Csi_sap2000_concrete Frame Design Tutorial

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Concrete Frame

Design Manual

Hong Kong Code of Practice forStructural Use of Concrete 2004

For SAP2000®

ISO SAP063008M12 Version 12.0.0Berkeley, California, USA June 2008



COPYRIGHT

Copyright Computers and Structures, Inc., 1978-2008

All rights reserved.

The CSI Logo®, SAP2000®, and ETABS® are registered trademarks of Computers and

Structures, Inc. SAFETM

and Watch & LearnTM

are trademarks of Computers and

Structures, Inc.

The computer programs SAP2000® and ETABS® and all associated documentation areproprietary and copyrighted products. Worldwide rights of ownership rest with Computers

and Structures, Inc. Unlicensed use of these programs or reproduction of documentation in

any form, without prior written authorization from Computers and Structures, Inc., is

explicitly prohibited.

No part of this publication may be reproduced or distributed in any form or by any means,

or stored in a database or retrieval system, without the prior explicit written permission of

the publisher.

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

Computers and Structures, Inc.1995 University Avenue

Berkeley, California 94704 USA

Phone: (510) 649-2200

FAX: (510) 649-2299

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

e-mail: [email protected] (for technical support questions)web: www.csiberkeley.com

http://www.csiberkeley.com/





DISCLAIMER

CONSIDERABLE TIME, EFFORT AND EXPENSE HAVE GONE INTO THE

DEVELOPMENT AND DOCUMENTATION OF CSI’S PROGRAMS. THE

PROGRAMS HAVE BEEN THOROUGHLY TESTED AND USED. IN USING THE

PROGRAMS, HOWEVER, THE USER ACCEPTS AND UNDERSTANDS THAT NO

WARRANTY IS EXPRESSED OR IMPLIED BY THE DEVELOPERS OR THEDISTRIBUTORS ON THE ACCURACY OR THE RELIABILITY OF THE

PROGRAMS.

THE PROGRAMS ARE VERY PRACTICAL TOOLS FOR THE DESIGN/CHECK OF

STRUCTURES. HOWEVER THE USER MUST THOROUGHLY READ THE

MANUALS AND MUST CLEARLY RECOGNIZE THE ASPECTS OF DESIGN THAT

THE PROGRAM ALGORITHMS DO NOT ADDRESS.

THE USER MUST EXPLICITLY UNDERSTAND THE ASSUMPTIONS OF THE

PROGRAMS AND MUST INDEPENDENTLY VERIFY THE RESULTS.

3





Contents

Chapter 1 Introduction

1.1 Organization 1-2

1.2 Recommended Reading/Practice 1-3

Chapter 2 Design Prerequisites

2.1 Design Load Combinations 2-1

2.2 Design and Check Stations 2-3

2.3 Identifying Beams and Columns 2-3

2.4 Design of Beams 2-3

2.5 Design of Columns 2-4

2.6 P-Delta Effects 2-5

2.7 Element Unsupported Length 2-6

2.8 Choice of Input Units 2-6

i



Design Manual Concrete Frame Hong Kong CP 2004

Chapter 3 Design Process

3.1 Notation 3-1

3.2 Design Load Combinations 3-4

3.3 Design Strength 3-4

3.4 Column Design 3-53.4.1 Generation of Biaxial Interaction Surface 3-53.4.2 Check Column Capacity 3-8

3.4.2.1 Determine Factored Moments andForces 3-9

3.4.2.2 Determine Additional Moments 3-93.4.2.3 Determine Capacity Ratio 3-11

3.4.3 Design Column Shear Reinforcement 3-13

3.5 Beam Design 3-153.5.1 Design Beam Flexural Reinforcement 3-15

3.5.1.1 Determine Factored Moments 3-153.5.1.2 Determine Required Flexural

Reinforcement 3-163.5.1.3 Minimum and Maximum Tensile

Reinforcement 3-233.5.2 Design Beam Shear Reinforcement 3-25

Chapter 4 Design Output

4.1 Overview 4-1

4.2 Graphical Display of Design Information 4-24.2.1 Input/Output 4-2

4.3 Tabular Display of Design output 4-4

4.4 Member Specific Information 4-64.4.1 Interactive Concrete Frame Design 4-8

4.5 Errors Messages and Warnings 4-9

ii



Contents

iii

Appendix A Second Order P-Delta Effects

Appendix B Member Unsupported Lengths and Computation ofK-Factors

Appendix C Concrete Frame Design Preferences

Appendix D Concrete Frame Overwrites

Appendix E Error Messages and Warnings

References



Chapter 1

Introduction

The design of concrete frames is seamlessly integrated within the program.

Initiation of the design process, along with control of various design parameters,

is accomplished using the Design menu.

Automated design at the object level is available for any one of a number of

user-selected design codes, as long as the structures have first been modeled and

analyzed by the program. Model and analysis data, such as material properties

and member forces, are recovered directly from the model database, and noadditional user input is required if the design defaults are acceptable.

The design is based on a set of user-specified loading combinations. However,

the program provides default load combinations for each design code supported

in the program. If the default load combinations are acceptable, no definition of

additional load combinations is required.

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

shear reinforcement. However, the user may specify the longitudinal steel, in

which case a column capacity ratio is reported. The column capacity ratio gives

an indication of the stress condition with respect to the capacity of the column.

The biaxial column capacity check is based on the generation of consistent

three-dimensional interaction surfaces. It does not use any empirical

1 - 1




formulations that extrapolate uniaxial interaction curves to approximate biaxial

action.

Interaction surfaces are generated for user-specified column reinforcing

configurations. The column configurations may be rectangular, square or

circular, with similar reinforcing patterns. The calculation of moment

magnification factors, unsupported lengths and strength reduction factors is

automated in the algorithm.

Every beam member is designed for flexure, shear, and torsion at output stations

along the beam span.

All beam-column joints are investigated for existing shear conditions.

For special moment resisting frames (ductile frames), the shear design of the

columns, beams and joints is based on the probable moment capacities of the

members. Also, the program will produce ratios of the beam moment capacities

with respect to the column moment capacities, to investigate weak beam/strong

column aspects, including the effects of axial force.

Output data can be presented graphically on the model, in tables for both input

and output data, or on the calculation sheet prepared for each member. For each

presentation method, the output is in a format that allows the engineer to quickly

study the stress conditions that exist in the structure and, in the event the member

reinforcing is not adequate, aid the engineer in taking appropriate remedial

measures, including altering the design member without rerunning the entire

analysis.

1.1 OrganizationThis manual is designed to help you quickly become productive with the

concrete frame design options of the Hong Kong Code of Practice for Structural

Use of Concrete 2004, which is referred to as HK CP 04 in this manual. Chapter

2 provides detailed descriptions of the Deign Prerequisites used for HK CP 04.

Chapter 3 provides detailed descriptions of the code specific process used for

HK CP 04. Chapter 4 documents the design output produced by the programs.The appendices provide details on certain topics referenced in this manual.

1 - 2 Organization



Chapter 1 - Introduct ion

Recommended Reading/Practice - 31

1.2 Recommended Reading/PracticeIt is strongly recommended that you read this manual and review any applicable

“Watch & Learn” Series™ tutorials, which are found on our web site,

http://www.csiberkeley.com, before attempting to design a concrete frame.

Additional information can be found in the on-line Help facility available from

within the program’s main menu.



Chapter 2

Design Prerequisites

This chapter provides an overview of the basic assumptions, design

preconditions, and some of the design parameters that affect the design of

concrete frames.

In writing this manual it has been assumed that the user has an engineering

background in the general area of structural reinforced concrete design and

familiarity with the HK CP 04 code.

2.1 Design Load CombinationsThe design load combinations are used for determining the various

combinations of the load cases for which the structure needs to be

designed/checked. The load combination factors to be used vary with the

selected design code. The load combination factors are applied to the forces and

moments obtained from the associated load cases and are then summed to obtain

the factored design forces and moments for the load combination.

For multi-valued load combinations involving response spectrum, time history,

moving loads and multi-valued combinations (of type enveloping, square-root

of the sum of the squares or absolute) where any correspondence between

interacting quantities is lost, the program automatically produces multiple sub

combinations using maxima/minima permutations of interacting quantities.

2 - 1




Separate combinations with negative factors for response spectrum cases are not

required because the program automatically takes the minima to be the negativeof the maxima for response spectrum cases and the above described

permutations generate the required sub combinations.

When a design combination involves only a single multi-valued case of time

history or moving load, further options are available. The program has an option

to request that time history combinations produce sub combinations for each

time step of the time history. Also an option is available to request that moving

load combinations produce sub combinations using maxima and minima of each

design quantity but with corresponding values of interacting quantities.

For normal loading conditions involving static dead load, live load, wind load,

and earthquake load, and/or dynamic response spectrum earthquake load, theprogram has built-in default loading combinations for each design code. The

combinations are based on the code recommendations and are documented for

each code in the corresponding manuals.

For other loading conditions involving moving load, time history, pattern live

loads, separate consideration of roof live load, snow load, etc., the user must

define design loading combinations either in lieu of or in addition to the default

design loading combinations.

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

additive. Similarly, all cases declared as live load are assumed additive.However, each load case declared as wind or earthquake, or response spectrum

cases, is assumed to be non additive with each other and produces multiple

lateral load combinations. Also wind and static earthquake cases produce

separate loading combinations with the sense (positive or negative) reversed. If

these conditions are not correct, the user must provide the appropriate design

combinations.

The default load combinations are included in design if the user requests them to

be included or if no other user defined combination is available for concrete

design. If any default combination is included in design, then all default

combinations will automatically be updated by the program any time the design

code is changed or if static or response spectrum load cases are modified.

2 - 2 Design Load Combinations



Chapter 2 - Design Prerequisites

Design and Check Stations 2 - 3

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

case on an element-by-element basis to reduce the contribution of the live loadto the factored loading.

The user is cautioned that if moving load or time history results are not requested

to be recovered in the analysis for some or all of the frame members, then the

effects of those loads will be assumed to be zero in any combination that

includes them.

2.2 Design and Check StationsFor each load combination, each element is designed or checked at a number of

locations along the length of the element. The locations are based on equallyspaced segments along the clear length of the element. The number of segments

in an element is requested by the user before the analysis is made. The user can

refine the design along the length of an element by requesting more segments.

2.3 Identifying Beams and ColumnsIn the program all beams and columns are represented as frame elements. But

design of beams and columns requires separate treatment. Identification for a

concrete element is done by specifying the frame section assigned to the element

to be of type beam or column. If any brace elements are in the frame, the brace

element also would be identified as either a beam or a column element based on

the section assigned to the brace element.

2.4 Design of BeamsIn 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 the code specific manuals. The reinforcement requirements are calculated at a

user-defined number of stations along the beam span.

All of the beams are designed for major direction flexure, shear and torsion only.

Effects due to any axial forces and minor direction bending 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 maximumfactored moments and the determination of the reinforcing steel. 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 a 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, then 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 due to 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.

2.5 Design of ColumnsIn the design of 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, which is a factor that gives an indication of the

stress condition of the column with respect to the capacity of the column. Thedesign procedure for the reinforced concrete columns of the structure involves

the following steps:

Generate axial force-biaxial moment interaction surfaces for all of the

different concrete section types of the model.

Check the capacity of each column for the factored axial force and bending

moments obtained from each loading 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.

The generation of the interaction surface is based on the assumed strain andstress distributions and some other simplifying assumptions. These stress and

strain distributions and the assumptions are documented in Chapter 3.

2 - 4 Design of Columns



Chapter 2 - Design Prerequisites

P-Delta Effects 2 - 5

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 capacityneeds to be considered.

For certain special seismic cases, the design of columns for shear is based on the

capacity shear. The capacity shear force in a particular direction is calculated

from the moment capacities of the column associated with the factored axial

force acting on the column. For each load combination, the factored axial load is

calculated using the load cases and the corresponding load combination factors.

Then, the moment capacity of the column in a particular direction under the

influence of the axial force is calculated using the uniaxial interaction diagram in

the corresponding direction, as documented in Chapter 3.

2.6 P-Delta EffectsThe program design process require that the analysis results include the P-delta

effects. The P-delta effects are considered differently for “braced” or “nonsway”

and “unbraced” or “sway” components of moments in columns or frames. For

the braced moments in columns, the effect of P-delta is limited to “individual

member stability”. For unbraced components, “lateral drift effects” should be

considered in addition to individual member stability effect. The program

assumes that “braced” or “nonsway” moments are contributed from the “dead”

or “live” loads. Whereas, “unbraced” or “sway” moments are contributed from

all other types of loads.

For the individual member stability effects, the moments are magnified with

moment magnification factors as documented in Chapter 3 of this manual.

For lateral drift effects, the program assumes that the P-delta analysis is

performed and that the amplification is already included in the results. The

moments and forces obtained from P-delta analysis are further amplified for

individual column stability effect if required by the governing code as in the HK

CP 04 codes.

The users of the program should be aware that the default analysis option in the

program is turned OFF for P-delta effect. The user can turn the P-delta analysis

ON and set the maximum number of iterations for the analysis. The default

number of iteration for P-delta analysis is 1. Further details on P-delta analysis

are provided in Appendix A of this design manual.




2 - 6 Element Unsupported Lengths

2.7 Element Unsupported LengthsTo account for column slenderness effect, the column unsupported lengths are

required. The two unsupported lengths are l33 and l22. 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).

Normally, the unsupported element length is equal to the length of the element,

i.e., the distance between END-I and END-J of the element. The program,

however, allows users to assign several elements to be treated as a single

member for design. This can be done differently for major and minor bending as

documented in Appendix B of this design manual.

The user has options to specify the unsupported lengths of the elements on an

element-by-element basis.

2.8 Choice of Input UnitsEnglish as well as SI and MKS metric units can be used for input. But the codes

are based on a specific system of units. All equations and descriptions presented

in the subsequent chapters correspond to that specific system of units unless

otherwise noted. For example, the HK CP 04 code is published in meter-kilo

Newton-second units. By default, all equations and descriptions presented in thechapter “Design for HK CP 04” correspond to meter-kilo Newton-second units.

However, any system of units can be used to define and design the structure in

the program.



Chapter 3Design for CP 2004 Hong Kong

This chapter describes in detail the various aspects of the concrete design

procedure that is used by the program when the user selects the Hong Kong

limit state design code CP 2004 (CP 2004). For simplicity, all equations and

descriptions presented in this chapter correspond to Newton-Millimeter-Second

units unless otherwise noted.

3.1 NotationThe various notations used in this chapter are described herein:

Acv Area of section for shear resistance, mm2

Ag Gross area of cross-section, mm2

As Area of tension reinforcement, mm2

A' s Area of compression reinforcement, mm2

Asc Total area of column longitudinal reinforcement, mm2

Asv Total cross-sectional area of links at the neutral axis, mm

2

Asv / sv Area of shear reinforcement per unit length of the member,

mm2 /mm

3 - 1



Design Manual Concrete Frame Design Hong Kong CP 2004

a Depth of compression block, mm

b Width or effective width of the section in the compression zone,mm

b' Shorter section dimension, mm

b f Width or effective width of flange, mm

bw Average web width of a flanged beam, mm

C Compression force, N

d Effective depth of tension reinforcement, mm

d' Depth to center of compression reinforcement, mm

E c Modulus of elasticity of concrete, MPa

E s Modulus of elasticity of reinforcement, assumed as 200,000 MPa

emin Minimum eccentricity, mm

f cu Characteristic cube strength at 28 days, MPa

'

s f Compressive stress in a beam compression steel, MPa

f y Characteristic strength reinforcement, MPa

f yv Characteristic strength of link reinforcement, MPa (< 460 MPa)

h Overall depth of a section in the plane of bending, mmh f Flange thickness, mm

K Normalized design moment, M u / bd 2 f cu

K' Maximum2

u

u

M

bd fcfor a singly reinforced concrete section,

assuming that moment redistribution is limited to 10%

k 1 Shear strength enhancement factor for support compression

k 2 Concrete shear strength factor, 3

1

25cu f

le Effective height of a column, mm

lo Clear height between end restraints, mm

3 - 2 Notation



Chapter 3 - Design for CP 2004 Hong Kong

M Design moment at a section, N-mm

M 1 , M 2 Smaller and larger end moments in slender column, N-mm

M i Initial moment at the point of maximum additional moment,

N-mm

M x, M y Applied moments about the major and minor axes of a column,

N-mm

N Ultimate axial load, N

sv Spacing of the links along the length of the beam, mm

T Tension force, N

V Design shear force at ultimate design load, Nv Design shear stress at a beam cross-section or at a punch critical

section, MPa

vc Design ultimate shear stress resistance of a concrete beam, MPa

v' c Design concrete shear stress corrected for axial forces, MPa

v x , v y Design ultimate shear stress of a concrete section, MPa

x Neutral axis depth, mm

xbal Depth of neutral axis in a balanced section, mm

z Lever arm, mm

Effective length factor

b Moment redistribution factor in a member

f Partial safety factor for load

m Partial safety factor for material strength

c Maximum concrete strain, 0.0035

s Strain in tension steel

' s Strain in compression steel

Notation 3 - 3




3.2 Design Load CombinationsThe design loading combinations define the various factored combinations of

the load cases for which the structure is to be checked. The design loading

combinations are obtained by multiplying the characteristic loads by

appropriate partial factors of safety, f (CP 2.3.1.3). If a structure is subjected

to dead load (DL) and live load (LL) only, the design will need only one

loading combination, namely 1.4 DL + 1.6 LL. However, in addition to the

dead load and live load, if the structure is subjected to wind (WL), and

considering that those loads are subject to reversals, the following load

combinations for ultimate limit state should be considered (CP 2.3.2, Table

2.1):

1.4 DL + 1.6 LL

1.0 DL ± 1.4 WL (CP 2.3.2.1)

1.4 DL ± 1.4 WL

1.2 DL + 1.2 LL ± 1.2 WL

These are the default load combinations. In addition to these load

combinations, the code requires that all buildings be capable of resisting a

notional design ultimate horizontal load applied at each floor or roof level. The

notional load should be equal to 0.015 times the dead load (CP 3.1.4.2). It is

recommended that the user define additional load cases to consider notional

load in the program.

Live load reduction factors, as allowed by some design codes, can be applied to

the member forces of the live load case on a member-by-member basis to

reduce the contribution of the live load to the factored loading.

3.3 Design StrengthThe design strength for concrete and steel are obtained by dividing the

characteristic strength of the material by a partial factor of safety, m. The

values of m used in the program are listed as follows (CP 2.4.3.2, Table 2.2).

1.15, for reinforcement,

1.50, for concrete in flexure and axial load, and

1.25, for shear strength without shear reinforcement.

m

(CP 2.4.3.2,

Table 2.2)

3 - 4 Design Load Combinations




3.4 Column DesignThe user may define the geometry of the reinforcing bar configuration of each

concrete column section. If the area of reinforcing is provided by the user, the

program checks the column capacity. However, if the area of reinforcing is not

provided by the user, the program calculates the amount of reinforcing required

for the column. The design procedure for the reinforced concrete columns of

the structure involves the following steps:

Generate axial force/biaxial moment interaction surfaces for all of the

different concrete section types of the model. A typical biaxial interaction

surface is shown in Figure 3-1. When the steel is undefined, the program

generates the interaction surfaces for the range of allowable reinforcement

from 0.8 to 6 percent (CP 9.5.1).

Calculate the capacity ratio or the required reinforcing area for the factored

axial force and biaxial (or uniaxial) bending moments obtained from each

loading combination at each station of the column. The target capacity

ratio is taken as one when calculating the required reinforcing area.

Design the column shear reinforcement.

The following three subsections describe in detail the algorithms associated

with these steps.

3.4.1 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 (CP 6.2.1.4a). A

typical interaction diagram is shown in Figure 3-1.

Column Design 3 - 5




3 - 6 Column Design

Figure 3-1 A typical column interaction surface

The coordinates of these points are determined by rotating a plane of linear

strain in three dimensions on the section of the column (CP 6.1.2.4). See Figure3-2. The linear strain diagram limits the maximum concrete strain, at the

extremity of the section, to c (CP 6.1.2.4) as shown by the following:

2

2

0.0035 for 60 /

0.0035 0.00006 60 for 60 /

cu

c

cu cu

f N mm

f f N m

m

The formulation is based consistently on the basic principles of ultimate

strength design and allows for any doubly symmetric rectangular, square, or

circular column section (CP 6.2.1.4a, CP Figure 6.1).

The stress in the steel is given by the product of the steel strain and the steel

modulus of elasticity, ,s s E and is limited to the design strength of the steel,

area associated with each reinforcing bar is placed atThe 1.15 0.87 . y y f f




c

c

c

c

c

c

c

c

c

c

Figure 3-2 Idealized strain distribution for generation of interaction surface

the actual location of the center of the bar and the algorithm does not assume

any simplifications in the manner in which the area of steel is distributed over

the cross-section of the column (such as an equivalent steel tube or cylinder).

See Figure 3-3.

Column Design 3 - 7




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

stress value of 0.65 0.45 cu m u f f (CP 6.1.2.4, CP Figure 6.1). See Figure3-3. The interaction algorithm provides corrections to account for the concrete

area that is displaced by the reinforcement in the compression zone.

Figure 3-3 Idealization of stress and strain distribution in a column section

3.4.2 Check Column Capacity

The column capacity is checked for each loading combination at each output

station of each column. In checking a particular column for a particular loading

combination at a particular location, the program uses the following steps:

Determine the factored moments and forces from the load cases and the

specified load combination factors to give , , , , and . x y x y N V V M M

Determine the additional moments due to slender column effect. Compute

moments due to minimum eccentricity.

Determine total design moments by adding the corresponding additional

moments to the factored moments obtained from the analysis. Determine

3 - 8 Column Design




Column Design 3 - 9

whether the point, defined by the resulting axial load and biaxial moment

set, lies within the interaction volume.

The following three subsections describe in detail the algorithms associated

with these steps.

3.4.2.1 Determine Factored Moments and Forces

Each load combination is defined with a set of load factors corresponding to

the load cases. The factored loads for a particular load combination are

obtained by applying the corresponding load factors to the load cases, giving

, , , , and . x y x y N V V M M

3.4.2.2 Determine Additional Moments

The determination of additional moments depends on whether the frame is

“braced” or “unbraced” against sidesway (CP 6.2.1.1(d)). For “unbraced”

columns, additional moment is automatically considered in the P-delta

analysis. But for “braced” columns, further calculation is required for stability

of individual column members.

3.4.2.2.1 Braced Column

The additional moment in a braced column in a particular plane is the productof the axial load and the lateral deflection of the column in that plane (CP

6.2.1.3),

,add u M Na (CP 6.2.1.3(a))

where, is the deflection at the ultimate limit state, which is obtained fromua

u aa Kh and (CP 6.2.1.3)

21

.2000

ea

l

b

(CP 6.2.1.3)

In the preceding equations,




3 - 10 Column Design

– el is the effective length in the plane under consideration. It is obtained

from

0 ,el l (CP 6.2.1.1(e))

where is the effective length factor, and is the unsupported length

corresponding to instability in the major or minor direction of the element,

. In calculating the value of the effective length, the

0l

factor is

conservatively taken as 1. However, the program allows the user to overwrite

this default value.

b is the dimension of the column in the plane of bending considered.

h is also the dimension of the column in the plane of bending considered.

K is the correction factor to the deflection to take care of the influence of the

axial force, and is conservatively taken as 1.K

The program then calculates the total design moments by combining the

factored moments obtained from analysis and the additional moments. If 1 M

and 2 M 2 1 M M are the initial end moments in a column member in a

particular plane, the maximum design moment for the column is taken as the

greatest of the following:

2 M (CP 6.2.1.3(b))

(CP 6.2.1.3(b))1 add M M

1 2 add M

M (CP 6.2.1.3(b))

(CP 6.2.1.3(b))min N e

where,

i M is the initial moment in a column due to design ultimate loads at the point

of maximum additional moment and is given by

1 20.4 0.6 0.4 .i 2 M M M M (CP 6.2.1.3(b))

and x yl l




Column Design 3 - 11

1 M and 2 M are the smaller and the larger end moments respectively. Both

moments are assumed to be positive if the column is in single curvature. If thecolumn is in double curvature, 1 M is assumed to be negative.

mine is the minimum eccentricity, which is taken as 0.05 times the overall

dimension of the column in the plane of bending considered, but not more than

20 mm (CP 6.2.1.2(d)).

min 20 .20

h

e mm (CP 6.2.1.2(d))

3.4.2.2.2 Unbraced Column

In the case of the unbraced column, it is assumed that the program analysis

includes P-delta effects so that the analysis results include the effects of the

additional moments. Therefore, no additional computation is required. That

means moment magnification factors for moments causing sidesway are taken

as unity. However, it is recommended that for P-delta analysis, a factor be used

to obtain a equivalent to 1.2 DL + 1.2 LL (White and Hajjar 1991).P

Also, the minimum eccentricity requirements are satisfied so the design

moment should be at least

min ,u M Ne (CP 6.2.1.2(d))

where, is the minimum eccentricity, which is described in the previous

section. In biaxial bending, the algorithm ensures that the eccentricity exceeds

the minimum about both the axes simultaneously.

mine

3.4.2.3 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, thedesign forces , ,and x y N M M

, ,

are obtained according to the previous subsections.

The point

is then placed in the interaction space shown as point L

in Figure 3-4. If the point lies within the interaction volume, the column x y N M M





capacity is adequate; however, if the point lies outside the interaction volume,

the column is overstressed.

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

location of point C. The point C is defined as the point where the line OL (if

extended outwards) will intersect the failure surface. This point is determined

by three-dimensional linear interpolation between the points that define the

failure surface. See Figure 3-4. The capacity ratio, CR, is given by the ratio

.OL

OC

Figure 3-4 Geometric representation of column capacity ratio

If OL = OC (or CR = 1), the point lies on the interaction surface and the

column is stressed to capacity.




Column Design 3 - 13

If OL < OC (or CR < 1), the point lies within the interaction volume and the

column capacity is adequate.

If OL > OC (or CR > 1), the point lies outside the interaction volume and the

column is overstressed.

The maximum of all of the values of CR calculated from each load

combination is reported for each check station of the column along with the

controlling , , and x y N M M set and associated load combination number.

If the reinforcing area is not defined, the program computes the reinforcement

that will giv ratio of unity.e an interaction

3.4.3 ement

The shear reinforcement is designed for each loading combination in the major

shear reinforcement for a

Design Column Shear Reinforc

and minor directions of the column. In designing the

particular column for a particular loading combination due to shear forces in a

particular direction, the following steps are involved (CP 6.2.1.4(e) and

6.1.2.5):

Calculate the design shear stress from

, ,cv

cv

v A bd

A

whereV

(CP 6.1.2.5(a))

0.8 , cuv f and (CP 6.1.2.5(a))

27 . N mm

v (CP 6.1.2.5(a))

– If exceeds 0.8 cu f or 2mm7 N , the section area should be increased.

Calculate the design concrete shear stress from (CP 6.1.2.5(a))

'0.6 , c c

c

N Vd 6.1.2.5(k))v v

A M

with (CP

1 13 4400

,

(CP 6.1.2.5(c))1 2 1000.79

s

c

m

Ak k v

bd d





where,

is the enhancement factor for support compression and taken

ively as 1, (CP 6.1.2.5(g))

1k

conservat

13

2 ,25

cu f

(CP 6.1.2.5(c))k

1.25. m (CP 2.4.3.2)

However the following limitations also apply:

100

0.15 3,

s A

bd (CP 6.1.2.5(c))

1,Vd

M (CP 6.1.2.5(u))

40.67for members without shear reinforcement

1.00for members withshear reinforcement, (CP 6.1.2.5(c))

400

d

280 N cu mm

f , (CP 6.1.2.5, 6.1.2.5(c))

s A is the area of tensile steel, which is assumed to be half of total rebar.

Calculate the design average shear stress that can

trans

be carried by minimum

verse rebar, r v , as follows:

2 2

23

0.4 if 40

N N cumm mm

f

f 2

23

2

0.4 if 40 < 8040

800.4 if 8040

cu N r cu mm

N cu mm

v f

f

(CP 6.1.2.5(b), Table CP 6.2)

– If '

, c r v v v provide minimum links defined by

,0.87

sv r

v yv

A v

s f (CP 6.1.2.5(b))




Beam Design 3 - 15

', c r v v v provide links given byelse if

'

.0.87

sv

v y

c

v

v v b A

s f (CP 6.1.2.5(b))

3.5 Beam DesignIn the design of concrete beams, the program calculates and reports the

for flexure and shear based on the beam moments and

on factors, and other criteria described herein or in the

3.5.1 orcement

The beam top and bottom flexural steel is designed at a user defined number of

lexural reinforcement for

ar section, the following

einforcing steel

3.5.1.1

In the design of flexural reinforcement of concrete frame beams, the factored

moments for each load combination at a particular beam station are obtained

required areas of steel

shears, load combinati

subsections that follow. The reinforcement requirements are calculated at a

user defined number of check stations along the beam span.

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

Effects due to any axial forces, minor direction bending, and torsion that may

exist in the beams must be investigated independently by the user.

The beam design procedure involves the following steps:

Design beam flexural reinforcement

Design beam shear reinforcement

Design Beam Flexural Reinf

check stations along the beam span. In designing the f

the major moment for a particular beam at a particul

steps are involved:

Determine the maximum factored moments

Determine the r

Determine Factored Moments




3 - 16 Beam Design

by factoring the corresponding moments for different load cases with the

such cases, the beam may be designed as a Rectangular section, or T

3.5.1.2 ocess, the program calculates both the

tension and compression reinforcement. Compression reinforcement is added

oment capacity of a

ion in the member does not exceed 10% (i.e., b 0.9) (CP

corresponding load factors.

The beam section is then designed for the maximum positive and maximum

negative factored moments obtained from all of the load combinations at that

section.

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

beam effects may be included.

Determine Required Flexural ReinforcementIn the flexural reinforcement design pr

when the applied design moment exceeds the maximum m

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 3-6 (CP 6.1.2.4(a)). Furthermore, it is assumed that moment

redistribut

6.1.2.4(b)). The code also places a limitation on the neutral axis depth,

2

2

0.5 for 45 /

0.4 for 45 < 70 /

cu

cu

f N mm x

f N mmd

20.33 for 70 < 100 / andnomoment redistribution

cu f N mm

to safeguard against non-ductile failures (CP 6.1.2.4(b)). In addition, the area

of compression reinforcement is calculated on the assumption that the neutral

xis depth remains at the maximum permitted value.

f cu Ag (CP

a

The design procedure used by the program, for both rectangular and flangedsections (L and T beams), is summarized in the subsections that follow. It is

assumed that the design ultimate axial force does not exceed 0.1




Beam Design 3 - 17

6.1.2.4(a)); hence, all of the beams are designed for major direction flexure and

shear only.

c

Figure 3-6 Rectangular beam design

3.5.1.2.1 Design of a Rectangu

For rectangular beams, the moment capacity as a singly reinforced beam,

ction. The reinforcing steel area is determined

an, less than, or equal to M single. See Figure

einforced.

lar Beam

M single, is obtained first for a se

based on whether M is greater th

3-2.

Calculate the ultimate moment of resistance of the section as singly

r

2single , where cu M K f bd (CP 6.1.2.4(c))




3 - 18 Beam Design

2

2

2and no moment redistribution

0.156 for 45 /

' 0.120 for 45 70 /

0.094 for 70 100 / .

cu

cu

cu

f N mm

K f N mm

f N mm

– If M M single, the area of tension reinforcement, As, is obtained from

,

0.87s

y

M A

f z

where (CP 6.1.2.4(c))

0.5 0.25 0.95 ,0.9

K z d d

2

2

2

, for 45 / ,0.45

, for 45 70 / ,0.40

, for 70 100 / ,0.36

cu

cu

cu

d z f N mm

d z x f N mm

d z f N mm

2.

cu

M K

f bd

This is the top steel if the section is under negative moment and the

bottom steel if the section is under positive moment.

– If M > M single, the area of compression reinforcement, 's A , is given by

single,

s

s

M M A

f d d

where d ' is the depth of the compression steel from the concrete

compression face, and

1 0.87 ,s s s yd f E

x f (CP 6.1.2.4 (c), 3.2.6, Fig. CP 3.9)




2

2

2

, for 45 / ,

0.45

, for 45 70 / ,0.40

, for 70 100 / ,0.36

cu

cu

cu

d z f N mm

d z x f N mm

d z f N mm

0.5 0.25 .0.9

K z d

This is the bottom steel if the section is under negative moment. From

equilibrium, the area of tension reinforcement is calculated as

single single

.( )0.87

s

y y

M M M A

f d d f z(CP 6.1.2.4(c))

3.5.1.2.2 Design as a T Beam

Flanged Beam Under Negative Moment

The contribution of the flange to the strength of the beam is ignored. The

design procedure is therefore identical to the one used for Rectangular beams,

except that in the corresponding equations, is replaced by See Figure 3-7.b .wb

Flanged Beam Under Posit ive Moment

With the flange in compression, the program analyzes the section by

considering alternative locations of the neutral axis. Initially, the neutral axis is

assumed to be located in the flange. Based on this assumption, the program

calculates the exact depth of the neutral axis. If the stress block does not extend

beyond the flange thickness, the section is designed as a rectangular beam of

width b f . If the stress block extends beyond the flange width, the contribution

of the web to the flexural strength of the beam is taken into account. See Figure

3-7.

Assuming the neutral axis is in the flange, the normalized moment is computed

as

Beam Design 3 - 19




2.

cu f

M K

f b d

Then the moment arm is computed as

0.5 0.25 0.95 ,0.9

K z d d

the depth of neutral axis is computed as

2

2

2

, for 45 / ,0.45

, for 45 70 / ,0.40

, for 70 100 / ,0.36

cu

cu

cu

d z f N mm

d z x f N mm

d z f N mm

the depth of compression block is given by

a =

2

2

2

0.9 for 5 N/mm

0.8 for 45 < 70 N/mm

0.72 for 70 < 100 N/mm

cu

cu

cu

x f

x f

x f

4 ,

,

.

If a h f , the subsequent calculations for As are exactly the same as

previously defined for the Rectangular section design. However, in that

case, the width of the compression flange, b f , is taken as the width of the

beam, b, for analysis. Whether compression reinforcement is required

depends on whether K K .

If a > h f , calculation for As is performed in two parts. The first part is for

balancing the compressive force from the flange, C f , and the second part is

for balancing the compressive force from the web, C w , as shown in Figure

3-3.

In that case, the ultimate resistance moment of the flange is given by

3 - 20 Beam Design




Beam Design 3 - 21

0.67

0.5 ,

f cu f w f

m

f M f b b h d h

the balance of moment taken by the web is computed as

, w f M M M and

the normalized moment resisted by the web is given by

2. w

w

cu w

M K

f b d

c

Figure 3-7 T beam design

If K w K 1, the beam is designed as a singly reinforced concrete beam. The

area of steel is calculated as the sum of two parts, one to balance

compression in the flange and one to balance compression in the web.

,

0.870.87 0.5

f w

s

y y f

M M A f z f d h

where




3 - 22 Beam Design

0.5 0.25 0.95 .0.9

wK z d d

If K w K' , compression reinforcement is required and is calculated as

follows:

The ultimate moment of resistance of the web only is given by

2.uw cu w M K f b d

The compression reinforcement is required to resist a moment of

magnitude

.w uw M M

The compression reinforcement is computed as

,

w uw

s

s

M M A

f d d

where,

d ' is the depth of the compression steel from the concrete

compression face, and

1 0.87 .s s c y

d f E f

x

The area of tension reinforcement is obtained from equilibrium

1,

0.87 0.5

f uw w uws

y f

M M M M A

f d h z d d where

0.5 0.25 0.95 .0.9

k z d d




Special Case

If 2

f cu M B f bd ,

0, s A

1 2

0.87 0.5

cu w f

s

y f

M k f b d k d h A

f d h(CP 6.1.2.5(d))

where,

cu

1

f

k =

2

2

2

0.100 for 45 /

0.072 for 45 70 /

0.054 for 70 100 / , and

cu

cu

N mm

f N mm

f N mm

2

2

2

0.45 for 45N/mm

0.32 for 45 70N/mm

0.24 for 70 100N/mm

cu

2 cu

cu

f

k = f

f

,

,

.

3.5.1.3 Minimum and Maximum Tensile Reinforcement

The minimum flexural tensile steel required for a beam section is given by thefollowing table, which is taken from CP Table 9.1 (CP 9.2.1.1), with interpolation

for reinforcement of intermediate strength:

Minimum percentage

Section SituationDefinition of

percentage f y = 250 MPa f y = 460 MPa

Rectangular 100bh

As 0.24 0.13

Beam Design 3 - 23




3 - 24 Beam Design

Minimum percentage

Section Situation Definition of percentage f y = 250 MPa f y = 460 MPa

f

w

b

b< 0.4 100

hb

A

w

s 0.32 0.18

T or L beam with

web in tension

f

w

b

b 0.4 100

hb

A

w

s 0.24 0.13

T beam with web

in compression 100

hb

A

w

s 0.48 0.26

L beam with web

in compression 100

hb

A

w

s 0.36 0.20

The minimum flexural compression steel, if it is required at all, provided in a

rectangular beam or T beam section is given by the following table, which is

taken from CP Table 9.1 (CP 9.2.1.1), with interpolation for reinforcement of

intermediate strength:

Section Situation Definition of percentage

Minimumpercentage

Rectangular

100

s A

bh 0.20

Web in tension 100

s

f f

A

b h 0.40

T beam

Web in compression 100

s

w

A

b h 0.20

In addition, an upper limit on both the tension reinforcement and compression

reinforcement has been imposed to be 0.04 times the gross cross-sectional area

(CP 9.2.1.3).




Beam Design 3 - 25

3.5.2 Design Beam Shear Reinforcement

The shear reinforcement is designed for each loading combination in the major

and minor directions of the column. In designing the shear reinforcement for a

particular beam for a particular loading combination due to shear forces in a

particular direction, the following steps are involved (CP 6.1.2.5):

Calculate the design shear stress as

, , wh cv

cv

V v A bd

Aere (CP 6.1.2.5(a))

0.8 , cuv f and (CP 6.1.2.5(a))

27 . N mm

v (CP 6.1.2.5(a) 6.1.2.5(k))

– If v exceeds either 0.8 cu f or 27 N mm

, the section area should be in-

creased.

Calculate the design concrete shear stress from

0.6 , with d c c

c

V N v v

A M (CP 6.1.2.5(k))

1 1

3 41 2 1000.79 400 ,

s

c

m

Ak k vbd d

(CP 6.1.2.5(c))

where,

is the enhancement factor for support compression,1k

and is conservatively taken as 1, (CP 6.1.2.5(g))1k

13

2 1, and25

cu f

k (CP 6.1.2.5(c))

1.25. m (CP 2.4.3.2)

However, the following limitations also apply:




1000.15 3, s A

bd

(CP 6.1.2.5(c))

40.67for memberswithoutshear reinforcement,

1.00 for members withshear reinforcement,

400

d

(CP 6.1.2.5(c))

1.d V

M (CP 6.1.2.5(k))

Calculate the design average shear stress that can be carried by minimum

transverse rebar, ,r v as follows:

2 2

23

2

23

2

0.4 if 40

0.4 if 40 8040

800.4 if 8040

N N cumm mm

cu N r cu mm

N cu mm

f

f v f

f

(CP 6.1.2.5(b), Table CP 6.2)

280 N cu

mm f (for calculation purpose only). (CP 6.1.2.5(c))

s A is the area of tensile steel.

– If , c r v v v provide minimum links defined by

,0.87

s r

v y

A v b

vs f

else if , provide links given by cv v vr

.0.87

csv

v y

v v b A

vs f

(CP 6.1.2.5)

3 - 26 Beam Design



Chapter 4Design Output

4.1 OverviewThe program creates design output in different formats – graphical display,

tabular output, and member specific detailed design information.

The graphical display of design output includes input and output design

information. Input design information includes design section labels,K -factors,live load reduction factors, and other design parameters. The output design

information includes longitudinal reinforcing, shear reinforcing, torsional

reinforcing and column capacity ratios. All graphical output can be printed.

The tabular output can be saved in a file or printed. The tabular output includes

most of the information that can be displayed. This is generated for added

convenience to the designer.

The member specific detailed design information shows the details of the

calculation from the designer’s point of view. It shows the design forces,

design section dimensions, reinforcement, and some intermediate results for all

of the load combinations at all of the design sections of a specific frame

member. For a column member, it also can show the position of the current

state of design forces on the column interaction diagram.

4 - 1




In the following sections, some of the typical graphical display, tabular output,

spreadsheet output, and member specific detailed design information aredescribed. The HK CP 04 design code is described in this manual.

4.2 Graphical Display of Design InformationThe graphical display of design output includes input and output design

information. Input design information includes design section label,K -factors,

live load reduction factor, and other design parameters. The output design

information includes longitudinal reinforcing, shear reinforcing, torsion

reinforcing, column capacity ratio, beam-column capacity ratio, joint shear

check, and other design information.

The graphical output can be produced in color or in gray-scaled screen display.

The active screen display can be sent directly to the printer.

4.2.1 Input and Output

Input design information for the HK CP 04 code includes the following:

Design sections

Design framing type

Live load reduction factors (RLLF)

Unbraced length, L-factors, for major and minor direction of bending

Effective length factors, K -factors, for major and minor direction of bend-

ing

C m factors, for major and minor direction of bending

ns factors, for major and minor direction of bending

s factors, for major and minor direction of bending

The output design information that can be displayed consists of the following:

Longitudinal reinforcing area

4 - 2 Graphical Display of Design Information



Chapter 4 - Design Output

Longitudinal reinforcing area as percent of concrete gross area

Shear reinforcing areas per unit spacing

Column P-M-M interaction ratios

Torsion reinforcing

General reinforcing details

Use the Design menu > Concrete Frame Design > Display Design Info

command to plot input and output values directly on the model in the active

window. Clicking this command will access the Display Design Results form.

Select the Design Output or Design Input option, and then use the drop-down

lists to choose the type of design data to be displayed, such as longitudinalreinforcement, rebar percentages, shear reinforcing and so on. Click the OK

button on the form to close the form and display the selected data in the active

window.

The graphical displays can be viewed in 2D or 3D mode. Use the various

toolbar buttons (e.g., Set Default 3D View, Set X-Y View) to adjust the view,

or use the View menu > Set 2D View or View menu > Set 3D View

commands to refine the display.

The graphical display in the active window can be printed by clicking theFile

menu > Print Graphics command, the Print Graphics button on the toolbar,or the Ctrl+G keyboard shortcut. The display also can be captured as a bit map

file (.bmp) using one of the subcommands on the File menu > Capture

Picture command, or as a metafile (.emf) using one of the subcommands on

the File menu > Capture Enhanced Metafile command. The captured picture

file can then be used in popular graphics programs, including Paint and

PowerPoint. Alternatively, the standard Windows screen capture command

(click the Print Screen button on the keyboard) can be used to create a screen

capture of the entire window, or use the Alt+Print Screen command to capture

only the "top layer," such as a form displayed from within the program.

By default, graphics are displayed and printed in color, assuming a color

printer is available. Use the Options menu > Colors > Output command to

change default colors, as necessary, including changing the background color

from the default black to white. A white background can be useful when

printing design output to save ink/toner. In addition, the Options menu >

Graphical Display of Design Information 4 - 3




Colors > Set Active Theme command can be used to view or print graphics in

grayscale.

4.3 Tabular Display of Design OutputThe tabular design output can be sent directly to a printer or saved to a file. The

printed form of the tabular output is the same as that produced for the file

output except that the font size is adjusted for the printed output.

The tabular design output includes input and output design information that

depends on the design code chosen. For the HK CP 04 code, the tabular output

includes the following. All tables have formal headings and are self-

explanatory, so further description of these tables is not given.

Input design information includes the following:

Concrete Column Property Data

- Material label

- Column dimensions

- Reinforcement pattern

- Concrete cover

- Bar area

Concrete Beam Property Data- Material label

- Beam dimensions

- Top and bottom concrete cover

- Top and bottom reinforcement areas

Concrete Column Property Data

- Material label

- Column dimensions

- Reinforcement pattern

- Concrete cover

- Bar area

Load Combination Multipliers

- Combination name

4 - 4 Tabular Display of Design Output




- Load types

- Load factors

Concrete Design Element Information

- Design section ID

- Factors for major and minor direction of bending

- Unbraced length ratios for major and minor direction of

bending, L-factors

- Live load reduction factors (RLLF)

Concrete Moment Magnification Factors

- Section ID

- Element type

- Framing type- ns -factors

- s -factors

The output design information includes the following:

Column design Information

- Section ID

- Station location

- Total longitudinal reinforcement and the governing load combina-

tion

- Major shear reinforcement and the governing load combination

- Minor shear reinforcement and the governing load combination

Beam Design Information

- Section ID

- Station location

- Top longitudinal reinforcement and the governing load combination

- Bottom reinforcement and the governing load combination

- Longitudinal torsional reinforcement and the governing load combi-

nation

- Major shear reinforcement and the governing load combination for

shear and torsion design

Tabular output can be printed directly to a printer or saved in a file using the

File menu > Print Tables command. A form will display when this command

is used. Depress the F1 key on the keyboard to access the Help topic specific to

Tabular Display of Design Output 4 - 5




that form, which will identify the types of output available (e.g., plain text with

or without page breaks, rich text format Word document, and so on).

4.4 Member Specific InformationMember specific design information shows the details of the calculation from

the designer's point of view. It includes the geometry and material data, other

input data, design forces, design section dimensions, reinforcement details, and

some of the intermediate results for the selected member. The design detail

information can be displayed for a specific load combination and for a specific

station of a column or beam member. For columns, member specific design

information also can show the position of the current state of design forces

using a column interaction diagram.

After an analysis has been performed and the Design menu > Concrete

Frame Design > Start Design/Check command has been used, access the

detailed design information by right clicking a frame member to display the

Concrete Column Design Information form if a column member was right

clicked or the Concrete Beam Design Information form if a beam member was

right clicked. Table 4-1 identifies the types of data provided by the forms.

The longitudinal and shear reinforcing area are reported in their current units,

which are displayed in the drop-down list in the lower right corner of the

program window. Typically, the longitudinal reinforcing area is reported inin

2

,mm

2, cm2 and so on. Shear reinforcing areas typically are reported in in

2 /in,

mm2 /mm, cm

2 /cm and so on.

Table 4-1 Member Specific Data for Columns and Beams

Column Beam

Load combination ID

Station locations

Longitudinal reinforcement area

Major shear reinforcement areas

Minor shear reinforcement areas

Load combination ID

Station location

Top reinforcement areas

Bottom reinforcement areas

Longitudinal reinforcement for torsion design

Shear reinforcement area for shear

Shear reinforcement area for torsion design

4 - 6 Member Specific Information




Table 4-1 Member Specific Data for Columns and Beams

Buttons on the forms can be used to access additional forms that provide the following data

Overwrites

– Element section ID

– Element framing type

– Code-dependent factors

– Live load reduction factors

– Effective length factors, K , for major

and minor direction bending

– C m factors for major and minor bend-

ing

– s factors for major and minor direc-

tions

Summary design data

– Geometric data and graphical represen-tation

– Material properties

– Minimum design moments

– Moment factors

– Longitudinal reinforcing areas

– Design shear forces

– Shear reinforcing areas

– Shear capacities of steel and concrete

– Torsion reinforcing

– Interaction diagram, with the axial

force and biaxial moment showing the

state of stress in the column

Detailed calculations for flexural details,

shear details, joint shear, and beam/ col-umn capacity ratios

Overwrites

– Element section ID

– Element framing type

– Code-dependent factors

– Live load reduction factors

– Effective length factors, K , for major and

minor direction bending

– C m factors for major and minor bending

– s factors for major and minor directions

Summary design data

– Geometric data and graphical representa-

tion

– Material properties– Design moments and shear forces

– Minimum design moments

– Top and bottom reinforcing areas

– Shear capacities of concrete and steel

– Shear reinforcing area

– Torsion reinforcing area

The load combination is reported by its name, while station data is reported by

its location as measured from the I-end of the column. The number of line

items reported is equal to the number of design combinations multiplied by the

number of stations. One line item will be highlighted when the form first

displays. This line item will have the largest required longitudinal reinforcing,

unless any design overstress or error occurs for any of the items. In that case,

the last item among the overstressed items or items with errors will be

highlighted. In essence, the program highlights the critical design item.

If a column has been selected and the column has been specified to be checked

by the program, the form includes the same information as that displayed for a

designed column, except that the data for a checked column includes the

capacity ratio rather than the total longitudinal reinforcing area. Similar to the

Member Specific Information 4 - 7




design data, the line item with the largest capacity ratio is highlighted when the

form first displays, unless an item has an error or overstress, in which case, thatitem will be highlighted. In essence, the program highlights the critical check

item.

The program can be used to check and to design rebar in a column member.

When the users specifies that the program is to check the rebar in the column,

the program checks the rebar as it is specified. When the user specifies that the

program design the rebar configuration, the program starts with the data

specified for rebar and then increases or decreases the rebar in proportion to the

relative areas of rebar at the different locations of rebar in the column.

4.4.1 Interactive Concrete Frame DesignThe interactive concrete frame design and review is a powerful mode that

allows the user to review the design results for any concrete frame design, to

revise the design assumptions interactively, and to review the revised results

immediately.

Before entering the interactive concrete frame design mode, the design results

must be available for at least one member. That means the design must have

been run for all the members or for only selected members. If the initial design

has not been performed yet, run a design by clicking the Design menu >

Concrete Frame Design > Start Design/Check of Structure command.

There are three ways to initiate the interactive concrete frame design mode:

Click the Design menu > Concrete Frame Design > Start Design/Check

of Structures command to run a design.

Click the Design menu > Concrete Frame Design > Display Design Info

command to access the Display Design Results form and select a type of

result.

Click the Design menu > Concrete Frame Design > Interactive Con-

crete Frame Design command.

After using any of the three commands, right click on a frame member to enter

the interactive Concrete Frame Design Mode and access the Concrete Column

Design Information form if a column member was right clicked or the

4 - 8 Member Specific Information




Error Messages and Warnings 4 - 9

Concrete Beam Design Information form if a beam member was right clicked.

These forms have Overwrites buttons that accesses the Concrete FrameDesign Overwrites form. The form can be used to change the design sections,

element type, live load reduction factor for reducible live load, and many other

design factors. See Appendix D for a detailed description of the overwrite

items. When changes to the design parameters are made using the Overwrites

form, the Concrete Beam or Column Design Information forms update

immediately to reflect the changes. Then other buttons on the Concrete Beam

or Column Design Information forms can be used to display additional forms

showing the details of the updated design. See the Member Specific

Information section of this chapter for more information.

In this way, the user can change the overwrites any number of times to produce

a satisfactory design. After an acceptable design has been produced by

changing the section or other design parameters, click the OK button on the

Concrete Beam or Column Design Information forms to permanently change

the design sections and other overwrites for that member. However, if the

Cancel button is used, all changes made to the design parameters using the

Concrete Frame Design Overwrites form are temporary and do not affect the

design.

4.5 Error Messages and WarningsIn many places of concrete frame design output, error messages and warnings

are displayed. The messages are numbered. A complete list of error messages

and warnings used in Concrete Frame Design for all the design codes is

provided in Appendix E. However, all of the messages are not applicable to the

HK CP 04 code.



APPENDICES





Appendix ASecond Order P-Delta Effects

Typically, design codes require that second order P-delta effects be considered

when designing concrete frames. They are the global lateral translation of the

frame and the local deformation of members within the frame.

Consider the frame object shown in Figure A-1, which is extracted from a story

level of a larger structure. The overall global translation of this frame object is

indicated by . The local deformation of the member is shown as . The total

second order P-delta effects on this frame object are those caused by both and

.

The program has an option to consider P-delta effects in the analysis. When

P-delta effects are considered in the analysis, the program does a good job of

capturing the effect due to the deformation shown in Figure A-1, but it does

not typically capture the effect of the deformation (unless, in the model, the

frame object is broken into multiple elements over its length).

A - 1




Figure A-1 The Total Second Order P-Delta Effects on a

Frame Element Caused by Both and

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

the following equation.

M CAP = aM nt + bM lt where,

M CAP = Flexural design capacity required

M nt = Required flexural capacity of the member assuming there isno joint translation of the frame (i.e., associated with the

deformation in Figure A-1)

M lt = Required flexural capacity of the member as a result of

lateral translation of the frame only (i.e., associated with the

deformation in Figure A-1)

a = Unitless factor multiplying M nt

b = Unitless factor multiplying M lt (assumed equal to 1 by the

program; see the following text)

When the program performs concrete frame design, it assumes that the factor b

is equal to 1 and calculates the factor a. That b = 1 assumes that P-delta effects

have been considered in the analysis, as previously described. Thus, in general,

when performing concrete frame design in this program, consider P-delta

effects in the analysis before running the program.

A - 2 Second Order P-Delta Effects



Appendix BMember Unsupported Lengths and

Computation of K -Factors

The column unsupported lengths are required to account for column slenderness

effects. The program automatically determines the unsupported length ratios,

which are specified as a fraction of the frame object length. Those ratios times

the frame object length give the unbraced lengths for the members. Those ratios

can also be overwritten by the user on a member-by-member basis, if desired,

using the overwrite option.

There are two unsupported lengths to consider. They are L33 and L22, as shown

in Figure B-1. These are the lengths between support points of the member 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).

B - 1




Figure B-1 Axis of bending and unsupported length

In determining the values for L22 and L33 of the members, 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 member support points and evaluates the

corresponding unsupported length.

It is possible for the unsupported length of a frame object to be evaluated by the

program as greater than the corresponding member length. For example, assume

a column has a beam framing into it in one direction, but not the other, at a floor

level. In that 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.

B - 2 Member Unsupported Lengths and Computation of K-Factors



Appendix C

Concrete Frame Design Preferences

Table C-1 Design Criteria

ItemPossibleValues

DefaultValue

Description

Time HistoryDesign

Envelopes,Step-by-Step

Envelopes

Toggle for design load combinationsthat include a time history designed for

the envelope of the time history, ordesigned step-by-step for the entiretime history. If a single design loadcombination has more than one timehistory case in it, that design loadcombination is designed for the enve-lopes of the time histories, regardlessof what is specified here.

NumberInteraction

Curves

Multiple of 4

424

Number of equally spaced interactioncurves used to create a full 360 deg interaction surface (this item should bea multiple of four). We recommend 24

for this item.

C - 1




C - 2 Preferences

ItemPossibleValues

DefaultValue

Description

NumberAny odd value

511

Number of points used to define asingle curve in a concrete frame;should be odd.

ConsiderMinimum

EccentricityNo, Yes Yes

Toggle to consider if minimum eccen-tricity should be considered in design.

SeismicA, B, C,D, E, F

D

This item varies with the SeismicHazard Exposure Group and the ef-fective Peak Velocity Related Accel-eration.

Phi(Tension

Controlled)> 0 0.9

Strength reduction factor for tensioncontrolled sections.

Phi(Compression

Controlled-Tied)> 0 0.65

The strength reduction factor forcompression controlled sections withspiral reinforcement.

Phi(Compression

Controlled-Spiral)> 0 0.70

The strength reduction factor forcompression controlled sections withspiral reinforcement.

Phi(Shear and/ or

Torsion)> 0 0.75

The strength reduction factor for shearand torsion.

Phi(Shear - Seismic)

> 0 0.60

The strength reduction factor for shearin structures that rely on specialmoment resisting frames or specialreinforced concrete structural walls toresist earthquake effects.

Phi (Joint Shear) > 0 0.75The strength reduction factor for shear

and torsion.



Appendix C - Concrete Frame Design Preferences

Preferences C - 3

ItemPossibleValues

DefaultValue

Description

Phi (Pattern LiveLoad Factor)

0 0.60

The strength reduction factor for shearin structures that rely on specialmoment resisting frames or specialreinforced concrete structural walls toresist earthquake effects.

Utilization FactorLimit

> 0 0.95Stress ratios that are less than or equalto this value are considered accept-able.





Appendix D

Concreter Frame Overwrites

The concrete frame design overwrites are basic assignments that apply only to

those elements to which they are assigned. Table D-1 lists concrete frame design

overwrites for Hong Kong CP 2004. Default values are provided for all

overwrite items. Thus, it is not necessary to specify or change any of the

overwrites. However, at least review the default values to ensure 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.

Table D-1 Design Criteria

ItemPossibleValues

DefaultValue

Description

CurrentDesignSection

Any definedconcretesection

Analysissection

The design section for the selectedframe objects. When this overwrite isapplied, any previous auto selectsection assigned to the frame objectis removed.

D - 1




D - 2 Concrete Frame Design Overwrites

ItemPossibleValues

DefaultValue

Description

ElementType

SwaySpecial, SwayIntermediate,

Sway OrdinaryNonSway

FromReference

Frame type per moment frame defi-nition given in ACI 21.1. The FramingType is used for ductility considera-tions in the design. The program de-termines its default value based onthe Seismic Design Category (SDC)assigned for the structure in thePreferences. If the assigned SDC isA or B, the Framing Type is set toOrdinary. If the assigned SDC is C,the Framing Type is set to Interme-diate. If the assigned SDC is D, E, or

F, the Framing Type is set to special(IBC 1908.1.2). These are defaultvalues, which the user can overwritesif needed.

Live LoadReduction

Factor 0 Calculated

The reduced live load factor. Areducible live load is multiplied by thisfactor to obtain the reduced live loadfor the frame object. Specifying 0means the value is program deter-mined.

UnbracedLength Ratio

(Major) 0 Calculated

Unbraced length factor for bucklingabout the frame object major axis.This item is specified as a fraction ofthe frame object length. Multiplyingthis factor times the frame objectlength gives the unbraced length forthe object. Specifying 0 means thevalue is program determined.

UnbracedLength Ratio

(Minor) 0 0.60

Unbraced length factor for bucklingabout the frame object minor axis.Multiplying this factor times the frameobject length gives the unbracedlength for the object. Specifying 0means the value is program deter-mined. This factor is also used in

determining the length forlateral-torsional buckling.



Appendix D

Concrete Frame Design Overwrites D - 3

ItemPossible

Values

Default

Value

Description

EffectiveLength Factor

(K Major)> 0 Calculated

See ACI 10.12, 10.13 and FigureR10.12.1. Effective length factor forbuckling about the frame object majoraxis. This item is specified as a frac-tion of the frame object length.





Appendix E

Error Messages and Warnings

Table E-1 provides a complete list of Concrete Errors messages and Warnings.

Table E-1 Error Messages

ErrorNumber

Description

1 Beam concrete compression failure

2 Reinforcing required exceeds maximum allowed

3 Shear stress exceeds maximum allowed

4 Column design moments cannot be calculated

5 Column factored axial load exceeds Euler Force

6 Required column concrete area exceeds maximum

7 Flexural capacity could not be calculated for shear design

8 Concrete column supports non-concrete beam/column

E - 1




E - 2 Error Messages and Warnings

ErrorNumber

Description

9 115 k L r , 2 0 zeta_ , 1 0 eta (GB50010 7.3.10)

10 Column is overstressed for P-M-M

11 Axial compressive capacity for concrete exceeded (TBM 6.4.2)

12 Beam frames into column eccentrically (11.6.3)

13 Torsion exceeds maximum allowed

14 Reinforcing provided is below minimum required

15 Reinforcing provided exceeds maximum allowed

16 Tension reinforcing provided is below minimum required

17 30 k L r (GB 7.3.10)

21The column is not ductile. Beam/column capacity ratio is notneeded.

22The load is not seismic. Beam/column capacity ratio is not

needed.

23There is no beam on top of column. Beam/column capacity ratiois not needed.

24At least one beam on top of column is not of concrete.Beam/column capacity ratio is not calculated.

25The column on top is not of concrete. Beam/column capacity ratiois not calculated.

26The station is not at the top of the column. Beam/column capacity

ratio is not needed.

27 The column is not ductile. Joint shear ratio is not needed.



Appendix E

ErrorNumber

Description

28 The load is not seismic. Joint shear ratio is not needed.

29There is no beam on top of column. Joint shear ratio is notneeded.

30At least one beam on top of column is not of concrete. Joint shearratio is not calculated.

31The column on top is not of concrete. Joint shear ratio is notneeded.

32 The station is not at the top of the column. Joint shear ratio is notneeded.

33 Beam/column capacity ratio exceeds limit.

34 Joint shear ratio exceeds limit.

35 Capacity ratio exceeds limit.

36All beams around the joint have not been designed.Beam/column capacity ratio is not calculated.

37 At least one beam around the joint has failed. Beam/column ca-pacity ratio is not calculated.

38The column above the joint has not been designed. Beam/columncapacity ratio is not calculated.

39The column above the joint has failed. Beam/column capacityratio is not calculated.

40All beams around the joint have not been designed. Joint shearratio is not calculated.

41 At least one beam around the joint has failed. Joint shear ratio isnot calculated.

42 The column above the joint has not been designed. Joint shear

Error Messages and Warnings F- 3




E - 4 Error Messages and Warnings

ErrorNumber

Description

ratio is not calculated.

43The column above the joint has failed. Joint shear ratio is notcalculated.

45Shear stress due to shear force and torsion together exceedsmaximum allowed.



References

HK CP, 2004. Code of Practice for Structural Use of Concrete 2004 (HK CP 04),

Building Department, 12/F-18/F Pioneer Centre, 750 Nathan Road,

Mongkok, Kowloon, Hong Kong.

CSI, 2005a. SAP2000 Getting Started, Computers and Structures, Inc., Berke-

ley, California.

CSI, 2005b. Welcome to ETABS, Computers and Structures, Inc., Berkeley,

California.

CSI, 2005c. CSI Analysis Reference Manual, Computers and Structures, Inc.,

Berkeley, California.

D. W. White 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, 1991.

Documents

Csi_sap2000_concrete Frame Design Tutorial