## Info

In both ESA and ERSA analyses, ''effective'' stiffness of the components shall be used in order to obtain realistic evaluation for the structure's period and displacement demands. The effective stiffness of ductile components shall represent the component's actual secant stiffness near first yield of rebar. The effective stiffness shall include the effects of concrete cracking, reinforcement, and axial load for concrete components; residual stresses, out-of-straightness, and axial load for steel components; and the restraints of the surrounding soil for piles. For ductile concrete column members, effective moments of inertia, If, shall be based on cracked section properties and can be determined from the initial slope of the M-f curve between the origin and the point designating first yield of the main column reinforcement. The torsional moment of inertia of concrete column Jeff may be taken as 0.2 times Jgross. For capacity-protected concrete members, Ieff shall be based on their level of cracking. For a conventionally reinforced concrete box girder superstructure, Ieff can be estimated between 0.5 and 0.75 times Igross, the moment of inertia of a gross section. For prestressed concrete superstructures, Ieff is assumed 1.0 times Igross.

The following are major considerations in seismic analysis and design practice:

• A beam-element model with three or more lumped masses for each member is usually used [25,26].

• Larger cap stiffness is often used to simulate a stiff deck.

• Compression and tension models are used to simulate the behavior of expansion joints. In the tension model, superstructure joints including abutments are released longitudinally but the restrainers are modeled as truss elements. In the compression model, all restrainers are considered to be inactive and all joints are locked longitudinally.

• Simplistic analysis models should be used for initial assessment of structural behavior. The results of more sophisticated models shall be compared for reasonableness with the results obtained from the simplistic models. The rotational and translational stiffness of abutments and foundations modeled in the seismic analysis must be compatible with their structural and geotechnical capacity. The energy dissipation capacity of the abutments should be considered for bridges whose response is dominated by the abutments [50].

• For elastic response spectrum analysis, the viscous damping ratio inherent in the specified ground spectra is usually 5%.

• For time history analysis, in lieu of measurements, a damping ratio of 5% for both concrete and timber constructions and 2% for welded and bolted steel construction may be used.

• For one- or two-span continuous bridges with abutment designed to activate significant passive pressure in the longitudinal direction, a damping ratio of up to 10% may be used in longitudinal analysis.

• Soil-spring elements should be used to the soil-foundation-structure interaction. Adjustments are often made to meet force-displacement compatibility, particularly for abutments. The maximum capacity of the soil behind abutments with heights larger than 2.5 m may be taken as 370 kPa and will be linearly reduced for the backwall height less than 2.5 m.

• Pile footing with pile cap and spread footing with soil types A and B [37] may be modeled as rigid. If footing flexibility contributes more than 20% to pier displacement, foundation springs shall be considered.

• For pile bent/drilled shaft, estimated depth to fixity or soil-spring based on idealized p-y curves should be used.

• Force-deformation behavior of a seismic isolator can be idealized as a bilinear relationship with two key variables: second slope stiffness and characteristic strength. For design, the forcedeformation relationship can be represented by an effective stiffness based on the secant stiffness and a damping coefficient. For more detailed information, references can be made ATC/MCEER Guidelines and AASHTO Guide Specifications [37,51] and a comprehensive chapter by Zhang [52].

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