Model details.

In previous studies, the strengthening effectiveness and feasibility of carbon fiber reinforced polymer (CFRP) were mainly evaluated through experimental research or numerical analysis. Although these methods can accurately provide estimates, both experimental and numerical assessment processes are costly in terms of time and cost. There is a need for reliable calculation formulae that can predict the static strengths of circular hollow section (CHS) stub columns in a more convenient and cost-saving manner. Therefore, this paper mainly conducted theoretical analysis and derived the calculation formulae. Furthermore, finite element (FE) analysis of CHS stub columns strengthened with CFRP was also conducted, and FE simulations were obtained. The accuracy of these formulae was validated by comparing the theoretical predictions with both FE simulations conducted by the authors and experimental results derived from previous studies. The maximum error was found to be no more than 10%. The cost-effective number of CFRP laminates bonded on the steel tube surface can be determined using the CFRP confinement coefficient λ, where λ balances the construction cost and the strengthening efficiency. A parametric study was also conducted to investigate the impact of steel strength, the number of CFRP laminates, and the bonding configuration of CFRP on the strengthening efficiency.