Modelling
Eightnode linear hexahedron element C3D8R is used for core concrete and conventional structural steel parts, and tennode quadratic tetrahedron element C3D10 is selected for ball table, table plate and pressure plate of the ball table. Steel components such as tower column, wrapped object, ball table and pressure plate of the ball table are simulated by the secondary plastic flow model 21 given by Han L.H., and the concrete stressstrain relationship model21 proposed by Han L.H. is taken for the core concrete in the tower column.
The joint tower column interacts with the core concrete in the form of "hard touching" and "penalty friction", and the friction coefficient is taken as 0.4. The bolt ball interacts with the ball table, pressure plate of the ball table, and the upper wrapped object in the form of "hard touching" and "penalty friction", and the friction coefficient is taken as 0.15. Other contacts are defined by Tie binding.
Seen from Table 3, we can know that the maximum error rate between the test value and the simulated value of the ultimate bearing capacity of the joint is about 10 %, thus indicating that the modelling, material property definition, analysis step establishment, interaction setting, load setting and mesh subdivision are reasonable, therefore, the parameter expansion analysis can be carried out.
Table 3 Comparison of ultimate bearing capacity
Specimen Number

Nut/kN

Nuc/kN

e/%

JD1

180

183.4

1.8

JD2

318

351.4

10.5

JD3

242

252.5

4.3

JD4

229

252.5

10.2

Parameter Expansion Analysis
Due to the limited test conditions and specimen number, the expansion analysis of key parameter of the joint is conducted by ABAQUS, 40 finite element analysis models are set up to control the change of two parameters, and the other parameters remain unchanged. The results of parameter expansion analysis are shown in Table 4.
Table 4 Parameter Expansion
Thickness of Pressure Plate/mm

Wall Thickness of the Ball Table/mm

Nuc/kN

Model Number

Thickness of Pressure Plate/mm

Wall Thickness of the Ball Table/mm

Nuc/kN

10

4

170.1

1

21

14

8

307.1

10

5

173.4

2

22

14

9

309.7

10

6

176.6

3

23

14

10

314.1

10

7

183

4

24

14

11

319.9

10

8

183.4

5

25

16

4

252.5

10

9

185.4

6

26

16

5

274.7

10

10

186.9

7

27

16

6

313.2

10

11

187.9

8

28

16

7

352.3

12

4

173.9

9

29

16

8

351.4

12

5

192.6

10

30

16

9

365.1

12

6

215.1

11

31

16

10

368.2

12

7

232.4

12

32

16

11

372.3

12

8

240.5

13

33

18

4

255.5

12

9

244.2

14

34

18

5

289.8

12

10

248.9

15

35

18

6

334.1

12

11

252.6

16

36

18

7

368.3

14

4

209.6

17

37

18

8

375.2

14

5

234.4

18

38

18

9

381.1

14

6

264.6

19

39

18

10

385.3

14

7

295.5

20

40

18

11

387.1

Wall Thickness of the Ball Table
According to the relationship curve between the ultimate bearing capacity and the wall thickness of the ball table in Figure 9, we can know that when the thickness of the pressure plate of the ball table is 10mm, 12mm, 14mm, 16mm and 18mm respectively, and the wall thickness of the ball table is increased from 4mm to 7mm, the growth range of the ultimate bearing capacity of the joint is 7.6%, 36.6%, 41%, 39.5% and 44.1% respectively, and the ultimate bearing capacity of the joint is increased by 13.1kN, 39.8kN, 85.9kN, 99.8kN and 112.8kN respectively; When the wall thickness of the ball table is increased from 7mm to 10mm, the growth range of the ultimate bearing capacity of the joint is 2.1%, 7%, 6.2%, 4.5% and 4.6% respectively, and the ultimate bearing capacity of the joint is increased by 3.9kN, 16.5kN, 18.6kN, 15.9kN and 17kN respectively; When the wall thickness of the ball table is increased from 10mm to 11mm, the growth range of the ultimate bearing capacity of the joint is 0.5%, 1.4%, 1.8%, 1.1% and 0.5% respectively, and the ultimate bearing capacity of the joint is increased by 1kN, 3.7kN, 5.8kN, 4.1kN and 1.8kN respectively.
To sum up, when the thickness of the pressure plate of the ball table remains unchanged and the bearing capacity is met, and the wall thickness of the ball table is less than 7mm, the wall of the ball table is thinner, and the failure mode of the joint is the strength failure of the table material. The wall thickness of the ball table is the key parameter affecting the ultimate bearing capacity of the joint, therefore the increase of the wall thickness of the ball table can greatly improve the ultimate bearing capacity of the joint; When the wall thickness of the ball table is greater than 7, the table plate at tension zone is destroyed by the larger loading. At this time, the increase of the wall thickness of the ball table cannot improve the bearing capacity of the table plate at tension zone, and the change of the wall thickness of the ball table has little effect on the ultimate bearing capacity of the joint.
Thickness of Pressure Plate of the Ball Table
It can be seen from Figure 10 that when the wall thickness of the ball table is 4mm, 6mm, 8mm and 10mm respectively, and the thickness of the pressure plate of the ball table is increased from 10mm to 12mm, the growth range of the ultimate bearing capacity of the joint is 2.2%, 21.8%, 31.1%, 33.1% respectively, and the ultimate bearing capacity of the joint is increased by 3.8kN, 38.5kN, 57.1kN and 62kN respectively; When the thickness of the pressure plate of the ball table is increased from 12mm to 14mm, the growth range of the ultimate bearing capacity of the joint is 20.5%, 23%, 27.6%, 26.1% respectively, and the ultimate bearing capacity of the joint is increased by 35.7kN, 49.5kN, 66.6kN and 65.2kN respectively; When the thickness of the pressure plate of the ball table is increased from 14mm to 16mm, the growth range of the ultimate bearing capacity of the joint is 20.4%, 18.4%, 14.4%, 17.2% respectively, and the ultimate bearing capacity of the joint is increased by 42.9kN, 48.6kN, 44.3kN and 54.1kN respectively; When the thickness of the pressure plate of the ball table is increased from 16mm to 18mm, the growth range of the ultimate bearing capacity of the joint is 1.1%, 6.6%, 6.7%, 4.6% respectively, and the ultimate bearing capacity of the joint is increased by 3kN, 20.9kN, 23.8 kN and 17.1kN respectively.
Fig.10 Relationship between ultimate bearing capacity and thickness of pressure plate of the ball table
To sum up, when the wall thickness of the ball table remains unchanged and the table wall meets the bearing capacity, and the thickness of the pressure plate of the ball table is less than 16mm, the pressure plate of the ball table is thinner, and the failure mode of the joint is the buckling failure of the pressure plate of the ball table at tension zone. At this time, the thickness of the pressure plate of the ball table is the key parameter affecting the ultimate bearing capacity of the joint, therefore, the increase of the thickness of the pressure plate of the ball table can greatly improve the ultimate bearing capacity of the joint; When the thickness of the pressure plate of the ball table is greater than 16mm, the table plate at tension zone is destroyed by the greater loading. At this time, the increase of the thickness of the pressure plate of the ball table cannot improve the bearing capacity of table plate at tension zone, and the change of the thickness of pressure plate of the ball table has little effect on the ultimate bearing capacity of the joint.