# Section 3104F Seismic Analysis and Structural Performance

The purpose of this section is to establish minimum standards for seismic analysis and structural performance. Seismic performance is evaluated at two criteria levels. Level 1 requirements define a performance criterion to ensure MOT functionality. Level 2 requirements safeguard against major structural damage or collapse.

Section 3104F applies to all new and existing MOTs structures. Structures supporting loading arms, pipelines, oil transfer and storage equipment, critical nonstructural systems and vessel mooring structures, such as mooring and breasting dolphins are included. Catwalks and similar components that are not part of the lateral load carrying system and do not support oil transfer equipment may be excluded.

Each MOT shall be designated as regular or irregular based on torsional irregularity criteria presented in ASCE/SEI 7 [4.1]. An MOT is defined to be irregular when maximum displacement at one end of the MOT transverse to an axis is more than 1.2 times the average of the displacement at the two ends of the MOT as described in Figure 31F-4-1. For MOTs with multiple segments separated by expansion joints, each segment shall be designated as regular or irregular using criteria in this section. Expansion joints in this context are defined as joints that separate each structural segment in such a manner that each segment will move independently during an earthquake.

If a MOT is divided into seismically isolated sections, an evaluation of the relative movement of pipelines and supports shall be considered, including phase differences (Section 3109F.3).

Two levels of design seismic performance shall be considered. 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 structural behavior with repairable damage

**• ** Prevention of structural collapse

**• ** Temporary loss of operations, restorable within months

**• ** Prevention of major spill (≥1200 bbls)

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.

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 push-over 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.

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.

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, Δ_{d}.

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.

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, Δ_{d}, shall be calculated by multiplying the spectral response acceleration, S_{A}, corresponding to the effective elastic structural period, T_{e} (see Equation (4-2) or Equation (4-8)), by . If T_{e} < T_{0}, where T_{0} 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 of ASCE/SEI 41 [4.3] that is based on the procedure presented in FEMA 440 [4.6], or the Substitute Structure Method presented in Priestley et al. [4.4]. Both of these methods utilize the pushover curve developed in Section 3104F.2.3.1.

The Coefficient Method is based on the ASCE/SEI 41 [4.3] procedure.

The first step in the Coefficient Method requires idealization of the pushover curve to calculate the effective elastic lateral stiffness, k_{e}, and effective yield strength, F_{y}, 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, k_{e}. The effective elastic lateral stiffness, k_{e}, shall be taken as the secant stiffness calculated at the lateral force equal to 60 percent of the effective yield strength, F_{y}, of the structure. The effective yield strength, F_{y}, 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 (α_{1}k_{e}) determined by a point (F_{d},Δ_{d}) and a point at the intersection with the first line segment such that the area above and below the actual curve area approximately balanced. (F_{d},Δ_{d}) 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 (α_{2}k_{e}), determined by the point at the end of the positive post-yield slope (F_{d}, Δ_{d}) and the point at which the lateral force degrades to 60 percent of the effective yield strength.

The target displacement shall be calculated from:

(4-1)

where:

S_{A} = spectral acceleration of the linear-elastic system at vibration period, which is computed from:

(4-2)

where:

m | = | seismic mass as defined in Section 3104F.2.3 |

k_{e} | = | effective elastic lateral stiffness from idealized pushover |

C_{1} | = | modification factor to relate maximum inelastic displacement to displacement calculated for linear elastic response. For period less than 0.2 s, C_{1} need not be taken greater than the value at T_{e} = 0.2 s. For period greater than 1.0 s, C_{1} = 1.0. For all other periods: |

(4-3)

where:

α | = | Site class factor |

= | 130 for Site Class A or B, | |

= | 90 for Site Class C, and | |

= | 60 for Site Class D, E, or F. | |

μ_{strength} | = | ratio of elastic strength demand to yield strength coefficient calculated in accordance with Equation (4-5). The Coefficient Method is not applicable where μ_{strength} exceeds μ_{max} computed from Equation (4-6). |

C_{2} | = | 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, C_{2} = 1.0. For all other periods: |

(4-4)

The strength ratio μ_{strength} shall be computed from:

(4-5)

where:

F_{y} = yield strength of the structure in the direction under consideration from the idealized pushover curve.

For structures with negative post-yield stiffness, the maximum strength ratio μ_{max} shall be computed from:

(4-6)

where:

Δ_{d} = larger of target displacement or displacement corresponding to the maximum pushover force,

Δ_{y} = displacement at effective yield strength

h = 1 + 0.15lnT_{e}, and

α_{e} = effective negative post-yield slope ratio which shall be computed from:

(4-7)

where:

α_{P-Δ}, and the maximum negative post-elastic stiffness ratio, α_{2}, 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, S_{1} greater than or equal to 0.6g and equal to 0.2 for sites with 1 second spectral value, S_{1} less than 0.6g.

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