This paper is devoted to the study of possibilities for assessing the metal structures of overhead cranes based on key performance criteria. Special attention is given to the issue of systematic overloads of the crane’s span system caused by intensive operation. As a result, the span part of the crane may develop residual deformations when the material operates in the elastic-plastic stage. For this purpose, a mathematical model of the span system of lifting machines was developed, considering that its elastic line, even in the absence of external load on the span, may have an initial curvature. The article derives equations for the deflection of the span beam, taking into account the acquired curvature. This enables the evaluation of the crane’s span system for strength and stiffness under the combined effect of longitudinal and transverse loads in the working plane. The results obtained in this study can be used at the stage of calculation and design of the geometric characteristics of beam cross-sections subjected to pre-stressing. Additionally, the authors’ recommendations can be applied during repair work on any span systems to extend their service life or modernize the crane.