In dynamics models for the railway tracks, the rails are considered as beams supported continuously or periodically mass-spring systems. Recently, the mass-spring systems are replaced by Euler-Bernoulli beams on viscoelastic foundation in order to study the dynamics of sleepers. This paper presents a development of this study by considering the Timoshenko beams for sleepers. We consider the dynamic equation in the steady-state of a sleeper subjected to the reaction forces. The rails are modelled by the periodically supported beams subjected to moving loads, leading to a relation between the sleeper displacements and the reaction forces. By substituting this relation into the dynamic equation, the sleeper responses can be obtained by using the Green’s function. Finally, numerical examples show the influences of beam models on sleeper responses. This development completes analytical choices for the dynamics of railway tracks where the rails and sleepers can be modelled by the two beam theories.

This paper investigates the effectiveness of machine learning (ML) models available in MATLAB Regression Learner app and MATLAB App Designer, both low-code applications, for accurately predicting punching shear strength (PSS) in reinforced concrete (RC) slabs. A database of 379 RC slab samples without transverse reinforcement was compiled from renowned publications. RandomSearch and Bayesian optimisation were employed for tuning hyperparameters. The performance of these models was compared with six empirical models, which included three current design codes, three equations from other researchers, and 227 finite-element simulations conducted by the authors. The ML models and finite-element method (FEM) demonstrated superior performance compared with the literature and practical codes. Furthermore, the results emphasised the exceptional performance of the Gaussian process regression (GPR) with optimised hyperparameters, exhibiting the best performance in validation, training, and testing datasets with R² values of 0.95, 0.99, and 0.98, respectively. A user-friendly standalone application was developed, providing real-time predictions of the PSS using the two best-developed ML models, GPR and support vector machine (SVM), as well as six empirical models from the literature. This tool offers users flexibility in choosing the most appropriate model for their specific needs, delivering reliable, and accurate results for estimating the PSS of RC slabs.