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

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.