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Behaviour of axially loaded tubular V-joints
J. Construct. Steel Research 16 (1990) 89-109
Behaviour of Axially Loaded Tubular V-Joints S. Scola, R. G. R e d w o o d Department of Civil Engineering and Applied Mechanics. McGill University. Montreal. Qurbec. Canada H3A 2K6
&
H. S. Mitri Department of Mining and Metallurgical Engineering, McGill University, Montreal. Qurbec, Canada H3A 2A7 (Received 18 September 1989; accepted 9 March 1990)
A BSTRA CT The results of an experimental test program comprising seven tubular V-joints and five tubular T-joints consisting of circular hollow sections and subject to branch axial loading are reported. The tested specimens had branch-to-chord diameter ratios varying from 0.22 to 0.65, and chord radius-to-thickness ratios of 13 to 23. The angle between branches of the V-joints was 60, 90 or 120 degrees. The behaviour of the joints is examined through a comparison of ultimate strengths, stiffness characteristics and hotspot stresses of comparable T and V specimens. Addition of a loaded out-of-plane branch member to a T-joint increases the strength of the T-joint when the angle between the branches is low, and decreases it when the angle is large.
NOTATION d D Fy gt L Pu
Branch diameter Chord diameter Yield stress Transverse gap dimension (measured around circumference) Chord length Ultimate strength 89
J. Construct. Steel Research 0143-974X/90/$03.50 ~ 1990 Elsevier Science Publishers Ltd, England. Printed in Great Britain
90
S. Scola, R. G. Redwood. H, S. Mitri
Qt3 t T
Dimensionless parameter (see Appendix 2) Branch wall thickness Chord wall thickness
o~ c~,, /3 y 7-/ p. r d~
Chord length parameter = 2L/D Chord ovalization parameter Diameter ratio = d/D Chord wall thinness ratio = D / 2 T V-joint to T-joint SCF ratio V-joint to T-joint strength ratio Wall thickness ratio = t/T Out-of-plane or included angle
INTRODUCTION The presence of multiplanar joints in steel off-shore platforms is virtually inevitable. For the purpose of design, engineers have historically treated complex, multiplanar joints as a series of planar joints. For example, V-joints can be viewed as a pair of T-joints separated by an angle ~ as shown in Fig. 1. This approach has led researchers to focus on uniplanar joints and as a result relatively few studies of multiplanar joint behaviour have been reported in the literature. A most comprehensive review of both research work and design codes applicable to tubular joints can be found in a 1985 report from the UK Underwater Engineering G r o u p ( U E G ) . ~ Research has been focused on two areas. These are (1) stress prediction and in particular hotspot stress calculations for use in fatigue design; (2) d e v e l o p m e n t of ultimate strength equations. Although different theoretical and experimental approaches have been used, the two most popular have been the finite element m e t h o d (FEM) and experimental tests on steel models. Linear elastic FEM programs have been used to carry out parametric studies and to develop stress concentration factor (SCF) equations. Early equations were proposed by Reber z and Visser. 3 More complete studies were carried out by Kuang et al., 4 Gibstein, 5 and Wordsworth and Smedley. 6 Their proposed SCF equations for T-joints loaded in compression are found in Appendix 1. Early experimental studies such as those carried out at the University of Texas 7"s were aimed at increasing knowledge of joint fatigue behaviour.
Behaviour of axially loaded tubular V-ioints
91
branchl ~ c r o w n --~
t
D
l
saddle --~
Z End
View
D E n d View
"?' =D/ET
a =2L/D
chord __7 Elevation
L Section
T =t,/T
•
A-A
/~ - d / D
Fig. 1. Tubular joint nomenclature: (a) T-joint; (b) V-joint.
As the limit states design approach became more popular, more joints were tested to their ultimate static strength. Current strength design equations tend to express the ultimate strength of the joint in terms of branch axial load. The 1984 API 9 and 1986 AWS I° codes for T-joints shown in Appendix 2 are derived from lower bound equations proposed by Yura et al. tt in 1980. Mean static strength equations proposed by
92
S. Scola. R. G. Redwood. H. S. M,'tri
P
Chord
Reference which
brace
for
C~o a p p l i e s
P Z = L / ( R T ) '/-"
P sinO c o s 2 0
exp(-Z/O.6T)
All b r a c e s at a joint
ao=l.O
+ 0.7P s i n O ] Ref~e~ braoe for
CXo) 1.0 ao = 1 . 7 f o r =1.35 =1.0 =1.35 =2.4
which ~, applies
T-joints 0=60 ° =90" =120 ° =180 °
Fig. 2. Chord ovalizing parameter, ao, as defined by AWS. m
93
Behaviour of axially loaded tubular V-joints
Billington et al., ~ 2 0 c h i et al., ~3 and Yura ~4 are also shown in Appendix 2. The A W S C o d e proposes a strength equation directly applicable to multiplanar joints by including a chord ovalizing parameter, ao. which is shown in Fig. 2. Makino et al. 15 have c o m p a r e d the measured strengths of double K-joints with those of c o m p a r a b l e planar K-joints. A constant angle of ~b = 60 ° b e t w e e n the planes of the individual K branches was considered. This study showed how the relative strength diminishes in proportion to the transverse gap dimension, gt, defined in Fig. 1. The small amount of available data on V-joints provided the incentive for this study. A series of uniaxial compression tests on T-joints and V-joints was carried out and the results are discussed in this paper. The strength, stiffness, and stress concentration characteristics of both types of joints are c o m p a r e d , and an assessment of current design equations for T-joints and their applicability to V-joint design is made.
TESTING PROGRAM Seven V-joint specimens and five T-joint specimens were tested in uniaxial compression. The p a r a m e t e r s / 3 , y, oh, which are defined in Fig. 1, were considered important to V-joint behaviour. The above parameters were varied in their practical range, each assuming three values. Table 1 lists the specified parametric values of each V-joint specimen. Also listed are the
TABLE 1
Parametric Values Used in Testing Program Specimen
[3
3'
da
v1 v2 v3 v4 V5 v6 v7 T1 T2 T3 T4 T5
0.405 0-405 0-645 0.220 0.405 0.405 0.405 0-405 0.405 0-645 0.220 0-405
22-90 13.40 17.25 17.25 17-25 17.25 17.25 22-90 13-40 17.25 17.25 17.25
90° 90° 90° 90° 60° 120° 90°
94
.G" Scola, R. G. Redwood, H. S. Mitri
: ttnl,+-et++~tte+tin.+ machine! T ~
sets
~--[ i=]
of
ehannels
....
i
I
!~ j ~ l o a d i n g
cap
.//,'" ///
~
"~~__short
base
It-base l>eatn resting on st,rong floor
[. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
i
Fig,3. SchematicV-jointsetup. corresponding values for the five T-joints which were tested for comparative purposes. All the joints tested had a nominal chord diameter of 219.1 mm and branch diameters varying from 48.3 to 168-3 mm. Measured geometric properties are given in Table 2 together with measured mechanical properties of the chord material. Nominal branch thicknesses are given since the interiors of the branch tubes were inaccessible. The chord sections were c o l d - f o r m e d and subsequently stress-relieved whereas the branch m e m b e r s were cold-formed to final shape. All chord sections were specified as A S T M A53 G R B steel. Welding was carried out with E 7 0 X X ( E 4 8 0 X X in SI) electrodes and fillet welds were used. No weld failure was o b s e r v e d during testing. A schematic of a V-joint test setup is shown in Fig. 3. Loads were applied at hinge supports and transferred to the chord m e m b e r through two loading caps, spaced at a distance 2D + d apart. The chord was
Behaviour of axially loaded tubular V-joinL~
95
(a) (b) Fig. 4. V-joint in testing position: (a) hinge supports, loading cap, and diaphragm (b) base supports, base beam, lateral bracing.
TABLE 2 Geometric and Mechanical Properties of Chord Material
Specimen
D(mm)
d(tnm) TOnm)
VI V2 V3 V4 V5 V6 V7 T1 T2 T3 T4 T5
219-95 220-00 220-25 221)-35 220-40 219.90 220.50 219.85 219-95 220-00 220-25 219-60
89.1 89-3 142.3 49.0 89.6 89.3 89-8 89-0 89-3 141.8 48.7 89-0
4.92 8-24 6-315 6.34 6-39 6.39 6-32 4.94 8-21 6.40 6-37 6.39
t(mm) ch(deg.) E~(,MPa) 4.78 4,78 6+55 4,78 4-78 4-78 4.78 4-78 4-78 6.55 4.78 4-78
90 91) 90 90 60 120 90
355 400 327 327 327 327 327 335 400 327 327 327
F,(MPa) 465 482 458 458 458 458 458 465 482 458 458 458
9~
5. 5celia. R. G. Red~*ood. H.
_S. ~,!,rr~
Fig. 5. T-joint in testing position.
reinforced at the loading points by close-fitting internal diaphragms to prevent distortion of the chord m e m b e r at its ends. The two branches rested on hinges, and short base supports were fitted to specimens to a c c o m m o d a t e the different angles, and were connected to a base beam which rested on the strong floor. A V-joint in testing position is shown in Fig. 4. The T-joints were tested in a similar a r r a n g e m e n t to that of the V-joints, except that they were in the position shown in Fig. 5. A ball joint on the test machine head compressed the branch and the chord ~vas supported by two hinges placed on the machine base, and spaced apart a distance of 2D+d.
All loads were applied by a 2000 kN universal testing machine. A n initial load of approximately 3 kN was applied before testing to settle in the specimen anti obtain initial readings. Load increments of 20 to 25 kN were than applied quasi-statically. The load was held constant while recording data. Smaller increments were applied as the response became m o r e inelastic and the joint approached its ultimate resistance. Loads were recorded to the nearest 0.5 kN using the load cell integral to the testing machine. Deflections were measured by means of linear variable differential transformers ( L V D T ) . Two LVDTs were used on
Behaviour of axially loaded tubular V-]oims
97
supp°rting~ / )
~'-j~braneh~ (a)
,
LVDT
aluminium bracket hose clamp
~
---- l e v e l
plate
(b) Fig. 6.
LVDT
setup for measurement of branchpenetration:(a) V-joint; (b) T-joint.
each specimen to measure axial branch penetration. These LVDTs were placed alongside the branch for T-joints or across the branch for V-joints as shown in Fig. 6. Eight resistance strain gauges were placed on a vertical line passing through the saddle of the connection on every T-joint (Fig. 7). When possible, five sets of four gauges were placed on each V-joint. Two gauges
98
S. Scola. R. G. Redwood, H. S. Mitri
20
End
View
I t (a)
I
Elevation
Plan
(b)
Fig. 7. Strain gauge location: (a) V-joint; (b) T-joint.
were placed vertically at 45 ° intervals around the branch. The chord gauges were placed on lines radiating from the center of the branch perpendicular to the weld as shown in Fig. 7. The spacing of all gauges was chosen to c o n f o r m with the location r e c o m m e n d e d by the U K D e p a r t m e n t of Energy for S C F determination•
99
Behaviour of axially loaded tubular V-joints
TEST RESULTS Ultimate strength
The peak load was recorded in each test. For V-joints. the loads are given in terms of the axial force component in a branch. Results are presented in Table 3. Also shown in Table 3 are the ultimate joint strengths as predicted by the formulae proposed by Billington et al., 12 Ochi et al., 13 Yura 14 and the AWS. m The T-joint formulae were used to estimate V-joint strength in all cases except for the AWS code equation which can be specifically applied to V-joints. It is readily seen in Fig. 8 that the predictions are generally lower than the experimental joint strengths for T-joints. Not surprisingly, AWS
[] O O A
350
z
O c h i e t al. B i l l i n g t o n e t al. Yura AWS
0 300 i i
%'
~"
I I
250
?
a: ~
A J
200
I
T3
7" .-2" 150 I
T5 100 1 I
' T4 T1
50
0
I 50
I lO0
I 150
I 200
I 250
I 300
I 3:50
EXPERIMENTAL ULTIMATE STRENGTH (KN) Fig. 8. Comparison of T-joint predicted and experimental strength.
S. Scola. R. G. Redwood, H. S. Mitri
100
1.6
1,4
--
1.2
-
1.0
--
0.8
--
0.6 50
13
I
I
I
I
60
70
80
90
I
I
I
100
II0
120
(a) 1.6
1.4
--
1.2
--
1.0
---"4
0.8
-
16
0.6 0.2
I
I
I
I
0.3
0.4
0.5
0.6
(b) Fig. 9. V a r i a t i o n of relative s t r e n g t h ratio/x.
Behaviour of axially loaded tubular V-joints
101
1.6
1.4
• 3
_ ~ 1 . 3 4 - 0 . 6 9
gt/D
~
e7
----<._
1.2
# 1.0
~ e6
0.8
O6 0.0
I 0.1
I 0.2
I 0.3
I 0.4
I 0.5
I 0.6
I 0.7
gt/D (c) Fig. 9--contd.
values are consistently the lowest as they are based on lower bound equations as previously mentioned. Differences between the remaining three mean strength equations can be attributed to both differences in database screening standards and ultimate strength definition. Yura, ~4for instance, included a deformation limit in identifying ultimate loads. The best a g r e e m e n t with the T-joint test results appears to be provided by Ochi et al. ~3
Six out of seven V-joints sustained as much, or more, axial load as their comparable T-joints. This can be expressed as the V-joint strength to T-joint strength ratio, p., being equal to or greater than one for six of the seven joints listed in Table 3. The A W S formula predicted increases of strength for V-joints which were in all cases greater than those observed experimentally. Of particular concern are the ~ = 120 ° results where the predicted ~ was 1.18 but a decreased strength was recorded. The variation of the relative strength ratio ~. with the angle ~ and with the diameter ratio/3 is shown in Fig. 9, a and b. Because of the limited data for values of 4~ and/3 greater and less than the central values, the trends cannot be considered as firmly established. H o w e v e r the reduced strength ratio for 4~above 90 ° may be attributed to the tendency of both branches to ovalize the chord in the same sense. W h e n ~ is less than 90 ° the branches may tend to act as one m e m b e r , and hence the joint behaviour is m o r e like
1),
S. Scola. R. G. R e d w o o d . H. S. Mitri
TABLE 3 Ultimate Strength Predictions and Test Results (kN) Specimen
Billington et al. l_"
Ochi et al. 1 ~
Y u r a 14
,4 W S m
A V¢S Ix
Test
Test Ix
V1 V2 V3 V4 V5 V6 V7 T1 T2 T3 T4 T5
99.0 335" 1 225-7 113-1 164-9 164-7 161-4 100-7 332-7 231-3 113-9 164-5
115.8 334.7 284.6 125.9 180-0 179.8 176-7 116-6 342-4 291)-5 126-8 179-3
93-8 314-6 216.4 101-7 154.8 154.7 151.6 94.5 312-3 221.9 102.4 154.4
132-8 445-5 314.2 138.1 174. I 173.9 214.7 90. l 297.8 208.7 100.3 147.2
1.48 1-48 1.54 1-38 1.18 I. 18 1-48
131.5 383.7 452.9 122.0 238.8 177-4 206-3 115-2 330-5 328.7 122.3 208.6
1'14 l"16
1"38 1"00 1"14 0" 85" 0"99"
"Obtained by dividing the V-joint value by that of T5.
that of a T-joint with a large /3 value. Fig. 10 illustrates cross-section deformations supporting this interpretation. Fig. 9b shows considerable scatter in p. values at the central value of/3, with a possible trend to increasing strength of the V-joint with increase in /3. However, Fig. 9c shows a clear variation between tt and the size of the transverse gap, gt- This parameter may be written gt = 0-5D(4,-2 arcsin/3) and the best fit line to the data is /x = 1-34 - 0 . 6 9 g ] D
/x exceeds unity for smaller values ofgt for the reason discussed above for ~b < 9 0 °. The parameter gt was identified by Makino et al. 15 as a primary factor influencing the strength of double K-joints when compared with that of planar K-joints. The effect on K-joint strength took a similar form to this result for V-joints. Load-deformation Load-deformation curves are plotted in Figs 11 to 12. With the exception of V3, the deformations given represent the average of the two L V D T readings for branch axial penetration. Loads are normalized bv dividing them by Fy T 2. When examining y effects, loads are divided by Fv 12.
Beha viour of" a_rially loaded tubular V@)ints
(a)
1I)3
ibt
°-?
(c)
(d)
Fig. 10. Post-failure cross-sections: (a) T3; (b) V5; (c) V7: (d) V6, It can be seen that V-joints are generally stiffer than similar T-joints. Most V-joints reached ultimate load with less than 2 m m penetration whereas T-joint resistance peaked after 5 to 6 mm branch penetration. Reducing the y ratio increases both load carrying capacity and stiffness in T-joints as well as V-joints as shown in Fig. l l . Similar effects were noted with an increasing/3 ratio although the increases were larger for the V specimens: T3 carried 2-7 times more branch load than T4 while V3 sustained 3.7 times more than V4. It is interesting to note that the large branches of V3 did not penetrate the chord but rather ovalized it in such a way that the measured diameters lengthened and therefore negative penetration, i.e. axial elongation, was recorded (Fig. 12). Figure 13 shows the impact of the angle ~b on the response of the joint. In particular, it should be noted that the response of V5, with its higher flexibility and ultimate load, was similar to that of a T-joint with a high value of/3.
:+ X
3 5"-':>Li. R. (;. R:'J";+'+'.'J. H S. Mitt:
= YI ~7=22.91 , TI ('Y=22.91
.: Y2 (7:13.41 a T2 U~=13.4}
s Y7 (7=17.251 ,,, T5 (7=17.25}
4+ .i 1 ~,e --
L
7= 13.'t
/
35
f -
; = 1.'.25
~
;/=17.25
,
i
!
, =:~z.r~
7 =1~2.9
-5!m
500
1500 251111 :t500 4500 CHOt-,'D DEI"OI:D,IATION ( ,00 1 trim)
5500
6500
Film 1 I. Effect of 7 on e x p e r i m e n t a l l o a d - d e f l e c t i o n response.
TABLE
4
Stress (7¢mcentration Factors in C h o r d Specimen
(;ihmWeitt +
Kuang et al. 4
Wordsworth & SmedleyO
'1"l VI 1"2 ;2 "I"3 ','3 T4 ',4 "F5 \:5 V6 V7
22.25
23.50
23-50
7.13
7.92
8-52
17-96
16.21
I8-42
1(1-64
14.52
10-78
12.48
l 3.53
14.02
Exp.
16-116 33.07 7.811 8-O3 14-4l 8.29 8.69 14.29 16.38 16.66 8-011 11.87
~1~
2,65 1,02 0,57 1,65 1.01 0,49 0.72
Behaviour of axially loaded tubular V-/oints
105
40 o v3 ~ = . s 4 s ) • T3 ~ = . s 4 5 )
~ v4 ~ = . 2 z o ) • T~ ~ = . 2 2 o )
o -
v7 (~=.-~o5) TS LS=.~OS)
,8=.64,5
35
3O
.'>, zs
~z ,o 5
0 -aooo
-zooo
- tooo CHORD
o
tooo
DEFORMATION
zooo
3ooo
.~ooo
5o0,>
sooo
(O.O01rnrN)
Fig. 12. Effect of/3 on experimental load-deflection response.
Strain measurements
Chord stress concentration factors determined in accordance with the UK D e p a r t m e n t of Energy guidance notes are presented in Table 4. SCFs were calculated at all early loading stages (under 15%) of ultimate load and the highest values were retained. A slow decrease in SCFs was usually recorded which indicates the shortness of the linear elastic range of response of tubular joints. Table 4 also lists the SCFs calculated using available formulae. It should be noted that the small value of ot for the test specimens puts them outside the validity range of the formulae. This restriction is not too severe since all three formulae proposed low dependence on a. Most of the predictions of Kuang et al. 4 and Gibstein 5 were within 25% of T-joint experimental results, while those of Wordsworth and Smedley 6 were less accurate with the exception of the prediction for T5. Strain gauge studies on V-joints have been carried out on steel models by Dijkstra and de Back t6 and by Wordsworth and Smedley. 6 Neither of
S. Scola. R. G. Redwood, H. S. 3htrt
106 22 5 --
V5
: :
V6 L'7
--
T5
2=!20 ~ ) 2 : 90 = )
o: 6 0 ~ 175 o=,
~
"50
<
125
7=:
tO0
~
75
q
•
T5
Z 50
~5
I]
i0 0 0
2000
3000
CHORI) DEFORMATION
.I000
riO00
6000
(O.O01mm)
Fig. 13. Effect of ¢bon experimental load-deflection response.
those studies included a symmetric compressive loading. Recho and Brozetti 17presented a series of 16 finite element analyses of V-joints, three of which considered symmetric compressive loading. Their results indicated a lower SCF than for a similar T-joint and in some cases a 22.5 ° shift of the hotspot location. The highest strain recorded on V-joints always occurred at the chord exterior saddle. High strains at 45 ° recorded on V2, a specimen with parametric values similar to one of Recho and Brozetti's models, indicate the possible existence of a hotspot between 0 and 45°: Specimen V6 was the only one with high strain on both the back and crotch sides of the branch (see Fig. 1); all other specimens had low strain in the crotch region. The experimental V-joint SCF to T-joint SCF ratio, ~c, varied from 0.5 to 2.6. This would indicate that the values of SCFs for V-joints cannot be predicted with T-joint formulae. Nevertheless, the influence of the various geometric parameters on the SCFs seems to be similar. For instance, SCFs increase with increasing y and decrease with increasing/3. Measured SCFs decreased with increasing ~.
Behavio,tr of ~ially loaded tubular V-joints
t07
CONCLUSIONS The following conclusions can be drawn from the results presented: (1) V-joints are typically three to four times stiffer than comparable T-joints. (2) T-joint strength formulae are generally conservative when applied to V-joints. However the measured ultimate strength of V-joints was lower than that of the corresponding T-joint when the transverse gap dimension, g~, exceeded 0.50D. (3) The AWS code So factor appears to be too generous in its prediction of strength increase for V-joints over their comparable T-joints. (4) Although the effects of geometric ratios on SCFs appear to be similar for both types of joints, T-joint SCF formulae cannot be used to predict V-joint SCF. (5) The hotspot always occurs on the back side of V-joints, most often at the saddle, while the stresses in the crotch region tend to be much lower.
ACKNOWLEDGEMENTS The authors wish to acknowledge the financial support of the Natural Science and Research Council of Canada, both through its scholarship program and Grant A-3366.
REFERENCES 1. Underwater Engineering Group, Design of Tubular Joints for Offshore Structures, Vols I, 2, and 3. UEG Offshore Research, 6, Storey's Gate, Westminster, London, SWlP 3AV, 1985. 2. Reber, J. B., Ultimate strength design of tubular joints. J. Struct. Div., ASCE, 99(ST6) (June 1973) 1223-40. 3. Visser, W., On the structural design of tubular joints. Proc. Offshore Technology Conf., Paper 2117, Houston, TX, 6-8 May 1974, pp. 881-94. 4. Kuang, J. G., Potvin, A. B. & Leick, R. D., Stress concentration in tubular joints. Proc. 7th Offshore Technology Conf., Paper OTC 2205, Houston, TX, 5-8 May 1975. 5. Gibstein, M. B., Parametric stress analysis of T-joints. Proc. European Offshore Steel Research Seminar, Paper 26, Cambridge, UK, Nov. 1978. 6. Wordsworth, A. C. & Smedley, G. P., Stress concentration of unstiffened tubular joints. Proc. European Offshore Steel Research Seminar, Paper 31, Cambridge. UK, Nov. 1978.
S. Scola. R. G. Redwood. H. S. Mitri
108
7. Toprac, A. A.. Johnston, L. P. & Noel, J., Welded tubular corm :ctions: an investigation of stresses in T-joints. Welding J., suppl. (January 1966) 1-12. 8. Toprac, A. A., Natarajan, M., Erzurumlu, H. & Kanoo, A. L. J., Research in tubular joints: static and fatigue loads. Proc. Offshore Technology Conf., Paper 1062. Houston. TX, l&-21 May 1969, pp. 667-80. 9. American Petroleum Institute, Recommended Practice jbr Planning, Designing and Constructing Fixed Offshore Platforms. API RP2A, 15th edn, 1984. 10. American Welding Society, Structural Welding Code--Steel. ANS/AWS D1.1-86, AWS, Miami, FL, 1986. 11. Yura, J. A., Zettlemoyer, N. & Edwards, I. E., Ultimate capacity of tubular joints. Proc. 12th Offshore Technology Conf., Paper OTC 3690. Houston, TX, 5-8 May 1980. 12. Billington, C. J., Lalani, M. & Tebbett, I. E., Background to new formulas for the ultimate limit state of tubular joints. A PIM J. Petroleum Technology, 37(1) (January 1984) 147-56. 13. Ochi, K., Makino, Y. & Kurobane, Y., Basis for design of unstiffened tubular joints under axial brace loading. IIW Doc. XV-561-84, International Institute of Welding Annual Assembly Boston, MA, 15-21 July 1984. 14. Yura, J., Connections with round tubes. Proc. Syrup. on Hollow Structural Sections in Building Structures. ASCE, Chicago, 15-17 Sept. 1985. 15. Makino, Y., Kurobane, Y. & Ochi, K., Ultimate Capacity of Tubular Double K-Joints. Proc. Welding of Tubular Structures Conf., International Institute of Welding, Boston, MA, July 1984, pp. 451-8. 16. Dijkstra, O. D. & de Back, J., Fatigue strength of tubular T-joint and X-joint. Proc. 12th Offshore Technology Cot(., Paper OTC 3696, Houston, TX, 5-8 May 1980. 17. Recho, N. & Brozetti, J., Stress concentrations at tubular V-joints. Proc. Welding of Tubular Structures Conf., International Institute of Welding, Boston, MA, July 1984, pp. 517-24.
A P P E N D I X 1: STRESS C O N C E N T R A T I O N F A C T O R S . T - J O I N T Kuang et al. :4 chord SCF
=
1.981aw°SVe- l t ¢ y °'sos r1"333
for
7_
Gibstein: 5 chord SCF = a"°6[1.44 - 3.72(/3 - 0.47)e]y"S7r ''37
for
7_
t t 19
Behaviour of axially loaded tubular V-joints
W o r d s w o r t h a n d S m e d l e y : 6 c h o r d saddle SCF =/33,~-(6-78 - 6.42/3 L';2)
for
8_
APPENDIX 2
Mean strength formulae Billington et al. :~2 P, = (4.1 + 20.3/3) Qt3 Fy T 2 where Qt3 = 1.0
for /3 < 0-6
0.3 Q~ = /3(1 - 0.833/3)
for/3 > 0-6
Ochi et al.: ~3 P, = 4.83(1 + 4.94/32)(2-),) °233 (a/2) -''45 Fy T 2
Yura: 14 Pu = (3.1 + 20.9/3) 6 T2
Lower bound strength formula AWS: L° P, = 18.85
--
+
Q~ x 0.7(a,, - 1) /3FvT 2
w h e r e Q~ is d e f i n e d as per Billington et al., a b o v e , and ao is defined in Fig. 2. (Note: the c o n s t a n t 18.85 includes the 1.8 factor of safety used by AWS.) A P I , 9 Y u r a et al.: II
e . = (3-4 + 19/3) Fy T z
Behaviour of Axially Loaded Tubular V-Joints S. Scola, R. G. R e d w o o d Department of Civil Engineering and Applied Mechanics. McGill University. Montreal. Qurbec. Canada H3A 2K6
&
H. S. Mitri Department of Mining and Metallurgical Engineering, McGill University, Montreal. Qurbec, Canada H3A 2A7 (Received 18 September 1989; accepted 9 March 1990)
A BSTRA CT The results of an experimental test program comprising seven tubular V-joints and five tubular T-joints consisting of circular hollow sections and subject to branch axial loading are reported. The tested specimens had branch-to-chord diameter ratios varying from 0.22 to 0.65, and chord radius-to-thickness ratios of 13 to 23. The angle between branches of the V-joints was 60, 90 or 120 degrees. The behaviour of the joints is examined through a comparison of ultimate strengths, stiffness characteristics and hotspot stresses of comparable T and V specimens. Addition of a loaded out-of-plane branch member to a T-joint increases the strength of the T-joint when the angle between the branches is low, and decreases it when the angle is large.
NOTATION d D Fy gt L Pu
Branch diameter Chord diameter Yield stress Transverse gap dimension (measured around circumference) Chord length Ultimate strength 89
J. Construct. Steel Research 0143-974X/90/$03.50 ~ 1990 Elsevier Science Publishers Ltd, England. Printed in Great Britain
90
S. Scola, R. G. Redwood. H, S. Mitri
Qt3 t T
Dimensionless parameter (see Appendix 2) Branch wall thickness Chord wall thickness
o~ c~,, /3 y 7-/ p. r d~
Chord length parameter = 2L/D Chord ovalization parameter Diameter ratio = d/D Chord wall thinness ratio = D / 2 T V-joint to T-joint SCF ratio V-joint to T-joint strength ratio Wall thickness ratio = t/T Out-of-plane or included angle
INTRODUCTION The presence of multiplanar joints in steel off-shore platforms is virtually inevitable. For the purpose of design, engineers have historically treated complex, multiplanar joints as a series of planar joints. For example, V-joints can be viewed as a pair of T-joints separated by an angle ~ as shown in Fig. 1. This approach has led researchers to focus on uniplanar joints and as a result relatively few studies of multiplanar joint behaviour have been reported in the literature. A most comprehensive review of both research work and design codes applicable to tubular joints can be found in a 1985 report from the UK Underwater Engineering G r o u p ( U E G ) . ~ Research has been focused on two areas. These are (1) stress prediction and in particular hotspot stress calculations for use in fatigue design; (2) d e v e l o p m e n t of ultimate strength equations. Although different theoretical and experimental approaches have been used, the two most popular have been the finite element m e t h o d (FEM) and experimental tests on steel models. Linear elastic FEM programs have been used to carry out parametric studies and to develop stress concentration factor (SCF) equations. Early equations were proposed by Reber z and Visser. 3 More complete studies were carried out by Kuang et al., 4 Gibstein, 5 and Wordsworth and Smedley. 6 Their proposed SCF equations for T-joints loaded in compression are found in Appendix 1. Early experimental studies such as those carried out at the University of Texas 7"s were aimed at increasing knowledge of joint fatigue behaviour.
Behaviour of axially loaded tubular V-ioints
91
branchl ~ c r o w n --~
t
D
l
saddle --~
Z End
View
D E n d View
"?' =D/ET
a =2L/D
chord __7 Elevation
L Section
T =t,/T
•
A-A
/~ - d / D
Fig. 1. Tubular joint nomenclature: (a) T-joint; (b) V-joint.
As the limit states design approach became more popular, more joints were tested to their ultimate static strength. Current strength design equations tend to express the ultimate strength of the joint in terms of branch axial load. The 1984 API 9 and 1986 AWS I° codes for T-joints shown in Appendix 2 are derived from lower bound equations proposed by Yura et al. tt in 1980. Mean static strength equations proposed by
92
S. Scola. R. G. Redwood. H. S. M,'tri
P
Chord
Reference which
brace
for
C~o a p p l i e s
P Z = L / ( R T ) '/-"
P sinO c o s 2 0
exp(-Z/O.6T)
All b r a c e s at a joint
ao=l.O
+ 0.7P s i n O ] Ref~e~ braoe for
CXo) 1.0 ao = 1 . 7 f o r =1.35 =1.0 =1.35 =2.4
which ~, applies
T-joints 0=60 ° =90" =120 ° =180 °
Fig. 2. Chord ovalizing parameter, ao, as defined by AWS. m
93
Behaviour of axially loaded tubular V-joints
Billington et al., ~ 2 0 c h i et al., ~3 and Yura ~4 are also shown in Appendix 2. The A W S C o d e proposes a strength equation directly applicable to multiplanar joints by including a chord ovalizing parameter, ao. which is shown in Fig. 2. Makino et al. 15 have c o m p a r e d the measured strengths of double K-joints with those of c o m p a r a b l e planar K-joints. A constant angle of ~b = 60 ° b e t w e e n the planes of the individual K branches was considered. This study showed how the relative strength diminishes in proportion to the transverse gap dimension, gt, defined in Fig. 1. The small amount of available data on V-joints provided the incentive for this study. A series of uniaxial compression tests on T-joints and V-joints was carried out and the results are discussed in this paper. The strength, stiffness, and stress concentration characteristics of both types of joints are c o m p a r e d , and an assessment of current design equations for T-joints and their applicability to V-joint design is made.
TESTING PROGRAM Seven V-joint specimens and five T-joint specimens were tested in uniaxial compression. The p a r a m e t e r s / 3 , y, oh, which are defined in Fig. 1, were considered important to V-joint behaviour. The above parameters were varied in their practical range, each assuming three values. Table 1 lists the specified parametric values of each V-joint specimen. Also listed are the
TABLE 1
Parametric Values Used in Testing Program Specimen
[3
3'
da
v1 v2 v3 v4 V5 v6 v7 T1 T2 T3 T4 T5
0.405 0-405 0-645 0.220 0.405 0.405 0.405 0-405 0.405 0-645 0.220 0-405
22-90 13.40 17.25 17.25 17-25 17.25 17.25 22-90 13-40 17.25 17.25 17.25
90° 90° 90° 90° 60° 120° 90°
94
.G" Scola, R. G. Redwood, H. S. Mitri
: ttnl,+-et++~tte+tin.+ machine! T ~
sets
~--[ i=]
of
ehannels
....
i
I
!~ j ~ l o a d i n g
cap
.//,'" ///
~
"~~__short
base
It-base l>eatn resting on st,rong floor
[. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
i
Fig,3. SchematicV-jointsetup. corresponding values for the five T-joints which were tested for comparative purposes. All the joints tested had a nominal chord diameter of 219.1 mm and branch diameters varying from 48.3 to 168-3 mm. Measured geometric properties are given in Table 2 together with measured mechanical properties of the chord material. Nominal branch thicknesses are given since the interiors of the branch tubes were inaccessible. The chord sections were c o l d - f o r m e d and subsequently stress-relieved whereas the branch m e m b e r s were cold-formed to final shape. All chord sections were specified as A S T M A53 G R B steel. Welding was carried out with E 7 0 X X ( E 4 8 0 X X in SI) electrodes and fillet welds were used. No weld failure was o b s e r v e d during testing. A schematic of a V-joint test setup is shown in Fig. 3. Loads were applied at hinge supports and transferred to the chord m e m b e r through two loading caps, spaced at a distance 2D + d apart. The chord was
Behaviour of axially loaded tubular V-joinL~
95
(a) (b) Fig. 4. V-joint in testing position: (a) hinge supports, loading cap, and diaphragm (b) base supports, base beam, lateral bracing.
TABLE 2 Geometric and Mechanical Properties of Chord Material
Specimen
D(mm)
d(tnm) TOnm)
VI V2 V3 V4 V5 V6 V7 T1 T2 T3 T4 T5
219-95 220-00 220-25 221)-35 220-40 219.90 220.50 219.85 219-95 220-00 220-25 219-60
89.1 89-3 142.3 49.0 89.6 89.3 89-8 89-0 89-3 141.8 48.7 89-0
4.92 8-24 6-315 6.34 6-39 6.39 6-32 4.94 8-21 6.40 6-37 6.39
t(mm) ch(deg.) E~(,MPa) 4.78 4,78 6+55 4,78 4-78 4-78 4.78 4-78 4-78 6.55 4.78 4-78
90 91) 90 90 60 120 90
355 400 327 327 327 327 327 335 400 327 327 327
F,(MPa) 465 482 458 458 458 458 458 465 482 458 458 458
9~
5. 5celia. R. G. Red~*ood. H.
_S. ~,!,rr~
Fig. 5. T-joint in testing position.
reinforced at the loading points by close-fitting internal diaphragms to prevent distortion of the chord m e m b e r at its ends. The two branches rested on hinges, and short base supports were fitted to specimens to a c c o m m o d a t e the different angles, and were connected to a base beam which rested on the strong floor. A V-joint in testing position is shown in Fig. 4. The T-joints were tested in a similar a r r a n g e m e n t to that of the V-joints, except that they were in the position shown in Fig. 5. A ball joint on the test machine head compressed the branch and the chord ~vas supported by two hinges placed on the machine base, and spaced apart a distance of 2D+d.
All loads were applied by a 2000 kN universal testing machine. A n initial load of approximately 3 kN was applied before testing to settle in the specimen anti obtain initial readings. Load increments of 20 to 25 kN were than applied quasi-statically. The load was held constant while recording data. Smaller increments were applied as the response became m o r e inelastic and the joint approached its ultimate resistance. Loads were recorded to the nearest 0.5 kN using the load cell integral to the testing machine. Deflections were measured by means of linear variable differential transformers ( L V D T ) . Two LVDTs were used on
Behaviour of axially loaded tubular V-]oims
97
supp°rting~ / )
~'-j~braneh~ (a)
,
LVDT
aluminium bracket hose clamp
~
---- l e v e l
plate
(b) Fig. 6.
LVDT
setup for measurement of branchpenetration:(a) V-joint; (b) T-joint.
each specimen to measure axial branch penetration. These LVDTs were placed alongside the branch for T-joints or across the branch for V-joints as shown in Fig. 6. Eight resistance strain gauges were placed on a vertical line passing through the saddle of the connection on every T-joint (Fig. 7). When possible, five sets of four gauges were placed on each V-joint. Two gauges
98
S. Scola. R. G. Redwood, H. S. Mitri
20
End
View
I t (a)
I
Elevation
Plan
(b)
Fig. 7. Strain gauge location: (a) V-joint; (b) T-joint.
were placed vertically at 45 ° intervals around the branch. The chord gauges were placed on lines radiating from the center of the branch perpendicular to the weld as shown in Fig. 7. The spacing of all gauges was chosen to c o n f o r m with the location r e c o m m e n d e d by the U K D e p a r t m e n t of Energy for S C F determination•
99
Behaviour of axially loaded tubular V-joints
TEST RESULTS Ultimate strength
The peak load was recorded in each test. For V-joints. the loads are given in terms of the axial force component in a branch. Results are presented in Table 3. Also shown in Table 3 are the ultimate joint strengths as predicted by the formulae proposed by Billington et al., 12 Ochi et al., 13 Yura 14 and the AWS. m The T-joint formulae were used to estimate V-joint strength in all cases except for the AWS code equation which can be specifically applied to V-joints. It is readily seen in Fig. 8 that the predictions are generally lower than the experimental joint strengths for T-joints. Not surprisingly, AWS
[] O O A
350
z
O c h i e t al. B i l l i n g t o n e t al. Yura AWS
0 300 i i
%'
~"
I I
250
?
a: ~
A J
200
I
T3
7" .-2" 150 I
T5 100 1 I
' T4 T1
50
0
I 50
I lO0
I 150
I 200
I 250
I 300
I 3:50
EXPERIMENTAL ULTIMATE STRENGTH (KN) Fig. 8. Comparison of T-joint predicted and experimental strength.
S. Scola. R. G. Redwood, H. S. Mitri
100
1.6
1,4
--
1.2
-
1.0
--
0.8
--
0.6 50
13
I
I
I
I
60
70
80
90
I
I
I
100
II0
120
(a) 1.6
1.4
--
1.2
--
1.0
---"4
0.8
-
16
0.6 0.2
I
I
I
I
0.3
0.4
0.5
0.6
(b) Fig. 9. V a r i a t i o n of relative s t r e n g t h ratio/x.
Behaviour of axially loaded tubular V-joints
101
1.6
1.4
• 3
_ ~ 1 . 3 4 - 0 . 6 9
gt/D
~
e7
----<._
1.2
# 1.0
~ e6
0.8
O6 0.0
I 0.1
I 0.2
I 0.3
I 0.4
I 0.5
I 0.6
I 0.7
gt/D (c) Fig. 9--contd.
values are consistently the lowest as they are based on lower bound equations as previously mentioned. Differences between the remaining three mean strength equations can be attributed to both differences in database screening standards and ultimate strength definition. Yura, ~4for instance, included a deformation limit in identifying ultimate loads. The best a g r e e m e n t with the T-joint test results appears to be provided by Ochi et al. ~3
Six out of seven V-joints sustained as much, or more, axial load as their comparable T-joints. This can be expressed as the V-joint strength to T-joint strength ratio, p., being equal to or greater than one for six of the seven joints listed in Table 3. The A W S formula predicted increases of strength for V-joints which were in all cases greater than those observed experimentally. Of particular concern are the ~ = 120 ° results where the predicted ~ was 1.18 but a decreased strength was recorded. The variation of the relative strength ratio ~. with the angle ~ and with the diameter ratio/3 is shown in Fig. 9, a and b. Because of the limited data for values of 4~ and/3 greater and less than the central values, the trends cannot be considered as firmly established. H o w e v e r the reduced strength ratio for 4~above 90 ° may be attributed to the tendency of both branches to ovalize the chord in the same sense. W h e n ~ is less than 90 ° the branches may tend to act as one m e m b e r , and hence the joint behaviour is m o r e like
1),
S. Scola. R. G. R e d w o o d . H. S. Mitri
TABLE 3 Ultimate Strength Predictions and Test Results (kN) Specimen
Billington et al. l_"
Ochi et al. 1 ~
Y u r a 14
,4 W S m
A V¢S Ix
Test
Test Ix
V1 V2 V3 V4 V5 V6 V7 T1 T2 T3 T4 T5
99.0 335" 1 225-7 113-1 164-9 164-7 161-4 100-7 332-7 231-3 113-9 164-5
115.8 334.7 284.6 125.9 180-0 179.8 176-7 116-6 342-4 291)-5 126-8 179-3
93-8 314-6 216.4 101-7 154.8 154.7 151.6 94.5 312-3 221.9 102.4 154.4
132-8 445-5 314.2 138.1 174. I 173.9 214.7 90. l 297.8 208.7 100.3 147.2
1.48 1-48 1.54 1-38 1.18 I. 18 1-48
131.5 383.7 452.9 122.0 238.8 177-4 206-3 115-2 330-5 328.7 122.3 208.6
1'14 l"16
1"38 1"00 1"14 0" 85" 0"99"
"Obtained by dividing the V-joint value by that of T5.
that of a T-joint with a large /3 value. Fig. 10 illustrates cross-section deformations supporting this interpretation. Fig. 9b shows considerable scatter in p. values at the central value of/3, with a possible trend to increasing strength of the V-joint with increase in /3. However, Fig. 9c shows a clear variation between tt and the size of the transverse gap, gt- This parameter may be written gt = 0-5D(4,-2 arcsin/3) and the best fit line to the data is /x = 1-34 - 0 . 6 9 g ] D
/x exceeds unity for smaller values ofgt for the reason discussed above for ~b < 9 0 °. The parameter gt was identified by Makino et al. 15 as a primary factor influencing the strength of double K-joints when compared with that of planar K-joints. The effect on K-joint strength took a similar form to this result for V-joints. Load-deformation Load-deformation curves are plotted in Figs 11 to 12. With the exception of V3, the deformations given represent the average of the two L V D T readings for branch axial penetration. Loads are normalized bv dividing them by Fy T 2. When examining y effects, loads are divided by Fv 12.
Beha viour of" a_rially loaded tubular V@)ints
(a)
1I)3
ibt
°-?
(c)
(d)
Fig. 10. Post-failure cross-sections: (a) T3; (b) V5; (c) V7: (d) V6, It can be seen that V-joints are generally stiffer than similar T-joints. Most V-joints reached ultimate load with less than 2 m m penetration whereas T-joint resistance peaked after 5 to 6 mm branch penetration. Reducing the y ratio increases both load carrying capacity and stiffness in T-joints as well as V-joints as shown in Fig. l l . Similar effects were noted with an increasing/3 ratio although the increases were larger for the V specimens: T3 carried 2-7 times more branch load than T4 while V3 sustained 3.7 times more than V4. It is interesting to note that the large branches of V3 did not penetrate the chord but rather ovalized it in such a way that the measured diameters lengthened and therefore negative penetration, i.e. axial elongation, was recorded (Fig. 12). Figure 13 shows the impact of the angle ~b on the response of the joint. In particular, it should be noted that the response of V5, with its higher flexibility and ultimate load, was similar to that of a T-joint with a high value of/3.
:+ X
3 5"-':>Li. R. (;. R:'J";+'+'.'J. H S. Mitt:
= YI ~7=22.91 , TI ('Y=22.91
.: Y2 (7:13.41 a T2 U~=13.4}
s Y7 (7=17.251 ,,, T5 (7=17.25}
4+ .i 1 ~,e --
L
7= 13.'t
/
35
f -
; = 1.'.25
~
;/=17.25
,
i
!
, =:~z.r~
7 =1~2.9
-5!m
500
1500 251111 :t500 4500 CHOt-,'D DEI"OI:D,IATION ( ,00 1 trim)
5500
6500
Film 1 I. Effect of 7 on e x p e r i m e n t a l l o a d - d e f l e c t i o n response.
TABLE
4
Stress (7¢mcentration Factors in C h o r d Specimen
(;ihmWeitt +
Kuang et al. 4
Wordsworth & SmedleyO
'1"l VI 1"2 ;2 "I"3 ','3 T4 ',4 "F5 \:5 V6 V7
22.25
23.50
23-50
7.13
7.92
8-52
17-96
16.21
I8-42
1(1-64
14.52
10-78
12.48
l 3.53
14.02
Exp.
16-116 33.07 7.811 8-O3 14-4l 8.29 8.69 14.29 16.38 16.66 8-011 11.87
~1~
2,65 1,02 0,57 1,65 1.01 0,49 0.72
Behaviour of axially loaded tubular V-/oints
105
40 o v3 ~ = . s 4 s ) • T3 ~ = . s 4 5 )
~ v4 ~ = . 2 z o ) • T~ ~ = . 2 2 o )
o -
v7 (~=.-~o5) TS LS=.~OS)
,8=.64,5
35
3O
.'>, zs
~z ,o 5
0 -aooo
-zooo
- tooo CHORD
o
tooo
DEFORMATION
zooo
3ooo
.~ooo
5o0,>
sooo
(O.O01rnrN)
Fig. 12. Effect of/3 on experimental load-deflection response.
Strain measurements
Chord stress concentration factors determined in accordance with the UK D e p a r t m e n t of Energy guidance notes are presented in Table 4. SCFs were calculated at all early loading stages (under 15%) of ultimate load and the highest values were retained. A slow decrease in SCFs was usually recorded which indicates the shortness of the linear elastic range of response of tubular joints. Table 4 also lists the SCFs calculated using available formulae. It should be noted that the small value of ot for the test specimens puts them outside the validity range of the formulae. This restriction is not too severe since all three formulae proposed low dependence on a. Most of the predictions of Kuang et al. 4 and Gibstein 5 were within 25% of T-joint experimental results, while those of Wordsworth and Smedley 6 were less accurate with the exception of the prediction for T5. Strain gauge studies on V-joints have been carried out on steel models by Dijkstra and de Back t6 and by Wordsworth and Smedley. 6 Neither of
S. Scola. R. G. Redwood, H. S. 3htrt
106 22 5 --
V5
: :
V6 L'7
--
T5
2=!20 ~ ) 2 : 90 = )
o: 6 0 ~ 175 o=,
~
"50
<
125
7=:
tO0
~
75
q
•
T5
Z 50
~5
I]
i0 0 0
2000
3000
CHORI) DEFORMATION
.I000
riO00
6000
(O.O01mm)
Fig. 13. Effect of ¢bon experimental load-deflection response.
those studies included a symmetric compressive loading. Recho and Brozetti 17presented a series of 16 finite element analyses of V-joints, three of which considered symmetric compressive loading. Their results indicated a lower SCF than for a similar T-joint and in some cases a 22.5 ° shift of the hotspot location. The highest strain recorded on V-joints always occurred at the chord exterior saddle. High strains at 45 ° recorded on V2, a specimen with parametric values similar to one of Recho and Brozetti's models, indicate the possible existence of a hotspot between 0 and 45°: Specimen V6 was the only one with high strain on both the back and crotch sides of the branch (see Fig. 1); all other specimens had low strain in the crotch region. The experimental V-joint SCF to T-joint SCF ratio, ~c, varied from 0.5 to 2.6. This would indicate that the values of SCFs for V-joints cannot be predicted with T-joint formulae. Nevertheless, the influence of the various geometric parameters on the SCFs seems to be similar. For instance, SCFs increase with increasing y and decrease with increasing/3. Measured SCFs decreased with increasing ~.
Behavio,tr of ~ially loaded tubular V-joints
t07
CONCLUSIONS The following conclusions can be drawn from the results presented: (1) V-joints are typically three to four times stiffer than comparable T-joints. (2) T-joint strength formulae are generally conservative when applied to V-joints. However the measured ultimate strength of V-joints was lower than that of the corresponding T-joint when the transverse gap dimension, g~, exceeded 0.50D. (3) The AWS code So factor appears to be too generous in its prediction of strength increase for V-joints over their comparable T-joints. (4) Although the effects of geometric ratios on SCFs appear to be similar for both types of joints, T-joint SCF formulae cannot be used to predict V-joint SCF. (5) The hotspot always occurs on the back side of V-joints, most often at the saddle, while the stresses in the crotch region tend to be much lower.
ACKNOWLEDGEMENTS The authors wish to acknowledge the financial support of the Natural Science and Research Council of Canada, both through its scholarship program and Grant A-3366.
REFERENCES 1. Underwater Engineering Group, Design of Tubular Joints for Offshore Structures, Vols I, 2, and 3. UEG Offshore Research, 6, Storey's Gate, Westminster, London, SWlP 3AV, 1985. 2. Reber, J. B., Ultimate strength design of tubular joints. J. Struct. Div., ASCE, 99(ST6) (June 1973) 1223-40. 3. Visser, W., On the structural design of tubular joints. Proc. Offshore Technology Conf., Paper 2117, Houston, TX, 6-8 May 1974, pp. 881-94. 4. Kuang, J. G., Potvin, A. B. & Leick, R. D., Stress concentration in tubular joints. Proc. 7th Offshore Technology Conf., Paper OTC 2205, Houston, TX, 5-8 May 1975. 5. Gibstein, M. B., Parametric stress analysis of T-joints. Proc. European Offshore Steel Research Seminar, Paper 26, Cambridge, UK, Nov. 1978. 6. Wordsworth, A. C. & Smedley, G. P., Stress concentration of unstiffened tubular joints. Proc. European Offshore Steel Research Seminar, Paper 31, Cambridge. UK, Nov. 1978.
S. Scola. R. G. Redwood. H. S. Mitri
108
7. Toprac, A. A.. Johnston, L. P. & Noel, J., Welded tubular corm :ctions: an investigation of stresses in T-joints. Welding J., suppl. (January 1966) 1-12. 8. Toprac, A. A., Natarajan, M., Erzurumlu, H. & Kanoo, A. L. J., Research in tubular joints: static and fatigue loads. Proc. Offshore Technology Conf., Paper 1062. Houston. TX, l&-21 May 1969, pp. 667-80. 9. American Petroleum Institute, Recommended Practice jbr Planning, Designing and Constructing Fixed Offshore Platforms. API RP2A, 15th edn, 1984. 10. American Welding Society, Structural Welding Code--Steel. ANS/AWS D1.1-86, AWS, Miami, FL, 1986. 11. Yura, J. A., Zettlemoyer, N. & Edwards, I. E., Ultimate capacity of tubular joints. Proc. 12th Offshore Technology Conf., Paper OTC 3690. Houston, TX, 5-8 May 1980. 12. Billington, C. J., Lalani, M. & Tebbett, I. E., Background to new formulas for the ultimate limit state of tubular joints. A PIM J. Petroleum Technology, 37(1) (January 1984) 147-56. 13. Ochi, K., Makino, Y. & Kurobane, Y., Basis for design of unstiffened tubular joints under axial brace loading. IIW Doc. XV-561-84, International Institute of Welding Annual Assembly Boston, MA, 15-21 July 1984. 14. Yura, J., Connections with round tubes. Proc. Syrup. on Hollow Structural Sections in Building Structures. ASCE, Chicago, 15-17 Sept. 1985. 15. Makino, Y., Kurobane, Y. & Ochi, K., Ultimate Capacity of Tubular Double K-Joints. Proc. Welding of Tubular Structures Conf., International Institute of Welding, Boston, MA, July 1984, pp. 451-8. 16. Dijkstra, O. D. & de Back, J., Fatigue strength of tubular T-joint and X-joint. Proc. 12th Offshore Technology Cot(., Paper OTC 3696, Houston, TX, 5-8 May 1980. 17. Recho, N. & Brozetti, J., Stress concentrations at tubular V-joints. Proc. Welding of Tubular Structures Conf., International Institute of Welding, Boston, MA, July 1984, pp. 517-24.
A P P E N D I X 1: STRESS C O N C E N T R A T I O N F A C T O R S . T - J O I N T Kuang et al. :4 chord SCF
=
1.981aw°SVe- l t ¢ y °'sos r1"333
for
7_
Gibstein: 5 chord SCF = a"°6[1.44 - 3.72(/3 - 0.47)e]y"S7r ''37
for
7_
t t 19
Behaviour of axially loaded tubular V-joints
W o r d s w o r t h a n d S m e d l e y : 6 c h o r d saddle SCF =/33,~-(6-78 - 6.42/3 L';2)
for
8_
APPENDIX 2
Mean strength formulae Billington et al. :~2 P, = (4.1 + 20.3/3) Qt3 Fy T 2 where Qt3 = 1.0
for /3 < 0-6
0.3 Q~ = /3(1 - 0.833/3)
for/3 > 0-6
Ochi et al.: ~3 P, = 4.83(1 + 4.94/32)(2-),) °233 (a/2) -''45 Fy T 2
Yura: 14 Pu = (3.1 + 20.9/3) 6 T2
Lower bound strength formula AWS: L° P, = 18.85
--
+
Q~ x 0.7(a,, - 1) /3FvT 2
w h e r e Q~ is d e f i n e d as per Billington et al., a b o v e , and ao is defined in Fig. 2. (Note: the c o n s t a n t 18.85 includes the 1.8 factor of safety used by AWS.) A P I , 9 Y u r a et al.: II
e . = (3-4 + 19/3) Fy T z