###### Abstract  
Web-tapered beams with I-sections, which are aesthetic and structurally efficient, have been widely used in steel structures. Web-tapered I-section beams bent about the strong axis may undergo out-of-plane buckling through lateral deflection and twisting. This primary stability failure mode in slender beams is known as lateral-torsional buckling (LTB). Unlike prismatic I-beams, the complex mode shape of web-tapered I-section beams makes it challenging or even impossible to derive a closed-form expression for the LTB load under certain transverse loading conditions. Therefore, the LTB assessment of web-tapered I-section beams is primarily performed using finite element analysis (FEA). However, this method involves multiple steps, requires specialized expertise, and demands significant computational resources, making it impractical in certain cases. This study proposes an analytical approach based on the Ritz method to evaluate the LTB of simply supported web-tapered beams with doubly or mono-symmetric I-sections. The proposed analytical method accounts for web tapering, I-section mono-symmetry, types and positions of transverse loads, and beam slenderness. The method was implemented in Mathematica to allow the rapid evaluation of the LTB capacity of web-tapered I-beams. The study validates the LTB loads computed using the developed Mathematica package against results from shell-based FEA. An excellent agreement was observed between the analytically and numerically calculated LTB loads. stability; lateral-torsional buckling; web-tapered I beam; FE analysis 2025 2 20  
level. During LTB, the compression flange tends to buckle laterally, while the remaining cross-section resists this lateral bending. As a result, the cross-section undergoes both twisting and lateral deflection. From a design perspective, LTB may occur well before the outer fibers of the cross-section reach their yield strength. Therefore, determining the elastic LTB load during the design stage is essential. The fundamental concepts of the LTB and classical differential equation solutions for beams, columns, beam-columns, and cantilevers under basic loading conditions are well-documented in the literature [1; 2; 3; 4; 5; 6; 7; 8; 9; 10]. The Ritz and Galerkin methods are energy-based techniques commonly used to analyze LTB behavior. The Ritz method works directly with the total potential energy, converting it from a functional to a function using an assumed deflected shape that satisfies the structure's kinematic boundary conditions. This transformation allows the use of standard calculus instead of the more complex variational calculus required for minimizing energy. This process enables the determination of the elastic critical LTB load. On the other hand, the Galerkin method originates from energy principles but employs the differential equilibrium equation during the solution process. Using a displacement function that satisfies kinematic and natural boundary conditions, the elastic critical LTB load is obtained via the Galerkin integral. These two energy approaches have been utilized to treat the LTB of beams, beam-columns subjected to combined axial and transverse load, castellated beams [11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23], beams with various cross-sections [24; 25; 26], and cantilevers [27; 28; 29; 30; 31; 32; 33]. A limited number of studies are related to the LTB of tapered beams, beam-columns, and cantilevers. [PERSON] and [PERSON] [34; 35] studied the LTB of web- or flange-tapered beams with I-sections. [PERSON] [36] proposed a finite element formulation to analyze the LTB response of tapered beam-columns under varying load cases and support configurations. A simplified formulation for the LTB resistance of web-tapered beams with symmetric I-profiles subjected to uniformly distributed loads was presented by [PERSON] et al. [37]. The power series approach was employed by [PERSON] et al. [38] to study the LTB response of tapered beams with general cross-sections and support configurations.