# Chapter 16 Seismic Response History Procedures

### 16.1 Linear Response History Procedure

Where linear response history procedure is performed the requirements of this chapter shall be satisfied.

### 16.1.1 Analysis Requirements

A linear response history analysis shall consist of an analysis of a linear mathematical model of the structure to determine its response, through methods of numerical integration, to suites of ground motion acceleration histories compatible with the design response spectrum for the site. The analysis shall be performed in accordance with the requirements of this section.

### 16.1.2 Modeling

Mathematical models shall conform to the requirements of Section 12.7.

### 16.1.3 Ground Motion

A suite of not less than three appropriate ground motions shall be used in the analysis. Ground motion shall conform to the requirements of this section.

### 16.1.3.1 Two-Dimensional Analysis

Where two-dimensional analyses are performed, each ground motion shall consist of a horizontal acceleration history, selected from an actual recorded event. Appropriate acceleration histories shall be obtained from records of events having magnitudes, fault distance, and source mechanisms that are consistent with those that control the maximum considered earthquake. Where the required number of appropriate recorded ground motion records are not available, appropriate simulated ground motion records shall be used to make up the total number required. The ground motions shall be scaled such that the average value of the 5% damped response spectra for the suite of motions is not less than the design response spectrum for the site for periods ranging from 0.2T to 1.5T where T is the natural period of the structure in the fundamental mode for the direction of response being analyzed.

### 16.1.3.2 Three-Dimensional Analysis

Where three-dimensional analyses are performed, ground motions shall consist of pairs of appropriate horizontal ground motion acceleration components that shall be selected and scaled from individual recorded events. Appropriate ground motions shall be selected from events having magnitudes, fault distance, and source mechanisms that are consistent with those that control the maximum considered earthquake. Where the required number of recorded ground motion pairs is not available, appropriate simulated ground motion pairs are permitted to be used to make up the total number required. For each pair of horizontal ground motion components, a square root of the sum of the squares (SRSS) spectrum shall be constructed by taking the SRSS of the 5% damped response spectra for the scaled components (where an identical scale factor is applied to both components of a pair). Each pair of motions shall be scaled such that in the period range from 0.2T to 1.5T, the average of the SRSS spectra from all horizontal component pairs does not fall below the corresponding ordinate of the response spectrum used in the design, determined in accordance with Section 11.4.5 or 11.4.7.
At sites within 3 miles (5 km) of the active fault that controls the hazard, each pair of components shall be rotated to the faultnormal and fault-parallel directions of the causative fault and shall be scaled so that the average of the fault-normal components is not less than the MCER response spectrum for the period range from 0.2T to 1.5T.

### 16.1.4 Response Parameters

For each ground motion analyzed, the individual response parameters shall be multiplied by the following scalar quantities:
1. Force response parameters shall be multiplied by Ie/R, where Ie is the importance factor determined in accordance with Section 11.5.1 and R is the response modification coefficient selected in accordance with Section 12.2.1.
2. Drift quantities shall be multiplied by Cd/R, where Cd is the deflection amplification factor specified in Table 12.2-1.
For each ground motion i, where i is the designation assigned to each ground motion, the maximum value of the base shear, Vi, member forces, QEi, and story drifts, △i, at each story scaled as indicated in the preceding text shall be determined. Story drifts at each story shall be determined at the locations defined in Section 12.8.6.
If at least seven ground motions are analyzed, the design member forces used in the load combinations of Section 12.4.2.3 and the design story drift used in the evaluation of drift in accordance with Section 12.12.1 are permitted to be taken respectively as the average of the scaled QEi and △i values determined from the analyses and scaled as indicated in the preceding text. If fewer than seven ground motions are analyzed, the design member forces and the design story drift shall be taken as the maximum value of the scaled QEi and △i values determined from the analyses.
Where this standard requires consideration of the seismic load effects including overstrength factor of Section 12.4.3, the value of Ω0QE need not be taken larger than the maximum of the unscaled value, QEi, obtained from the analyses.

### 16.1.4.1 Additional Scaling of Forces

Where the maximum scaled base shear predicted by the analysis, Vi, is less than 85% of the calculated base shear, V, using the equivalent lateral force procedure, the scaled member forces, QEi, shall be additionally multiplied by 0.85V/Vi.
Where V = the equivalent lateral force procedure base shear, calculated in accordance with Section 12.8.

### 16.1.4.2 Additional Scaling of Drifts

Where the maximum scaled base shear predicted by the analysis, Vi, is less than 0.85CsW, and where Cs is determined in accordance with Section 12.8.1.1, the scaled story drifts, △i, shall be additionally multiplied by 0.85CsW/Vi.

### 16.1.5 Horizontal Shear Distribution

The distribution of horizontal shear shall be in accordance with Section 12.8.4 except that amplification of torsion in accordance with Section 12.8.4.3 is not required where accidental torsion effects are included in the dynamic analysis model.

### 16.2 Nonlinear Response History Procedure

Where nonlinear response history procedure is performed the requirements of Section 16.2 shall be satisfied.

### 16.2.1 Analysis Requirements

A nonlinear response history analysis shall consist of an analysis of a mathematical model of the structure that directly accounts for the nonlinear hysteretic behavior of the structure's elements to determine its response through methods of numerical integration to suites of ground motion acceleration histories compatible with the design response spectrum for the site. The analysis shall be performed in accordance with this section. See Section 12.1.1 for limitations on the use of this procedure.

### 16.2.2 Modeling

A mathematical model of the structure shall be constructed that represents the spatial distribution of mass throughout the structure. The hysteretic behavior of elements shall be modeled consistent with suitable laboratory test data and shall account for all significant yielding, strength degradation, stiffness degradation, and hysteretic pinching indicated by such test data. Strength of elements shall be based on expected values considering material overstrength, strain hardening, and hysteretic strength degradation. Linear properties, consistent with the requirements of Section 12.7.3, are permitted to be used for those elements demonstrated by the analysis to remain within their linear range of response. The structure shall be assumed to have a fixed base, or alternatively, it is permitted to use realistic assumptions with regard to the stiffness and load-carrying characteristics of the foundations consistent with site-specific soils data and rational principles of engineering mechanics.
For regular structures with independent orthogonal seismic force-resisting systems, independent 2-D models are permitted to be constructed to represent each system. For structures having a horizontal structural irregularity of Type 1a, 1b, 4, or 5 in Table 12.3-1 or structures without independent orthogonal systems, a 3-D model incorporating a minimum of three dynamic degrees of freedom consisting of translation in two orthogonal plan directions and torsional rotation about the · vertical axis at each level of the structure shall be used. Where the diaphragms are not rigid compared with the vertical elements of the seismic force-resisting system, the model should include representation of the diaphragm's flexibility and such additional dynamic degrees of freedom as are required to account for the participation of the diaphragm in the structure's dynamic response.

Ground motion shall conform to the requirements of Section 16.1.3. The structure shall be analyzed for the effects of these ground motions simultaneously with the effects of dead load in combination with not less than 25% of the required live loads.

### 16.2.4 Response Parameters

For each ground motion analyzed, individual response parameters consisting of the maximum value of the individual member forces, QEi, member inelastic deformations,Ψi, and story drifts, △i, at each story shall be determined, where i is the designation assigned to each ground motion.
If at least seven ground motions are analyzed, the design values of member forces, QE, member inelastic deformations, Ψ, and story drift, △, are permitted to be taken as the average of the QEi, Ψi, and △i values determined from the analyses. If fewer than seven ground motions are analyzed, the design member forces, QE, design member inelastic deformations, Ψ, and the design story drift, △, shall be taken as the maximum value of the QEi, Ψi, and △i values determined from the analyses.

### 16.2.4.1 Member Strength

The adequacy of members to resist the combination of load effects of Section 12.4 need not be evaluated.
EXCEPTION: Where this standard requires consideration of the seismic load effects including overstrength factor of Section 12.4.3, the maximum value of QEi obtained from the suite of analyses shall be taken in place of the quantity Ω0QE .

### 16.2.4.2 Member Deformation

The adequacy of individual members and their connections to withstand the estimated design deformation values, Ψi, as predicted by the analyses shall be evaluated based on laboratory test data for similar elements. The effects of gravity and other loads on member deformation capacity shall be considered in these evaluations. Member deformation shall not exceed two-thirds of a value that results in loss of ability to carry gravity loads or that results in deterioration of member strength to less than 67% of the peak value.

### 16.2.4.3 Story Drift

The design story drift, △i, obtained from the analyses shall not exceed 125% of the drift limit specified in Section 12.12.1.

### 16.2.5 Design Review

A design review of the seismic force-resisting system and the structural analysis shall be performed by an independent team of registered design professionals in the appropriate disciplines and others experienced in seismic analysis methods and the theory and application of nonlinear seismic analysis and structural behavior under extreme cyclic loads. The design review shall include, but need not be limited to, the following:
1. Review of any site-specific seismic criteria employed in the analysis, including the development of site-specific spectra and ground motion time histories;
2. Review of acceptance criteria used to demonstrate the adequacy of structural elements and systems to withstand the calculated force and deformation demands, together with laboratory and other data used to substantiate these criteria;
3. Review of the preliminary design, including the selection of structural system and the configuration of structural elements; and
4. Review of the final design of the entire structural system and all supporting analyses.
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