Elastic Bending of a Strip Under the Action of Applied Forces

The flexural deformation of the rod involves restoring its elastic axis to its original state once the deforming forces cease. Typically, the initial position of the elastic axis is assumed to be rectilinear, reflecting the common use of rectilinear structures in the construction industry, serving various roles such as bridges and spans. Excessive deflection in such structures can lead to failure, making it crucial to establish permissible deflection limits for these building elements. The allowable deflection for rectilinear elements is extremely small, disproportionate to the element's length. As a result, simplified theoretical formulas were employed to calculate deflection values that align with practical considerations. This simplification entails replacing the second-order differential equations of the elastic axis with first-order differential equations, providing acceptably accurate results for the deflection of rectilinear elements with minor deformations. However, in engineering practice, rectilinear rods undergo significant deformations, making the use of simplified formulas inappropriate for calculating their deflections. Moreover, curvilinear elastic elements with an initial curved shape of the elastic axis become prevalent. These include risers of cultivator tines designed to smooth pulsating dynamic loads and springs and piston rings. The article focuses on determining the shape of the elastic axis of the piston ring.