Heads up:
There are no amended sections in this chapter.

B |
= | bias factor to adjust nominal strength to seismic target reliabilities |

D_{u} |
= | ultimate deformation capacity; the largest deformation at which the hysteresis model is deemed valid given available laboratory data or other substantiating evidence |

f'_{ce} |
= | expected compressive strength of concrete, psi |

√f'_{ce} |
= | square root of expected compressive strength of concrete, psi |

f_{ue} |
= | expected tensile strength for nonprestressed reinforcement, psi |

f_{ye} |
= | expected yield strength for nonprestressed reinforcement, psi |

ℓ_{p} |
= | plastic-hinge length for analysis purposes, in. |

R_{ne} |
= | expected yield strength |

V_{ne} |
= | expected shear strength, lb |

θ_{y} |
= | yield rotation, radians |

ϕ_{s} |
= | seismic resistance factor for force-controlled actions |

**distributed plasticity (fiber) model**—component model consisting of discrete fibers explicitly representing nonlinear stress-strain or force-deformation responses.

**structural wall panel zone**—portion of a structural wall common to intersecting wall segments where forces from adjacent wall segments are resolve.

The following actions shall be as defined by ASCE/SEI 7 Chapter 16:

**action, deformation-controlled**

**action, force-controlled**

**action, force-controlled critical**

**action, force-controlled ordinary**

**action, force-controlled noncritical**

This appendix shall supplement the requirements of Chapter 16 of ASCE/SEI 7 when performing nonlinear response history analysis to determine the design of earthquake-resistant concrete structures.

This appendix shall be used in conjunction with Chapter 16 of ASCE/SEI 7 for additional general requirements, ground motions, load combinations, modeling, and analysis for design of new reinforced concrete structures, including:

(a) Structural systems designated as part of the seismic-force-resisting system, including diaphragms, moment-resisting frames, structural walls, and foundations.

(b) Members not designated as part of the seismic-force-resisting system but required to support other loads while sustaining deformations and forces associated with earthquake effects.

All concrete structures designed or verified by this Appendix shall be proportioned and detailed as required by Chapter 18 and the requirements of A.12 when applicable.

It shall be permitted to use the provisions of Appendix A to demonstrate the adequacy of a structural system as required by 18.2.1.7.

Independent structural design review consistent with A.13 shall be required for use of Appendix A.

The licensed design professional shall provide justification for any interpretation required for the application of Appendix A, and if accepted by the independent structural design reviewers, justification shall be provided to the building official for acceptance.

Action Classification and Criticality in A.7, and Acceptance Criteria in A.10 and A.11 provide a comprehensive design approach following the intent of Chapter 16 of ASCE/SEI 7 and the general building code, and shall take precedence over those of Chapter 16 of ASCE/SEI 7.

Nonlinear response history analysis shall include the effects of horizontal earthquake ground motions.

Vertical earthquake ground motion shall be considered simultaneously with horizontal earthquake ground motions where inclusion of vertical ground motion will substantially affect the structural design requirements.

Earthquake ground motion acceleration histories shall be selected and modified in accordance with procedures established by the general building code.

Load combinations for nonlinear response history analysis shall conform to the requirements of the general building code.

Models for analysis shall be three-dimensional and shall conform to the requirements of the general building code.

Modeling of member nonlinear behavior, including effective stiffness, expected strength, expected deformation capacity, and hysteresis under force or deformation reversals, shall be substantiated by applicable physical test data and shall not be extrapolated beyond the limits of testing.

Degradation in member strength or stiffness shall be included in the numerical models unless it can be demonstrated that the demand is not sufficiently large to produce these effects. If degradation in component strength is included in the numerical model, the model formulation shall be such that structural deformation at onset of strength loss is not affected by mesh configuration in the finite element model.

For structural walls with aspect ratio

**, the numerical model of the wall and its connection to surrounding elements shall represent kinematic effects associated with wall rotation and uplift, including the effect of migration of the neutral axis as a function of applied axial force and lateral deformation, unless it can be demonstrated that such effects do not affect the structural design requirements.***h*/_{w}*ℓ*≥ 2_{w}All actions shall be classified as deformation-controlled or force-controlled in accordance with A.7.2 and A.7.3.

Deformation-controlled actions shall satisfy the requirements of A.10.

The following shall be designated as deformation-controlled actions:

Force-controlled actions shall satisfy the requirements of A.11.

The following shall be designated as ordinary force-controlled actions:

(a) Shear and moment in perimeter basement walls

(b) In-plane shear in non-transfer diaphragms

(c) In-plane normal forces in diaphragms other than collectors

(d) Moment in shallow foundation members, including spread footings and mat foundations

(e) Moment in deep foundation members

Noncritical force-controlled actions shall be designated as actions in any component where failure will not result in: (a) collapse of the structure; (b) loss of the earthquake resistance of the structure; and (c) falling hazard.

All actions not designated as deformation controlled, ordinary force-controlled, or noncritical force-controlled shall be classified as critical-force controlled.

Member stiffness shall include effects of deformations due to flexure, shear, axial elongation or shortening, and reinforcement slip along its development length.

If cracking is anticipated as a result of combined effects of applied forces, displacements, and volume change effects associated with shrinkage, temperature, or creep, effects of concrete cracking on effective member stiffness shall be modeled.

If yielding of reinforcement or nonlinear response of concrete is anticipated as a result of combined effects of applied forces, displacements, and volume change effects associated with shrinkage, temperature, or creep, the structural model shall be capable of representing member stiffness for loading near the onset of inelastic response, as well as behavior past the onset of inelastic response.

It shall be permitted to represent member stiffness near the onset of inelastic response using an effective stiffness based on analysis substantiated by physical test data. Alternatively, it shall be permitted to represent member stiffness near the onset of inelastic response using the effective stiffness values in Table A.8.4.

**Table A.8.4—Effective stiffness values**

^{[1]}Component | Axial | Flexural | Shear | |
---|---|---|---|---|

Beams | nonprestressed | 1.0E_{c}A_{g} | 0.3E_{c}I_{g} | 0.4E_{c}A_{g} |

prestressed | 1.0E_{c}A_{g} | 1.0E_{c}I_{g} | 0.4E_{c}A_{g} | |

Columns with compression caused by design gravity loads^{[2]} | ≥0.5A'_{g}f_{c} | 1.0E_{c}A_{g} | 0.7E_{c}I_{g} | 0.4E_{c}A_{g} |

≤0.1A' or with tension_{g}f_{c} | 1.0E (compression) 1.0_{c}A_{g}E (tension)_{s}A_{st} | 0.3E_{c}I_{g} | 0.4E_{c}A_{g} | |

Structural walls^{[3]} | in-plane | 1.0E_{c}A_{g} | 0.35E_{c}I_{g} | 0.2E_{c}A_{g} |

out-of-plane | 1.0E_{c}A_{g} | 0.25E_{c}I_{g} | 0.4E_{c}A_{g} | |

Diaphragms (in-plane only)^{[4]} | nonprestressed | 0.25E_{c}A_{g} | 0.25E_{c}I_{g} | 0.25E_{c}A_{g} |

prestressed | 0.5E_{c}A_{g} | 0.5E_{c}I_{g} | 0.4E_{c}A_{g} | |

Coupling beams | with or without diagonal reinforcement | 1.0E_{c}A_{g} | 0.4E_{c}A_{g} | |

Mat foundations | in-plane | 0.5E_{c}A_{g} | 0.5E_{c}I_{g} | 0.4E_{c}A_{g} |

out-of-plane^{[5]} | 0.5E_{c}I_{g} |

^{[1]}Tabulated values for axial, flexural, and shear shall be applied jointly in defining effective stiffness of an element, unless alternative combinations are justified.

^{[2]}For columns with axial compression falling between the limits provided, flexural stiffness shall be determined by linear interpolation.

^{[3]}Tabulated values are appropriate where members are modeled using line elements to represent their properties.

^{[4]}Diaphragms shall be permitted to be modeled as rigid in-plane if this does not result in differences in analysis outcomes.

In beam-column joints if joint flexibility is not modeled explicitly, it shall be permitted to model joint flexibility implicitly by defining the effective stiffness of beams and columns framing into the joint to include joint flexibility and by introducing beam and column rigid end offsets that extend to the center of the joint.

Expected material strength shall be defined based on applicable project-specific data or data from projects using similar materials and construction. If applicable data are not available, the expected material strengths in Table A.9.1 shall be permitted.

**Table A.9.1—Expected material strengths**

Material | Expected strength | ||
---|---|---|---|

Concrete | f' = 1.3_{ce}f'_{c}^{[1]} | ||

Reinforcing steel | Expected yield strength, f, psi_{ye} | Expected tensile strength, f, psi_{ue} | |

A615 | Grade 60 | 70,000 | 106,000 |

A706 | Grade 60 | 69,000 | 95,000 |

Grade 80 | 85,000 | 112,000 |

^{[1]}Expected strength

*f*' is strength expected at approximately 1 year or longer.

_{ce}Deformations in any of the response history analyses shall not exceed the ultimate deformation capacity

**unless (a) or (b) is satisfied.***D*_{u}(a) The analysis assumes the strength associated with this mode of deformation is negligible for the remainder of that analysis, and the structure is evaluated for stability and strength.

(b) The analysis is considered to have an unacceptable response as defined by ASCE/SEI 7.

**shall be determined by (a), (b), or (c):**

*D*_{u}(a)

**of the component shall be taken as the valid range of modeling as demonstrated by comparison of the hysteresis model with suitable laboratory test data including the appropriate gravity load effect.***D*_{u}(b) If special structural walls are modeled using distributed plasticity (fiber) models,

**shall be evaluated using the average vertical strain. The strain shall be evaluated over a height of the plastic hinge length,***D*_{u}**, where***ℓ*_{p}**is the longer of (i) and (ii):***ℓ*_{p}(i) ℓ = 0.2_{p}ℓ + 0.03_{w}h_{w} |
(A.10.2.a) |

(ii) ℓ = 0.08_{p}h + 0.00015_{w}f_{y}d_{b} |
(A.10.2.b) |

but not exceeding the story height, where

**and***d*_{b}**are determined based on the wall longitudinal reinforcement.***f*_{y}(c) If structural components are modeled using lumped plasticity (concentrated hinge) or distributed plasticity (fiber) models,

**shall be permitted to be in accordance with ACI 369.1 or as substantiated by laboratory testing.***D*_{u}Force-controlled actions shall be evaluated in accordance with the general building code, with expected strength taken as

**ϕ**._{s}BR_{n}**ϕ**shall be in accordance with Table A.11.2, with

_{s}**ϕ**determined in accordance with Chapter 21, except that 21.2.4.1 shall not apply.

**Table A.11.2—Seismic resistance factor**

Force-controlled action |
ϕ_{s} |
---|---|

Critical | ϕ |

Ordinary | ϕ/0.9 ≤ 1.0 |

Noncritical | ϕ/0.85 ≤ 1.0 |

Bias factor,

**, shall be taken as 1.0. Alternatively, it shall be permitted to calculate***B**B*using Eq. (A.11.3):B = 0.9R /_{ne}R ≥ 1.0_{n} | (A.11.3) |

The expected strength,

**, is permitted to be defined in accordance with the nominal strength provisions of Chapters 18, 22, or 23, with***R*_{ne}**substituted for***f*'_{ce}**and***f*'_{c}**substituted for***f*_{ye}**or***f*_{y}**, except as provided in A.11.3.2.1 and A.11.3.2.2.***f*_{yt}For structural walls where

**meeting (a) through (d), the requirements of A.11.3.2.1.1 and A.11.3.2.1.2 shall apply.***h*/_{w}*ℓ*≥ 2_{w}(b) Strains calculated as the mean of the maximum demand from a suite of response history analyses

(c) Calculated concrete compressive strain < 0.005

(d) Calculated longitudinal tensile strain < 0.01

For all vertical wall segments sharing a common lateral force,

**shall not be taken greater than . For any individual vertical wall segments,***V*_{ne}**shall not be taken greater than .***V*_{ne}For structural wall panel zones,

**shall be calculated in accordance with A.11.3.2.1.1.***V*_{ne}**shall not be taken greater than .***V*_{ne}If the mean maximum deformation from the set of response history analyses exceeds

**0.5**of confined concrete, members shall be subject to the added detailing requirements of this section.*D*_{u}For beams of special moment frames, the spacing of transversely supported flexural reinforcing bars as required by 18.6.4.2 shall not exceed 8 in.

For tied columns of special moment frames, every longitudinal bar shall have lateral support by a corner of a hoop or a seismic hook as required in 18.7.5.2(f) regardless of axial load or concrete strength.

When deformations of beams of special moment frames exceed

**0.5**, the column dimension parallel to the beam longitudinal reinforcement required in 18.8.2.3 shall be increased by 20 percent.*D*_{u}Boundary elements shall be provided in accordance with 18.10.6 with transverse reinforcement conforming with A.12.2.3.

If boundary elements are required, splices of shear reinforcement shall be made with mechanical or welded splices, or lap splices enclosed in transverse reinforcement spaced at the smaller of

**6**of the spliced bars or 6 in.*d*_{b}If the floor or roof slab is shown by analysis to undergo inelastic response at a slab-wall connection, the slab flexural reinforcement shall be extended through the slab-wall joint and anchored for structural integrity.

The analysis and design shall be reviewed by an independent structural design reviewer. The independent structural design reviewer shall act under the direction of the building official.

The independent structural design review shall be performed by one or more individuals acceptable to the building official and possessing knowledge of (a) through (d):

(a) Selection and scaling of ground motions for use in nonlinear response history analysis.

(b) Behavior of structural systems of the type under consideration when subjected to earthquake loading.

(c) Analytical structural modeling for use in nonlinear response history analysis, including use of physical tests in the creation and calibration of the structural analysis models, and knowledge of soil-structure interaction if used in the analysis or in the development of ground motions.

(d) The requirements of Appendix A as they pertain to design of the type of structure under consideration.

The scope of the independent structural design review shall be approved by the building official and shall include a minimum of (a) through (h):

(a) Basis of design document, including the earthquake-performance objectives, the overall earthquake-resistant design methodology, and acceptance criteria

(b) Proposed structural system

(c) Earthquake hazard determination, and selection and modification of earthquake ground motions

(d) Modeling approaches for components

(e) Structural analysis model, including soil-structure interaction as applicable, and verification that the structural analysis model adequately represents the properties of the structural system

(f) Review of structural analysis results and determination of whether calculated response meets approved acceptance criteria

(g) Design and detailing of structural components

(h) Drawings, specifications, and quality control/quality assurance and inspection provisions in the design documents

The independent structural design review shall be documented as follows:

(a) The independent structural design reviewer shall issue comments and questions to the licensed design professional.

(b) The licensed design professional shall provide written responses to the independent structural design reviewer.

(c) The independent structural design reviewer shall summarize the review in a letter addressed to the building official that shall include a log of all questions or comments and responses. Any items that lack resolution or consensus shall be clearly explained with reasons for lack of agreement.