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This paper presents an efficient numerical methodology in probabilistically solving the governing partial differential equation of solid mechanics with uncertainties in both the material parameter and forcing function in the time domain using the stochastic Galerkin approach. The methodology hypothesizes the input forcing function and the elastic modulus of the solid to be a nonstationary random process and a heterogeneous random field, respectively, and efficiently represents them in terms of multidimensional Hermite polynomial chaos -orthogonal and uncorrelated polynomials of zero-mean, unit variance Gaussian random variables -by taking advantage of the optimality of the Kosambi-Karhunen-Loève theorem. The methodology allows for any non-Gaussian marginal distributions and any arbitrary correlation structures for the input process and field. The solution random processes (displacement, velocity, and acceleration) are also represented in

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Research was conducted to investigate how the inclination angle of the diagonal tension field action varies in steel plate shear walls (SPSWs) and to determine what optimum constant angle best matches the demands obtained from finite-element (FE) analysis. An FE model was first calibrated against experimental results that surveyed inclination angles across the web plate of an idealized SPSW as a function of drift and that showed significant differences in inclination angles at different locations across the web plate. Then, four real SPSWs with varying aspect ratios and numbers of stories were designed and modeled for FE analyses. The variations in angle in the web plate and along the boundary elements were documented as a function of drift and showed significant variations. Combined moment-axial force demand ratios in the SPSW boundary elements were calculated and compared for all real SPSWs to determine the preferable value of single angle that could be used in design. Overall, using 45°was found to be a reasonable compromise for both horizontal and vertical boundary element (HBE and VBE, respectively) design if a single constant angle is desired. Furthermore, the demand on the web plate is not sensitive to the variation of inclination angle. Consequently, the single angle of 45°is recommended for the design of the entire SPSW.