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Shear Wall Design Manual Turkish TS 500-2000 with Seismic Code 2007

Shear Wall

Design Manual Turkish TS 500-2000

with Turkish Seismic Code 2007 For ETABS® 2016

ISO ETA122815M51 Rev. 0 Proudly developed in the United States of America December 2015

Copyright

Copyright Computers & Structures, Inc., 1978-2015 All rights reserved. The CSI Logo®, SAP2000®, ETABS®, and SAFE® are registered trademarks of Computers & Structures, Inc. Watch & LearnTM is a trademark of Computers & Structures, Inc. The computer programs SAP2000® and ETABS® and all associated documentation are proprietary and copyrighted products. Worldwide rights of ownership rest with Computers & Structures, Inc. Unlicensed use of these programs or reproduction of documentation in any form, without prior written authorization from Computers & Structures, Inc., is explicitly prohibited.

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DISCLAIMER

CONSIDERABLE TIME, EFFORT AND EXPENSE HAVE GONE INTO THE DEVELOPMENT AND DOCUMENTATION OF THIS SOFTWARE. HOWEVER, THE USER ACCEPTS AND UNDERSTANDS THAT NO WARRANTY IS EXPRESSED OR IMPLIED BY THE DEVELOPERS OR THE DISTRIBUTORS ON THE ACCURACY OR THE RELIABILITY OF THIS PRODUCT.

THIS PRODUCT IS A PRACTICAL AND POWERFUL TOOL FOR STRUCTURAL DESIGN. HOWEVER, THE USER MUST EXPLICITLY UNDERSTAND THE BASIC ASSUMPTIONS OF THE SOFTWARE MODELING, ANALYSIS, AND DESIGN ALGORITHMS AND COMPENSATE FOR THE ASPECTS THAT ARE NOT ADDRESSED.

THE INFORMATION PRODUCED BY THE SOFTWARE MUST BE CHECKED BY A QUALIFIED AND EXPERIENCED ENGINEER. THE ENGINEER MUST INDEPENDENTLY VERIFY THE RESULTS AND TAKE PROFESSIONAL RESPONSIBILITY FOR THE INFORMATION THAT IS USED.

Contents

1 Introduction 1.1 Notation 1-2 1.2 Design Station Locations 1-7 1.3 Default Design Load Combinations 1-8

1.3.1 Dead Load Component 1-8 1.3.2 Live Load Component 1-9 1.3.3 Wind Load Component 1-9 1.3.4 Earthquake Load Component 1-9 1.3.5 Combinations that Include a Response Spectrum 1-9 1.3.6 Combinations that Include Time History Results 1-10 1.3.7 Combinations that Include Static Nonlinear Results 1-11

1.4 Shear Wall Design Preferences 1-12 1.5 Shear Wall Design Overwrites 1-12 1.6 Choice of Units 1-12

2 Pier Design 2.1 Wall Pier Shear Design 2-1

2.1.1 Determine the Concrete Shear Capacity 2-2 2.1.2 Determine the Require Shear Reinforcing 2-2

2.2 Wall Pier End Zones 2-3 2.2.1 Details of Check for Wall End Zone Requirements 2-3

i

Shear Wall Design TS 500-2000

2.2.2 Reinforcement for Wall End Zones 2-4 2.3 Wall Pier Flexural Design 2-5

2.3.1 Designing a Simplified Pier Section 2-5 2.3.2 Checking a General or Uniform Reinforcing

Pier Section 2-10 2.3.3 Wall Pier Demand/Capacity Ratio 2-18 2.3.4 Designing a General Reinforcing Pier Section 2-19

3 Spandrel Design 3.1 Spandrel Flexural Design 3-1

3.1.1 Determine the Maximum Factored Moments 3-2 3.1.2 Determine the Required Flexural Reinforcing 3-2

3.2 Spandrel Shear Design 3-10 3.2.1 Determine the Concrete Shear Capacity 3-10 3.2.2 Determine the Required Shear Reinforcing 3-11

Appendix A Shear Wall Design Preferences

Appendix B Design Procedure Overwrites

Appendix C Analysis Sections and Design Sections

Bibliography

ii

Chapter 1 Introduction

This manual describes the details of the shear wall design and stress check algorithms used by the program when the user selects the TS 500-2000 de-sign code. The various notations used in this manual are described in Section 1.1.

The design is based on loading combinations specified by the user (Section 1.2). To facilitate the design process, the program provides a set of default load combinations that should satisfy requirements for the design of most building type structures.

The program performs the following design, check, or analysis procedures in accordance with TS 500-2000 requirements:

Design and check of concrete wall piers for flexural and axial loads (Chap-ter 2)

Design of concrete wall piers for shear (Chapter 2)

Design of concrete shear wall spandrels for flexure (Chapter 3)

Design of concrete wall spandrels for shear (Chapter 3)

Consideration of the wall end zones requirements for concrete wall piers using an approach based on the requirements of Turkish Earthquake code 2007 Section 3.6.2 in TS 500-2000 (Chapter 3)

1-1


The program provides detailed output data for Simplified pier section design, Section Designer pier section design, Section Designer pier section check, and Spandrel design (Chapter 4).

1.1. Notation Following is the notation used in this manual.

Acv Area of concrete used to determine shear stress, mm2

Ag Gross area of concrete, mm2

Ah-min Minimum required area of distributed horizontal reinforcing steel required for shear in a wall spandrel, mm2 / mm

As Area of tension reinforcing steel, mm2

Asc Area of reinforcing steel required for compression in a pier edge member, or the required area of tension steel required to balance the compression steel force in a wall spandrel, mm2

Asc-max Maximum area of compression reinforcing steel in a wall pier edge member, mm2

Asf The required area of tension reinforcing steel for balancing the concrete compression force in the extruding portion of the concrete flange of a T-beam, mm2

Ast Area of reinforcing steel required for tension in a pier edge member, mm2

Ast-max Maximum area of tension reinforcing steel in a wall pier edge member, mm2

Asw /s Area of reinforcing steel required for shear, mm2 / mm

Aswd Area of diagonal shear reinforcement in a coupling beam, mm2

Asw-min/s Minimum required area of distributed vertical reinforcing steel required for shear in a wall spandrel, mm2 / mm

1-2 Notation


Astw The required area of tension reinforcing steel for balancing the concrete compression force in a rectangular concrete beam, or for balancing the concrete compression force in the concrete web of a T-beam, mm2

A's Area of compression reinforcing steel in a spandrel, mm2

B1, B2... Length of a concrete edge member in a wall with uniform thickness, mm

Cc Concrete compression force in a wall pier or spandrel, pounds

Cf Concrete compression force in the extruding portion of a T-beam flange, pounds

Cs Compression force in wall pier or spandrel reinforcing steel, pounds

Cw Concrete compression force in the web of a T-beam, pounds

D/C Demand/Capacity ratio as measured on an interaction curve for a wall pier, unitless

DB1 Length of a user-defined wall pier edge member, mm. This can be different on the left and right sides of the pier, and it also can be different at the top and the bottom of the pier.

DB2 Width of a user-defined wall pier edge member, mm. This can be different on the left and right sides of the pier, and it also can be different at the top and the bottom of the pier.

Es Modulus of elasticity of reinforcing steel, MPa

IP-max The maximum ratio of reinforcing considered in the design of a pier with a Section Designer section, unitless

IP-min The minimum ratio of reinforcing considered in the design of a pier with a Section Designer section, unitless

LBZ Horizontal length of the wall end zone at each end of a wall pier, mm

Notation 1-3


Lw Horizontal length of wall pier, mm. This can be different at the top and the bottom of the pier

Ls Horizontal length of wall spandrel, mm

LL Live load

Mr Bending resistance, N-mm

Md Designed bending moment at a design section, N-mm

Mdc In a wall spandrel with compression reinforcing, the designed bending moment at a design section resisted by the couple between the concrete in compression and the tension steel, N-mm

Mds In a wall spandrel with compression reinforcing, the designed bending moment at a design section resisted by the couple between the compression steel and the tension steel, N-mm

Mdw In a wall spandrel with a T-beam section and compression reinforcing, the designed bending moment at a design sec-tion resisted by the couple between the concrete in compres-sion in the web and the tension steel, N-mm

Nb Axial load capacity at balanced strain conditions, N

NCmax Maximum ratio of compression steel in an edge member of a wall pier, unitless

Nd Designed factored axial load at a section, N

Nleft Equivalent axial force in the left edge member of a wall pier used for design, N. This may be different at the top and the bottom of the wall pier.

Nmax Limit on the maximum compressive design strength speci-fied by TS 500-2000, N

Nmax Factor Factor used to reduce the allowable maximum compressive design strength, unitless. The TS 500-2000 specifies this factor to be 1.0. This factor can be revised in the prefer-ences.

1-4 Notation


N0 Axial load capacity at zero eccentricity, N

Noc The maximum compression force a wall pier can carry with strength reduction factors set equal to one, N

Not The maximum tension force a wall pier can carry with strength reduction factors set equal to one, N

Nright Equivalent axial force in the right edge member of a wall pier used for design, pounds. This may be different at the top and the bottom of the wall pier.

NTmax Maximum ratio of tension steel in an edge member of a wall pier, unitless

OC On a wall pier interaction curve the "distance" from the origin to the capacity associated with the point considered

OL On a wall pier interaction curve the "distance" from the origin to the point considered

RLW Shear strength reduction factor as specified in the concrete material properties, unitless. This reduction factor applies to light-weight concrete. It is equal to 1 for normal weight con-crete.

RLL Reduced live load

Ts Tension force in wall pier reinforcing steel, N

Vcr Shear at inclined cracking, N

Vds The portion of the shear force in a spandrel carried by the shear reinforcing steel, N

Vd Designed shear force at a design section, N

WL Wind load

a Depth of the wall pier or spandrel compression block, mm

a1 Depth of the compression block in the web of a T-beam, mm

Notation 1-5


bs Width of the compression flange in a T-beam, mm. This can be different on the left and right ends of the T-beam

c Distance from the extreme compression fiber of the wall pier or spandrel to the neutral axis, mm

dr-bot Distance from bottom of spandrel beam to centroid of the bottom reinforcing steel, mm. This can be different on the left and right ends of the beam.

dr-top Distance from top of spandrel beam to centroid of the top reinforcing steel, mm. This can be different on the left and right ends of the beam.

ds Depth of the compression flange in a T-beam, mm. This can be different on the left and right ends of the T-beam.

dspandrel Depth of spandrel beam minus cover to centroid of reinforc-ing, mm

fy Yield strength of steel reinforcing, N/mm2. This value is used for flexural and axial design calculations.

fys Yield strength of steel reinforcing, N/mm2. This value is used for shear design calculations.

f'c Concrete compressive strength, N/mm2. This value is used for flexural and axial design calculations.

f'cs Concrete compressive strength, N/mm2. This value is used for shear design calculations.

f's Stress in compression steel of a wall spandrel, N/mm2.

hs Height of a wall spandrel, mm. This can be different on the left and right ends of the spandrel.

pmax Maximum ratio of reinforcing steel in a wall pier with a Sec-tion Designer section that is designed (not checked), unit-less.

pmin Minimum ratio of reinforcing steel in a wall pier with a Sec-tion Designer section that is designed (not checked), unit-less.

1-6 Notation


tw Thickness of a wall pier, mm. This can be different at the top and bottom of the pier.

ts Thickness of a wall spandrel, mm. This can be different on the left and right ends of the spandrel.

ΣDL The sum of all dead load cases

ΣLL The sum of all live load cases

ΣRLL The sum of all reduced live load cases

α The angle between the diagonal reinforcing and the longitu-dinal axis of a coupling beam

ε Reinforcing steel strain, unitless

εs Reinforcing steel strain in a wall pier, unitless

ε's Compression steel strain in a wall spandrel, unitless

γm Material factor

γmc Material factor for concrete

γms Material factor for steel

1.2. Design Station Locations The program designs wall piers at stations located at the top and bottom of the pier only. To design at the mid-height of a pier, break the pier into two separate "half-height" piers.

The program designs wall spandrels at stations located at the left and right ends of the spandrel only. To design at the mid-length of a spandrel, break the spandrel into two separate "half-length" piers. Note that if a spandrel is into broken into pieces, the program will calculate the seismic diagonal shear reinforcing separately for each piece. The angle used to calculate the seismic diagonal shear reinforcing for each piece is based on the length of the piece, not the length of the entire spandrel. This can cause the required area of di-agonal reinforcing to be significantly underestimated. Thus, if you break a

Design Station Locations 1-7


spandrel into pieces, calculate the seismic diagonal shear reinforcing sepa-rately by hand.

1.3. Default Design Load Combinations The design load combinations are the various combinations of the load cases for which the structure is to be checked. For this code, if a structure is sub-jected to dead (G), live (Q), wind (W), and earthquake (E), and considering that wind and earthquake forces are reversible, the following load combina-tions may need to be defined (TS 6.2.6):

1.4G + 1.6Q (TS 6.3)

0.9G ± 1.3W (TS 6.6)

1.0G + 1.3Q ± 1.3W (TS 6.5)

0.9G ± 1.0E (TS 6.8a)

1.0G + 1.0Q ± 1.0E (TS 6.7a)

1.0G + 1.0Q – 1.0E (TS 6.7b)

These also are 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.

1.3.1. Dead Load Component The dead load component of the default design load combinations consists of the sum of all dead loads multiplied by the specified factor. Individual dead load cases are not considered separately in the default design load combina-tions.

See the description of the earthquake load component later in this chapter for additional information.

1-8 Default Design Load Combinations


1.3.2. Live Load Component The live load component of the default design load combinations consists of the sum of all live loads, both reducible and unreducible, multiplied by the specified factor. Individual live load cases are not considered separately in the default design load combinations.

1.3.3. Wind Load Component The wind load component of the default design load combinations consists of the contribution from a single wind load case. Thus, if multiple wind load cases are defined in the program model, the preceding equations will con-tribute multiple design load combinations, one for each wind load case that is defined.

1.3.4. Earthquake Load Component The earthquake load component of the default design load combinations con-sists of the contribution from a single earthquake load case. Thus, if multiple earthquake load cases are defined in the program model, the preceding equa-tions will contribute multiple design load combinations, one for each earth-quake load case that is defined.

The earthquake load cases considered when creating the default design load combinations include all static load cases that are defined as earthquake loads and all response spectrum cases. Default design load combinations are not created for time history cases or for static nonlinear cases.

1.3.5. Combinations that Include a Response Spectrum In the program all response spectrum cases are assumed to be earthquake load cases. Default design load combinations are created that include the re-sponse spectrum cases.

The output from a response spectrum is all positive. Any program shear wall design load combination that includes a response spectrum load case is checked for all possible combinations of signs on the response spectrum val-ues. Thus, when checking shear in a wall pier or a wall spandrel, the response spectrum contribution of shear to the design load combination is considered once as a positive shear and then a second time as a negative shear. Similar-ly, when checking moment in a wall spandrel, the response spectrum contri-

Default Design Load Combinations 1-9


bution of moment to the design load combination is considered once as a positive moment and then a second time as a negative moment. When check-ing the flexural behavior of a two-dimensional wall pier or spandrel, four possible combinations are considered for the contribution of response spec-trum load to the design load combination. They are:

+N and +M

+N and −M

−N and +M

−n and −M

where N is the axial load in the pier and M is the moment in the pier. Simi-larly, eight possible combinations of N, M2 and M3 are considered for three-dimensional wall piers.

Note that based on the preceding, TS 6.8a and TS 6.8b are redundant for a load combination with a response spectrum, and similarly, TS 6.7a and TS 6.7b are redundant for a load combination with a response spectrum. For this reason, the program creates default design load combinations based on TS 6.8a and TS 6.7a only for response spectra. Default design load combinations using TS 6.8b and TS 6.7b are not created for response spectra.

1.3.6. Combinations that Include Time History Results The default shear wall design load combinations do not include any time his-tory results. To include time history forces in a design load combination, the user must define the load combination.

When a design load combination includes time history results, the design can be for the envelope of those results or for each step of the time history. The type of time history design can be specified in the shear wall design preferences (Appendix A).

When envelopes are used, the design is for the maximum of each response quantity (axial load, moment, and the like) as if they occurred simultaneous-ly. Typically, this is not the realistic case, and in some instances, it may be unconservative. Designing for each step of a time history gives the correct correspondence between different response quantities, but designing for each step can be very time consuming.

1-10 Default Design Load Combinations


When the program gets the envelope results for a time history, it gets a maximum and a minimum value for each response quantity. Thus, for wall piers it gets maximum and minimum values of axial load, shear and moment; and for wall spandrels, it gets maximum and minimum values of shear and moment. For a design load combination in the program shear wall design module, any load combination that includes a time history load case in it is checked for all possible combinations of maximum and minimum time history design values. Thus, when checking shear in a wall pier or a wall spandrel, the time history contribution of shear to the design load combination is considered once as a maximum shear and then a second time as a minimum shear. Similarly, when checking moment in a wall spandrel, the time history contribution of moment to the design load combination is considered once as a maximum moment and then a second time as a minimum moment. When checking the flexural behavior of a wall pier, four possible combinations are considered for the contribution of time history load to the design load combination. They are:

Nmax and Mmax

Nmax and Mmin

Nmin and Mmax

Nmin and Mmin

where N is the axial load in the pier and M is the moment in the pier.

If a single design load combination has more than one time history case in it, that design load combination is designed for the envelopes of the time histo-ries, regardless of what is specified for the Time History Design item in the preferences.

1.3.7. Combinations That Include Static Nonlinear Results The default shear wall design load combinations do not include any static nonlinear results. To include static nonlinear results in a design load combi-nation, define the load combination yourself.

If a design load combination includes a single static nonlinear case and noth-ing else, the design is performed for each step of the static nonlinear analysis. Otherwise, the design is performed for the last step of the static nonlinear analysis only.

Default Design Load Combinations 1-11


1.4. Shear Wall Design Preferences The shear wall design preferences are basic properties that apply to all wall pier and spandrel elements. Appendix A identifies shear wall design prefer-ences for TS 500-2000. Default values are provided for all shear wall design preference items. Thus, it is not required that preferences be specified. How-ever, at least review the default values for the preference items to make sure they are acceptable. Please consult the program-specific on-line Help for in-formation about reviewing and updating preferences.

1.5. Shear Wall Design Overwrites The shear wall design overwrites are basic assignments that apply only to those piers or spandrels to which they are assigned. The overwrites for piers and spandrels are separate. Appendix B identifies the shear wall overwrites for TS 500-2000. Note that the available overwrites change depending on the pier section type (Uniform Reinforcing, General Reinforcing, or Simplified T and C). Default values are provided for all pier and spandrel overwrite items. Thus, it is not necessary to specify or change any of the overwrites. How-ever, at least review the default values for the overwrite items to make sure they are acceptable. When changes are made to overwrite items, the program applies the changes only to the elements to which they are specifically assigned; that is, to the elements that are selected when the overwrites are changed. Please consult the program-specific on-line Help for information about reviewing and updating preferences.

1.6. Choice of Units For shear wall design in this program, any set of consistent units can be used for input. Also, the system of units being used can be changed at any time. Typically, design codes are based on one specific set of units.

The TS 500-2000 code is based on Newton-Millimeter-Second units. For simplicity, all equations and descriptions presented in this manual correspond to Newton-Millimeter-Second units unless otherwise noted.

The shear wall design preferences allow the user to specify special units for concentrated and distributed areas of reinforcing. These units are then used for reinforcing in the model, regardless of the current model units displayed in the drop-down list on the status bar (or within a specific form). The special

1-12 Shear Wall Design Preferences


units specified for concentrated and distributed areas of reinforcing can only be changed in the shear wall design preferences.

The choices available in the shear wall design preferences for the units asso-ciated with an area of concentrated reinforcing are in2, cm2, mm2, and current units. The choices available for the units associated with an area per unit length of distributed reinforcing are in2/ft, cm2/m. mm2/m, and current units.

The current units option uses whatever units are currently displayed in the drop-down list on the status bar (or within a specific form). If the current length units are m, this option means concentrated areas of reinforcing are in m2 and distributed areas of reinforcing are in m2/m. Note that when using the "current" option, areas of distributed reinforcing are specified in Length2/Length units, where Length is the currently active length unit. For example, if you are working in kN and m units, the area of distributed rein-forcing is specified in m2/m. If you are in Newton and mm, the area of dis-tributed reinforcing is specified in mm2/mm.

Choice of Units 1-13

Chapter 2 Pier Design

This chapter describes how the program designs each leg of concrete wall piers for shear using TS 500-2000. Note that in this program shear reinforcing can-not be specified and then checked by the program. The program only designs the pier for shear and reports how much shear reinforcing is required. The shear design is performed at stations at the top and bottom of the pier.

This chapter also describes how the program designs and checks concrete wall piers for flexural and axial loads using TS 500-2000. The menu option “TS 500-2000” also covers the “Specification for Structures to be Built in SEISMIC Areas, Part III - Earthquake Disaster Prevention” (TCS 2007). First we de-scribe how the program designs piers that are specified by a Simplified Section. Next we describe how the program checks piers that are specified by a Section Designer Section. Then we describe how the program designs piers that are specified by a Section Designer Section.

2.1 Wall Pier Shear Design The wall pier shear reinforcing is designed for each of the design load combi-nations. The following steps are involved in designing the shear reinforcing for a particular wall pier section for a particular design loading combination.

Determine the design factored forces Nd, Md and Vd that are acting on the wall pier section.

2-1


Determine the shear force, Vc, that can be carried by the concrete.

Determine the required shear reinforcing to carry the balance of the shear force.

Step 1 needs no further explanation. The following two sections describe in de-tail the algorithms associated with the Steps 2 and 3.

2.1.1 Determine the Concrete Shear Capacity Given the design force set Nd, Md and Vd acting on a wall pier section, the shear force carried by the concrete, Vc, is calculated as.

0.65c ctd chV f A= (TS 8.1.3, EDP 3.6.7.2)

The shear force is limited to a maximum of

max 0.22 cd chV f A= (TS 8.1.5b, TCS 3.6.7.2)

2.1.2 Determine the Required Shear Reinforcing Given Vd and Vc, the following equation provides the required shear reinforcing in area per unit length (e.g., mm2/mm) for both seismic and nonseismic wall piers (as indicated by the "Design is Seismic" item in the pier design over-writes). Note that additional requirements for seismic piers are provided later in this section.

(0.8 )d c

shyd w

V VA

f L−

= (TS 8.1.4, TCS 3.6.7.2)

where,

r 0.65 must not exceed 0.22ctd ch sh yd cd chV f A A f f A= + in accordance with TCS Section 3.6.7.2, Eqn. 3.17b.

For walls 2.0≥w

w

Hl

, Ash shall be 0.0025 of the gross section area of the wall

web remaining in between the wall end zones. In cases where 2.0w

w

Hl

≤ , the

wall web section is the full section of the wall.

2-2 Wall Pier Shear Design


2.2 Wall Pier End Zones This section describes how the program considers the wall end zones require-ments for each leg of concrete wall piers using TCS 2007 code. The program uses an approach based on the requirements of Section 3.6.2 of TCS 2007.

Note that the wall end zones requirements are considered separately for each design load case that includes seismic load.

2.2.1 Details of a Check for Wall End Zone Requirements The following information is available for the wall end zone check:

The height of the entire wall, Hw, length of the wall pier, lw, and the gross ar-ea of the pier, Ag. (Refer to Figure 2-5 later in this chapter for an illustration of the dimensions lw and bw, the thickness of the wall pier.)

The area of steel in the pier, Ast. This area of steel is calculated by the pro-gram, or it is provided by the user.

The symmetry of the wall pier (i.e., is the left side of the pier the same as the right side of the pier). Only the geometry of the pier is considered, not the re-inforcing, when determining if the pier is symmetrical. Figure 2-1 shows some examples of symmetrical and unsymmetrical wall piers. Note that a pier defined using Section Designer is assumed to be unsymmetrical, unless it is made up of a single rectangular shape.

Figure 2-1 Example Plan Views of Symmetrical and Unsymmetrical Wall Piers

The critical wall height is measured from the foundation or Base level in ETABS using the following criteria:

Wall Pier End Zones 2-3


/ 6w

crw

lH

H

≥

(TCS 3.6.2, Eqn 3.15a and 3.15b)

2cr wH l≤ (TCS 3.6.2)

In structural walls with rectangular cross-sections, the wall end zone length ul is computed as follows:

20.2

≥ wu

w

bl

l along the critical wall height, and

0.1≥ w

uw

bl

l outside the critical wall height (TCS 3.6.2.3)

If wall end zones are required, the program calculates the minimum required length of the wall end zone at each end of the wall, lu, in accordance with the requirements of TCS Section 3.6.2. Figure 2-2 illustrates the boundary zone length lu.

Figure 2-2 Illustration of Wall End Zone Length, lu

2.2.2 Reinforcement for Wall End Zones The vertical reinforcement at each wall end zone is required by TCS Sections 3.6.5.1. The program computes and reports the total cross-sectional area of ver-tical reinforcement as follows:

0.02 , along critical wall height0.01 , outside critical wall height

w us

w u

b lA

b l

≥

(TCS 3.6.5.1)

0.0025sv gA s A≥ (TCS 3.6.3.1)

2-4 Wall Pier End Zones


2.3 Wall Pier Flexural Design For both designing and checking piers, it is important to understand the local axis definition for the pier. Access the local axes assignments using the Assign menu.

2.3.1 Designing a Simplified Pier Section This section describes how the program designs a pier that is assigned a simpli-fied section. The geometry associated with the simplified section is illustrated in Figure 2-3. The pier geometry is defined by a length, thickness and size of the edge members at each end of the pier (if any).

Figure 2-3 Typical Wall Pier Dimensions Used for Simplified Design

A simplified C and T pier section is always planar (not three-dimensional). The dimensions shown in the figure include the following:

Wall Pier Flexural Design 2-5


The length of the wall pier is designated lw. This is the horizontal length of the wall pier in plan.

The thickness of the wall pier is designated bw. The thickness specified for left and right edge members (DB2left and DB2right) may be different from this wall thickness.

DB1 represents the horizontal length of the pier end zone. DB1 can be differ-ent at the left and right sides of the pier.

DB2 represents the horizontal width (or thickness) of the pier end zone. DB2 can be different at the left and right sides of the pier.

The dimensions illustrated are specified in the shear wall overwrites (Appendix B) and can be specified differently at the top and bottom of the wall pier.

If no specific end zone dimensions have been specified by the user, the program assumes that the end zone is the same width as the wall, and the program determines the required length of the end zone. In all cases, whether the end zone size is user-specified or program-determined, the program reports the required area of reinforcing steel at the center of the end zone. This section describes how the program-determined length of the end zone is determined and how the program calculates the required reinforcing at the center of the end zone.

Three design conditions are possible for a simplified wall pier. These condi-tions, illustrated in Figure 2-4, are as follows:

The wall pier has program-determined (variable length and fixed width) end zones on each end.

The wall pier has user-defined (fixed length and width) end zones on each end.

The wall pier has a program-determined (variable length and fixed width) end zone on one end and a user-defined (fixed length and width) end zone on the other end.

2.3.1.1 Design Condition 1 Design condition 1 applies to a wall pier with uniform design thickness and program-determined end zone length. For this design condition, the design al-gorithm focuses on determining the required size (length) of the end zones, while limiting the compression and tension reinforcing located at the center of

2-6 Wall Pier Flexural Design


the end zones to user-specified maximum ratios. The maximum ratios are spec-ified in the shear wall design preferences and the pier design overwrites as Edge Design PC-Max and Edge Design PT-Max.

Design Condition 2Wall pier with user-defined edgemembers

Design Condition 1Wall pier with uniform thickness andETABS-determined (variable length)edge members

Design Condition 3Wall pier with a user-defined edgemember on one end and an ETABS-determined (variable length) edgemember on the other end

Note:In all three conditions, the onlyreinforcing designed by ETABS is thatrequired at the center of the edgemembers

Figure 2-4 Design Conditions for Simplified Wall Piers

Consider the wall pier shown in Figure 2-5. For a given design section, say the top of the wall pier, the wall pier for a given design load combination is de-signed for a factored axial force Nd-top and a factored moment Md-top.

The program initiates the design procedure by assuming an end zone at the left end of the wall of thickness bw and width B1-left, and an end zone at the right end of the wall of thickness bw and width B1-right. Initially B1-left = B1-right = bw.

The moment and axial force are converted to an equivalent force set Nleft-top and Nright-top using the relationships shown below. (Similar equations apply at the bottom of the pier.)

( )

-top -topleft-top

1-lef 1-right2 0.5 0.5d d

w t

N MN

l B B= +

− −

( )

-top -topright-top

1-left 1-right2 0.5 0.5d d

w

N MN

l B B= −

− −

For any given loading combination, the net values for Nleft-top and Nright-top could be tension or compression.



B1-right

tp

t p

B2-right

B3-right

0.5Lp

0.5tptp

0.5tp

B1-left

B2-left

B3-left

CLWall Pier Plan

Pu-top

Mu-top

Pu-bot

Mu-bot

Pright-botPleft-bot

Pright-topPleft-top

Left e

dge m

embe

r

Righ

t edg

e mem

ber

Wall Pier Elevation

Lp

Top of pier

Bottom of pier

Figure 2-5 Wall Pier for Design Condition 1



Note that for dynamic loads, Nleft-top and Nright-top are obtained at the modal level and the modal combinations are made before combining with other loads. Also for design loading combinations involving SRSS, the Nleft-top and Nright-top forces are obtained first for each load case before the combinations are made.

If any value of Nleft-top or Nright-top is tension, the area of steel required for ten-sion, Ast, is calculated as:

styd

NAf

= .

If any value of Nleft-top or Nright-top is compression, for section adequacy, the area of steel required for compression, Asc, must satisfy the following relationship.

( )maxAbs ( ) Factor [0.85 ( ) ]cd g sc yd scN N f A A f A= − +

where N is either Nleft-top or Nright-top, Ag = bwB1, and the Nmax Factor is defined in the shear wall design preferences (the default is 0.80). In general, we recom-mend use of the default value.

max

Abs ( ) 0.85( Factor)

0.85

cd g

scyd cd

N f AN

Af f

−=

−.

If Asc calculates as negative, no compression reinforcing is needed.

The maximum tensile reinforcing to be packed within the bp times B1 concrete end zone is limited by:

-max max 1.st wA NT b B=

Similarly, the compression reinforcing is limited by:

-max max 1.sc wA NC b B=

If Ast is less than or equal to Ast-max and Asc is less than or equal to Asc-max, the program will proceed to check the next loading combination; otherwise the program will increment the appropriate B1 dimension (left, right or both, de-pending on which end zone is inadequate) by one-half of the wall thickness to B2 (i.e., 1.5bw) and calculate new values for Nleft-top and Nright-top resulting in new values of Ast and Asc. This iterative procedure continues until Ast and Asc are within the allowed steel ratios for all design load combinations.



If the value of the width of the end zone B increments to where it reaches a value larger than or equal to lw /2, the iteration is terminated and a failure con-dition is reported.

This design algorithm is an approximate but convenient algorithm. Wall piers that are declared overstressed using this algorithm could be found to be ade-quate if the reinforcing steel is user-specified and the wall pier is accurately evaluated using interaction diagrams.

2.3.1.2 Design Condition 2 Design condition 2 applies to a wall pier with user-specified end zones at each end of the pier. The size of the end zones is assumed to be fixed; that is, the program does not modify them. For this design condition, the design algorithm determines the area of steel required in the center end zones and checks if that area gives reinforcing ratios less than the user-specified maximum ratios. The design algorithm used is the same as described for condition 1; however, no it-eration is required.

2.3.1.3 Design Condition 3 Design condition 3 applies to a wall pier with a user-specified (fixed dimen-sion) end zone at one end of the pier and a variable length (program-determined) end zone at the other end. The width of the variable length end zone is equal to the width of the wall.

The design is similar to that which has previously been described for design conditions 1 and 2. The size of the user-specified end zone is not changed. Iter-ation occurs on the size of the variable length end zone only.

2.3.2 Checking a General or Uniform Reinforcing Pier Section When a General Reinforcing or Uniform Reinforcing pier section is specified to be checked, the program creates an interaction surface for that pier and uses that interaction surface to determine the critical flexural demand/capacity ratio for the pier. This section describes how the program generates the interaction surface for the pier and how it determines the demand/capacity ratio for a given design load combination.

Note: In this program, the interaction surface is defined by a series of PMM interac-tion curves that are equally spaced around a 360-degree circle.



2.3.2.1 Interaction Surface In this program, a three-dimensional interaction surface is defined with refer-ence to the Nd, M2d and M3d axes. The surface is developed using a series of interaction curves that are created by rotating the direction of the pier neutral axis in equally spaced increments around a 360-degree circle. For example, if 24 PMM curves are specified (the default), there is one curve every 15 degrees (360°/24 curves = 15°). Figure 2-6 illustrates the assumed orientation of the pier neutral axis and the associated sides of the neutral axis where the section is in tension (designated T in the figure) or compression (designated C in the fig-ure) for various angles.

a) Angle is 0 degrees 45°

Interaction curve isfor a neutral axisparallel to this axis

3

2

Pier section

b) Angle is 45 degrees


3

2

Pier section

a) Angle is 180 degrees 225°


3

2

Pier section

b) Angle is 225 degrees


3

2

Pier section

T C

T C

C TC T

Figure 2-6 Orientation of the Pier Neutral Axis for Various Angles

Note that the orientation of the neutral axis is the same for an angle of θ and θ+180°. Only the side of the neutral axis where the section is in tension or compression changes. We recommend use of 24 interaction curves (or more) to define a three-dimensional interaction surface.

Each PMM interaction curve that makes up the interaction surface is numeri-cally described by a series of discrete points connected by straight lines. The coordinates of these points are determined by rotating a plane of linear strain



about the neutral axis on the section of the pier. Details of this process are de-scribed later in the section entitled "Details of the Strain Compatibility Analy-sis."

By default, 11 points are used to define a PMM interaction curve. This number can be changed in the preferences; any odd number of points greater than or equal to 11 can be specified, to be used in creating the interaction curve. If an even number is specified for this item in the preferences, the program will in-crement up to the next higher odd number.

Note that when creating an interaction surface for a two-dimensional wall pier, the program considers only two interaction curvesthe 0° curve and the 180° curveregardless of the number of curves specified in the preferences. Fur-thermore, only moments about the M3 axis are considered for two-dimensional walls.

2.3.2.2 Formulation of the Interaction Surface The formulation of the interaction surface in this program is based consistently on the basic principles of ultimate strength design given in Sections 7.1 of TS 500-2000. The program uses the requirements of force equilibrium and strain compatibility to determine the strength axial load and moment strength (Nr, M2r, M3r) of the wall pier. For the pier to be deemed adequate, the required strength (Nd, M2d, M3d) must be less than or equal to the design strength, i.e.,

(Nd, M2d, M3d) ≤ (Nr, M2r, M3r)

The design strength for concrete and steel is obtained by dividing the character-istic 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.

The theoretical maximum compressive force that the wall pier can carry is des-ignated Noc and is given by:

Noc = [0.85fcd (Ag − Ast) + fydAst].



The theoretical maximum tension force that the wall pier can carry is designat-ed Not and is given by:

Not = fydAst.

If the wall pier geometry and reinforcing is symmetrical in plan, the moments associated with both Noc and Not are zero. Otherwise, a moment associated will be with both Noc and Not.

The maximum compressive axial load is limited to Nr(max), where

Nr(max) = 0.6 fck Ag for gravity combinations (TS 7.4.1)

Nr(max) = 0.5 fck Ag for seismic combinations

Note: The number of points to be used in creating interaction diagrams can be speci-fied in the shear wall preferences and overwrites.

As previously mentioned, by default, 11 points are used to define a single in-teraction curve. When creating a single interaction curve, the program includes the points at Nb, Noc and Not on the interaction curve. Half of the remaining number of specified points on the interaction curve occur between Nb and Noc at approximately equal spacing along the N axis. The other half of the remaining number of specified points on the interaction curve occur between Nb and Not at approximately equal spacing along the N axis.

Figure 2-7 shows a plan view of an example two-dimensional wall pier. Notice that the concrete is symmetrical but the reinforcing is not symmetrical in this example. Figure 2-8 shows several interaction surfaces for the wall pier illus-trated in Figure 2-7.

f’c = 4 ksify = 60 ksi

1'

12'-6"

3"

# 5@12” o.c.,each face, exceptas noted3"12 spaces at 1'-0" = 12'-0"

2-#9

2-#9

2-#6

Figure 2-7 Example Two-Dimensional Wall Pier With Unsymmetrical Reinforcing



Figure 2-8 Interaction Curves for Example Wall Pier Shown in Figure 2-7

Note the following about Figure 2-8:

Because the pier is two-dimensional, the interaction surface consists of two interaction curves. One curve is at 0° and the other is at 180°. Only M3d mo-ments are considered because this is a two-dimensional example.

In this program, compression is negative and tension is positive.

The 0° and 180° interaction curves are not symmetric because the wall pier reinforcing is not symmetric.

The smaller interaction surface (drawn with a heavier line) has the strength reduction factor, as specified by TS 500-2000.

The dashed line shows the effect of setting the NmaxFactor to 1.0.

The larger interaction surface has both the strength reduction factor and the NmaxFactor set to 1.0.



The interaction surfaces shown are created using the default value of 11 points for each interaction curve.

Figure 2-9 shows the 0° interaction curves for the wall pier illustrated in Figure 2-7. Additional interaction curves are also added to Figure 2-9.

Figure 2-9 Interaction Curves for Example Wall Pier Shown in Figure 2-7

The smaller, heavier curve in Figure 2-9 has the strength reduction factor as specified in TS 500-2000.

2.3.2.3 Details of the Strain Compatibility Analysis As previously mentioned, the program uses the requirements of force equilibri-um and strain compatibility to determine the nominal axial load and moment strength (Nd, M2d, M3d) of the wall pier. The coordinates of these points are de-termined by rotating a plane of linear strain on the section of the wall pier.

Figure 2-10 illustrates varying planes of linear strain such as those that the pro-gram considers on a wall pier section for a neutral axis orientation angle of 0 degrees.



Varyingneutral axislocations

Varying Linear Strain Diagram

Plan View of Wall Pier

-0.003

0.000

+ ε

- ε

Varyingneutral axislocations

Varying Linear Strain Diagram


-0.003

0.000

+ ε

- ε

Figure 2-10 Varying Planes of Linear Strain

In these planes, the maximum concrete strain is always taken as −0.003 and the maximum steel strain is varied from −0.003 to plus infinity. (Recall that in this program compression is negative and tension is positive.) When the steel strain is −0.003, the maximum compressive force in the wall pier, Noc, is obtained from the strain compatibility analysis. When the steel strain is plus infinity, the maximum tensile force in the wall pier, Not, is obtained. When the maximum steel strain is equal to the yield strain for the reinforcing (e.g., 0.00207 for fyk = 460 MPa), Nb is obtained.

Figure 2-11 illustrates the concrete wall pier stress-strain relationship that is obtained from a strain compatibility analysis of a typical plane of linear strain shown in Figure 2-10. In Figure 2-11 the compressive stress in the concrete, Cc, is calculated using section 7.2 of TS 500-2000.

Cc = 0.85fcdk1cbw (TS 7.1)

In Figure 2-10, the value for maximum strain in the reinforcing steel is as-sumed. Then the strain in all other reinforcing steel is determined based on the assumed plane of linear strain. Next the stress in the reinforcing steel is calcu-lated using the following equation, where εs is the strain, Es is the modulus of elasticity, σs is the stress, and fys is the yield stress of the reinforcing steel.



Linear Strain Diagram


c

ε = 0.

003

εs1εs

2εs3εs

4

εs5εs

6εs7εs

8εs9εs

10εs11εs

12εs13

a = β1cCc

0.85f'

c

Stress Diagram

Cs1Ts

5 Cs2Cs

3Cs4Ts

6Ts7Ts

8Ts9Ts

10Ts11Ts

12Ts13

t p

Linear Strain Diagram


c

ε = 0.

003

εs1εs1εs

2εs2εs

3εs3εs

4εs4

εs5εs5εs

6εs6εs

7εs7εs

8εs8εs

9εs9εs

10εs10εs

11εs11εs

12εs12εs

13εs13

a = β1cCc

0.85f'

c

Stress Diagram

Cs1Cs1Ts

5Ts5 Cs

2Cs2Cs

3Cs3Cs

4Cs4Ts

6Ts6Ts

7Ts7Ts

8Ts8Ts

9Ts9Ts

10Ts10Ts

11Ts11Ts

12Ts12Ts

13Ts13

t p

Figure 2-11 Wall Pier Stress-Strain Relationship

σs = εsEs ≤ fys

The force in the reinforcing steel (Ts for tension or Cs for compression) is cal-culated by:

Ts or Cs = σsAs

For the given distribution of strain, the value of Nr is calculated as:

Nr = (ΣTs − Cc − ΣCs) ≤ Nmax



In the preceding equation , the tensile force Ts and the compressive forces Cc and Cs are all positive. If Nr is positive, it is tension, and if it is negative, it is compression.

The value of M2r is calculated by summing the moments due to all of the forces about the pier local 2 axis. Similarly, the value of M3r is calculated by summing the moments due to all of the forces about the pier local 3 axis. The forces whose moments are summed to determine M2r and M3r are Nr, Cc, all of the Ts forces and all of the Cs forces.

The Nr, M2r and M3r values calculated as described in the preceding paragraph make up one point on the wall pier interaction diagram. Additional points on the diagram are obtained by making different assumptions for the maximum steel stress; that is, considering a different plane of linear strain, and repeating the process.

When one interaction curve is complete, the next orientation of the neutral axis is assumed and the points for the associated new interaction curve are calculat-ed. This process continues until the points for all of the specified curves have been calculated.

2.3.3 Wall Pier Demand/Capacity Ratio Refer to Figure 2-12, which shows a typical two-dimensional wall pier interac-tion diagram. The forces obtained from a given design load combination are Nd and M3d. The point L, defined by (Nd, M3d), is placed on the interaction dia-gram, as shown in the figure. If the point lies within the interaction curve, the wall pier capacity is adequate. If the point lies outside of the interaction curve, the wall pier is overstressed.

As a measure of the stress condition in the wall pier, the program calculates a stress ratio. The ratio is achieved by plotting the point L and determining the location of point C. The point C is defined as the point where the line OL (ex-tended outward if needed) intersects the interaction curve. The de-mand/capacity ratio, D/C, is given by D/C = OL / OC where OL is the "dis-tance" from point O (the origin) to point L, and OC is the "distance" from point O to point C. Note the following about the demand/capacity ratio:

If OL = OC (or D/C = 1), the point (Nd, M3d) lies on the interaction curve and the wall pier is stressed to capacity.

If OL < OC (or D/C < 1), the point (Nd, M3d) lies within the interaction curve and the wall pier capacity is adequate.



φPn

φM3nO

L

C

M3u

Pu

AxialCompression

AxialTension

Figure 2-12 Two-Dimensional Wall Pier Demand/Capacity Ratio

If OL > OC (or D/C > 1), the point (Nd, M3d) lies outside of the interaction curve and the wall pier is overstressed.

The wall pier demand/capacity ratio is a factor that gives an indication of the stress condition of the wall with respect to the capacity of the wall.

The demand/capacity ratio for a three-dimensional wall pier is determined in a similar manner to that described here for two-dimensional piers.

2.3.4 Designing a General Reinforcing Pier Section When a General Reinforcing pier section is specified to be designed, the pro-gram creates a series of interaction surfaces for the pier based on the following items:

The size of the pier as specified in Section Designer.

The location of the reinforcing specified in Section Designer.

The size of each reinforcing bar specified in Section Designer relative to the size of the other bars.

The interaction surfaces are developed for eight different ratios of reinforcing-steel-area-to-pier-area. The pier area is held constant and the rebar area is mod-



ified to obtain these different ratios; however, the relative size (area) of each rebar compared to the other bars is always kept constant.

The smallest of the eight reinforcing ratios used is that specified in the shear wall design preferences as Section Design IP-Min. Similarly, the largest of the eight reinforcing ratios used is that specified in the shear wall design prefer-ences as Section Design IP-Max.

The eight reinforcing ratios used are the maximum and the minimum ratios plus six more ratios. The spacing between the reinforcing ratios is calculated as an increasing arithmetic series in which the space between the first two ratios is equal to one-third of the space between the last two ratios. Table 1 illustrates the spacing, both in general terms and for a specific example, when the mini-mum reinforcing ratio, IPmin, is 0.0025 and the maximum, IPmax, is 0.02.

After the eight reinforcing ratios have been determined, the program develops interaction surfaces for all eight of the ratios using the process described earlier in the section entitled "Checking a General or Uniform Reinforcing Pier Sec-tion."

Next, for a given design load combination, the program generates a de-mand/capacity ratio associated with each of the eight interaction surfaces. The program then uses linear interpolation between the eight interaction surfaces to determine the reinforcing ratio that gives a demand/capacity ratio of 1 (actually the program uses 0.99 instead of 1). This process is repeated for all design load combinations and the largest required reinforcing ratio is reported.

Design of a Uniform Reinforcing pier section is similar to that described herein for the General Reinforcing section.

Table 2-1 The Eight Reinforcing Ratios Used by the Program Curve Ratio Example

1 IPmin 0.0025

2 IPmax IPminIPmin +

14− 0.0038

3 7 IPmax IPminIPmin +3 14

−

0.0054

4 IPmax IPminIPmin + 4

14−

0.0075


14−

0.0100

6 25 IPmax IPminIPmin +3 14

−

0.0129



Table 2-1 The Eight Reinforcing Ratios Used by the Program Curve Ratio Example


14−

0.0163

8 IPmax 0.0200


Chapter 3 Spandrel Design

This chapter describes how the program designs concrete shear wall spandrels for flexure and shear when TS 500-2000 is the selected design code. The program allows consideration of rectangular sections and T-beam sections for shear wall spandrels. Note that the program designs spandrels at stations located at the ends of the spandrel. No design is performed at the center (mid-length) of the spandrel. The program does not allow shear reinforcing to be specified and then checked. The program only designs the spandrel for shear and reports how much shear reinforcing is required.

3.1 Spandrel Flexural Design In this program, wall spandrels are designed for major direction flexure and shear only. Effects caused by any axial forces, minor direction bending, torsion or minor direction shear that may exist in the spandrels must be investigated by the user independent of the program. Spandrel flexural reinforcing is designed for each of the design load combinations. The required area of reinforcing for flexure is calculated and reported only at the ends of the spandrel beam.

The following steps are involved in designing the flexural reinforcing for a par-ticular wall spandrel section for a particular design loading combination at a particular station.

Determine the maximum factored moment Md.

3-1


Determine the required flexural reinforcing.

These steps are described in the following sections.

3.1.1 Determine the Maximum Factored Moments In the design of flexural reinforcing for spandrels, the factored moments for each design load combination at a particular beam station are first obtained.

The beam section is then designed for the maximum positive and the maximum negative factored moments obtained from all of the design load combinations.

3.1.2 Determine the Required Flexural Reinforcing In this program, negative beam moments produce top steel. In such cases, the beam is always designed as a rectangular section.

In this program, positive beam moments produce bottom steel. In such cases, the beam may be designed as a rectangular section, or as a T-beam section. Indicate that a spandrel is to be designed as a T-beam by specifying the appro-priate slab width and depth dimensions are provided in the spandrel design overwrites (Appendix B).

The flexural design procedure is based on a simplified rectangular stress block, as shown in Figure 3-1. 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):

cu sb

cu s yd

Ec dE fε

=ε +

(TS 7.1)

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

max 10.85 ba k c= (TS 7.11, 7.3, Eqn. 7.4)

where k1 is calculated as follows:

k1 = 0.85 − 0.006 ( )25ckf − , 0.70 ≤ k1 ≤ 0.85. (TS 7.1, Table 7.1)

3-2 Spandrel Flexural Design


Figure 3-1 Rectangular Spandrel Beam Design, Positive Moment

It is assumed that the compression depth carried by the concrete is less than or equal to amax. When the applied moment exceeds the moment capacity at amax, the program calculates an area of compression reinforcement assuming that the additional moment is carried by compression reinforcing and additional tension reinforcing.

The procedure used by the program for both rectangular and T-beam sections is given in the subsections that follow.

3.1.2.1 Rectangular Beam Flexural Reinforcing Refer to Figure 3-1. For a rectangular beam, the factored moment, Md, is resist-ed by a couple between the concrete in compression and the tension in reinforc-ing steel. This is expressed as:

spandrel 2d caM C d = −

(TS 7.1)

where 0.85=c cd sC f a t and dspandrel is equal to hs − dr-bot for positive bending and hs − dr-top for negative bending.

The depth of the compression block, a, is given by:

Spandrel Flexural Design 3-3


2spandrel spandrel

20.85

= − − d

cd s

Ma d df t

The program uses the preceding equation to determine the depth of the com-pression block, a. The depth of the compression block, a, is compared with amax.

3.1.2.1.1 Tension Reinforcing Only Required If a ≤ amax, no compression reinforcing is required and the program calculates the area of tension reinforcing,

spandrel 2

= −

ds

yd

MAaf d

The steel is placed at the bottom for positive moment and at the top for nega-tive moment.

Note: The program reports the ratio of top and bottom steel required in the web area. When compression steel is required, those ratios may be large because there is no limit on them. However, the program reports an overstress when the ratio exceeds 4%.

3.1.2.1.2 Tension and Compression Reinforcing Required If a > amax, compression reinforcing is required and the program calculates re-quired compression and tension reinforcing as follows.

The depth of the concrete compression block, a, is set equal to a = amax. The compressive force developed in the concrete alone is given by

max0.85=c cd sC f a t (TS 7.1)

The moment resisted by the couple between the concrete in compression and the tension steel, Mdc, is given by

maxspandrel 2

= −

dc caM C d

Therefore, the additional moment to be resisted by the couple between the compression steel and the additional tension steel, Mds, is given by



= −ds d dcM M M

The force carried by the compression steel, Cs, is given by,

spandrel

=−

dss

r

MCd d

Referring to Figure 3-1, the strain in the compression steel, ε's, is given by.

( )0.003 rs

c dc−′ε =

The stress in the compression steel, f 's, is given by.

max

max.s s cu yd

c dE fc

′−′σ ε ≤

The term dr in the preceding equations is equal to dr-top for positive bending and equal to dr-bot for negative bending. The term c is equal to max 1.a k

The total required area of compression steel, A's, is calculated using the follow-ing equation.

( 0.85 )σ

′ =′ −

ss

s cd

CAf

The required area of tension steel for balancing the compression in the concrete web, Asw, is:

max

spandrel 2

= −

dcsw

yd

MAaf d

The required area of tension steel for balancing the compression steel, Asc, is:

( )spandrel

=−

dssc

yd r

MAf d d

In the preceding equations, dspandrel is equal to hs − dr-bot for positive bending and hs − dr-top for negative bending. In the preceding equations, dr is equal to dr-top for positive bending and dr-bot for negative bending.



The total tension reinforcement As is given by:

s sw scA A A= +

Thus, the total tension reinforcement, As, and the total compression reinforce-ment, As'. As is to be placed at the bottom of the beam, and As' at the top for positive bending and vice versa for negative bending.

3.1.2.2 T-Beam Flexural Reinforcing T-beam action is considered effective for positive moment only. When design-ing T-beams for negative moment (i.e., designing top steel), the calculation of required steel is as described in the previous section for rectangular sections. No T-beam data is used in this design. The width of the beam is taken equal to the width of the web.

For positive moment, the depth of the compression block, a, is given by

2 2 .0.85

d

cd f

Ma d df b

= − −

If a ≤ ds, the subsequent calculations for the reinforcing steel are exactly the same as previously defined for rectangular section design. However, in that case, the width of the compression block is taken to be equal to the width of the compression flange, bs. Compression reinforcement is provided when the dimension "a" exceeds amax.

If a > ds, the subsequent calculations for the required area of reinforcing steel are performed in two parts. First, the tension steel required to balance the compressive force in the flange is determined, and second, the tension steel required to balance the compressive force in the web is determined. If neces-sary, compression steel is added to help resist the design moment.

The remainder of this section describes in detail the design process used by the program for T-beam spandrels when a > ds.

Refer to Figure 3-2. The compression force in the protruding portion of the flange, Cf, is given. The protruding portion of the flange is shown cross-hatched.

( )0.85= −f cd s s sC f b t d



Figure 3-2 Design of a Wall Spandrel with a T-Beam Section, Positive Moment

The required area of tension steel for balancing the compression force in the concrete flange, Asf, is:

= fsf

yd

CA

f

The portion of the total moment, Md, that is resisted by the flange, Mdf, is given by

spandrel .2

sdf f

dM C d = −

Therefore, the balance of the moment to be carried by the web, Mdw, is given by

.dw d dfM M M= −

The web is a rectangular section of width ts and depth hs for which the design depth of the compression block, a1, is recalculated as:

21 spandrel spandrel

20.85

= − − dw

cd s

Ma d df t



3.1.2.2.1 Tension Reinforcing Only Required If a1 ≤ amax, no compression reinforcing is required and the program calculates the area of tension steel for balancing the compression force in the concrete web, Asw.

1

2

= −

dwsw

yd spandrel

MAaf d

The total tension reinforcement As is given by.

s sf swA A A= +

The total tension reinforcement, As, is to be placed at the bottom of the beam for positive bending.

3.1.2.2.2 Tension and Compression Reinforcing Required If a1 > amax, where a1 is calculated using the equation in Section 3.1.2.2, com-pression reinforcing is required. In that case, the required reinforcing is com-puted as follows.

The depth of the concrete compression block, a, is set equal to amax, a = amax. The compressive force developed in the web concrete alone is given by

0.85 .w cd sC f at=

The moment resisted by the couple between the concrete web in compression and the tension steel, Mdc, is given by

spandrel .2dc waM C d = −

Therefore, the additional moment to be resisted by the couple between the compression steel and the tension steel, Mds, is given by

= −ds dw dcM M M

Referring to Figure 3-2, the force carried by the compression steel, Cs, is given by



spandrel -

.dss

r top

MCd d

=−

The strain in the compression steel, εs', is given by

( )-0.003

.r tops

c dc−′ =ε

The stress in the compression steel, fs', is given by

( )-top0.003

.s rs s s

E c df E

c−′ ′= ε =

The term c is equal to max 1 .a k

The required area of compression steel, As', is calculated as,

.ss

s

CA ′ =′σ

The required area of tension steel for balancing the compression in the concrete web, Asw, is

spandrel

.

2

dcsw

yd

MAaf d

= −

The required area of tension steel for balancing the compression steel, Asc, is

( )spandrel -top

.dssc

yd r

MAf d d

=−

The total tension reinforcement As is given by

.s sf sw scA A A A= + +

As is to be placed at the bottom of the beam, and As' at the top of the beam.



3.2 Spandrel Shear Design The program allows consideration of rectangular sections and T-beam sections for wall spandrels. The shear design for both of these types of spandrel sections is identical.

The wall spandrel shear reinforcing is designed for each of the design load combinations. The required area of reinforcing for vertical shear is calculated only at the ends of the spandrel beam.

In this program, wall spandrels are designed for major direction flexure and shear forces only. Effects caused by any axial forces, minor direction bending, torsion or minor direction shear that may exist in the spandrels must be investi-gated by the user independent of the program.

The following steps are involved in designing the shear reinforcing for a par-ticular wall spandrel section for a particular design loading combination at a particular station.

Determine the factored shear force Vd.

Determine the shear force, Vc, that can be carried by the concrete.

Determine the required shear reinforcing to carry the balance of the shear force.

Step 1 needs no further explanation. The following two sections describe in de-tail the algorithms associated with Steps 2 and 3.

3.2.1 Determine the Concrete Shear Capacity Given Vd and Vc, the required shear reinforcement in the form of stirrups or ties within a spacing, s, is given for rectangular beam by the following:

The shear force is limited to a maximum of

max 0.22 cd wV f A= (TS 8.1.5b, TCS 3.3.7.5)

The required shear reinforcement per unit spacing, Asw /s, is calculated as fol-lows:

If ,d crV V≤

3-10 Spandrel Shear Design


0.3 ,sw ctdw

ywd

A f bs f

= (TS 8.1.5, Eqn. 8.6)

else if max ,cr dV V V< ≤

( )d csw

ywd

V VAs f d

−= , (TS 8.1.4, Eqn. 8.5)

0.3sw ctdw

ywd

A f bs f

≥ (TS 8.1.5, Eqn. 8.6)

else if max ,dV V>

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).

3.2.2 Determine the Required Shear Reinforcing One of the terms used in calculating the spandrel shear reinforcing is dspandrel, which is the distance from the extreme compression fiber to the centroid of the tension steel. For shear design, the program takes dspandrel to be equal to the smaller of hs − dr-top and hs − dr-bot.

3.2.2.1 Seismic and Nonseismic Spandrels Given Vd and Vcr, the required force to be carried by the shear reinforcing, Vds, is calculated using (TS 8.1.4).

= −ds d crV V V (TS 8.1.4)

If Vds exceeds spandrel1.5 ,ctd sf t d a failure condition is reported in accordance with TCS Section 3.6.8.4.

Given Vds, the preceding equation initially calculates the required vertical shear reinforcing in area per unit length (e.g., square mm per meter) for both seismic and nonseismic wall spandrels (as indicated in the preferences). Note that addi-tional requirements that are checked for both seismic and nonseismic wall spandrels are given as.

Spandrel Shear Design 3-11


spandrel

= dsv

yd

VAf d

Note: The output units for the distributed shear reinforcing can be set in the shear wall design preferences.

3.2.2.2 Seismic Spandrels Only For seismic spandrels only, in addition to the requirements of the previous sub-section, an area of diagonal shear reinforcement in coupling beams is also cal-

culated when spandrel

3≤sLd

using the following equation.

2 sin

dvd

yd

VAf

=γ

, (TCS 3.6.8.4(b))

where,

2 2

0.8sin(0.8 )

s

s s

h

L hγ =

+,

where hs is the height of the spandrel and Ls is the length of the spandrel.

In the output, the program reports the diagonal shear reinforcing as required or not required (i.e., optional). The diagonal shear reinforcing is reported as re-quired when spandrel1.5f .>d ctdV db

3-12 Spandrel Shear Design

Chapter 4 Design Output

The program has the capacity to create design output in four major ways – graphical display, file output, tabular display, and member specific detailed design information. The graphical display includes input and output design information for members visible in the active window; the display can be sent directly to a printer or saved to a file. The file output includes both summary and detail design data that can be saved in RTF, HTML and plain text formats. The tabular display output includes both summary and detail design data that can be displayed or saved in many formats, including Excel, Access, RTF, HTML and plain text. The member specific detailed design in-formation shows the details of the calculation.

The following sections describe some of the typical graphical display, file output, tabular display output, and member specific detailed design infor-mation. Some of the design information is very specific to the chosen shear wall design code. This manual addresses "TS 500-200" design code related output information only.

4.1 Graphical Display of Design Information The graphical display of design output includes input and output design in-formation for all shear wall members that are visible in the active window. The graphical output can be produced in color or in gray-scaled screen dis-

4-1

Shear Wall Design Manual TS 500-2000

play. The active screen display can be sent directly to the printer or saved to a file in several formats.

Use the Design menu > Shear Wall Design > Display Design Info com-mand to display on-screen output plotted directly on the model. If desired, the screen graphics can then be printed using the File menu > Print Graphics command. The on-screen display data is organized into two main groups, as follows.

Design Input

Material

Thickness

Pier length/spandrel depth

Section Designer pier sections

Design Output

Simplified pier longitudinal reinforcing

Simplified pier edge members

Section Designer pier reinforcing ratios

Section Designer pier D/C ratios

Spandrel longitudinal reinforcing

Shear reinforcing

Pier demand/capacity ratios

Pier boundary zones

Note that you cannot display more than one of the listed items on the model at the same time.

The output plotted directly on piers is plotted along an invisible line that ex-tends from the centroid of the pier section at the bottom of the pier to the centroid of the pier section at the top of the pier. Similarly, the output plotted directly on spandrels is plotted along an invisible line that extends from the

4-2 Graphical Display of Design Information


centroid of the spandrel section at the left end of the spandrel to the centroid of the spandrel section at the top of the spandrel.

The onscreen graphical display can be sent to printer using any of the follow-ing commands. Use the File menu > Print Graphics command to print the active window. To capture the graphical display in a file for printing through another application, use the File menu > Capture Enhanced Metafile command to create an .emf file, or use the File menu > Capture Picture command to create a bitmap (.bmp) file. Create a screen capture of the active window using the Alt+ Print Screen keyboard keys or create a screen cap-ture of the entire window using the Ctrl + Print Screen keyboard keys. Then use the Ctrl+V keyboard keys to paste the saved image into Paint or other graphical program.

4.2 Tabular Display of Design Information In addition to model definition and analysis results, the design information for all piers and spandrels or for only selected piers and spandrels can be dis-played in tabular spreadsheet format. Currently, the program generates de-sign pier location data, pier basic overwrite data, uniform reinforcing sec-tions, general reinforcing sections, simplified T and C sections, spandrel lo-cation data, spandrel basic overwrite data, and spandrel geometry data. The tabular spreadsheet output can be displayed by selecting the Display menu > Show Tables command to access the Choose Tables for Display form. That form can be used to choose which tables or sets of tables are to be displayed.

The names of the tables are displayed in a tree structure, which can be col-lapsed or expanded by clicking on an item in the tree. Click on the small check boxes preceding the items to select those tables for display. If a branch of the tree is selected, all of the tables under that branch are selected. The se-lected set of tables can be saved as a Named Set using the Save Named Set button. This named set can be used in the future for quick selection. If one or more frame members are selected on the structural model before accessing the Choose Tables for Display form, the Selection Only check box will be checked when the form displays and, the program will display information for the selected members only; uncheck the check box to display information for all applicable "unselected" members in the model. If the Show Unformat-ted check box is checked, the numbers will be displayed unformatted, instead of being displayed using a limited number of decimal digits. The unformatted option provides higher precision output that can then be copied into other programs.

Tabular Display of Design Information 4-3


Use the other buttons in the form to tailor the data display. For example, click the Select Load Cases button to specify which load cases are to be in-cluded in the display of model definition data; click the Select Analysis Case and Modify/Show Options to specify which analysis cases are to be includ-ed and how analysis results are displayed.

After selecting all of the tables for shear wall design and the display options, click the OK button to display a form showing one of the selected design ta-bles, with a drop-down list in the upper right-hand corner of the form that can be used to select other tables for display.

Use the scroll bars on the bottom and right side of the tables to scroll right and left or up and down if portions of the data table can not be displayed in the form's display area. The columns can be resized by clicking the left mouse button on the separator of the headers, holding down the left mouse button and then dragging the mouse to the left or right. Reset the column widths to their default values by selecting the Format-Filter-Sort menu > Reset Default Column Widths command on the form. The table can be split into two or more tables by clicking on the small black rectangular area near the bottom-left corner of the table, holding down the left mouse button, and then dragging the mouse button to the left or right. Repeat this process to add more splits. Use the split and horizontal scroll bar to put two columns side by side for easier comparison. The splits can be removed by selecting the For-mat-Filter-Sort menu > Remove Splits command on the form. Alternative-ly, remove the split by clicking, holding and dragging the left mouse button to merge the split key to its original location.

Select multiple consecutive columns by putting the cursor on the header, holding down the mouse button, and then dragging the mouse button left or right. Alternatively, depress the Shift key and click the left mouse button to select a range of columns.

Each of the individual fields (columns) can be formatted. Fields with text in-formation can be set for specific types of alignment (center, left, right) and to specific widths. In addition to setting the alignment and column widths, fields with numeric data can be set for the maximum number of characters, zero tolerance, number of decimal digits and so forth. The tables can be for-matted, filtered and sorted using multiple criteria accessed using the Format-Filter-Sort menu on the form. Filtering and sorting features can be useful in identifying critical cases. After specifying the table formatting information, save it to a format file that can be used in the future by selecting the appro-priate feature available under the Format-Filter-Sort menu.

4-4 Tabular Display of Design Information


The current table (i.e., the table in the active window) can be exported to Ex-cel, Access, .rtf., .html, and plain text formats. In both Excel spreadsheet and Access database formats, the tables can have many columns, making the ta-bles very wide. In .rft and .html formats, the tables are split at convenient points to make a reasonably printable document. In plain text format, the ta-bles can be saved with or without the splits. To export a table to Excel, for example, select the File menu > Export Current Table > To Excel com-mand. The program will export the entire table to an Excel spreadsheet workbook and will automatically open the file in MS Excel. Similarly, if the table is exported to other formats, the default editor specific to that format will open the document, provided that the editor is available in the computer. The table will be saved in that format only if the relevant editor is not availa-ble. Instead of exporting or displaying the currently displayed table, the en-tire set of available tables can be exported and displayed in the afore-mentioned formats by selecting the File menu and the appropriate submenu command. With these exporting and display features, the tables can be saved in many required formats and can be printed. Many other features of the de-sign tables are left for the user to discover by using the program.

4.3 Detailed Display of Member Specific Information Interactive design is a powerful mode that allows quick, on-screen review of design results for a specific pier or spandrel. This mode allows easy modifi-cation to design parameters (overwrites) and immediate review of the new results.

Note that a design must have been run for the interactive design mode to be available. To run a design, click the Design menu > Shear Wall Design > Start Design/Check of Structure command.

To enter the interactive design and review mode, right click on a wall pier or spandrel while the design results are displayed. If design results are not cur-rently displayed (and the design has been run), click the Design menu > Shear Wall Design > Interactive Wall Design command and then right click a pier or spandrel to enter the interactive design and review mode for that pier or spandrel.

Note that if both a pier and a spandrel label are assigned to the right-clicked object, a pop-up box offers the choice to enter the interactive design and re-view mode for the pier or for the spandrel. Appendix E provides additional information about interactive shear wall design.

Detailed Display of Member Specific Information 4-5


4.4 Output of Design Information In addition to model definition and analysis results, the design information for all piers and spandrels or for selected piers and spandrels only can be saved in tabular format. For AIC 318-02 code, the program saves simplified pier longitudinal reinforcing, simplified pier edge members, Section Design-er pier reinforcing ratios, section Designer pier D/C ratios, spandrel longitu-dinal reinforcing, shear reinforcing, sier demand/capacity ratios and pier boundary zones. Save the file output by selecting the File menu > Print Tables command to access the Choose Tables for Printing form. Use the op-tions on the form to choose which table or set of tables to save in a file or print. This form is very similar to the Choose Tables for Display form, which has been described earlier in this chapter in the "Tabular Display of Design Information" section.

The name of the tables are displayed in a tree structure, which can be col-lapsed or expanded by clicking on an item in the tree. Click on the small check boxes preceding the items to select those tables for printing or saving to a file. If a branch of the tree is selected, all of the tables under that branch are selected. When all options for printing or saving the data to file have been specified, the settings can be saved as a Named Set using the Save Named Set button. The Named Set can be easily recalled in the future, re-ducing the need to reselect the options and ensuring that output is consistent from one printing effort to another.

If one or more structural members are selected before the Choose Tables for Printing form is accessed, the Selection Only check box will be checked, and the program will save or print the data for the selected members only; un-check the check box to save or print the data for all appropriate "unselected" members.

The output can be generated in a variety of formats, including rich text for-mat (.rft), plain text with and without splits or page breaks (.txt), and hyper-link text markup language (.htm) by choosing the appropriate option on the right side of the form.

Printed output can be specified to have a landscaped orientation, in which the width of the resulting printout on a given page is longer than the height of the printout.

Filtering criteria can be applied if those criteria were specified using the Format-Filter-Sort menu > Format Table command when the selected da-ta tables were displayed using the Display menu > Show Tables command.

4-6 Output of Design Information


The output also can be specified to include a hyperlinked contents to facili-tate accessing specific areas of the printout.

There are other buttons on the form that do not affect saving or printing de-sign information. For example, the Select Load Cases button affects only saving/printing model definition data. The Select Analysis Cases and Modi-fy/Show Options buttons affect only saving/printing analysis results.

After clicking all the necessary tables for steel frame design and all necessary options, clicking the OK button will save/print the design tables.

Although the File name > Print Tables command path is dedicated for sav-ing/printing design information, it is not the only path to do so. Design tables can be saved in different formats using the path Display menu > Show Ta-bles command.

4.5 Error Messages and Warnings Error messages and warnings may be displayed in the shear wall design out-put. The messages are numbered. A list of error messages and warnings used in Shear Wall Design for all the design codes is provide in Appendix I. How-ever, all of the messages are not applicable to the TS 500-200.

Error Messages and Warnings 4-7

Appendix A Shear Wall Design Preferences

The shear wall design preferences are basic properties that apply to all wall pier and spandrel elements. Table A1 identifies shear wall design preferences for TS-500-2000. Default values are provided for all shear wall design preference items. Thus, it is not required that preferences be specified. However, at least review the default values for the preference items to make sure they are acceptable. Refer to the program Help for an explanation of how to change a preference.

Table A1 Shear Wall Preferences

Item Possible Values

Default Value

Description

Design Code Any code in the program

ACI 318-14 Design code used for design of concrete shear wall elements (wall piers and spandrels)

A-1

Shear Wall Design TS-500-2000



Default Value

Description

Multi-Response Case Design

Envelopes, Step-by-Step,

Last Step, Envelopes-All,

Step-by-Step-All

Envelopes

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. - Envelopes - considers enveloping values for Time History and Multi-step static and last step values for Nonlinear static. - Step-by-Step - considers step by step values for Time History and Multi-step static and last step values for Nonlinear static. - Last Step - considers last values for Time History, Multi-step static and Nonlinear static. - Envelopes - All - considers enveloping values for Time History, Multi-step static and Nonlinear static. - Step-by-Step - All - considers step by step values for Time History, Multi-step static and Nonlinear static. Step-by-Step and Step-by-Step - All default to the corresponding Envelope if more than one multivalued case is present in the combo.

Rebar Material Rebar Material Name

Rebar Material Name

Rebar material for flexural and boundary zone (if applicable) design.

Rebar Shear Material

Rebar Material Name

Rebar Material Name

Rebar material for shear design.

Gamma (Steel) > 0 1.15 The strength reduction factor for reinforcement in a wall pier or spandrel.

Gamma (Concrete)

> 0 1.50 The strength reduction factor for concrete in a wall pier or spandrel.

Nmax Factor > 0 1.0 A factor used to reduce the allowable maximum compressive design strength.

Number of Curves ≥ 4 24 Number of equally spaced interaction curves used to create a full 360-degree interaction surface (this item should be a multiple of four). We recommend that you use 24 for this item.

Number of Points ≥ 11 11 Number of points used for defining a single curve in a wall pier interaction surface (this item should be odd)..

Edge Design PT-max

> 0 0.06 Maximum ratio of tension reinforcing allowed in edge members, PTmax..

Edge Design PC-max

> 0 0.04 Maximum ratio of compression reinforcing allowed in edge members, PCmax.

A-2

Appendix A Preferences



Default Value

Description

Section Design IP-Max

≥ Section Design IP-Min

0.02 The maximum ratio of reinforcing considered in the design of a pier with a Section Designer section.

Section Design IP-Min

> 0 0.0025 The minimum ratio of reinforcing considered in the design of a pier with a Section Designer section.

Utilization Factor Limit

> 0 0.95 Stress ratios that are less than or equal to this value are considered acceptable.

A-3

Appendix B Design Procedure Overwrites

The shear wall design overwrites are basic assignments that apply only to those piers or spandrels to which they are assigned. The overwrites for piers and spandrels are separate. Tables B1 and B2 identify the shear wall overwrites for piers and spandrels, respectively, for TS-500-2000. Note that the available overwrites change depending on the pier section type (Uniform Reinforcing, General Reinforcing, or Simplified T and C).

Default values are provided for all pier and spandrel overwrite items. Thus, it is not necessary to specify or change any of the overwrites. However, at least review the default values for the overwrite items to make sure they are accept-able. When changes are made to overwrite items, the program applies the changes only to the elements to which they are specifically assigned; that is, to the elements that are selected when the overwrites are changed. Refer to the program Help for an explanation of how to change the overwrites.

Table B-1: Pier Design Overwrites Pier Overwrite


Default Value

Pier Overwrite Description

Design this Pier Yes or No Yes Toggle for design of the pier when you click the Design menu > Shear Wall Design > Start Design/Check command.

B-1




Default Value


LL Reduction Factor

Program calculated,

> 0

Program calculated

A reducible live load is multiplied by this factor to obtain the reduced live load. Entering 0 for this item means that it is program calculated. See the subsection entitled "LL Reduction Factor" for more information.

Design is Seismic Yes or No Yes Toggle for design as seismic or nonseismic. Additional design checks are performed for seismic elements compared to nonseismic elements. Also, in some cases, the strength reduction factors are different.

Pier Section Type Uniform Reinforcing,

General Reinforcing, Simplified T and C

Uniform Reinforcing

This item indicates the type of pier. The General Reinforcing option is not available unless General pier sections have previously been defined in Section Designer.

Overwrites Applicable to Uniform Reinforcing Pier Sections Edge Bar Name Any defined bar

size Varies The size of the uniformly spaced edge bars.

Edge Bar Spacing >0 250 mm The spacing of the uniformly spaced edge bars. End/Corner Bar

Name Any defined bar

size Varies The size of end and corner bars.

Clear Cover >0 40 mm The clear cover for the edge, end and corners bars.

Material Any defined concrete material

property

Varies The material property associated with the pier.

Check/Design Reinforcing

Check or Design

Design This item indicate whether the pier section is to be designed or checked.

Overwrites Applicable to General Reinforcing Pier Sections Section Bottom Any general pier

section defined in Section Designer

The first pier in the list of Section Designer piers

Name of a pier section, defined in Section Designer that is assigned to the bottom of the pier.

Section Top Any general pier section defined in

Section Designer

The first pier in the list of

Section Designer piers

Name of a pier section, defined in Section Designer, that is assigned to the top of the pier.

Check/Design Reinforcing

Check or Design

Design This item indicates whether the pier section is to be designed or checked.

Overwrites Applicable to Simplified T and C Pier Sections ThickBot Program

calculated, or > 0

Program calculated

Wall pier thickness at bottom of pier, tp. Inputting 0 means the item is to be program calculated.

LengthBot Program calculated,

or > 0

Program calculated

Wall pier length at bottom of pier, Lp. Inputting 0 means the item is to be program calculated.

DB1LeftBot ≥ 0 0 Length of the bottom of a user-defined edge member on the left side of a wall pier, DB1left.

B-2

Appendix B Overwrites



Default Value


DB2LeftBot ≥ 0 0 Width of the bottom of a user-defined edge member on the left side of a wall pier, DB2left. See Figure 2-3 in Chapter 2 for more information.

DB1RightBot ≥ 0 Same as DB1-left-bot

Length of the bottom of a user-defined edge member on the right side of a wall pier, DB1right.

DB2RightBot ≥ 0 Same as DB2-left-bot

Width of the bottom of a user-defined edge member on the right side of a wall pier, DB2right.

ThickTop Program calculated,

or > 0

Program calculated

Wall pier thickness at top of pier, tp. Inputting 0 means the item is to be program calculated.

LengthTop Program calculated,

or > 0

Program calculated

Wall pier length at top of pier, Lp. Inputting 0 means the item is to be program calculated.

DB1LeftTop ≥ 0 0 Length of the top of a user-defined edge member on the left side of a wall pier, DB1left.

DB2LeftTop ≥ 0 0 Width of the top of a user-defined edge member on the left side of a wall pier, DB2left.

DB1RightTop ≥ 0 Same as DB1-left-bot

Length of the top of a user-defined edge member on the right side of a wall pier, DB1right.

DB2RightTop ≥ 0 Same as DB2-left-bot

Width of the top of a user-defined edge member on the right side of a wall pier, DB2right.

Material Any defined concrete material property

Material property associated with the pier.

Edge Design NC-max

> 0 Specified in Preferences

Maximum ratio of compression reinforcing allowed in edge members, NCmax.

Edge Design NT-max

> 0 Specified in Preferences

Maximum ratio of tension reinforcing allowed in edge members, NTmax.

B.1 LL Reduction Factor If the LL Reduction Factor is program calculated, it is based on the live load reduction method chosen in the live load reduction preferences. If you specify your own LL Reduction Factor, the program ignores any reduction method specified in the live load reduction preferences and simply calculates the reduced live load for a pier or spandrel by multiplying the specified LL Reduction Factor times the reducible live load.

Note that options are available to define a load case as a reducible live load.

Important Note: The LL reduction factor is not applied to any load combination that is included in a design load combination. For example, assume you have two static load cases labeled DL and RLL. DL is a dead load and RLL is a reducible live load. Now assume that you create a design load combination named DESCOMB1 that includes DL and RLL. Then for

B-3


design load combination DESCOMB1, the RLL load is multiplied by the LL reduction factor. Next assume that you create a load combination called COMB2 that includes RLL. Now assume that you create a design load combination called DESCOMB3 that included DL and COMB2. For design load combination DESCOMB3, the RLL load that is part of COMB2 is not multiplied by the LL reduction factor.

B.2 User-Defined Edge Members When defining a user-defined edge member, you must specify both a nonzero value for DB1 and a nonzero value for DB2. If either DB1 or DB2 is specified as zero, the edge member width is taken as the same as the pier thickness and the edge member length is determined by the program.

Table B-2 Spandrel Design Overwrites

Spandrel Overwrite


Default Value

Spandrel Overwrite Description

Design this Spandrel

Yes or No Yes Toggle for design of the spandrel when you click the Design menu > Shear Wall Design > Start Design/Check command.

LL Reduction Factor

Program calculated,

> 0

Program calculated

A reducible live load is multiplied by this factor to obtain the reduced live load. Entering 0 for this item means that it is program calculated. See the subsection entitled "LL Reduction Factor" for more information.

Design is Seismic Yes or No Yes Toggle for design as seismic or nonseismic. Additional design checks are performed for seismic elements compared to nonseismic elements. Also, in some cases the strength reduction factors are different.

Length Program calculated,

or > 0

Program calculated

Wall spandrel length, Ls. Inputting 0 means the item is to be program calculated.

ThickLeft Program calculated,

or > 0

Program calculated

Wall spandrel thickness at left side of spandrel, ts. Inputting 0 means the item is to be program calculated.

DepthLeft Program calculated,

or > 0

Program calculated

Wall spandrel depth at left side of spandrel, hs. Inputting 0 means the item is to be program calculated.

CoverBotLeft Program calculated,

or > 0

Program calculated

Distance from bottom of spandrel to centroid of bottom reinforcing, dr-bot left on left side of beam. Inputting 0 means the item is to be program calculated as 0.1hs.

CoverTopLeft Program calculated,

or > 0

Program calculated

Distance from top of spandrel to centroid of top reinforcing, dr-top left on left side of beam. Inputting 0 means the item is to be program calculated as 0.1hs.

SlabWidthLeft ≥ 0 0 Slab width for T-beam at left end of spandrel, bs.

B-4

Appendix B Overwrites

Table B-2 Spandrel Design Overwrites

Spandrel Overwrite


Default Value

Spandrel Overwrite Description

SlabDepthLeft ≥ 0 0 Slab depth for T-beam at left end of spandrel, ds. ThickRight Program

calculated, or > 0

Program calculated

Wall spandrel thickness at right side of spandrel, ts. Inputting 0 means the item is to be program calculated.

DepthRight Program calculated,

or > 0

Program calculated

Wall spandrel depth at right side of spandrel, hs. Inputting 0 means the item is to be program calculated.

CoverBotRight Program calculated,

or > 0

Program calculated

Distance from bottom of spandrel to centroid of bottom reinforcing, dr-bot right on right side of beam. Inputting 0 means the item is to be program calculated as 0.1hs.

Cover- TopRight

Program calculated,

or > 0

Program calculated

Distance from top of spandrel to centroid of top reinforcing, dr-top right on right side of beam. Inputting 0 means the item is to be program calculated as 0.1hs.

SlabWidthRight ≥ 0 0 Slab width for T-beam at right end of spandrel, bs. SlabDepthRight ≥ 0 0 Slab depth for T-beam at right end of spandrel,

ds. Material Any defined

concrete material property

Material property associated with the spandrel.

Consider Vuc Yes or No Yes Toggle switch to consider Vuc (concrete shear capacity) when computing the shear capacity of the spandrel.

B-5

Appendix C Analysis Sections and Design Sections

It is important to understand the difference between analysis sections and design sections when performing shear wall design. Analysis sections are simply the objects defined in your model that make up the pier or spandrel section. The analysis section for wall piers is the assemblage of wall and column sections that make up the pier. Similarly, the analysis section for spandrels is the assemblage of wall and beam sections that make up the spandrel. The analysis is based on these section properties, and thus, the design forces are based on these analysis section properties.

The design section is completely separate from the analysis section. Two types of pier design sections are available. They are:

Uniform Reinforcing Section: For flexural designs and/or checks, the program automatically (and internally) creates a Section Designer pier section of the same shape as the analysis section pier. Uniform reinforcing is placed in this pier. The reinforcing can be modified in the pier overwrites. The Uniform Reinforcing Section pier may be planar or it may be three-dimensional.

For shear design and boundary zone checks, the program automatically (and internally) breaks the analysis section pier up into planar legs and then performs the design on each leg separately and reports the results separately for each leg. Note that the planar legs are derived from the area objects defined in the model, not from the pier section defined in Section Designer.

C-1


The pier section defined in Section Designer is only used for the flexural design/check.

General Reinforcing Section: For flexural designs and/or checks, the pier geometry and the reinforcing is defined by the user in the Section Designer utility. The pier defined in Section Designer may be planar or it may be three-dimensional.

For shear design and boundary zone checks, the program automatically (and internally) breaks the analysis section pier up into planar legs and then performs the design on each leg separately and reports the results separately for each leg. Note that the planar legs are derived from the area objects defined in the model, not from the pier section defined in Section Designer. The pier section defined in Section Designer is only used for the flexural design/check.

Simplified Pier Section: This pier section is defined in the pier design overwrites. The simplified section is defined by a length and a thickness. The length is in the pier 2-axis direction and the thickness is in the pier 3-axis direction.

In addition, you can, if desired, specify thickened edge members at one or both ends of the simplified pier section. You cannot specify reinforcing in a simplified section. Thus, the simplified section can only be used for design, not for checking user-specified sections. Simplified sections are always planar.

Only one type of spandrel design section is available. It is defined in the spandrel design overwrites. A typical spandrel is defined by a depth, thickness and length. The depth is in the spandrel 2-axis direction; the thickness is in the spandrel 3-axis direction; and the length is in the spandrel 1-axis direction. Spandrel sections are always planar.

In addition, you can, if desired, specify a slab thickness and depth, making the spandrel design section into a T-beam. You cannot specify reinforcing in a spandrel section. Thus, you can only design spandrel sections, not check them.

The pier and spandrel design sections are designed for the forces obtained from the program's analysis, which is based on the analysis sections. In other words, the design sections are designed based on the forces obtained for the analysis sections.

C-2

Bibliography

CSI, 2012. CSI Analysis Reference Manual. Computers and Structures, Inc., Berkeley, California.

TCS, 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.

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