Curved steel beams are commonly used in the construction of modern bridges, highway ramps and interchanges, major buildings, ships, and air space structures and as of today there is no closed-from solution to this class of problems. The mathematical expression of the problem as shown in literature is very complex and its numerical solution may not be accurate.

This Thesis presents a closed form solution to the problem of the lateral stability against buckling of horizontally curved beams with or without constant radius of curvature. This theoretical analysis was performed under the assumption that, the lateral and angular displacements in the buckling state are very small compared to the initial radius of curvature where the second order terms can be neglected and the cross-section in the strained state retains its original shape.

Solving the differential equation of equilibrium for this type of elastic stability problem by common methods was an improbable task. Therefore, it has become necessary to implement a new method to overcome these difficulties.