The structural elements of buildings have recently required the development of efficient design solutions due to increased dynamic and thermal loads. The main solution for improving the efficiency of such elements involves creating lightweight non-uniform beam and arch structures from alloyed steel, which has better mechanical characteristics. The most promising approach is the use of welded beams and arches with perforated partitions and composite beams, which are often used together, for instance, as structural elements of cylindrical shells. The development of an effective cross-sectional shape for perforated beams and crane girders is considered, taking into account the strength, local stability, resistance to flat bending, and fatigue deformation. It has been shown that the effective form for perforated beams is a box-shaped structure made of perforated shvellers. Calculations for selecting a rational design from the assortment of hot-rolled shveller profiles have demonstrated that a significant reduction in the weight of the structure can be achieved by using the proposed cross-sectional shape. An evaluation of the fatigue strength of composite metal crane girders operating in harsh conditions has shown the effectiveness of using hot-rolled I-beams as their upper flange, as well as the necessity of using hot-rolled I-beams to ensure strength in their lower part. When choosing the rational parameters of an arch design, multiple recalculations of its bending with respect to technological cutouts in the thickness are necessary; hence, simplified calculation schemes are commonly used. Some authors simplify this process by replacing an arch with a cutout with a solid arch reduced in height by the cutout radius. We have shown that this model does not accurately describe the actual distribution of forces and displacements, leading to inadequate results. We have developed a simplified methodology for the preliminary calculation of a circular arch with a cutout, which includes correction coefficients calculated by us. A calculation of the flat stress–strain state of an elastic circular metal arch with a central semicircular cutout under various ratios of design parameters and uniform external pressure was conducted. A dependence of the stress concentration coefficient at the cutout’s apex on the ratio of the cutout radius and arch thickness was obtained. These results can be generalized for reinforced non-uniform shells and for the fuzzy application of external influences.
