Due to inherent defects in the steel, as well as processing techniques or design issues, there may be cracks in the steel, which can potentially lead to brittle failure of steel members. Therefore, to avoid the severe consequences caused by brittle failure of steel members, it is particularly important to evaluate the importance degree of potential brittle failure members in steel structures. The risk achievement worth was introduced to study the importance degree of potential brittle failure members in statically determinate structures and an evaluation method was proposed for the importance degree. By analyzing the relationship between parameters such as the total number of members, correlation coefficients, the number of potential brittle failure members, reliability indices, and the importance degree of potential brittle failure members, relevant patterns have been summarized. The results indicate that as the total number of members, correlation coefficients, and the number of potential brittle failure members increase, the importance degree of potential brittle failure members also increases. On the contrary, as the reliability index increases, the importance degree of potential brittle failure members decreases. By applying the method to an engineering case truss structure, its feasibility and effectiveness have been demonstrated, and a theoretical reference for the evaluation of such issues have also been provided.