Calculation of Displacements of Plate Elements of Box-Shape Structure of Buildings

The article investigates the dynamic behaviour of a box-shaped building structure subjected to seismic excitation modelled as a sinusoidal base displacement. The structure is represented as a spatial system of interconnected plate and beam elements, accounting for bending, shear, and torsional effects. The problem is solved numerically using the finite difference method. Calculations are performed for three dimensionless excitation frequencies β₁ = 16, β₂ = 17, and β₃ = 17.5, with a base displacement amplitude of A₀ = 0.02 m. Material properties are taken as Eb = 20000 MPa and Ec = 7500 MPa, with geometric parameters a = 3.5 m, b = 5 m, and hc = 0.2 m. Results show that as the excitation frequency approaches the natural frequency (β ≈ 17.5), resonance leads to a significant increase in displacements. Maximum dimensionless deflections (W/A₀) occur in the upper regions of bending panels and are notably higher near openings compared to solid sections. The presence of openings increases displacement values, particularly along their edges, while beam and plate elements exhibit consistent deformation patterns.