Vector-valued intensity measures for incremental dynamic analysis

In incremental dynamic analysis (IDA), use of an efficient intensity measure (IM) is of vital importance. Efficiency means good explanatory power of the IM in regard to specific engineering demand parameter (EDP) that can help reduce the number of records used to estimate response of structures under given accuracy. According to dimension of the parameters, intensity measures can be classified into scalar-valued IMs and vector-valued IMs. While scalar-valued IMs have been studied systematically, vector-valued IMs have not been investigated comprehensively. Besides, vector-valued IMs considering the effect of higher modes have not been proposed. Hence in order to provide a systematic investigation on vector-valued IMs, this paper proposes five vector-valued IMs with two considering higher mode effect and three incorporating period elongation effect. Then a low-rise and a middle-rise reinforced concrete frames are modeled and analysed by PERFORM-3D and IDA under fifteen suites ground motion records for each structure. To evaluate efficiency of the proposed IMs, residual sum of squares (RSS) and R2 were calculated by logistic regression of IDA data. Results verified the better efficiency of vector-valued IMs than scalar-valued IMs. It is also proved that the relationship between IM and EDP can be expressed as a linear regression of logarithm for both scalar-valued IMs and vector-valued IMs. It turns out that a desirable IM should be selected based on the features of the specific structure. For structures dominated by the first mode, the impact of nonlinearity is of vital importance and should be mainly considered when choosing desirable IMs. Furthermore, for IMs considering nonlinearity effect, efficiency is relevant to the number of spectral acceleration incorporated; for IMs incorporating higher mode effect, the proposed multi-valued IM is more efficient than the two-valued type.