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3104F.2 Existing MOTs
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3104F.2.1 Seismic Performance Criteria
Two levels of seismic performance shall be considered, except for critical systems (Section 3104F.5.1). These levels are defined as follows:
Level 1 Seismic Performance:
• Minor or no structural damage
• Temporary or no interruption in operations
Level 2 Seismic Performance:
• Controlled inelastic behavior with repairable damage
• Prevention of collapse
• Temporary loss of operations, restorable within months
• Prevention of major spill (≥ 1200 bbls)
The Level 1 and Level 2 seismic performance criteria are defined in Table 31F-4-1.
3104F.2.2 Basis for Evaluation
Component capacities shall be based on existing conditions, calculated as "best estimates," taking into account the mean material strengths, strain hardening and degradation overtime. The capacity of components with little or no ductility, which may lead to brittle failure scenarios, shall be calculated based on lower bound material strengths. Methods to establish component strength and deformation capacities for typical structural materials and components are provided in Section 3107F. Geotechnical considerations are discussed in Section 3106F.
3104F.2.3 Analytical Procedures
The objective of the seismic analysis is to verify that the displacement capacity of the structure is greater than the displacement demand, for each performance level defined in Table 31F-4-1. For this purpose, the displacement capacity of each element of the structure shall be checked against its displacement demand including the orthogonal effects of Section 3104F.4.2. The required analytical procedures are summarized in Table 31F-4-2.
The displacement capacity of the structure shall be calculated using the nonlinear static (pushover) procedure. For the nonlinear static (pushover) procedure, the pushover load shall be applied at the target node defined as the center of mass (CM) of the MOT structure. It is also acceptable to use a nonlinear dynamic procedure for capacity evaluation, subject to peer review in accordance with Section 3101F.8.2.
Methods used to calculate the displacement demand are linear modal, nonlinear static and nonlinear dynamic.
Mass to be included in the displacement demand calculation shall include mass from self-weight of the structure, weight of the permanent equipment, and portion of the live load that may contribute to inertial mass during earthquake loading, such as a minimum of 25% of the floor live load in areas used for storage.
Any rational method, subject to the Division's approval, can be used in lieu of the required analytical procedures shown in Table 31F-4-2.
3104F.2.3.1 Nonlinear Static Capacity Procedure (Pushover)
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 pushover 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.
3104F.2.3.1.1 Modeling
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.
3104F.2.3.1.2 Timber Pile Supported Structures
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.
3104F.2.3.2 Nonlinear Static Demand Procedure
A nonlinear static procedure shall be used to determine the displacement demand for all concrete and steel structures, with the exception of irregular configurations with high or moderate spill classifications. A linear modal procedure is required for irregular structures with high or moderate spill classifications, and may be used for all other classifications in lieu of the nonlinear static procedure.
In the nonlinear static demand procedure, deformation demand in each element shall be computed at the target node displacement demand. The analysis shall be conducted in each of the two orthogonal directions and results combined as described in Section 3104F.4.2.
The target displacement demand of the structure, Δd, shall be calculated from:
(4-1)
Te = effective elastic structural period defined in Equation (4-3) or Equation (4-9)
SA = spectral response acceleration corresponding to Te
If Te < T0, where T0 is the period corresponding to the peak of the acceleration response spectrum, a refined analysis (see Section 3104F.2.3.2.1 or 3104F.2.3.2.2) shall be used to calculate the displacement demand. In the refined analysis, the target node displacement demand may be computed from the Coefficient Method (Section 3104F.2.3.2.1) or the Substitute Structure Method (Section 3104F.2.3.2.2). Both of these methods utilize the pushover curve developed in Section 3104F.2.3.1.
3104F.2.3.2.1 Coefficient Method
The Coefficient Method is based on the procedures presented in ASCE/SEI 41 [4.3] and FEMA 440 [4.4].
The first step in the Coefficient Method requires idealization of the pushover curve to calculate the effective elastic lateral stiffness, ke, and effective yield strength, Fy, of the structure as shown in Figure 31F-4-4.
The first line segment of the idealized pushover curve shall begin at the origin and have a slope equal to the effective elastic lateral stiffness, ke. The effective elastic lateral stiffness, ke, shall be taken as the secant stiffness calculated at the lateral force equal to 60 percent of the effective yield strength, Fy, of the structure. The effective yield strength, Fy, shall not be taken as greater than the maximum lateral force at any point along the pushover curve.
The second line segment shall represent the positive post-yield slope (α1ke) determined by a point (Fd,Δd) and a point at the intersection with the first line segment such that the area above and below the actual curve area approximately balanced. (Fd,Δd) shall be a point on the actual pushover curve at the calculated target displacement, or at the displacement corresponding to the maximum lateral force, whichever is smaller.
The third line segment shall represent the negative post-yield slope (α2ke), determined by the point at the end of the positive post-yield slope (Fd,Δd) and the point at which the lateral force degrades to 60 percent of the effective yield strength.
The target displacement shall be calculated from:
(4-2)
SA = spectral acceleration of the linear-elastic system at vibration period, which is computed from:
(4-3)
m = seismic mass as defined in Section 3104F.2.3
ke = effective elastic lateral stiffness from idealized pushover
C1 = modification factor to relate maximum inelastic displacement to displacement calculated for linear elastic response. For period less than 0.2 s, C1 need not be taken greater than the value at Te = 0.2 s. For period greater than 1.0 s, C1 = 1.0. For all other periods:
(4-4)
a = Site class factor
= 130 for Site Class A or B,
= 90 for Site Class C, and
= 60 for Site Class D, E or F.
µstrength = ratio of elastic strength demand to yield strength coefficient calculated in accordance with Equation (4-6). The Coefficient Method is not applicable where µstrength exceeds µmax computed from Equation (4-7). µstrength shall not be taken as less than 1.0.
C2 = modification factor to represent the effects of pinched hysteresis shape, cyclic stiffness degradation and strength deterioration on the maximum displacement response. For periods greater than 0.7s, C2 = 1.0. For all other periods:
(4-5)
(4-6)
(4-7)
Δd = larger of target displacement or displacement corresponding to the maximum pushover force,
Δy = displacement at effective yield strength
(4-8)
αe = effective negative post-yield slope ratio which shall be computed from:
(4-9)
αP-Δ, and the maximum negative post-elastic stiffness ratio, α2, are estimated from the idealized force-deformation curve, and λ is a near-field effect factor equal to 0.8 for sites with 1 second spectral value, S1 greater than or equal to 0.6g and equal to 0.2 for sites with 1 second spectral value, S1 less than 0.6g.
3104F.2.3.2.2 Substitute Structure Method
The Substitute Structure Method is based on the procedure presented in Priestley et al. [4.5] and ASCE/COPRI 61 [4.2]. This method is summarized below.
- Idealize the pushover curve from nonlinear pushover analysis, as described in Section 3104F.2.3.2.1, and estimate the effective yield strength, Fy, and yield displacement, Δy.
- Compute the effective elastic lateral stiffness, ke, as the effective yield strength, Fy, divided by the yield displacement, Δy.
- Compute the structural period in the direction under consideration from:
(4-10)m = seismic mass as defined in Section 3104F.2.3ke = effective elastic lateral stiffness in direction under consideration - Determine target displacement, Δd , of the effective linear elastic system from:
(4-11)SA = the 5 percent damped spectral displacement corresponding to the linear elastic structural period, TeSelect the initial estimate of the displacement demand as Δd, i = Δd. - The ductility level, µΔ,i , is found from Δd,i /Δy. Use the appropriate relationship between ductility and damping, for the component undergoing inelastic deformation, to estimate the effective structural damping, ξeff,i. In lieu of more detailed analysis, Equation (4-12) may be used for concrete and steel piles connected to the deck through dowels embedded in the concrete. Note that the idealized pushover curves in Figure 31F-4-4 shall be utilized in Figure 31F-4-5, which illustrates the iterative procedure.Equation (4-12) for effective damping was developed by Kowalsky et al. [4.6] for the Takeda hysteresis model of system's force-displacement relationship.
- Compute the force, Fd,i, on the force-deformation relationship associated with the estimated displacement, Δd,i (see Figure 31F-4-5).
- Compute the effective stiffness, keff,i, as the secant stiffness from:
(4-13) - Compute the effective period, Teff,i, from:
(4-14)m = seismic mass as defined in Section 3104F.2.3 - For the effective structural period, Teff,i, and the effective structural damping, ξeff,i, compute the spectral acceleration SA(Teff,i, ξeff,i) from an appropriately damped design acceleration response spectrum.
- Compute the new estimate of the displacement, Δd, j, from:
(4-15) - Repeat steps 5 to 10 with Δd, i = Δd, j until displacement, Δd, j, computed in step 10 is sufficiently close to the starting displacement, Δd, i, in step 5 (Figure 31F-4-5).
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