This study investigates the impact of uncertain load positions through an innovative optimization technique. It seamlessly integrates reliability-based design into the optimization of the structural topology, with a specific focus on the web portion of steel I-beams and including geometrical imperfection analysis. The study operates under the premise that the applied load is randomly positioned, engaging in a comprehensive probabilistic analysis. This methodology extends its considerations to additional factors, such as material properties, volume fraction, and geometric imperfections. The assumption of a normal distribution for each of these parameters aids in quantifying uncertainties. Moreover, the proposed work leverages the notion of plastic ultimate load multipliers to illustrate how the algorithm can improve the performance of steel beams. To evaluate the algorithm, the results of a benchmark problem were meticulously analyzed. While exploring the probabilistic nature of externally applied force positions, a numerical example was conducted involving a steel I-beam within the context of reliability-based imperfect geometry topology optimization. The outcomes of the proposed method underscore that the integration of probabilistic design significantly influences the topology optimization process.