CFD NTC 2008

User Manual: CFD-NTC-2008

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Concrete Frame Design Manual

Italian NTC 2008

Concrete Frame

Design Manual

Italian NTC 2008

For ETABS® 2016

ISO ETA122815M32 Rev. 0

Proudly developed in the United States of America December 2015

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

Structures, Inc. SAFETM and Watch & LearnTM are trademarks of Computers and

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proprietary and copyrighted products. Worldwide rights of ownership rest with Computers

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

Computers and Structures, Inc.

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DISCLAIMER

CONSIDERABLE TIME, EFFORT AND EXPENSE HAVE GONE INTO THE

DEVELOPMENT AND TESTING OF THIS SOFTWARE. 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 THIS PRODUCT.

THIS PRODUCT IS A PRACTICAL AND POWERFUL TOOL FOR STRUCTURAL

DESIGN. HOWEVER, THE USER MUST EXPLICITLY UNDERSTAND THE BASIC

ASSUMPTIONS OF THE SOFTWARE MODELING, ANALYSIS, AND DESIGN

ALGORITHMS AND COMPENSATE FOR THE ASPECTS THAT ARE NOT

ADDRESSED.

THE INFORMATION PRODUCED BY THE SOFTWARE MUST BE CHECKED BY A

QUALIFIED AND EXPERIENCED ENGINEER. THE ENGINEER MUST

INDEPENDENTLY VERIFY THE RESULTS AND TAKE PROFESSIONAL

RESPONSIBILITY FOR THE INFORMATION THAT IS USED.

Contents

Chapter 1 Introduction

1.1 Organization 1-2

1.2 Recommended Reading/Practice 1-2

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 Lengths 2-5

Concrete Frame Design Eurocode 2-2004

2.8 Choice of Input Units 2-6

Chapter 3 Design Process

3.1 Notation 3-1

3.2 Assumptions / Limitations 3-4

3.3 Design Load Combinations 3-5

3.4 Column Design 3-7

3.4.1 Generation of Biaxial Interaction Surface 3-8

3.4.2 Calculate Column Capacity Ratio 3-11

3.4.3 Design Longitudinal Reinforcement 3-18

3.4.4 Design Column Shear Reinforcement 3-18

3.5 Beam Design 3-19

3.5.1 Design Beam Flexural Reinforcement 3-19

3.5.2 Design Beam Shear Reinforcement 3-28

3.5.3 Design Beam Torsion Reinforcement 3-30

Chapter 4 Seismic Provisions

4.1 Notations 4-1

4.2 Design Preferences 4-3

4.3 Overwrites 4-3

4.4 Supported Framing Types 4-3

4.5 Member Design 4-4

4.5.1 Ductility Class High – Moment-Resisting Frames 4-4

4.5.2 Ductility Class Low – Moment-Resisting

Frames 4-17

4.5.3 Special Consideration for Seismic Design 4-20

Contents

Appendix A Second Order P-Delta Effects

Appendix B Member Unsupported Lengths and Computation of

-Factors

Appendix C Concrete Frame Design Preferences

Appendix D Concrete Frame Overwrites

Appendix E Error Messages and Warnings

Appendix F Nationally Determined Parameters (NDPs)

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 structure has 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 no

additional 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.

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 load 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 formula-

tions that extrapolate uniaxial interaction curves to approximate biaxial action.

1 - 1

Concrete Frame Design NTC 2008

Interaction surfaces are generated for user-specified column reinforcing con-

figurations. The column configurations may be rectangular, square, or circular,

with similar reinforcing patterns. The calculation of second order moments,

unsupported lengths, and material partial factors is automated in the algorithm.

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

along the beam span.

Input and output data can be presented graphically on the model, in tables, or on

the calculation sheet prepared for each member. For each presentation method,

the data is in a format that allows the engineer to quickly study the stress con-

ditions that exist in the structure and, in the event the member reinforcing is not

adequate, aids the engineer in taking appropriate remedial measures, including

altering the design member without rerunning the entire analysis.

1.1 Organization

This manual is designed to help the user quickly become productive with the

concrete frame design options of NTC 2008. Chapter 2 provides detailed de-

scriptions of the Design Prerequisites used for NTC 2008. Chapter 3 provides

detailed descriptions of the code-specific process used for NTC 2008. Chapter 4

provides a detailed description of the algorithms related to seismic provisions in

the design/check of structures in accordance with § 7.4 of the NTC 2008. The

appendices provide details on certain topics referenced in this manual.

1.2 Recommended Reading/Practice

It is strongly recommended that you read this manual and review any applicable

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

www.csiamerica.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.

1 - 2 Organization

Chapter 2

Design Prerequisites

This chapter provides an overview of the basic assumptions, design precondi-

tions, 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 NTC 2008 design code and the seismic provisions in the

design/check of structures in accordance with § 7.4 of the NTC 2008.

2.1 Design Load Combinations

The design load combinations are used for determining the various combina-

tions 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 in-

teracting quantities is lost, the program automatically produces multiple sub

2 - 1

Concrete Frame Design NTC 2008

combinations using maxima/minima permutations of interacting quantities.

Separate combinations with negative factors for response spectrum cases are not

required because the program automatically takes the minima to be the negative

of the maxima for response spectrum cases and the previously described per-

mutations 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, or dynamic response spectrum earthquake load, the pro-

gram has built-in default loading combinations for each design code. These are

based on the code recommendations and are documented for each code in the

corresponding manual.

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

loads, separate consideration of roof live load, snow load, and so on, 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 static load cases declared as dead load

to be additive. Similarly, all cases declared as live load are assumed additive.

However, each static 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 appro-

priate design combinations.

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

them to be included or if no other user-defined combinations are available for

concrete design. If any default combination is included in design, 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

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

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

to 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, the effects

of those loads will be assumed to be zero in any combination that includes them.

2.2 Design and Check Stations

For 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 equally

spaced output stations along the clear length of the element. The number of

output stations in an element is requested by the user before the analysis is

performed. The user can refine the design along the length of an element by

requesting more output stations.

2.3 Identifying Beams and Columns

In 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 accomplished by specifying the frame section assigned to

the element to be of type beam or column. If any brace member exists in the

frame, the brace member also would be identified as a beam or a column ele-

ment, depending on the section assigned to the brace member.

2.4 Design of Beams

In the design of concrete beams, in general, the program calculates and reports

the required areas of reinforcing steel for flexure, shear, and torsion based on the

beam moments, shears, load combination factors, and other criteria, which are

described in detail in Chapters 3 and 4 (seismic). The reinforcement require-

ments are calculated at a user-defined number of stations along the beam span.

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

Effects resulting from any axial forces and minor direction bending that may

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

Design and Check Stations 2 - 3

Concrete Frame Design NTC 2008

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

station of a particular beam, the steps involve the determination of the maximum

factored 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 beam or a T-beam. For the design of

flexural reinforcement, the beam is first designed as a singly reinforced beam. If

the singly reinforced beam is not adequate, the required compression rein-

forcement is calculated.

In designing the shear reinforcement for a particular beam for a particular set of

loading combinations at a particular station because of 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 any

reinforcement steel required to carry the balance.

2.5 Design of Columns

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

steel, or if the longitudinal steel is specified, the column stress condition is

reported in terms of a column capacity ratio, which is a factor that gives an

indication of the load condition of the column with respect to the capacity of 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 dif-

ferent concrete section types in 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 col-

umn. This step is also used to calculate the required steel reinforcement (if

none was specified) that will produce a column capacity ratio of 1.0.

The generation of the interaction surface is based on the assumed strain and

stress distributions and 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

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 is

considered.

2.6 P-Delta Effects

The program design process requires that the analysis results include P-Delta

effects. For the individual member stability effects, the first order analysis

moments are increased with additional second order moments, as documented in

Chapter 3. As an alternative, the user can turn off the calculation of second order

moments for individual member stability effects. If this calculation is turned off,

the user should apply another method, such as equivalent lateral loading or

P-Delta analysis with vertical members divided into at least two segments, to

capture the member stability effects in addition to the global P-Delta effects.

Users of the program should be aware that the default analysis option is that

P-Delta effect are not included. The user can specify that P-Delta analysis be

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

number of iteration for P-Delta analysis is 1. Further details about P-Delta

analysis are provided in Appendix A of this design manual.

2.7 Element Unsupported Lengths

To account for column slenderness effects, 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 cor-

responds 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 accomplished differently for major and minor

bending, as documented in Appendix B.

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

element-by-element basis.

P-Delta Effects 2 - 5

Concrete Frame Design NTC 2008

2.8 Choice of Input Units

Imperial, as well as SI and MKS metric units can be used for input and output.

The codes are based on a specific system of units. The NTC 2008 design code is

published in Newton-millimeter-second units and all equations and descriptions

presented in the “Design Process” chapter correspond to these units. However,

any system of units can be used to define and design a structure in the program.

2 - 6 Choice of Input Units

Chapter 3

Design Process

This chapter provides a detailed description of the code-specific algorithms used

in the design of concrete frames when the NTC 2008 code has been selected. For

simplicity, all equations and descriptions presented in this chapter correspond to

Newton-millimeter-second units unless otherwise noted.

3.1 Notation

The various notations used in this chapter are described herein:

Area of concrete used to determine shear stress, mm2

Gross area of concrete, mm2

Area enclosed by centerlines of connecting walls for torsion, mm2

Area of tension reinforcement, mm2

′

Area of compression reinforcement, mm2

Area of longitudinal torsion reinforcement, mm2

Area of transverse torsion reinforcement (closed stirrups) per unit

length of the member, mm2/mm

3 - 1

Concrete Frame Design NTC 2008

Area of shear reinforcement per unit length of the member,

mm2/mm

Modulus of elasticity of concrete, MPa

Modulus of elasticity of reinforcement, assumed as 200 GPa

Moment of inertia of gross concrete section about centroidal axis,

neglecting reinforcement, mm4

Smaller factored end moment in a column, N-mm

Larger factored end moment in a column, N-mm

Design moment, including second order effects to be used in

design, N-mm

0Ed

Equivalent first order end moment (EC2 5.8.8.2), N-mm

Second order moment from the Nominal Curvature method (EC2

5.8.8), N-mm

First order factored moment at a section about the 2-axis, N-mm

First order factored moment at a section about the 3-axis, N-mm

Buckling load, N

Factored axial load at a section, N

Factored torsion at a section, N-mm

Factored shear force at a section, N

Rd,c

Design shear resistance without shear reinforcement, N

Rd,max

Shear force that can be carried without crushing of the notional

concrete compressive struts, N

Depth of compression block, mm

max

Maximum allowed depth of compression block, mm

Width of member, mm

Effective width of flange (T-beam section), mm

Width of web (T-beam section), mm

Distance from compression face to tension reinforcement, mm

3 - 2 Notation

Chapter 3 - Design Process

′

Concrete cover-to-center of reinforcing, mm

Thickness of slab/flange (T-beam section), mm

Deflection due to curvature for the Nominal Curvature method

(EC2 5.8.8), mm

Eccentricity to account for geometric imperfections (EC2 5.2),

min

Minimum eccentricity (EC2 6.1), mm

Design concrete compressive strength (EC 3.1.6), MPa

ctm

Mean value of axial tensile strength of concrete, MPa

Design yield strength of reinforcement (EC2 3.2), MPa

Overall depth of a column section, mm

Member effective length, mm

Member unsupported length, mm

Radius of gyration of column section, mm

Effective wall thickness for torsion, mm

Outer perimeter of cross-section, mm

Outer perimeter of area A

, mm

Depth to neutral axis, mm

Material coefficient taking account of long-term effects on the

compressive strength (EC2 3.1.6)

Material coefficient taking account of long-term effects on the

tensile strength (EC2 3.1.6)

lcc

Light-weight material coefficient taking account of long-term

effects on the compressive strength (EC2 11.3.5)

lct

Light-weight material coefficient taking account of long-term

effects on the tensile strength (EC2 11.3.5)

Strain in concrete

cu2

Ultimate strain allowed in extreme concrete fiber (0.0035

mm/mm)

Notation 3 - 3

Concrete Frame Design NTC 2008

Strain in reinforcing steel

Material partial factor for concrete (EC2 2.4.2.4)

Material partial factor for steel (EC2 2.4.2.4)

Factor defining effective height of concrete stress block (EC2

3.1.7)

Factor defining effective strength of concrete stress block (EC2

3.1.7)

Angle between concrete compression strut and member axis

perpendicular to the shear force

Inclination due to geometric imperfections (EC2 5.2), ratio

Basic inclination for geometric imperfections (EC2 5.2), ratio

3.2 Assumptions / Limitations

The following general assumptions and limitations exist for the current imple-

mentation of NTC 2008 within the program. Limitations related to specific parts

of the design are discussed in their relevant sections.

 Design of plain or lightly reinforced concrete sections is not handled.

 Design of prestressed or post-tensioned sections currently is not handled.

 The serviceability limit state currently is not handled.

 Design for fire resistance currently is not handled.

 By default, the Persistent & Transient design situation (

=1.5

and

=1.15

) is considered. Other design situations can be considered and

may require modification of some of the concrete design preference values.

 It is assumed that the structure being designed is a building type structure.

Special design requirements for special structure types (such as bridges,

pressure vessels, offshore platforms, liquid-retaining structures, and the

like) currently are not handled.

 It is assumed that the load actions are based on NTC 2008.

3 - 4 Assumptions / Limitations

Chapter 3 - Design Process

 The program works with cylinder strength as opposed to cube strength.

 The program does not check depth-to-width ratios (EC2 5.3.1) or effective

flange widths for T-beams (EC2 5.3.2). The user needs to consider these

items when defining the sections.

 It is assumed that the user will consider the maximum concrete strength

limit, Cmax, specified in the design code (NTC Tab. 4.1.I).

 It is assumed that the cover distances input by the user satisfy the minimum

cover requirements (NTC § 4.1.6.1.3).

 The design value of the modulus of elasticity of steel reinforcement, Es, is

assumed to be 200 GPa.

3.3 Design Load Combinations

The design load combinations are the various combinations of the prescribed

load cases for which the structure is to be checked. The program creates a

number of default design load combinations for a concrete frame design. Users

can add their own design load combinations as well as modify or delete the

program default design load combinations. An unlimited number of design load

combinations can be specified.

To define a design load combination, simply specify one or more load patterns,

each with its own scale factor. The scale factors are applied to the forces and

moments from the load cases to form the design forces and moments for each

design load combination. There is one exception to the preceding. For spectral

analysis modal combinations, any correspondence between the signs of the

moments and axial loads is lost. The program uses eight design load combina-

tions for each such loading combination specified, reversing the sign of axial

loads and moments in major and minor directions.

As an example, if a structure is subjected to dead load, D, and live load, L, only,

the NTC 2008 design check would require two design load combinations only.

However, if the structure is subjected to wind, earthquake, or other loads, nu-

merous additional design load combinations may be required.

Design Load Combinations 3 - 5

Concrete Frame Design NTC 2008

The program allows live load reduction factors to be applied to the member

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

the contribution of the live load to the factored responses.

The design load combinations are the various combinations of the load cases for

which the structure needs to be checked. NTC 2008 allows strength load com-

binations to be defined based on NTC 2008 Eq. 2.5.1:

γ +γ +γ +γ + γ ψ

∑

11 22 1 1 0

G G P Q k Qi i ki

G GPQ Q

(NTC Eq. 2.5.1)

Load combinations considering seismic loading are automatically generated

based on NTC 2008 Eq. 2.5.5:

≥

+ +++ ψ

∑

12 2

i ki

G G PE Q

(NTC Eq. 2.5.5)

The symbols used in the previous equations refer to:

G1 self weight of the structural members

G2 self weight of the non-structural members

P pre-post tension

Qi live loads

E seismic action

The variable values and factors used in the load combinations are defined as:

γG1,sup = 1.30 (NTC Tab. 2.6.I)

γG1,inf = 1.00 (NTC Tab. 2.6.I)

γG2,sup = 1.50 (NTC Tab. 2.6.I)

γG2,inf = 0.00 (NTC Tab. 2.6.I)

γQ,1,sup = 1.50 (NTC Tab. 2.6.I)

γQ,1,inf = 0.00 (NTC Tab. 2.6.I)

3 - 6 Design Load Combinations

Chapter 3 - Design Process

0.7 (live load, not storage)

0.6 (wind load)



ψ=





(NTC Tab. 2.5.I)

ψ2,i = 0.3 (assumed office/residential) (NTC Tab. 2.5.I)

The user should apply other appropriate design load combinations if roof live

load is separately treated, or if other types of loads are present. PLL is the live

load multiplied by the Pattern Live Load Factor. The Pattern Live Load Factor

can be specified in the Preferences.

When using the NTC 2008 design code, the program design assumes that a

P-Delta analysis has been performed.

3.4 Column Design

The program can be used to check column capacity or to design columns. If the

geometry of the reinforcing bar configuration of the concrete column section has

been defined, the program can check the column capacity. Alternatively, the

program can calculate the amount of reinforcing required to design the column

based on a provided reinforcing bar configuration. The reinforcement require-

ments are calculated or checked at a user-defined number of output stations

along the column height. The design procedure for reinforced concrete columns

involves the following steps:

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

ferent concrete section types of the model. A typical biaxial interaction di-

agram is shown in Figure 3-1. For reinforcement to be designed, the

program generates the interaction surfaces for the range of allowable rein-

forcement from a minimum of 0.2 percent to a maximum of 4 percent (NTC

§ 7.4.6.2.2).

 Calculate the capacity ratio or the required reinforcement area for the fac-

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

each load combination at each output station of the column. The target ca-

pacity ratio is taken as the Utilization Factor Limit when calculating the

required reinforcing area.

 Design the column shear reinforcement.

Column Design 3 - 7

Concrete Frame Design NTC 2008

The following subsections describe in detail the algorithms associated with this

process.

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. A typical interaction

surface is shown in Figure 3-1.

Figure 3-1 A typical column interaction surface

The coordinates of the points on the failure surface are determined by rotating a

plane of linear strain in three dimensions on the column section, as shown in

Figure 3-2. The linear strain diagram limits the maximum concrete strain, εcu, at

the extremity of the section to 0.0035 (NTC § 4.1.2.1.2.2).

3 - 8 Column Design

Chapter 3 - Design Process

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

The formulation is based consistently upon the general principles of ultimate

strength design (NTC § 4.1.2.1.2.1).

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, fyd (NTC

§ 4.1.2.1.2.3). 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

Column Design 3 - 9

Concrete Frame Design NTC 2008

assume any further simplifications with respect to distributing the area of steel

over the cross-section of the column, as shown in Figure 3-2.

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

effective strength of:

cd cc

f= α γ

50 /≤

f N mm

0.85

α=

1.5

γ=

50 N/mm

(NTC 2008), refer to Eurocode 2:

=αη

cd cc

η = 1.0 – (fck – 50)/200 for 50 < fck ≤ 90 MPa (EC2 Eq. 3.22)

The concrete compression stress block is assumed to have an effective height of

βx, as shown in Figure 3-3, where β = 0.8.

Concrete Section Strain Diagram Stress Diagram

′

ε3

fη

ε1

ε2

ε3

ε4

ax= β

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

3 - 10 Column Design

Chapter 3 - Design Process

The interaction algorithm provides correction to account for the concrete area

that is displaced by the reinforcement in the compression zone. The depth of the

equivalent rectangular block is further referred to as a, such that:

a = βx (NTC § 4.1.2.1.2.4)

where x is the depth of the stress block in compression, as shown in Figure 3-3.

The effect of the material partial factors, γc and γs , and the material coefficient,

αcc, are included in the generation of the interaction surface (NTC § 4.1.2).

Default values for γc, γs, and αcc are provided by the program but can be over-

written using the Preferences.

3.4.2 Calculate Column Capacity Ratio

The column capacity ratio is calculated for each design 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 design load combina-

tion, at a particular location:

 Determine the factored first order moments and forces from the analysis cases

and the specified load combination factors to give Ned, M22, and M33.

 Determine the second order moment based on the chosen Second Order

Method, using the Preferences. The available options are “Nominal

Curvature” (NTC 2008 § 4.1.2.1.7.3 and EC2 5.8.8) or “None,” if the user

wants to explicitly ignore second order effects within the design calculations.

This last option may be desirable if the second order effects have been

simulated with equivalent loads or if a P-Delta analysis has been undertaken

and each column member is divided into at least two elements, such that M22

and M33 already account for the second order effects.

 Add the second order moments to the first order moments if the column is

determined to be slender (NTC 2008 § 4.1.2.1.7.3). A column is considered to

be slender if:

lim 15.4

λλ ν

>= C

Column Design 3 - 11

Concrete Frame Design NTC 2008

where

is the buckling length in the considered direction

is the radius of gyration relative to the uncracked section in the

considered direction

1.7

= − m

and is a parameter that depends on the distribution of

bending moments along the element (

0.7 2.7≤≤C

and is the ratio of the first order end moments, with

01 02 .MM≤

c cd

and is the dimensional axial force.

 Determine whether the point, defined by the resulting axial load and biaxial

moment set, lies within the interaction volume.

The following subsections describe in detail the algorithms associated with this

process.

3.4.2.1 Determine Factored Moments and Forces

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

corresponding factors to all of the analysis cases, giving NEd, M22, and M33.

These first order factored moments are further increased to account for geo-

metric imperfections (NTC § 4.1.2.1.2.4 e § 4.1.2.1.7.3). The eccentricity to

account for geometric imperfections, ei, is defined as:

( )

max 0.05 ;20mm; / 300

e hH=

where h is the height of the section and H is the height of the column.

The resulting first order moments, including geometric imperfections, are cal-

culated as:

3 - 12 Column Design

Chapter 3 - Design Process

M22 = M22 + ei2 NEd

M33 = M33 + ei3 NEd

The moment generated because of the geometric imperfection eccentricity, or

the min eccentricity if greater, is considered only in a single direction at a time.

3.4.2.2 Second Order Moments

The global incidence of the second order effects must be evaluated by the user in

accordance with NTC § 4.1.1.4.

If the global second order effects are relevant, the moments M22 and M33 must be

obtained from a second order elastic (P-∆) analysis or by applying fictitious,

magnified horizontal forces following the recommendations of Eurocode 2

Annex H. For more information about P-∆ analysis, refer to Appendix A.

In addition, if the column is slender (NTC 2008 § 4.1.2.1.7.3), the computed

moments are further increased for individual column stability effects (NTC 2008

§ 4.1.2.1.7.3) by computing a moment magnification factor based on the

“Nominal Curvature method” (NTC 2008 § 4.1.2.1.7.3 and EC2 5.8.8).

The user can manually specify to exclude the calculation of the second order

moment if a P-Δ analysis has been performed and if the elements have been

divided into, at least, two segments (see Appendix A of this manual).

3.4.2.2.1 Nominal Curvature Method

The overall design moment, MEd, based on the Nominal Curvature method is

computed as specified in Eurocode 2:

MEd = M0Ed + M2 (EC2 Eq. 5.31)

where M0Ed is defined as:

M0Ed = 0.6 M02 + 0.4 M01 ≥ 0.4 M02 (EC2 Eq. 5.32)

M02 and M01 are the moments at the ends of the column, and M02 is numerically

larger than M01.

01 02

is positive for single curvature bending and negative

for double curvature bending. The preceding expression of M0Ed is valid if no

transverse load is applied between the supports.

Column Design 3 - 13

Concrete Frame Design NTC 2008

The additional second order moment associated with the major or minor direc-

tion of the column is defined as:

M2 = NEd e2, (EC2 Eq. 5.33)

where NEd is the design axial force, and e2, the deflection due to the curvature, is

defined as:

( )

e rl c=

(EC2 5.8.8.2(3))

The effective length, lo, is taken equal to β

l lu. The factor c depends on the cur-

vature distribution and is taken equal to 8, corresponding to a constant first order

moment. The term

is the curvature and is defined as:

lr K K r

(EC2 Eq. 5.34)

The correction factor, Kr, depends on the axial load and is taken as 1 by default.

The factor Kφ is also taken as 1, which represents the situation of negligible

creep. Both of these factors can be overwritten on a member-by-member basis.

The term

is defined as:

( )

1 0 45

r . d.= ε

(EC2 5.8.8.3(1))

The preceding second order moment calculations are performed for major and

minor directions separately.

3.4.2.3 Determine Capacity Ratio

As a measure of the load condition of the column, a capacity ratio is calculated.

The capacity ratio is a factor that gives an indication of the load condition of the

column with respect to the load capacity of the column.

Before entering the interaction diagram to check the column capacity, the sec-

ond order moments are added to the first order factored loads to obtain NEd, MEd2,

and MEd3. The point (NEd, MEd2, MEd3) 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 capacity is adequate. However, if the point lies outside the interac-

tion volume, the column is overloaded.

3 - 14 Column Design

Chapter 3 - Design Process

Figure 3-4 Geometric representation of column capacity ratio

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

cation of point C. 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, as shown in Figure 3-4. The capacity ratio, CR, is given by the ratio

OL OC .

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

column is loaded to capacity.

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

the column capacity is adequate.

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

the column is overloaded.

Column Design 3 - 15

Concrete Frame Design NTC 2008

The maximum of all the values of CR calculated from each design load com-

bination is reported for each check station of the column, along with the con-

trolling NEd, MEd2, and MEd3 set and associated design load combination name.

3.4.3 Design Longitudinal Reinforcement

If the user has specified that a column is to be designed, the program computes

the required reinforcement that will give a column capacity ratio equal to the

Utilization Factor Limit, which is set to 0.95 by default.

3.4.4 Design Column Shear Reinforcement

The shear reinforcement is designed for each design 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 design

load combination resulting from shear forces in a particular direction:

 Determine the design forces acting on the section, NEd and VEd. Note that NEd

is needed for the calculation of VRcd.

 Determine the maximum design shear force that can be carried without

crushing of the notional concrete compressive struts, VRcd.

 Determine the required shear reinforcement as area per unit length,

A s.

The following subsections describe in detail the algorithms associated with this

process.

3.4.4.1 Determine Design Shear Force

In the design of the column shear reinforcement of concrete frames, the forces

for a particular design load combination, namely, the column axial force, NEd,

and the column shear force, VEd, in a particular direction are obtained by fac-

toring the load cases with the corresponding design load combination factors.

3 - 16 Column Design

Chapter 3 - Design Process

3.4.4.2 Determine Design Shear Resistance

To prevent crushing of the concrete compression struts, the design shear force

VEd is limited by the maximum sustainable design shear force, VRcd. If the design

shear force exceeds this limit, a failure condition occurs. The maximum sus-

tainable shear force is defined as:

cot cot

0.9 1 cot

Rcd w c cd

V db f α+ ϑ

= ⋅ ⋅ ⋅α ⋅ +ϑ

(NTC Eq. 4.1.19)

= 1 for members not subjected to axial compression

= +

for

0 0.25

≤≤

cp cd

1.25=

for

0.25 0.5

≤≤

cd cp cd

2.5 1



= +





for

0.5

≤≤

cd cp cd

0.5=

cd cd

angle between the shear reinforcement and the column axis. In the case of

vertical stirrups,

degrees.

angle between the concrete compression struts and the column axis. NTC

2008 allows θ to be taken between 21.8 and 45 degrees. The program

assumes the conservative value of 45 degrees.

Column Design 3 - 17

Concrete Frame Design NTC 2008

RECTANGULAR

SQUARE WITH CIRCULAR REBAR

CIRCULAR

DIRECTION

OF SHEAR

FORCE

DIRECTION

OF SHEAR

FORCE

DIRECTION

OF SHEAR

FORCE

RECTANGULAR

SQUARE WITH CIRCULAR REBAR

Acv

CIRCULAR

DIRECTION

OF SHEAR

FORCE

DIRECTION

OF SHEAR

FORCE

DIRECTION

OF SHEAR

FORCE

DIRECTION

OF SHEAR

FORCE

DIRECTION

OF SHEAR

FORCE

DIRECTION

OF SHEAR

FORCE

RECTANGULAR

SQUARE WITH CIRCULAR REBAR

CIRCULAR

DIRECTION

OF SHEAR

FORCE

DIRECTION

OF SHEAR

FORCE

DIRECTION

OF SHEAR

FORCE

RECTANGULAR

SQUARE WITH CIRCULAR REBAR

Acv

CIRCULAR

DIRECTION

OF SHEAR

FORCE

DIRECTION

OF SHEAR

FORCE

DIRECTION

OF SHEAR

FORCE

DIRECTION

OF SHEAR

FORCE

DIRECTION

OF SHEAR

FORCE

DIRECTION

OF SHEAR

FORCE

Figure 3-6 Shear stress area, Ac

3.4.4.3 Determine Required Shear Reinforcement

If VEd is less than VRcd, the required shear reinforcement in the form of stirrups or

ties per unit spacing,

A s,

is calculated as:

( )

0.9 cot cot sin

sw Ed

ywd

s df

= ⋅

⋅ α+ ϑ α

(NTC Eq. 4.1.18)

with

90α=

degrees.

In the preceding expressions, for a rectangular section, b is the width of the

column, d is the effective depth of the column, and Ac is the effective shear area,

which is equal to bd. For a circular section, b is replaced with D, which is the

3 - 18 Column Design

Chapter 3 - Design Process

external diameter of the column, d is replaced with 0.8D, and Ac is replaced with

the gross area

The maximum of all of the calculated

values, obtained from each design

load combination, is reported for the major and minor directions of the column,

along with the controlling combination name.

The column shear reinforce ment requirements reported by the program are

based solely on shear strength consideration. Any minimum stirrup requirements

to satisfy spacing considerations or transverse reinforcement volumetric con-

siderations must be investigated independently by the user.

3.5 Beam Design

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, shear forces,

torsions, design load combination factors, and other criteria described in the text

that follows. The reinforcement requirements are calculated at a user-defined

number of output stations along the beam span.

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

Effects resulting from any axial forces and minor direction bending that may

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

The beam design procedure involves the following steps:

 Design flexural reinforcement

 Design shear reinforcement

 Design torsion reinforcement

3.5.1 Design Beam Flexural Reinforcement

The beam top and bottom flexural reinforcement is designed at output stations

along the beam span. The following steps are involved in designing the flexural

reinforcement for the major moment for a particular beam, at a particular sec-

tion:

 Determine the maximum factored moments

Beam Design 3 - 19

Concrete Frame Design NTC 2008

 Determine the required reinforcing steel

3.5.1.1 Determine Factored Moments

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

for each design load combination at a particular beam section are obtained by

factoring the corresponding moments for different load cases with the corre-

sponding design load combination factors.

The beam section is then designed for the factored moments obtained from each

of the design load combinations. Positive moments produce bottom steel. In

such cases, the beam may be designed as a rectangular or a T-beam section.

Negative moments produce top steel. In such cases, the beam is always designed

as a rectangular section.

3.5.1.2 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 can avoid the need for compression rein-

forcement by increasing the effective depth, the width, or the grade of concrete.

The design procedure is based on a simplified rectangular stress block, as shown

in Figure 3-7 (NTC Fig. 4.1.3). When the applied moment exceeds the moment

capacity, the area of compression reinforcement is calculated on the assumption

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 (T-beams) is summarized in the following subsections. It is assumed

that the design ultimate axial force is negligible, hence all beams are designed

ignoring axial force.

3 - 20 Beam Design

Chapter 3 - Design Process

Beam Section Strain Diagram Stress Diagram

A′

f′

Beam Section Strain Diagram Stress Diagram

3cu

A′

f′

Figure 3-7 Rectangular beam design

In designing for a factored negative or positive moment, MEd (i.e., designing top

or bottom steel), the effective strength and depth of the compression block are

given by αccfcd and βx (see Figure 3-7) respectively, where:

β = 0.8 (NTC § 4.1.2.1.2.2)

αcc = 0.85 (NTC § 4.1.2.1.2.2)

cd cc

f= α γ

50N/mm

f≤

0.85

α=

1.5

γ=

50N/mm

(NTC 2008), refer to Eurocode 2:

cd cc

f=αη

η = 1.0 – (fck – 50)/200 for 50 < fck ≤ 90 MPa (EC2 Eq. 3.22)

x0=βx

Beam Design 3 - 21

Concrete Frame Design NTC 2008

For the design of the beams a ductility criterion, suggested in Eurocode 2 § 5.5,

is followed.

The limiting value of the ratio of the neutral axis depth at the ultimate limit state

to the effective depth, (x/d)lim, is expressed as a function of the ratio of the re-

distributed moment to the moment before redistribution, δ, as follows:

( )

lim

xd k k= δ−

for fck ≤ 50 MPa (EC2 Eq. 5.10a)

( )

lim

xd k k= δ−

for fck > 50 MPa (EC2 Eq. 5.10b)

No redistribution is assumed, such that δ is assumed to be 1. The four factors, k1,

k2, k3, and k4 [NDPs], are defined as:

k1 = 0.44 (EC2 5.5(4))

( )

21.25 0.6 0.0014 cu

k= +ε

(EC2 5.5(4))

k3 = 0.54 (EC2 5.5(4))

( )

41.25 0.6 0.0014 cu

k= +ε

(EC2 5.5(4))

where the ultimate strain, εcu2 [NDP], is determined from Eurocode 2 Table 3.1

as:

εcu2 = 0.0035 for fck < 50 MPa (NTC § 4.1.2.1.2.2)

εcu2 = 2.6 + 35

( )

90 100



−



for fck ≥ 50 MPa (NTC § 4.1.2.1.2.2)

3.5.1.2.1 Rectangular Beam Flexural Reinforcement

For rectangular beams, the normalized moment, m, and the normalized section

capacity as a singly reinforced beam, mlim, are determined as:

mbd f

lim

lim lim

mdd



 

=β−



 

 



3 - 22 Beam Design

Chapter 3 - Design Process

The reinforcing steel area is determined based on whether m is greater than, less

than, or equal to mlim.

 If m

≤

mlim, a singly reinforced beam will be adequate. Calculate the nor-

malized steel ratio, ω, and the required area of tension reinforcement, As, as:

ω = 1−

m21−

As = ω







f bd

This area of reinforcing steel is to be placed at the bottom if MEd is positive, or

at the top if MEd is negative.

 If m > mlim, compression reinforcement is required. Calculate the normalized

steel ratios, ω', ωlim, and ω, as:

ωlim = β

lim







= 1 −

lim

m−

ω' =

−

′

−

lim

ω = ωlim + ω'

where d' is the depth to the compression steel, measured from the concrete

compression face.

Calculate the required area of compression and tension reinforcement, As' and

As, as:

As' = ω'





′





f bd

As = ω







f bd

where

f′

the stress in the compression steel, is calculated as:

Beam Design 3 - 23

Concrete Frame Design NTC 2008

′

= Es εc

′



−





lim

≤ fyd

As is to be placed at the bottom and As' is to be placed at the top if MEd is pos-

itive, and As' is to be placed at the bottom and As is to be placed at the top if MEd

is negative.

3.5.1.2.2 T-Beam Flexural Reinforcement

In designing a T-beam, a simplified stress block, as shown in Figure 3-8, is

assumed if the flange is in compression, i.e., if the moment is positive. If the

moment is negative, the flange is in tension, and therefore ignored. In that case, a

simplified stress block, similar to that shown in Figure 3-8, is assumed on the

compression side.

Cax

f′

3cu

A′

Beam Section Strain Diagram Stress Diagram

Cax

f′

3cu

A′

Beam Section Strain Diagram Stress Diagram

Figure 3-8 T-beam design

Flanged Beam Under Negative Moment

In designing for a factored negative moment, MEd (i.e., designing top steel), the

calculation of the reinforcing steel area is exactly the same as described for a

rectangular beam, i.e., no specific T-beam data is used.

=β

3 - 24 Beam Design

Chapter 3 - Design Process

Flanged Beam Under Positive Moment

In designing for a factored positive moment, MEd, the program analyzes the

section by considering the depth of the stress block. If the depth of the stress

block is less than or equal to the flange thickness, the section is designed as a

rectangular beam with a width bf. If the stress block extends into the web, addi-

tional calculation is required.

For T-beams, the normalized moment, m, and the normalized section capacity as

a singly reinforced beam, mlim, are calculated as:

f cd

mbd f

lim lim lim

mdd



 

=β−



 

 



Calculate the normalized steel ratios ωlim and ω, as:

ωlim =β

lim







ω = 1 −

m21−

Calculate the maximum depth of the concrete compression block, xmax, and the

effective depth of the compression block, x, as:

xmax = ωlim d

x = ωd

The reinforcing steel area is determined based on whether m is greater than, less

than, or equal to mlim.

 If x ≤ hf , the subsequent calculations for As are exactly the same as previ-

ously defined for rectangular beam design. However, in this case, the width

of the beam is taken as bf , as shown in Figure 3-8. Compression rein-

forcement is required if m > mlim.

Beam Design 3 - 25

Concrete Frame Design NTC 2008

 If x > hf , the calculation for As has two parts. The first part is for balancing

the compressive force from the flange, and the second part is for balancing

the compressive force from the web, as shown in Figure 3-8.

 The required reinforcing steel area, As2, and corresponding resistive mo-

ment, M2, for equilibrating compression in the flange outstands are calcu-

lated as:

()

−

f w f cd

b b hf











−= 2

yds

dfAM

Now calculate the required reinforcing steel area As1 for the rectangular

section of width bw to resist the remaining moment M1 = MEd – M2. The

normalized moment, m1 is calculated as:

w cd

mbd f

The reinforcing steel area is determined based on whether m1 is greater than,

less than, or equal to mlim.

 If m1

≤

mlim, a singly reinforced beam will be adequate. Calculate the

normalized steel ratio, ω

, and the required area of tension rein-

forcement, As1, as:

ω1 = 1−

m21−

As1 = ω1







f bd

 If m1 > mlim, compression reinforcement is required. Calculate the

normalized steel ratios, ω', ωlim, and ω, as:

ωlim = β

lim













3 - 26 Beam Design

Chapter 3 - Design Process

ω′ =

−

′

−

lim

ω1 = ωlim + ω′

where d' is the depth to the compression steel, measured from the

concrete compression face.

Calculate the required area of compression and tension reinforcement,

As′ and As, as:

As′ = ω'





′





f bd

As1 = ω1







f bd

where fs′, the stress in the compression steel, is calculated as:

′

= Esεc

lim

′



−





≤ fyd

The total tensile reinforcement is As = As1 + As2, and the total compression

reinforcement is As′. As is to be placed at the bottom and As′ is to be placed at

the top of the section.

3.5.1.3 Minimum and Maximum Tensile Reinforcement

The minimum flexural tensile steel reinforcement, As,min, required in a beam

section is given as the maximum of the following two values:

As,min = 0.26

( )

ctm yk

bt d (NTC Eq. 4.1.43)

As,min = 0.0013bt d (NTC Eq. 4.1.43)

where bt is the mean width of the tension zone, equal to the web width for

T-beams, and fctm is the mean value of axial tensile strength of the concrete,

calculated as:

Beam Design 3 - 27

Concrete Frame Design NTC 2008

fctm = 0.30fck(2/3) for fck

≤

50 MPa (NTC Eq. 11.2.3a)

fctm = 2.12 ln

( )

1 10

for fck > 50 MPa (NTC Eq. 11.2.3b)

fcm = fck + 8 MPa (NTC Eq. 11.2.2)

The maximum flexural steel reinforcement, As,max, permitted as either tension or

compression reinforcement is defined as:

As,max = 0.04Ac (NTC § 4.1.6.1.1)

where Ac is the gross cross-sectional area.

3.5.2 Design Beam Shear Reinforcement

The required beam shear reinforcement is calculated for each design load com-

bination at each output station along the beam length. The following assump-

tions are made for the design of beam shear reinforcement:

 The beam section is assumed to be prismatic. The shear capacity is based on

the beam width at the output station and therefore a variation in the width of

the beam is neglected in the calculation of the concrete shear capacity at

each particular output station.

 All shear reinforcement is assumed to be perpendicular to the longitudinal

reinforcement. Inclined shear steel is not handled.

The following steps are involved in designing the shear reinforcing for a par-

ticular beam, for a particular design load combination resulting from shear

forces in a particular direction:

 Determine the design forces acting on the section, NEd and VEd. Note that NEd

is needed for the calculation of VRcd.

 Determine the maximum design shear force that can be carried without

crushing of the notional concrete compressive struts, VRcd.

 Determine the required shear reinforcement as area per unit length,

A s.

The following subsections describe in detail the algorithms associated with this

process.

3 - 28 Beam Design

Chapter 3 - Design Process

3.5.2.1 Determine Design Shear Force

In the design of the beam shear reinforcement, the shear forces and moments for

a particular design load combination at a particular beam section are obtained by

factoring the associated shear forces and moments with the corresponding

design load combination factors.

3.5.2.2 Determine Maximum Design Shear Force

To prevent crushing of the concrete compression struts, the design shear force

VEd is limited by the maximum sustainable design shear force, VRcd. If the design

shear force exceeds this limit, a failure condition occurs. The maximum sus-

tainable shear force is defined as:

cot cot

0.9 1 cot

Rcd w c cd

V db f α+ ϑ

= ⋅ ⋅ ⋅α ⋅ +ϑ

(NTC Eq. 4.1.19)

= 1 for members not subjected to axial compression

= +

for

0 0.25

≤≤

cp cd

1.25=

for

0.25 0.5

≤≤

cd cp cd

2.5 1



= +





for

0.5

≤≤

cd cp cd

f′

0.5

angle between the shear reinforcement and the column axis. In the case of

vertical stirrups

90α=

degrees

angle between the concrete compression struts and the beam axis. NTC

2008 allows θ to be taken between 21.8 and 45 degrees.

If torsion is significant, i.e., TEd > Tcr where Tcr is defined as:

1Ed

cr Rd c Rd c

TT V



= −





(EC2 Eq. 6.31)

Beam Design 3 - 29

Concrete Frame Design NTC 2008

and if the load combination includes seismic, the value of θ is taken as 45°.

However, for other cases, θ is optimized using the following relationship:

( )

cot tan 0.9

cw cd Ed

vf vθ+ θ = α

where

21.8 45 .°≤θ≤ °

3.5.2.3 Determine Required Shear Reinforcement

If VEd is less than VRcd, the required shear reinforcement in the form of stirrups or

ties per unit spacing,

A s,

is calculated as:

( )

0.9 cot cot sin

sw Ed

ywd

s df

= ⋅

⋅ α+ ϑ α

(NTC Eq. 4.1.18)

with

90α=

degrees and ϑ as given in the previous section.

The maximum of all of the calculated

values, obtained from each design

load combination, is reported for the major and minor directions of the beam,

along with the controlling combination name.

The calculated shear reinforcement must be greater than the minimum rein-

forcement:

,min

1.5

Ab= ⋅

with b in millimeters and Asw,min in m/mm2.

The beam 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 consid-

erations must be investigated independently by the user.

3.5.3 Design Beam Torsion Reinforcement

The torsion reinforcement is designed for each design load combination at a

user-defined number of output stations along the beam span. The following steps

3 - 30 Beam Design

Chapter 3 - Design Process

are involved in designing the longitudinal and shear reinforcement for a partic-

ular station due to beam torsion:

 Determine the factored torsion, TEd.

 Determine torsion section properties.

 Determine the reinforcement steel required.

3.5.3.1 Determine Factored Torsion

In the design of torsion reinforcement of any beam, the factored torsions for each

design load combination at a particular design station are obtained by factoring

the corresponding torsion for different load cases with the corresponding design

load combination factors.

3.5.3.2 Determine Torsion Section Properties

For torsion design, special torsion section properties, including A, t, u, and um are

calculated. These properties are described as follows (NTC § 4.1.2.1.4).

A = area enclosed by centerlines of the connecting walls, where the

centerline is located a distance of

from the outer surface

t =

= effective wall thickness

Ac = area of the section

u = outer perimeter of the cross-section

um = perimeter of the area A

For torsion design of T-beam sections, it is assumed that placing torsion rein-

forcement in the flange area is inefficient. With this assumption, the flange is

ignored for torsion reinforcement calculation. However, the flange is considered

during calculation of the torsion section properties.

With this assumption, the special properties for a Rectangular beam section are

given as follows:

Ac = bh

A = (b – t)(h – t)

Beam Design 3 - 31

Concrete Frame Design NTC 2008

u = 2b + 2h

um = 2(b – t) + 2(h – t)

where, the section dimensions b, h, and t are shown in Figure 3-9. Similarly, the

special section properties for a T-beam section are given as follows:

Ac =

( )

+−

w f ws

bh b b d

A = (bf – t)(h – t)

u = 2bf + 2h

um = 2(bf – t) + 2(h – t)

where the section dimensions bf, bw, h, and ds for a T-beam are shown in

Figure 3-9.

2−

cb 2−

Closed Stirrup in

Rectangular Beam Closed Stirrup in

T-Beam Section

ch 2−h

ch 2−

2−

cb 2−

Closed Stirrup in

Rectangular Beam Closed Stirrup in

T-Beam Section

ch 2−h

ch 2−

Figure 3-9 Closed stirrup and section dimensions for torsion design

3.5.3.3 Determine Torsion Reinforcement

It is assumed that the torsional resistance is provided by closed stirrups, longi-

tudinal bars, and compression diagonals.

The ultimate resistance of compression diagonals is:

3 - 32 Beam Design

Chapter 3 - Design Process

cot

21 cot

Rcd cd

T At f ϑ

′

= ⋅ ⋅⋅ ⋅+ϑ

(NTC Eq. 4.1.27)

0.5

cd cd

′=

is the angle of the compression diagonals, as previously defined for

beam shear. The code allows any value between 21.8° and 68.2° (NTC Eq.

4.1.30), while the program assumes the conservative value of 45°.

An upper limit of the combination of VEd and TEd that can be carried by the sec-

tion without exceeding the capacity of the concrete struts is checked using the

following equation.

1.0

Ed Ed

Rcd Rcd

+≤

(NTC Eq. 4.1.32)

If the combination of VEd and TEd exceeds this limit, a failure message is de-

clared. In that case, the concrete section should be increased in size.

The ultimate resistance of the closed stirrups is:

2 cot

Rsd yd

T Af

=⋅⋅ ⋅ ⋅ ϑ

(NTC Eq. 4.1.28)

= stirrups’ area.

By reversing the equation 4.1.28 and imposing

Ed Rsd

it is possible to cal-

culate the necessary steel area.

Finally the resistance of longitudinal bars is:

2cot

Rld m

=⋅⋅ ⋅ ϑ

∑

(NTC Eq. 4.1.28)

∑

area of the total longitudinal bars

By reversing the equation 4.1.28 and imposing

Ed Rsd

it is possible to cal-

culate the necessary steel area.

Beam Design 3 - 33

Concrete Frame Design NTC 2008

The maximum of all the calculated A1 and

values obtained from each

design load combination is reported along with the controlling combination

names.

The beam torsion reinforcement requirements reported by the program are based

solely on strength considerations. Any minimum stirrup requirements and

longitudinal rebar requirements to satisfy spacing considerations must be

investigated independently of the program by the user.

3 - 34 Beam Design

Chapter 4

Seismic Provisions

This chapter provides a detailed description of the algorithms related to seismic

provisions in the design/check of structures in accordance with the "NTC 2008

– Norme Tecniche per le Costruzioni."

4.1 Notations

The following notations are used in this chapter.

Ash

Total area of horizontal hoops in a beam-column joint, mm

Asv,i

Total area of column vertical bars between corner bars in one direc-

tion through a joint, mm2

ΣM

Sum of design values of moments of resistance of the beams fram-

ing into a joint in the direction of interest, N-mm

MRc

Sum of design values of the moments of resistance of the columns

framing into a joint in the direction of interest, N-mm

4 - 1

Concrete Frame Design NTC 2008

i,d

End moment of a beam or column for the calculation of its capacity

design shear, N-mm

Rb,i

Design value of beam moment of resistance at end i, N-mm

Rc,i

Design value of column moment of resistance at end i, N-mm

Ed,max

Maximum acting shear force at the end section of a beam from

capacity design calculation, N

VEd,min

Minimum acting shear force at the end section of a beam from

capacity design calculation, N

Cross-section depth, mm

Cross-sectional depth of the column in the direction of interest, mm

hjc

Distance between extreme layers of the column reinforcement in a

beam-column joint, mm

Distance between beam top and bottom reinforcement, mm

Clear length of a beam or a column, mm

Basic value of the behavior factor

Prevailing aspect ratio of the walls of the structural design

Multiplier of the horizontal design seismic action at formation of

the first plastic hinge in the system

αu

Multiplier of the horizontal seismic design action at formation of

the global plastic mechanism

Model uncertainty factor on the design value of resistance in the

estimation of the capacity design action effects, accounting for var-

ious sources of overstrength

Ratio,

min maxEd , Ed,

, between the minimum and maximum acting

shear forces at the end section of a beam

Curvature ductility factor

4 - 2 Notations

Chapter 4 - Seismic Provisions

Displacement ductility factor

Tension reinforcement ratio

4.2 Design Preferences

The concrete frame design Preferences are basic assignments that apply to all

of the concrete frame members. The following steel frame design Preferences

are relevant to the special seismic provisions.

 Framing Type

 Ignore Seismic Code?

4.3 Overwrites

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

those elements to which they are assigned. The following concrete frame de-

sign overwrite is relevant to the special seismic provisions.

 Frame Type

4.4 Supported Framing Types

The code (NTC 2008) now recognizes the following types of framing systems

(NTC 2008 § 7.4.3.1). With regard to these framing types, the program has im-

plemented specifications for the types of framing systems listed.

Framing Type References

DCH MRF (Ductility Class High – Moment-Resisting Frame) NTC § 7.4.4

DCL MRF (Ductility Class Low – Moment-Resisting Frame) NTC § 7.4.4

Secondary

The program default frame type is Ductility Class High – Moment-Resisting

Frame (DCH MRF). However, that default can be changed in the Preference

for all frames or in the Overwrites on a member-by-member basis. If a frame

type Preference is revised in an existing model, the revised frame type does not

Design Preferences 4 - 3

Concrete Frame Design NTC 2008

apply to frames that have already been assigned a frame type through the

Overwrites; the revised Preference applies only to new frame members added

to the model after the Preference change and to the old frame members that

were not assigned a frame type though the Overwrites.

4.5 Member Design

This section describes the special requirements for designing a member.

4.5.1 Ductility Class High – Moment-Resisting Frames (DCH MRF)

For this framing system

( )

45 11 13

o uu

q . , ..= = −

αααα

(NTC § 7.4.3.2,

Table 7.4.I), the following additional requirements are checked or reported

(NTC § 7.4.4.1-6).

NOTE: The geometrical constraints and material requirements given in NTC § 7.4.6

should be checked independently by the user because the program does not perform

those checks.

4.5.1.1 Design Forces

4.5.1.1.1 Beams

The design values of bending moments and axial forces are obtained from the

analysis of the structure for the seismic design situation, taking into account

second order effects and the capacity design requirements (NTC § 7.4.4). The

design values for shear forces of primary seismic beams and columns are

determined in accordance with NTC § 7.4.4.1.1 and NTC § 7.4.4.2.1,

respectively.

In primary seismic beams, the design shear forces are determined in accord-

ance with the capacity design rule, on the basis of the equilibrium of the beam

under (a) the transverse load acting on it in the seismic design situation and (b)

end moments Mi,d (with i = 1,2 denoting the end sections of the beam), corre-

sponding to plastic hinge formation for positive and negative directions of

seismic loading. The plastic hinges should be taken to form at the ends of the

beams (see Figure 4-1) (NTC § 7.4.4.1.1).

4 - 4 Member Design

Chapter 4 - Seismic Provisions

2Rd Rh,

( )

1Rd Rh, Rc Rb

M MM

−

∑∑

∑

Rb Rc

MM<

∑∑

Rb Rc

MM>

∑∑

1 2

2Rd Rh,

( )

1Rd Rh, Rc Rb

M MM

−

∑∑

∑

Rb Rc

MM<

∑∑

Rb Rc

MM>

∑∑

1 2

Figure 4-1 Capacity Design Shear Force for beams

The preceding condition has been implemented as follows:

a) At end section i, two values of the acting shear force should be calculated,

i.e. the maximum VEd,max,i and the minimum VEd,min,i corresponding to the

maximum positive and the maximum negative end moments Mi,d that can

develop at ends 1 and 2 of the beam.

max

Rd Rd bi Rd bj

id g qo

−+

+ψ



γ+



= +

min Rd Rd bi Rd bj

id g qo

+−

+ψ



γ+



= +

As the moments and shears on the right-hand side of the preceding equa-

tions are positive, the outcome may be positive or negative. If it is positive,

the shear at any section will not change the sense of action despite the cy-

clic nature of seismic loading; if it is negative, the shear does change sense.

The ratio:

min

max

is used in the dimensioning of shear reinforcement of DCH beams as a

measure of the reversal of the shear force at end i (similarly at end j).

Member Design 4 - 5

Concrete Frame Design NTC 2008

is the factor accounting for possible overstrength because of steel

strain hardening, which in the case of DCH beams is taken as equal to 1.2;

MRb,i is the design value of the beam moment of resistance at end i in the

sense of the seismic bending moment under the considered sense of the

seismic action;

b) At a beam end where the beam is supported indirectly by another beam in-

stead of framing into a vertical member, the beam end moment, Mi,d, may

be taken as equal to the acting moment at the beam end section in a seismic

design situation.

4.5.1.1.2 Columns

In primary seismic columns, the design values of shear forces are determined

in accordance with the capacity design rule, on the basis of the equilibrium of

the column under end moments Mi,d (with i = 1.2 denoting the end stations of

the column), corresponding to plastic hinge formation for positive and negative

directions of seismic loading. The plastic hinges should be taken to form at the

ends of the columns (see Figure 4-2).

,1 ,2

max Rd Rd c Rd c

CD c



γ+



where

is the factor accounting for possible overstrength due to steel strain

hardening, which in the case of DCH beams is taken as equal to

1.3;

MRc,i is the design value of the column moment of resistance at end i in

the sense of the seismic bending moment under the considered

sense of the seismic action.

4 - 6 Member Design

Chapter 4 - Seismic Provisions

( )

2Rd Rb Rc Rc,

M MM

∑∑

∑

Rb Rc

MM>

∑∑

∑

1Rd Rc,

∑

Rb Rc

MM<

∑∑

( )

2Rd Rb Rc Rc,

M MM

∑∑

∑

Rb Rc

MM>

∑∑

∑

1Rd Rc,

∑

Rb Rc

MM<

∑∑

Figure 4-2 Capacity Design Shear Force for Columns

4.5.1.2 Design Resistance

The beam and column bending resistance is computed in accordance with NTC

2008 § 4.1.2.1.2 with the following exceptions (NTC § 7.4.4.2.2.1):

 In primary seismic columns, the value of the normalized axial force

should not exceed 0.55. Otherwise the program generates a warning message.

Member Design 4 - 7

Concrete Frame Design NTC 2008

dcd g

vfA

The beam shear resistance is computed in accordance with NTC 2008

§ 4.1.2.1.3 with the following exceptions (NTC § 7.4.4.1.2.2):

(1) In the critical regions of primary seismic beams, the strut inclination, θ,

in the truss model is 45°.

(2) With regard to the arrangement of shear reinforcement within the critical

region at an end of a primary seismic beam where the beam frames into a

column, the following cases should be distinguished, depending on the

algebraic value of the ratio:

VEd,min/VEd,max ratio between the minimum and maximum acting

shear forces, as derived in accordance with NTC § 7.4.4.1.2.2.

(a) If VEd,min/VEd,max ≥−0.5, the shear resistance provided by the rein-

forcement should be computed in accordance with NTC 2008 §

4.1.2.1.3.

(b) If VEd,min/VEd,max < −0.5, i.e. when an almost full reversal of shear

forces is expected, then:

(i) if

,min

max ,max

2Ed

E ctd w

V f bd



≤−





(NTC Eq. 7.4.2)

where fctd is the design value of the concrete tensile strength the

same rule as in (a) of this section applies.

(ii) if |VE|max exceeds the limit value in expression (NTC Eq. 7.4.2),

inclined reinforcement should be provided in two directions, ei-

ther at ±45° to the beam axis, and half of |VE|max should be re-

sisted by stirrups and half by inclined reinforcement.

 In such a case, the verification is carried out by means of the condition:

max 2

s yd

V≤

(NTC Eq. 7.4.3)

4 - 8 Member Design

Chapter 4 - Seismic Provisions

where,

As is the area of the inclined reinforcement in one direction, crossing

the potential sliding plane (i.e., the beam end section).

NOTE: Inclined stirrups are not designed at this time. Only vertical

stirrups are designed for case (b)(ii) for the full shear force.

The column shear resistance is computed in accordance with NTC 2008

§ 4.1.2.1.3.

4.5.1.3 Joint Design

To ensure that the beam-column joint of a Ductility Class High Moment

Resisting Frame (DCH MRF) 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 checked. The material proper-

ties 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,

jhd

• Determine the effective area of the joint

• Design panel zone shear rebar/stirrup

The algorithms associated with these steps are described in detail in the follow-

ing three sections.

4.5.1.3.1 Determine the Panel Zone Shear Force

Figure 4-3 illustrates the free body stress condition of a typical beam-column

intersection for a column direction, major or minor.

Member Design 4 - 9

Concrete Frame Design NTC 2008

The force

jhd

is the horizontal panel zone shear force that is to be calculated.

The forces that act on the joint are NEd, VC,

and

The forces NEd and

VC are the design axial force and design shear force, respectively, from the

column framing into the top of the joint. The moments

and

are

obtained from the beams framing into the joint. The program calculates the

joint shear force

jhd

by resolving the moments into C and T forces. Noting

that TL = CL and TR = CR:

=+−

jhd L R C

V TTV

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 prin-

ciples of ultimate strength theory.

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 di-

rections 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 Ductility Class High Moment Resisting Frames (DCH MRF),

the evaluation of the design shear force is based on the moment capacities with

a reinforcing steel overstrength factor due to steel strain hardening, γRd, which

in the case of DCH MRF beams is taken as equal to 1.2 (NTC § 7.4.4.3). The C

and T force are based on those moment capacities. The program calculates the

column shear force VC from the beam moment capacities, as follows (see

Figure 4-3):

Ed Ed

It should be noted that the points of inflection shown on Figure 4-3 are taken as

midway between actual lateral support points for the columns. If no column exists

at the top of the joint, the shear force from the top of the column is taken as zero.

4 - 10 Member Design

Chapter 4 - Seismic Provisions

POINT OF

INFLECTION

ELEVATION

POINT OF

INFLECTION

PANEL

ZONE

COLUMN

ABOVE

TOP OF BEAM

COLUMN

HEIGHT

(H)

COLUMN

BELOW

jhd

POINT OF

INFLECTION

ELEVATION

POINT OF

INFLECTION

PANEL

ZONE

COLUMN

ABOVE

TOP OF BEAM

COLUMN

HEIGHT

(H)

COLUMN

BELOW

jhd

Figure 4-3 Column shear force VC

The effects of load reversals, as illustrated in Case 1 and Case 2 of Figure 4-4,

are investigated and the design is based on the maximum of the joint shears

obtained from the two cases.

Member Design 4 - 11

Concrete Frame Design NTC 2008

Figure 4-4 Beam-column joint analysis

4 - 12 Member Design

Chapter 4 - Seismic Provisions

4.5.1.3.2 Determine the Effective Area of Joint

The joint area that resists 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 cal-

culation is limited as follows:

{ } { }

{ }

min max ; ;min ; ;

j cw c cw c

b bb b hb h= ++

(NTC § 7.4.4.3.1)

bc = cross-sectional dimension of column,

bw = width of web of a beam, and

hc = cross-sectional depth of column in the direction of interest.

The joint area for joint shear along the major and minor directions is calculated

separately.

It should be noted that if the beam frames into the joint eccentrically, the pre-

ceding assumptions may not be conservative, and the user should investigate

the acceptability of the particular joint.

4.5.1.3.3 Check Panel Zone Shear Force

The panel zone shear force is evaluated by comparing it with the following

design shear strengths (EC85.5.3.3(2)).

jhd cd j jc

V f bh≤η − η

(NTC Eq. 7.4.8)

where,

( )

1 250

j ck

fη=α −

0.6

α=

for interior joints and

0.48

α=

for exterior joints

is the distance between extreme layers of column reinforcement;

is as defined by NTC § 7.4.4.3.1 (see § 4.5.1.3.2 of this manual);

Member Design 4 - 13

Concrete Frame Design NTC 2008

is the normalized axial force in the column above the joint; and

is given in MPa.

4.5.1.4 Design Panel Zone Confinement Reinforcing

The panel zone confinement reinforcing (horizontal hoops) is computed as fol-

lows (NTC § 7.4.4.3.1).

jhd

j jc j jw

sh ctd

ctd d cd ywd

bh bh

f vf f













= −





(NTC Eq. 7.4.10)

where,

is the total area of the horizontal hoops;

jhd

is the horizontal shear force acting on the concrete core of the joint

is the distance between the top and the bottom reinforcement of the

beam;

is the distance between the extreme layers of column reinforcement;

is as defined in NTC § 7.4.4.3.1 (see § 4.5.1.3.2 of this manual);

is the normalized design axial force of the column above

( )

d Ed c cd

v N Af=

The horizontal hoops should be uniformly distributed within the depth

between the top and bottom bars of the beam. In exterior joints, they should

enclose the ends of beam bars bent toward the joint.

4 - 14 Member Design

Chapter 4 - Seismic Provisions

Additional requirements for horizontal confinement reinforcement in joints of

primary seismic beam with columns as stipulated in NTC 2008 § 7.4.6.2.3 are

NOT enforced by the program.

4.5.1.5 Beam-Column Flexural Capacity Ratios

The program calculates the ratio of the sum of the beam moment capacities to

the sum of the column moment capacities. For Ductility Class High Moment

Resisting Frames (DCH MRF), at a particular joint for a particular column di-

rection, major or minor (NTC § 7.4.4.2.1):

1.3 1.0

M≤

∑

(NTC Eq. 7.4.4)

∑c

= Sum of nominal flexural strengths of columns framing into the

joint, evaluated at the faces of the joint. Individual column flex-

ural strength is calculated for the associated factored axial force.

∑b

= Sum of nominal flexural strengths of the beams framing into the

joint, evaluated at the faces of the joint.

The beam capacities are calculated for reversed situations (Cases 1 and 2) as il-

lustrated in Figure 4-3, 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,

in each of the

columns is calculated from the program design load combinations. For each

design load combination, the moment capacity of each column under the influ-

ence of the corresponding axial load is then determined separately for the ma-

jor and minor directions of the column, using the uniaxial column interaction

diagram; see Figure 4-5. The moment capacities of the two columns are added

to give the capacity summation for the corresponding design load combination.

Member Design 4 - 15

Concrete Frame Design NTC 2008

The maximum capacity summations obtained from all of the design load com-

binations is used for the beam-column capacity ratio.

Figure 4-5 Moment capacity MEd at a given axial load NEd

The beam-column capacity ratio is determined for a beam-column joint only

when the following conditions are met:

• the frame is a Ductility Class High Moment Resisting Frame (DCH MRF)

• when a column exists above the beam-column joint, the column is concrete

• all of the beams framing into the column are concrete beams

• the connecting member design results are available

• the load combo involves seismic load

The beam-column flexural capacity ratios

( )

1.3

∑∑

are reported only

for Ductility Class High Moment Resisting Frames involving seismic design

4 - 16 Member Design

Chapter 4 - Seismic Provisions

load combinations. If this ratio is greater than 1.0, a warning message is printed

in the output.

4.5.1.6 Minimum and Maximum Tensile Reinforcement

The minimum and maximum flexural tensile reinforcement ratio in a beam sec-

tion are limited to the following values (NTC § 7.4.6.2.1):

1.4 3.5

comp

yk yk

≤ρ≤ρ +

(NTC Eq. 7.4.25)

with

in [MPa].

The minimum and maximum flexural tensile reinforcement ratio required in a

column section is limited to the following (NTC § 7.4.6.2.1):

0.01 0.04≤ρ≤

(NTC Eq. 7.4.27)

4.5.2 Ductility Class Low – Moment-Resisting Frames (DCL MRF)

For this framing system

( )

30 11 13

o uu

q. , ..

αααα

= = −

(NTC § 7.4.3.2,

Table 7.4.I), the additional requirements described in the sections that follow

are checked or reported (NTC § 7.4.4.1-6).

NOTE: The geometrical constraints and material requirements given in NTC § 7.4.6

should be independently checked by the user because the program does not perform

those checks.

4.5.2.1 Design Forces

4.5.2.1.1 Beams

The design values of bending moments and axial forces are obtained from the

analysis of the structure for the seismic design situation, taking into account

second order effects and the capacity design requirements (NTC § 7.4.4). The

design values for shear forces of primary seismic beams and columns are

Member Design 4 - 17

Concrete Frame Design NTC 2008

determined in accordance with NTC § 7.4.4.1.1 and NTC § 7.4.4.2.1,

respectively.

In primary seismic beams, the design shear forces are determined in accord-

ance with the capacity design rule, on the basis of the equilibrium of the beam

under (a) the transverse load acting on it in the seismic design situation and (b)

end moments Mi,d (with i = 1,2 denoting the end sections of the beam), corre-

sponding to plastic hinge formation for positive and negative directions of

seismic loading. The plastic hinges should be taken to form at the ends of the

beams (see Figure 4-1) (NTC § 7.4.4.1.1).

The preceding condition has been implemented as follows:

a) At end section i, two values of the acting shear force should be calculated,

i.e., the maximum VEd,max,i and the minimum VEd,min,i corresponding to the

maximum positive and the maximum negative end moments Mi,d that can

develop at ends 1 and 2 of the beam.

max

Rd Rd bi Rd bj

id g qo

−+

+ψ



γ+



= +

min Rd Rd bi Rd bj

id g qo

+−

+ψ



γ+



= +

is the factor accounting for possible overstrength because of steel

strain hardening, which in the case of DCL beams is taken as equal

to 1.0;

MRb,i is the design value of the beam moment of resistance at end i in the

sense of the seismic bending moment under the considered sense of

the seismic action;

b) At a beam end where the beam is supported indirectly by another beam in-

stead of framing into a vertical member, the beam end moment, Mi,d, may

be taken as equal to the acting moment at the beam end section in a seismic

design situation.

4 - 18 Member Design

Chapter 4 - Seismic Provisions

4.5.2.1.2 Columns

In primary seismic columns, the design values of shear forces are determined

in accordance with the capacity design rule, on the basis of the equilibrium of

the column under end moments Mi,d (with i=1.2 denoting the end stations of the

column), corresponding to plastic hinge formation for positive and negative

directions of seismic loading. The plastic hinges should be taken to form at the

ends of the columns (see Figure 4-2).

,1 ,2

max Rd Rd c Rd c

CD c cl



γ+



where

is the factor accounting for possible overstrength due to steel strain hard-

ening, which in the case of DCL beams is taken as equal to 1.1;

MRc,i is the design value of the column moment of resistance at end i in the

sense of the seismic bending moment under the considered sense of the

seismic action.

4.5.2.2 Design Resistance

The beam and column bending resistance is computed in accordance with NTC

2008 § 4.1.2.1.2 with the following exceptions (NTC § 7.4.4.2.2.1):

 In primary seismic columns, the value of the normalized axial force

should not exceed 0.65. Otherwise the program generates a warning mes-

sage.

The beam and column shear resistance is computed in accordance with NTC

2008 § 4.1.2.1.3.

4.5.2.3 Minimum and Maximum Tensile Reinforcement

The minimum and maximum flexural tensile reinforcement ratio in a beam sec-

tion is limited to the following values (NTC § 7.4.6.2.1):

Member Design 4 - 19

Concrete Frame Design NTC 2008

comp

1.4 3.5

yk yk

≤ρ≤ρ +

(NTC Eq. 7.4.25)

with

in [MPa].

The minimum and maximum flexural tensile reinforcement ratio required in a

column section is limited to the following (NTC § 7.4.6.2.1):

0.01 0.04.≤ρ≤

(NTC Eq. 7.4.27)

4.5.3 Special Consideration for Seismic Design

For Special Moment Resisting Concrete Frames (seismic design), the beam

design satisfies the following additional conditions (see also Table 4-1):

Table 4-1: Design Criteria

Type of

Check/

Design

Ductility Class Low

Moment Resisting Frames

(DCL MRF)

Ductility Class High

Moment Resisting Frames

(DCH MRF)

Column Check (interaction)

Specified Combinations Specified Combinations

Column Design (interaction)

Specified Combinations

1% < ρ < 4%

Specified Combinations

1% < ρ < 4%

Column Shears

Specified Combinations

Column Capacity Shear

= 1.1

Specified Combinations

Column Capacity Shear

= 1.3

Beam Design Flexure

Specified Combinations

comp

1.4 3.5

yk yk

≤ρ≤ρ +

Specified Combinations

comp

1.4 3.5

yk yk

≤ρ≤ρ +

4 - 20 Member Design

Chapter 4 - Seismic Provisions

Table 4-1: Design Criteria

Type of

Check/

Design

Ductility Class Low

Moment Resisting Frames

(DCL MRF)

Ductility Class High

Moment Resisting Frames

(DCH MRF)

Beam Min. Moment Override Check

end

comp,end 2

ρ ≥ρ

comp 4

ρ ≥ρ

end

comp,end 2

ρ ≥ρ

comp 4

ρ ≥ρ

Beam Design Shear

Specified Combinations

Beam Capacity Shear (Ve)

γRd = 1.0

Specified Combinations

Beam Capacity Shear (Ve)

γRd = 1.2

Joint Design

No Requirement Checked for shear

Beam/Column Capacity Ratio

No Requirement Checked

• ρcomp is the compressed reinforcement, while ρ is the tensioned reinforce-

ment.

Member Design 4 - 21

APPENDICES

Appendix A

Second Order P-Delta Effects

Typically, design codes require that second order P-∆ 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-∆ effects on this frame object (P-∆) are those caused by both ∆

and δ.

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

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 δ deformation (unless, in the model, the frame object is

broken into multiple elements over its length).

Consideration of the second order P-∆ effects is generally achieved by compu-

ting the flexural design capacity using a formula similar to that shown in the

following equation.

A - 1

Concrete Frame Design NTC 2008

Figure A-1 The Total Second Order P-Delta Effects on a Frame Element Caused by

Both

∆

and

MCAP = aMnt + bMlt where,

MCAP = Flexural design capacity required

Mnt = Required flexural capacity of the member assuming there is

no joint translation of the frame (i.e., associated with the δ

deformation in Figure A-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 A-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 calculates the factor a. That b = 1 assumes that P-∆ effects have

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

performing concrete frame design in this program, consider P-∆ effects in the

analysis before running the program.

A - 2 Second Order P-Delta Effects

Appendix B

Member 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).

In determining the values for L22 and L33 of the members, the program recog-

nizes various aspects of the structure that have an effect on these lengths, such as

member connectivity, diaphragm constraints, and support points. The program

automatically locates the member support points and evaluates the corre-

sponding unsupported length.

B - 1

Concrete Frame Design NTC 2008

Figure B-1 Axis of bending and 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

The Concrete Frame Design Preferences are basic assignments that apply to all

of the concrete frame members. Table C-1 lists the Concrete Frame Design

Preferences for the KBC 2009 code. Default values are provided for all

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

preferences. However, at least review the default values to ensure they are

acceptable. Some of the preference items also are available as member specific

overwrite items. The Overwrites are described in Appendix D. Overwritten

values take precedence over the preferences.

Table C-1 Design Criteria Table

Item

Possible

Values

Default

Value

Description

Multi-Response

Case Design Envelopes,

Step-by-Step Envelopes

This is either "Envelopes", "Step-by-Step",

"Last Step", "Envelopes - All",

"Step-by-Step - All" indicating how results

for multivalued cases (Time history, Non-

linear static or Multi-step static) are con-

sidered in the design.

Envelope - considers enveloping values for

Time History and Multi-step static and last

step values for Nonlinear static.

C - 1

Concrete Frame Design NTC 2008

Item

Possible

Values

Default

Value

Description

Step-by-Step - considers step by step

values for Time History and Multi-step

static and last step values for Nonlinear

static.

Last Step - considers last values for Time

History, Multi-step static and Nonlinear

static.

Envelope - All - considers enveloping val-

ues for Time History, Multi-step static and

Nonlinear static.

Step-by-Step - All - considers step by step

values for Time History, Multi-step static

and Nonlinear static.

Step-by-Step and Step-by-Step - All default

to the corresponding Envelope if more then

one multivalued case is present in the

combo.

Number

Interaction Curves

Multiple of 4

≥ 4 24

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.

Number Any odd value

≥ 5 11 Number of points used for defining a single

curve in a concrete frame should be odd

Consider

Minimum No, Yes Yes Toggle to consider if minimum eccentricity

should be considered in design.

Phi

(Tension

Controlled) > 0 0.85 Strength reduction factor for tension con-

trolled sections.

Phi

(Compression

Controlled-Tied) > 0 0.65 The strength reduction factor for compres-

sion controlled sections with spiral rein-

forcement.

Phi

(Compression

> 0 0.70 The strength reduction factor for compres-

sion controlled sections with spiral rein-

C - 2 Preferences

Appendix C - Concrete Frame Design Preferences

Item

Possible

Values

Default

Value

Description

Controlled-Spiral)

forcement.

Phi

(Shear and/ or Tor-

sion) > 0 0.75 The strength reduction factor for shear and

torsion.

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

torsion.

Phi (Pattern Live

Load Factor) ≥ 0 0.75

The strength reduction factor for shear in

structures that rely on special moment

resisting frames or special reinforced

concrete structural walls to resist

earthquake effects.

Utilization Factor

Limit > 0 0.95 Stress ratios that are less than or equal to

this value are considered acceptable.

Preferences C - 3

Appendix D

Concrete 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 KBC 2009. 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. Refer to the program help for information

about changing overwrites.

Table D-1 Design Criteria Table

Item Possible

Values Default

Value Description

Current

Design

Section

Any defined

concrete

section

Analysis

section

The design section for the selected

frame objects. When this overwrite

is applied, any previous auto select

section assigned to the frame

object is removed.

Element

Type

Sway

Special, Sway

Intermediate,

Sway Ordinary

NonSway

From

Reference

Frame type per moment frame

definition given in KBC 0520. The

Framing Type is used for ductility

considerations in the design.

These are default values, which

the user can overwrites if needed.

D - 1

Concrete Frame Design NTC 2008

Item Possible

Values Default

Value Description

Live Load Re-

duction Factor

≥ 0 Calculated

The reduced live load factor. A

reducible live load is multiplied by

this factor to obtain the reduced

live load for the frame object.

Specifying 0 means the value is

program determined.

Unbraced

Length Ratio

(Major) ≥ 0 Calculated

Unbraced length factor for buckling

about the frame object major axis.

This item is specified as a fraction

of the frame object length.

Multiplying this factor times the

frame object length gives the

unbraced length for the object.

Specifying 0 means the value is

program determined.

Unbraced

Length Ratio

(Minor) ≥ 0 0.60

Unbraced length factor for buckling

about the frame object minor axis.

Multiplying this factor times the

frame object length gives the

unbraced length for the object.

Specifying 0 means the value is

program determined. This factor is

also used in determining the length

for lateral-torsional buckling.

Effective

Length Factor

(K Major) > 0 Calculated

See KBC 0506.5.3.1. Effective

length factor for buckling about the

frame object major axis. This item

is specified as a fraction of the

frame object length.

D - 2 Overwrites

Appendix E

Error Messages and Warnings

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

Table E-1 Error Messages

Error

Number

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

Concrete Frame Design NTC 2008

Error

Number

Description

115k Lr∗/>

20zeta_ <

10eta <.

(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

30k Lr∗/>

(GB 7.3.10)

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

needed.

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

needed.

There is no beam on top of column. Beam/column capacity ratio

is not needed.

24 At least one beam on top of column is not of concrete.

Beam/column capacity ratio is not calculated.

The column on top is not of concrete. Beam/column capacity ratio

is not calculated.

The 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.

E - 2 Appendix E

Appendix E – Error Messages and Warnings

Error

Number

Description

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

29 There is no beam on top of column. Joint shear ratio is not

needed.

At least one beam on top of column is not of concrete. Joint shear

ratio is not calculated.

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

needed.

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

needed.

33 Beam/column capacity ratio exceeds limit.

34 Joint shear ratio exceeds limit.

35 Capacity ratio exceeds limit.

36 All beam s around the joint have not been designed.

Beam/column capacity ratio is not calculated.

37 At least one beam around the joint have failed. Beam/column

capacity ratio is not calculated.

38 The column above the joint have not been designed.

Beam/column capacity ratio is not calculated.

39 The column above the joint have failed. Beam/column capacity

ratio is not calculated.

40 All beams around the joint have not been designed. Joint shear

ratio is not calculated.

At least one beam around the joint have failed. Joint shear ratio is

not calculated.

The column above the joint have not been designed. Joint shear

Output Details E - 3

Concrete Frame Design NTC 2008

Error

Number

Description

ratio is not calculated.

43 The column above the joint have failed. Joint shear ratio is not

calculated.

45 Shear stress due to shear force and torsion together exceeds

maximum allowed.

E - 4 Appendix E

CFD NTC 2008

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