PSI - Issue 81

Volodymyr Romaniuk et al. / Procedia Structural Integrity 81 (2026) 276–281

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composite profiles with increased section moduli, and forms ensuring overall and local stability, these methods do not fully address stress redistribution at connections. One of the design solutions that allows the design forces in structural elements to be reduced is the de-centering of their fastening in both hinged and rigid nodes. That is, the axes of the elements do not intersect at one point, and this creates bending moments in the nodes, which reduce the stresses in certain cross-sections and prolong the elastic state of operation of individual structural elements. However, no data exist on the optimal value of tie vertical displacement, and its effect on stress distribution remains unquantified. This study investigates the influence of tie vertical displacement on the stress-strain state of the arch upper chord. The optimal vertical tie placement is theoretically determined and validated through experimental data. 2. Analysis of recent research and publications As provided by design standards DBN V.2.6-198 (2014) and EN 1993-1-8 (2005), the calculation of structures in engineering practice is carried out by developing their structural schemes and applying external loads to them. Moreover, the connections of individual elements in the nodes are assumed to be perfectly hinged or absolutely rigid. The de-centering of hinged nodes creates a bending moment in them, which actually changes the structural scheme of such structures. Theoretical and experimental aspects of the influence of node de-centering on the condition of span structures of roofing, in particular perforated arches, were investigated in Romaniuk et al. (2024a) and Romaniuk (2008). In particular, Romaniuk et al. (2024a) and Pidgurskyi et al. (2021) present experimental studies of the stress-strain state of the perforated arch as a whole and its individual elements taking into account the pre-stressing and displacement of the tie, but there are no data on the study and determination of the optimal value of the vertical displacement of the tie, which requires additional investigation. In Romaniuk et al. (2024b), the authors conducted a study of the features of the performance of a continuous perforated beam near an intermediate support, which is actually the upper chord of the arch, and the intermediate support is the node for fastening the spacer to the chord. The issues of theoretical and experimental study of the behavior of perforated structures under load are discussed in Tsavdaridis, D’Mello (2011 a), Tsavdaridis, D’Mello (2011b), Morkhade, Gupta (2015). It is also worth noting the influence of the actual stiffness of nodal bolted connections, where their opening also contributes to a change in the stress state of the sections and affects the overall stress-strain state and the actual performance of structures under external loading (Wang 2018, Shardakov et al. 2018a, Shardakov et al. 2018b). 3. Research purpose and tasks The aim of the research is to conduct an experimental and theoretical study of the actual performance of the elements of a steel perforated arch, taking into account the vertical displacement of the tie rod. The tasks are: determination of experimental and theoretical stresses in the critical cross-sections of arch elements; comparative analysis of theoretical and experimental stresses; assessment of the effect of tie rod displacement on the load-bearing capacity of a steel arch with a perforated upper chord. In this article, the influence of the vertical displacement of the tie on the stress-strain state of only the upper chord of the arch is investigated in detail. Accordingly, the value of the optimal vertical placement of the tie is theoretically determined, which is confirmed by experimental data. The tasks of calculating structures very often coincide with the tasks of optimizing their stress state at different stages of loading in order to obtain the greatest effect with the least material consumption. Therefore, issues related to optimal material distribution, finding the optimal stress state, optimal load application sequences, and other aspects are very important when designing steel structures. 4. Main results In the design of an arch with a perforated upper chord (Fig. 1), a tie rod 2 is used, which is designed to absorb the thrust force. If it is moved in the vertical direction, the support hinge nodes B and C will be de-centered and, as a result, a bending moment will arise at these nodes, the magnitude of which is

(1)

0 0 M Pe =

where P – is the force in the tie rod; e 0 – is the eccentricity of the tie displacement. The most stressed nodes in the arch are nodes D , where the spacer is attached to the chords of the half-arches. The bending moment at the attachment point is

2 cos

qf

f







(

)

(2)

1

1

0 1 M P e f

f

,

= + −

2  −   

sin

