Modeling of building structures loaded by movable mass by the example of the single span hingedly fixed beam

Problem statement. Publications review of methods for determining the dynamic loads on buildings and structures has shown that there is no clear agreed terminology in this field of expertise yet. In addition, different approaches to determining the dynamic loads have been used in various fields. Moreover, the existing techniques had insufficient attention to dynamic loads modelling based on non-linearity properties of the systems. For many years mathematical investigations were limited to mathematical models based upon measured values by some means. Measurements statistics were produced in a probabilistic way. Not only formula for the function in a deterministic form, but also such terms as spectral density and correlation functions have been established. Purpose. To undertake a comparative study of interactions in system structure-loads, considering the inertia of the movable load and damping (shock-absorbing) characteristics of the beam. Methods. Estimates have been provided by three methods: analytical, finite element method (FEM) using SCAD software and the method of straight lines with the help of Mathcad software. All calculations were performed according to three schemes: 1) analytical solution – without taking into account the inertia of the movable mass and beam, damping characteristics of the beam; the model of the building structure is continual; 2) finite element analysis using SCAD software – without taking into account the inertia of the movable mass but considering damping characteristics of the beam; the model of the building structure is discrete (the number of finite elements – 22); 3) the solution of straight lines method using Mathcad – taking into account the inertia of the movable mass and damping characteristics of the beam; the model of the building structure is discrete (the number of degrees of freedom – 21) Conclusion. Despite all simplifications, analytical results equal to FEM results without internal friction. Internal friction can reduce design beam deflection in the mid-point (by the assigned parameters) by 1,9 %. Introduction of the inertial forces of the movable mass instead increases design beam deflection in the mid-point (by the assigned parameters) by 1,2 %.