Report - PEER - University of California, Berkeley

6. DAMAGE AND LIMIT DEFORMATIONSThe structural limit deformation is defined for each limit state in each horizontaldirection as the corresponding equivalent SDF lateral deformation, when any of theinter-story deformations first attained to its story limit deformation. The story limitdeformations shall be evaluated based on the damage level of the members, whichshall be classified into the following four levels with the corresponding limit states:(1) Level I: serviceability limit, (2) Level II: reparability limit I, (3) Level III:reparability limit II, and (4) Level IV: safety limit. These limit states shall beevaluated based on the residual damage states as:(1) Serviceability limit state: the residual crack width shall be less than 0.2mmand the reinforcing bar shall remain elastic at maximum.(2) Reparability limit state I: the residual crack width shall be less than 0.5mm to1.0mm and the reinforcing bar shall remain within small inelastic strain at maximum.Slight damage to concrete may occur.(3) Reparability limit state II: the residual crack width shall be less than 1.0mm to2.0mm and the reinforcing bar may be with large inelastic strain but without buckling.Falling-off of cover concrete may occur but no damage to core concrete.(4) Safety limit state: deformability limit without significant decay of seismicresistance (not less than 80% of maximum strength), which may be caused bycrushing of concrete, buckling or rupture of reinforcing bars, shear failure or bondfailure.The above limit states are expressed on the skeleton of typical hysteretic relationsof ductile member, such as flexural yielding beam, as shown in Figure 3. Practicalmethods of evaluating the limit deformations in terms of member end rotation anglesare shown in the level 2 documents of the Guidelines, separately for each member,such as beam, column, wall, beam-column joint, and non-structural element. As forevaluation of the serviceability and the safety limit states, past AIJ guidelines mayalso be available, while the method of evaluating reparability, especially maximumand residual crack widths, are based on the following concept and models, which arenewly introduced into the Guidelines.Ductile inelastic deformations of reinforced concrete members are caused mostlyby the tensile deformation, or widening of cracks. It has been pointed out from manypast experimental research that total sum of crack widths along the member couldeasily be related to the overall deformation of the members by a simple deformationmodel, each for decomposed deformation modes, such as flexural, shear or axialdeformations. Based on recent experimental data and observation, maximum crackwidths can be related to the member deformations, assuming a simple deformationmodel with cracks of equal spacing, which are dependent on the reinforcement ratioacross the cracks, as shown in Figure 4. Then the maximum crack widths areformulated using the number of cracks and the averaged crack widths. The residualcrack widths are derived from the maximum widths at the peak proportionally to themaximum and unloading deformation points based on the unloading rules of typical33