Ultimate In-plane moment capacity of T and Y tubular joints

J. Construct. Steel Research 12 (1989) 69--80

Ultimate In-Plane Moment Capacity of T and Y Tubular Joints H. S. Mitri Department of Miningand MetallurgicalEngineering,McGillUniversity, Montreal, Quebec, Canada H3A 2A7 (Received 29 February 1988;accepted 20 May 1988)

ABSTRACT A punching shear model is developed to predict the ultimate strength of Tand Y-joints between steel circular tubular members subjected to in-plane bending moment. An empirical adjustment is included to extend the application to thin-walled members. The predictions of the theoretical model are compared with experimental results of 45 joint tests reported in the literature. A comparison of performance between the presented equation and those currently used in design is made.

1 INTRODUCTION The ultimate strength design of joints between circular steel truss members in fixed offshore structures is usually carried out using empirical relations based on very extensive test data. Such data serve to establish mathematical models from which prediction equations are derived. While some current design recommendations are based on semi-empirical models making use of the concept of punching shear, L2 there has been a recent trend to reject these simplified physical models in favour of a purely empirical basis for design. 3-6 Empirical joint strength formulae can be refined as additional test data become available; in addition, different formulae may be proposed for design of the same form of joint depending on the choice of database. This screening of data may be influenced by the scale of the test specimens, the geometrical similitude between these and the prototype and on judgement related to validity of the data due to test inadequacies (premature failure of 69 j. Construct. Steel Research 0143-974X/89/$03.50O 1989Elsevier Science Publishers Ltd, England. Printed in Great Britain

70

H. S. Mitri

cl

--I

BRANCH

j

Criticot Section

D

CHORD

(a)

d

-

-

D

CHORD

(b)

1

Fig. 1. T and Y tubular joints: (a) T-joint; (b) Y-joint.

test rig or secondary components of the test specimen). Given an accepted database, the superior strength formulation will be that providing the lowest coefficient of variation when compared with test data, subject to consideration of simplicity in design use. In the following, one loading case, that of in-plane bending, is considered for T or Y tubular joints (Fig. 1). A simple theoretical model is developed to predict the ultimate bending moment over part of a practical range of

Ultimate in-plane moment capacity of T and Y tubular joints

71

geometrical parameters applicable to steel offshore platforms, and empirical data are used to extend this to the full practical range. This approach is then compared with other recently proposed design formulations.

2 ULTIMATE STRENGTH FORMULATION A typical failure of an in-plane moment loaded joint usually involves a shear fracture through the chord wall on the tension side of the brace and plastic bending/instability on the compression side of the chord wall.5 For relatively thick chord walls (i.e. low D/2T --- ~/values) it is anticipated that such mode of failure is related to yield in shear of the chord wall. With this assumption, the shear yield stresses developed through the thickness produce a couple equilibrating the applied bending moment, as shown in Fig. 2. For a tubular branch connected to a fiat plate, the ultimate

Bronch

/ Flot Plote t

I

'"

mu

Jr ~£.ritico! Sect ions

Fig. 2. Punching shear model.

72

H. S. Mitri

moment, Mu, can be calculated as the moment of the boundary shearing forces about the y-axis. Thus Mo =

1

F, r d 2

O)

In the above, the shear yield stress is taken as Fflx/3 and the critical section is assumed to be just on the outside of the branch perimeter. If a fillet weld of size tw is deposited around the branch, the effective diameter of the brace will be (d + 2t,,) and eqn (1) becomes Mo =

1

F, r a

(2)

2tw \2 1 +---~-)

(3)

in which F(w)=

The attachment of tubular members may not be made by fillet welds, and if full or partial penetration groove welds were employed this adjustment of the diameter would not be necessary. In a typical T-joint, the length of the saddle-shaped line of the bracechord intersection is obviously greater than that of a circle produced by a plane cut. It follows that an increase in strength would be anticipated if the true length of the saddle were accounted for. In order to account for this effect, the saddle is approximated by two elliptic planes each making an angle ~b with the horizontal as illustrated in Fig. 3. The solution is approximate, for while the perimeter of the inclined ellipse is larger than the horizontal circle it is slightly smaller than the true length of the saddle. It can be shown that, after integrating the contributions to the ultimate moment based on the configuration shown in Fig. 3, the following result is obtained: 1

Mu = - ~ Fy Td 2 F(w)

tanh-l(sin6) sin 6

(4)

A comparison between eqns (3) and (4) shows that the effect of the chord curvature (and also the effect of the branch-to-chord diameter ratio/3) can be expressed as a function F(/3) where tanh-l(sin~b) F(B) = sin6 in which 25 = sin-t/3.

(5)

~j

~°

~J

~r C~

Q~

0

.~"

/

7L

0 "TI

~m

\

H. S. Mitri

74

Finally, to account for the angle between the chord and the bracing m e m b e r , 0, the length along the x-axis can be adjusted to (d + 2tw)/sin 0. Integration of the m o m e n t of shear yield forces along the perimeter yields

M,

= l--L- F Td2 tan-l;(1 -c°s2g}/sin2°)l/2 x/3 y s-~nOF(w) (sin2 0 -- COs2 6 ) 1/2

(6)

W h e n d~ = 90°, eqn (6) reduces to eqn (4). In general, F(/3, 0) =

tanh -~(1 - cos2~/sin 2 0) 1/2 (sin2 0 - cos26) 1/2

(7)

w h e n cos d} < sin 0. If this is not the case, then

F(/3, 0) =

tan-1 (cos 2 4~/sin2 0 - 1)1/2 (cos2 ~b- sin2 0) 1/2

(8)

3 SIMPLIFIED FORMULATION T h e function given in eqn (5) cannot be reduced to a simple function of/3, but can be closely represented by F,(/3) = 0.25(5 - (1 -/32) 1/2)

(9)

w h e r e the subscript a denotes an approximate fit. In spite of the coupling of/3 and 0 in eqns (7) and (8), the variations of F(/3, 0) s h o w n in Fig. 4 indicate that the coupling effects are relatively weak. T h u s an approximation of eqns (7) and (8) of the form Fa(/3). Fa(O) can be postulated, where F.(/3) is given by eqn (9) and a possible form of F~(O) is

F~(O) = 1 + 0.2

(2)2 - 0

(10)

w h e r e 0 is in radians. These results are shown by dotted lines in Fig. 4. T h e ultimate m o m e n t m a y then be written as

1 Td 2 M. = - ~ Fy s-~nOF(w) F~(~) F,(O) <-Mpb

(11)

w h e r e Mpb = plastic m o m e n t of the branch m e m b e r . For thin-chord walls it can be anticipated that chord wall deformations, especially near the crown of the joint, will be predominantly in a flexural

Ultimate in-plane moment capacity of T and Y tubular joints

75

1.5

1.459 1.4 Eqa. (7) and (8)

1.317

1.3 F, (~) • F, (0) - - - ~ 1.2

1.246

f

0=40- . - ~

L'/

1.0

0 =90' 0.9 I 0

I 0.2

I 0.4

t 0.6

I 0.8

1.0

B Fig. 4. E x a c t a n d a p p r o x i m a t e v a r i a t i o n s o f F([3,0).

m o d e and the shear failure m o d e assumed above will no longer apply. In the absence of a theoretical model accounting for this behaviour, a best-fit analysis with test results has been carried out to determine a further function F(y). It was found that F(y) = C/y would best represent the behaviour of thin-walled joints having y > C, where C = constant. A least-squares analysis yielded a value of C = 22.5. Thus, F(y) = 1.0 for y _ 22.5 (12) F(y) = 22"5for y > 22.5 y in which y =

D/2T. Equation (12) can now be included in eqn (11). 4 COMPARISON WITH OTHER RESULTS

For the purpose of comparison with test results, the ultimate strength is considered to be the maximum moment attained during the test, since this is the one usually reported in the literature. The author is aware of a total of 52

H. S. Mitri

76

TABLE 1 Database

Reference

No. of tests

No. of tests considered

7 8 9 10 11 12a

2 19 1 17 7 6

2 15 1 17 6 4

Total

52

45

aJapanese tests reported by Yura et al.12

TABLE 2 Tested Joint Specimen Data

No. 1 2 3 4 5 6

7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

Specimen no. 4C 1-90 4C1-135 8C1-135 8T1-90 8C2-90 8T2-90

4 5 6 7 8 9 10 11 12 13 14 16 17 18 19 A2 B2 C2 D2 E2

Ref.

D (mm)

T d (ram) (mm)

11

114.6 114.6 220.0 220.0 219"7 219-7

5.87 5.87 7.09 7.09 8.20 7.62

8

219-1 219-1 298"5 219.1 219.1 219.1 219.1 219.1 219"1 219.1 298"5 298.5 219"1 219-1 219.1 114.2 114.1 114.3 113.9 114.1

5.9 8"8 7.1 5"9 8.8 10-0 12-5 5-9 8.8 12.5 7.1 10.0 5"9 8-8 12.5 3.44 4.95 5.41 6.01 3.45

10

t (mm)

0

F (MPa)

[3

1 1 4 - 6 5.87 114.6 5.87 220.0 7.09 220.0 7.09 219"7 8.20 219-7 7-62

90 45 45 90 90 90

210 207 276 276 172 328

1.0 1"0 1"0 1.0 1"0 1.0

9.8 15 414 9-8 17 713 15.5 95 819 15.5 83 587 13.4 65 691 14.4 113 374

71-6 71-6 101"6 101-6 101.6 101.6 101.6 139.7 139.7 139.7 193"7 193.7 177.8 177.8 177.8 48.3 48-3 48-3 48-3 60-3

90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90

314 422 294 305 367 368 404 314 422 392 296 294 314 422 392 347 329 333 352 388

0.33 0.33 0.34 0-46 0"46 0"46 0.46 0.64 0-64 0.64 0-65 0-81 0-81 0.81 0.81 0.42 0.42 0.42 0.42 0.53

18.6 12.4 21"0 18.6 12.4 11"0 8"8 18"6 12"4 8.8 21-0 14-9 18-6 12-4 8"8 16.6 11.5 10.5 9.5 16.5

18.5 18"5 16"0 16.0 16.0 16.0 16-0 17.5 17.5 17.5 7" 1 7.1 16"0 16.0 16.0 4.0 4.0 4-0 4.0 5-0

y

M (kNmm)

8 240 17 756 14 323 11 674 25 800 34924 53 955 25 800 58 860 88 290 53 465 85 641 40 515 98 100 160 884 2 240 2 060 2 350 2 980 3 870

77

Ultimate in-plane moment capacity of T and Y tubular joints TABLE 2.--contd.

No.

Specimen no.

D (ram)

T d (ram) (mm)

t (ram)

0

F (MPa)

27 28 29 30 31 32 33 34 35 36 37 38

F2 G2 H2 J2 K2 L2 M2 N2 P2 Q2 R2 $2

10

114.1 114.0 114.2 114.1 114.3 114.1 114.2 114.3 114.0 114.2 114.1 114.1

4.92 6.05 3-45 4.92 5-41 6-03 3-42 5.41 5-96 3-42 4.95 5.93

60.3 60.3 76-1 76.1 76.1 76-1 88-9 88.9 88-9 114-3 114.3 114.3

5.0 5-0 4.5 4.5 4.5 5.0 5.0 5.0 5.0 5.0 5.0 5.0

90 90 90 90 90 90 90 90 90 90 90 90

320 349 356 330 342 362 347 345 361 341 335 359

0.53 0-53 .0-67 0.67 0.67 0.67 0-78 0.78 0.78 1.0 1-0 1.0

39

1-7

9

407.7

8.05

274.3

6.6

90

331

0.67 25.3

40 41 42 43

B-70--0.2 B-70--0.4 B-100-0.2 B-100--0.4

12

318.5 318.5 457-2 457.2

4.4 4.4 4.8 4.8

60.5 139-8 89.1 165.2

nr a nr nr nr

90 90 90 90

441 441 402 402

0.19 0.44 0-20 0-36

36.2 36.2 47.6 47.6

3 332 14 896 6 082 18 040

44 45

A17 A19

7

508.0 508.0

7-9 7.9

168.3 168.3

nr nr

90 90

324 324

0.33 32-2 0.33 32.2

36 890 35 903

Ref.

[3

M ~/ (kNmm) 11-5 9.4 16.6 11.5 10-5 9-0 16-0 10.5 9.5 16-7 11-5 9.6

5 5 4 7 9 9 7 12 12 12 18 19

660 220 470 450 700 090 020 810 740 500 980 800

119603

Conversion factors: 1 mm = 0.039 4 in, 1 MPa = 0-145 ksi, I kN mm = 8.84 Ib in. anr = N o t reported.

joints between circular tubes which have been tested under in-plane bending. 7-12 Forty-five of these were considered to form a sound database. Table 1 lists the sources, and the complete physical joint data are given in Table 2. The tests that were ruled out were as follows: (1) Specimen 8C1-90 tested by Toprac 11experienced a premature failure due to the short length of the chord leg used on one side. The chord was deformed to an oval with its larger diameter in the plane of the joint. (2) Tests 1, 2 and 3 of Gibstein 8 were excluded as a result of branch failure. Joint No. 15 was also eliminated due to accidental cracks in the weld. (3) Two of the six tests carried out in Japan were excluded by Yura et al. 12 The theoretical ultimate moment Mu was calculated using eqn (11) with the function of eqns (12) included. Some difficulty was encountered in the evaluation of F(w), since weld sizes are seldom reported in the literature. As a measure of weld size, therefore, twin eqn (3) was taken as the smaller of the

78

H. S. Mitri

150

-

M

(Mo/

ave

1 021

/

- -

:

/ o.1o,

100

M (kN-m) (test)

/

• • • []

/

• / /

50

--

/.,

Ref. 11 Ref.8 Ref.lO Ref.9

z~ R e f . 1 2 o Ref.7

I 50

I 100

I 150

M. ( k N - m )

Fig. 5. Comparisonwith test results.

branch or chord thicknesses.13 In the case of six tests (Nos 40-45), the brace wall thicknesses were not given, and t,, was taken as the chord wall thickness. Figure 5 compares the calculated and test values of M.. The mean value of the test to theory ratio is 1.021 with a coefficient of variation of 0.102. Some design recommendations5'6'14 for in-plane bending make use of the following formula with some minor variations:

( r: d ] ~T":

M, = 6.1Fr \ sinO ]

(13)

Comparison of this with the database given in Table 1 gives a test-topredicted mean of 0.948 with a coefficient of variation of 0-156. While a smaller variation of 0.121 based on a sample of 40 results has been given in Ref. 6 for eqn (13), the coefficient of variation of 0-102 found for eqn (11) represents a significant improvement over either of these results.

Ultimate in-plane moment capacityof T and Y tubularjoints

79

5 CONCLUSIONS T h e ultimate in-plane bending m o m e n t on a T o r Y t u b u l a r obtained from 1

Td 2

M~ = --~ Fy s-~nO F(w) F~(fl) Fa(O)F(3~)<-Mpb

joint can be

(14)

w h e r e the four functions are given in eqns (3), (9), (10) and (12), respectively. While of m o r e complex form, this gives a significantly improved correlation with test data than a widely used design formula. The database contained only two results for Y joints (0 ~: ~-/2) and additional data for such cases are needed. The use of Fa(O) = 1.0 for such cases should provide a conservative strength estimate.

REFERENCES 1. British Standards Institution, BS 6235: Code of practice for fixed offshore structures, London, BSI, 1982. 2. Det Norske Veritas, Rules for the design, construction and inspection of fixed offshore structures, 1977. 3. American Petroleum Institute, Recommended practice for planning, designing and constructing fixed offshore platforms, APIRP2A, 15th edition, October 1984. 4. Kurobane, Y., Makino, Y. & Ochi, K., Ultimate resistance of unstiffened tubular joints, J. Struct. Engng, Trans. ASCE, 110, no. 2 (1984) 385--400. 5. Underwater Engineering Group Offshore Research, Design of tubular joints for offshore structures, Construction Industry Research and Information Service, UK, 3 volumes, 1985. 6. Yura, J., Connections with Round Tubes, Proc. Symp. on Hollow Structural Sections in Building Construction, ASCE, Chicago, September 1985. 7. Billington, C. J., Research into composite tubular construction for offshore jacket structures, J. Construct. Steel Res., 1, no. 1 (September 1980) 18-26. 8. Gibstein, M. B., The static strength of T-joints subjected to in-plane bending, DnV Report No. 76-137, 1976. 9. Hoadley, P. W. & Yura, J., Ultimate strength of tubular joints subjected to combined loads, Department of Civil Engineering, The University of Texas at Austin, PMFSEL Report 83-3, 1983. 10. Stamenkovic, A. & Sparrow, K. D., Load interaction in T-joints of steel circular hollow sections, J. Struct. Engng, Trans. ASCE, 109, no. 9 (1983) 2192-204. 11. Toprac, A. A., An investigation of welded steel pipe connections, WRC Bull., 71 (August 1961) 15-34.

80

H. S. Mitri

12. Yura, J., Zettlemoyer, N. & Edwards, I. F., Ultimate capacity of circular tubular joints, J. Struct. Div., Trans. A S C E , 107, no. ST10 (1981) 1965--84. 13. Wardenier, J., Hollow Section Joints, Delft University Press, Delft, The Netherlands, 1982. 14. Billington, C. J., Minaz, L. W. & Tebett, I. E., Background to new formulas for the ultimate limit state of tubular joints, J. Petroleum Techn., January (1984) 147-56.