In this research the tail-equivalent linearization method (TELM) has been applied to a structure with biaxial behavior of materials, using the biaxial Bouc-Wen material model. The modeled structure has been subjected to independent bidirectional excitation with the incident angle θ with major axes of structure. The direct differentiation method (DDM) has been developed for calculating the response and its derivatives for the first time for the biaxial Bouc-Wen material model, where the application of DDM is more difficult compared with uniaxial Bouc-Wen models due to its coupled constitutive law of material. The method is applied to a structure with a rigid diaphragm, supported by four different columns. The structure is subjected to bidirectional and modulated filtered white noise excitations. The cumulative probability distribution function (CDF), probability density function (PDF), average rate of crossing, and first passage probability of displacement response are calculated for a column in the roof level of the structure. The results have been compared with those of Monte Carlo simulation presenting good agreement. The effects of nonlinearity degree and the levels of threshold have been investigated on the tail-equivalent linear system (TELS). The importance and effects of considering biaxial nonlinear behavior have been assessed by changing its relevant parameter in the Bouc-Wen model to obtain and compare different TELSs. The effects of incident angle have been investigated for independent components of excitation to find the most critical angle related to the minimum reliability index in TELM. Furthermore, system eccentricity, most critical incident angle for different responses, nonlinearity, and spectral intensity ratio of bidirectional excitation are considered.
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