Abstract: Equal stiffness verification is an important basis for material replacement of various engineering structures. In this paper, an efficient and reliable equal stiffness verification method is obtained by designing and verifying the stiffness of carbon fiber-reinforced plastics (CFRP) replace steel shape tubes. Firstly, by the theoretical calculation, the deformation of the shape tube structure in different loading conditions is obtained, the influencing factors and degree of deformation are analyzed. Then, according to the theoretical deformation of the shape tube and the equal stiffness design principles, equal stiffness carbon fiber-reinforced plastics (CFRP) shape tube and steel shape tube are obtained. Finally, an efficient and reliable equal stiffness verification method, i.e., the modal verification method, is proposed. According to the theoretical derivation, the verification conditions of equal stiffness are used to verify the stiffness of CFRP shape tube and steel shape tube which have met the equal stiffness requirement. The results show that the CFRP shape tube and the steel shape tube satisfy the stiffness verification conditions, and the effectiveness of the method is verified. Compared with the previous multi-case loading verification method, main advantages of the equal stiffness mode verification method are as follows: ① The analysis process is simpler, which only includes the modal analysis of replacement parts and original parts, and this can greatly improve the verification efficiency; ② The validity of this method is not limited by the loaded condition of the structure, and it can be applied in the equal stiffness verification of variable-loading structure; ③ The verification results, which are based on the theory of the stiffness matrix, are more reliable, and the all-round equal stiffness verification can be obtained.

Key words: shape tube, equal stiffness design, equal stiffness verification, the modal verification method