To assess displacement capacity, two-dimensional nonlinear static (pushover) analyses shall be performed; three-dimensional analyses are optional. A model that incorporates the nonlinear load deformation characteristics of all components for the lateral force-resisting system shall be used in the pushover analysis.
Alternatively, displacement capacity of a pile in the MOT structure may be estimated from pushover analysis of an individual pile with appropriate axial load and pile-to-deck connection.
The displacement capacity of a pile from the push-over analysis shall be defined as the displacement that can occur at the top of the pile without exceeding plastic rotation (or material strain) limits, either at the pile-deck hinge or in-ground hinge, as defined in Section 3107F. If pile displacement has components along two axes, as may be the case for irregular MOTs, the pile displacement capacity shall be defined as the resultant of its displacement components along the two axes.
SEISMIC PERFORMANCE CRITERIA1, 2
|SPILL CLASSIFICATION3||SEISMIC PERFORMANCE LEVEL||PROBABILITY OF EXCEEDANCE||RETURN PERIOD|
|High||Level 1||50% in 50 years||72 years|
|Level 2||10% in 50 years||475 years|
|Medium||Level 1||65% in 50 years||48 years|
|Level 2||15% in 50 years||308 years|
|Low||Level 1||75% in 50 years||36 years|
|Level 2||20% in 50 years||224 years|
MINIMUM REQUIRED ANALYTICAL PROCEDURES
|SPILL CLASSIFICATION1||CONFIGURATION||SUBSTRUCTURE MATERIAL||DISPLACEMENT DEMAND PROCEDURE||DISPLACEMENT CAPACITY PROCEDURE|
|High/Medium||Irregular||Concrete/Steel||Linear Modal||Nonlinear Static|
|High/Medium||Regular||Concrete/Steel||Nonlinear Static2||Nonlinear Static|
|Low||Regular/Irregular||Concrete/Steel||Nonlinear Static||Nonlinear Static|
|High/Medium/Low||Regular/Irregular||Timber||Nonlinear Static||Nonlinear Static|
- See Section 3101F.6 for spill classification.
- Linear modal demand procedure may be required for cases where more than one mode is expected to contribute to the displacement demand.
A series of nonlinear pushover analyses may be required depending on the complexity of the MOT structure. At a minimum, pushover analysis of a two-dimensional model shall be conducted in both the longitudinal and transverse directions. The piles shall be represented by nonlinear elements that capture the moment-curvature/rotation relationships for components with expected inelastic behavior in accordance with Section 3107F. The effects of connection flexibility shall be considered in pile-to-deck connection modeling. For prestressed concrete piles, Figure 31F-4-2 may be used. A nonlinear element is not required to represent each pile location. Piles with similar lateral force-deflection behavior may be lumped in fewer larger springs, provided that the overall torsional effects are captured.
Linear material component behavior is acceptable where nonlinear response will not occur. All components shall be based on effective moment of inertia calculated in accordance with Section 3107F. Specific requirements for timber pile structures are discussed in the next section.
For all timber pile supported structures, linear elastic procedures may be used. Alternatively, the nonlinear static procedure may be used to estimate the target displacement demand, Δd.
A simplified single pile model for a typical timber pile supported structure is shown in Figure 31F-4-3. The pile-deck connections may be assumed to be "pinned." The lateral bracing can often be ignored if it is in poor condition. These assumptions shall be used for the analysis, unless a detailed condition assessment and lateral analysis indicate that the existing bracing and connections may provide reliable lateral resistance.
A series of single pile analyses may be sufficient to establish the nonlinear springs required for the pushover analysis.