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# 3104F.2.3.2.2 Substitute Structure Method

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The Substitute Structure Method is based on the procedure presented in Priestley et al. [4.4] and is briefly summarized below.

- Idealize the pushover curve from nonlinear pushover analysis, as described in Section 3104F.2.3.2.1, and estimate the yield force, F
_{y}, and yield displacement, Δ_{y}. - Compute the effective elastic lateral stiffness, k
_{e}, as the yield force, F_{y}, divided by the yield displacement, Δ_{y}. - Compute the structural period in the direction under consideration from:(4-8)where:m =seismic mass as defined in Section 3104F.2.3k
_{e}=effective elastic lateral stiffness in direction under consideration - Determine target displacement Δ
_{d}, from:(4-9)S_{A}= spectral displacement corresponding tostructural period, T_{e} *The ductility level,*µ_{Δ}, is found from Δ_{d}/Δ_{y}. Use the appropriate relationship between ductility and damping, for the component undergoing inelastic deformation, to estimate the effective structural damping, ξ_{eff}. In lieu of more detailed analysis, the relationship shown in Figure 31F-4-5 or Equation (4-10) may be used for concrete and steel piles connected to the deck through dowels embedded in the concrete.(4-10)where:Equation (4-10) for effective damping was developed by Kowalsky et al. [4.5] for the Takeda hysteresis model of system's force-displacement relationship.- From the acceleration response spectra, create elastic displacement spectra, S
_{D}, using Equation (4-11) for various levels of damping.(4-11) - Using the curve applicable to the effective structural damping, ξ
_{eff}, find the effective period, T_{d}(see Figure 31F-4-6). - In order to convert from a design displacement response spectra to another spectra for a different damping level, the adjustment factors in Section 3103F.4.2.9 shall be used.
- The effective secant stiffness, k
_{eff}, can then be found from:(4-12)where:m = seismic mass as defined in Section 3104F.2.3T_{d}= effective structural period - The required strength, F
_{u}, can now be estimated by:(4-13) - F
_{u }*and*Δ_{d }can be plotted on the force-displacement curve established by the pushover analysis. Since this is an iterative process, the intersection of F_{u}and Δ_{d}most likely will not fall on the force-displacement curve and a second iteration will be required. An adjusted value of Δ_{d}, taken as the intersection between the force-displacement curve and a line between the origin and F_{u}and Δ_{d}, can be used to find µ_{Δ}. - Repeat the process until a satisfactory solution is obtained (see Figure 31F-4-7).
- From pushover data, calculate the displacement components of an element along the two axis of the system.

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3104F.2.3.2.2 [SLC] Marine Oil Terminals, Substitute Structure Method

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*Substitute**Structure**Method*is based on the procedure presented in Priestley et al. [4.4] and is briefly summarized below. Idealize ...
California Building Code 2016 (Vol 1 & 2) > 31F [SLC] Marine Oil Terminals > 3104F Seismic Analysis and Structural Performance > 3104F.2 Existing MOTs > 3104F.2.3 Analytical Procedures > 3104F.2.3.2 Nonlinear Static Demand Procedure > 3104F.2.3.2.2 Substitute Structure Method

3104F.2.3.2.2 [SLC] Marine Oil Terminals, Substitute Structure Method

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*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 ...
California Building Code 2022 (Vol 1 & 2) > 31F [SLC] Marine Oil Terminals > 3104F Seismic Analysisand Structural Performance > 3104F.2 Existing MOTs > 3104F.2.3 Analytical Procedures > 3104F.2.3.2 Nonlinear Static Demand Procedure > 3104F.2.3.2.2 Substitute Structure Method

3104F.2.3.2.2 [SLC] Marine Oil Terminals,

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*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 ...
California Building Code 2019 (Vol 1 & 2) > 31F [SLC] Marine Oil Terminals > 3104F

*Seismic Analysis and Structural Performance*> 3104F.2*Existing MOTs*> 3104F.2.3*Analytical Procedures*> 3104F.2.3.2*Nonlinear Static Demand Procedure*> 3104F.2.3.2.2*Substitute Structure Method*
3104F.2.3.2 [SLC] Marine Oil Terminals,

*Nonlinear Static Demand Procedure*
, 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 ...
California Building Code 2019 (Vol 1 & 2) > 31F [SLC] Marine Oil Terminals > 3104F

*Seismic Analysis and Structural Performance*> 3104F.2*Existing MOTs*> 3104F.2.3*Analytical Procedures*> 3104F.2.3.2*Nonlinear Static Demand Procedure*
3104F.2.3 [SLC] Marine Oil Terminals,

*Analytical Procedures*
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 ...
California Building Code 2019 (Vol 1 & 2) > 31F [SLC] Marine Oil Terminals > 3104F

*Seismic Analysis and Structural Performance*> 3104F.2*Existing MOTs*> 3104F.2.3*Analytical Procedures*