Comparative Finite Element Modal Analysis of Reinforced Concrete Cantilever Beams with Four- and Six-Bar Longitudinal Reinforcement Layouts

Abstract

This study compares the elastic modal characteristics of reinforced-concrete cantilever beams containing four and six 12 mm longitudinal reinforcing bars using three-dimensional finite element analysis (FEA) and an exploratory machine learning (ML) exercise. Beam geometry, material properties, bond assumptions, and boundary conditions were held constant. Mesh refinement from a 50 mm to a 25 mm nominal element size changed the fundamental natural frequency by 0.18%, satisfying the adopted 1% convergence criterion. The Fine mesh FEA fundamental frequency of 36.048 Hz differed by 1.49% from the Euler–Bernoulli transformed-section estimate of 35.52 Hz. Block Lanczos extraction provided the first six natural frequencies and corresponding normalised mode shapes. Increasing the longitudinal steel area from 452.39 to 678.58 mm2 changed the calculated frequencies by −0.02% to +0.19%, while the two layouts exhibited similar mode-shape topology under the assumed intact, linear-elastic, perfectly bonded conditions. Four regression algorithms were fitted to the 12 correlated mode–configuration records using only mode number and reinforcement count as inputs and natural frequency as the output. The reported R2, MAE, and RMSE values describe complete dataset fitting or interpolation and do not establish generalisation to unseen configurations. No physical modal displacement, strain, or stress amplitude is reported because eigenvector scaling is arbitrary and no forced-response analysis with defined excitation and damping was performed.