Traditional damage analysis of steel truss structures requires detailed finite element meshing, and there is a coupling between stress-strain and damage solving, resulting in complex damage analysis and massive computations. In this paper, the element bearing ratio (EBR) reflecting the bearing state of components was defined, and the concept of the element damage factor was introduced based on the principle of deformation energy conservation. A homogeneous generalized yield function (HGYF) for box-section components was constructed to establish adaptive damage factors and the criterion under multi-force combinations. Combined with linear elastic iterative analysis, an adaptive damage evolution method for simulating steel truss structures with box section was proposed. Through numerical examples, the damage criterion in the method was able to adaptively determine whether component stiffness degradation occurred, eliminating the requirement to consider the interaction between stress-strain fields and damage, thereby reducing the difficulty of coupled calculations and enhancing computational efficiency in structural damage analysis. Based on the linear elastic iterative analysis, the calculated ultimate bearing capacity showed good agreement with experimental results.