Standard Requirements for Seismic Evaluation and Retrofit of Existing Concrete Buildings Public Discussion Draft
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369.1 Public Discussion Draft 1 2
Standard Requirements for Seismic Evaluation and Retrofit of Existing Concrete Buildings
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(369.1) and Commentary
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Reported by Committee 369
5 Wassim Ghannoum, Chair Anna Birely
Adolfo Matamoros
Sergio Brena
Steven McCabe
Casey Champion
Murat Melek
Jeffrey Dragovich
Jack Moehle
Kenneth Elwood
Arif Ozkan
Una Gilmartin
Robert Pekelnicky
Garrett Hagen
Jose Pincheira
Arne Halterman Wael Hassan
Mario Rodriguez
Mohammad Iqbal
Murat Saatcioglu
Jose Izquierdo-Encarnacion
Siamak Sattar
Afshar Jalalian
Halil Sezen
Thomas Kang
Roberto Stark
Dominic Kelly
Andreas Stavridis
Insung Kim
John Wallace
Laura Lowes
Tom Xia
Kenneth Luttrell
This draft is not final and is subject to revision. This draft is for public review and comment only. Page 1 of 217
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Keywords: ASCE 41; acceptance criteria; anchorage; axial failure; bond-strength; concrete;
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connection; deformation-controlled; demand-capacity ratio; force-controlled; foundation;
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dynamic analysis; earthquake; effective flexural strength; stiffness; effective width; linear static
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analysis; load-deformation relationship; m-factor; modeling parameters; moment-frames;
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nonlinear analysis; plastic hinge; plastic rotation; probability of failure; posttensioned; prestress;
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shear strength; slab-column moment frames; seismic rehabilitation; retrofit; retrofit measure;
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stiffness; structural wall.
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PREFACE
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In this standard, reference to ASCE 41 implies reference to the ASCE/SEI 41-17 standard. In this
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standard, reference to ACI 318 implies reference to the ACI 318-14 Building Code.
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This standard provides retrofit and rehabilitation criteria for reinforced concrete buildings based
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on results from the most recent research on the seismic performance of existing concrete
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buildings. The intent of the ACI 369.1 standard is to provide a continuously updated resource
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document for modifications to Chapter 10 of ASCE 41, similar to how the National Earthquake
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Hazards Reduction Program (NEHRP) Recommended Seismic Provisions produced by the
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Federal Emergency Management Agency (FEMA) (FEMA 450) have served as source
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documents for the International Building Code (IBC) and its predecessor building codes.
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Specifically, this version of ACI 369.1 serves as the basis for Chapter 10, “Concrete” of ASCE
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41.
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This standard should be used in conjunction with Chapters 1 through 7 of ASCE/SEI 41-
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17. Chapter 1 of ASCE 41 provides general requirements for evaluation and retrofit, including
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the selection of performance objectives and retrofit strategies. Chapter 2 of ASCE 41 defines
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performance objectives and seismic hazards. Chapter 3 of ASCE 41 provides the requirements
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for evaluation and retrofit, including treating as-built information and selecting the appropriate
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screening procedures. Chapter 4 of ASCE 41 summarizes Tier 1 screening procedures, while
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Chapters 5 and 6 summarize Tier 2 deficiency-based procedures and Tier 3 systematic
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procedures for evaluation and retrofit, respectively. Chapter 7 of ASCE 41 details analysis
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procedures referenced in ACI 369.1, including, linear and nonlinear analysis procedures,
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acceptance criteria, and alternative methods for determining modeling parameters and
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acceptance criteria. Chapter 8 of ASCE 41 provides geotechnical engineering provisions for
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building foundations and assessment of seismic-geologic site hazards. References to these
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chapters can be found throughout the standard. The design professional is referred to the FEMA
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report, FEMA 547, for detailed information on seismic rehabilitation measures for concrete
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buildings. Repair techniques for earthquake-damaged concrete components are not included in
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ACI 369.1. The design professional is referred to FEMA 306, FEMA 307, and FEMA 308 for
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information on evaluation and repair of damaged concrete wall components.
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This standard does not provide modeling procedures, acceptance criteria, and rehabilitation
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measures for concrete-encased steel composite components. Future versions will provide
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provision updates for concrete moment frames and will add provisions for concrete components
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and systems omitted in the present version of the standard.
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INTRODUCTION
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This draft is not final and is subject to revision. This draft is for public review and comment only. Page 3 of 217
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Earthquake reconnaissance has clearly demonstrated that existing concrete buildings designed
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before the introduction of seismic design codes in the 1980’s are more vulnerable to severe
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damage or collapse when subjected to strong ground motion than concrete buildings built after
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that period. Seismic rehabilitation of existing buildings where new components are added or
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existing components are modified or retrofitted with new materials, or both, can be used to
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mitigate the risk to damage in future earthquakes. Seismic rehabilitation is encouraged not only
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to reduce the risk of damage and injury in future earthquakes, but also to extend the life of
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existing buildings and reduce using new materials in the promotion of sustainability objectives.
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It is not possible to codify all problems encountered in the process of performing the seismic
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evaluation and retrofit of reinforced concrete buildings, nor is the intent of the standard to do so.
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The standard provides a basic framework for modeling and evaluation of structures that reflects
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the latest information available from researchers and practicing engineers, so that seismic
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evaluation and retrofit can be performed with a consistent set of criteria. Many provisions in the
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standard rely on the use of sound engineering judgement for their implementation. The
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commentary of the standard provides references that describe in detail the implementation of
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methodologies adopted in the standard.
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CHAPTER 1 - GENERAL
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1.1―ScopeThis standard sets forth requirements for the seismic evaluation and retrofit of concrete
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components of the seismic-force-resisting system of an existing building. These building standard
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requirements apply to existing concrete components, retrofitted concrete components, and new
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concrete components. Provisions of this standard do not apply to concrete-encased steel composite
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components.
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Chapter 2 specifies data collection procedures for obtaining material properties and performing
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condition assessments. Chapter 3 provides general analysis and design requirements for concrete
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components. Chapters 4 through 9 provide modeling procedures, component strengths, acceptance
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criteria, and retrofit measures for cast-in-place and precast concrete moment frames, concrete
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frames with masonry infills, cast-in-place and precast concrete shear walls, and concrete braced
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frames. Chapters 10 through 12 provide modeling procedures, strengths, acceptance criteria, and
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retrofit measures for concrete diaphragms and concrete foundation systems.
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C1.1—Scope
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These standard requirements were developed based on the best knowledge of the seismic
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performance of existing concrete buildings at the time of publication. These requirements are not
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intended to restrict the licensed design professional from using new information that becomes
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available before the issuance of the next edition of this standard. Such new information can
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include tests conducted to address specific building conditions.
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This standard provides short descriptions of potential seismic retrofit measures for each concrete
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building system. The licensed design professional, however, is referred to FEMA 547 for detailed
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information on seismic retrofit measures for concrete buildings. Repair techniques for earthquake‐
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damaged concrete components are not included in this standard. The licensed design professional
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is referred to FEMA 306, FEMA 307, and FEMA 308 for information on evaluation and repair of
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damaged concrete wall components.
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Concrete‐encased steel composite components behave differently from concrete sections reinforced
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with reinforcing steel. Concrete‐encased steel composite components frequently behave as over‐
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reinforced sections. This type of component behavior was not represented in the data sets used
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to develop the force–deformation modeling relationships and acceptance criteria in this
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standard and is not covered in this standard. Concrete encasement is often provided for fire
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protection rather than for strength or stiffness and typically lacks transverse reinforcement. In
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some cases, the transverse reinforcement does not meet detailing requirements in AISC 360.
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Lack of adequate confinement can result in lateral expansion of the core concrete, which exacerbates
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bond slip and, undermines the fundamental principle that plane sections remain plane.
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Testing and analysis used to determine acceptance criteria for concrete‐encased steel composite
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components should include the effect of bond slip between steel and concrete, confinement ratio,
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confinement reinforcement detailing, kinematics, and appropriate strain limits.
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To preserve historic buildings, exercise care in selecting the appropriate retrofit approaches and
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techniques for application.
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CHAPTER 2―MATERIAL PROPERTIES AND CONDITION ASSESSMENT
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2.1―General
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Mechanical properties of materials shall be obtained from available drawings, specifications, and
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other documents for the existing building in accordance with the requirements of ASCE 41 Section
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3.2. Where these documents fail to provide adequate information to quantify material properties,
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such information shall be supplemented by materials testing based on requirements of Chapter 2.
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The condition of the concrete components of the structure shall be determined using the
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requirements of Section 2.3.
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Material properties of existing concrete components shall be determined in accordance with
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Section 2.2. The use of default material properties based on historical information is permitted This draft is not final and is subject to revision. This draft is for public review and comment only. Page 6 of 217
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in accordance with Section 2.2.5. A condition assessment shall be conducted in accordance with
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Section 2.3. The extent of materials testing and condition assessment performed shall be used to
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determine the knowledge factor as specified in Section 2.4.
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C2.1―General
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Chapter 2 identifies properties requiring consideration and provides requirements for determining
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building properties. Also described is the need for a thorough condition assessment and utilization of
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knowledge gained in analyzing component and system behavior. Personnel involved in material
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property quantification and condition assessment should be experienced in the proper
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implementation of testing practices and the interpretation of results.
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When modeling a concrete building, it is important to investigate local practices relative to seismic
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design. Specific benchmark years can be determined for the implementation of earthquake‐
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resistant design in most locations, but caution should be exercised in assuming optimistic
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characteristics for any specific building. Particularly with concrete materials, the date of original
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building construction significantly influences seismic performance. Without deleterious conditions
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or materials, concrete gains compressive strength from the time it is originally cast and in place.
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Strengths typically exceed specified design values (28‐day or similar). In older construction,
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concrete strength was often very low (less than 3000 psi) and it was rarely specified in the
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drawings.. Early adoptions of concrete in buildings often used reinforcing steel with relatively low
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strength and ductility, limited continuity, and reduced bond development. Continuity between
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specific existing components and elements, such as beams, columns, diaphragms, and shear walls,
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can be particularly difficult to assess because of concrete cover and other barriers to inspection. This draft is not final and is subject to revision. This draft is for public review and comment only. Page 7 of 217
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Properties of welded wire reinforcement for various periods of construction can be obtained
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from the Wire Reinforcement Institute (WRI 2009).
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Documentation of the material properties and grades used in component and connection
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construction is invaluable and can be effectively used to reduce the amount of in‐place testing
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required. The licensed design professional is encouraged to research and acquire all available
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records from original construction, including photographs, to confirm reinforcement details shown
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on the plans.
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Further guidance on the condition assessment of existing concrete buildings can be found in the
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following:
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11
structures;
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13
structures before retrofit; and
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including analytical and load test methods.
ACI 201.1R, which provides guidance on conducting a condition survey of existing concrete
ACI 364.1R, which describes the general procedures used for the evaluation of concrete
ACI 437R, which describes methods for strength evaluation of existing concrete buildings,
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2.2 Properties of In-Place Materials and Components
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2.2.1 Material Properties
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2.2.1.1 General―The following component and connection material properties shall be obtained
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for the as-built structure:
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1.
Concrete compressive strength; and
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2.
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Yield and ultimate strength of conventional and prestressing reinforcing steel, cast-in place and post-installed anchors, and metal connection hardware.
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Where materials testing is required by ASCE 41 Section 6.2, the test methods to quantify material
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properties shall comply with the requirements of Section 2.2.3. The frequency of sampling,
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including the minimum number of tests for property determination, shall comply with the
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requirements of Section 2.2.4.
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C2.2.1.1 General―Other material properties and conditions of interest for concrete components
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include
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1. Tensile strength and modulus of elasticity of concrete;
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2. Ductility, toughness, and fatigue properties of concrete;
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3. Carbon equivalent present in the reinforcing steel; and
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4. Presence of any degradation such as corrosion or deterioration of bond between concrete and
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reinforcement.
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The extent of effort made to determine these properties depends on availability of accurate, updated
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construction documents and drawings; construction quality and type; accessibility; and material
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conditions. The analysis method selected—for example, linear static procedure (LSP) or nonlinear
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static procedure (NSP)—might also influence the testing scope. Concrete tensile strength and
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modulus of elasticity can be estimated based on the compressive strength and may not warrant the
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damage associated with any extra coring required.
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The sample size and removal practices followed are referenced in FEMA 274, Sections C6.3.2.3
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and C6.3.2.4. ACI 228.1R provides guidance on methods to estimate the in‐place strength of
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concrete in existing structures, whereas ACI 214.4R provides guidance on coring in existing
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structures and interpretation of core compressive strength test results. Generally, mechanical
3
properties for both concrete and reinforcing steel can be established from combined core and
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specimen sampling at similar locations, followed by laboratory testing. Core drilling should minimize
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damage to the existing reinforcing steel.
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2.2.1.2 Nominal or Specified Properties―Nominal material properties, or properties specified in
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construction documents, shall be taken as lower-bound material properties. Corresponding
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expected material properties shall be calculated by multiplying lower-bound values by a factor
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taken from Table 1 to translate from lower-bound to expected values. Alternative factors shall be
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permitted where justified by test data.
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2.2.2 Component Properties―The following component properties and as-built conditions shall
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be established:
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1.
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Cross-sectional dimensions of individual components and overall configuration of the structure;
2.
Configuration of component connections, size, embedment depth, and type of
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anchors, thickness of connector material, anchorage and interconnection of
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embedments and the presence of bracing or stiffening components;
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3.
Modifications to components or overall configuration of the structure;
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4.
Most recent physical condition of components and connections, and the extent of
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any deterioration;
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5.
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Deformations beyond those expected because of gravity loads, such as those caused by settlement or past earthquake events; and
6.
Presence of other conditions that influence building performance, such as
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nonstructural components that can interact with structural components during
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earthquake excitation.
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C2.2.2 Component Properties―Component properties are required to properly characterize
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building performance in seismic analysis. The starting point for assessing component properties
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and condition is retrieval of available construction documents. A preliminary review should
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identify primary gravity‐ and seismic‐force‐resisting elements and systems and their critical
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components and connections. If there are no drawings of the building, the licensed design
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professional should perform a thorough investigation of the building to identify these elements,
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systems, and components as described in Section 2.3.
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2.2.3 Test Methods to Quantify Material Properties
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2.2.3.1 General―Destructive and nondestructive test methods used to obtain in-place mechanical
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properties of materials identified in Section 2.2.1 and component properties identified in Section
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2.2.2 are specified in this section. Samples of concrete and reinforcing and connector steel shall
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be examined for physical condition as specified in Section 2.3.2.
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When determining material properties with the removal and testing of samples for laboratory
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analysis, sampling shall take place in primary gravity- and seismic-force-resisting components in
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regions with the least stress.
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Where Section 2.2.4.2.1 does not apply and the coefficient of variation is greater than 20%, the
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expected concrete strength shall not exceed the mean less one standard deviation. This draft is not final and is subject to revision. This draft is for public review and comment only. Page 11 of 217
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2.2.3.2 Sampling―For concrete material testing, the sampling program shall include the removal
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of standard cores. Core drilling shall be preceded by nondestructive location of the reinforcing
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steel, and core holes shall be located to avoid damage to or drilling through the reinforcing steel. Core
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holes shall be filled with concrete or grout of comparable strength having nonshrinkage properties. If
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conventional reinforcing steel is tested, sampling shall include removal of local bar segments and
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installation of replacement spliced material to maintain continuity of the reinforcing bar for
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transfer of bar force unless an analysis confirms that replacement of the original components is
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not required.
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Removal of core samples and performance of laboratory destructive testing shall be permitted to
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determine existing concrete strength properties. Removal of core samples shall use the procedures
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included in ASTM C42. Testing shall follow the procedures contained in ASTM C42, ASTM C39,
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and ASTM C496. Core strength shall be converted to in-place concrete compressive strength by
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an approved procedure.
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Removal of bar or tendon samples and performance of laboratory destructive testing shall be
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permitted to determine existing reinforcing steel strength properties. The tensile yield and ultimate
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strengths for reinforcing and prestressing steels shall follow the procedures included in ASTM
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A370. Reinforcing samples that are slightly damaged during removal are permitted to be machined
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to a round bar as long as the tested area is at least 70% of the gross area of the original bar.
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Prestressing materials shall meet the supplemental requirements in ASTM A416, ASTM A421, or
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ASTM A722, depending on material type. Properties of connector steels shall be permitted to be
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determined by wet and dry chemical composition tests and direct tensile and compressive strength
22
tests as specified by ASTM A370. Where strength, construction quality or both of anchors or
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embedded connectors are required to be determined, in-place testing shall satisfy the provisions of
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ASTM E488-96.
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C2.2.3.2 Sampling―ACI 214.4R and FEMA 274 provide further guidance on correlating concrete
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core strength to in‐place strength and provide references for various test methods that can be
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used to estimate material properties. Chemical composition can be determined from retrieved
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samples to assess the condition of the concrete. Section C6.3.3.2 of FEMA 274 (1997b) provides
8
references for these tests.
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When concrete cores are taken, care should be taken when patching the holes. For example, a
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core through the thickness of a slab should have positive anchorage by roughening the surface
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and possibly dowels for anchorage. For that case, the holes should be filled with concrete or grout
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and the engineer should provide direction for filling the hole so that the added concrete or grout
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bonds to the substrate.
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The reinforcing steel system used in the construction of a specific building is usually of uniform
15
grade and similar strength. One grade of reinforcement is occasionally used for small‐diameter
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bars, like those used for stirrups and hoops, and another grade for large‐diameter bars, like those
17
used for longitudinal reinforcement. In some cases, different concrete design strengths or classes
18
are used. Historical research and industry documents contain insight on material mechanical
19
properties used in different construction eras (Section 2.2.5). This information can be used with
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laboratory and field test data to gain confidence in in‐place strength properties. Undamaged
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reinforcing steel can be reduced to a smooth bar, as long as the samples meet the requirements
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of ASTM A370, excluding the limitations of Annex 9. This type of reinforcing would occur in a
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situation where only a limited length of bar can be removed for testing.
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2.2.4 Minimum Number of Tests―Materials testing is not required if material properties are
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available from original construction documents that include material test records or reports.
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Material test records or reports shall be representative of all critical components of the building
7
structure.
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Based on Section 6.2 of ASCE 41, data collection from material tests is classified as either
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comprehensive or usual. The minimum number of tests for usual data collection is specified in
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Section 2.2.4.1. The minimum number of tests necessary to quantify properties by in-place testing
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for comprehensive data collection is specified in Section 2.2.4.2. If the existing gravity-load-
12
resisting-system or seismic-force-resisting system is replaced during the retrofit process, material
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testing is only required to quantify properties of existing materials at new connection points.
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C2.2.4 Minimum Number of Tests―To quantify in‐place properties accurately, it is essential that
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a minimum number of tests be conducted on primary components of the seismic‐force‐resisting
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system. The minimum number of tests is dictated by the availability of original construction data,
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structural system type used, desired accuracy, quality and condition of in‐place materials, level of
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seismicity, and target performance level. Accessibility to the structural system can influence the
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testing program scope. The focus of testing should be on primary seismic‐force‐resisting
21
components and specific properties for analysis. Test quantities provided in this section are
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minimal; the licensed design professional should determine whether further testing is needed to
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evaluate as‐built conditions. This draft is not final and is subject to revision. This draft is for public review and comment only. Page 14 of 217
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Testing is generally not required on components other than those of the seismic‐force‐resisting
2
system.
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The licensed design professional and subcontracted testing agency should carefully examine test
4
results to verify that suitable sampling and testing procedures were followed and appropriate
5
values for the analysis were selected from the data.
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2.2.4.1 Usual Data Collection―The minimum number of tests to determine concrete and
8
reinforcing steel material properties for usual data collection shall be based on the following
9
criteria:
10
1.
If the specified design strength of the concrete is known, at least one core shall be
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taken from samples of each different concrete strength used in the construction of the
12
building, with a minimum of three cores taken for the entire building;
13
2.
If the specified design strength of the concrete is not known, at least one core shall be
14
taken from each type of seismic-force-resisting component, with a minimum of six
15
cores taken for the entire building;
16
3.
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If the specified design strength of the reinforcing steel is known, nominal or specified material properties shall be permitted without additional testing; and
4.
If the specified design strength of the reinforcing steel is not known, at least two
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strength test coupons of reinforcing steel shall be removed from the building for
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testing.
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5.
Cast-in-place or post-installed anchors shall be classified in groups of similar type,
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size, geometry and structural use. In groups of anchors used for out-of-plane wall
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anchorage and in groups of anchors whose failure in tension or shear would cause This draft is not final and is subject to revision. This draft is for public review and comment only. Page 15 of 217
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the structure not to meet the selected Performance Objective, 5% of the anchors with
2
a minimum of three anchors of each anchor group shall be tested in-place in tension
3
to establish an available strength, construction quality or both. The test load shall be
4
specified by the licensed design professional and shall be based on the anticipated
5
demand or strength in accordance with available construction information. If the test
6
load is used as the basis for anchor strength calculation, the available anchor strength
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shall not be taken greater than 2/3 of the test load. Testing of the anchors to failure is
8
not required and a test load lower than the expected failure load shall be permitted.
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If the test load is not achieved in one or more anchors tested in a group, anchors in
10
that group shall be tested under a tensile load smaller than that specified for the
11
preceding tests. Otherwise, the strength of the tested anchor group shall be ignored.
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Testing in accordance with 2.2.4.2.5 shall be permitted to determine the available
13
strength based on a statistical distribution of the test results.
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2.2.4.2 Comprehensive Data Collection
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2.2.4.2.1 Coefficient of Variation―Unless specified otherwise, a minimum of three tests shall be
3
conducted to determine any property. If the coefficient of variation exceeds 20%, additional tests
4
shall be performed until the coefficient of variation is equal to or less than 20%. If additional
5
testing does not reduce the coefficient of variation below 20%, a knowledge factor reduction per
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Section 4.4 shall be used. In determining coefficient of variation, cores shall be grouped by grades
7
of concrete and element type. The number of tests in a single component shall be limited so as not
8
to compromise the integrity of the component.
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2.2.4.2.2 Concrete Materials―For each concrete element type of the seismic-force-resisting
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system, as well as secondary systems for which failure could result in a collapse hazard, a
11
minimum of three core samples shall be taken and subjected to compression tests. A minimum of
12
six total tests shall be performed on a building for concrete strength determination, subject to the
13
limitations of this section. If varying concrete classes or grades were used in the building
14
construction, a minimum of three samples and tests shall be performed for each class and grade.
15
The modulus of elasticity and tensile strength shall be permitted to be estimated from the
16
compressive strength testing data. Samples shall be taken from components, distributed throughout
17
the building, that are critical to the structural behavior of the building.
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Tests shall be performed on samples from components that are identified as damaged or degraded
19
to quantify their condition. Test results from areas of degradation shall be compared with strength
20
values specified in the construction documents. If test values less than the specified strength in the
21
construction documents are found, further strength testing shall be performed to determine the cause
22
or identify the degree of damage or degradation.
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The minimum number of tests to determine compressive strength of each concrete element type
2
shall conform to one of the following criteria:
3
1.
For concrete elements for which the specified design strength is known and test results
4
are not available, a minimum of three core tests shall be conducted for each floor level,
5
400 yd3 (306 m3) of concrete, or 10,000 ft2 (930 m2) of surface area, whichever requires
6
the most frequent testing; or
7
2.
For concrete elements for which the specified design strength is unknown and test
8
results are not available, a minimum of six core tests shall be conducted for each floor
9
level, 400 yd3 (306 m3) of concrete, or 10,000 ft2 (930 m2) of surface area, whichever
10
requires the most frequent testing. Where the results indicate that different classes of
11
concrete were used, the degree of testing shall be increased to confirm class use.
12
3.
Alternately, for concrete elements for which the design strength is known or unknown,
13
and test results are not available, it is permitted to determine the lower bound
14
compressive strength based on core sample testing and applying the provisions in
15
Section 6.4.3 of ACI 562-16. If the lower bound compressive strength is determined in
16
this manner, the expected compressive strength shall be determined as the lower bound
17
compressive strength value obtained from ACI 562-16 Equation 6.4.3 plus one standard
18
deviation of the strength of the core samples. When following the provisions in Section
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6.4.3 of ACI 562-16, the minimum number of samples per element type shall be four.
20
The sample locations shall be:
21 22 23
a. Distributed to quantify element material properties throughout the height of the building b. Distributed to quantify element material properties in locations critical to the This draft is not final and is subject to revision. This draft is for public review and comment only. Page 18 of 217
structural system being investigated.
1 2 3
Quantification of concrete strength via ultrasonics or other nondestructive test methods shall not
4
be substituted for core sampling and laboratory testing.
5
6
C2.2.4.2.2 Concrete Materials―ACI 214.4R provides guidance on coring in existing structures and
7
interpretation of core compressive strength test results.
8
If a structure was constructed in phases or if construction documents for different parts of the
9
structure were issued at separate times, the licensed design professional, for the purpose of
10
determining sampling size, should consider the concrete in each construction phase or in each set
11
of construction documents as of different type. Section 6.4.3 of ACI 562‐16 provides a method to
12
calculate an equivalent specified concrete strength f’c based on statistical analysis of compression
13
strength test results from core samples. ASTM E178 provides guidance on consideration of
14
outliers in a set of core samples. Equation 6.4.3 in Section 6.4.3 of ACI 562‐16 defines the
15
equivalent specified compressive strength of concrete as a function of the number of tests, the
16
coefficient of variation of the samples, and a factor to account for the number of samples. Section
17
6.4.3 of ACI 562‐16 permits the engineer to select the number of samples used to evaluate
18
concrete compressive strength but imposes a penalty to the results to account for the uncertainty
19
associated with the number of samples.
20
Equation 6.4.3 of ACI 562‐16 was derived with the objective of calculating the 13% fractile of the
21
in‐place concrete compressive strength, which some studies have shown to be approximately
22
equal to the specified compressive strength of concrete f’c (Bartlett and MacGregor, 1996). The This draft is not final and is subject to revision. This draft is for public review and comment only. Page 19 of 217
1
first term in Equation 6.4.3 of ACI 562‐16 represents the effect of sample size on the uncertainty
2
of the mean in‐place strength, where the coefficient kc is obtained from a Student’s t distribution
3
with n‐1 degrees of freedom and a 90% confidence level. The second term in Equation 6.4.3 of ACI
4
562‐16 represents the uncertainty attributable to correction factors relating cylinder strength to
5
specified compressive strength, which were assumed to have a normal distribution, also
6
estimated with a 90% confidence level. The study by Bartlett and MacGregor (1996) showed that
7
the specified compressive strength f’c corresponds approximately to the 13% fractile of the 28‐
8
day in‐place strength in walls and columns, and approximately the 23% fractile of the 28‐day in‐
9
place compressive strength in beams and slabs. The former was considered to be a more
10
appropriate measure of specified compressive strength f’c than the latter because the nominal
11
strength of columns is more sensitive to concrete compressive strength than the strength of
12
beams and slabs (ACI 214.4).
13
In Section 2.2.1.2 of this standard it is stated that nominal material properties or properties
14
specified in construction documents shall be taken as lower‐bound material properties unless
15
otherwise specified. The method to estimate of the specified concrete compressive strength f’c in
16
Section 6.4.3 of ACI 562‐16 was adopted in this standard to obtain the lower bound compressive
17
strength consistent with the provisions in Section 2.2.1.2.
18
ACI 214.4R provides guidance on coring in existing structures and interpretation of core
19
compressive strength test results. The minimum of 4 samples was adopted based on the
20
recommendations in ACI 214.4. The following equation is provided in ACI 214.4
21
This draft is not final and is subject to revision. This draft is for public review and comment only. Page 20 of 217
1
(C1)
2
3
where nsamples represents the minimum number of samples, COVpopulation represents the estimated
4
coefficient of variation of the population, and epopulation represents the predetermined maximum
5
error expressed as a percentage of the population average. For a total of 4 samples the previous
6
equation dictates that the maximum error is equal to the estimate of the coefficient of variation
7
of the population. Bartlett and MacGregor (1995) report that for many batches of cast‐in‐place
8
concrete, and samples obtained from many members, the coefficient of variation was
9
approximately 13%. If the maximum error is equal to the coefficient of variation, a maximum error
10
of 13% corresponds to approximately 1.13 standard deviations, which is considered adequate for
11
an estimate of lower bound material properties.
12
Users of the document are cautioned that for coefficients of variation between 13 and 20%, the
13
minimum number of samples needed to limit the error below one standard deviation according
14
to the recommendations in ACI 214.4 is higher than 4. For example, for a coefficient of variation
15
of 20% a minimum of 7 samples is recommended to limit the error to one standard deviation. If
16
the maximum error is reduced to 10% the minimum number of samples recommended is
17
significantly higher. For a coefficient of variation of 15.87% (one standard deviation away from
18
the mean) and a maximum error of 10%, the minimum number of samples recommended is 11,
19
and for a coefficient of variation of 20% and a maximum error of 10%, the minimum number of
20
samples recommended is 16. If the coefficient of variation exceeds 20%, the requirements in
21
Section 2.2.4.2.1 shall be satisfied.
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1
2 3
Ultrasonics and nondestructive test methods should not be substituted for core sampling and
4
laboratory testing as they do not yield accurate strength values directly. These methods should
5
only be used for confirmation and comparison. Guidance for nondestructive test methods is
6
provided in ACI 228.2R.
7 8
2.2.4.2.3 Conventional Reinforcing and Connector Steels―Tests shall be conducted to determine
9
both yield and ultimate strengths of reinforcing and connector steel. Connector steel is defined as
10
additional structural steel or miscellaneous metal used to secure precast and other concrete shapes
11
to the building structure. A minimum of three tensile tests shall be conducted on conventional
12
reinforcing steel samples from a building for strength determination, subject to the following
13
supplemental conditions:
14
1.
If original construction documents defining properties exist, then at least three strength
15
coupons shall be removed from random locations from each element or component
16
type and tested; or
17
2.
If original construction documents defining properties are unavailable, but the
18
approximate date of construction is known and a common material grade is confirmed,
19
at least three strength coupons shall be removed from random locations from each
20
element or component type for every three floors of the building; and
21 22 23
3.
If the construction date is unknown, at least six strength coupons for every three floors shall be performed.
Refer to Section 2.2.3.2 for replacement of sampled material.
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1
2.2.4.2.4 Prestressing Steel―Sampling prestressing steel tendons for laboratory testing shall only
2
be performed on prestressed components that are part of the seismic-force-resisting system.
3
Prestressed components in diaphragms shall be permitted to be excluded.
4
Tendon or prestress removal shall be avoided if possible. Any sampling of prestressing steel
5
tendons for laboratory testing shall be done with extreme care. It shall be permitted to determine
6
material properties without tendon or prestress removal by careful sampling of either the tendon
7
grip or the extension beyond the anchorage, if sufficient length is available.
8
All sampled prestressed steel shall be replaced with new, fully connected, and stressed material
9
and anchorage hardware, unless an analysis confirms that replacement of original components is
10
not required.
11
2.2.4.2.5 Cast-in-place or post-installed anchors― Cast-in-place or post-installed anchors shall
12
be classified in groups in accordance with 2.2.4.1. In groups of anchors used for out-of-plane
13
wall anchorage and in groups of anchors whose failure in tension or shear would cause the
14
structure not to meet the selected Performance Objective, 10% of the anchors with a minimum of
15
six anchors of each anchor group shall be tested in-place to in tension to establish an available
16
strength, construction quality or both. Testing of the anchors to failure is not required. The test
17
load shall be specified by the licensed design professional and shall be based on the anticipated
18
demand or strength in accordance with available construction information. If the test load is
19
used as the basis for anchor strength calculation, the available anchor strength shall not be taken
20
greater than 2/3 of the test load. Testing of the anchors to failure is not required and a test load
21
lower than the expected failure load shall be permitted.
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1
2
C2.2.4.2.5 Cast‐in‐place or post‐installed anchors― To estimate ultimate strength of the
3
anchors in accordance with Section 3.6, the frequency of the test should be increased to at least
4
25% of the anchors and the test load should be at least the nominal design strength in
5
accordance with Chapter 17 of ACI 318. In‐place anchor testing performed in accordance with
6
2.2.4.2.5 provides the minimum available tensile strength of a single anchor, which is likely
7
governed by pullout or bond strength in tension. Other failure modes and parameters that affect
8
the strength of the anchors, such as proximity to edges, group effect, presence of cracks, or
9
eccentricity of applied loads, should be considered in accordance with Chapter 17 of ACI 318.
10 11
2.2.5 Default Properties―Default material properties to determine component strengths shall be
12
permitted to be used in conjunction with the linear analysis procedures of ASCE 41 Chapter 7.
13
Default lower-bound concrete compressive strengths are specified in Table 2. Default expected
14
concrete compressive strengths shall be determined by multiplying lower-bound values by an
15
appropriate factor selected from Table 1, unless another factor is justified by test data. The
16
appropriate default compressive strength, lower-bound strength, or expected strength as specified
17
in ASCE 41 Section 7.5.1.3, shall be used to establish other strength and performance
18
characteristics for the concrete as needed in the structural analysis.
19
Default lower-bound values for reinforcing steel are specified for various ASTM specifications
20
and periods in Tables 3 or 4. Default expected strength values for reinforcing steel shall be
21
determined by multiplying lower-bound values by an appropriate factor selected from Table 1,
22
unless another factor is justified by test data. Where default values are assumed for existing
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1
reinforcing steel, welding or mechanical coupling of new reinforcement to the existing reinforcing
2
steel shall not be permitted.
3
The default lower-bound yield strength for steel connector material shall be taken as 27,000 lb/in.2
4
(186 MPa). The default expected yield strength for steel connector material shall be determined
5
by multiplying lower-bound values by an appropriate factor selected from Table 1, unless another
6
value is justified by test data.
7
The default lower-bound yield strength for cast-in-place or post-installed anchor material shall be
8
taken as 27,000 lb/in.2 (186 MPa) unless another value is justified by test data. Component actions
9
on the connections shall be considered as force-controlled actions and default expected yield
10
strength shall not be used.
11
The use of default values for prestressing steel in prestressed concrete construction shall not be
12
permitted.
13 14
C2.2.5 Default Properties―Default values provided in this standard are generally conservative.
15
Whereas the strength of reinforcing steel can be fairly consistent throughout a building, the
16
strength of concrete in a building could be highly variable, given variability in concrete mixtures
17
and sensitivity to water–cement ratio and curing practices. A conservative assumption based
18
upon the field observation of the concrete compressive strength in the given range is
19
recommended, unless a higher strength is substantiated by construction documents, test reports,
20
or material testing. For the capacity of an element in question, the lower value within the range
21
can be conservative. It can be appropriate to use the maximum value in a given range where
22
determining the force‐controlled actions on other components.
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1
Until about 1920, a variety of proprietary reinforcing steels was used. Yield strengths are likely to
2
be in the range of 33,000 to 55,000 lb/in.2 (230 to 380 MPa), but higher values are possible and
3
actual yield and tensile strengths can exceed minimum values. Once commonly used to designate
4
reinforcing steel grade, the terms “structural,” “intermediate,” and “hard” became obsolete in
5
1968. Plain and twisted square bars were occasionally used between 1900 and 1949.
6
Factors to convert default reinforcing steel strength to expected strength include consideration of
7
material overstrength and strain hardening.
8 9
2.3 Condition Assessment
10
2.3.1 General―A condition assessment of the existing building and site conditions shall be
11
performed as specified in this section.
12
The condition assessment shall include the following:
13
1.
14 15
presence of any degradation shall be noted; 2.
16 17
3.
A review and documentation of other conditions, including neighboring party walls and buildings, presence of nonstructural components and mass, and prior remodeling;
4.
20 21
Verification of the presence and configuration of components and their connections, and the continuity of load paths between components, elements, and systems;
18 19
Examination of the physical condition of primary and secondary components, and the
Collection of information needed to select a knowledge factor in accordance with Section 4.4; and
5.
Confirmation of component orientation, plumbness, and physical dimensions.
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1
2
C2.3.1 General―The condition assessment also affords an opportunity to review other
3
conditions that can influence concrete elements and systems and overall building performance.
4
Of particular importance is the identification of other elements and components that can
5
contribute to or impair the performance of the concrete system in question, including infills,
6
neighboring buildings, and equipment attachments. Limitations posed by existing coverings, wall
7
and ceiling space, infills, and other conditions shall also be defined such that prudent retrofit
8
measures can be planned.
9
10
2.3.2 Scope and Procedures―The scope of the condition assessment shall include critical
11
structural components as described in the following subsections.
12
2.3.2.1 Visual Condition Assessment―Direct visual inspection of accessible and representative
13
primary components and connections shall be performed to
14
Identify configuration issues;
15
Determine if degradation is present;
16
Establish continuity of load paths;
17
Establish the need for other test methods to quantify the presence and degree of
18 19 20
degradation; and
Measure dimensions of existing construction to compare with available design information and reveal any permanent deformations.
21
A visual building inspection shall include visible portions of foundations, seismic-force-resisting
22
members, diaphragms (slabs), and connections. As a minimum, a representative sampling of at
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1
least 20% of the components and connections shall be visually inspected at each floor level. If
2
significant damage or degradation is found, the assessment sample of all similar-type critical
3
components in the building shall be increased to 40% or more, as necessary, to accurately assess the
4
performance of components and connections with degradation.
5
If coverings or other obstructions exist, partial visual inspection through the obstruction shall be
6
permitted to be performed using drilled holes and a fiberscope.
7
8
C2.3.2.1 Visual Condition Assessment―Further guidance can be found in ACI 201.1R, which
9
provides a system for reporting the condition of concrete in service.
10 11
2.3.2.2 Comprehensive Condition Assessment―Exposure is defined as local minimized removal
12
of cover concrete and other materials to inspect reinforcing system details. All damaged concrete
13
cover shall be replaced after inspection. The following criteria shall be used for assessing primary
14
connections in the building for comprehensive data collection:
15
1.
If detailed design drawings exist, exposure of at least three different primary
16
connections shall occur, with the connection sample including different types of
17
connections (for example, beam–column, column–foundation, beam–diaphragm, and
18
diaphragm-wall). If no deviations from the drawings exist or if the deviations from the
19
drawings are consistently similar, it shall be permitted to consider the sample as being
20
representative of installed conditions. If inconsistent deviations are noted, then at least
21
25% of the specific connection type shall be inspected to identify the extent of
22
deviation; or
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1
2.
In the absence of detailed design drawings, at least three connections of each primary
2
connection type shall be exposed for inspection. If common detailing among the three
3
connections is observed, it shall be permitted to consider this condition as representative
4
of installed conditions. If variations are observed among like connections, additional
5
connections shall be inspected until an accurate understanding of building construction
6
is gained.
7
2.3.2.3 Additional Testing―If additional destructive and nondestructive testing is required to
8
determine the degree of damage or presence of deterioration, or to understand the internal
9
condition and quality of concrete, test methods approved by the licensed design professional shall
10
be used.
11
12
C2.3.2.3 Additional Testing―The physical condition of components and connectors affects their
13
performance. The need to accurately identify the physical condition can dictate the need for
14
certain additional destructive and nondestructive test methods. Such methods can be used to
15
determine the degree of damage or presence of deterioration and to improve understanding of
16
the internal condition and concrete quality. Further guidelines and procedures for destructive and
17
nondestructive tests that can be used in the condition assessment are provided in ACI 228.1R, ACI
18
228.2R, FEMA 274 (Section C6.3.3.2), and FEMA 306(Section 3.8).
19
The nondestructive examination (NDE) methods having the greatest use and applicability to
20
condition assessment are listed below:
21 22
Surface NDE methods include infrared thermography, delamination sounding, surface hardness measurement, and crack mapping. These methods can be used to find surface
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1
degradation in components such as service‐induced cracks, corrosion, and construction
2
defects;
3
Volumetric NDE methods, including radiography and ultrasonics, can be used to identify
4
the presence of internal discontinuities and loss of section. Impact‐echo ultrasonics is often
5
used and is a well‐understood technology;
6
On‐line monitoring using acoustic emissions, strain gauges, in‐place static or dynamic load
7
tests, and ambient vibration tests can be used to assess structural condition and
8
performance. Monitoring is used to determine if active degradation or deformations are
9
occurring, whereas nondestructive load testing provides direct insight on load‐carrying
10 11
capacity;
Electromagnetic methods using a pachometer or radiography can be used to locate, size,
12
or perform an initial assessment of reinforcing steel. Further assessment of suspected
13
corrosion activity should use electrical half‐cell potential and resistivity measurements;
14
and
15
Lift‐off testing (assuming original design and installation data are available), or another
16
nondestructive method such as the “coring stress relief” specified in SEI/ASCE 11, can
17
be used where absolutely essential to determine the level of prestress remaining in an
18
unbonded prestressed system.
19 20
2.3.3 Basis for the Mathematical Building Model―Results of the condition assessment shall be
21
used to quantify the following items needed to create the mathematical building model:
22
1.
Component section properties and dimensions;
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1
2.
2
Component configuration and the presence of any eccentricities or permanent deformation;
3
3.
Connection configuration and the presence of any eccentricities;
4
4.
Presence and effect of alterations to the structural system since original
5 6
construction; and 5.
7
Interaction of nonstructural components and their involvement in seismic force resistance.
8
All deviations between available construction records and as-built conditions obtained from visual
9
inspection shall be accounted for in the structural analysis.
10
Unless concrete cracking, reinforcement corrosion, or other mechanisms of degradation are
11
observed in the condition assessment as the cause for damage or reduced capacity, the cross-
12
sectional area and other sectional properties shall be assumed to be those from the design drawings
13
after adjustment for as-built conditions. If some sectional material loss has occurred, the loss shall
14
be quantified by direct measurement and sectional properties reduced accordingly using the
15
principles of structural mechanics.
16
2.4 Knowledge Factor―A knowledge factor () for computation of concrete component
17
acceptance criteria shall be selected in accordance with ASCE 41 Section 6.2.4 with additional
18
requirements specific to concrete components. A knowledge factor, equal to 0.75 shall be used if
19
any of the following criteria are met:
20
1.
Components are found to be damaged or deteriorated during assessment, and
21
further testing is not performed to quantify their condition or justify the use of
22
higher values of ;
23
2.
Mechanical properties have a coefficient of variation exceeding 20%; and
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1
3.
Components contain archaic or proprietary material and the condition is uncertain.
2 3
CHAPTER 3 – GENERAL ASSUMPTIONS AND REQUIREMENTS
4
3.1―Modeling and Design
5
3.1.1 General―Seismic retrofit of a concrete building involves the design of new components
6
connected to the existing structure, seismic upgrading of existing components, or both. New
7
components shall comply with ACI 318, except as otherwise indicated in this standard.
8
Original and retrofitted components of an existing building are not expected to satisfy provisions
9
of ACI 318 but shall be assessed using the provisions of this standard. Brittle or low-ductility
10
failure modes shall be identified as a part of the seismic evaluation.
11
Evaluation of demands and capacities of reinforced concrete components shall include
12
consideration of locations along the length where seismic force and gravity loads produce
13
maximum effects; where changes in cross section or reinforcement result in reduced strength; and
14
where abrupt changes in cross section or reinforcement, including splices, can produce stress
15
concentrations that result in premature failure.
16
C3.1.1 General―Brittle or low‐ductility failure modes typically include behavior in direct or nearly
17
direct compression; shear in slender components and in‐component connections; torsion in
18
slender components; and reinforcement development, splicing, and anchorage. The stresses,
19
forces, and moments acting to cause these failure modes should be determined from a limit‐state
20
analysis, considering probable resistances at locations of nonlinear action.
21
22
3.1.2 Stiffness―Component stiffnesses shall be calculated considering shear, flexure, axial
23
behavior, and reinforcement slip deformations. Stress state of the component, cracking extent This draft is not final and is subject to revision. This draft is for public review and comment only. Page 32 of 217
1
caused by volumetric changes from temperature and shrinkage, deformation levels under gravity
2
loads and seismic forces shall be considered. Gravity load effects considered for effective
3
stiffnesses of components shall be determined using ASCE/SEI 41 Equation 7-3.
4 5
C3.1.2 Stiffness―For columns with low axial loads (below approximately 0.1Agfc), deformations
6
caused by bar slip can account for as much as 50% of the total deformations at yield. Further
7
guidance regarding calculation of the effective stiffness of reinforced concrete columns that
8
include the effects of flexure, shear, and bar slip can be found in Elwood and Eberhard (2009).
9
Flexure‐controlled wall stiffness can vary from approximately 0.15EcEIg to 0.5EcEIg, depending on
10
wall reinforcement and axial load. A method for calculating wall stiffness which provides
11
compatibility with fiber section analysis is offered in C7.2.2.
12 13
3.1.2.1 Linear Procedures―Where design actions are determined using the linear procedures of
14
ASCE 41 Chapter 7, component effective stiffnesses shall correspond to the secant value to the
15
yield point of the component. Alternate stiffnesses shall be permitted where it is demonstrated by
16
analysis to be appropriate for the design loading. Alternatively, effective stiffness values in Table
17
5 shall be permitted.
18 19
C3.1.2.1 Linear Procedures―The effective flexural rigidity values in Table 5 for beams and
20
columns account for the additional flexibility from reinforcement slip within the beam–column
21
joint or foundation before yielding. The values specified for columns were determined based on a
22
database of 221 rectangular reinforced concrete column tests with axial loads less than 0.67Agfc
23
and shear span–depth ratios greater than 1.4. Measured effective stiffnesses from the laboratory This draft is not final and is subject to revision. This draft is for public review and comment only. Page 33 of 217
1
test data suggest that the effective flexural rigidity for low axial loads could be approximated as
2
0.2EIg; however, considering the scatter in the effective flexural rigidity and to avoid
3
underestimating the shear demand on columns with low axial loads, 0.3EIg is recommended in
4
Table 5 (Elwood et al. 2007). In addition to axial load, the shear span–depth ratio of the column
5
influences the effective flexural rigidity. A more refined estimate of the effective flexural rigidity
6
can be determined by calculating the displacement at yield caused by flexure, slip, and shear
7
(Elwood and Eberhard 2009).
8
The modeling recommendations for beam–column joints (Section 6.2.2.1) do not include the
9
influence of reinforcement slip. When the effective stiffness values for beams and columns from
10
Table 5 are used in combination with the modeling recommendations for beam–column joints,
11
the overall stiffness is in close agreement with results from beam–column subassembly tests
12
(Elwood et al. 2007).
13
The effect of reinforcement slip can be accounted for by including rotational springs at the ends
14
of the beam or column elements (Saatcioglu et al. 1992). If this modeling option is selected, the
15
effective flexural rigidity of the column element should reflect only the flexibility from flexural
16
deformations. In this case, for axial loads less than 0.3Agfc, the effective flexural rigidity can be
17
estimated as 0.5EIg, with linear interpolation to the value given in Table 5 for axial loads greater
18
than 0.5Agfc.
19
Because of low bond stress between concrete and plain reinforcement without deformations,
20
components with plain longitudinal reinforcement and axial loads less than 0.5Agfc can have lower
21
effective flexural rigidity values than in Table 5.
This draft is not final and is subject to revision. This draft is for public review and comment only. Page 34 of 217
1 2
3.1.2.2 Nonlinear Procedures―Where design actions are determined using the nonlinear
3
procedures of ASCE 41 Chapter 7, component load-deformation response shall be represented by
4
nonlinear load-deformation relations. Linear relations shall be permitted where nonlinear response
5
does not occur in the component. The nonlinear load-deformation relation shall be based on
6
experimental evidence or taken from quantities specified in Chapters 4 through 12. For the nonlinear
7
static procedure (NSP), the generalized load-deformation relation shown in Fig. 1 or other curves
8
defining behavior under monotonically increasing deformation shall be permitted. For the nonlinear
9
dynamic procedure (NDP), load-deformation relations shall define behavior under monotonically
10
increasing lateral deformation and under multiple reversed deformation cycles as specified in Section
11
3.2.1.
12
The generalized load-deformation relation shown in Fig. 1 shall be described by linear response from
13
A (unloaded component) to an effective yield B, then a linear response at reduced stiffness from
14
point B to C, then sudden reduction in seismic force resistance to point D, then response at reduced
15
resistance to E, and final loss of resistance thereafter. The slope from point A to B shall be
16
determined according to Section 3.1.2.1. The slope from point B to C, ignoring effects of gravity
17
loads acting through lateral displacements, shall be taken between zero and 10% of the initial slope,
18
unless an alternate slope is justified by experiment or analysis. Point C shall have an ordinate equal
19
to the strength of the component and an abscissa equal to the deformation at which significant
20
strength degradation begins. Representation of the load-deformation relation by points A, B, and
21
C only (rather than all points A–E) shall be permitted if the calculated response does not exceed
22
point C. Numerical values for the points identified in Fig. 1 shall be as specified in Sections 3.2.2.2
23
for beams, columns, and joints, 3.3.2.2 for post-tensioned beams, 3.4.2.2 for slab–column
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1
connections, and 7.2.2 for shear walls, wall segments, and coupling beams. Other load-
2
deformation relations shall be permitted if justified by experimental evidence or analysis.
3 4
C3.1.2.2 Nonlinear Procedures―Typically, the response shown in Fig. 1 is associated with flexural
5
response or tension response. In this case, the resistance at Q/Qy = 1.0 is the yield value, and
6
subsequent strain hardening is accommodated by hardening in the load‐deformation relation as
7
the member is deformed toward the expected strength. Where the response shown in Fig. 1 is
8
associated with compression, the resistance at Q/Qy = 1.0 typically is the value where concrete
9
begins to spall, and strain hardening in well‐confined sections can be associated with strain
10
hardening of the longitudinal reinforcement and an increase in strength from the confinement of
11
concrete. Where the response shown in Fig. 1 is associated with shear, the resistance at Q/Qy =
12
1.0 typically is the value at which the design shear strength is reached and, typically, no strain
13
hardening follows.
14
The deformations used for the load‐deformation relation of Fig. 1 shall be defined in one of two
15
ways, as follows:
16
Deformation, or Type I: In this curve, deformations are expressed directly using terms such as
17
strain, curvature, rotation, or elongation. The parameters anl and bnl refer to deformation
18
portions that occur after yield, or plastic deformation. The parameter cnl is the reduced resistance
19
after the sudden reduction from C to D. Parameters anl, bnl, and cnl are defined numerically in
20
various tables in this standard. Alternatively, parameters anl, bnl, and cnl can be determined
21
directly by analytical procedures justified by experimental evidence.
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1
Deformation Ratio, or Type II: In this curve, deformations are expressed in terms such as shear
2
angle and tangential drift ratio. The parameters dnl and enl refer to total deformations measured
3
from the origin. Parameters cnl, dnl, and enl are defined numerically in various tables in this
4
standard. Alternatively, parameters cnl, dnl, and enl can be determined directly by analytical
5
procedures justified by experimental evidence.
6
Provisions for determining alternative modeling parameters and acceptance criteria based on
7
experimental evidence are given in ASCE 41 Section 7.6.
8
Displacement demands determined from nonlinear dynamic analysis are sensitive to the rate of
9
strength degradation included in the structural model. Unless there is experimental evidence of
10
sudden strength loss for a particular component under consideration, the use of a model with a
11
sudden strength loss from point C to D in Fig. 1 can result in overestimation of the drift demands
12
for a structural system and individual components. A more realistic model for many concrete
13
components would have a linear degradation in resistance from point C to E.
14
Strength loss that occurs within a single cycle can result in dynamic instability of the structure,
15
whereas strength loss that occurs between cycles is unlikely to cause such instability. Fig. 1 does not
16
distinguish between these types of strength degradation and may not accurately predict the
17
displacement demands if the two forms of strength degradation are not properly considered.
18 19
3.1.3 Flanged Construction―In beams consisting of a web and flange that act integrally, the
20
combined stiffness and strength for flexural and axial loading shall be calculated considering a
21
width of effective flange on each side of the web equal to the smallest of:
22
1.
The provided flange width;
This draft is not final and is subject to revision. This draft is for public review and comment only. Page 37 of 217
1
2.
Eight times the flange thickness;
2
3.
Half the distance to the next web; or
3
4.
One-fifth of the beam span length.
4
Where the flange is in compression, the concrete and reinforcement within the effective width
5
shall be considered effective in resisting flexure and axial load. Where the flange is in tension,
6
longitudinal reinforcement within the effective width of the flange and developed beyond the
7
critical section shall be considered fully effective for resisting flexural and axial loads. The portion
8
of the flange extending beyond the width of the web shall be assumed ineffective in resisting
9
shear.
10
In walls, effective flange width should be computed using Chapter 18 of ACI 318.
11 12
3.2 Strength and Deformability
13
3.2.1 General―Actions in a structure shall be classified as being either deformation-controlled or
14
force-controlled. Deformation-controlled actions are defined by the designation of linear and
15
nonlinear acceptance criteria in Tables 7 through 10 and 13 through 22. Where linear and nonlinear
16
acceptance criteria are not specified in the tables, actions shall be taken as force-controlled unless
17
component testing is performed in accordance with ASCE 41 Section 7.6. Strengths for deformation-
18
controlled and force-controlled actions shall be calculated in accordance with Sections 3.2.2 and 3.2.3,
19
respectively.
20
Components shall be classified as having low, moderate, or high ductility demands, according to
21
Section 3.2.4.
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1
Where strength and deformation capacities are derived from test data, the tests shall be representative
2
of proportions, details, and stress levels for the component and comply with Section 7.6.1 of
3
ASCE 41.
4
The strength and deformation capacities of concrete members shall correspond to values resulting
5
from a loading protocol involving three fully reversed cycles to the design deformation level, in
6
addition to similar cycles to lesser deformation levels, unless a larger or smaller number of
7
deformation cycles is determined considering earthquake duration and dynamic properties of the
8
structure.
9 10
C3.2.1 General―In this standard, actions are classified as either deformation‐controlled or force‐
11
controlled. Actions are considered to be deformation‐controlled where the component behavior
12
is well documented by test results. Where linear or nonlinear acceptance criteria are tabulated in
13
this standard, the committee has judged the action to be deformation‐controlled and expected
14
material properties should be used. Where such acceptance criteria are not specified, the action
15
should be assumed force‐controlled, thereby requiring the use of lower‐bound material
16
properties, or the licensed design professional can opt to perform testing to validate the
17
classification of deformation‐controlled. ASCE 41 Section 7.6 provides guidance on procedures to
18
be followed during testing, and ASCE 41 Section 7.5.1.2 provides a methodology based on the test
19
data to distinguish force‐controlled from deformation‐controlled actions. Further guidance on the
20
testing of moment‐frame components can be found in ACI 374.1.
21
In some cases, including short‐period buildings and those subjected to a long‐duration design
22
earthquake, a building can be expected to be subjected to additional cycles to the design deformation
23
levels beyond the three cycles recommended in Section 3.2.1. The increased number of cycles can This draft is not final and is subject to revision. This draft is for public review and comment only. Page 39 of 217
1
lead to reductions in resistance and deformation capacity. The effects on strength and deformation
2
capacity of additional deformation cycles should be considered in design.
3 4
3.2.2 Deformation-Controlled Actions―Strengths used for deformation-controlled actions shall
5
be taken as equal to expected strengths QCE obtained experimentally or calculated using accepted
6
principles of mechanics. Unless specified in this standard, other procedures specified in ACI 318 to
7
calculate strengths shall be permitted, except that the strength reduction factor ϕ shall be taken
8
equal to unity. Deformation capacities for acceptance of deformation-controlled actions
9
calculated by nonlinear procedures shall be as specified in Chapters 4 through 12 of this standard. For
10
components constructed of lightweight concrete, QCE shall be modified in accordance with ACI 318
11
procedures for lightweight concrete.
12
13
C3.2.2 Deformation‐Controlled Actions―Expected yield strength of reinforcing steel, as specified
14
in Section 4.2.1.2, includes material overstrength considerations.
15
16
3.2.3 Force-Controlled Actions―Strengths used for force-controlled actions shall be taken as
17
lower-bound strengths QCL, obtained experimentally or calculated using established principles of
18
mechanics. Lower-bound strength is defined as the mean less one standard deviation of
19
resistance expected over the range of deformations and loading cycles to which the concrete
20
component is likely to be subjected. Where calculations are used to define lower-bound
21
strengths, lower-bound estimates of material properties shall be used. Unless other procedures
22
are specified in this standard, procedures specified in ACI 318 to calculate strengths shall be
23
permitted, except that the strength reduction factor shall be taken equal to unity. For This draft is not final and is subject to revision. This draft is for public review and comment only. Page 40 of 217
1
components constructed of lightweight concrete, QCL shall be modified in accordance with ACI
2
318 procedures for lightweight concrete.
3
4
3.2.4 Component Ductility Demand Classification―Table 6 provides classification of component
5
ductility demands as low, moderate, or high based on the maximum value of the demand–capacity
6
ratio (DCR) defined in ASCE 41 Section 7.3.1.1 for linear procedures or the calculated
7
displacement ductility for nonlinear procedures.
8 9
3.3―Flexure and Axial Loads
10
Flexural strength of members with and without axial loads shall be calculated according to ACI
11
318 or by other demonstrated rational methods, such as sectional analysis using appropriate
12
concrete and steel constitutive models. Deformation capacity of members with and without axial
13
loads shall be calculated considering shear, flexure, and reinforcement slip deformations, or based
14
on acceptance criteria given in this standard. Strengths and deformation capacities of components
15
with monolithic flanges shall be calculated considering concrete and developed longitudinal
16
reinforcement within the effective flange width, as defined in Section 3.1.3.
17
Strength and deformation capacities shall be determined based on the available development of
18
longitudinal reinforcement. Where longitudinal reinforcement has embedment or development
19
length that is insufficient for reinforcement strength development, flexural strength shall be
20
calculated based on limiting stress capacity of the embedded bar as defined in Section 3.5.
21
Where flexural deformation capacities are calculated from basic principles of mechanics,
22
reductions in deformation capacity caused by applied shear shall be considered. Where using
23
analytical models for flexural deformability that do not directly account for the effect of shear on This draft is not final and is subject to revision. This draft is for public review and comment only. Page 41 of 217
1
deformation capacity and if the design shear equals or exceeds 6 f c' Aw , lb/in.2 ( 0.5 f c' Aw , MPa),
2
the design flexural deformation capacity shall not exceed 80% of the value calculated using the
3
analytical model.
4
For concrete columns or walls under combined axial load and biaxial bending, the combined
5
strength shall be evaluated considering biaxial bending. When using linear procedures, the axial
6
load PUF or PUD shall be calculated as a force-controlled action or deformation-controlled action
7
per ASCE 41 Section 7.5.2. The design moments MUD should be calculated about each of two
8
orthogonal axes. Combined strength shall be based on principles of mechanics with applied
9
bending moments calculated as MUDx/(mxκ) and MUDy/(myκ) about the x- and y-axes, respectively.
10
Acceptance shall be based on the applied bending moments lying within the expected strength
11
envelope calculated at an axial load level of PUF if the member is in compression or PUD /
12
[(minimum of mx and my)κ] if the member is in tension.
13 14
C3.3 Flexure and Axial Loads―Laboratory tests indicate that flexural deformability can be reduced
15
as coexisting shear forces increase. As flexural ductility demands increase, shear capacity
16
decreases, which can result in a shear failure before theoretical flexural deformation capacities
17
are reached. Use caution where flexural deformation capacities are determined by calculation.
18
FEMA 306 (ASCE 41 Section 5.2) is a resource for guidance on the interaction between shear and
19
flexure.
20
The combined strength under uniaxial or biaxial bending with axial load is difficult to generalize
21
in a closed‐form solution, given the range of column section geometries encountered. For a
22
particular class of rectangular column sections, closed‐form solutions based on section capacities
23
about the principal axes have been developed that provide excellent agreement when compared This draft is not final and is subject to revision. This draft is for public review and comment only. Page 42 of 217
1
to a more generalized analysis (Hsu 1988, Furlong et al. 2004). A circular envelope provides a poor
2
prediction of the strength for all but circular columns. For general sections, the strength envelope
3
should be developed based on principles of mechanics.
4
When flexural strength of an axially loaded member needs to be calculated in the linear
5
procedure, compressive load level should be considered as a force‐controlled action due to its
6
non‐ductile nature while, tensile load level should be considered as a deformation‐controlled
7
action because the tensile strength and stiffness of the member are based on steel reinforcement
8
contribution only. The m‐factor for the flexural behavior can be conservatively used to estimate
9
the deformation‐controlled action due to the tension.
10 11
3.3.1 Usable Strain Limits―For deformation- and force-controlled actions in elements without
12
confining transverse reinforcement, the maximum usable strain at the extreme concrete
13
compression fiber used to calculate the moment and axial strength shall not exceed:
14
a) 0.002 for members in nearly pure compression
15
b) 0.005 for other members
16
Larger values of maximum usable strain in the extreme compression fiber shall be allowed where
17
substantiated by experimental evidence.
18
For deformation- and force-controlled actions in elements with confined concrete, the maximum
19
usable strain at the extreme concrete compression fiber used to calculate moment and axial strength
20
shall be based on experimental evidence and consider limitations posed by transverse
21
reinforcement fracture, longitudinal reinforcement buckling, and degradation of component
22
resistance at large deformation levels. In the case of force-controlled actions in elements with
23
confined concrete, it shall be permitted to adopt usable strain limits for unconfined concrete. This draft is not final and is subject to revision. This draft is for public review and comment only. Page 43 of 217
1
For deformation-controlled actions the maximum compressive strains in the longitudinal
2
reinforcement used to calculate the moment and axial strength shall not exceed 0.02, and
3
maximum tensile strains in longitudinal reinforcement shall not exceed 0.05. Monotonic coupon test
4
results shall not be used to determine reinforcement strain limits. If experimental evidence is used to
5
determine strain limits for reinforcement, the effects of low-cycle fatigue and transverse
6
reinforcement spacing and size shall be included in testing procedures.
7 8
C3.3.1
9
Early research on the stress‐strain behavior of unconfined concrete (Hognestad, 1952) has shown
10
that the stress‐strain behavior of concrete is different in members subjected to flexure than in
11
members subjected to nearly pure compression. Concrete subjected to concentric compression
12
exhibits crushing shortly after the maximum stress is reached at strains of approximately 0.0015
13
to 0.0020 (Hognestad, 1952), while crushing in the extreme compression fiber of members
14
subjected to flexure and axial load is observed at higher strains, ranging between 0.003 to 0.005
15
(Hognestad, 1952). The maximum usable strain limits established in this section are intended to
16
caution engineers when using stress‐strain relationships for concrete to calculate moment and
17
axial strengths. In members subjected to nearly pure compression, redistribution of stresses
18
within the compression zone after the strain in the concrete exceeds the strain corresponding to
19
peak stress (0.0015 to 0.0020 for unconfined concrete) (Hognestad, 1952) is not possible because
20
most of the concrete in the cross section will be on the descending branch of the stress‐strain
21
curve for concrete.
22
Usable strain limits specified in this section do not preclude engineers from using the provisions
23
in Section 22.2 of ACI 318. Section 22.2.2.1 of ACI 318 stipulates that to calculate the moment and
Usable Strain Limits
This draft is not final and is subject to revision. This draft is for public review and comment only. Page 44 of 217
1
axial strength of reinforced concrete members, the maximum usable strain in the extreme
2
compression fiber of reinforced concrete shall be assumed to be 0.003. This usable strain is within
3
the limit of 0.005 specified in Section 3.3.1 of this standard. In the case of members subjected to
4
nearly pure compression, provisions in Section 22.4.2 of ACI 318 establish that the design axial
5
strength of columns with unconfined concrete shall not exceed 80% of the nominal axial strength.
6
According to the commentary of Section 22.4.2.1 of ACI 318, the reduced nominal axial strength
7
corresponds to a minimum eccentricity of 5% of the column depth. The usable strain limit of 0.002
8
specified in Section 3.3.1 of this standard is intended to prevent overestimating the flexural
9
strength of columns with very small eccentricities, so the provisions in Section 22.4.2.1 for the ACI
10
318 Code can be used in lieu of calculating the axial and moment strength based on stress‐strain
11
models for concrete.
12
While provisions in Section 21.2.2 of ACI 318 establish that for tension‐controlled members the
13
strain in the reinforcement at failure shall be at least 0.005, there is no upper limit in the code for
14
the usable strain in the reinforcement of beams and columns. Although an upper limit in the strain
15
at failure of beams and columns is implied in the provisions for minimum reinforcement in
16
Sections 9.6 and 10.6 of ACI 318, those limits are not intended for members that will be subjected
17
to deformation cycles in the nonlinear range of response. The reinforcement tensile strain limit in
18
Section 5.3.1 of this standard is based on consideration of the effects of material properties and
19
low‐cycle fatigue. Low‐cycle fatigue is influenced by spacing and size of transverse
20
reinforcement and strain history. Using extrapolated monotonic test results to develop tensile
21
strains greater than those specified above is not recommended. California Department of
22
Transportation (Caltrans) “Seismic Design Criteria” (Caltrans 2006) recommends an ultimate This draft is not final and is subject to revision. This draft is for public review and comment only. Page 45 of 217
1
tensile strain of 0.09 for No. 10 (No. 32) bars and smaller, and 0.06 for No. 11 (No. 36) bars and
2
larger, for ASTM A706 60 kip/in.2 (420 MPa) reinforcing bars. A lower bound is selected here
3
considering the variability in materials and details typically found in existing structures.
4
Refer to Brown and Kunnath (2004) for incorporating the effects of low‐cycle fatigue and
5
transverse reinforcing for determining strain limits based on testing.
6 7
3.4―Shear and Torsion
8
Strengths in shear and torsion shall be calculated according to ACI 318, except as modified in this
9
standard.
10
Within yielding regions of components with moderate or high ductility demands, shear and
11
torsional strength shall be calculated according to procedures for ductile components, such as the
12
provisions in Chapter 18 of ACI 318. Within yielding regions of components with low ductility
13
demands per Table 6 and outside yielding regions for all ductility demands, procedures for
14
effective elastic response, such as the provisions in Chapter 22 of ACI 318, shall be permitted to
15
calculate the design shear strength.
16
Unless otherwise noted, where the longitudinal spacing of transverse reinforcement exceeds half
17
the component effective depth measured in the direction of shear, transverse reinforcement shall
18
be assumed to have reduced effectiveness in resisting shear or torsion by a factor of 2(1-s/d).
19
Where the longitudinal spacing of transverse reinforcement exceeds the component effective
20
depth measured in the direction of shear, transverse reinforcement shall be assumed ineffective in
21
resisting shear or torsion. For beams and columns, lap-spliced transverse reinforcement shall be
22
assumed not more than 50% effective in regions of moderate ductility demand and ineffective in
23
regions of high ductility demand, and applies in addition to the effectiveness factor due to spacing. This draft is not final and is subject to revision. This draft is for public review and comment only. Page 46 of 217
1
Shear friction strength shall be calculated according to ACI 318, considering the expected axial
2
load from gravity and earthquake effects. Where retrofit involves the addition of concrete requiring
3
overhead work with dry pack, the shear friction coefficient shall be taken as equal to 70% of the
4
value specified by ACI 318.
5 6
C3.4 Shear and Torsion―The reduction in the effectiveness of transverse reinforcement in this
7
section accounts for the limited number of ties expected to cross an inclined crack when ties are
8
provided at large spacing. Furthermore, reduction in the effectiveness of the transverse
9
reinforcement is needed since the widely spaced ties may not be fully developed both above and
10
below the crack. For tie spacing equal to the effective depth of the member, it is possible to
11
develop an inclined crack that does not cross any ties, and hence the contribution of the transverse
12
reinforcement should be ignored.
13 14
3.5―Development and Splices of Reinforcement
15
Development of straight bars, hooked bars, and lap-spliced bars shall be calculated according to
16
the provisions of ACI 318, with the following modifications:
17
1.
Deformed straight, hooked, and lap-spliced bars satisfying the development
18
requirements of Chapter 25 of ACI 318 using expected material properties, shall be
19
deemed capable of developing their yield strength, except as adjusted in the
20
following: (a) the development of lapped straight bars in tension without
21
consideration of lap splice classifications is permitted to be used as the required lap
22
splice length; (b) for columns, where deformed straight and lap-spliced bars pass
23
through regions where inelastic deformations and damage are expected, the bar
This draft is not final and is subject to revision. This draft is for public review and comment only. Page 47 of 217
1
length within those regions shall be considered effective for anchorage only until
2
inelastic deformations occur. In such cases, the development length obtained using
3
ACI 318 procedures shall be compared with a degraded available development
4
length (lb-deg) as defined in (2) below;
5
2.
Where existing deformed straight bars, hooked bars, and lap-spliced bars do not
6
meet the development requirements of (1) above, the capacity of existing
7
reinforcement shall be calculated using Eq. 1:
8
1.25
9
(1a)
/
If the maximum applied bar stress is larger than fs given in Eq. (1a), members shall
10
be deemed controlled by inadequate development or splicing.
11
For columns, where deformed straight and lap-spliced longitudinal bars pass
12
through regions where inelastic deformations and damage are expected, the bar
13
length within those regions shall be considered effective for anchorage only until
14
inelastic deformations occur. In such cases, if fs = fylL/E from Eq. (1a), the degraded
15
reinforcement capacity fs-deg accounting for the loss of anchorage in the damaged
16
region shall be evaluated using a degraded available development length (lb-deg). lb-
17
deg
18
maximum flexural demand in any direction damage is anticipated within the
19
column.
20
shall be evaluated by subtracting from lb a distance of 2/3d from the point of
1.25
/
(1b)
21
In cases where fs = fylL/E from Eq. (1a) but the maximum applied longitudinal bar
22
stress is larger than fs-deg given in Eq. (1b), columns shall be deemed controlled by This draft is not final and is subject to revision. This draft is for public review and comment only. Page 48 of 217
1
inadequate development or splicing and the capacity of the existing reinforcement
2
taken as fylL/E;
3
3.
For inadequate development or splicing of straight bars in beams and columns: for
4
nonlinear procedures it shall be permitted to assume that the reinforcement retains
5
the calculated maximum stress evaluated using Eq. (1a) up to the deformation levels
6
defined by anl in Tables 7, 8 and 9; for linear procedures, the calculated maximum
7
stress evaluated using Eq. (1a) shall be used for strength calculations. For members
8
other than beams and columns controlled by inadequate development or splicing
9
and hooked anchorage the developed stress shall be assumed to degrade from 1.0fs,
10
at a ductility demand or DCR equal to 1.0, to 0.2fs at a ductility demand or DCR
11
equal to 2.0;
12
4.
Strength of deformed straight, discontinuous bars embedded in concrete sections or
13
beam–column joints, with clear cover over the embedded bar not less than 3db, shall
14
be calculated according to Eq. 2:
15
/
(lb/in.2 units)
16
/
(MPa units)
(2)
17
Where fs is less than fyL/E and the calculated stress in the bar caused by design loads
18
equals or exceeds fs, the maximum developed stress shall be assumed to degrade
19
from 1.0fs, at a ductility demand or DCR equal to 1.0, to 0.2fs at a ductility demand
20
or DCR equal to 2.0. In beams with bottom bar embedment length into beam–
21
column joints less than the requirements of ACI 318, flexural strength shall be
22
calculated considering the stress limitation of Eq. 2;
This draft is not final and is subject to revision. This draft is for public review and comment only. Page 49 of 217
1
5.
For plain straight, hooked, and lap-spliced bars, development and splice lengths
2
shall be taken as twice the values determined in accordance with ACI 318, unless
3
other lengths are justified by approved tests; and
4
6.
Doweled bars added in seismic retrofit shall be assumed to develop yield stress
5
where all the following conditions are satisfied:
6
a.
Drilled holes for dowel bars are cleaned;
7
b.
Embedment length le is not less than 10db and;
8
c.
Minimum dowel bar spacing is not less than 4le and minimum edge distance
9
is not less than 2le.
10
Design values for dowel bars not satisfying these conditions shall be verified by
11
test data. Field samples shall be obtained to ensure that design strengths are
12
developed in accordance with Chapter 3.
13
7.
Square reinforcing bars in a building should be classified as either twisted or
14
straight. The developed strength of twisted square bars shall be as specified for
15
deformed bars in this Section, using an effective diameter calculated based on the
16
area of the square bar. Straight square bars shall be considered as plain bars, and
17
the developed strength shall be as specified for plain bars in this Section.
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1
C3.5 Development and Splices of Reinforcement―Development requirements in accordance with
2
Chapter 25 of ACI 318 are applicable to development of bars in all components. Chapter 18 of ACI
3
318 provides development requirements that are intended only for use in yielding components of
4
reinforced concrete moment frames that comply with the cover and confinement provisions of
5
Chapter 18 of ACI 318. Chapter 25 of ACI 318 permits reductions in lengths if minimum cover and
6
confinement are present in an existing component. For additional information on development and
7
lap splices, see ACI 408R‐03, and for hooked anchorage, see Sperry et al. (2005).
8
Eq. (1a), which is a modified version of the model presented by Cho and Pincheira (2006), reflects
9
the intent of ACI 318 development and splice equations to develop 1.25 times the nominal bar
10
strength, referred to in this standard as the expected yield strength. The nonlinear relation
11
between developed stress and development length reflects the effect of increasing slip, and hence,
12
reduced unit bond strength, for longer development lengths. Refer to Elwood et al. (2007) for
13
more details.
14
Bond strength can be significantly curtailed in damaged regions within plastic hinges (Sokoli and
15
Ghannoum 2015, Ichinose 1992). The length where bond capacity is curtailed during inelastic
16
deformations is recommended to be 2/3 of the section effective depth (d) (Sokoli and Ghannoum
17
2015). If fs evaluated using Eq. (1a) equals fylL/E, then bond failure is not expected prior to inelastic
18
hinging and the bar under consideration can be expected to resist the full yield stress fylL/E.
19
However, fs should be re‐evaluated using a degraded effective anchorage length (lb‐deg) using Eq.
20
(1b), which is reduced by the bar length within the region expected to be damaged. If fs‐deg remains
21
equal to fylL/E even after the anchorage length is reduced, then no anchorage failure is expected
22
even during inelastic deformations. If, however, fs‐deg becomes smaller than fylL/E when the This draft is not final and is subject to revision. This draft is for public review and comment only. Page 51 of 217
1
available anchorage length is reduced, then anchorage failure is expected, but only after inelastic
2
deformations occur. In such cases, the limiting stress in longitudinal bars will be fylL/E but the
3
modeling parameters in Tables 8 and 9 for columns with inadequate development or splicing
4
should be used.
5
For buildings constructed before 1950, the bond strength developed between reinforcing steel
6
and concrete can be less than present‐day strength. Present equations for development and splices
7
of reinforcement account for mechanical bond from deformations present in deformed bars as
8
well as chemical bond. The length required to develop plain bars is much greater than for deformed
9
bars and more sensitive to cracking in concrete. Testing and assessment procedures for tensile lap
10
splices and development length for plain reinforcing steel are found in CRSI (1981).
11 12
3.6―Connections to Existing Concrete
13
Connections used to connect two or more components shall be classified according to their
14
anchoring systems as cast-in-place or as post-installed and shall be evaluated and designed
15
according to Chapter 17 of ACI 318 as modified in this section. The properties of the existing
16
anchors and connection systems obtained in accordance with Section 2.2 shall be considered in
17
the evaluation. These provisions do not apply to connections in plastic hinge zones.
18
This draft is not final and is subject to revision. This draft is for public review and comment only. Page 52 of 217
1
C3.6 Connections to Existing Concrete―Chapter 17 of ACI 318 accounts for the influence of
2
cracking on the load capacity of connectors; however, cracking and spalling expected in plastic
3
hinge zones is likely to be more severe than the level of damage for which Chapter 17 is
4
applicable. ACI 355.2 and ACI 355.4 describe simulated seismic tests that can be used for
5
qualification of post‐installed anchors. Such tests do not simulate the conditions expected in
6
plastic hinge zones.
7
ASCE/SEI 41‐06 Section 6.3.6.1, required the load capacity of anchors placed in areas where
8
cracking is expected to be reduced by a factor of 0.5. This provision was included in FEMA 273 for
9
both cast‐in‐place and post‐installed anchors, before the introduction of ACI 318‐02 Appendix D.
10
Because cracking is now accounted for in ACI 318, the 0.5 factor is not required in Section 3.6 of
11
this standard.
12
Capacities of existing anchors should be evaluated based on the obtained properties in
13
accordance with Section 2.2 and Chapter 17 of ACI 318. If the anchors are not tested to failure
14
but to a load based on the force‐controlled action determined by the engineer for the seismic
15
hazard under consideration, the procedure in Chapter 17 of ACI 318 can be used to calculate
16
available strength based on the test results and the geometry of anchors measured or assumed
17
by the engineer.
18
To evaluate the capacity of existing cast‐in‐place and post‐installed anchors using ACI 318
19
Chapter 17, it is necessary to know the geometry of the anchor (i.e., embedment, edge distance,
20
spacing, and anchor diameter) and material properties. Edge distance, spacing, and anchor
21
diameter can be established from construction documents or by visual inspection. Unless known
22
from construction documents, embedment and material properties of the anchor are more This draft is not final and is subject to revision. This draft is for public review and comment only. Page 53 of 217
1
difficult to determine. Where failure of the anchor is not critical to meeting the target
2
performance level, embedment of post‐installed anchors can be assumed equal to the minimum
3
embedment required by manufacturer’s specifications for the anchor type in question. For cast‐
4
in‐place anchors, embedment can be taken as less than or equal to the minimum embedment
5
from the original design code for an embedded bolt of the same diameter. It is recommended that
6
where the consequence of failure of an anchor is critical to satisfying the target performance level,
7
anchor embedment not known from construction documents is determined by nondestructive
8
testing (e.g., ultrasonic testing).
9
Lower‐bound properties for steel connector materials and concrete strength based on default
10
values, construction documents, or test values can be assumed for anchor strength calculations.
11
It is noted that direct testing of anchors can provide greater certainty and can provide higher
12
capacities. Judgment should be exercised in the use of default lower‐bound material properties,
13
since doing so may not yield a conservative estimate of anchor capacity in cases where the steel
14
strength is determined to govern the anchor capacity, and additional requirements of ACI 318,
15
Chapter 17, for ductile behavior are waived as a result.
16
Not all manufacturers of post‐installed anchors publish information on the mean and the
17
standard deviation of the ultimate anchor capacity. Older testing for existing post‐installed
18
anchors is often reported at allowable stress design levels and may not comply with the
19
requirements of Chapter 17 of ACI 318 for simulated seismic tests. It is recommended that care
20
and judgment should be used in determining pullout strength for anchors, particularly those that
21
are critical to satisfying the target performance level. Where necessary, in situ strengths of
This draft is not final and is subject to revision. This draft is for public review and comment only. Page 54 of 217
1
anchors can be obtained or verified by static testing of representative anchors. ACI 355.2 and ACI
2
355.4 can be used for guidance on testing.
3
Proper installation of post‐installed anchors is critical to their performance and should be verified
4
in all cases.
5 6
3.6.1 Cast-in-Place Anchors and Connection Systems―All component actions on cast-in-
7
place anchors and connection systems shall be considered force-controlled. Lower-bound
8
strength of the anchors and connections shall be nominal strength as specified in Chapter 17 of
9
ACI 318 for the connections of structural components. The amplification factor to account for
10
the seismic overstrength, Ω0, shall be taken equal to unity for the connections of structural
11
components.
12
A strength reduction factor, and amplification factor, Ω0, shall be used for the connections of
13
non-structural components.
14
15
C3.6.1 Cast‐in‐Place Anchors and Connection Systems―The strength reduction factor, in ACI
16
318 shall be taken equal to unity for the lower bound connection strength of structural
17
components but the requirements in Section 17.2.3 of ACI 318 shall be satisfied including the
18
reduction of the strength due to cracked concrete and cyclic loading. The component actions on
19
the anchors and connection systems for structural components are considered as force‐
20
controlled actions according to Sections 7.5.2 and 7.5.3 of ASCE 41 so further amplification of
21
the seismic demand is not necessary.
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1
However, the seismic demand on non‐structural components in Chapter 13 of ASCE 41 is based
2
on that in ASCE/SEI 7. A strength reduction factor, , and amplification factor, Ω0, should be
3
consistent with the demand.
4 5
3.6.2 Post-installed Anchors―All component actions on post-installed anchor connection systems
6
shall be considered force-controlled. The lower-bound capacity of post-installed anchors shall be
7
nominal strength, as specified in Chapter 17 of ACI 318, or mean less one standard deviation of
8
ultimate values published in approved test reports for the connections of structural components.
9
The amplification factor to account for the seismic overstrength, Ω0, shall be taken equal to unity
10
for the connections of structural components.
11
A strength reduction factor,and amplification factor, Ω0, shall be used for the connections of
12
non-structural components.
13 14
C3.6.2 Post‐installed Anchors and Connection Systems―The strength reduction factor, in ACI
15
318 shall be taken equal to unity for the lower bound connection strength of structural
16
components but the requirements in Section 17.2.3 of ACI 318 shall be satisfied including the
17
reduction of the strength due to cracked concrete and cyclic loading. The component actions on
18
post‐installed anchors for structural components are considered as force‐controlled actions
19
according to Sections 7.5.2 and 7.5.3 of ASCE 41 so further amplification of the seismic demand
20
is not necessary.
21
However, the seismic demand on non‐structural components in Chapter 13 of ASCE 41 is based
22
on that in ASCE/SEI 7. Strength reduction factor,and amplification factor, Ω0, should be
23
consistent with the demand. This draft is not final and is subject to revision. This draft is for public review and comment only. Page 56 of 217
1 2
3.7―Retrofit Measures
3
Seismic retrofit measures for concrete buildings shall meet the requirements of this section and
4
other provisions of this standard.
5
Retrofit measures shall include replacement or retrofit of the component or modification of the
6
structure so that the component is no longer deficient for the selected Performance Objective. If
7
component replacement is selected, the new component shall be designed in accordance with this
8
standard and detailed and constructed in compliance with the applicable building code.
9
Retrofit measures shall be evaluated to ensure that the completed retrofit achieves the selected
10
performance objective. The effects of retrofit on stiffness, strength, and deformability shall be
11
taken into account in an analytical model of the rehabilitated structure. The compatibility of new
12
and existing components shall be checked at displacements consistent with the selected
13
Performance Level.
14
Connections required between existing and new components shall satisfy the requirements of Section
15
3.6 and other requirements of this standard.
16 17 18
4―CONCRETE MOMENT FRAMES 4.1―Types of Concrete Moment Frames
19
Concrete moment frames are defined as elements composed primarily of horizontal frame
20
components, such as beams, slabs, or both; vertical frame components, such as columns; and joints
21
connecting horizontal and vertical frame components. To resist seismic forces, these elements act
22
alone or in conjunction with shear walls, braced frames, or other elements.
23
Frames that are cast monolithically, including monolithic concrete frames created by the addition
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1
of new material, are addressed in this chapter. Frames addressed include reinforced concrete
2
beam–column moment frames, post-tensioned concrete beam–column moment frames, and slab–
3
column moment frames.
4
The frame classifications in Sections 4.1.1 through 4.1.3 include existing construction, new
5
construction, existing construction that has been retrofitted, frames intended as part of
6
the seismic-force-resisting system, and frames not intended as part of the seismic-force-resisting
7
system in the original design.
8
4.1.1 Reinforced Concrete Beam–Column Moment Frames―Reinforced concrete beam–column
9
moment frames, addressed in Section 4.2, are defined by the following conditions:
10
1.
Frame components are beams with or without slabs, columns, and their connections;
11
2.
Frames are of monolithic construction that provide for moment and shear transfer between
12 13
beams and columns; and 3.
14
Primary reinforcement in components contributing to seismic-force resistance is nonprestressed.
15
4.1.2 Post-tensioned Concrete Beam–Column Moment Frames―Post-tensioned concrete beam–
16
column moment frames, addressed in Section 4.3, are defined by the following conditions:
17
1.
Frame components are beams (with or without slabs), columns, and their connections;
18
2.
Frames are of monolithic construction that provide for moment and shear transfer between
19 20 21
beams and columns; and 3.
Primary reinforcement in beams contributing to seismic-force resistance includes posttensioned reinforcement with or without non prestressed reinforcement.
22
4.1.3 Slab–Column Moment Frames―Slab–column moment frames, addressed in Section 2.4, are
23
defined by the following conditions:
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1
1.
2 3
and their connections; 2.
4 5 6
Frame components are slabs with or without beams in the transverse direction, columns,
Frames are of monolithic construction that provide for moment and shear transfer between slabs and columns; and
3.
Primary reinforcement in slabs contributing to seismic-force resistance includes nonprestressed reinforcement, prestressed reinforcement, or both.
7 8
4.2―Reinforced Concrete Beam–Column Moment Frames
9
4.2.1 General―The analytical model for a beam–column frame element shall represent strength,
10
stiffness, and deformation capacity of beams, columns, beam–column joints, and other
11
components of the frame, including connections with other elements. Potential failure in flexure,
12
shear, and reinforcement development at any section along the component length shall be
13
considered. Interaction with other elements, including nonstructural components, shall be included.
14
Analytical models representing a beam–column frame using line elements with properties
15
concentrated at component centerlines shall be permitted. Where beam and column centerlines do
16
not intersect, the eccentricity effects between frame centerlines shall be considered. Where the
17
centerline of the narrower component falls within the middle third of the adjacent frame component
18
measured transverse to the framing direction, this eccentricity need not be considered. Where
19
larger eccentricities occur, the effect shall be represented either by reductions in effective stiffness,
20
strength, and deformation capacity or by direct modeling of the eccentricity.
21
The beam–column joint in monolithic construction is the zone having horizontal dimensions
22
equal to the column cross-sectional dimensions and vertical dimension equal to the beam depth. A
23
wider joint is acceptable where the beam is wider than the column. The beam–column joint shall
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1
be modeled according to Section 4.2.2 or as justified by experimental evidence. The model of the
2
connection between columns and foundation shall be selected based on details of the column–
3
foundation connection and rigidity of the foundation–soil system.
4
Action of the slab as a diaphragm interconnecting vertical components shall be considered.
5
Action of the slab as a composite beam flange shall be considered in developing stiffness, strength,
6
and deformation capacities of the beam component model per Section 3.1.3.
7
Inelastic action shall be restricted to those components and actions listed in Tables 7, 8, and 9,
8
except where it is demonstrated by experimental evidence and analysis that other inelastic action
9
is acceptable for the selected performance level. Acceptance criteria are specified in Section 4.2.4.
10 11
C4.2.1 General―Nonstructural components should be included in the analytical model if such
12
elements contribute significantly to building stiffness, modify dynamic properties, or have
13
significant impact on the behavior of adjacent structural elements. Section 7.2.3.3 of ASCE 41
14
suggests that nonstructural components should be included if their lateral stiffness exceeds 10%
15
of the total initial lateral stiffness of a story. Partial infill walls and staircases are examples of
16
nonstructural elements that can alter the behavior of adjacent concrete structural elements.
17 18
4.2.2 Stiffness of Reinforced Concrete Beam–Column Moment Frames
19
4.2.2.1 Linear Static and Dynamic Procedures―Beams shall be modeled considering flexural
20
and shear stiffnesses, including the effect of the slab acting as a flange in monolithic construction
21
according to the provisions in Section 3.1.3. Columns shall be modeled considering flexural, shear,
22
and axial stiffnesses. Refer to Section 3.1.2 to compute the effective stiffnesses. Where joint
23
stiffness is not modeled explicitly, it shall be permitted to be modeled implicitly by adjusting a This draft is not final and is subject to revision. This draft is for public review and comment only. Page 60 of 217
1
centerline model (Fig. 2):
2
1.
For ΣMColE/ΣMnBE > 1.2, column offsets are rigid and beam offsets are not;
3
2.
For ΣMColE/ΣMBE < 0.8, beam offsets are rigid and column offsets are not; and
4
3.
For 0.8 ≤ ΣMColE/ΣMBE ≤ 1.2, half of the beam and column offsets are considered rigid.
5
MColE shall be calculated considering axial force from the gravity loads specified in Equation 7-
6
3 of ASCE 41. Because this modeling approach accounts only for joint shear flexibility, stiffness
7
values used for the beams and columns shall include the flexibility resulting from bar slip.
8 9
C4.2.2.1 Linear Static and Dynamic Procedures―Various approaches to explicitly model beam–
10
column joints are available in the literature (El‐Metwally and Chen 1988; Ghobarah and Biddah
11
1999; Shin and LaFave 2004; Mitra and Lowes 2007, Lin and Restrepo, 2002). For simplicity of
12
implementation in commercial structural analysis software and agreement with calibration
13
studies performed in the development of this standard, this section defines an implicit beam–
14
column joint modeling technique using centerline models with semirigid joint offsets. Fig. 2
15
shows an example of an explicit joint model and illustrates the implicit joint modeling approach.
16
In the implicit joint model, only a portion of the beam and column, or both, within the geometric
17
joint region is defined as rigid. In typical commercial software packages, this portion can range
18
from 0, in which case the model is a true centerline model, to 1.0, where the entire joint region
19
is rigid. Further commentary is provided in Section C5.1.2.1, and background material is provided
20
in Elwood et al. (2007) and Birely et al. (2009).
21 22
4.2.2.2 Nonlinear Static Procedure―Nonlinear load-deformation relations shall comply with
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1
Section 3.1.2. Nonlinear modeling parameters for beams, columns, and beam–column joints are
2
provided in Tables 7, 8, 9, and 10, respectively.
3
Beams and columns shall be modeled using concentrated or distributed plastic hinge models.
4
Other models whose behavior represents the behavior of reinforced concrete beam and column
5
components subjected to seismic loading shall be permitted. The beam and column model shall be
6
capable of representing inelastic response along the component length, except where it is shown
7
by equilibrium that yielding is restricted to the component ends. Where nonlinear response is
8
expected in a mode other than flexure, the model shall be established to represent such effects.
9
Monotonic load-deformation relations shall be established according to the generalized load-
10
deformation relation shown in Fig. 1, with the exception that different relations shall be permitted
11
where verified by experiments. The overall load-deformation relation shall be established so that
12
maximum resistance is consistent with the strength specifications of Sections 3.2 and 4.2.3.
13
For beams and columns, the generalized deformation in Fig. 1 is plastic hinge rotation. For
14
beam–column joints, the generalized deformation is shear strain. Values of the generalized
15
deformation at points B, C, and D shall be derived from experiments or rational analyses and shall
16
take into account the interactions among flexure, axial load, and shear.
17 18
C4.2.2.2 Nonlinear Static Procedure―The modeling parameters and acceptance criteria
19
specified in Tables 8 and 9 reflect results from research on reinforced concrete columns and an
20
updated database of columns tests that includes 319 rectangular and 171 circular column tests
21
without lap‐splices (Ghannoum and Sivaramakrishnan 2012 a,b), and a database of 39
22
rectangular columns containing lap‐splices (Al Awaar 2015). Most circular columns in the
23
database contained spiral reinforcement. Separate tables are given for rectangular columns This draft is not final and is subject to revision. This draft is for public review and comment only. Page 62 of 217
1
(Table 8) and spirally reinforced circular columns (Table 9). For circular columns reinforced with
2
ties not conforming to ACI 318 seismic hoop designation, Table 8 should be used. The three
3
parameters that are used in Tables 8 and 9 to calculate modeling parameters and acceptance
4
criteria for columns not controlled by inadequate development or splicing are: axial load ratio,
5
transverse reinforcement ratio, and ratio of shear demand at flexural yielding to shear capacity
6
(VyE/VCol0E). For columns controlled by inadequate development or splicing, the same modeling
7
parameters were introduced for rectangular and circular columns in Tables 8 and 9 and are
8
related to: axial load ratio, transverse reinforcement ratio, and the ratio of transverse
9
reinforcement to longitudinal reinforcement strength.
10
The modeling parameters in Tables 8 and 9 define the plastic rotations according to Fig. 1a. As
11
shown in Fig. 1a, modeling parameter anl provides the plastic rotation at significant loss of lateral
12
force capacity. For the purposes of determining anl values based on test data, it was assumed
13
that this point represented a 20% or greater reduction in the lateral force resistance from the
14
measured peak shear capacity. For columns expected to experience flexural failures (VyE/ VCol0E ≤
15
0.6), such loss of lateral load resistance can be caused by concrete crushing, bar buckling, and
16
other flexural damage mechanisms. For columns expected to experience shear failures, either
17
before or after flexural yielding (VyE/ VCol0E > 0.6), loss of lateral load resistance is commonly
18
caused by severe diagonal cracking indicative of shear damage. For columns with inadequate
19
anchorage or splicing, loss of lateral load resistance is caused by bond splitting failures that
20
gradually unload the longitudinal bars. Consistent with Section 7.5.1.2 of ASCE 41, modeling
21
parameter bnl provides an estimate of the plastic rotation at the loss of gravity load support, that
22
is, axial load failure. This draft is not final and is subject to revision. This draft is for public review and comment only. Page 63 of 217
1
Modeling parameters given in Tables 8 and 9 represent median estimates of parameters
2
extracted from columns in the database (Ghannoum and Sivaramakrishnan 2012 a,b). For
3
columns with longitudinal bars that are adequately anchored or spliced, equations for modeling
4
parameter anl were obtained from a weighted regression analysis of the data (Ghannoum and
5
Matamoros 2014). An upper bound on the transverse reinforcement ratio (ρt) of 0.0175 was
6
selected because few columns in the database contained a ratio exceeding that limit, as well as
7
to limit the maximum deformation capacity of highly confined columns. Equations for modeling
8
parameters cannot be used for columns with a transverse reinforcement ratio below 0.0005 as
9
they are not intended for unreinforced columns. For columns with ties not adequately anchored
10
into the core, an upper bound on the transverse reinforcement ratio of 0.0075 was selected to
11
limit their contribution to deformation capacity. A lower limit on VyE/ VCol0E of 0.2 is prescribed
12
because few columns in the database have lower values of VyE/ VCol0E.
13
Due to the scarcity of collapse tests, equations for modeling parameter bnl were obtained from
14
a behavioral model adapted from Elwood and Moehle (2005) (Ghannoum and Matamoros 2014).
15
Recent test data from columns tested to axial failure (Matamoros et al. 2008; Woods and
16
Matamoros 2010; Henkhaus 2010; and Simpson and Matamoros 2012) show that the drift ratio
17
at axial failure for columns with various configurations and loading histories is estimated
18
adequately using the failure model proposed by Elwood and Moehle (2005). The set of columns
19
evaluated included slender and short columns, as well as shear‐critical columns and columns
20
failing in shear after flexural yielding. Table C1 presents the practical range of modeling
21
parameters for concrete columns evaluated using the equations in Tables 8 and 9.
22
The tabulated relations for modeling parameters were evaluated using the data from This draft is not final and is subject to revision. This draft is for public review and comment only. Page 64 of 217
1
laboratory tests (Ghannoum and Matamoros 2014). The An error ratio was is defined as the
2
modeling parameters evaluated from tables divided by the experimental modeling parameter
3
values for the column tests. The error ratios were found to follow lognormal probability
4
distributions for all modeling parameters (Ghannoum and Matamoros 2014). Fitted lognormal
5
distributions were used to produce multipliers for the tabulated modeling parameter relations
6
to achieve specific probabilities of exceedance (Table C2).
7
Acceptance criteria in Tables 8 and 9 were selected as 15% of the anl values for Immediate
8
Occupancy, 50% of the bnl values for Life Safety, and 70% of the bnl values for Collapse Prevention.
9
The fractions of bnl values were selected based on Table C2 to achieve low probabilities of axial
10
failure for columns satisfying the acceptance criteria. These probabilities were 10% and 25% for
11
Life Safety and Collapse Prevention, respectively.
12
Note that the probabilities of exceedance in Table C1 correspond to the probability of failure
13
for a column given a plastic rotation demand equal to the modeling parameter scaled by the
14
appropriate multiplier in Table C2.
15
Most laboratory tests ignore some factors that can influence the drift capacity, such as loading
16
history and bidirectional loading. The probabilities of exceedance in Table C2 can therefore be
17
larger if these factors are considered. Databases used to assess the model conservatism consist
18
of rectangular and circular columns subjected to unidirectional lateral forces applied parallel to
19
either one of the column principal axes. Actual columns have configurations and loadings that
20
differ from those used in the databases. Note that bidirectional loading on corner columns and
21
long duration seismic motions is expected to result in lower deformation capacities (Matamoros
22
et al. 2008; Henkhaus 2010, Woods and Matamoros 2010; Simpson and Matamoros 2012; and This draft is not final and is subject to revision. This draft is for public review and comment only. Page 65 of 217
1
Ghannoum and Matamoros 2014). Test data has shown that the drift ratio at axial failure of
2
columns subjected to biaxial loading and/or a large number of cycles per drift ratio can be lower
3
than that of column with loading histories consisting of uniaxial loading with three cycles per drift
4
ratio. Limited data exist, however, to assess the degree of reduction anticipated.
5
The acceptance criteria for linear procedures in Table 10 were determined based on the
6
modeling parameters for nonlinear procedures in Tables 8 and 9 in accordance with ASCE 41
7
Section 7.6.
8
The licensed design professional is referred to the following reports for further guidance
9
regarding determination of modeling parameters and acceptance criteria for reinforced concrete
10
columns: Lynn et al. 1996; Panagiotakos and Fardis 2001; Sezen 2002; Fardis and Biskinis 2003;
11
Biskinis et al. 2004; Elwood and Moehle 2004, 2005a, and 2005b; Berry and Eberhard 2005;
12
Henkhaus, 2010; Matamoros et al. 2008; Woods and Matamoros 2010; and Ghannoum and
13
Matamoros 2014.
14 15
4.2.2.3 Nonlinear Dynamic Procedure―For NDP, the complete hysteretic behavior of each
16
component shall be modeled using properties verified by experimental evidence. The use of the
17
generalized load-deformation relation described by Fig. 1 to represent the envelope relation for the
18
analysis shall be permitted. Refer to Section 4.2.2.2 for the application of parameters for columns
19
in Tables 8 and 9. Unloading and reloading properties shall represent significant stiffness and
20
strength-degradation characteristics.
21 22
4.2.3 Strength of Reinforced Concrete Beam–Column Moment Frames―Component strengths
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1
shall be computed according to the general requirements of Section 3.2, as modified in this section.
2
The maximum component strength shall be determined considering potential failure in flexure,
3
axial load, shear, torsion, bar development, and other actions at all points along the length of the
4
component, under the actions of design gravity load and seismic force combinations.
5 6
4.2.3.1 Columns―For columns, the shear strength Vcol shall be permitted to be calculated using
7
Eq. (3).
8 9
(3)
10
11
12
/
⁄
13
14
1
.
/
⁄
1
.
0.8
⁄ .
(3)
/
/
/
0.8
/
15 16 17
in which knl = 1.0 in regions where displacement ductility demand is less than or equal to 2, 0.7 in
18
regions where displacement ductility demand is greater than or equal to 6, and varies linearly for This draft is not final and is subject to revision. This draft is for public review and comment only. Page 67 of 217
1
displacement ductility between 2 and 6;
2
0.75 for lightweight aggregate concrete and 1.0 for normal-weight aggregate concrete;
3
NUG is the axial compression force calculated using Eq. 7-3 of ASCE 41 (set to zero for tension
4
force);
5
MUD/VUDd is the largest ratio of moment to shear times effective depth for the column under design
6
loadings evaluated using Eq. (7-34) of ASCE 41, but shall not be taken greater than 4 or less
7
than 2; and
8 9 10
αCol = 1.0 for s/d ≤ 0.75, 0.0 for s/d ≥ 1.0, and varies linearly for s/d between 0.75 and 1.0. Alternative formulations for column strength that consider effects of reversed cyclic inelastic deformations and that are verified by experimental evidence shall be permitted.
11
For columns satisfying the detailing and proportioning requirements of ACI 318, Chapter 18,
12
and for which shear is classified as a deformation-controlled action, as well as for columns in
13
which shear is classified as a force-controlled action, it shall be permitted to use the shear strength
14
equations in Chapter 18 of ACI 318.
15 16
C4.2.3.1 Columns―The use of shear strength equations and material properties to calculate the
17
shear strength VCol0E in this standard is illustrated in Figure C‐1.
18
As discussed in Section C5.3, experimental evidence indicates the possibility that flexural
19
deformability can be reduced as coexisting shear forces increase. As flexural ductility demands
20
increase, shear capacity decreases, which can result in a shear failure before theoretical flexural
21
deformation capacities are reached. Caution should be exercised when flexural deformation
22
capacities are determined by calculation.
23
Eq. (3) illustrates the reduction in column shear capacity with increasing nonlinear This draft is not final and is subject to revision. This draft is for public review and comment only. Page 68 of 217
1
deformations and provides an estimate of the mean observed shear strength for 51 rectangular
2
reinforced concrete columns subjected to unidirectional lateral forces parallel to one face of the
3
column (Sezen and Moehle 2004). The coefficient of variation for the ratio of measured to
4
calculated shear strength is 0.15.
5
For a column experiencing flexural yielding before shear failure (VyE 3.0 and shall be considered short
5
or squat if their aspect ratio is d/2
0.0030
0.01
0.2
0.0015
0.005
0.01
Condition iii. Beams Controlled by Inadequate Development or Splicing Along the Span Stirrup spacing d/2
0.0030
0.02
0.0
0.0015
0.01
Stirrup spacing > d/2
0.0030
0.01
0.0
0.0015
0.005
b
0.02 0.01 b
Condition iv. Beams Controlled by Inadequate Embedment into Beam–Column Joint 0.015
0.03
0.2
0.01
0.02
0.03
Note: fc in lb/in. (MPa) units. a Values between those listed in the table shall be determined by linear interpolation. b Where more than one of Conditions i, ii, iii, and iv occur for a given component, use the minimum appropriate numerical value from the table. c “C” and “NC” are abbreviations for conforming and nonconforming transverse reinforcement, respectively. Transverse reinforcement is conforming if, within the flexural plastic hinge region, hoops are spaced at d/3, and if, for components of moderate and high ductility demand, the strength provided by the hoops (Vs) is at least 3/4 of the design shear. Otherwise, the transverse reinforcement is considered nonconforming. d V is the shear force from NSP or NDP. 2
This draft is not final and is subject to revision. This draft is for public review and comment only. Page 195 of 217
1 2 3
Table 8—Modeling parameters and numerical acceptance criteria for nonlinear procedures— reinforced concrete columns other than circular with spiral reinforcement or seismic hoops as defined in ACI 318 Modeling Parameters Plastic rotation angles, anl and bnl ( radians) Residual strength ratio, cnl
Acceptance criteria Plastic rotation angle (radians) Performance level IO LS CP Columns not controlled by inadequate development or splicing along the clear height‡
V yE N a nl 0.042 0.043 UD' 0.63 t 0.023 VColOE Ag f cE For
N UD 0 .5 0.5 bnl 0.01 a nl ' Ag f cE N 1 f cE' UD 5 0.8 A g f cE' t f ytE
cnl 0.24 0.4
0 .0 a
0.15 anl ≤ 0.005
0.5 bnlb
0.7 bnlb
NUD 0.0 Ag fcE'
Columns controlled by inadequate development or splicing along the clear heightc
1 t f ytE anl 8 f l ylE
0 .0 d 0.025
0.0 N e bnl 0.012 0.085 UD' 12t anl Ag fcE 0.06
0.0
0.5 bnl
0.7 bnl
cnl 0.15 36t 0.4
4 5 6 7 8 9 10 11 12 13 14 15 16 17
ρt shall not be taken greater than 0.0175 in any case nor greater than 0.0075 when ties are not adequately anchored in the core. Equations in the table are not valid for columns with ρt smaller than 0.0005. VyE/VColOE shall not be taken less than 0.2. NUD shall be the maximum compressive axial load accounting for the effects of lateral forces as described in Eq. (7-34) of ASCE 41. Alternatively, it shall be permitted to evaluate NUD based on a limit-state analysis. a bnl shall be reduced linearly for NUD/(Agf’cE) > 0.5 from its value at NUD/(Agf’cE) = 0.5 to zero at NUD/(Agf’cE) = 0.7 but shall not be smaller than anl b
NUD/(Agf’cE) shall not be taken smaller than 0.1. Columns are considered to be controlled by inadequate development or splices where the calculated steel stress at the splice exceeds the steel stress specified by Eqs. (1a) or (1b). Modeling parameter for columns controlled by inadequate development or splicing shall never exceed those of columns not controlled by inadequate development or splicing. d anl for columns controlled by inadequate development or splicing shall be taken as zero if the splice region is not crossed by at least two tie groups over its length. e ρt shall not be taken greater than 0.0075. c
This draft is not final and is subject to revision. This draft is for public review and comment only. Page 196 of 217
1 2 3
Table 9—Modeling parameters and numerical acceptance criteria for nonlinear procedures— reinforced concrete circular columns with spiral reinforcement or seismic hoops as defined in ACI 318 Modeling Parameters Plastic rotation angles, anl and bnl ( radians) Residual strength ratio, cnl
Acceptance criteria Plastic rotation angle (radians) Performance level IO LS Columns not controlled by inadequate development or splicing along the clear height‡
V N a nl 0.06 0.06 UD' 1.3 t 0.037 yE A f V g cE ColOE For
0 .0
N UD 0.65 0.5 bnl 0.01 a nl ' Ag f cE N 1 f cE' UD 5 ' 0.8 Ag f cE t f ytE
cnl 0.24 0.4
CP
a
0.15 anl ≤ 0.005
0.5 bnlb
0.7 bnlb
NUD 0.0 Ag fcE'
Columns controlled by inadequate development or splicing along the clear heightc
1 t f ytE anl 8 f l ylE
0 .0 d 0.025
0.0 NUD e bnl 0.012 0.085 12t anl Ag f cE' 0.06
4 5 6 7 8 9 10 11 12 13 14 15 16
0.0
0.5 bnl
0.7 bnl
cnl 0.15 36t 0.4 ρt shall not be taken greater than 0.0175 in any case nor greater than 0.0075 when ties are not adequately anchored in the core. Equations in the table are not valid for columns with ρt smaller than 0.0005. VyE/VColOE shall not be taken less than 0.2. NUD shall be the maximum compressive axial load accounting for the effects of lateral forces as described in Eq. (7-34) of ASCE 41. Alternatively, it shall be permitted to evaluate NUD based on a limit-state analysis. a bnl shall be reduced linearly for NUD/(Agf’cE) > 0.5 from its value at NUD/(Agf’cE) = 0.5 to zero at NUD/(Agf’cE) = 0.7 but shall not be smaller than anl b NUD/(Agf’cE) shall not be taken smaller than 0.1. c Columns are considered to be controlled by inadequate development or splices where the calculated steel stress at the splice exceeds the steel stress specified by Eqs. (1a) or (1b). Modeling parameter for columns controlled by inadequate development or splicing shall never exceed those of columns not controlled by inadequate development or splicing. d anl for columns controlled by inadequate development or splicing shall be taken as zero if the splice region is not crossed by at least two tie groups over its length. e ρt shall not be taken greater than 0.0075.
This draft is not final and is subject to revision. This draft is for public review and comment only. Page 197 of 217
1
Table 10a - Numerical Acceptance Criteria for Linear Procedures—Reinforced concrete columns
2
other than circular with spiral reinforcement or seismic hoops as defined in ACI 318
m-factorsa Performance Level
NUD A f' g cE
Component Type
t
Primary VyE/VColOE
IO
LS
Secondary CP
LS
CP ‡
Columns not controlled by inadequate development or splicing along the clear height 0.1
0.0175
≥ 0.2 < 0.6
1.7
3.4
4.2
6.8
8.9
0.7
0.0175
≥ 0.2 < 0.6
1.2
1.4
1.7
1.4
1.7
0.1
0.0005
≥ 0.2 < 0.6
1.5
2.6
3.2
2.6
3.2
0.7
0.0005
≥ 0.2 < 0.6
1.0
1.0
1.0
1.0
1.0
0.1
0.0175
≥ 0.6 < 1.0
1.5
2.7
3.3
6.8
8.9
0.7
0.0175
≥ 0.6 < 1.0
1.0
1.0
1.0
1.0
1.0
0.1
0.0005
≥ 0.6 < 1.0
1.3
1.9
2.3
1.9
2.3
0.7
0.0005
≥ 0.6 < 1.0
1.0
1.0
1.0
1.0
1.0
0.1
0.0175
≥ 1.0
1.3
1.8
2.2
6.8
8.9
0.7
0.0175
≥ 1.0
1.0
1.0
1.0
1.0
1.0
0.1
0.0005
≥ 1.0
1.1
1.0
1.1
1.7
2.1
0.7
0.0005
≥ 1.0
1.0
1.0
1.0
1.0
1.0
Columns controlled by inadequate development or splicing along the clear height‡
3 4 5 6 7
0.1
0.0075
1.0
1.7
2.0
5.3
6.8
0.7
0.0075
1.0
1.0
1.0
2.8
3.5
0.1
0.0005
1.0
1.0
1.0
1.4
1.6
0.7
0.0005
1.0
1.0
1.0
1.0
1.0
a
Values between those listed in the table shall be determined by linear interpolation. ‡ Columns are considered to be controlled by inadequate development or splicing where the calculated steel stress at the splice exceeds the steel stress specified by Eqs. (1a) or (1b). Acceptance criteria for columns controlled by inadequate development or splicing shall never exceed those of columns not controlled by inadequate development or splicing.
This draft is not final and is subject to revision. This draft is for public review and comment only. Page 198 of 217
1
Table 10b - Numerical Acceptance Criteria for Linear Procedures—Reinforced concrete circular
2
columns with spiral reinforcement or seismic hoops as defined in ACI 318
m-factorsa Performance Level
NUD A f' g cE
Component Type
t
Primary VyE/VColOE
IO
LS
Secondary CP
LS
CP ‡
Columns not controlled by inadequate development or splicing along the clear height 0.1
0.0175
≥ 0.2 < 0.6
1.7
4.8
6.2
8.9
11.6
0.7
0.0175
≥ 0.2 < 0.6
1.4
2.1
2.6
2.1
2.6
0.1
0.0005
≥ 0.2 < 0.6
1.6
3.2
4.0
3.2
4.0
0.7
0.0005
≥ 0.2 < 0.6
1.0
1.0
1.0
1.0
1.0
0.1
0.0175
≥ 0.6 < 1.0
1.7
3.7
4.7
8.9
11.6
0.7
0.0175
≥ 0.6 < 1.0
1.1
1.0
1.1
1.0
1.1
0.1
0.0005
≥ 0.6 < 1.0
1.4
2.1
2.5
2.3
2.8
0.7
0.0005
≥ 0.6 < 1.0
1.0
1.0
1.0
1.0
1.0
0.1
0.0175
≥ 1.0
1.4
2.3
2.9
8.9
11.6
0.7
0.0175
≥ 1.0
1.0
1.0
1.0
1.0
1.0
0.1
0.0005
≥ 1.0
1.0
0.8
0.8
2.3
2.8
0.7
0.0005
≥ 1.0
1.0
1.0
1.0
1.0
1.0
Columns controlled by inadequate development or splicing along the clear height‡
3 4 5 6 7
0.1
0.0075
1.0
1.7
2.0
5.3
6.8
0.7
0.0075
1.0
1.0
1.0
2.8
3.5
0.1
0.0005
1.0
1.0
1.0
1.4
1.6
0.7
0.0005
1.0
1.0
1.0
1.0
1.0
a
Values between those listed in the table shall be determined by linear interpolation. ‡ Columns are considered to be controlled by inadequate development or splicing where the calculated steel stress at the splice exceeds the steel stress specified by Eqs. (1a) or (1b). Acceptance criteria for columns controlled by inadequate development or splicing shall never exceed those of columns not controlled by inadequate development or splicing.
This draft is not final and is subject to revision. This draft is for public review and comment only. Page 199 of 217
Table 11. Modeling Parameters and Numerical Acceptance Criteria for Nonlinear Procedures—Reinforced Concrete Beam–Column Joints Modeling Parametersa
Acceptance Criteriaa Plastic Rotations Angle (radians)
Plastic Rotations Angle (radians) a
Conditions
Performance Level
Residual Strength Ratio
b
c
IO
LS
CP
Condition i. Interior joints (Note: for classification of joints, refer to Fig. 3) P A g f ' cE
Transverse reinforcementc
V VJ
0.1
C
1.2
0.015
0.03
0.2
0.0
0.02
0.03
0.1
C
1.5
0.015
0.03
0.2
0.0
0.015
0.02
0.4
C
1.2
0.015
0.025
0.2
0.0
0.015
0.025
0.4
C
1.5
0.015
0.2
0.2
0.0
0.015
0.02
0.1
NC
1.2
0.005
0.2
0.2
0.0
0.015
0.02
0.1
NC
1.5
0.005
0.015
0.2
0.0
0.01
0.015
0.4
NC
1.2
0.005
0.015
0.2
0.0
0.01
0.015
0.4
NC
1.5
0.005
0.015
0.2
0.0
0.01
0.015
b
d
Condition ii. Other joints (Note: for classification for joints, refer to Fig. 3) P A g f ' cE
Transverse reinforcementc
V VJ
0.1
C
1.2
0.01
0.02
0.2
0.0
0.015
0.02
0.1
C
1.5
0.01
0.015
0.2
0.0
0.01
0.015
0.4
C
1.2
0.01
0.02
0.2
0.0
0.015
0.02
0.4
C
1.5
0.01
0.015
0.2
0.0
0.01
0.015
0.1
NC
1.2
0.005
0.01
0.2
0.0
0.0075
0.01
0.1
NC
1.5
0.005
0.01
0.2
0.0
0.0075
0.01
0.4
NC
1.2
0.0
0.0075
0.0
0.0
0.005
0.0075
0.4
NC
1.5
0.0
0.0075
0.0
0.0
0.005
0.0075
b
d
a
Values between those listed in the table shall be determined by linear interpolation. P is the design axial force on the column above the joint calculated using limit-state analysis procedures in accordance with Section 4.2.4, and Ag is the gross cross-sectional area of the joint. c “C” and “NC” are abbreviations for conforming and nonconforming transverse reinforcement. Joint transverse reinforcement is conforming if hoops are spaced at hc/2 within the joint. Otherwise, the transverse reinforcement is considered nonconforming. d V is the shear force from NSP or NDP, and VJ is the shear strength for the joint. The shear strength shall be calculated according to Section 4.2.3. b
1 This draft is not final and is subject to revision. This draft is for public review and comment only. Page 200 of 217
1 2 3
This draft is not final and is subject to revision. This draft is for public review and comment only. Page 201 of 217
1 Table 12. Values of for Joint Strength Calculation
Value of Condition i: Interior Jointsa Transverse Reinforcementb
Condition ii: other joints
Interior Joint Exterior Joint Knee Joint with or Interior Joint with Without Transverse Exterior Joint with Without Transverse Without Transverse Transverse Beams Beams Transverse Beams Beams Beams
C
20
15
15
12
8
NC
12
10
8
6
4
a
For classification of joints, refer to Fig. 3. b “C” and “NC” are abbreviations for conforming and nonconforming transverse reinforcement. Joint transverse reinforcement is conforming if hoops are spaced at hc/2 within the joint. Otherwise, the transverse reinforcement is considered nonconforming.
2 3
This draft is not final and is subject to revision. This draft is for public review and comment only. Page 202 of 217
Table 13. Numerical Acceptance Criteria for Linear Procedures—Reinforced Concrete Beams m-factorsa
Performance Level Component Type Primary Conditions
IO
LS
Secondary CP
LS
CP
Condition i. Beams Controlled by Flexureb V
d
– ------------- bal
Transverse reinforcementc
0.0
C
3 (0.25)
3
6
7
6
10
0.0
C
6 (0.5)
2
3
4
3
5
0.5
C
3 (0.25)
2
3
4
3
5
0.5
C
6 (0.5)
2
2
3
2
4
0.0
NC
3 (0.25)
2
3
4
3
5
0.0
NC
6 (0.5)
1.25
2
3
2
4
0.5
NC
3 (0.25)
2
3
3
3
4
0.5
NC
6 (0.5)
1.25
2
2
2
3 4
bw d
f 'cE
Condition ii. Beams Controlled by Shearb Stirrup spacing d/2
1.25
1.5
1.75
3
Stirrup spacing > d/2
1.25
1.5
1.75
2
3
Condition iii. Beams Controlled by Inadequate Development or Splicing Along the Span Stirrup spacing d/2
1.25
1.5
1.75
3
Stirrup spacing > d/2
1.25
1.5
1.75
2
b
4 3 b
Condition iv. Beams Controlled by Inadequate Embedment into Beam–Column Joint 2
2
3
3
4
Note: fc in lb/in. (MPa) units. a Values between those listed in the table shall be determined by linear interpolation. b Where more than one of Conditions i, ii, iii, and iv occurs for a given component, use the minimum appropriate numerical value from the table. c “C” and “NC” are abbreviations for conforming and nonconforming transverse reinforcement. Transverse reinforcement is conforming if, within the flexural plastic hinge region, hoops are spaced at d/3, and if, for components of moderate and high ductility demand, the strength provided by the hoops (Vs) is at least 3/4 of the design shear. Otherwise, the transverse reinforcement is considered nonconforming. d V is the shear force calculated using limit-state analysis procedures in accordance with Section 4.2.4.1. 2
1 2
This draft is not final and is subject to revision. This draft is for public review and comment only. Page 203 of 217
Table 14—Numerical acceptance criteria for linear procedures—reinforced concrete beam–column joints m-Factorsa
Performance Level Component Type Primary Conditions
IO
LS
Secondary CP
LS
CP
Condition i. Interior Joints (for classification of joints, refer to Fig. 3) P A g f ' cE
b
Transverse reinforcementc
V VJ
d
0.1
C
1.2
1
1
1
3
4
0.1
C
1.5
1
1
1
2
3
0.4
C
1.2
1
1
1
3
4
0.4
C
1.5
1
1
1
2
3
0.1
NC
1.2
1
1
1
2
3
0.1
NC
1.5
1
1
1
2
3
0.4
NC
1.2
1
1
1
2
3
0.4
NC
1.5
1
1
1
2
3
Condition ii. Other Joints (for classification of joints, refer to Fig. 3) P A g f ' cE
b
Transverse reinforcementc
V VJ
d
0.1
C
1.2
1
1
1
3
4
0.1
C
1.5
1
1
1
2
3
0.4
C
1.2
1
1
1
3
4
0.4
C
1.5
1
1
1
2
3
0.1
NC
1.2
1
1
1
2
3
0.1
NC
1.5
1
1
1
2
3
0.4
NC
1.2
1
1
1
1.5
2
0.4
NC
1.5
1
1
1
1.5
2
a
Values between those listed in the table shall be determined by linear interpolation. P is the design axial force on the column above the joint calculated using limit-state analysis procedures in accordance with Section 10.4.2.4. Ag is the gross cross-sectional area of the joint. c V is the shear force and VJ is the shear strength for the joint. The design shear force and shear strength shall be calculated according to Section 4.2.4.1 and Section 4.2.3, respectively. d “C” and “NC” are abbreviations for conforming and nonconforming transverse reinforcement, respectively. Transverse reinforcement is conforming if hoops are spaced at hc/2 within the joint. Otherwise, the transverse reinforcement is considered nonconforming. b
1 2
This draft is not final and is subject to revision. This draft is for public review and comment only. Page 204 of 217
Table 15. Modeling Parameters and Numerical Acceptance Criteria for Nonlinear Procedures—Two-Way Slabs and Slab–Column Modeling Parametersa
Acceptance Criteriaa Plastic Rotation Angle (radians)
Plastic Rotation Angle (radians) Conditions
a
b
Performance Level
Residual Strength Ratio c
Secondary IO
LS
CP
b
Condition i. Reinforced Concrete Slab–Column Connections Vg ----Vo c
Continuity reinforceme ntd
0
Yes
0.2 0.4
0.035
0.05
0.2
0.01
0.035
0.05
Yes
0.03
0.04
0.2
0.01
0.03
0.04
Yes
0.02
0.03
0.2
0
0.02
0.03
0.6
Yes
0
0.02
0
0
0
0.02
0
No
0.025
0.025
0
0.01
0.02
0.025
0.2
No
0.02
0.02
0
0.01
0.015
0.02
0.4
No
0.01
0.01
0
0
0.008
0.01
0.6
No
0
0
0
0
0
0
> 0.6
No
0
0
0
—
e
e
—
—e
0.05
Condition ii. Post-tensioned Slab–Column Connectionsb Vg ----Vo c
Continuity reinforceme ntd|
0
Yes
0.035
0.05
0.4
0.01
0.035
0.6
Yes
0.005
0.03
0.2
0
0.025
0.03
> 0.6
Yes
0
0.02
0.2
0
0.015
0.02
0
No
0.025
0.025
0
0.01
0.02
0.025
0.6
No
0
0
0
0
0
0
> 0.6
No
0
0
0
—
e
e
—e
—
Condition iii. Slabs Controlled by Inadequate Development or Splicing Along the Spanb 0
0.02
0
0
0.01
0.02 b
Condition iv. Slabs Controlled by Inadequate Embedment into Slab–Column Joint 0.015
0.03
0.2
0.01
0.02
0.03
a
Values between those listed in the table shall be determined by linear interpolation. Where more than one of Conditions i, ii, iii, and iv occur for a given component, use the minimum appropriate numerical value from the table. c Vg is the gravity shear acting on the slab critical section as defined by ACI 318, and Vo is the direct punching shear strength as defined by ACI 318. b
This draft is not final and is subject to revision. This draft is for public review and comment only. Page 205 of 217
d
“Yes” shall be used where the area of effectively continuous main bottom bars passing through the column cage in each direction is greater than or equal to 0.5Vg/(fy). Where the slab is posttensioned, “Yes” shall be used where at least one of the post-tensioning tendons in each direction passes through the column cage. Otherwise, “No” shall be used. e Action shall be treated as force-controlled.
1 2
This draft is not final and is subject to revision. This draft is for public review and comment only. Page 206 of 217
Table 16. Numerical Acceptance Criteria for Linear Procedures—Two-Way Slabs and Slab–Column m-Factorsa
Performance Level Component Type Primary Conditions
IO
LS
Secondary CP
LS
CP
Condition i. Reinforced Concrete Slab–Column Connectionsb Vg ----Vo c
Continuity reinforcementd
0
Yes
2
2.75
3.5
3.5
4.5
0.2
Yes
1.5
2.5
3
3
3.75
0.4
Yes
1
2
2.25
2.25
3
0.6
Yes
1
1
1
1
2.25
0
No
2
2.25
2.25
2.25
2.75
0.2
No
1.5
2
2
2
2.25
0.4
No
1
1.5
1.5
1.5
1.75
0.6
No
1
1
1
1
1
> 0.6
No
—
e
—
e
—
e
—
e
—e
Condition ii. Post-tensioned Slab–Column Connectionsb Vg ----Vo c
Continuity reinforcementd
0
Yes
1.5
2
2.5
2.5
3.25
0.6
Yes
1
1
1
2
2.25
> 0.6
Yes
1
1
1
1.5
1.75
0
No
1.25
1.75
1.75
1.75
2
0.6
No
1
1
1
1
1
> 0.6
No
—
e
—
e
—
e
—
e
—e
Condition iii. Slabs Controlled by Inadequate Development or Splicing Along the Spanb —e
—e
—e
3
4
Condition iv. Slabs Controlled by Inadequate Embedment into Slab–Column Jointb
1 2 3 4 5 6 7 8 9
2
2
3
3
a
4
Values between those listed in the table shall be determined by linear interpolation. Where more than one of conditions i, ii, iii, and iv occur for a given component, use the minimum appropriate numerical value from the table. c Vg is the the gravity shear acting on the slab critical section as defined by ACI 318, and Vo is the direct punching shear strength as defined by ACI 318. d “Yes” shall be used where the area of effectively continuous main bottom bars passing through the column cage in each direction is greater than or equal to 0.5Vg/(ϕfy). Where the slab is post-tensioned, “Yes” shall be used where at least one of the posttensioning tendons in each direction passes through the column cage. Otherwise, “No” shall be used. e Action shall be treated as force controlled. b
This draft is not final and is subject to revision. This draft is for public review and comment only. Page 207 of 217
Table 17. Modeling Parameters and Numerical Acceptance Criteria for Nonlinear Procedures—Reinforced Concrete Infilled Frames Modeling Parametersa
Total Strain Conditions d e b i. Columns Modeled as Compression Chords Columns confined along entire 0.02 0.04 lengthc All other cases 0.003 0.01
Residual Strength Ratio c
Acceptance Criteria Total Strain Performance Level IO LS CP
0.4
0.003
0.03
0.04
0.2
0.002
0.01
0.01
0.0
0.01
0.04
0.05
ii. Columns Modeled as Tension Chordsb Columns with well-confined splices or no splices All other cases
0.05
0.05
See 0.03 0.2 See 0.02 0.03 note d note d a Interpolation shall not be permitted. b If load reversals result in both Conditions i and ii applying to a single column, both conditions shall be checked. c A column shall be permitted to be considered to be confined along its entire length where the quantity of hoops along the entire story height including the joint is equal to threequarters of that required by ACI 318 for boundary components of concrete shear walls. The maximum longitudinal spacing of sets of hoops shall not exceed either h/3 or 8db. d Potential for splice failure shall be evaluated directly to determine the modeling and acceptance criteria. For these cases, refer to the generalized procedure of Section 6.3.2.
1 2
This draft is not final and is subject to revision. This draft is for public review and comment only. Page 208 of 217
Table 18. Frames
Numerical Acceptance Criteria for Linear Procedures—Reinforced Concrete Infilled
m-Factorsa
Performance Level Component Type Primary
Secondary
Conditions i. Columns Modeled as Compression Chordsb
IO
LS
CP
LS
CP
Columns confined along entire lengthc
1
3
4
4
5
All other cases
1
1
1
1
1
ii. Columns Modeled as Tension Chordsb Columns with well-confined splices or no splices
3
4
5
5
6
All other cases 1 2 2 3 4 a Interpolation shall not be permitted. b If load reversals result in both Conditions i and ii applying to a single column, both conditions shall be checked. c A column is permitted to be considered to be confined along its entire length where the quantity of hoops along the entire story height, including the joint, is equal to three-quarters of that required by ACI 318 for boundary components of concrete shear walls. The maximum longitudinal spacing of sets of hoops shall not exceed either h/3 or 8db.
1
This draft is not final and is subject to revision. This draft is for public review and comment only. Page 209 of 217
Table 19. Modeling Parameters and Numerical Acceptance Criteria for Nonlinear Procedures— R/C Shear Walls and Associated Components Controlled by Flexure
Acceptable Plastic Hinge Rotationa (radians)
Plastic Hinge Rotation (radians) Conditions
Residual Strength Ratio
Performance Level
a
b
c
IO
LS
CP
0.015 0.010 0.009 0.005 0.008 0.006 0.003 0.002
0.020 0.015 0.012 0.010 0.015 0.010 0.005 0.004
0.75 0.40 0.60 0.30 0.60 0.30 0.25 0.20
0.005 0.004 0.003 0.0015 0.002 0.002 0.001 0.001
0.015 0.010 0.009 0.005 0.008 0.006 0.003 0.002
0.020 0.015 0.012 0.010 0.015 0.010 0.005 0.004
0.75
0.010
0.025
0.050
0.50
0.005
0.020
0.040
0.50
0.006
0.020
0.035
0.25
0.005
0.010
0.025
i. Shear Walls and Wall Segments
As A's f yE P
V
twlw f 'cE
twlw f 'cE
Confined Boundaryb
0.1 0.1 0.25 0.25 0.1 0.1 0.25 0.25
4 6 4 6 4 6 4 6
Yes Yes Yes Yes No No No No
ii. Shear Wall Coupling Beamsc Longitudinal reinforcement and transverse reinforcementd
V twlw
0.050
f ' cE
Conventional longitudinal reinforcement with conforming transverse reinforcement
3
0.025
6
0.020
Conventional longitudinal reinforcement with nonconforming transverse reinforcement
3
0.020
6
0.010
0.040 0.035 0.025 0.050
NA 0.030 0.050 0.80 0.006 0.030 0.050 Diagonal reinforcement a Linear interpolation between values listed in the table shall be permitted. b A boundary element shall be considered confined where transverse reinforcement exceeds 75% of the requirements given in ACI 318 and spacing of transverse reinforcement does not exceed 8db. It shall be permitted to take modeling parameters and acceptance criteria as 80% of confined values where boundary elements have at least 50% of the requirements given in ACI 318 and spacing of transverse reinforcement does not exceed 8db. Otherwise, boundary elements shall be considered not confined. c For coupling beams spanning
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