Curved Beam Stiffness Coefficients

A three-dimensional stiffness coefficient matrix for constant cross section curved beams is derived. This matrix relates the beam end point rotations and translations to the internal moments, torques, shears, and axial forces. The stiffness matrix is transformed into a three-dimensional spatial coordinate system by means of a coordinate transformation matrix. The transformation matrix is derived by rotating the orthogonal coordinate axis through three consecutive rotations. Finally an example problem, simulating a spherical dome is worked to demonstrate the application of the curved beam stiffness matrix coefficients.