###### Abstract
The study considered the effects of the initial stresses and load eccentricities. Additionally, several numerical examples validated by the FEA were presented. [PERSON] [39] examined the lateral-torsional buckling response of beams with simultaneous tapering in both the flanges and the web. [PERSON] and [PERSON] [40] investigated the LTB response of web-tapered I-section beam-columns subjected to combined axial and transverse loads, incorporating shear deformation effects into their analysis. [PERSON] and [PERSON] [41] presented a general variational formulation to analyze the LTB behavior of singly symmetric thin-walled tapered beams. The study extended kinematical assumptions developed for the LTB of prismatic beams, derived the total potential of the tapered beam, and employed [PERSON]'s criterion for stability analysis. The study included numerical examples to unveil the LTB behavior of tapered beams and cantilevers. The study concluded that tapered beams may exhibit higher or lower critical moments than their prismatic counterparts depending on the tapering ratio and loading conditions. Another important outcome was that tapering reduces the distance between the load application point and the torsional center for cantilevers, increasing stability despite the material reduction. [PERSON] et al. [42] evaluated the validity and underlying assumptions of a one-dimensional (1D) analytical model designed to investigate the LTB behavior of singly symmetric, web-tapered, thin-walled I-beams. The 1D model, which incorporated the effects of pre-buckling deflections, was benchmarked against results obtained from two-dimensional shell finite element analyses (FEA) performed using the ABAQUS software. The primary objective was to assess the accuracy of the 1D model's predictions regarding critical loads and associated buckling modes across various geometric configurations and loading conditions. The study revealed that the 1D model provided accurate predictions for the critical LTB loadsand buckling modes for longer beams. However, significant discrepancies were observed for shorter beams due to local effects, such as web or flange distortion, which the 1D model was unable to capture. The study also concluded that pre-buckling deflections influenced LTB loads, especially in web-tapered cantilevers subjected to transverse loads at the centroid or bottom flange. [PERSON] and [PERSON] [43] introduced a variational principle for the LTB analysis of web-tapered beams with symmetric I-sections, which derives the total potential energy by considering all relevant longitudinal, shear, and transverse stresses. The proposed theory encompasses the effects of tapering, nonlinearities, and detailed deformation mechanics, providing a comprehensive and realistic approach for analyzing the LTB of web-tapered I-beams. [PERSON] [44] introduced an analytical method to assess the LTB load of flanges and/or web-tapered I-section cantilevers, developed a Mathematica package, and validated analytical solutions using FEA, where shell elements were employed. [PERSON] et al. [45] examined the LTB of web-tapered T-section cantilevers. The study highlighted that these cantilevers exhibit remarkable differences from those with I-sections. They expressed that the lack of the bottom flange compressed the lower part of the web, increasing buckling instability. Additionally, the study revealed that web tapering can increase or decrease critical lateral-torsional buckling loads depending on the flange width of the beam. Numerous studies have demonstrated that the lateral-torsional buckling (LTB) behavior of web-tapered beams is qualitatively distinct from that of prismatic members. Simplified modeling approaches that represent tapered beams as equivalent or piecewise prismatic segments have been shown to yield unreliable or inaccurate buckling predictions, as they fail to account for critical geometric variations and deformation modes inherent to tapered geometries [41; 42; 43].