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An extensive field and laboratory study is carried out to evaluate the concrete strength of existing building stock in Turkey. The concrete strength of each building was determined by core sampling and laboratory testing. Randomly selected components for core sampling were identified to meet with minimum requirements of standards or pre-standards for number of tests. A total of 1679 randomly selected core samples were extracted from 167 public buildings for laboratory testing. The average and coefficient of variation values of each building were obtained. The upper-bound value of the expected concrete strength is calculated as the mean less one standard deviation. It is observed that the expected concrete strength values are drastically lower than the specified ones. Also, the variability in concrete strength values is considerably high compared to the specified strength of buildings. Almost one-half of the investigated buildings have concrete strength values as low as that of the collapsed buildings during past earthquakes in Turkey. Considering that the current study validates low concrete strength in a significant number of existing buildings as observed in different buildings from various regions of Turkey during the earthquakes at Duzce and Kocaeli in 1999 and at Bingol in 2003, a considerable portion of existing building stock is at serious risk in the case of a seismic event.

The computation of constant ductility (or isoductile) response spectra for single-degree-of-freedom systems can require numerous individual response history analyses. Recognising that the same ductility response may be obtained for different strength oscillators of a given period, greater computational effort is required to reduce the possibility that a desired solution is not overlooked. Even a single solution may not exist if a local discontinuity in the strength-ductility relationship coincides with the desired value of ductility. This paper describes a two-phase algorithm to identify the highest strength solution for which the corresponding ductility equals (or does not exceed) the desired ductility. The first phase adopts a "check-reject" approach to reject intervals of strength where the possibility of unidentified higher-strength solutions is considered to be remote, thereby narrowing the strength interval in which the solution will be found. The second phase identifies a solution within this interval as rapidly as possible using a bisection approach. The algorithm is implemented in the USEE software program. The efficiency and accuracy of the algorithm are demonstrated by comparison to results obtained with other software programs.