Seismic Design Practice in Japan

The following symbols are used in this chapter. The section number in parentheses after definition of a symbol refers to the section where the symbol first appears or is defined. a space of tie reinforcement ( Section 44.4.4 ) A CF sectional area of carbon fiber ( Figure 44.19 ) A h area of tie reinforcements ( Section 44.4.4 ) A w sectional area of tie reinforcement ( Section 44.4.4 ) b width of section ( Section 44.4.4 ) c B coefficient to evaluate effective displacement ( Section 44.4.7 ) c B modification coefficient for clearance ( Section 44.4.11 ) C df modification coefficient ( Section 44.4.2 ) C c modification factor for cyclic loading ( Section 44.4.4 ) C D modification coefficient for damping ratio ( Section 44.4.6 ) c e modification factor for scale effect of effective width ( Section 44.4.4 ) C E modification coefficient for energy-dissipating capability ( Section 44.4.7 ) C p coefficient depending on the type of failure mode ( Section 44.4.2 ) C pt modification factor for longitudinal reinforcement ratio ( Section 44.4.4 ) C R factor depending on the bilinear factor r ( Section 44.4.2 ) c W corrective coefficient for ground motion characteristics ( Section 44.4.9 ) C Z modification coefficient for zone ( Section 44.4.3 ) d effective width of tie reinforcements ( Section 44.4.4 ) d height of section ( Section 44.4.4 ) D a width or a diameter of a pier ( Section 44.4.4 ) D E coefficient to reduce soil constants according to F L value ( Section 44.4.11 ) E c elastic modules of concrete ( Section 44.4.4 ) E CF elastic modulus of carbon fiber ( Figure 44.19 ) E des gradient at descending branch ( Section 44.4.4 ) F L liquefaction resistant ratio ( Section 44.4.9 ) F ( u ) restoring force of a device at a displacement u ( Section 44.4.7 ) h height of a pier ( Section 44.4.4 ) h B height of the center of gravity of girder from the top of bearing ( Figure 44.13 ) k B equivalent damping of a Menshin device ( Section 44.4.7 ) h i damping ratio of i th mode ( Section 44.4.6 ) h ij damping ratio of j th substructure in i th mode ( Section 44.4.6 ) h Bi damping ratio of i th damper ( Section 44.4.7 ) h Pi damping ratio of i th pier or abutment ( Section 44.4.7 ) h Fui damping ratio of i th foundation associated with translational displacement ( Section 44.4.7 ) h F θ i damping ratio of i th foundation associated with rotational displacement( Section 44.4.7 ) H distance from a bottom of pier to a gravity center of a deck ( Section 44.4.7 ) H 0 shear force at the bottom of footing ( Figure 44.12 ) I importance factor ( Section 44.5.2 ) k hc lateral force coefficient ( Section 44.4.2 ) k hc design seismic coefficient for the evaluation of liquefaction potential ( Section 44.4.9 ) K hc 0 standard modification coefficient ( Section 44.4.3 ) k hcm lateral force coefficient in Menshin design ( Section 44.4.7 ) k he equivalent lateral force coefficient ( Section 44.4.2 ) k hem equivalent lateral force coefficient in Menshin design ( Section 44.4.7 ) k hp lateral force coefficient for a foundation ( Section 44.4.2 ) k j stiffness matrix of jth substructure ( Section 44.4.6 ) K stiffness matrix of a bridge ( Section 44.4.6 ) K B equivalent stiffness of a Menshin device ( Section 44.4.7 ) K Pi equivalent stiffness of i th pier or abutment ( Section 44.4.7 ) K Fui translational stiffness of i th foundation ( Section 44.4.7 ) K F θ i rotational stiffness of i th foundation ( Section 44.4.7 ) L shear stress ratio during an earthquake ( Section 44.4.9 ) L A redundancy of a clearance ( Section 44.4.11 ) L E clearance at an expansion joint ( Section 44.4.11 ) L P plastic hinge length of a pier ( Section 44.4.4 ) M 0 moment at the bottom of footing ( Figure 44.12 ) P a lateral capacity of a pier ( Section 44.4.2 ) P s shear capacity in consideration of the effect of cyclic loading ( Section 44.4.4 ) P s 0 shear capacity without consideration of the effect of cyclic loading ( Section 44.4.4 ) P u bending capacity ( Section 44.4.2 ) r bilinear factor defined as a ratio between the first stiffness (yield stiffness) and the second stiffness (postyield stiffness) of a pier ( Section 44.4.2 ) r d modification factor of shear stress ratio with depth ( Section 44.4.9 ) R dynamic shear strength ratio ( Section 44.4.9 ) R priority ( Section 44.5.2 ) R d dead load of superstructure ( Section 44.4.11 ) R heq and R veq vertical reactions caused by the horizontal seismic force and vertical force ( Section 44.4.11 ) R L cyclic triaxial strength ratio ( Section 44.4.9 ) R U design uplift force applied to the bearing support ( Section 44.4.11 ) s space of tie reinforcements ( Section 44.4.4 ) S earthquake force ( Section 44.5.2 ) S c shear capacity shared by concrete ( Section 44.4.4 ) S I and S II acceleration response spectrum for Type-I and Type-II ground motions ( Section 44.4.6 ) S I 0 and S II 0 standard acceleration response spectrum for Type-I and Type-II ground motions ( Section 44.4.6 ) S E seat length ( Section 44.4.11 ) S EM minimum seat length (cm) ( Section 44.4.11 ) S s shear capacity shared by tie reinforcements ( Section 44.4.4 ) T natural period of fundamental mode ( Table 44.3 ) Δ T difference of natural periods ( Section 44.4.11 ) T 1 and T 2 natural periods of the two adjacent bridge systems ( Section 44.4.11 ) u B design displacement of isolators ( Section 44.4.7 ) U Be effective design displacement ( Section 44.4.7 ) U Bi design displacement of i th Menshin device ( Section 44.4.7 ) u G relative displacement of ground along the bridge axis ( Section 44.4.11 ) U R relative displacement (cm) developed between a superstructure and a substructure ( Section 44.4.11 ) V 0 vertical force at the bottom of footing ( Figure 44.12 ) v T structural factor ( Section 44.5.2 ) v RP 1 design specification ( Section 44.5.2 ) V RP 2 pier structural factor ( Section 44.5.2 ) V RP 3 aspect ratio ( Section 44.5.2 ) V MP steel pier factor ( Section 44.5.2 ) V FS unseating device factor ( Section 44.5.2 ) V F foundation factor ( Section 44.5.2 ) W v weighting factor on structural members ( Section 44.5.2 ) W equivalent weight ( Section 44.4.2 ) W elastic strain energy ( Section 44.4.7 ) W P weight of a pier ( Section 44.4.2 ) W U weight of a part of superstructure supported by the pier ( Section 44.4.2 ) Δ W energy dissipated per cycle ( Section 44.4.7 ) α safety factor ( Section 44.4.4 ) α, β coefficients depending on shape of pier ( Section 44.4.4 ) α m safety factor used in Menshin design ( Section 44.4.7 ) δ y yield displacement of a pier ( Section 44.4.2 ) δ R residual displacement of a pier after an earthquake ( Section 44.4.2 ) δ Ra allowable residual displacement of a pier ( Section 44.4.2 ) δ u ultimate displacement of a pier ( Section 44.4.4 ) ε c strain of concrete ( Section 44.4.4 ) ε cc strain at maximum strength ( Section 44.4.4 ) ε G ground strain induced during an earthquake along the bridge axis ( Section 44.4.11 ) ε s strain of reinforcements ( Section 44.4.4 ) ε sy yield strain of reinforcements ( Section 44.4.4 ) θ angle between vertical axis and tie reinforcement ( Section 44.4.4 ) θ Pu ultimate plastic angle ( Section 44.4.4 ) μ a allowable displacement ductility factor of a pier ( Section 44.4.2 ) μ m allowable ductility factor of a pier in Menshin design ( Section 44.4.7 ) μ R response ductility factor of a pier ( Section 44.4.2 ) ρ s tie reinforcement ratio ( Section 44.4.4 ) σ c stress of concrete ( Section 44.4.4 ) σ cc strength of confined concrete ( Section 44.4.4 ) σ CF stress of carbon fiber ( Figure 44.19 ) σ ck design strength of concrete ( Section 44.4.4 ) σ s stress of reinforcements ( Section 44.4.4 ) σ sy yield strength of reinforcements ( Section 44.4.4 ) σ v total loading pressure ( Section 44.4.9 ) https://www.w3.org/1998/Math/MathML" display="inline"> σ v ′ https://www.w3.org/1999/xlink" xlink:href=" https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429287244/bd1d3abd-8bd4-4d0a-8cef-0f1d46f01738/content/eq874.tif "/> effective loading pressure ( Section 44.4.9 ) τ c shear stress capacity shared by concrete ( Section 44.4.4 ) ϕ ij mode vector of jth substructure in i th mode ( Section 44.4.6 ) ϕ i mode vector of a bridge in i th mode ( Section 44.4.6 ) ϕ y yield curvature of a pier at bottom ( Section 44.4.4 ) ϕ u ultimate curvature of a pier at bottom ( Section 44.4.4 )