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Numerous studies have been carried out on the axially loaded circular concrete-filled steel tube (CCFST) stub columns. However, to date, no clear evaluation criterion for the compatibility of its design parameters has been established. In the present study, the compatibility of the design parameters (concrete compressive strength <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>f</mi><mi>c</mi></msub></semantics></math></inline-formula>, steel yield strength <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>f</mi><mi>y</mi></msub></semantics></math></inline-formula>, diameter <i>D</i> and thickness of steel tube <i>t</i>) of axially loaded CCFST stub columns was quantitatively investigated in terms of the contribution of the composite actions to the axial bearing capacity of the columns. The composite ratio <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>λ</mi></semantics></math></inline-formula> was proposed as an indicator to represent the effectiveness of the composite actions. A numerical framework of the determination of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>λ</mi></semantics></math></inline-formula> was established, making use of a series of existing widely recognized constitutive models of structural steel and concrete. Some modifications were carried out on these models to ensure the numerical stability of the presented analysis. Moreover, the rationality of the combined use of these models was verified. The analytical results show that excessive or very small <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>D</mi><mo>/</mo><mi>t</mi></mrow></semantics></math></inline-formula> ratio should be avoided in design. Meanwhile, the combined use of low-strength steel and high-strength concrete should be avoided. A table of optimal <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>D</mi><mo>/</mo><mi>t</mi></mrow></semantics></math></inline-formula> ratios corresponding to different material strength matches was provided for designers. Finally, an optimization of the design parameters using the proposed method and the existing design specification was performed.