Internal Force Calculation Method for a Complex Curved Beam Under a Vertical Load

Abstract

In design, curved beams are popular owing to their aesthetic appearance. They are found to be in a state of coupled bending, shear and torsion when subjected to vertical loads. This complex behavior makes it difficult to perform force analysis in structural design. In this article, a set of equations are derived to calculate the internal forces at any position of a curved beam that consists of two orthogonal straight segments and one circular arc axis segment under a vertical load based on the force method. To simplify the calculation in practice, a simplified internal force analysis method is further developed by transforming the arc section into an equivalent straight beam model. The simplified formula is derived by fitting the internal force of 729 different curved beams, and it can be used quickly and accurately for hand calculation of internal force in a curved beam. Finally, the effectiveness of the proposed methods is verified by three engineering examples. The results show that the proposed force method can reasonably estimate internal forces at different locations of a complex curved beam, and the proposed simplified method can provide a convenient and practical approach to calculating the internal force distribution of curved beams.

Keywords:

• curved beam
• internal force calculation
• uniform load
• force method
• parameter analysis
• equivalent straight beam model

Disclosure Statement

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this article.

Data Availability Statement

The data used in this study can be provided upon request. We will provide the data in a timely manner in accordance with ethical and legal requirements, and in a format that is compatible with most statistical software packages. If you require access to the data and code, please contact the corresponding author directly. We will make every effort to ensure that the data is accessible and secure.

Additional information

Funding

The research is supported by the National Natural Science Foundation of China: [Grant Number 52108112]; Natural Science Foundation for Distinguished Young Scholars of Hunan Province: [Grant Number 2022JJ10050]; Natural Science Foundation of Hunan Province: [Grant Number 2021JJ30716].