PSI - Issue 73

Lenka Koubova et al. / Procedia Structural Integrity 73 (2025) 66–72 Lenka Koubova / Structural Integrity Procedia 00 (2025) 000–000

67

2

Resistance to lateral forces is provided primarily by rigid frame action – that is, by the development of bending moment and shear force in the frame members and joints. By virtue of the rigid beam–column connections, a moment frame cannot displace laterally without bending the beams or columns, depending on the geometry of the connection. The bending rigidity and strength of the frame members is therefore the primary source of lateral stiffness and strength for the entire frame (Bruneau et al. (2011)). MRF structures are discussed, for example, in a study by the authors Siddika et al. (2019). It is based on modal analysis of MRF structures using ANSYS software to study the natural frequency and deflection pattern with their controlling parameters. A simplified model equation for prediction of natural frequency of MRF structures is proposed, with considering the structure height, lateral dimension and mass of the MRF structure simultaneously. This model is helpful for prediction of natural frequency easily and can be applied for different types of materials. Other authors also deal with MRF structures. The results of a shake table test program on two Steel Moment Resisting Frame (SMRF) structures alternatively equipped with and without nonstructural elements are presented in the article published by Landolfo et al. (2025). Shi et al. (2025) presents the numerical multi-scale modelling and verification of high-strength-steel (HSS) structures moment-resisting frames, and the subsequent companion study provides a detailed parametric study with nonlinear static and dynamic analyses. In the paper published by Norouzi et al. (2024), the seismic collapse fragility analysis of special steel moment-resisting frame (MRF) buildings with strength and stiffness deterioration is comprehensively evaluated, considering the effect of record selection based on the spectral shape parameters. The study from Tao et al. (2025) investigated the influence of slab composite effect on the seismic performance of a six-story timber moment-resisting frame (TMF) with concrete slabs through nonlinear time history analysis in OpenSees. Hud et al. (2024) deals with the influence of mass distribution on natural vibrations of a reinforced concrete building frame. The results of their study highlight how variations in mass distribution can lead to significant shifts in natural frequencies and mode shapes, emphasizing the importance of accounting for this factor in structural design and assessment. This article deals with determining the dependence of the natural frequency of MRF structures on their parameters. It deals with their dependence on the number of floors of the frame structure, the number of columns on the floor, and the total weight. The stiffness constant method is used for the solution. Calculations are performed using MS Excel. 2. Solution procedure The task is solved as a planar problem. The solution is based on the stiffness constant method published in Koubova (2024). By solving the system of equations (1), we obtain the natural frequencies and mode shapes. [ ] � ̈ ( ) � +[ ] � ( ) � = {0}. (1) In Eq. (1), { u ( t ) } is the displacement vector. Its second derivation � ̈ ( ) � determines the acceleration vector. The stiffness matrix [ k] is obtained by localizing the global stiffness matrices of the elements [ k i ] into which the structure is divided. The global stiffness matrix [ k i ] of the i -th element is obtained by the transformation of the local stiffness matrix [ ∗ ] in Eq. (2). [ ∗ ] = ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎡ ∆ 0 0 − ∆ 0 0 0 1∆2 3 − ∆6 2 0 − 1∆2 3 − ∆6 2 0 − ∆6 2 4∆ 0 ∆6 2 2∆ − ∆ 0 0 ∆ 0 0 0 − 1∆2 3 ∆6 2 0 1∆2 3 ∆6 2 0 − ∆6 2 2∆ 0 ∆6 2 4∆ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎤ (2)