# Analytical and simplified models for dynamic analysis of short skew bridges under moving loads

## TL;DR

This paper develops analytical and simplified models to analyze the dynamic response of skew bridges under moving loads, highlighting the influence of skewness and torsional stiffness on vertical displacements and accelerations.

## Contribution

It introduces a 3D beam theory-based analytical model and a simplified 2D model for skew bridge dynamics, validated against finite element results, with a parametric study on skewness effects.

## Key findings

- Skewness significantly affects vertical displacement.
- Torsional stiffness influences displacement at large skew angles.
- Span length reduces skewness impact on dynamic response.

## Abstract

Skew bridges are common in highways and railway lines when non perpendicular crossings are encountered. The structural effect of skewness is an additional torsion on the bridge deck which may have a considerable effect, making its analysis and design more complex. In this paper, an analytical model following 3D beam theory is firstly derived in order to evaluate the dynamic response of skew bridges under moving loads. Following, a simplified 2D model is also considered which includes only vertical beam bending. The natural frequencies, eigenmodes and orthogonality relationships are determined from the boundary conditions. The dynamic response is determined in time domain by using the "exact'" integration. Both models are validated through some numerical examples by comparing with the results obtained by 3D FE models. A parametric study is performed with the simplified model in order to identify parameters that significantly influence the vertical dynamic response of the skew bridge under traffic loads. The results show that the grade of skewness has an important influence on the vertical displacement, but hardly on the vertical acceleration of the bridge. The torsional stiffness really has effect on the vertical displacement when the skew angle is large. The span length reduces the skewness effect on the dynamic behavior of the skew bridge.