of dimensions bw and d, for which the design depth of the compression block is recalculated as
a1 = d -
ƒ
d2 −
2Muw
0.85f ci ϕbw
.
If a1 ≤ amax, the area of tensile steel reinforcement is then given by
As2 =
Muw
a 

ϕf y  d − 1 
2 

Technical Note 21 - 6
, and
Design Beam Flexural Reinforcement
Concrete Frame Design ACI-318-99
Beam Design
As = As1 + As2.
This steel is to be placed at the bottom of the T-beam.
ƒ
If a1 > amax, compression reinforcement is required (ACI 10.3.3) and is
calculated as follows:
−
The compressive force in web concrete alone is given by
C = 0.85 f c' bamax.
−
(ACI 10.2.7.1)
Therefore, the moment resisted by concrete web and tensile steel
is
a


Muc = C  d − max ϕ , and
2


the moment resisted by compression steel and tensile steel is
Mus = Muw - Muc.
−
Therefore, the compression steel is computed as
As' =
Mus
f s' (d
− d' )ϕ
, where
 c − d' 
f s' = 0.003Es 
.
 c 
−
(ACI 10.2.4)
The tensile steel for balancing compression in web concrete is
As2 =
Muc
, and
amax
)ϕ
f y (d −
2
the tensile steel for balancing compression in steel is
As3 =
Mus
.
f y (d − d' )ϕ
Design Beam Flexural Reinforcement
Technical Note 21 - 7
Beam Design
−
Concrete Frame Design ACI-318-99
The total tensile reinforcement, As = As1 + As2 + As3, and total
compression reinforcement is As' . As is to be placed at bottom and
As' 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 '
200


c
As ≥ max 
bw d and
bw d  or
f
f
y

 y
As ≥ (4/3)As(required).
(ACI 10.5.1)
(ACI 10.5.3)
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):
ƒ
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 As(min) (ACI 21.3.2.1).
3 f '

200


c
As(min) ≥ max 
bw d and
bw d  or
f
f
y
 y

As(min) ≥
ƒ
(ACI 10.5.1)
4
As(required).
3
(ACI 10.5.3)
The beam flexural steel is limited to a maximum given by
As ≤ 0.025 bwd.
(ACI 21.3.2.1)
ƒ
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 21.3.2.2).
ƒ
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
Concrete Frame Design ACI-318-99
Beam Design
maximum of positive or negative moment capacities of any of the beam
end (support) stations (ACI 21.3.2.2).
For Intermediate moment resisting concrete frames (i.e., seismic design), the
beam design would satisfy the following conditions:
ƒ
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 21.10.4.1).
ƒ
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 21.10.4.1).
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, Vu.
•
Determine the shear force, Vc, 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
Beam Design
Concrete Frame Design ACI-318-99
Table 1 Design Criteria Table
Type of
Check/
Design
Ordinary Moment
Resisting Frames
(non-Seismic)
Intermediate Moment
Resisting Frames
(Seismic)
Special Moment
Resisting Frames
(Seismic)
Column
Check
(interaction)
NLDa Combinations
NLDa Combinations
NLDa Combinations
Column
Design
(interaction)
NLDa Combinations
1% < ρ < 8%
NLDa Combinations
1% < ρ < 8%
NLDa Combinations
α = 1.0
1% < ρ < 6%
NLDa Combinations
Modified NLDa Combinations
(earthquake loads doubled)
Column capacity
ϕ = 1.0 and α = 1.0
Column
Shears
Beam
Design
Flexure
Beam Min.
Moment
Override
Check
NLDa Combinations
NLDa Combinations
ρ ≤ 0.025
NLDa Combinations
ρ≥
1 −
M u END
3
1
≥ max M u+ , M u−
5
+
≥
M uEND
No Requirement
+
MuSPAN
−
M uSPAN
{
1
≥ max{M
5
NLDa Combinations
Column shear capacity
ϕ = 1.0 and α = 1.25
3 f c'
fy
, ρ ≥ 200
fy
1 −
M u END
2
1
≥ max Mu+ , Mu−
4
+
≥
M uEND
}
}
END
+
MuSPAN
+
−
u , M u END
−
MuSPAN
{
}
1
≥ max{M , M }
4
−
u
Beam
Design
Shear
NLDa Combinations
Modified NLDa Combinations
(earthquake loads doubled)
Beam Capacity Shear (Vp)
with α = 1.0 and ϕ = 1.0
plus VD+L
Joint Design
No Requirement
No Requirement
Checked for shear
Beam/Column
Capacity
Ratio
No Requirement
No Requirement
Reported in output file
END
−
u END
NLDa Combinations
Beam Capacity Shear (Vp)
with α = 1.25 and ϕ = 1.0
plus VD+L
Vc = 0
NLDa = Number of specified loading
Technical Note 21 - 10
Design Beam Shear Reinforcement
Concrete Frame Design ACI-318-99
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, Vp, 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 ACI318-99 Technical Note 20
Column Design. See also Table 1 for details.
The design shear force Vu is then given by (ACI 21.3.4.1)
Vu = Vp + VD+L
(ACI 21.3.4.1)
where Vp 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, Vp is the maximum of VP1 and VP2 ,
where
VP1
=
M I− + M J+
, and
L
VP2
=
M I+ + M J−
, where
L
M I−
= Moment capacity at end I, with top steel in tension, using a
steel yield stress value of αfy 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 αfy and no ϕ factors (ϕ = 1.0),
Design Beam Shear Reinforcement
Technical Note 21 - 11
Beam Design
Concrete Frame Design ACI-318-99
M I+
= Moment capacity at end I, with bottom steel in tension, using
a steel yield stress value of αfy 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 αfy 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,
R21.3.4.1). VD+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 21.10.3.a,
R21.10). The modified factored shear forces are based on the specified
load factors, except the earthquake load factors are doubled (ACI
21.10.3.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
ACI318-99 Technical Note 20 Column Design. See also Table 1 for details.
Determine Concrete Shear Capacity
The allowable concrete shear capacity is given by
Vc = 2 f c' bwd.
(ACI 11.3.1.1)
For Special moment resisting frame concrete design, Vc is set to zero if both
the factored axial compressive force, including the earthquake effect Pu, is
less than f c' Ag/20 and the shear force contribution from earthquake VE is
more than half of the total maximum shear force over the length of the member Vu (i.e., VE ≥ 0.5Vu) (ACI 21.3.4.2).
Technical Note 21 - 12
Design Beam Shear Reinforcement
Concrete Frame Design ACI-318-99
Beam Design
Determine Required Shear Reinforcement
Given Vu and Vc, the required shear reinforcement in area/unit length is calculated as
Av =
(Vu / ϕ − Vc )s
.
f ys d
(ACI 11.5.6.1, 11.5.6.2)
The shear force resisted by steel is limited by
(Vu / ϕ - Vc) ≤ 8 f c' bd.
(ACI 11.5.6.9)
Otherwise, redimensioning of the concrete section is required. Here, ϕ, the
strength reduction factor for shear, is 0.85 by default (ACI 9.3.2.3). The
maximum of all the calculated Av 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
©COMPUTERS AND STRUCTURES, INC., BERKELEY, CALIFORNIA DECEMBER 2001
CONCRETE FRAME DESIGN ACI318-99
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:
ƒ
Determine the panel zone design shear force, Vuh
ƒ
Determine the effective area of the joint
ƒ
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
Joint Design
Concrete Frame Design ACI318-99
Figure 1 Beam-Column Joint Analysis
Technical Note 22 - 2
Determine the Panel Zone Shear Force
Concrete Frame Design ACI318-99
Joint Design
The force Vuh is the horizontal panel zone shear force that is to be calculated.
The forces that act on the joint are Pu, Vu, MuL and MuR. The forces Pu and Vu
are axial force and shear force, respectively, from the column framing into the
top of the joint. The moments MuL and MuR are obtained from the beams
framing into the joint. The program calculates the joint shear force Vuh by resolving the moments into C and T forces. Noting that TL = CL and TR = CR,
Vuh = TL + TR - Vu
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, Cmax, and the
maximum moment, Mmax, that can be carried by the beam.
C max = 0.85f ' c bd
Mmax = C max
d
2
Then the program conservatively determines C and T forces as follows:

abs( M ) 
C = T = C max 1 − 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 21.5.1.1, UBC 1921.5.1.1). The C and T force are based on these
moment capacities. The program calculates the column shear force Vu from
the beam moment capacities, as follows:
Determine the Panel Zone Shear Force
Technical Note 22 - 3
Joint Design
Concrete Frame Design ACI318-99
L
Vu =
Mu + Mu
H
R
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 Vuh by
the effective area of the joint and comparing it with the following design shear
strengths (ACI 21.5.3, UBC 1921.5.3):
v =
{
Technical Note 22 - 4
20ϕ
f 'c
for joints confirmed on all four sides
15ϕ
f 'c
for joints confirmed on three faces or on two
opposite faces
12ϕ
f 'c
for all other joints
Determine the Effective Area of Joint
Concrete Frame Design ACI318-99
Joint Design
Figure 2 Column Shear Force Vu
where ϕ = 0.85 (by default).
(ACI 9.3.2.3, UBC 1909.3.2.3,1909.3.4.1)
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 21.5.3.1, UBC
1921.5.3.1).
Determine the Effective Area of Joint
Technical Note 22 - 5
Joint Design
Concrete Frame Design ACI318-99
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 f c' ,3 / 4 f c' 


(ACI 21.5.3.2, UBC 1921.5.3.2)
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 21.4.2.2).
∑Me ≥
6
∑Mg
5
(ACI 21.4.2.2)
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, Pu, 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 Pu 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
Concrete Frame Design ACI318-99
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 Mu at a Given Axial Load Pu
Beam/Column Flexural Capacity Ratios
Technical Note 22 - 7
©COMPUTERS AND STRUCTURES, INC., BERKELEY, CALIFORNIA DECEMBER 2001
CONCRETE FRAME DESIGN ACI318-99
Technical Note 23
Input Data
This Technical Note describes the concrete frame design input data for
ACI318-99. 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
DESCRIPTION
Load Combination Multipliers
Combo
Design load combination. See Technical Note 8.
Type
Load type: dead, live, superimposed dead, earthquake, wind,
snow, reduced live load, other.
Case
Name of load case.
Factor
Load combination scale factor.
Code Preferences
Phi_bending
Bending strength reduction factor.
Phi_tension
Tensile strength reduction factor.
Phi_compression
(Tied)
Compressive strength reduction factor for tied columns.
Phi_compression (Spiral)
Compressive strength reduction factor for reinforced columns.
Phi_shear
Shear strength reduction factor.
Input Data
Technical Note 23 - 1
Input Data
Concrete Frame Design ACI318-99
Table 1 Concrete Frame Design Input Data
COLUMN HEADING
DESCRIPTION
Material Property Data
Material Name
Concrete, steel, other.
Material Type
Isotropic or orthotropic.
Design Type
Modulus of Elasticity
Poisson's Ratio
Thermal Coeff
Coefficient of thermal expansion.
Shear Modulus
Material Property Mass and Weight
Material Name
Concrete, steel, other.
Mass Per Unit Vol
Used to calculate self-mass of structure.
Weight Per Unit Vol
Used to calculate self-weight of structure.
Material Design Data for Concrete Materials
Material Name
Concrete, steel, other.
Lightweight Concrete
Concrete FC
Concrete compressive strength.
Rebar FY
Bending reinforcing steel yield strength.
Rebar FYS
Shear reinforcing steel yield strength.
Lightwt Reduc Fact
Shear strength reduction factor for light weight concrete; default
= 1.0.
Concrete Column Property Data
Section Label
Label applied to section.
Mat Label
Material label.
Column Depth
Column Width
Rebar Pattern
Layout of main flexural reinforcing steel.
Concrete Cover
Minimum clear concrete cover.
Bar Area
Area of individual reinforcing bar to be used.
Technical Note 23 - 2
Table 1 Concrete Frame Design Input Data
Concrete Frame Design ACI318-99
Input Data
Table 1 Concrete Frame Design Input Data
COLUMN HEADING
DESCRIPTION
Concrete Column Design Element Information
Story ID
Column assigned to story level at top of column.
Column Line
Grid line.
Section ID
Name of section assigned to column.
Framing Type
Lateral or gravity.
RLLF Factor
L_Ratio Major
Unbraced length about major axis.
L_Ratio Minor
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
Story level at which beam occurs.
Bay ID
Grid lines locating beam.
Section ID
Section number assigned to beam.
Framing type
Lateral or gravity.
RLLF Factor
L_Ratio Major
Unbraced length about major axis.
L_Ratio Minor
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
Input Data
Concrete Frame Design ACI318-99
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
©COMPUTERS AND STRUCTURES, INC., BERKELEY, CALIFORNIA DECEMBER 2001
CONCRETE FRAME DESIGN ACI318-99
Technical Note 24
Output Details
This Technical Note describes the concrete frame design output for ACI318-99
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
Grid lines.
Section ID
Name of section assigned to column.
Station ID
Required Reinforcing
Longitudinal
Area of longitudinal reinforcing required.
Combo
Load combination for which the reinforcing is designed.
Shear22
Shear reinforcing required.
Combo
Load combination for which the reinforcing is designed.
Shear33
Shear reinforcing required.
Table 1 Concrete Column Design Output
Technical Note 24 - 1
Output Details
Concrete Frame Design ACI318-99
Table 1 Concrete Column Design Output
COLUMN HEADING
DESCRIPTION
Combo
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
Story level at which joint occurs.
Column Line
Grid line.
Section ID
Assigned section name.
Beam-Column Capacity Ratios
Major
Ratio of beam moment capacity to column capacity.
Combo
Load combination upon which the ratio of beam moment capacity to column capacity is based.
Minor
Ratio of beam moment capacity to column capacity.
Combo
Load combination upon which the ratio of beam moment capacity to column capacity is based.
Joint Shear Capacity Ratios
Major
Ratio of factored load versus allowed capacity.
Combo
Load combination upon which the ratio of factored load versus
allowed capacity is based.
Minor
Ratio of factored load versus allowed capacity.
Combo
Load combination upon which the ratio of factored load versus
allowed capacity is based.
Technical Note 24 - 2
Table 2 Concrete Column Joint Output
Concrete Frame Design ACI318-99
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