Analytical analysis on the static support reactions of single-column pier bridges using the grey wolf optimizer

To obtain the support reactions of single-column pier girder bridges for studying the bridge stability against overturning, the bridge deck can be treated as an orthotropic thin plate with point supports in the domain. A semi-analytical formula for support reactions is then derived by a hybrid method using the grey wolf optimizer. To avoid calculation errors and improve the computational efficiency, dimensionless parameters α and β are introduced. Compared with the finite element analysis results, the maximum error resulting from the derived analytical formula is about ± 15% with the larger error occurring in the cases with small support reactions, which is considered practically acceptable. The analytical solution is then used in the parametric analysis to investigate the effects of span, support location, and bearing width on the single-column pier bridge under four vehicles. The analysis shows that the proposed method is reasonably accurate, highly efficient, and effective.