Study of the Impact of Loads on the Deformation of Building Structures using Differential Equations

The paper investigates the influence of different types of loads on the deformation of building structures, particularly beams, using second-order differential equations that allow modeling deformation processes. For this purpose, we considered two beam deflection equations under concentrated and distributed loads. Several experiments were conducted under different geometrical conditions (variable parameters of the beam cross-section, length, and loads). The solutions were studied using graph-analytical methods: constructing a graph of solutions reflecting the system's behaviour, a hodograph allowing tracking of additional nuances of the studied process, and amplitude and phase-frequency characteristics. The influence of conditions on the nature of system behavior is determined. The study's results can be used to optimise design solutions in construction.