Report - PEER - University of California, Berkeley

EC8-Part 1. The verifications should provide a margin against memberultimate capacity.• “Damage Limitation” (DL), corresponding to “Immediate Occupancy” in theUS. Members should be verified to remain elastic.The “Seismic Hazard” levels for which the three Limit States are required will bedecided nationally as NDPs, or by the owner, if the National Annex does not choose.The Eurocode itself gives no recommendation, but mentions that the performanceobjective recommended as suitable to ordinary new buildings is a 225yr earthquake(20% in 50 years), a 475yr event (10% in 50 years), or a 2475yr one (2% in 50 years),for the DL, the SD or the NC “Limit State”, respectively. National Authorities willdecide too whether all three Limit States will need to be verified, or whether checkingone or two Limit States at the corresponding seismic hazard level will suffice. It ishoped that National Authorities will set the performance requirements for existingbuildings in their territory so that the chance that owners will retrofit their propertyincreases and the population of buildings to be retrofitted is acceptable for the societyand the national economy. The same spectral shape holds for all hazard levels.3.2 Compliance Criteria for Concrete BuildingsInformative Annex A in (CEN 2004b) specifies for members of concrete buildings theperformance requirements mentioned already with the definition of the three LimitStates, as shown in Table 1. Flexure is always considered as a ductile mechanism andchecked in terms of deformations - in this case in terms of chord-rotations at memberends. Shear is considered as a brittle mechanism and checked in terms of forces.The mean value of the chord rotation at yielding, θ y , or ultimate, θ u,m (total orplastic part) is given as (Biskinis and Fardis 2004, Fardis and Biskinis 2003):Ly b yfor beams, rectangular columns:s + aVz ⎛ h ⎞ 0.13φd fθ y = φ y + 0.0013 1 1.5 +3⎜ +L⎟(8)⎝ s ⎠ f cfor walls, rectangular, bar-belled:Ls+ aVz ⎛ Ls⎞ 0.13φydbf yθ y = φ y + 0.002⎜1− 0.125 ⎟ + (9)3 ⎝ h ⎠ fθ⎛ fyw⎞0.225 0.35 ⎜αρ⎟fdum = 0sx⎛ 3 ⎞ ν ⎡max(0.01;ω2) ⎤ ⎛ Ls⎞ ⎜ ⎟c 100ρ.016 1 (0.3 )c25⎝⎠⎜ − a w ⎟ ⎢f ⎥ ⎜ ⎟(1.25 ) (10)⎝ 8 ⎠ ⎣ max(0,01; ω1) ⎦ ⎝ h ⎠sxplν ⎡max(0.01;ω2) ⎤ 0.2⎛Ls⎞ ⎜ ⎟c 100 ρdθumθumθy0.0145( 1 0.4 )(0.25)c 25⎝f= − = − a⎠w ⎢⎥ f ⎜ ⎟(1.275 ) (11)⎣ max(0.01; ω1) ⎦ ⎝ h ⎠The new variables in Eqs.(8)–(11) are: a V =1 if the shear force at flexuralyielding, M y /L s , exceeds the shear at diagonal cracking, or 0 otherwise; z: internallever arm = 0.9d in beams or columns, 0.8l w in walls; d b : diameter of longitudinalbars; a w =1 for walls, 0 otherwise; ρ sx : confining reinforcement ratio in the direction ofbending; ρ d : diagonal reinforcement ratio. All other variables have been defined0.30.35⎛⎜αρfyw⎞⎟c9