Numerical Methods in Structural Load Analysis for Civil Engineering Projects in Rivers State

This study investigates the application of advanced numerical methods to structural load analysis for civil engineering infrastructure projects in Rivers State, South South Nigeria, a region experiencing rapid infrastructure development driven by oil revenues and urban population growth. Structural analysis of bridges, flyovers, and multi-storey commercial buildings requires the solution of large systems of linear equations and eigenvalue problems arising from the finite element discretisation of structural members, and numerical accuracy is of paramount importance given the life-safety consequences of structural failure. The study examines the performance of the Gaussian elimination, LU decomposition, and Cholesky factorisation methods in solving stiffness matrix equations derived from finite element models of three representative civil structures in the Port Harcourt metropolitan area. Condition numbers are computed to assess the numerical stability of each stiffness matrix, and iterative refinement procedures are applied to improve solution accuracy for ill-conditioned systems. The study also evaluates the numerical performance of the Lanczos eigenvalue algorithm in computing natural frequencies for dynamic load analysis of a pedestrian bridge model. Verification is conducted by comparing numerical results against analytical solutions for standard benchmark structures and against results from the SAP2000 structural analysis software. Results indicate that LU decomposition with partial pivoting provides the most reliable numerical performance across the structural problem types examined. The study recommends the adoption of structured numerical method training in professional engineering programmes. Keywords: numerical methods, structural load analysis, finite element, LU decomposition, Rivers State