CFD TS 500 2000

User Manual: CFD-TS-500-2000

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Concrete Frame Design Manual
Turkish TS 500-2000 with Seismic Code 2007

Concrete Frame
Design Manual
Turkish TS 500-2000
with Turkish Seismic Code 2007
For SAP2000®

ISO SAP102816M37 Rev. 0
Proudly developed in the United States of America

October 2016

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Contents

Chapter 1

Chapter 2

Introduction
1.1

Organization

1-2

1.2

Recommended Reading/Practice

1-3

Chapter 2
Design Prerequisites

This chapter provides an overview of the basic assumptions, design preconditions, and some of the design parameters that affect the design of concrete
frames.
In writing this manual it has been assumed that the user has an engineering
background in the general area of structural reinforced concrete design and familiarity with TS 500-2000 codes.

2.1

Design Load Combinations
The design load combinations are used for determining the various combinations of the load cases for which the structure needs to be designed/checked. The
load combination factors to be used vary with the selected design code. The load
combination factors are applied to the forces and moments obtained from the
associated load cases and are then summed to obtain the factored design forces
and moments for the load combination.
For multi-valued load combinations involving response spectrum, time history,
moving loads and multi-valued combinations (of type enveloping, square-root
of the sum of the squares or absolute) where any correspondence between interacting quantities is lost, the program automatically produces multiple sub

2-1

Concrete Frame Design TS 500-2000

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 permutations just described
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, snow load,
wind load, and earthquake load, or dynamic response spectrum earthquake load,
the program 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 manuals.
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 load cases declared as dead load to be
additive. Similarly, all cases declared as live load are assumed additive. However, each load case declared as wind or earthquake, or response spectrum cases,
is assumed to be non additive with each other and produces multiple lateral load
combinations. Also wind and static earthquake cases produce separate loading
combinations with the sense (positive or negative) reversed. If these conditions
are not correct, the user must provide the appropriate design combinations.
The default load combinations are included in design if the user requests them to
be included or if no other user-defined combination is available for concrete
design. If any default combination is included in design, 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 segments along the clear length of the element. The number of segments
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 segments.
When using the TS 500-2000 design code, requirements for joint design at the
beam-to-column connections are evaluated at the top most station of each
column. The program also performs a joint shear analysis at the same station to
determine if special considerations are required in any of the joint panel zones.
The ratio of the beam flexural capacities with respect to the column flexural
capacities considering axial force effect associated with the weak- beam/strongcolumn aspect of any beam/column intersection are reported.

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 element exists in the
frame, the brace element also would be identified as a beam or a column element, depending on the section assigned to the brace element.

Design and Check Stations

2-3

Concrete Frame Design TS 500-2000

2.4

Design of Beams
In the design of concrete beams, in general, the program calculates and reports
the required areas of steel for flexure and shear based on the beam moments,
shears, load combination factors, and other criteria, which are described in detail
in the code-specific manuals. The reinforcement requirements 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 caused by any axial forces and minor direction bending that may exist in
the beams must be investigated independently by the user.
In designing the flexural reinforcement for the major moment at a particular
section of a particular beam, the steps involve the determination of the 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 beam section is not adequate, the required compression reinforcement is calculated.
In designing the shear reinforcement for a particular beam for a particular set of
loading combinations at a particular station associated with beam major shear,
the steps involve the determination of the factored shear force, the determination
of the shear force that can be resisted by concrete, and the determination of the
reinforcement steel required to carry the balance.
Special considerations for seismic design are incorporated into the program for
the TS 500-2000 code.

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 stress condition of the column with respect to the capacity of the

2-4

Design of Beams

Chapter 2 - Design Prerequisites

column. The design procedure for the reinforced concrete columns of the
structure involves the following steps:


Generate axial force-biaxial moment interaction surfaces for all of the different concrete section types 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 column. This step is also used to calculate the required reinforcement (if none
was specified) that will produce a capacity ratio of 1.0.

The generation of the interaction surface is based on the assumed strain and
stress distributions and some other simplifying assumptions. These stress and
strain distributions and the assumptions are documented in Chapter 3.
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
must be considered.
For certain special seismic cases, the design of columns for shear is based on the
capacity shear. The capacity shear force in a particular direction is calculated
from the moment capacities of the column associated with the factored axial
force acting on the column. For each load combination, the factored axial load is
calculated using the load cases and the corresponding load combination factors.
Then, the moment capacity of the column in a particular direction under the influence of the axial force is calculated, using the uniaxial interaction diagram in
the corresponding direction, as documented in Chapter 3.

2.6

Design of Joints
To ensure that the beam-column joint of special moment resisting frames possesses adequate shear strength, the program performs a rational analysis of the
beam-column panel zone to determine the shear forces that are generated in the
joint. The program then checks this against design shear strength.
Only joints that have a column below the joint are designed. The material
properties of the joint are assumed to be the same as those of the column below
the joint. The joint analysis is performed in the major and the minor directions of
the column. The joint design procedure involves the following steps:

Design of Joints

2-5

Concrete Frame Design TS 500-2000



Determine the panel zone design shear force



Determine the effective area of the joint



Check panel zone shear stress

The joint design details are documented in Chapter 3.

2.7

P-Delta Effects
The program design process requires that the analysis results include P-delta
effects. The P-delta effects are considered differently for “braced” or
“non-sway” and “unbraced” or “sway” components of moments in columns or
frames. For the braced moments in columns, the effect of P-delta is limited to
“individual member stability.” For unbraced components, “lateral drift effects”
should be considered in addition to individual member stability effect. The
program assumes that “braced” or “nonsway” moments are contributed from the
“dead” or “live” loads, whereas, “unbraced” or “sway” moments are contributed
from all other types of loads.
For the individual member stability effects, the moments are magnified with
moment magnification factors, as documented in Chapter 3 of this manual.
For lateral drift effects, the program assumes that the P-delta analysis is performed and that the amplification is already included in the results. The moments and forces obtained from P-delta analysis are further amplified for
individual column stability effect if required by the governing code, as in the TS
500-2000 codes.
Users of the program should be aware that the default analysis option is P-delta
effects are not included. The user can include P-delta analysis 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.

2.8

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

2-6

P-Delta Effects

Chapter 2 - Design Prerequisites

between support points of the element in the corresponding directions. The
length l33 corresponds to instability about the 3-3 axis (major axis), and l22 corresponds to instability about the 2-2 axis (minor axis).
Normally, the unsupported element length is equal to the length of the element,
i.e., the distance between END-I and END-J of the element. The program,
however, allows users to assign several elements to be treated as a single
member for design. This can be accomplished differently for major and minor
bending, as documented in Appendix B of this design manual.
The user has options to specify the unsupported lengths of the elements on an
element-by-element basis.

2.9

Choice of Input Units
English as well as SI and MKS metric units can be used for input. The codes are
based on a specific system of units. All equations and descriptions presented in
this manual correspond to that specific system of units unless otherwise noted.
For example, the TS 500-2000 code is published in Millimeter-Newton-Second
units. By default, all equations and descriptions presented in the “Design Process” chapter correspond to Millimeter-Newton-Second units. However, any
system of units can be used to define and design a structure in the program.

Choice of Input Units

2-7

Chapter 3
Design Process

This chapter provides a detailed description of the code-specific algorithms used
in the design of concrete frames when the TS 500-2000 codes have been selected. The menu option “TS 500-2000” also covers the “Specification for
Buildings to be Built in Earthquake Areas” (2007). For simplicity, all equations
and descriptions presented in this chapter correspond to Millimeter-Newton-Second units unless otherwise noted.
For referring to pertinent sections of the corresponding code, a unique prefix is
assigned for each code.

3.1



Reference to the TS 500-2000 code is identified with the prefix “TS.”



Reference to the Specification for Turkish Seismic Code (2007) code is
identified with the prefix “TSC.”

Notation
The various notations used in this chapter are described herein:

Gross area of concrete, mm2

3-1

Concrete Frame Design TS 500-2000

Area enclosed by centerline of the outermost closed transverse
torsional reinforcement, mm2

Area of tension reinforcement, mm2

A′s

Area of compression reinforcement, mm2

Asl

Area of longitudinal torsion reinforcement, mm2

Aot /s

Area of transverse torsion reinforcement (closed stirrups) per unit
length of the member, mm2/mm

Aov /s

Area of transverse shear reinforcement per unit length of the
member, mm2/mm

As(required) Area of steel required for tension reinforcement, mm2

3-2

Ast

Total area of column longitudinal reinforcement, mm2

Asw

Area of shear reinforcement, mm2

Asw/s

Area of shear reinforcement per unit length of the member,
mm2/mm

Coefficient, dependent upon column curvature, used to calculate
moment magnification factor

Modulus of elasticity of concrete, N/mm2

Modulus of elasticity of reinforcement, 2x105 N/mm2

Moment of inertia of gross concrete section about centroidal axis,
neglecting reinforcement, mm4

Ise

Moment of inertia of reinforcement about centroidal axis of
member cross-section, mm4

Clear unsupported length, mm

Smaller factored end moment in a column, N-mm

Larger factored end moment in a column, N-mm

Factored moment to be used in design, N-mm

Mns

Non-sway component of factored end moment, N-mm

Notation

Chapter 3 - Design Process

Sway component of factored end moment, N-mm

Designed factored moment at a section, N-mm

Md2

Designed factored moment at a section about 2-axis, N-mm

Md3

Designed factored moment at a section about 3-axis, N-mm

Axial load capacity at balanced strain conditions, N

Critical buckling strength of column, N

Nmax

Maximum axial load strength allowed, N

Axial load capacity at zero eccentricity, N

Designed factored axial load at a section, N

Rdns

Absolute value of ratio of maximum factored axial dead load to
maximum factored axial total load, i.e., creep coefficient

Shear force resisted by concrete, N

Shear force caused by earthquake loads, N

VG+Q

Shear force from span loading, N

Vmax

Maximum permitted total factored shear force at a section, N

Shear force computed from probable moment capacity, N

Shear force resisted by steel, N

Designed factored shear force at a section, N

Depth of compression block, mm

Depth of compression block at balanced condition, mm

amax

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

Depth to neutral axis, mm

Notation

3-3

Concrete Frame Design TS 500-2000

3-4

Depth to neutral axis at balanced conditions, mm

Distance from compression face to tension reinforcement, mm

d′

Concrete cover to center of reinforcing, mm

Thickness of slab (T-beam section), mm

emin

Minimum eccentricity, mm

fcd

Designed compressive strength of concrete, N/mm2

fck

Characteristic compressive strength of concrete, N/mm2

fctk

Characteristic tensile strength of concrete, N/mm2

fyd

Designed yield stress of flexural reinforcement, N/mm2.

fyk

Characteristic yield stress of flexural reinforcement, N/mm2.

fywd

Designed yield stress of transverse reinforcement, N/mm2.

Overall depth of a column section, mm

Effective length factor

Factor for obtaining depth of compression block in concrete

Perimeter of centerline of outermost closed transverse torsional
reinforcement, mm

Radius of gyration of column section, mm

Reinforcing steel overstrength factor

βs

Moment magnification factor for sway moments

βns

Moment magnification factor for non-sway moments

εc

Strain in concrete

εcu,

Maximum usable compression strain allowed in extreme concrete
fiber (0.003 mm/mm)

εs

Strain in reinforcing steel

γm

Material factor

Notation

Chapter 3 - Design Process

3.2

γmc

Material factor for concrete

γms

Material factor for steel

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 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 cases,
each with its own scale factor. The scale factors are applied to the forces and
moments from the load cases to form the factored 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 combinations 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, G, and live load, Q, only,
the TS 500-2000 design check may need one design load combination only,
namely, 1.4G +1.6Q. However, if the structure is subjected to wind, earthquake,
or other loads, numerous additional design load combinations may be required.
The program allows live load reduction factors to be applied to the member
forces obtained form a load case that includes reducible live load 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. For this code, if a structure is subjected
to dead (G), live (Q), wind (W), and earthquake (E), and considering that wind
and earthquake forces are reversible, the following load combinations may need
to be defined (TS 6.2.6):

Design Load Combinations

3-5

Concrete Frame Design TS 500-2000

1.4G + 1.6Q

(TS 6.3)

0.9G ± 1.3W
1.0G + 1.3Q ± 1.3W

(TS 6.6)
(TS 6.5)

0.9G ± 1.0E
1.0G + 1.0Q ± 1.0E

(TS 6.8)
(TS 6.7)

These are also the default design load combinations in the program whenever the
TS 500-2000 code is used. The user should use other appropriate design load
combinations if roof live load is separately treated, or if other types of loads are
present.
Live load reduction factors can be applied to the member forces of the live load
case on a member-by-member basis to reduce the contribution of the live load to
the factored loading.
When using the TS 500-2000 code, the program design assumes that a P-Delta
analysis has been performed.

3.3

Limits on Material Strength
The characteristic compressive strength of concrete, fck, should not be less than
20 N/mm2 (TS 3.1.1, TSC 3.2.5.1). The upper limit of the reinforcement yield
stress, fy, is taken as 420 N/mm2 (TSC 3.2.5.3) and the upper limit of the reinforcement shear strength, fyk is taken as 420 N/mm2 (TSC 3.2.5.3).
The program enforces the upper material strength limits for flexure and shear
design of beams and columns or for torsion design of beams. The input material
strengths are taken as the upper limits if they are defined in the material properties as being greater than the limits. The user is responsible for ensuring that
the minimum strength is satisfied.

3-6

Limits on Material Strength

Chapter 3 - Design Process

3.4

Design Strength
The design strength for concrete and steel is obtained by dividing the characteristic strength of the material by a partial factor of safety, γmc and γms. The
values used in the program are as follows:
Partial safety factor for steel, γms = 1.15, and

(TS 6.2.5)

Partial safety factor for concrete, γmc = 1.5.

(TS 6.2.5)

These factors are already incorporated in the design equations and tables in the
code. Although not recommended, the program allows them to be overwritten. If
they are overwritten, the program uses them consistently by modifying the
code-mandated equations in every relevant place.

3.5

Column Design
The program can be used to check column capacity or to design columns. If the
geometry of the reinforcing bar configuration of each concrete column section
has been defined, the program will check the column capacity. Alternatively, the
program can calculate the amount of reinforcing required to design the column
based on provided reinforcing bar configuration. The reinforcement requirements are calculated or checked at a user-defined number of check/design stations along the column span. The design procedure for the reinforced concrete
columns of the structure involves the following steps:
 Generate axial force-biaxial moment interaction surfaces for all of the different concrete section types of the model. A typical biaxial interacting diagram is shown in Figure 3-1. For reinforcement to be designed, the program
generates the interaction surfaces for the range of allowable reinforcement: 1
to 4 percent for Ordinary, Nominal Ductility and High Ductility Moment Resisting frames (TS 7.4.1).
 Calculate the capacity ratio or the required reinforcing area for the factored
axial force and biaxial (or uniaxial) bending moments obtained from each
loading combination at each station of the column. The target capacity ratio is
taken as the Utilization Factor Limit when calculating the required reinforcing
area.

Design Strength

3-7

Concrete Frame Design TS 500-2000

 Design the column shear reinforcement.
The following four sections describe in detail the algorithms associated with this
process.

3.5.1

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

3-8

Column Design

Chapter 3 - Design Process

The coordinates of these points are determined by rotating a plane of linear strain
in three dimensions on the section of the column, as shown in Figure 3-2. The
linear strain diagram limits the maximum concrete strain, εcu, at the extremity of
the section, to 0.003 (TS 7.1). The formulation is based consistently on the
general principles of ultimate strength design (TS 7.1).

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

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 (TS
7.1). The area associated with each reinforcing bar is assumed to be placed at the
actual location of the center of the bar, and the algorithm does not assume any

Column Design

3-9

Concrete Frame Design TS 500-2000

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 a stress
value of 0.85fcd (TS 7.1), as shown in Figure 3-3.

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

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, a, is taken as:
a = k1 c

(TS 7.1)

where c is the depth of the stress block in compression strain and,
k1 = 0.85 − 0.006 ( f ck − 25 ) ,

0.70 ≤ k1 ≤ 0.85.

(TS 7.1, Table 7.1)

The effect of the material factors, γmc and γms, are included in the generation of
the interaction surface.
Default values for γmc and γms are provided by the program but can be overwritten
using the Preferences.
The maximum compressive axial load is limited to Nr(max), where

3 - 10

Column Design

Chapter 3 - Design Process

Nr(max) = 0.6 fck Ag for gravity combinations

(TS 7.4.1)

Nr(max) = 0.5 fck Ag for seismic combinations

3.5.2

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 combination
at a particular location:


Determine the factored moments and forces from the load cases and the
specified load combination factors to give Nd, Md2, and Md3.



Determine the moment magnification factors for the column moments.



Apply the moment magnification factors to the factored moments. Determine if the point, defined by the resulting axial load and biaxial moment set,
lies within the interaction volume.

The factored moments and corresponding magnification factors depend on the
identification of the individual column as either “sway” or “non-sway.”
The following three sections describe in detail the algorithms associated with
that process.

3.5.2.1 Determine Factored Moments and Forces
The loads for a particular design load combination are obtained by applying the
corresponding factors to all of the load cases, giving Nd, Md2, and Md3. The
factored moments are further increased, if required, to obtain minimum eccentricities of (15mm + 0.03h), where h is the dimension of the column in mm in the
corresponding direction (TS 6.3.10). The minimum eccentricity is applied in
both directions simultaneously. The minimum eccentricity moments are amplified for second order effects (TS 6.3.10, 7.6.2).

Column Design

3 - 11

Concrete Frame Design TS 500-2000

3.5.2.2 Determine Moment Magnification Factors
The moment magnification factors are calculated separately for sway (overall
stability effect), βs, and for non-sway (individual column stability effect), βns.
Also, the moment magnification factors in the major and minor directions are, in
general, different (TS 7.6.2.5, 7.6.2.6).
The moment obtained from analysis is separated into two components: the sway
Ms and the non-sway Mns components. The non-sway components, which are
identified by “ns” subscripts, are primarily caused by gravity load. The sway
components are identified by the “s” subscript. The sway moments are primarily
caused by lateral loads and are related to the cause of sidesway.
For individual columns or column-members, the magnified moments about two
axes at any station of a column can be obtained as
M2 = Mns +βs Ms

(TS 7.6.2.5)

The factor βs is the moment magnification factor for moments causing sidesway.
The program takes this factor to be 1 because the component moments Ms and
Mns are assumed to be obtained from a second order elastic ( P-∆ ) analysis (TS
7.6.1). For more information about P-∆ analysis, refer to Appendix A.
For the P-∆ analysis, the analysis combination should correspond to a load of 1.4
(dead load) + 1.6 (live load) (TS 6.2.6). See also White and Hajjar (1991). The
user should use reduction factors for the moments of inertia in the program as
specified in TS 6.3.7. The default moment of inertia factor in this program is 1.
The computed moments are further amplified for individual column stability
effect (TS 7.6.2.5) by the non-sway moment magnification factor, βns, as follows:
Md = βnsM2

(TS 7.6.2.5)

Md is the factored moment to be used in design.
The non-sway moment magnification factor, βns, associated with the major or
minor direction of the column is given by (TS 7.6.2.5)

3 - 12

Column Design

Chapter 3 - Design Process

=
βns

Cm
1 − 1.3

Nd
Nk

Cm =+
0.6 0.4

≥ 1.0

where

(TS 7.6.2.5, Eqn. 7.24)

M1
≥ 0.4,
M2

(TS 7.6.2.5, Eqn. 7.25)

M1 and M2 are the moments at the ends of the column, and M2 is numerically
larger than M1. M1 ⁄ M2 is positive for single curvature bending and negative for
double curvature bending. The preceding expression of Cm is valid if there is no
transverse load applied between the supports. If transverse load is present on the
span, or the length is overwritten, Cm = 1. The user can overwrite Cm on an object-by-object basis.

Nk =

π2 EI

( klu )

(TS 7.6.2.4, Eqn. 7.19)

k is conservatively taken as 1; however, the program allows the user to overwrite
this value (TS7.6.2.2). lu is the unsupported length of the column for the direction of bending considered. The two unsupported lengths are l22 and l33,
corresponding to instability in the minor and major directions of the object,
respectively, as shown in Figure B-1 in Appendix B. These are the lengths
between the support points of the object in the corresponding directions.
Refer to Appendix B for more information about how the program automatically
determines the unsupported lengths. The program allows users to overwrite the
unsupported length ratios, which are the ratios of the unsupported lengths for the
major and minor axes bending to the overall member length.
EI is associated with a particular column direction:

EI =
=
Rm

0.4 Ec I g
1 + Rm

(TS 7.6.2.4, Eqn. 7.21)

maximumfactored axial sustained (dead) load
maximum factored axial total load

≤ 1.0

(TS 7.6.2.4, Eqn. 7.22)

Column Design

3 - 13

Concrete Frame Design TS 500-2000

The magnification factor, βns, must be a positive number and greater than one.
Therefore, Nd must be less than Nk /1.3. If Nd is found to be greater than or equal
to Nk /1.3, a failure condition is declared.
The preceding calculations are performed for major and minor directions separately. That means that βn, βns, Cm, k, lu, EI, and Rm assume different values for
major and minor directions of bending.
If the program assumptions are not satisfactory for a particular member, the user
can explicitly specify values of βn and βns.

3.5.2.3 Determine Capacity Ratio
As a measure of the stress condition of the column, a capacity ratio is calculated.
The capacity ratio is basically a factor that gives an indication of the stress
condition of the column with respect to the capacity of the column.
Before entering the interaction diagram to check the column capacity, the moment magnification factors are applied to the factored loads to obtain Nd, Md2,
and Md3. The point (Nd, Md2, and Md3) 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 interaction
volume, the column is overstressed.
This capacity ratio is achieved by plotting the point L and determining the
location 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 stressed to capacity.
 If OL < OC (or CR < 1), the point lies within the interaction volume and the
column capacity is adequate.
 If OL > OC (or CR > 1), the point lies outside the interaction volume and the
column is overstressed.

3 - 14

Column Design

Chapter 3 - Design Process

The maximum of all values of CR calculated from each design load combination
is reported for each check station of the column along with the controlling Nd,
Md2, and Md3 set and the associated design load combination name.

Figure 3-4 Geometric representation of column capacity ratio

3.5.3 Required Reinforcing Area
If the reinforcing area is not defined, the program computes the reinforcement
that will give a column capacity ratio equal to the Utilization Factor Limit, which
is set to 0.95 by default.

Column Design

3 - 15

Concrete Frame Design TS 500-2000

3.5.4 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 factored forces acting on the section, Nd and Vd. Note that Nd is
needed for the calculation of Vc.
 Determine the shear force, Vc, which can be resisted by concrete alone.
 Calculate the reinforcement steel required to carry the balance.
For High Ductility and Nominal Ductility moment resisting frames, the shear
design of the columns is also based on the maximum probable moment resistance and the nominal moment resistance of the members, respectively, in
addition to the factored shear forces (TS 8.1.4, TSC 3.3.7. 3.7.5). Effects of the
axial forces on the column moment capacities are included in the formulation.
The following three sections describe in detail the algorithms associated with
this process.

3.5.4.1 Determine Section Forces
 In the design of the column shear reinforcement of an Ordinary Moment
Resisting concrete frame, the forces for a particular design load combination,
namely, the column axial force, Nd, and the column shear force, Vd, in a
particular direction are obtained by factoring the load cases with the
corresponding design load combination factors.
 In the shear design of High Ductility and Nominal Ductility Moment Resisting
frames (i.e., seismic design), the shear capacity of the column is checked for
capacity shear in addition to the requirement for the Ordinary Moment
Resisting frames. The maximum design shear force (force to be considered in
the design) in the column, Vd, is determined from consideration of the
maximum forces that can be generated at the column. Two different capacity
shears are calculated for each direction (major and minor). The first is based
on the maximum probable moment strength of the column, while the second is
computed from the maximum probable moment strengths of the beams

3 - 16

Column Design

Chapter 3 - Design Process

framing into the column. The design strength is taken as the minimum of these
two values, but never less than the factored shear obtained from the design
load combination.

{

}

=
Vd min Vec ,Veb ≥ Vd ,factored

(TSC 3.3.7.1, Eqn. 3.5)

where

Vec = Capacity shear force of the column based on the maximum probable
maximum flexural strengths of the two ends of the column.

Veb = Capacity shear force of the column based on the maximum probable
moment strengths of the beams framing into the column.
In calculating the capacity shear of the column, Vec , the maximum probable
flexural strength at the two ends of the column is calculated for the existing
factored axial load. Clockwise rotation of the joint at one end and the associated
counter-clockwise rotation of the other joint produces one shear force. The reverse situation produces another capacity shear force, and both of these situations are checked, with the maximum of these two values taken as the Vec .
For each design load combination, the factored axial load, Nd, is calculated.
Then, the maximum probable positive and negative moment strengths,
+
−
, of the column in a particular direction under the influence of the
M pr
and M pr
axial force Nd is calculated using the uniaxial interaction diagram in the corresponding direction. Then the capacity shear force is obtained by applying the
calculated maximum probable ultimate moment strengths at the two ends of the
column acting in two opposite directions. Therefore, Vec is the maximum of

Vec1 and Vec2 ,

{

}

=
Vec max Vec1 , Vec2 ≤ 0.22 f cd Aw

(TSC 3.3.7.1, 3.3.7.5)

where,

V =
c
e1

M I− + M J+
L

(TSC 3.3.7.1, Fig. 3.3,3.5)

Column Design

3 - 17

Concrete Frame Design TS 500-2000

Vec2 =

M I+ + M J−
,
L

(TSC 3.3.7.1, Fig. 3.3, 3.5)

M I+ , M I− = Positive and negative probable maximum moment strengths

+
pr

)

−
at end I of the column using a steel yield stress
, M pr

value of fyd and a concrete stress fcd,

M J+ , M J− = Positive and negative probable maximum moment strengths

+
pr

)

−
at end J of the column using a steel yield stress
, M pr

value of fyd and a concrete stress fcd, and
L

= Clear span of the column.

If the column section was identified as a section to be checked, the user-specified
reinforcing is used for the interaction curve. If the column section was identified
as a section to be designed, the reinforcing area envelope is calculated after
completing the flexural (P-M-M) design of the column. This envelope of reinforcing area is used for the interaction curve.
If the column section is a variable (non-prismatic) section, the cross-sections at
the two ends are used, along with the user-specified reinforcing or the envelope
of reinforcing for check or design sections, as appropriate. If the user overwrites
the length factor, the full span length is used. However, if the length factor is not
overwritten by the user, the clear span length will be used. In the latter case, the
maximum of the negative and positive moment capacities will be used for both
the positive and negative moment capacities in determining the capacity shear.
In calculating the capacity shear of the column based on the flexural strength of
the beams framing into it, Veb , the program calculates the maximum probable
positive and negative moment strengths of each beam framing into the top joint
of the column. Then the sum of the beam moments is calculated as a resistance to
joint rotation. Both clockwise and counter-clockwise rotations are considered
separately, as well as the rotation of the joint in both the major and minor axis
directions of the column. The shear force in the column is determined assuming
that the point of inflection occurs at mid-span of the columns above and below
the joint. The effects of load reversals are investigated and the design is based on
the maximum of the joint shears obtained from the two cases.

3 - 18

Column Design

Chapter 3 - Design Process

{

Veb = max Veb1 , Veb2

}

(TSC 3.3.7.1, Fig. 3.3, 3.5)

where,

Veb1 = Column capacity shear based on the maximum probable flexural
strengths of the beams for clockwise joint rotation,

Veb2 = Column capacity shear based on the maximum probable flexural
strengths of the beams for counter-clockwise joint rotation,

Veb1 =

M r1
,
H

Veb2 =

Mr2
,
H

M r1 = Sum of beam moment resistances with clockwise joint rotations,
M r 2 = Sum of beam moment resistances with counter-clockwise joint rotations, and

Distance between the inflection points, which is equal to the mean
height of the columns above and below the joint. If there is no column at
the top of the joint, the distance is taken as one-half of the height of the
column at the bottom of the joint.

For the case shown in Figure 3-5, Ve1 can be calculated as follows:

Veb1 ==

M rL + M rR
H

It should be noted that the points of inflection shown in Figure 3-5 are taken at
midway between actual lateral support points for the columns, and H is taken as
the mean of the two column heights. If no column is present at the top of the
joint, H is taken to be equal to one-half the height of the column below the joint.
The expression Veb is applicable for determining both the major and minor
direction shear forces. The calculated shear force is used for the design of the
column below the joint. When beams are not oriented along the major and minor
Column Design

3 - 19

Concrete Frame Design TS 500-2000

axes of the column, the appropriate components of the flexural capacities are
used. If the beam is oriented at an angle θ with the column major axis, the
appropriate component—Mpr cosθ or Mpr sinθ—of the beam flexural strength is
used in calculating Mr1 and Mr2. Also the positive and negative moment
capacities are used appropriately based on the orientation of the beam with
respect to the column local axis.
 For Nominal Ductility Moment Resisting frames, the shear capacity of the
column is same as for Ordinary Moment Resisting frames.
Vd ≤ 0.22 Aw f cd

(TSC 3.3.7.5, 3.7.5.3, Eqn. 3.5)

Figure 3-5 Column shear force Vd

3 - 20

Column Design

Chapter 3 - Design Process

where, Ve is the capacity shear force in the column determined from the
probable moment capacities of the column and the beams framing into it.


Ve = min Vec ,Veb 



(TSC 3.4.5.1, 3.4.5.2)

where, Vec is the capacity shear force of the column based on the probable
flexural strength of the column ends alone. Veb is the capacity shear force of
the column based on the probable flexural strengths of the beams framing into
it. The calculation of Vec and Veb is the same as that described for High Ductility Moment Resisting frames.
 For Ordinary Moment Resisting frames, the shear capacity for those columns
is checked based on the factored shear force.

3.5.4.2 Determine Concrete Shear Capacity
Given the design force set Nd and Vd, the shear force carried by the concrete, Vc,
is calculated as follows:
 If the column is subjected to axial loading, Nd is positive in this equation
regardless of whether it is a compressive or tensile force,

γ Nd
=
Vcr 0.65 f ctd bw d  1 +

Ag



 ,


(TS 8.1.3, Eqn. 8.1)

where,

0.07 for axial compression

γ = −0.3for axial tension
0 when tensile stress < 0.5 MPa
Vc = 0.8Vcr ,

(TS 8.1.4, Eqn. 8.4)

 For High Ductility Moment Resisting concrete frame design, if the factored
axial compressive force, Nd, including the earthquake effect, is small
N d < 0.05 f ck Ag and if the shear force contribution from earthquake, VE, is

(

)

Column Design

3 - 21

Concrete Frame Design TS 500-2000

more than half of the total factored maximum shear force Vd (VE ≥ 0.5Vd )
over the length of the member, and if the station is within a distance lo from the
face of the joint, then the concrete capacity Vc is taken as zero (TSC 3.7.6).
Note that for capacity shear design, VE is considered to be contributed solely
by earthquakes, so the second condition is automatically satisfied. The length
lo is taken as the section width, one-sixth the clear span of the column, or
500 mm, whichever is larger (TSC 3.3.4.1, 3.3.7.6).
d'
DIRECTION
OF SHEAR
FORCE

A cv

RECTANGULAR

DIRECTION
OF SHEAR
FORCE

A cv

SQUARE WITH CIRCULAR REBAR

DIRECTION
OF SHEAR
FORCE

A cv

CIRCULAR

Figure 3-6 Shear stress area, Acv

3.5.4.3 Determine Required Shear Reinforcement
Given Vd and Vc, the required shear reinforcement in the form of stirrups or ties
within a spacing, s, is given for rectangular and circular columns by the following:
3 - 22

Column Design

Chapter 3 - Design Process

 The shear force is limited to a maximum of
Vmax = 0.22 f cd Aw

(TS 8.1.5b, TSC 3.3.7.5)

 The required shear reinforcement per unit spacing, Av /s, is calculated as
follows:
If Vd ≤ Vcr ,
Asw
f
= 0.3 ctd bw ,
s
f ywd

(TS 8.1.5, Eqn. 8.6)

else if Vcr < Vd ≤ Vmax ,
Asw (Vd − Vc )
,
=
s
f ywd d

(TS 8.1.4, Eqn. 8.5)

Asw
f
≥ 0.3 ctd bw
s
f ywd

(TS 8.1.5, Eqn. 8.6)

else if Vd > Vmax ,
a failure condition is declared.

(TS 8.1.5b)

In the preceding expressions, for a rectangular section, bw is the width of the
column, d is the effective depth of the column. For a circular section, bw is replaced with D, which is the external diameter of the column, and d is replaced
with 0.8D and Aw is replaced with the gross area.
If Vd exceeds its maximum permitted value Vmax, the concrete section size should
be increased (TS 8.1.5b).
The maximum of all calculated Asw s 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 reinforcement requirements reported by the program are
based purely on shear strength consideration. Any minimum stirrup require-

Column Design

3 - 23

Concrete Frame Design TS 500-2000

ments to satisfy spacing considerations or transverse reinforcement volumetric
considerations must be investigated independently of the program by the user.

3.6

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 check/design 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

3.6.1

Design Beam Flexural Reinforcement
The beam top and bottom flexural steel is designed at check/design stations
along the beam span. The following steps are involved in designing the flexural
reinforcement for the major moment for a particular beam for a particular section:
 Determine the maximum factored moments
 Determine the reinforcing steel

3.6.1.1 Determine Factored Moments
In the design of flexural reinforcement of Special, Intermediate, or Ordinary
Moment Resisting concrete frame beams, the factored moments for each design
load combination at a particular beam section are obtained by factoring the

3 - 24

Beam Design

Chapter 3 - Design Process

corresponding moments for different load cases with the corresponding design
load combination factors.
The beam section is then designed for the factored moments obtained from all 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. Negative
moments produce top steel. In such cases, the beam is always designed as a
rectangular section.

3.6.1.2 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 has the option of avoiding the compression
reinforcement by increasing the effective depth, the width, or the grade of concrete.
The design procedure is based on the simplified rectangular stress block, as
shown in Figure 3-7 (TS 7.1). When the applied moment exceeds the moment
capacity at this design condition, 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 does not exceed ( 0.1 f ck Ag ) (TS 7.3); hence,
all of the beams are designed ignoring axial force.
3.6.1.2.1

Design for Rectangular Beam

In designing for a factored negative or positive moment, Md (i.e., designing top
or bottom steel), the depth of the compression block is given by a (see Figure
3-7), where,
a =−
d
d2 −

2 Md
0.85 f cd b

(TS 7.1)

Beam Design

3 - 25

Concrete Frame Design TS 500-2000

Figure 3-7 Rectangular beam design

The maximum depth of the compression zone, cb, is calculated based on the
compressive strength of the concrete and the tensile steel tension using the following equation (TS 7.1):
cb =

ε cu Es

ε cu Es + f yd

(TS 7.1)

The maximum allowable depth of the rectangular compression block, amax, is
given by
amax = 0.85k1cb

(TS 7.11, 7.3, Eqn. 7.4)

where k1 is calculated as follows:
k1 = 0.85 − 0.006 ( f ck − 25 ) ,

0.70 ≤ k1 ≤ 0.85.

(TS 7.1, Table 7.1)

 If a ≤ amax, the area of tensile steel reinforcement is then given by:

3 - 26

Beam Design

Chapter 3 - Design Process

As =

Md
a

f yd  d − 
2


This steel is to be placed at the bottom if Md is positive, or at the top if Md is
negative.
 If a > amax, compression reinforcement is required (TS 7.1) and is calculated
as follows:
The compressive force developed in concrete alone is given by:
C = 0.85 f cd bamax ;

(TS 7.1)

the moment resisted by concrete compression and tensile steel is:
a 

M
=
C  d − max  .
dc
2 


Therefore, the moment resisted by compression steel and tensile steel is:
M=
M d − M dc .
ds

So the required compression steel is given by:
As′ =

(

M ds
σ's

− 0.85 f cd

) ( d − d ′)

, where

c − d′
σ's = Es εcu  max
 ≤ f yd .
 cmax 

(TS 7.1)

The required tensile steel for balancing the compression in concrete is:
As1 =
f yd

M ds
, and
amax 

d
−

2 


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

Beam Design

3 - 27

Concrete Frame Design TS 500-2000

Therefore, the total tensile reinforcement is As = As1 + As2, and the total
compression reinforcement is
. As is to be placed at the bottom and
is
is to be placed at the bottom
to be placed at the top if Md is positive, and
and As is to be placed at the top if Md is negative.
3.6.1.2.2

Design for T-Beam

In designing a T-beam, a simplified stress block, as shown in Figure 3-8, is
assumed if the flange is under compression, i.e., if the moment is positive. If the
moment is negative, the flange comes under tension, and the flange is
ignored. In that case, a simplified stress block similar to that shown in Figure 3-8
is assumed in the compression side (TS 7.1).

Figure 3-8 T-beam design

Flanged Beam Under Negative Moment
In designing for a factored negative moment, Md (i.e., designing top steel), the
calculation of the steel area is exactly the same as described for a rectangular
beam, i.e., no T-beam data is used.

3 - 28

Beam Design

Chapter 3 - Design Process

Flanged Beam Under Positive Moment
If Md > 0, the depth of the compression block is given by
a =−
d
d2 −

2M d
.
0.85 f cd b f

The maximum depth of the compression zone, cb, is calculated based on the
compressive strength of the concrete and the tensile steel tension using the following equation (TS 7.1):
cb =

ε c Es

ε cu Es + f yd

(TS 7.1)

The maximum allowable depth of the rectangular compression block, amax, is
given by
amax = 0.85k1cb

(TS 7.11, 7.3, Eqn. 7.4)

where k1 is calculated as follows:
k1 = 0.85 − 0.006 ( f ck − 25 ) ,

0.70 ≤ k1 ≤ 0.85.

(TS 7.1, Table 7.1)

If a ≤ ds, the subsequent calculations for As are exactly the same as previously
defined for the Rectangular section design. However, in that case, the width of
the beam is taken as bf, as shown in Figure 3-8. Compression reinforcement is
required if a > amax.
 If a > ds, the calculation for As has two parts. The first part is for balancing the
compressive force from the flange, Cf , and the second part is for balancing the
compressive force from the web, Cw, as shown in Figure 3-8. Cf is given by:

(

)

=
C f 0.85 f cd b f − bw × min ( d s , amax )

Therefore, As1 =

Cf
f yd

(TS 7.1)

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

given by:

min ( d s , amax ) 
=
M df C f  d −

2



Beam Design

3 - 29

Concrete Frame Design TS 500-2000

Therefore, the balance of the moment, Md, to be carried by the web is given by:
M=
M d − M df .
dw

The web is a rectangular section of dimensions bw and d, for which the design
depth of the compression block is recalculated as:
a1 =−
d
d2 −

2 M dw
0.85 f cd bw

(TS 7.1)

 If a1 ≤ amax (TS 7.1), the area of tensile steel reinforcement is then given by:
As 2 =

M dw
, and
a1 

f yd  d − 
2


A
=
As1 + As 2 .
s

This steel is to be placed at the bottom of the T-beam.
 If a1 > amax, compression reinforcement is required and is calculated as
follows:
The compression force in the web concrete alone is given by:
C = 0.85 f cd bw amax .

(TS 7.1)

Therefore the moment resisted by the concrete:
a

M
=
C  d − max
dc
2



;


the tensile steel for balancing compression in the web concrete is:
As 2 =
f yd

M dc
;
amax 

d
−

2 


the moment resisted by compression steel and tensile steel is:

3 - 30

Beam Design

Chapter 3 - Design Process

M
=
M dw − M dc .
ds
Therefore, the compression steel is computed as:
As′ =

(

M ds
σ's

− 0.85 f cd

) ( d − d ′)

, where

c − d′
σ's = Es εcu  max
 ≤ f yd , and
 cmax 

(TS 7.1)

the tensile steel for balancing the compression steel is:
As 3 =

M ds
.
f yd ( d − d ′ )

The total tensile reinforcement is As = As1 + As 2 + As 3 , and the total compression reinforcement is As′ . As is to be placed at the bottom and As′ is to be
placed at the top.
3.6.1.2.3

Minimum and Maximum Tensile Reinforcement

The minimum and maximum flexural tensile steel required in a beam section is
given by the following limits:
0.8 f ctd
bw d
f yd

(minimum)

As − As' ≤ 0.85ρb bd .

(maximum)

As ≥

(TS 7.3, Eqn. 7.3)

An upper limit of 0.02 times the gross web area on both the tension reinforcement and the compression reinforcement is imposed as follows:
0.02bd Rectangular Beam
As ≤ 
0.02bw d T-Beam
0.02bd Rectangular Beam
As′ ≤ 
0.02bw d T-Beam

Beam Design

3 - 31

Concrete Frame Design TS 500-2000

3.6.1.2.4

Special Consideration for Seismic Design

For High Ductility and Nominal Ductility Resisting concrete frames (seismic
design), the beam design satisfies the following additional conditions (see also
Table 3-1):
Table 3-1: Design Criteria
Type of
Check/
Design

Nominal Ductility
Moment Resisting
Frames
(Seismic)

High Ductility
Moment Resisting
Frames
(Seismic)

Specified
Combinations

1% < ρ < 4%

1% < ρ <4%

Specified
Combinations

Ordinary
Moment Resisting
Frames
(Non-Seismic)

Column Check (interaction)
Specified
Combinations
Column Design (interaction)

Column Shears
Specified
Combinations

Column Capacity Shear
Vc = 0 (conditional)
Beam Design Flexure
Specified
Combinations

Specified
Combinations

ρ ≤ 0.02

ρ≥

0.8 f ctd
f yd

ρ≥

0.8 f ctd
f yd

ρ≥

0.8 f ctd
f yd

Beam Minimum Moment Override Check
No Requirement

1 −
+
M d ,end ≥ M d ,end zone 1, 2

+
−
M d ,end ≥ 0.3M d ,end zone 3, 4

{

}

1
+
+
−
M d ,span ≥ max M d ,M d
end
4
1
−
+
−
M
≥ max M d ,M d
d ,span
max
4

{

3 - 32

Beam Design

}

{

1
+
+
−
M d ,span ≥ max M d ,M d
end
4
1
−
+
−
M
≥ max M d ,M d
d ,span
max
4

{

}

Chapter 3 - Design Process

Table 3-1: Design Criteria
Type of
Check/
Design

Ordinary
Moment Resisting
Frames
(Non-Seismic)

Nominal Ductility
Moment Resisting
Frames
(Seismic)

High Ductility
Moment Resisting
Frames
(Seismic)

Specified
Combinations

Beam Design Shear
Specified
Combinations

Beam Capacity Shear (VE)
plus VD+L
Vc = 0 (conditional)

Joint Design
No Requirement

No Requirement

To be checked for shear

No Requirement

To be checked for shear

Beam/Column Capacity Ratio
No Requirement

 The minimum longitudinal reinforcement refers to tension reinforcement.
Longitudinal reinforcement shall be provided at both the top and bottom. Any
of the top and bottom reinforcement shall not be less than As(min) (TS 7.3).
0.8 f ctd
As ≥ As (min) =
bw d
f yd

(TS 7.3)

 The beam flexural steel is limited to a maximum given by
As ≤ 0.02 bw d .

(TS 7.3)

 At any end (support) of the beam, the beam positive moment capacity (i.e.,
associated with the bottom steel) would not be less that 50 percent of the beam
negative moment capacity (i.e., associated with the top steel) at that end (TSC
3.4.2.3) in Zones 1 and 2 and 30 percent of the beam negative moment
capacity in Zones 3 and 4.
 Neither the negative moment capacity nor the positive moment capacity at any
of the sections within the beam would be less than 1/4 of the maximum of
positive or negative moment capacities of any of the beam end (support)
stations (TSC 3.4.3.1a).

Beam Design

3 - 33

Concrete Frame Design TS 500-2000

3.6.2 Design Beam Shear Reinforcement
The shear reinforcement is designed for each design load combination at a
user-defined number of stations along the beam span. The following steps are
involved in designing the shear reinforcement for a particular station because of
beam major shear:
 Determine the factored shear force, Vd.
 Determine the shear force, Vc, that can be resisted by the concrete.
 Determine the reinforcement steel required to carry the balance.
For high ductility moment frames, the shear design of the beams is also based on
the maximum probable moment strengths and the nominal moment strengths of
the members, respectively, in addition to the factored design. Effects of axial
forces on the beam shear design are neglected.
The following three sections describe in detail the algorithms associated with
this process.

3.6.2.1 Determine Shear Force and Moment
 In the design of the beam shear reinforcement of nominal ductility concrete
frame, 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.
 In the design of High Ductility Moment Resisting concrete frames (i.e.,
seismic design), the shear capacity of the beam is also checked for the capacity
shear resulting from the maximum probable moment strength at the ends
along with the factored gravity load. This check is performed in addition to the
design check required for Ordinary moment resisting frames. The capacity
shear force, Vp, is calculated from the maximum probable moment strength of
each end of the beam and the gravity shear forces. The procedure for
calculating the design shear force in a beam from the maximum probable
moment strength is the same as that described for a column earlier in this
chapter. See Table 3-1 for a summary.
The design shear force is then given by (TSC 3.4.5.3):

3 - 34

Beam Design

Chapter 3 - Design Process

Vd = max {Ve1 ,Ve 2 }

(TSC 3.4.5.3, Fig 3.9)

V=
V p1 + VG +Q
e1

(TSC 3.4.5.3, Fig 3.9)

V=
V p 2 + VG +Q
e2

(TSC 3.4.5.3, Fig 3.9)

where Vp is the capacity shear force obtained by applying the calculated maximum probable ultimate moment capacities at the two ends of the beams acting in
two opposite directions. Therefore, Vp is the maximum of Vp1 and Vp2, where
Vp1 =

M I− + M J+
, and
L

Vp 2 =

M I+ + M J−
, where
L

M I− = Moment capacity at end I, with top steel in tension, using a steel
yield stress fyd and a concrete stress fcd.

M J+ = Moment capacity at end J, with bottom steel in tension, using a
steel yield stress fyd and a concrete stress fcd.

M I+ = Moment capacity at end I, with bottom steel in tension, using a
steel yield stress fyd and a concrete stress fcd.

M J− = Moment capacity at end J, with top steel in tension, using a steel
yield stress fyd and a concrete stress fcd.
L

= Clear span of beam.

If the reinforcement area has not been overwritten for ductile beams, the value of
the reinforcing area envelope is calculated after completing the flexural design
of the beam for all the design load combinations. Then this enveloping reinforcing area is used in calculating the moment capacity of the beam. If the reinforcing area has been overwritten for ductile beams, this area is used in
calculating the moment capacity of the beam. If the beam section is a variable
cross-section, the cross-sections at the two ends are used along with the
user-specified reinforcing or the envelope of reinforcing, as appropriate. If the

Beam Design

3 - 35

Concrete Frame Design TS 500-2000

user overwrites the major direction length factor, the full span length is used.
However, if the length factor is not overwritten, the clear length will be used. In
the latter case, the maximum of the negative and positive moment strengths will
be used in determining the capacity shear.
VG+Q is the contribution of shear force from the in-span distribution of gravity
loads, with the assumption that the ends are simply supported.
The computation of the design shear force in a Nominal Ductility Moment Resisting frame is the same as described for columns earlier in this chapter. See
Table 3-1 for a summary.

3.6.2.2 Determine Concrete Shear Capacity
Given the design force set Nd and Vd, the shear force carried by the concrete, Vc,
is calculated as follows:
 If the beam is subjected to axial loading, Nd is positive in this equation
regardless of whether it is a compressive or tensile force,

γN d
Vcr 0.65 f ctd bw d  1 +
=

Ag



 ,


(TS 8.1.3, Eqn. 8.1)

where,

 0.07 for axial compression

γ = −0.3 for axial tension
 0
when tensile stress < 0.5 MPa

Vc = 0.8Vcr ,

(TS 8.1.4, Eqn. 8.4)

(

)

3 - 36

Beam Design

Chapter 3 - Design Process

earthquakes, so the second condition is automatically satisfied. The length lo is
taken as the section width, one-sixth the clear span of the column, or 500 mm,
whichever is larger (TSC 3.3.4.1, 3.3.7.6).

3.6.2.3 Determine Required Shear Reinforcement
Given Vd and Vc, the required shear reinforcement in the form of stirrups or ties
within a spacing, s, is given for rectangular and circular columns by the following:
 The shear force is limited to a maximum of
Vmax = 0.22 f cd Aw

(TS 8.1.5b, TSC 3.3.7.5)

 The required shear reinforcement per unit spacing, Av /s, is calculated as follows:
If Vd ≤ Vcr ,
Asw
f
= 0.3 ctd bw ,
s
f ywd

(TS 8.1.5, Eqn. 8.6)

else if Vcr < Vd ≤ Vmax ,
Asw (Vd − Vc )
,
=
s
f ywd d

(TS 8.1.4, Eqn. 8.5)

Asw
f
≥ 0.3 ctd bw
s
f ywd

(TS 8.1.5, Eqn. 8.6)

else if Vd > Vmax ,
a failure condition is declared.

(TS 8.1.5b)

If Vd exceeds its maximum permitted value Vmax, the concrete section size should
be increased (TS 8.1.5b).
Note that if torsion design is performed and torsion rebar is needed, the equation
given in TS 8.1.5 does not need to be satisfied independently. See the next section Design of Beam Torsion Reinforcement for details.
Beam Design

3 - 37

Concrete Frame Design TS 500-2000

The maximum of all of the calculated Asw/s values, obtained from each design
load combination, is reported along with the controlling shear force and associated design load combination name.
The beam shear reinforcement requirements reported by the program are based
purely on shear strength considerations. Any minimum stirrup requirements to
satisfy spacing and volumetric consideration must be investigated independently
of the program by the user.

3.6.3 Design Beam Torsion Reinforcement
The torsion reinforcement is designed for each design load combination at a
user-defined number of stations along the beam span. The following steps are
involved in designing the shear reinforcement for a particular station because of
beam torsion:
 Determine the factored torsion, Td.
 Determine special section properties.
 Determine critical torsion capacity.
 Determine the reinforcement steel required.
Note that the torsion design can be turned off by choosing not to consider torsion
in the Preferences.

3.6.3.1 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 (TS 8.2).
In a statistically indeterminate structure where redistribution of the torsional
moment in a member can occur due to redistribution of internal forces upon
cracking, the design Td is permitted to be reduced in accordance with code (TS
8.2.3). However, the program does not try to redistribute the internal forces and
to reduce Td. If redistribution is desired, the user should release the torsional
DOF in the structural model.
3 - 38

Beam Design

Chapter 3 - Design Process

3.6.3.2 Determine Special Section Properties
For torsion design, special section properties such as Ae, S and ue are calculated.
These properties are described as follows (TS 8.2.4).
Ae = Area enclosed by centerline of the outermost closed transverse
torsional reinforcement
S

= Shape factor for torsion

ue = Perimeter of area Ae
In calculating the section properties involving reinforcement, such as Aov /s,
Aot /s, and ue, it is assumed that the distance between the centerline of the
outermost closed stirrup and the outermost concrete surface is 30 mm. This is
equivalent to 25-mm clear cover and a 10-mm-diameter stirrup placement. For
torsion design of T-beam sections, it is assumed that placing torsion reinforcement in the flange area is inefficient. With this assumption, the flange is ignored
for torsion reinforcement calculation. However, the flange is considered during
Tcr calculation. With this assumption, the special properties for a Rectangular
beam section are given as follows:
Ae =

( b − 2c )( h − 2c ) ,

ut = 2 ( b − 2c ) + 2 ( h − 2c ) ,
S

= x2y/3

(TS 8.2.4)
(TS 8.2.4)
(TS 8.2.4 )

where, the section dimensions b, h and c are shown in Figure 3-9. Similarly, the
special section properties for a T-beam section are given as follows:
Ae =

( bw − 2c )( h − 2c ) ,

ut = 2 ( h − 2c ) + 2 ( bw − 2c ) ,
S

= Σx2y/3

(TS 8.2.4)
(TS 8.2.4)
(TS 8.2.4)

where the section dimensions bw, h and c for a T-beam are shown in
Figure 3-9.

Beam Design

3 - 39

Concrete Frame Design TS 500-2000

b − 2c

h − 2c

c
bw − 2c

bw
Closed Stirrup in
Rectangular Beam

Closed Stirrup in
T-Beam Section

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

3.6.3.3 Determine Critical Torsion Capacity
Design for torsion may be ignored if either of the following is satisfied:
(i) The critical torsion limits, Tcr, for which the torsion in the section can be
ignored, is calculated as follows:
Td ≤ Tcr =
0.65 f ctd S

(TS 8.2.3, Eqn 8.12 )

In that case, the program reports shear reinforcement based on TS 8.1.5,
Eqn. 8.6. i.e.,
Asw
f
≥ 0.3 ctd bw
s
f ywd

(TS 8.1.5, Eqn. 8.6)

(ii) When design shear force and torsional moment satisfy the following equation, there is no need to compute torsional stirrups. However, the minimum
stirrups and longitudinal reinforcement shown below must be provided:
2

 Vd   Td 

 +
 ≤1
 Vcr   Tcr 

where Tcr is computed as follows:
3 - 40

Beam Design

(TS 8.2.2, Eqn 8.10)

Chapter 3 - Design Process

Tcr = 1.35 f ctd S

(TS 8.2.2, Eqn 8.11)

The required minimum closed stirrup area per unit spacing, Ao /s, is calculated
as:
Ao
f  1.3Td 
(TS 8.2.4, Eqn. 8.17)
=
0.15 ctd 1 +
 bw
s
f ywd  Vd bw 
Td
≤ 1.0 and for the case of statistically indeterminate structure
Vd bw
where redistribution of the torsional moment in a member can occur due to
redistribution of internal forces upon cracking, minimum reinforcement will be
obtained by taking Td equal to Tcr .

In Eqn. 8.17,

And the required minimum longitudinal rebar area, Asl, is calculated as:
Asl =

Td ue
.
2 Ae f yd

(TS 8.2.5, Eqn. 8.18 )

3.6.3.4 Determine Torsion Reinforcement
If the factored torsion Td is less than the threshold limit, Tcr, torsion can be safely
ignored (TS 8.2.3), when the torsion is not required for equilibrium. In that case,
the program reports that no torsion is required. However, if Td exceeds the
threshold limit, Tcr, it is assumed that the torsional resistance is provided by
closed stirrups, longitudinal bars, and compression diagonals (TS 8.2.4 and
8.2.5).
If Td > Tcr, the required longitudinal rebar area, Asl, is calculated as:
Asl =

Td ue
2 Ae f yd

(TS 8.2.4, Eqn. 8.16 )

and the required closed stirrup area per unit spacing, Aot /s, is calculated as:
Ao Aov Aot
=
+
s
s
s

(TS 8.2.4, Eqn. 8.13)

Beam Design

3 - 41

Concrete Frame Design TS 500-2000

Aov (Vd − Vc )
=
s
df ywd

(TS 8.2.4, Eqn. 8.14)

Aot
Td
=
s
2 Ae f ywd

(TS 8.2.4, Eqn. 8.15)

where, the minimum value of Ao /s is taken as:
Ao
f
=
0.15 ctd
s
f ywd

where,

 1.3Td
1 +
 Vd bw


 bw


(TS 8.2.4, Eqn. 8.17)

1.3Td
≤ 1.0.
Vd bw

An upper limit of the combination of Vd and Td that can be carried by the section
also is checked using the following equation.
Td Vd
+
≤ 0.22 f cd .
S bw d

(TS 8.2.5b, Eqn. 8.19)

The maximum of all the calculated Asl and Ao s 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
purely 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.

3.7

Joint Design
To ensure that the beam-column joint of High Ductility Moment Resisting
frames possesses adequate shear strength, the program performs a rational
analysis of the beam-column panel zone to determine the shear forces that are
generated in the joint. The program then checks this against design shear
strength.

3 - 42

Joint Design

Chapter 3 - Design Process

Only joints having a column below the joint are checked. The material properties
of the joint are assumed to be the same as those of the column below the joint.
The joint analysis is completed in the major and the minor directions of the
column. The joint design procedure involves the following steps:
 Determine the panel zone design shear force, Veh
 Determine the effective area of the joint
 Check panel zone shear stress
The algorithms associated with these three steps are described in detail in the
following three sections.

3.7.1 Determine the Panel Zone Shear Force
Figure 3-10 illustrates the free body stress condition of a typical beam-column
intersection for a column direction, major or minor.
The force Veh is the horizontal panel zone shear force that is to be calculated.
The forces that act on the joint are Nd, Vkol, M dL and M dR . The forces Nd and Vkol
are axial force and shear force, respectively, from the column framing into the
top of the joint. The moments M dL , and M dR are obtained from the beams
framing into the joint. The program calculates the joint shear force Veh by
resolving the moments into C and T forces. Noting that TL = CL and TR = CR,

Veh = TL + TR − Vkol
The location of C or T forces is determined by the direction of the moment. The
magnitude of C or T forces is conservatively determined using basic principles
of ultimate strength theory (TS 7.1).
The moments and the forces from 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, thereby contributing force components to the analysis.

Joint Design

3 - 43

Concrete Frame Design TS 500-2000

Figure 3-10 Beam-column joint analysis

3 - 44

Joint Design

Chapter 3 - Design Process

In the design of Highly Ductile Moment Resisting concrete frames, the evaluation of the design shear force is based on the moment capacities (with reinforcing steel overstrength factor, α, where, α = 1.25) of the beams framing into
the joint (TSC 3.5.2.1). The C and T forces are based on these moment capacities. The program calculates the column shear force Vkol from the beam moment
capacities, as follows (see Figure 3-5):

Vkol

M dL + M dR
=
H

It should be noted that the points of inflection shown on Figure 3-5 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.
The effects of load reversals, as illustrated in Case 1 and Case 2 of Figure 3-10,
are investigated and the design is based on the maximum of the joint shears
obtained from the two cases.

3.7.2

Determine the Effective Area of Joint
The joint area that resists the shear forces is assumed always to be rectangular in
plan view. The dimensions of the rectangle correspond to the major and minor
dimensions of the column below the joint, except if the beam framing into the
joint is very narrow. The effective width of the joint area to be used in the calculation is limited to the width of the beam plus the depth of the column. The
area of the joint is assumed not to exceed the area of the column below. The joint
area for joint shear along the major and minor directions is calculated separately
(TSC 3.5.1).
It should be noted that if the beam frames into the joint eccentrically, the preceding assumptions may not be conservative and the user should investigate the
acceptability of the particular joint.

Joint Design

3 - 45

Concrete Frame Design TS 500-2000

3.7.3

Check Panel Zone Shear Stress
The panel zone shear stress is evaluated by dividing the shear force by the
effective area of the joint and comparing it with the following design shear
strengths (TSC 3.5.2.2).
0.60 f cd for joints confined on all four sides,
v=
0.45 f cd for all other joints

(TSC 3.5.2.2)

A beam that frames into a face of a column at the joint is considered in this
program to provide confinement to the joint if at least three-quarters of the face
of the joint is covered by the framing member (TSC 3.5.2.2).
For joint design, the program reports the joint shear, the joint shear stress, the
allowable joint shear stress, and a capacity ratio.

3.7.4

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 high ductility frames, at a particular joint for a particular column direction, major or minor (TSC 3.3.5):

∑M

≥

6
∑ M rb
5

(TSC 3.3.5)

= Sum of probable flexural strengths of columns framing into the
joint, evaluated at the faces of the joint. Individual column
flexural strength is calculated for the associated factored axial
force.

∑M

= Sum of probable 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
illustrated in Figure 3-10 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

3 - 46

Joint Design

Chapter 3 - Design Process

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, N d , 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 influence of the corresponding axial load is then determined separately for the
major and minor directions of the column, using the uniaxial column interaction
diagram; see Figure 3-11. The moment capacities of the two columns are added
to give the capacity summation for the corresponding design load combination.
The maximum capacity summations obtained from all of the design load combinations is used for the beam-column capacity ratio.
The beam-column capacity ratio is determined for a beam-column joint only
when the following conditions are met:
 the frame is a High Ductility moment resisting frame
 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

( ∑ M ∑ M ) are reported only for
rb

high ductility frames involving seismic design load combinations. If this ratio is
greater than 5/6, a warning message is printed in the output. The ratio is also

( 5)∑ M

reported in the form of 6

M rc and ∑ M rc ∑ M rb .

Joint Design

3 - 47

Concrete Frame Design TS 500-2000

Figure 3-11 Moment capacity Md at a given axial load Nd

3 - 48

Joint Design

Chapter 4
Design Output

4.1

Overview
The program creates design output in different formats – graphical display,
tabular output, and member specific detailed design information.
The graphical display of design output includes input and output design information. Input design information includes design section labels, K-factors, live
load reduction factors, and other design parameters. The output design information includes longitudinal reinforcing, shear reinforcing, torsional reinforcing
and column capacity ratios. All graphical output can be printed.
The tabular output can be saved in a file or printed. The tabular output includes
most of the information that can be displayed. This is generated for added
convenience to the designer.
The member specific detailed design information shows the details of the calculation from the designer’s point of view. It shows the design forces, design
section dimensions, reinforcement, and some intermediate results for all of the
load combinations at all of the design sections of a specific frame member. For a
column member, it also can show the position of the current state of design
forces on the column interaction diagram.

4-1

Concrete Frame Design TS 500-2000

In the following sections, some of the typical graphical display, tabular output,
spreadsheet output, and member specific detailed design information are described. The TS 500-2000 design code is described in this manual.

4.2

Graphical Display of Design Information
The graphical display of design output includes input and output design information. Input design information includes design section label, K-factors, live
load reduction factor, and other design parameters. The output design information includes longitudinal reinforcing, shear reinforcing, torsion reinforcing,
column capacity ratio, beam-column capacity ratio, joint shear check, and other
design information.
The graphical output can be produced in color or in gray-scaled screen display.
The active screen display can be sent directly to the printer.

4.2.1 Input and Output
Input design information for the TS 500-2000 code includes the following:


Design sections



Design framing type



Live load reduction factors (RLLF)



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



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



Cm factors, for major and minor direction of bending



βns factors, for major and minor direction of bending



βs factors, for major and minor direction of bending

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

4-2



Longitudinal reinforcing area



Longitudinal reinforcing area as percent of concrete gross area

Graphical Display of Design Information

Chapter 4 - Design Output



Shear reinforcing areas per unit spacing



Column P-M-M interaction ratios



6
5

Beam-column capacity ratios



Column-beam capacity ratios



Joint shear capacity ratios



Torsion reinforcing



General reinforcing details

Use the Design menu > Concrete Frame Design > Display Design Info
command in the program to plot input and output values directly on the model in
the active window. Clicking this command will access the Display Design Results form. Select the Design Output or Design Input option, and then use the
drop-down lists to choose the type of design data to be displayed, such as longitudinal reinforcement, rebar percentages, shear reinforcing and so on. Click
the OK button on the form to close the form and display the selected data in the
active window.
The graphical displays can be viewed in 2D or 3D mode. Use the various toolbar
buttons (e.g., Set Default 3D View, Set X-Y View) to adjust the view, or use the
View menu > Set 2D View or View menu > Set 3D View commands in program and the Home > View > Set 2D View to refine the display.
The graphical display in the active window can be printed by clicking the File
menu > Print Graphics command in the program, the Print Graphics button
on the toolbar, or the Ctrl+G keyboard shortcut. The display also can be captured
as a bit map file (.bmp) using one of the subcommands on the File menu >
Capture Picture command in the program, or as a metafile (.emf) using one of
the subcommands on the File menu > Capture Enhanced Metafile command.
The captured picture file can then be used in popular graphics programs, including Paint and PowerPoint. Alternatively, the standard Windows screen
capture command (click the Print Screen button on the keyboard) can be used
to create a screen capture of the entire window, or use the Alt+Print Screen
command to capture only the "top layer," such as a form displayed from within
the program.

Graphical Display of Design Information

4-3

Concrete Frame Design TS 500-2000

By default, graphics are displayed and printed in color, assuming a color printer
is available. Use the Options menu > Colors > Output command to change
default colors, as necessary, including changing the background color from the
default black to white. A white background can be useful when printing design
output to save ink/toner. In addition, the Options menu > Colors > Set Active
Theme command can be used to view or print graphics in grayscale in the program.

4.3

Tabular Display of Design Output
The tabular design output can be sent directly to a printer or saved to a file. The
printed form of the tabular output is the same as that produced for the file output
except that the font size is adjusted for the printed output.
The tabular design output includes input and output design information that
depends on the design code chosen. For the TS 500-2000 code, the tabular
output includes the following. All tables have formal headings and are
self-explanatory, so further description of these tables is not given.
Input design information includes the following:


4-4

Concrete Column Property Data
- Material label
- Column dimensions
- Reinforcement pattern
- Concrete cover
- Bar area



Concrete Beam Property Data
- Material label
- Beam dimensions
- Top and bottom concrete cover
- Top and bottom reinforcement areas



Load Combination Multipliers
- Combination name
- Load types
- Load factors

Tabular Display of Design Output

Chapter 4 - Design Output



Concrete Design Element Information
- Design section ID
- Factors for major and minor direction of bending
- Unbraced length ratios for major and minor direction of
bending, L-factors
- Live load reduction factors (RLLF)



Concrete Moment Magnification Factors
- Section ID
- Element type
- Framing type
- βns -factors
- βs -factors

The output design information includes the following:


Column design Information
- Section ID
- Station location
- Total longitudinal reinforcement and the governing load combination
- Major shear reinforcement and the governing load combination
- Minor shear reinforcement and the governing load combination



Beam Design Information
- Section ID
- Station location
- Top longitudinal reinforcement and the governing load combination
- Bottom reinforcement and the governing load combination
- Longitudinal torsional reinforcement and the governing load combination
- Major shear reinforcement and the governing load combination for
shear and torsion design



Concrete Column Joint Information
- Section ID
- (6/5) Beam/column capacity ratios for major and minor direction and
the governing load combination
- Joint shear capacity for major and minor direction and the governing
load combination
Tabular Display of Design Output

4-5

Concrete Frame Design TS 500-2000

Tabular output can be printed directly to a printer or saved in a file using the File
menu > Print Tables command. A form will display when this command is
used. Depress the F1 key on the keyboard to access the Help topic specific to that
form, which will identify the types of output available (e.g., plain text with or
without page breaks, rich text format Word document, and so on).

4.4

Member Specific Information
Member specific design information shows the details of the calculation from
the designer's point of view. It includes the geometry and material data, other
input data, design forces, design section dimensions, reinforcement details, and
some of the intermediate results for the selected member. The design detail information can be displayed for a specific load combination and for a specific
station of a column or beam member. For columns, member specific design
information also can show the position of the current state of design forces using
a column interaction diagram.
After an analysis has been performed and the Design menu > Concrete Frame
Design > Start Design/Check command has been used, access the detailed design information by right clicking a frame member to display the Concrete
Column Design Information form if a column member was right clicked or the
Concrete Beam Design Information form if a beam member was right clicked.
Table 4-1 identifies the types of data provided by the forms.
The longitudinal and shear reinforcing area are reported in their current units,
which are displayed in the drop-down list in the lower right corner of the program window. Typically, the longitudinal reinforcing area is reported in in2,
mm2, cm2 and so on. Shear reinforcing areas typically are reported in in2/in,
mm2/mm, cm2/cm and so on.
Table 4-1 Member Specific Data for Columns and Beams
Column
 Load combination ID
 Station locations
 Longitudinal reinforcement area
 Major shear reinforcement areas

4-6

Member Specific Information

Beam





Load combination ID
Station location
Top reinforcement areas
Bottom reinforcement areas

Chapter 4 - Design Output

Table 4-1 Member Specific Data for Columns and Beams
 Minor shear reinforcement areas

 Longitudinal reinforcement for torsion design
 Shear reinforcement area for shear
 Shear reinforcement area for torsion design

Buttons on the forms can be used to access additional forms that provide the following data
 Overwrites
– Element section ID
– Element framing type
– Live load reduction factors
– Effective length factors, K, for major
and minor direction bending
– Cm factors for major and minor bending
– βs factors for major and minor
directions
 Summary design data
– Geometric data and graphical
representation
– Material properties
– Minimum design moments
– Moment factors
– Longitudinal reinforcing areas
– Design shear forces
– Shear reinforcing areas
– Shear capacities of steel and concrete
– Torsion reinforcing
– Interaction diagram, with the axial force
and biaxial moment showing the state
of stress in the column

 Overwrites
– Element section ID
– Element framing type
– Live load reduction factors
– Effective length factors, K, for major and
minor direction bending
– Cm factors for major and minor bending
– βs factors for major and minor directions
 Summary design data
– Geometric data and graphical
representation
– Material properties
– Design moments and shear forces
– Minimum design moments
– Top and bottom reinforcing areas
– Shear capacities of concrete and steel
– Shear reinforcing area
– Torsion reinforcing area

 Detailed calculations for flexural details,
shear details, joint shear, and beam/
column capacity ratios

The load combination is reported by its name, while station data is reported by
its location as measured from the I-end of the column. The number of line items
reported is equal to the number of design combinations multiplied by the number
of stations. One line item will be highlighted when the form first displays. This
line item will have the largest required longitudinal reinforcing, unless any design overstress or error occurs for any of the items. In that case, the last item
among the overstressed items or items with errors will be highlighted. In essence, the program highlights the critical design item.
If a column has been selected and the column has been specified to be checked
by the program, the form includes the same information as that displayed for a
designed column, except that the data for a checked column includes the caMember Specific Information

4-7

Concrete Frame Design TS 500-2000

pacity ratio rather than the total longitudinal reinforcing area. Similar to the
design data, the line item with the largest capacity ratio is highlighted when the
form first displays, unless an item has an error or overstress, in which case, that
item will be highlighted. In essence, the program highlights the critical check
item.
The program can be used to check and to design rebar in a column member.
When the users specifies that the program is to check the rebar in the column, the
program checks the rebar as it is specified. When the user specifies that the
program design the rebar configuration, the program starts with the data specified for rebar and then increases or decreases the rebar in proportion to the relative areas of rebar at the different locations of rebar in the column.

4.4.1 Interactive Concrete Frame Design
The interactive concrete frame design and review is a powerful mode that allows
the user to review the design results for any concrete frame design, to revise the
design assumptions interactively, and to review the revised results immediately.
Before entering the interactive concrete frame design mode, the design results
must be available for at least one member. That means the design must have
been run for all the members or for only selected members. If the initial design
has not been performed yet, run a design by clicking the Design menu > Concrete Frame Design > Start Design/Check of Structure.
There are three ways to initiate the interactive concrete frame design mode:


Click the Design menu > Concrete Frame Design > Start Design/Check
of Structures command to run a design.



Click the Design menu > Concrete Frame Design > Display Design Info
command to access the Display Design Results form and select a type of
result.



Click the Design menu > Concrete Frame Design > Interactive Concrete
Frame Design command.

After using any of the three commands, right click on a frame member to enter
the interactive Concrete Frame Design Mode and access the Concrete Column
Design Information form if a column member was right clicked or the Concrete

4-8

Member Specific Information

Chapter 4 - Design Output

Beam Design Information form if a beam member was right clicked. These
forms have Overwrites buttons that accesses the Concrete Frame Design
Overwrites form. The form can be used to change the design sections, element
type, live load reduction factor for reducible live load, and many other design
factors. See Appendix D for a detailed description of the overwrite items. When
changes to the design parameters are made using the Overwrites form, the
Concrete Beam or Column Design Information forms update immediately to
reflect the changes. Then other buttons on the Concrete Beam or Column Design
Information forms can be used to display additional forms showing the details of
the updated design. See the Member Specific Information section of this chapter
for more information.
In this way, the user can change the overwrites any number of times to produce a
satisfactory design. After an acceptable design has been produced by changing
the section or other design parameters, click the OK button on the Concrete
Beam or Column Design Information forms to permanently change the design
sections and other overwrites for that member. However, if the Cancel button is
used, all changes made to the design parameters using the Concrete Frame Design Overwrites form are temporary and do not affect the design.

4.5

Error Messages and Warnings
In many places of concrete frame design output, error messages and warnings
are displayed. The messages are numbered. A complete list of error messages
and warnings used in Concrete Frame Design for all the design codes is provided
in Appendix E. However, all of the messages are not applicable to TS 500-2000
code.

Error Messages and Warnings

4-9

APPENDICES

Appendix A
Second Order P-Delta Effects

Typically, design codes require that second order P-Delta effects be considered
when designing concrete frames. These effects 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 δ. The total
second order P-Delta effects on this frame object are those caused by both ∆ and
δ.
The program has an option to consider P-Delta effects in the analysis. When
P-Delta effects are considered in the analysis, the program does a good job of
capturing the effect due to the ∆ deformation shown in Figure A-1, but it does
not typically capture the effect of the δ deformation (unless, in the model, the
frame object is broken into multiple elements over its length).
Consideration of the second order P-Delta effects is generally achieved by
computing the flexural design capacity using a formula similar to that shown in
the following equation.

A-1

Concrete Frame Design TS 500-2000

Figure A-1 The total second order P-delta effects on a
frame element caused by both ∆ and δ

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)

Unitless factor multiplying Mnt

Unitless factor multiplying Mlt (assumed equal to 1 by the program;
see the following text)

When the program performs concrete frame design, it assumes that the factor b
is equal to 1 and calculates the factor a. That b = 1 assumes that P-Delta
effects have been considered in the analysis, as previously described. Thus, in
general, when performing concrete frame design in this program, consider
P-Delta effects in the analysis before running the program.

A-2

Appendix A

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 also can 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 recognizes
various aspects of the structure that have an effect on those lengths, such as
member connectivity, diaphragm constraints and support points. The program
automatically locates the member support points and evaluates the corresponding unsupported length.

B-1

Concrete Frame Design TS 500-2000

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.

Figure B-1 Axis of bending and unsupported length

B-2

Appendix B

Appendix C
Concrete Frame Design Preferences

The concrete frame design preferences are general assignments that are applied
to all of the concrete frame members. The design preferences should be
reviewed and any changes from the default values made before performing a
design. The following table lists the design preferences that are specific to using
TS 500-2000; the preferences that are generic to all codes are not included in this
table.
Table C-1 Preferences
Item

Multi-Response
Case Design

Possible
Values

Envelopes,
Step-by-Step
Last Step Envelopes – All
Step-by-Step All

Default
Value

Envelopes

Description
Toggle for design load combinations. This
is either "Envelopes", "Step-by-Step", "Last
Step", "Envelopes - All", "Step-by-Step All" indicating how results for multivalued
cases (Time history, Nonlinear static or
Multi-step static) are considered in the
design. If a single design load combination
has more than one time history, Nonlinear
static or Multi-step static case in it, that
design load combination is designed for the
envelopes of the time histories, regardless
of what is specified here.

C-1

Concrete Frame Design TS 500-2000

Item

Possible
Values

Default
Value

Description

Number
Interaction Curves

Multiple of 4
≥4

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

Number

Any odd value
≥5

Number of points used for defining a single
curve in a concrete frame; should be odd.

Consider
Minimum
Eccentricity

No, Yes

Yes

Seismic Zone

Zone1, Zone2,
Zone3, Zone 4

Zone 4

Gamma (Steel)

1.15

Gamma
(Concrete)

1.5

Gamma (Concrete
Shear)

1.25

Toggle to specify if minimum eccentricity is
considered in design.

This item varies with the Seismic Zone for
detailing.
Material factor for reinforcing steel.
Material factor for concrete.

Material factor for concrete shear strength.

Pattern Live
Load Factor

≥0

0.75

The pattern load factor is used to compute
positive live load moment by multiplying
Live load with Pattern Load Factor (PLF)
and assuming that beam is simply
supported. This option provides a limited
pattern loading to frames. Use zero to turn
off this option.

Utilization
Factor Limit

0.95

Stress ratios that are less than or equal to
this value are considered acceptable.

C-2

Appendix C

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 TS 500-2000. Default values are provided for all overwrite items.
Thus, it is not necessary to specify or change any of the overwrites. However, at
least review the default values to ensure they are acceptable. When changes are
made to overwrite items, the program applies the changes only to the elements to
which they are specifically assigned.
Table D-1 Overwrites
Item

Possible
Values

Default
Value

Current
Design
Section

Any defined
concrete
section

Analysis
section

Framing
Type

High Ductile,
Normal Ductile,
Ordinary
NonSway

Live Load
Reduction
Factor

≥0

High Ductile

Calculated

Description
The design section for the selected frame
objects.
The Framing Type is used for ductility
considerations in the design.

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.

D-1

Concrete Frame Design TS 500-2000

Item

Unbraced
Length Ratio
(Major)

Possible
Values

≥0

Default
Value

Description

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

Calculated

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)

Calculated

Effective length factor for buckling about the
frame object major axis. This item is specified
as a fraction of the frame object length.

Effective
Length Factor
(k Minor)

Calculated

Effective length factor for buckling about the
frame object major axis. This item is specified
as a fraction of the frame object length.

NonSway
Moment
Factor
(Bns major)

Calculated

Nonsway moment magnification about the
frame object major axis.

NonSway
Moment
Factor
(Bns minor)

Calculated

Sway Moment
Factor
(Bs major)

Calculated

Sway moment magnification about the frame
object major axis.

Sway Moment
Factor
(Bs minor)

Calculated

Sway moment magnification about the frame
object minor axis.

D-2

Appendix D

Nonsway moment magnification about the
frame object minor axis.

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

Beam concrete compression failure

Reinforcing required exceeds maximum allowed

Shear stress exceeds maximum allowed

Column design moments cannot be calculated

Column factored axial load exceeds Euler Force

Required column concrete area exceeds maximum

Flexural capacity could not be calculated for shear design

Concrete column supports non-concrete beam/column

k ∗ L/r > 115 , zeta_ 2 < 0 , eta < 1.0 (GB50010 7.3.10)

E-1

Concrete Frame Design TS 500-2000

Error
Number

E-2

Description

Column is overstressed for P-M-M

Axial compressive capacity for concrete exceeded (TBM 6.4.2)

Beam frames into column eccentrically (11.6.3)

Torsion exceeds maximum allowed

Reinforcing provided is below minimum required

Reinforcing provided exceeds maximum allowed

Tension reinforcing provided is below minimum required

k ∗ L/r > 30 (GB 7.3.10)

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

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.

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 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.

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

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

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

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

Appendix E

Appendix E – Error Messages and Warnings

Error
Number

Description

The column on top is not concrete. Joint shear ratio is not needed.

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

Beam/column capacity ratio exceeds limit.

Joint shear ratio exceeds limit.

Capacity ratio exceeds limit.

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

At least one beam around the joint has failed. Beam/column capacity
ratio is not calculated.

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

The column above the joint has failed. Beam/column capacity ratio is not
calculated.

All beams around the joint have not been designed. Joint shear ratio is
not calculated.

At least one beam around the joint has failed. Joint shear ratio is not
calculated.

The column above the joint has not been designed. Joint shear ratio is
not calculated.

The column above the joint has failed. Joint shear ratio is not calculated.

Shear stress due to shear force and torsion together exceeds maximum
allowed.

Appendix E

E- 3

References

CSI, 2008. CSI Analysis Reference Manual. Computers and Structures, Inc.,
Berkeley, California.
TSC, 2007. Specification for Turkish Seismic code. Official Gazette No. 26454
and 26511. Ministry of Public Works and Settlement. Government of the
Republic of Turkey.
TS 500, 2000. Requirements for Design and Construction of Reinforced Concrete Structures. Turkish Standard Institute. Necatibey Street No. 112, Bakanliklar, Ankara.
White, D. W. and J. F. Hajjar, 1991. “Application of Second-Order Elastic
Analysis in LRFD: Research to Practice.” Engineering Journal. American
Institute of Steel Construction, Inc., Vol. 28, No. 4.

References - i

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