Table 6 Comparison of SCFs between proposed formulae(\(SCF_{{{\text{pro}}}}\)) and FE analysis(\(SCF_{{{\text{FE}}}}\)).

From: Experimental and numerical investigations on stress concentration factors of concrete filled steel tube X-joints

Specimens

\(SCF_{{{\text{pro}}}}/SCF_{{{\text{FE}}}}\)

AT

IPB

A

B

C

D

E

A

B

C

D

E

C110X8.8-B44X2.2

1.07

1.04

1.10

1.07

0.99

1.20

0.78

1.05

1.08

1.13

C110X8.8-B44X4.4

1.01

1.10

1.02

1.05

0.86

1.03

0.92

1.10

0.93

0.87

C110X8.8-B44X6.6

1.02

1.20

1.11

0.85

0.94

0.99

1.11

1.24

1.08

0.80

C110X8.8-B44X8.8

0.99

0.72

0.70

0.77

1.05

1.18

1.12

1.16

0.92

0.82

C110X6.88-B44X1.72

0.98

1.00

1.05

0.96

1.01

1.05

0.83

0.99

1.04

1.04

C110X6.88-B44X3.44

0.96

1.11

1.04

1.04

0.96

1.01

1.05

1.12

1.04

0.90

C110X6.88-B44X5.16

0.92

0.91

1.03

1.03

0.93

1.11

1.03

1.05

1.09

0.94

C110X6.88-B44X6.88

1.06

1.00

0.92

0.89

1.13

1.09

1.05

1.14

1.06

0.91

C110X5.5-B44X1.38

1.02

1.01

1.05

1.04

1.11

1.14

0.85

0.91

1.03

1.25

C110X5.5-B44X2.75

0.96

1.02

0.97

1.07

0.85

0.96

1.01

0.89

1.08

0.97

C110X5.5-B44X4.13

0.96

1.08

1.14

1.07

0.96

0.95

1.11

0.95

0.94

0.94

C110X5.5-B44X5.5

0.94

0.98

1.12

1.00

1.02

0.98

1.48

1.09

1.15

0.99

C110X4.4-B44X1.1

1.06

0.96

0.98

1.03

1.07

1.03

0.99

1.09

1.15

1.13

C110X4.4-B44X2.2

1.00

1.00

1.05

0.94

0.90

0.88

0.95

0.91

0.97

0.93

C110X4.4-B44X3.3

0.98

0.96

0.91

0.95

0.91

1.05

1.05

1.03

1.02

1.04

C110X4.4-B44X4.4

1.06

0.98

0.99

0.95

1.04

0.86

0.89

0.97

0.91

0.86

C110X8.8-B60X2.2

1.03

0.91

0.95

1.06

1.00

1.11

0.68

0.80

0.97

1.17

C110X8.8-B60X4.4

0.99

1.06

1.00

1.05

0.91

0.91

0.79

0.95

0.96

0.92

C110X8.8-B60X6.6

0.96

1.07

1.09

1.01

0.91

0.94

1.02

0.97

1.03

0.86

C110X8.8-B60X8.8

0.96

0.71

0.79

0.79

1.11

0.95

0.65

0.65

0.71

0.95

C110X6.88-B60X1.72

0.88

0.90

0.98

0.94

1.04

1.08

0.82

0.83

0.92

1.04

C110X6.88-B60X3.44

0.91

0.95

0.92

1.01

0.91

1.05

0.89

0.96

0.97

0.96

C110X6.88-B60X5.16

0.95

1.04

1.01

1.00

0.97

0.98

0.87

0.88

0.79

0.90

C110X6.88-B60X6.88

1.01

0.92

0.93

0.86

1.00

1.05

0.81

0.86

0.91

0.93

C110X5.5-B60X1.38

0.96

0.91

0.93

0.95

0.90

1.05

1.11

1.22

1.19

0.97

C110X5.5-B60X2.75

0.98

0.91

0.92

1.00

0.94

1.07

1.11

1.05

1.06

1.02

C110X5.5-B60X4.13

1.01

0.98

1.01

1.04

0.99

1.09

1.30

1.20

1.21

1.06

C110X5.5-B60X5.5

0.99

1.07

1.10

0.98

0.95

1.05

1.16

1.07

1.19

1.02

C110X4.4-B60X1.1

1.00

0.96

0.97

0.94

1.03

0.94

1.01

1.07

0.99

0.87

C110X4.4-B60X2.2

0.97

0.94

0.95

0.95

0.92

1.01

0.99

0.88

0.86

0.98

C110X4.4-B60X3.3

0.96

0.91

0.94

0.98

0.94

0.95

0.96

1.01

1.03

0.95

C110X4.4-B60X4.4

0.97

0.94

0.96

1.06

1.12

0.99

0.92

0.99

0.96

1.04

C110X8.8-B77X2.2

0.97

1.11

1.10

1.07

1.05

1.09

1.32

1.25

1.39

1.07

C110X8.8-B77X4.4

1.04

1.09

1.24

1.13

0.93

0.86

1.33

1.12

1.16

1.06

C110X8.8-B77X6.6

0.98

1.04

1.08

1.09

0.99

0.80

1.63

1.24

1.29

1.02

C110X8.8-B77X8.8

1.01

0.77

0.72

0.89

1.05

0.93

0.99

0.90

0.76

0.94

C110X6.88-B77X1.72

1.12

1.05

1.13

1.11

1.07

1.21

1.24

1.38

1.26

1.15

C110X6.88-B77X3.44

0.98

1.15

1.17

1.22

0.97

0.89

0.83

0.85

0.88

0.95

C110X6.88-B77X5.16

1.00

1.23

1.32

1.09

0.99

0.85

0.85

0.89

0.88

0.81

C110X6.88-B77X6.88

1.07

0.91

0.92

0.91

1.06

0.98

0.87

0.78

0.85

0.94

C110X5.5-B77X1.38

1.07

0.99

1.07

1.01

1.03

1.26

1.33

1.37

1.54

1.11

C110X5.5-B77X2.75

1.05

1.01

0.98

1.10

0.99

1.08

1.06

1.17

1.13

1.07

C110X5.5-B77X4.13

1.04

1.17

1.14

1.12

1.03

1.08

1.38

1.41

1.40

1.23

C110X5.5-B77X5.5

1.06

1.10

1.16

0.98

1.11

1.33

1.56

1.58

1.49

1.19

C110X4.4-B77X1.1

1.05

1.02

1.04

0.91

1.06

0.79

0.76

0.75

0.70

0.76

C110X4.4-B77X2.2

0.97

0.88

0.91

0.94

0.92

1.07

1.25

1.04

0.93

1.05

C110X4.4-B77X3.3

1.01

1.01

1.02

0.98

1.00

1.08

0.90

0.97

0.96

1.12

C110X4.4-B77X4.4

1.03

1.03

1.00

1.01

1.05

1.07

0.88

0.87

1.01

1.15

C110X8.8-B93X2.2

0.95

1.14

1.19

1.11

1.02

1.18

1.35

1.51

1.17

1.07

C110X8.8-B93X4.4

1.00

1.30

1.56

1.21

0.88

0.97

1.47

1.21

1.15

1.02

C110X8.8-B93X6.6

0.96

0.90

0.95

1.01

0.96

0.94

1.21

1.16

1.04

0.92

C110X8.8-B93X8.8

1.00

0.84

0.83

0.83

1.11

0.98

1.30

0.96

1.13

0.97

C110X6.88-B93X1.72

1.00

1.11

1.13

1.03

1.03

0.86

0.64

0.62

0.67

0.80

C110X6.88-B93X3.44

0.97

1.06

1.18

1.03

0.99

0.98

0.59

0.64

0.78

0.98

C110X6.88-B93X5.16

0.91

0.99

1.01

0.90

1.03

0.91

0.64

0.84

0.81

0.97

C110X6.88-B93X6.88

0.95

0.81

0.75

0.87

1.09

1.12

0.66

0.80

0.62

1.02

C110X5.5-B93X1.38

1.04

0.95

0.95

0.96

1.01

1.09

1.02

0.92

0.93

0.97

C110X5.5-B93X2.75

1.05

0.89

0.88

1.12

0.99

1.11

0.67

0.84

1.18

1.00

C110X5.5-B93X4.13

1.00

1.00

0.87

0.89

0.96

1.14

0.84

0.88

1.40

1.09

C110X5.5-B93X5.5

0.99

0.99

0.97

1.03

0.94

1.13

1.05

0.89

1.10

1.02

C110X4.4-B93X1.1

0.96

1.00

0.91

1.04

1.04

1.54

1.83

1.37

1.73

1.45

C110X4.4-B93X2.2

1.01

1.08

1.03

1.05

0.95

0.95

1.20

1.31

1.05

0.94

C110X4.4-B93X3.3

0.98

1.04

1.03

0.95

0.95

0.98

1.20

1.17

1.05

0.94

C110X4.4-B93X4.4

0.98

0.95

1.15

1.12

1.03

1.04

1.37

1.19

0.90

0.90

Average

1.00

1.00

1.02

1.00

0.99

1.03

1.04

1.03

1.04

1.00

Standard Deviation

0.045

0.108

0.135

0.091

0.067

0.124

0.264

0.209

0.204

0.119

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