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. 2026 May 15;16:22198. doi: 10.1038/s41598-026-49985-z

Table 6.

Equations of design codes and literatures.

Codes Shape Equation
EC45 General CFST Inline graphic (11)
EC45 Octagonal CFST short column

Inline graphic (12)

Inline graphic (13)

Inline graphic (14)

where, the relative slenderness ratio is Inline graphic

GB5093670 General CFST

Inline graphic (15)

Inline graphic (16)

Inline graphic (17)

Inline graphic (18)

ACI318-99 and AISC 360 − 165,71 General CFST Inline graphic (19)
AISC 360 − 166 Octagonal CFST short column

Inline graphic (20)

Inline graphic, where Inline graphic (21)

Inline graphic (22)

Inline graphic (23)

Inline graphic (24)

DBJ72 General CFST

Inline graphic (25)

Inline graphic (26)

Inline graphic (27)

AIJ-200873 General CFST Inline graphic (28)
Equation 10 of Ding et al.26 Octagonal CFST Inline graphic (29)
Equation 14 of Ding et al.29 Hexagonal CFST Inline graphic (30)
Equation of Yu et al.59 Solid, Holow, Circle, and Polygonal CFST

Inline graphic (31)

where, Inline graphic

Inline graphic (32)

Equation of Patel et al.25,74 Octagonal CFST

Inline graphic (33)

where, Inline graphic (34)

Equation Li et al.30 Rectangular CFST

Inline graphic (35)

Inline graphic (36)

Inline graphic (37)

Inline graphic (38)

Equation of Ahmed and Liang40 Octagonal CFST short column Inline graphic (39)
Equation Nic J. Chen and T. M. Chan8 Octagonal CFST Inline graphic (40)
Equation J. Chen and T. M. Chan8 Octagonal CFST Inline graphic (41)
Equation Zhu and Chan60 Octagonal CFST

Inline graphic (42)

where, Inline graphic is insribed diameter of octagonal section; Inline graphic and Inline graphic are the modification factors based on the inscribed circularsection of an octagonal section.

Equation Liu et al.60,75 Octagonal CFST

Inline graphic (43)

Inline graphic (44)

where, Inline graphic is confining pressure and Inline graphic is hoop stress in steel tube.

Equation Ramadan et al.28 Hexagonal CFST Inline graphic (45)
Equation Nu with fscy modified MOHURD28,76 Hexagonal CFST

Inline graphic (46)

Inline graphic (47)

Inline graphic (48)

Inline graphic (49)

Inline graphic (50)

Equation Nu with fscy modified Han et al.28,77 Hexagonal CFST

Inline graphic (51)

Inline graphic (52)

Inline graphic (53)

Inline graphic (54)

Inline graphic (55)

Inline graphic (56)

Inline graphic (57)

Equation Nu with fscy modified Shen et al.28,31 Hexagonal CFST

Inline graphic (58)

Inline graphic (59)

Inline graphic (60)

Inline graphic (61)

Inline graphic (62)