Dzhanov L. Rational Steel Beams with Variable Web Height and Flange Width

Dissertation for the degree of Doctor of Philosophy in specialty 192 Construction and Civil Engineering (19 – Architecture and Construction) – Kyiv National University of Construction and Architecture, 2025. The dissertation is devoted to determining rational designs of beam elements of frames and structures made of welded I-beams with variable web height and flange width. Chapter 1 provides a review and analysis of scientific data presented in the literature regarding the search for optimal and rational web heights of steel I-beams with constant and variable cross-sectional areas.. Chapter 2 considers a new class of steel beams with variable flange width, web height, and web thickness. The chapter is dedicated to selecting the optimal and rational topology of variable cross-section steel beam elements used in frame structures of building frameworks. The beam is assumed to be laterally restrained out of the loading plane by a system of horizontal and vertical bracings, which prevents the loss of flexural stability and minimizes the emergence of bimoment stresses from restrained torsion due to accidental eccentricities in the application of external static loads between the horizontal bracings. These additional stresses from restrained torsion are considered in the working design either through detailed structural steelwork or by applying additional coefficients. It is also assumed that no loss of stability occurs due to longitudinal forces that may arise from the inclination of the axis of the variable cross-section element. Local stability of the web and flange is considered ensured by the element’s cross- section, and, where necessary, vertical stiffeners are used to ensure the web’s local stability. Chapter 3 is devoted to the investigation of the optimal structural form of a welded steel beam with a symmetrical cross-section, featuring variable web height and variable flange width, under the constraints of the second limit state—compliance with deflection limitations. The problem is formulated using a continuous modeling approach based on the Euler–Lagrange method as a nonlinear programming problem, considering strength requirements for each cross-section and aiming to minimize steel consumption. New analytical relationships are obtained for determining the optimal height of a welded steel I-beam with variable web height and flange width at the cross-section where the maximum bending moment occurs, while satisfying the specified deflection limits. Chapter 4 presents studies on the practical application of welded steel I-beams with variable web height and variable flange width. The focus is on the rational selection of the cross-section and the optimal structural form of a portal frame element made of a welded I-beam with variable web height and flange width, taking into account the effects of bending moment and axial force under a relative eccentricity of mx>15. The in-plane stability of the variable cross-section girder is considered using the Timoshenko–Yasinsky method. Local stability of the web and flanges is ensured by maintaining the appropriate flange width-to-thickness ratio and by providing stiffeners, while the global out-of-plane stability of the frame element is ensured through constructive measures, including the arrangement of vertical and horizontal bracing elements. The practical significance of the conducted research and the obtained new scientific results lies in establishing regularities for selecting the optimal structural form of welded steel I-beams with variable web height and flange width. Furthermore, the newly derived analytical expressions allow for the direct determination of the optimal section height at the initial design stage based on the two limit states where the maximum bending moment occurs. The developed methodological approach and the results of numerical studies enable the assignment of the optimal gradient of variation for the web and flange dimensions under the two limit states along the element’s length, depending on the applied internal forces. This facilitates the design of a rational welded I-beam configuration as a structural component of a frame system, taking into account the effects of both bending moments and axial forces..