66
STRENGTH AND STIFFNESS OF RHS BEAM TO RHS CONCRETE FILLED COLUMN JOINTS J. K. Szlendak, Bialystok Technical University, Poland ABSTRACT Composite connection made with RHS chord or column filled by concrete and branches with RHS steel profile are studied herein. The aim of this paper is deriving a simple theoretical formula for calculating the strength and stiffness of such joints. Test results of twelve connections in natural scale are described. Geometry and material properties of the tested joints are given. Theoretical solution of the joint strength and stiffness are proposed and the comparisons between theoretical and experimental results are presented. INTRODUCTION European Code EC 4 (1 ) makes possibility to design much more effective structures which combined advantages of steel structural sections and concrete structures. However many of structural problems are not included in this regulation. If the steel Vierendeel girder should be loaded by the significant load the interesting solution is such design where RHS or box chords section are concrete filling. From the structural point of view the box chords section ought to have the possibly large dimensions and their wall thickness ought to as small as possible. However in such situation two problems arise. Local instability of section walls leads to degradation of chord resistance and very thin walls decrease the strength and stiffness of joints. It leads to decreasing the overall carrying capacity of such structure. The strengthening of joints is possible by the steel plate welded to the face of chord. This however, does not strength the slender webs of box section. The other possibility is concrete filling of hollow section. Such filling leads also to increasing the thermal capacity of structure and its fire resistance. The comparison of these two ways of strengthening is given in (2 ). Strength and stiffness of T concrete filled joints made with RHS are the aim of this paper. TEST RIG, TEST SPECIMENS AND MEASUREMENTS Test rig is shown in figure 1. Twelve joints in natural scale were tested here up to failure.Ten of specimens, made with RHS, have the concrete filling chords. Two additional specimens are not concrete filling and are used for comparison how the concrete filling is effective compare with the pure steel RHS joints. The compression load equal to 420 kN, simulating the load in real structure, was applied to chord before the branch was loaded. Therefore in several steps the branch was loaded up to the reach the failure load. After each loading step, the joint was unloaded to measure the permanent deformations of the tested specimen. Typical type of joint failure was the inelastic deformation of the flange in the tension zone and finally cracking of welds, see figure 2. In Table 1 the geometry of the specimens, mechanical properties, and failure moment are given. The mechanical properties are the medium value from three tension coupons tests. The concrete mechanical properties were obtained from tests of five concrete standard cubes 100x100x100mm. Results obtained shown that the filling concrete has characteristic stress 42 MPa. Thickness of welds was equal to a = 1,2 t n . Connections in Steel Structures V - Amsterdam - June 3-4, 2004 403

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STRENGTH AND STIFFNESS OF RHS BEAM TO RHS CONCRETE FILLED COLUMN JOINTS

J. K. Szlendak, Bialystok Technical University, Poland

ABSTRACT Composite connection made with RHS chord or column filled by concrete and branches with RHS steel profile are studied herein. The aim of this paper is deriving a simple theoretical formula for calculating the strength and stiffness of such joints. Test results of twelve connections in natural scale are described. Geometry and material properties of the tested joints are given. Theoretical solution of the joint strength and stiffness are proposed and the comparisons between theoretical and experimental results are presented.

INTRODUCTION European Code EC 4 (1) makes possibility to design much more effective structures which combined advantages of steel structural sections and concrete structures. However many of structural problems are not included in this regulation. If the steel Vierendeel girder should be loaded by the significant load the interesting solution is such design where RHS or box chords section are concrete filling. From the structural point of view the box chords section ought to have the possibly large dimensions and their wall thickness ought to as small as possible. However in such situation two problems arise. Local instability of section walls leads to degradation of chord resistance and very thin walls decrease the strength and stiffness of joints. It leads to decreasing the overall carrying capacity of such structure. The strengthening of joints is possible by the steel plate welded to the face of chord. This however, does not strength the slender webs of box section. The other possibility is concrete filling of hollow section. Such filling leads also to increasing the thermal capacity of structure and its fire resistance. The comparison of these two ways of strengthening is given in (2). Strength and stiffness of T concrete filled joints made with RHS are the aim of this paper. TEST RIG, TEST SPECIMENS AND MEASUREMENTS Test rig is shown in figure 1. Twelve joints in natural scale were tested here up to failure.Ten of specimens, made with RHS, have the concrete filling chords. Two additional specimens are not concrete filling and are used for comparison how the concrete filling is effective compare with the pure steel RHS joints. The compression load equal to 420 kN, simulating the load in real structure, was applied to chord before the branch was loaded. Therefore in several steps the branch was loaded up to the reach the failure load. After each loading step, the joint was unloaded to measure the permanent deformations of the tested specimen. Typical type of joint failure was the inelastic deformation of the flange in the tension zone and finally cracking of welds, see figure 2. In Table 1 the geometry of the specimens, mechanical properties, and failure moment are given. The mechanical properties are the medium value from three tension coupons tests. The concrete mechanical properties were obtained from tests of five concrete standard cubes 100x100x100mm. Results obtained shown that the filling concrete has characteristic stress 42 MPa. Thickness of welds was equal to a = 1,2 tn.

Connections in Steel Structures V - Amsterdam - June 3-4, 2004 403

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Four LVDT gauges were used to measure the displacements and rotations, see figure 2. Registrations of the results were made permanently during full loading and unloading process, up to failure. After each loading step the joint was unloaded to measure the permanent deformations. For the control of obtained data from LVDT, the additional dial gauges were used, see figure 1. Table 1. Geometrical dimensions and mechanical properties.

Geometrical dimensions Yield stress Parameters

No of joint

RHS chord bo x ho

mm

RHS branch bn x hn

mm

chord wall thick

to mm

branch wall thick

tn mm

branch

fyn

MPa

chord

fyo

MPa

β η λo

length of

branch

m

ultimatefailure

moment

kNm BS1 140x140 80x80 5,2 4,3 400 479 0,57 0,57 26,9 0,415 8,51 S2

steel 140x140 100x100 7,1 5,1 380 457 0,71 0,71 19,7 0,415 20,23

BS3 140x140 120x120 7,05 5,15 369 404 0,86 0,86 19,9 0,41 32,80 BS4 140x140 100x100 5,1 5,1 373 457 0,71 0,71 27,5 0,415 14,94 BS5 140x140 100x100 7,05 5,15 380 457 0,71 0,71 19,9 0,405 23,49 BS6 140x140 80x80 7,1 4,4 392 479 0,57 0,57 19,7 0,408 13,06 BS7 140x140 100x100 5,35 4,3 373 457 0,71 0,71 26,2 0,407 14,25 BS8 140x140 100x100 7 4,3 369 457 0,71 0,71 20 0,4 20,00 BS9 140x140 120x120 7 5,2 375 404 0,86 0,86 20 0,41 31,78

BS10 140x140 120x120 5,2 5,2 373 404 0,86 0,86 26,9 0,41 26,24 BS11 140x140 80x80 7 4,15 400 479 0,57 0,57 20 0,411 14,39 S12 steel 140x140 100x100 7,15 4,15 380 460 0,71 0,71 19,6 0,408 16,73

Figure 1. Specimen during test. Figure 2. Joint failure (crack of welds).

404 Connections in Steel Structures V - Amsterdam - June 3-4, 2004

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THEORETICAL ESTIMATIONS Strength prediction For prediction the theoretical strength of filled joints, from the observations which were done during experimental tests, the following assumptions are adopted:

Figure 3. Failure model of joint – yield line mechanism. 1. Yield line mechanism, which is created in the tension zone of joint, is deceived. Erasing

inelastic deformations leads finally to situation that steel loaded flange looses the contact with filled concrete.

2. In compression zone the connection is almost absolutely stiff. So, for the simplicity could be assumed that this part of joint is compact.

3. In tension zone range of yield line mechanism is larger then in compression one. From the tests the assumption is adopted that in tension zone range of yield line mechanism is equal to 0,65hn

For the prediction of theoretical strength the yield line mechanism is proposed, similar to that as for unstrengthen steel joints (3). Proposed theoretical model is shown in figure 3. From the equation that the virtual work dissipated in the hinges by inner forces on the virtual rotations and deformations is equal to outer forces work on the virtual displacements the formula to predict strength of joints is given From the condition dMip,1,Rd/dx = 0 occurs

Mip,1,Ed

Φ

hn

bo

ho

bnto

0,65hn

concrete

df 3 f 1

f 2

f 2

Legend:φ1, φ2 , φ3

- virtual rotations in plastic hingesδ- virtual displacement0,65hn - range of the tension zone

xbo

)1(08,3)65,0(1

82,1, ++−

+= xxmb

M

plo

Rdip

βη

)2(2

1 β−=x

Connections in Steel Structures V - Amsterdam - June 3-4, 2004 405

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After substitution (2) to (1) the design formula is obtained

Initial stiffness Initial stiffness Sj,ini is a coefficient in the linear function between the bending moment applied to the joint and its local rotation (M = Sj,ini Φ). For pure steel joints the power function is assumed to predict the initial stiffness of the joints when β > 0,4, see (4). Analysis of the influence of particular parameters leads to the following formula:

Sj,ini = ks E to3β y4η y5λoy6 (4)

After the numerical simulation the followings exponents were obtained: y4 = 2, y5 = 3, y6 = 1. For eliminating the false results the Chauvenet rule was used (4). For assumption that the level of confidence will be 0,95 and when coefficient γM5 = 1,1 the coefficient ks = 6 was obtained. Then, the design value of the joints initial stiffness could be calculated as below:

Sj,ini = 6 E to3 β 2η 3 λo (5) However, for the concrete filled joints, after the numerical simulation, the increasing coefficient 1,3 is suggested and the design value of the joints initial stiffness could be calculated as below:

Sj,ini = 7.8 E to3 β 2η 3 λo (6)

Secant stiffness According the recommendations which are given in EC-3, see part 5.1.2 (5), as a simplification, the rotational, secant stiffness may be taken as Sj,ini /η in the analysis for all values of the design moment. Therefore, the secant stiffness of concrete filled joints is suggested to be calculated using coefficient η = 2, see Table 5.2 (5), as below:

Sj,sec = 3.9 E to3 β 2η 3 λo (7)

COMPARISON OF EXPERIMENTAL RESULTS AND THEORETICAL ESTIMATIONS In figure 4 to 15 the moment-rotation curves (M - Θ) for each tested joints are presented. They are shown not only loading but also unloading curves registered by LVDT and dial gauges. Unloading curves gives possibility to obtain the end of its elastic behaviour and show the arising of the joint permanent deformations. In Table 2 the comparison between the theoretical prediction and the test results is presented.

)3(08,3)1

65,01(1

8,1, +−

+−

=ββη plo

Rdip

mbM

406 Connections in Steel Structures V - Amsterdam - June 3-4, 2004

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BS1

0

2

4

6

8

10

0 1,5 3 4,5 6Rotation x 10-2 rad

Mom

ent k

Nm

LVDT Loading

LVDT Unloading

Dial gauge Loading

Dial gauge Unloading

Initial stif fness (6)

Secant stiffness (7)

Design load (3)

BS3

0

5

10

15

20

25

30

35

0 1,5 3 4,5 6Rotation x 10-2 rad

Mom

ent k

Nm

LVDT Loading

LVDT Unloading

Dial gauge Loading

Dial gauge Unloading

Welds failure

Initial stif fness (6)

Secant stif fness (7)

Figure 4. Joint BS1 β = 0.57, λo=26.9. Figure 5. Joint BS3 β = 0.86, λo=19.9.

BS4

0

4

8

12

16

0,0 1,5 3,0 4,5Rotation x 10-2 rad

Mom

ent k

Nm

LVDT Loading

LVDTUnloading

Dial gauge Loading

Dial gauge Unloading

Initial stif fness (6)

Secant stif fness (7)

Design load (3)

BS5

0

3

6

9

12

15

18

21

24

27

0 1,5 3 4,5 6 7,5Rotation x 10-2 rad

Mom

ent k

Nm

LVDT Loading

LVDT Unloading

Dial gauge Loading

Dial gauge Unloading

Welds failure

Initial stiffness (6)

Secant stif fness (7)

Design load (3)

Figure 6. Joint BS4 β = 0.71, λo=27.5. Figure 7. Joint BS5 β = 0.71, λo=19.9.

BS6

0

3

6

9

12

15

0 1,5 3 4,5 6Rotation x 10-2 rad

Mom

ent k

Nm

LVDT Loading

LVDT Unloading

Dial gauge Loading

Dial gauge Unloading

Welds failure

Initial stif fness (6)

Secant stiffness (7)

Design load (3)

BS7

0

3

6

9

12

15

0 1,5 3 4,5 6 7,5Rotation x 10-2 rad

Mom

ent k

Nm

LVDT Loading

LVDT Unloading

Dial gauge Loading

Dial gauge Unloading

Welds failure

Initial stif fness (6)

Secant stiffness (7)

Design load (3)

Figure 8. Joint BS6 β = 0.57, λo=19.7. Figure 9. Joint BS7 β = 0.71, λo=26,2.

Connections in Steel Structures V - Amsterdam - June 3-4, 2004 407

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BS8

0

3

6

9

12

15

18

21

0 1,5 3 4,5 6 7,5Rotation x 10-2 rad

Mom

ent k

Nm

LVDT Loading

LVDT Unloading

Dial gauge Loading

Dial gauge Unloading

Welds failure

Initial stif fness (6)

Secant stiffness (7)

Design load (3)

BS9

0

5

10

15

20

25

30

35

0 0,5 1 1,5 2 2,5Rotation x 10-2 rad

Mom

ent k

Nm

LVDT Loading

LVDT Unloading

Dial gauge Loading

Dial gaugeUnloadingWelds failure

Initial stif fness (6)

Secant stiffness (7)

Design load (3)

Figure 10. Joint BS8 β = 0.71, λo=20. Figure 11. Joint BS9 β = 0.86, λo=20.

BS10

0

3

6

9

12

15

18

21

24

27

0 1,6 3,2 4,8 6,4Rotation x 10-2 rad

Mom

ent k

Nm

LVDT Loading

LVDT Unloading

Dial gauge Loading

Dial gaugeUnloadingWelds failure

Initial stif fness (6)

Secant stiffness (7)

Design load (3)

BS11

0

3

6

9

12

15

0 1,5 3 4,5 6 7,5 9 10,5Rotation x 10-2 rad

Mom

ent k

Nm

LVDT Loading

LVDT Unloading

Dial gaugeLoadingDial gaugeUnloadingWelds failure

Serie6

Serie7

Serie8

Figure 12. Joint BS10 β = 0.86, λo=26,9. Figure 13. Joint BS11 β = 0.57, λo=20.

S2

0

5,5

11

16,5

22

0 1,5 3 4,5 6Rotation x 10-2 rad

Mom

ent k

Nm

LVDT Loading

LVDT Unloading

Dial gaugeLoadingDial gaugeUnloadingWelds failure

Initial stiffness (5)

Secant stif fness

Design load

S12

0

3

6

9

12

15

18

21

0 1,5 3 4,5 6 7,5Rotation x 10-2 rad

Mom

ent k

Nm

LVDT Loading

LVDT Unloading

Dial gaugeLoadingDial gaugeUnloadingWelds failure

Initial stiffness (5)

Secant stif fness

Design load

Figure 14. Joint S2 β = 0.71, λo=19,7. Figure 15. Joint S12 β = 0.71, λo=19,6.

408 Connections in Steel Structures V - Amsterdam - June 3-4, 2004

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Table 2. Comparison between theoretical and experimental strength of joints.

No of

joint

Theoretical strength

of joint (3) Mip,1,Rd kNm

Theoretical strength of

welds Mw,Rd kNm

Experimental strength Mexp kNm

Mexp / Mip,1,Rd

Mode of failure

BS1 5,91 13,83 5,75 0,97 yield of chord face BS3 33,89 30,87 - - welds cracking BS4 8,70 24,34 9,90 1,14 yield of chord face BS5 16,94 24,60 17,1 1,01 yield of chord face BS6 10,81 14,19 10,45 0,97 yield of chord face BS7 9,57 20,10 10,00 1,05 yield of chord face BS8 16,21 20,38 16,50 1,02 yield of chord face BS9 33,95 31,19 - - welds cracking BS10 18,64 31,19 19,5 1,05 yield of chord face BS11 10,72 14,19 11,2 1,05 yield of chord face

S2 12,8 24,34 15,2 1,18 yield of chord face S12 12,98 19,12 14,5 1,11 yield of chord face

Theoretical strength of pure steel joints S2 and S12 is estimated from the formula presented in (3) but initial stiffness is calculated from formula (5). Secant stiffness of these joints are equal to Sj,ini /η , where η = 2. CONCLUSIONS a. Table 2 shown that formula (3) good predicts the strength of T RHS joints which chords

are filled by concrete. b. Filled joints could be classified as the joints with full strength (see joints BS 3 and BS 9 in

Table 2), where the parameter β < 0,85 and if the wall slenderness of the chord section λo is not slender then 20. With regard to the unfilled, pure steel joints, the joints could be classified as the full strength if they are more compact i.e. parameter β < 1 and λo < 16.

c. As it could be expected, it was noticed that the rotation capacity of filled joints is much smaller than the adequate steel joint. However, all the tested joints have the rotation capacity over 1,5 x 10-2 rad, what guarantee to reach the serviceability limit of beam. For very flexible joints, for example BS 1, the rotation capacity is only equal to 6 x 10-2 rad, see figure 4, when for the adequate unfilled steel joint it is much larger and equal at least to 20 x 10-2 rad.

d. After the opening the RHS it was observed very good condition of the concrete. It was not worse then the similar concrete curing in more wet environment.

e. As it is shown, see formula (6), that the stiffness of filled joints is about 30 % larger then adequate steel joint. The test results show that such estimation could be accepted. However, more tests are needed for confirmation of this data.

ACKNOWLEDGEMENT This research project No W/IIB/10/01 was financially supported by Bialystok Technical University, Poland NOTATION fy yield stress of (fyn – branch member, fyo – chord member) ks coefficient

Connections in Steel Structures V - Amsterdam - June 3-4, 2004 409

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mpl plastic moment of resistance per unit length in the chord face (mpl = fyoto2/4) y1, y2, y3 unknown exponents β branch to chord width ratio (β = bn/bo) η branch depth to chord width ratio (η = hn / bo) λo slenderness of chord face ( λo = bo/to) REFERENCES (1) prEN 1994-1-1 "Design of composite steel and concrete structures". Part 1.1 "General

rules and rules for buildings", CEN, 18 March 2002. (2) Szlendak J. Improve the joints strength in steel frames with RHS Columns by concrete

filling. Proc. Int. Conf. on “Steel Structures of the 2000’s”, Istanbul, 2000, pp.345-352. (3) Szlendak J., Bródka J. "Investigation into the static strength of welded T moment

unreinforced joints in rectangular hollow sections“, International Institute of Welding, IIW-Doc. XV 538-83, March 1982.

(4) Szlendak J.K.: Design models of welded joints in steel structures with rectangular hollow sections. DSc thesis, Bialystok Technical University Press, 2004 (in Polish)

(5) prEN 1993-1-8 Eurocode 3: Design of steel structures: Part 1.8: Design of joints, CEN, 31 January 2003 (Stage 34 draft).

410 Connections in Steel Structures V - Amsterdam - June 3-4, 2004

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STRENGTH AND STIFFNESS OF 3D PLATES TO RHS COLUMN PIN JOINTS

J. K. Szlendak, Bialystok Technical University, Poland

ABSTRACT Nominally pinned joints where longitudinal plates are welded to the walls of RHS column are studied herein. The earlier results of such experiments made by Jarrett, where tension loading is applied to the joints, are reminded. A design formula for prediction the strength of joints, more optimistic, than one given by Jarrett is proposed. Results of experimental tests, where connections are loaded by the shear forces and secondary bending moments, are further discussed. Three types of joint failure were observed in tests. Models for these joint failures are given. For inelastic failure of chord face, proposed formulas for prediction the strength and stiffness of the joint have not reference to EC-3.

INTRODUCTION Braced frameworks with nominally pinned joints could be the proper solution for the saving of labour, manufacturing and erection costs. If in such structures the columns are made with box section (RHS), and the beam is the I - type profile, one of the easiest joint between them is the longitudinal plate welded to column, figure 1. This plate usually is connected with web of beam by using a bolted connection. Such joints are given in Table 7.13 (1). It ought to be remember that they are very flexible (2, 3) and sensitive on the cracks in the tension area. So, they should be rather used for the structures with predominantly static loading. Such joints are usually loaded by shear forces and secondary bending moments. Furthermore, they should be also able to carry the incidental tension load (2). If a carrying capacity for such loading is too small the failure of joint, as in figure 2, is available. When the semi-continuous framing is considered, than the design formulas to predict the strength, stiffness and rotation capacity of joints ought to be developed. From the reason of complex behaviour of described here joints such formulas are often semi-empirical. TENSION LOADING OF JOINTS Test results Tests of joints, where the tension load Nt is applied from the I beam web by the steel longitudinal gusset plate to the wall of RHS, are rather rare. One of it as in figure 2, for 13 joints, has been undertaken by Jarrett (2). In figure 3 results of these experiments for two joints sign 6T and 12T are shown. For joint 6T n = 0 but for 12T n = 0,52. It is easy to noticed that the prestressing of chord n = No/Aofyo decreased the ultimate load of joint. It could be also seen that such joints have a significant “overstrength”, which increases for large deformations of the loaded flanges of joint, see figures 2 and 3.

Connections in Steel Structures V - Amsterdam - June 3-4, 2004 411

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Strength prediction Prediction of the joint strength is given from the yield line bending-squash mechanism, which occurs on the face walls of the RHS. In this mechanism the initial energy is dissipated not only by the bending moments but also by the membrane forces in the yield lines, see Groeneveld (4), Szlendak and Brodka (5) and Szlendak (6).

Figure 1. Geometry of joint with Figure 2. Typical failure of joint (2). longitudinal plate (2).

0

50

100

150

200

250

0 5 10 15 20 25 30 35 40 45Deformation of loaded wall "w" [mm]

N e jt,

ult

Joint 6T ( n=0)

Joint 12T ( n = 0,52)

Ntjt from (10)

for joint 6T

Ntjt from (10) for

joint 12T

Figure 3. Experimental ultimate load Ne

jt, ult as a function of (w) 6T and 12T, (2) and theoretical strength Nt

jt estimated from (10). Strength of joint Nt

jt, as in figure 1, is estimated from formula:

( ) )1()1(224 2nDCmN nnpljtt −+= η

where coefficients Cn and Dn are calculated as below:

412 Connections in Steel Structures V - Amsterdam - June 3-4, 2004

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for value of parameter

)2()1(

)1()1(22

2222

βλβ

−−−+

=G

GC on

)3()1(

)1()1(312

2

2222

β

λβ

−−+=

G

GD

o

n

)4()1(5.21 22

2

o

Gλβ−

+=

but when

)5()1)(1(

)1(21βλβ

−+−+

=BBC o

n

)6()1)(1(

)1(31)1(1

βλβ

λβ

−+−

+−+=

BB

BD o

o

n

)7(]10)1(17[)1(

]10)1(17[)1(11−−−

−−−++=

oo

ooBλβλβ

λβλβ

Furthermore, when

)8(,2 onon DC λλ == When the pure bending model occurs, what is the typical assumption (1), the particular solution is obtained for which Cn is calculated as below:

)9(1

2β−

=nC

If a deformation of loaded wall “w” arises then the strength of the joint increases due to the membrane effect. As a good approximation could be assumed that for deformations such that w < to/2, the coefficient increasing the strength of the joint due to the membrane effect is equal to (1+4(w/to)2), (4). If one assumes that the maximum deformations of the loaded walls is equal to 1% bo, (3), this coefficient could be written as (1 + 4 (0,01bo/to)2) = (1 + 0,0004 λo

2). Then, more optimistic estimation of the joint strength is suggested. Proposed below formula is the extension of formula (1) and includes the increasing coefficient from the membrane effect:

[ ]( ) )10(0004,01)1(224 22onnpljt

t nDCmN λη +−+=

In figure 4 the comparison between this theoretical estimation and the experimental strength of joints tested by Jarrett (2), is shown. The experimental strength Ne

jt,pl, for the moment of creating the yield line mechanism and ultimate strength Ne

jt,ult, for large deformations and full membrane action is given for the joints 6T and 12T. As the illustration the results of ultimate strength Ne

jt,ult for the other from 13 joints are also included.

o

o

λλβ

25.12 −

<

o

o

o

o

λλβ

λλ

171017

25.12 −

<≤−

117

1017≤<

− βλ

λ

o

o

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0

20

40

60

80

100

120

140

0 20 40 60 80 100 120 140

Theoretical estimation Nttj/mpl

Exp

erim

enta

l res

ults

Ne tj,

pl/m

pl

Jarrett (2) - ultimate load (13 joints)

Joint 6T - design load (10)

Joint 12T - design load (10)

Joint 6T - ultimate load

Joint 12T - ultimate load

Figure 4. Comparison: theoretical estimation (10) and the experimental strength from (2).

SHEAR LOADING OF JOINTS Test results Test rig is shown in figure 5. Six joints were tested here in natural scale.

Figure 5. Test rig.

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Three specimens have two gusset plates (on opposite sides of RHS, sign 2D) and three other four gusset plates (on each side of RHS, sign 3D). Thickness of gusset plates were tn = 6 mm and the fillet welds 3,5 - 4 mm. Plates were connected, with using 3 M16 bolts grade 8.8., to more stiff plates, which simulate the webs of beams, see figure 8. Step by step compression force is applied by hydraulic jack to the RHS column, which was inside the rig tube diameter 406/8.8 mm. Because stiff plates were supported on strengthen walls of rig tube, the gusset plates of joint were loaded by shear load from the reactions, as in the real structure. Eight LVDT gauges were used to measure the displacements and the rotations of each gusset plate. Registrations of the results were made permanently (one registration per one second) during the full loading and unloading process up to failure. After each loading step the joint was unloaded to measure the permanent deformations of the tested specimen. Three types of joint failure, as described below, were observed in tests. Table 1. Geometrical dimensions and mechanical properties.

Geometrical dimensions Mechanical properties Parameters

No speci- men

RHS chord bo x ho x to

mm

Plate bn x hn x tn

mm

chord fyo

N/mm2

chord fuo

/mm2

plate fyn

N/mm2

plate fun

/mm2 β η λo

3D/1 150x150x10 130x60x6 394 516 308 435 0,04 0,87 15

2D/1 150x150x10 130x60x6 395 513 308 435 0,04 0,87 15

3D/2 180x180x8 130x60x6 374 509 308 435 0,033 0,72 22,5

2D/2 180x180x8 130x60x6 377 512 308 435 0,033 0,72 22,5

3D/3 150x150x5 130x60x6 410 549 308 435 0,04 0,87 30

2D/3 150x150x5 130x60x6 408 542 308 435 0,04 0,87 30

Figure 6. Bearing of gusset plate – view. Figure 7. Welds failure – view.

25

Ø1740

35

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Bearing of plate material failure occurred for specimens’ 3D/1 and 2D/1. These failure occurs when column section is compact, here λo = 15, and welds has the adequate strength. In such situation connection failed by the shear of bolts or bearing of gusset plate, see figure 6 and 9, where the example of moment - rotation curve is shown. It is obtained for one of the gusset plates of the joint 3D/1. Welds failure occurred for specimens 3D/2 and 2D/2. These failure occurs when column section is compact enough, here λo = 22,5, and strength of bolts is larger then the strength of welds. In such situation connection failed by cracking welds in the corners, in tension zone of gusset plate, see figure 7 and 9, where the moment-rotation curve for joint 3D/2 is shown.

Figure 8. Inelastic deformations of RHS flanges – view.

Flange yield failure occurred for specimens’ 3D/3 and 2D/3. This failure occurs when walls of section are slender, here λo = 30. Inelastic mechanism arises on the loaded flanges and sufficient membrane action was noticed, see figure 8. Large permanent deformations were observed during the unloading process. In figure 10 the examples of moment - rotation curves are shown. They are obtained for three of the gusset plates of joint 3D/3.

Joint 3D/1 and 3D/2

0123456789

10111213

0 25 50 75 100 125 150 175 200 225Local rotation x mrad

Mom

ent k

Nm Test results for joint 3D/1

Test results for joint 3D/2

Initial stiffness for joint 3D/1

Secant stiffness for joint 3D/1

Initial stiffness for joint 3D/2

Secant stiffness for joint 3D/2

Plate theoretical strength from (12)

Weld theoretical strength from (13)

Figure 9. Moment-rotation curves (bearing of gusset plate material and welds cracking).

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Joint 3D/3

0

1

2

3

4

5

6

7

8

0 50 100 150 200 250 300Local rotation x mrad

Mom

ent

kNm

Results for plate nr 1

Results for plate nr 3

Results for plate nr 4

Initial stiffness (19)

Secant stiffness (20)

Design load (16)

Figure 10. Moment-rotation curves (yielding of the loaded flanges of RHS).

Strength prediction Model 1: Bearing of plate material Formulas for design resistance for individual fasteners subjected to shear are shown in Table 1, (1). For Category A (bearing type) connections the below relations occur: Fv,Ed ≤ Fv,Rd Fv,Ed ≤ Fb,Rd where,

Fv,Rd = 2M

ubv Afγ

α (11)

For strength grades 4.6, 5.6 and 8.8: αv = 0,6 and,

Fb,Rd = 2

1

M

ub tdfakγ

(12)

where αb is the smaller of αd; u

ub

ff

or 1,0;

Model 2: Welds failure According the formula (4.1) part 4.5 (1), the resistance of the fillet weld will be sufficient if the following are both satisfied:

[σ┴2 + 3 (τ┴2 + τ║2)] 0,5 ≤ fu / (βw γM2 ) and σ┴ ≤ fu / γM2 (13)

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Model 3: Yield failure of loaded flanges Estimation of strength the RHS joints with longitudinal gusset plates is included, loaded by normal forces, is given in EC-3 (see Table 7.13 (1). However, up to now, the design formula for such joints, loaded by shear forces and bending moments, is not proposed there. Theoretical investigations into the static strength of RHS to RHS beam-column welded joints were undertaken in earlier works see e.g. (3, 6). The new design formula, presented in (6), could be used in case of joints studied here, when β < 0,2. Proposed formula has easy form for the direct calculation by the designers as below:

)14(),,( ,, ypln

yn

yooMMpljy

t Mff

fkM ληβ=

From different possible functions fM the power function is chosen. Then, the strength of joint Mt

jy,pl could be calculated from formula:

)15(,321

, ypln

yn

yoyo

yyMpljy

t Mff

kM ληβ=

After the numerical simulations the following exponents were obtained: y1=1/6, y2=1/2, y3= - 4/3. For eliminating the false results the Chauvenet rule was used, see (6). For assumption that the level of confidence will be 0,95 the coefficient kM = 27,5 was obtained. Furthermore, when the coefficient γM5 = 1,1 ( in EC-3 (1) it is assumed γM5 = 1) then the design value of the joints strength could be calculated as below:

)16(25 ,6 8

3

, ypln

yn

yo

o

pljyt M

ff

Mλβη

=

Comparison of this estimation with 186 test results of the static strength of RHS to RHS beam-column welded connections, collected in the data-bank (7), is given in (6). Results of 27 tests are ignored as false if level of confidence will be 0,95. This simplified estimation good predicts the experimental results (6). Initial stiffness Initial stiffness Sj,ini is a coefficient in the linear function between the bending moment applied to the joint and its local rotation (M = Sj,ini Φ). The power function is assumed to predict the initial stiffness of the joints when β > 0,4, see (6). Analysis of the influence of particular parameters leads to the following formula:

Sj,ini = ks E to3β y4η y5λoy6 (17)

After the numerical simulations the following exponents were obtained: y4 = 2, y5 = 3, y6 = 1. For eliminating the false results the Chauvenet rule was used (6). For assumption that the level of confidence will be 0,95 and when coefficient γM5 = 1,1 the coefficient ks = 6 was obtained. Then, the design value of the joints initial stiffness could be calculated as below:

Sj,ini = 6 E to3 β 2η 3 λo (18)

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Comparison of this estimation with 202 test results of the static strength of RHS to RHS beam-column welded connections, collected in the data-bank (7), shows that this simplified estimation good predicts the experimental results (6). However, for the longitudinal gusset plate joints parameter β should follow the condition β < 0,2; see Table 7.13 (1). Even if the thickness of gusset plates changed the value of β is still very small and influence of that parameter on the initial stiffness of joint is negligible. So, in the formula (18) it is assumed that β2 = 0,04. Therefore for 0,03 < β < 0,2 the initial stiffness of longitudinal gusset plate joints could be calculated as below:

Sj,ini = 0.24 E to3 η 3 λo (19) Secant stiffness According the recommendations which are given in EC-3, see part 5.1.2 (1), as a simplification, the rotational, secant stiffness may be taken as Sj,ini /η in the analysis for all values of the design moment. From Table 5.2 (1) the stiffness modification coefficient is equal to η = 2. Therefore for 0,03 < β < 0,2 the secant stiffness of longitudinal gusset plate joints could be calculated as below:

Sj,sec = 0.12 E to3 η 3 λo (20)

Joint 3D/3 (focus)

0,0

0,5

1,0

1,5

2,0

2,5

3,0

0 5 10 15 20 25 30 35 40 45 50Local rotation x mrad

Mom

ent

kNm

Results for plate nr 1

Results foir plate nr 3

Results for plate nr 4

Initial stiffness (19)

Secant stiffness (20)

Design load (16)

Figure 11. Moment-rotation curve (yielding of the loaded flange of RHS)

– details of assumed stiffness and design load of joint.

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CONCLUSIONS

a. New design formula (10) for joints loaded by tension load Nt, is suggested. Strength of the joint increases due to the membrane effect. Proposed estimation is more optimistic, than one given by Jarrett (2) and in Table 7.13 EC 3 (1). For compact RHS, when λo = 10 this strengthening is negligible and equal to 4%. However for slender wall RHS, when λo = 30 it is significant and equal to 36%.

b. Joints loaded by shear load and by additional bending moment failed from: bearing of plate material, shear of bolts and welds cracking. However, the yield failure of loaded flanges was specially research in this paper. From figure 9 and 10 could be easy noticed that the rotation of joints is large enough to reach the serviceability limit state. It is reminded that for typical load the rotation of beam supports about 15 mrad leads to exceeding this limit. Deflection of beam could be calculated with including the initial stiffness of beam supports, which is given by (19).

c. For ultimate limit state the minimum strength of joints calculated from formula (11-13) and (16) ought to be checked. Moreover, when the semi-continuous framing is considered the secant stiffness of joints given by the formula (20) could be included. Design model of such joint is given in figure 11.

NOTATION a throat thickness of welds fM function fy yield stress of (fyn – gusset plate, fyo – chord member) kM , ks coefficient mpl plastic moment of resistance per unit length in the chord face (mpl = fyoto2/4) n dimensionless prestressing in chord (n = No/Aofyo), y1, y2, y3 unknown exponents Mn

pl,y plastic moment of resistance of branch member (gusset plate) β branch to chord width ratio (β = bn/bo) η branch depth to chord width ratio (η = hn / bo) λo slenderness of chord face ( λo = bo/to) ACKNOWLEDGEMENT This research project No W/IIB/10/01 was financially supported by Bialystok Technical University, Poland REFERENCES (1) European Committee for Standardisation (CEN): Eurocode 3: Design of steel

structures: Part 1.8: Design of joints, European Standard, prEN 1993-1-8:2003, 31 January 2003 (Stage 34 draft).

(2) Jarrett N.D., Malik A.S.: Fin plate connections between RHS columns and I beams. Proceedings of the 5th International Symposium on Tubular Structures, Nottingham, Ed. M.G. Coutie and G. Davies, 1993.

(3) Wardenier J.: Hollow section joints, Delft University Press, 1982. (4) Groeneveld H.: Rigid plastic 2nd order calculation of horizontally restrained beam and

plates. Delft University of Technology, 1981.

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(5) Szlendak J., Bródka J.: Yield and buckling strength of T, Y and X joints in rectangular hollow section trusses. Proceedings of Institution of Civil Engineers, Part 2, 79, Mar., 167-180, 1985.

(6) Szlendak J.K.: Design models of welded joints in steel structures with rectangular hollow sections. DSc thesis, Bialystok Technical University Press, 2004 (in Polish)

(7) Szlendak J. Broniewicz M.: Data bank of connections. Beam to column welded connections. Part 1: RHS column to RHS beam. Bialystok Technical University, June 1995.

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AN EFFECTIVE EXTERNAL REINFORCEMENT SCHEME

FOR CIRCULAR HOLLOW SECTION JOINTS

Y. S. Choo, National University of Singapore, Singapore J. X. Liang, National University of Singapore, Singapore

G. J. van der Vegte, Delft University of Technology, The Netherlands

INTRODUCTION This paper presents an external reinforcement scheme, termed a collar, for strengthening circular hollow section (CHS) joints. Choo et al. (1) first investigated plate reinforcement schemes which may be used for field installation of auxiliary structures for offshore structures. The collar plate may be suitable to provide reinforcement to a pre-fabricated joint that is found to be under-designed. This concept may also find potential applications for reinforcing joints in older offshore platforms and large span structures. Fig. 1 illustrates the schematic arrangement for the collar reinforcement for a X-joint which may be found to be under-strength. In the figure, the collar plate reinforcement, assumed to be square in this case, is shown to be placed outside the foot-print of the brace-chord intersection, with thickness tc and length lc. The usual notations for the outside diameter and wall thickness of the brace (d1 and t1) and chord (d0 and t0), and associated geometric ratios are also indicated. The details 1 and 2, with additional weld shown hatched in Fig. 1, are indicative welding arrangement to connect the collar plate to the brace and chord. The edges of collar plate can be profiled to accommodate the existing full penetration weld at the brace-chord intersection. For the externally placed collar reinforcement plate which may be bent to be compatible with the chord curvature, Fig. 2 shows three possible schemes: 4 parts, 2 parts (parallel) and 2 parts (perpendicular). For the 4 part scheme, for example, the solid lines indicated in Fig. 2 denote the lines of weld connecting the collar plate to the brace and chord. Indicative weld details shown in Fig. 1 (details 1 and 2) can be sized appropriately for the design requirements. For a joint loaded predominantly by in-plane bending, the 2 parts (parallel) arrangement may be an option if the welding requirement needs to be minimized. For a joint loaded predominantly by brace axial load or out-of-plane bending, the 2 parts (perpendicular) arrangement may be considered. For collar plates with large lc/d1 ratio, additional slot welds may be placed within the boundaries to provide supplementary ties between the collar plate and the chord.

ABSTRACT This paper presents an effective external reinforcement scheme for circular hollow section joints. The collar plate reinforcement is a scheme which may be applied to newly fabricated or existing joints which are found to be under-strength. The paper first introduces the structural scheme and then presents results of extensive numerical studies on the static strength of circular hollow section (CHS) joints reinforced with a collar plate. The results show that significant strength enhancement of the reinforced joints can be achieved through proper proportioning of the reinforcement plate.

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Figure 1. Collar plate reinforced CHS X-joint.

4 parts 2 parts (parallel) 2 parts (perpendicular)

A

C

B

D

Figure 2. Arrangement of collar plate parts.

This paper presents results of numerical studies on the behaviour of CHS T- and X-joints with collar plate reinforcement. The accuracy of the numerical results is verified against the T-joint tests reported by Choo et al. (1, 2). The results show that significant strength enhancement for collar reinforced joints can be achieved through proper proportioning of the reinforcement plate. Selected plots are presented to demonstrate the strength enhancement of X-joints under brace axial compression, in-plane and out-of-plane moments. COMPARISON WITH REFERENCE TEST RESULTS Reference information on T-joint Tests Choo et al. (1) presented results from an experimental programme investigating the strength enhancement to a simple T-joint by provision of reinforcement around the intersection region, in the form of a doubler plate or a collar plate. The experimental programme consisted of eight tests with brace axial load with four pairs of tests, each pair with brace compression and tension. The chord length was chosen such that joint failure occurred prior to chord member failure, with particular reference to recommendations by Zettlemoyer (3).

0d

t

1t

0

l

t

c

c

d1

0d

t 1

l c

d1

bracechord

platecollar

α = 2l0/d0 τ = t1/t0

β = d1/d0 τc = tc/t0 2γ = d0/t0 lc/d1

21

Detail 1 Detail 2

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Detailed investigations into the behaviour of the test specimens and strength enhancement offered by the doubler and collar reinforcement for T-joints, are presented by Choo et al. (2) and van der Vegte et al. (4). In this paper, the experimental result for the collar reinforced T-joint specimen EX-03 and the calibration of the nonlinear finite element model are provided for illustration. Details can be referenced in our papers (2, 4).

Mesh densities and element type For a particular joint subjected to given loading, an analyst can consider the appropriate symmetry in geometry, loading and boundary conditions to determine the finite element (FE) model for analysis. For a X-joint subjected to brace axial load, only one-eighth of the joint modelled (as shown in Fig. 3) with appropriate symmetry conditions and load specification is required. For each FE model, more refined mesh is generated where stress gradient is more critical. The automatic mesh generator for reinforced joints in this study is an extension of that presented by Qian et al. (5). For the present FE models, two layers of 20-noded solid elements, type C3D20R with reduced integration in ABAQUS (6), are specified through the thickness of all members to provide good description of possible non-linearity in the thickness direction. Depending on the actual joint geometry, 500 to 1000 elements are created to represent one-eighth of a whole joint. Such mesh density has been proven to be able to produce results with good accuracy (7). Weld geometries As three-dimensional solid elements are used in the FE models, it is possible to simulate the weld geometries with high accuracy. The actual geometric definition of the welds is included in all FE models. The geometry of the penetration weld between the brace and the chord is modelled following the American Welding Society (8) recommendations. The depth of the fillet welds between the reinforcing plate and the chord surface is taken the same as the thickness of the plate, with two layers of finite elements specified. The welds connecting the collar plate and chord (along the chord circumferential or longitudinal directions) are not explicitly modeled. These are reflected in the FE model by specifying the appropriate spatially common nodes to be tied.

Figure 3. FE model for one eighth of a collar plate reinforced CHS X-joint 2γ = 50.8, β = 0.64, lc/d1 = 1.50 and τc = 1.0.

Y

X

Z

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Geometric and material specifications The geometrical non-linearity is included to predict possible buckling in the chord wall through the NLGEOM parameter in the *STEP option in ABAQUS input file. The material nonlinearity is specified using the “true stress” and associated logarithmic strain to define the plasticity with isotropic hardening (6). Contact interaction When a collar plate reinforced joint is loaded, contact may occur between the bottom of the collar parts and the chord outer surface. The contact interaction plays an important role in the load transferring mechanism of plate reinforced joints and thus non-linear contact analysis is required. Since both of the reinforcing plate and the chord wall are deformable bodies, a deformable-deformable contact interaction was defined using a “master-slave” algorithm in the numerical analysis (6). Comparison between test and FE results Fig. 4a shows the cut-section of the collar-reinforced Specimen EX-03 after completion of the test. It can be observed that the collar reinforcement has relocated the chord plastic hinges away from the brace-chord intersection, and that the brace has deformed extensively adjacent to the intersection. Fig. 4b shows the deformed shape predicted by the nonlinear FE analysis, and very good agreement with the experimental result is observed. Figure 4. Comparison between test and FE results, (a) Cut-section of EX-03 after test, and

(b) FE prediction. The load-ovalisation curves (in which ovalisation at particular load level is based on the change in diameter of the chord section) for Specimen EX-03 are shown in Fig. 5. The numerical prediction is found to correspond very closely with the experimental curve, and this serves to verify the accuracy of the numerical method. Programme set-up Parametric studies to investigate the static strength of collar plate reinforced X-joints have been conducted by the authors. The chord diameter of all joints was taken as do=508 mm, with β varying from 0.25 to 0.80 (β= 0.25, 0.43, 0.64 and 0.80), α = 12, and 2γ= 31.8 and 50.8. The brace-to-chord thickness ratio τ =1.0, and the brace length was kept at 4d1. The thickness of the reinforcing plate was assumed equal or larger than the chord wall thickness t0. For each combination of 2γ and β ratios, three values of plate thickness parameter (τc=1.00, 1.25 and 1.60) and five values of plate length parameter (lc /d1=1.25, 1.5, 2.0, 2.5 and 3.0) have been considered. The corresponding un-reinforced joints were also included to provide the appropriate reference strength. A total of 8 un-reinforced joints and 120 collar

a b

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reinforced joints were analyzed, with each joint subjected to brace axial compression, in-plane moment or out-of-plane moment separately. The un-bent collar plate was assumed to be square in shape, except for large β cases, where the plate width exceeded half the perimeter of the chord section, and for this case, the plate width was limited to half the chord perimeter with welds along its edges. In the following sections, selected results shown for the various loading conditions are focussed on joints with 2γ = 50.8 and β = 0.25 and 0.64.

Figure 5. Experimental and numerical load-ovalisation curves for EX-03. STRENGTH OF REINFORCED X-JOINT UNDER AXIAL COMPRESSION Failure mechanisms and load-indentation curves Fig. 6a to 6b show the deformed shapes of two collar reinforced X-joints subjected to axial brace compression. Due to the weld at the brace-chord intersection, and the collar-chord segments along the longitudinal (crown) and circumferential (saddle) segments, the collar plate is effective in stiffening the chord and enhancing the load transfer from the brace.

Figure 6. Deformed shapes of collar reinforced X-joints with lc=2.0d1 and 2γ=50.8 with (a) β = 0.25, (b) β = 0.64.

0 20 40 60 80 100 1200

100

200

300

400

500

Load

[kN

]

Ovalisation [mm]

β=0.54, 2γ=50.6, Collar, Compression Experimental Numerical

β = 0.64 τ = 1.00 lc = 2.00d1 τc = 1.00

β = 0.25 τ = 1.00 lc = 2.00d1 τc = 1.00

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In Fig. 7a and 7b, the non-dimensionalised loads F/fy0t02 for the joint with β= 0.25 and 0.64 and plate sizes lc=1.25d1 to 2.5d1 are plotted against the displacement δ/d0, where δ is the indentation of the chord wall at the crown position. It can be seen that significant strength enhancement is achievable for plate reinforced joints. For a joint with β= 0.64 and lc=2.5d1, a “jump” in joint strength can be observed when the collar plate width reaches half of the chord section perimeter due to a more direct and effective load transfer mechanism through the welds.

0.00 0.02 0.04 0.06 0.080

5

10

15

F/f y0

*t02

δ/d0

Unreinforced joint lc/d1=1.25 α =12.0 lc/d1=1.50 2γ=50.8 lc/d1=2.00 τ c=1.00 lc/d1=2.50 β =0.25

0.00 0.02 0.04 0.06 0.080

10

20

30

40

F/f y0

*t02

δ/d0

Unreinforced joint lc/d1=1.25 α =12.0 lc/d1=1.50 2γ=50.8 lc/d1=2.00 τ c=1.00 lc/d1=2.50 β =0.64

Figure 7. Normalised load-indentation curves for collar reinforced X-joints with different plate

width to brace diameter ratios (a) β = 0.25 (b) β = 0.64. The deformation limit proposed by Yura et al. (9), which is defined as 60fyd1/E, is adopted to determine the ultimate strength of a joint without a pronounced peak value in the load-displacement curve. It is noted that the collar plate reinforcement can provide substantial strength enhancement to the joint. Effects of τc and lc /d1 Fig. 8a and 8b present the strength enhancement due to provision of collar plate for joints with 2γ=50.8 and β=0.25 and 0.64, with the corresponding un-reinforced joint strength as reference strength. Each of the strength ratios is plotted against the plate parameters τc and lc/d1 in a three-dimensional diagram for each β. As noted in Fig. 8b, the reinforced joint strength, obtained by the provision of an appropriately dimensioned collar plate, can be up to 3 times of the strength of an un-reinforced joint. The strength of a collar plate reinforced joint may be improved either by increasing the collar plate length or by using a thicker plate. For joints with small values of lc/d1, the effect of the plate thickness is insignificant. The effect of plate thickness becomes more important as the collar plate length increases. BEHAVIOUR OF REINFORCED X-JOINTS UNDER IN-PLANE BENDING In this section, the failure mechanisms for un-reinforced and collar reinforced X-joints under in-plane bending are presented to highlight the differences. The geometric parameters of the joints considered are 2γ = 50.8 and β = 0.25 and 0.64. More details are reported by Choo et al. (10).

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Figure 8. The effects of τd and ld/d1 on the strength of axially loaded collar plate reinforced X-joints with 2γ = 50.8 (a) β = 0.25 (b) β = 0.64.

Failure mechanisms Fig. 9a and 9d show the deformed shapes of collar plate reinforced joints with different combination of β and lc/d1. The collar plate reinforced joint is observed to fail with relatively large plastic zones formed near the brace-chord intersection. Because of the welds between the collar plate parts and the chord surface parallel to the chord axis, the collar plate acts closely with the chord wall on both compressive and tensile sides. For joints with short collar plates (Fig. 9a and 9c), plastic hinges are observed near the welds between the collar plate and the chord. The strength enhancement due to the short collar plate may be regarded as an equivalent increase in β. No obvious plastic hinge is found for a joint with long collar plates (Fig. 9b and 9d).

Figure 9. Deformed shapes of collar plate reinforced X-joints under in-plane bending.

a β = 0.25 lc = 1.25d1

b β = 0.25 lc = 2.00d1

c β = 0.64 lc = 1.25d1

d β = 0.64 lc = 2.00d1

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Effects of τc and lc /d1 Fig. 10a and 10b present the strength enhancement due to provision of collar plate for joints with 2γ=50.8 and β=0.25 and 0.64. As noted in Fig. 10b, the reinforced joint strength, obtained by the provision of an appropriately dimensioned collar plate can be up to 2.8 times of the strength of an un-reinforced joint. For joints with small values of lc/d1, the effect of the plate thickness is insignificant. The effect of plate thickness becomes more important as the collar plate length increases and more deformation of the collar plate takes place.

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Mi,u

,c /M

i,u,u

l d/d 1

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Figure 10. The effects of τc and lc /d1 on the strength of collar plate reinforced X-joints under IPB with 2γ = 50.8 (a) β = 0.25 (b) β = 0.64.

STRENGTH OF REINFORCED X-JOINTS UNDER OUT-OF-PLANE BENDING Failure mechanisms Fig. 11a and 11b show the deformed shapes of collar plate reinforced joints loaded by out-of- plane bending. It can be observed that the weld connecting the collar plate to the chord, from the saddle positions along the chord circumferential direction is effective in transferring the brace moment.

Figure 11. Deformed shapes of collar plate reinforced X-joints under out-of-plane bending

with 2γ = 50.8 (a) β = 0.25 (b) β = 0.64.

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Effects of τc and lc /d1 Fig. 12a and 12b show the potential strength enhancement for collar plate reinforced X-joints. It can be seen that the strength ratio of the reinforced joint to the corresponding un-reinforced joint varies from 1.6 to 3.6. The plate thickness parameter τc and length parameter lc /d1 have significant effects on the strength of the reinforced joints for cases with large lc/d1 ratios. Equivalent strength enhancement can be obtained by either increasing the plate length or by using a thicker collar plate.

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Figure 12. The effect of τd and ld/d1 on the strength of collar plate reinforced X-joints under OPB with 2γ = 50.8 (a) β = 0.25 (b) β = 0.64.

SUMMARY AND CONCLUSIONS Extensive numerical studies have been conducted to evaluate the behaviour of circular hollow section (CHS) X-joint reinforced with a collar plate, subjected to axial brace compression, in-plane bending or out-of-plane bending respectively. From the presented results of un-reinforced and collar plate reinforced CHS T- and X-joints, the following may be concluded: 1. The collar plate is an effective reinforcement scheme, and can improve the static strength

of CHS T- and X-joints considerably. 2. Each of the parameters: the brace-to-chord diameter ratio β, the plate-to-chord wall

thickness ratio τc, and the plate length-to-brace diameter ratio lc/d1 have significant influence on the strength of collar plate reinforced joints.

3. For a reinforced joint with fixed brace and chord dimensions, equivalent strength enhancement can be obtained by either appropriately increasing the plate length or using a thicker reinforcement plate.

RECOMMENDATIONS FOR FUTURE RESEARCH Based on the present studies, the following are possible recommendations for future research on the collar plate reinforced joints: 1. Since only part of the geometric parameters and loading conditions have been covered in

the current study, more extensive parametric studies will provide a comprehensive understanding of collar plate reinforced joints.

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2. Fatigue analyses of collar plate reinforced joints are proposed. The current study concentrated on the static strength of plate reinforced joints. It is important to investigate the behavior of plate reinforced joints under fatigue loading.

3. Experimental investigations on plate reinforced joints subjected to different loading cases will provide reliable reference results for parametric numerical investigation. Due to lack of experimental data on plate reinforced joints, this study used available test results on reinforced T-joints and published numerical results to verify the numerical methods.

ACKNOWLEDGEMENTS The authors wish to record their appreciation to Dr Nick Zettlemoyer of ExxonMobil Upstream Research (USA) for initiating the research on reinforced joints in the National University of Singapore. They like to thank Professor Jaap Wardenier in Delft University of Technology and Professor Richard Liew in National University of Singapore for their contributions towards the studies. REFERENCES 1. Choo, Y.S., B.H. Li, G.J. van der Vegte, N. Zettlemoyer & J.Y.R. Liew (1998). Static

strength of T-joints reinforced with doubler plate or collar plate. Tubular Structures VIII: Proceedings Eighth International Symposium on Tubular Structures, Singapore, pp. 139-145.

2. Choo, Y.S., G.J. van der Vegte, B.H. Li, N. Zettlemoyer & J.Y.R. Liew (2005). Static strength of T-joints reinforced with doubler or collar plates - Part I: Experimental investigations. Journal of Structural Engineering, ASCE, Vol. 131, No. 1, pp. 119-128.

3. Zettlemoyer, N. (1988). Developments in ultimate strength technology for simple tubular joints. Proc. Offshore Tubular Joints Conference (OTJ’88), Surrey, UK.

4. van der Vegte, G.J., Y.S. Choo, J.X. Liang, N. Zettlemoyer and J.Y.R.Liew (2004). Static strength of T-joints reinforced with doubler or collar plates - Part II: Numerical simulations. Journal of Structural Engineering, ASCE (accepted for publication).

5. Qian X.D., Romeijn A., Wardenier J. and Choo Y.S. (2002). An automatic FE mesh generator for CHS tubular joints. Proc. 12th International Offshore and Polar Engineering Conference. Kita-Kyushu, Japan.

6. Abaqus/Standard User’s Manual Version 6.2 (2001). Hibbitt, Karlsson and Sorensen Inc., Rhode Island, USA.

7. van der Vegte, G.J. (1995). The static strength of uniplanar and multiplanar tubular T- and X-joints. PhD thesis. Delft University Press.

8. A.W.S. (1996). Structural Welding Code, AWS D1.1-96. American Welding Society Inc., Miami, USA.

9. Yura, J.A., N. Zettlemoyer & I.F. Edwards (1980). Ultimate capacity equations for tubular joints. Proc. Offshore Technology Conference, Paper OTC 3690, Houston, U.S.A.

10. Choo Y.S., Liang J.X., van der Vegte G.J., Liew J.Y.R. (2004). Static strength of collar plate reinforced CHS X-joints loaded by in-plane bending. Journal of Constructional Steel Research, Vol. 60, No. 12, pp. 1745-1760.

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THE INFLUENCE OF BOUNDARY CONDITIONS ON THE CHORD LOAD EFFECT FOR CHS GAP K-JOINTS

G.J. van der Vegte

Kumamoto University, Japan / Delft University of Technology, The Netherlands Y. Makino, Kumamoto University, Japan

J. Wardenier, Delft University of Technology, The Netherlands

ABSTRACT In the framework of a larger programme to establish new chord load functions for circular hollow section joints, this study evaluates the effects of various sets of boundary conditions and chord pre-load on the static strength of axially loaded gap K-joints. The influence of boundary conditions on the chord stress contours is made clear for four different combinations of the geometric parameters β and 2γ. It is concluded that a better understanding of the effects of chord pre-stress on the strength of K-joints is obtained by considering the maximum chord stress as the governing variable, instead of the chord stress due to externally applied pre-loads.

INTRODUCTION In current design rules, insufficient emphasis is put on the consistency of various design equations. For circular hollow section (CHS) joints, the external chord “pre-load” (i.e. the additional load in the chord which is not necessary to resist the horizontal components of the brace forces) is used to account for the effects of chord loading. However, for rectangular hollow section (RHS) joints, the chord stress formulation is based on the maximum chord stress i.e. the stresses as a result of axial forces and (where applicable) bending moments. To a designer, it is confusing that different approaches should be used for different categories of joints, which may lead to misinterpretations and errors. Hence, it has been proposed in the framework of a CIDECT (Comité International pour le Développement et l’Étude de la Construction Tubulaire) programme, to re-analyse the effects of chord stress on the ultimate strength of tubular joints in order to establish a chord stress formulation as a function of the maximum chord stress, consistent for CHS and RHS joints. As reported by van der Vegte and Makino (1), in the past, research into the effects of chord pre-load on the strength of tubular joints was limited. Three experimental studies are available in the literature regarding the effects of pre-load on the ultimate strength of tubular X-joints. Although for CHS K-joints, the number of experiments outnumbers the data available for uniplanar X-joints, in most of the K-joint tests, chord stress was simply a result of horizontal equilibrium loads and was not meant as a prime variable. Only a few researchers e.g. Kurobane and Makino (2) and de Koning and Wardenier (3) explicitly applied a chord pre-load to the joints. More recent investigations into the effects of chord pre-load on CHS joints were conducted by Dier and Lalani (4) and Pecknold et al (5, 6). Since numerical tools offer the flexibility to vary various parameters and at the same time

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exclude the scatter usually observed between different series of tests, additional data on axially loaded uniplanar K-joints subjected to chord pre-load were generated by van der Vegte et al (7) using numerical methods. Twelve K-joint configurations were analysed, using the software package ABAQUS/Standard (8). The brace-to-chord diameter ratio β ranged from 0.25 to 0.67, while the chord thinness ratio 2γ was taken as 25.4 or 63.5. The brace angle θ was set to 45˚ or 60˚. For each of the K-joints considered, the uniformly applied chord stress varied from –0.9 fy to +0.9 fy (tensile pre-stresses are referred to as positive). The boundary conditions employed for the set of twelve K-joint configurations are shown in figure 1. The chord stress contours obtained from the numerical analyses were presented not only as a function of the chord pre-stress due to external loads but also as a function of the maximum chord stress. Both contours appeared to be considerably different for the joints where large chord loads were introduced to maintain horizontal equilibrium.

Figure 1. Boundary conditions for K-joints used by van der Vegte et al (7). Various researchers assessed the effects of boundary conditions on the ultimate strength of uniplanar K-joints and came to the conclusion that the influence of restraints could be significant. A brief overview of some of the investigations is presented in the section hereafter. Additional FE analyses were conducted to evaluate the effects of various sets of boundary conditions on the static strength of uniplanar K-joints subjected to chord pre-load. The current study addresses the research programme, the FE strategy and the failure criteria. Finally, the numerical results are presented as a function of either the chord pre-stress due to external loads or the maximum chord stress. PREVIOUS RESEARCH INTO THE EFFECT OF BOUNDARY CONDITIONS ON CHS AND RHS K-JOINTS In 1989, Connelly and Zettlemoyer (9) performed numerical research into the static behaviour of various overlap and gap K-joint configurations. Each joint was analysed twice : at first the K-joints were restrained and loaded in a manner consistent with laboratory tests on such joints. In the second analysis, the K-joint models were mounted into a braced frame with the load being applied directly to the frame instead of the K-joint. Connelly and Zettlemoyer found that for this specific configuration with β = 1.0, the frame-mounted K-joints showed axial capacities which were between 11 to 26 % higher compared to the isolated joints. The authors suggested that, if possible, future tests on isolated joints should consider a more accurate replication of the boundary conditions found in actual frames. In 1992, Bolt et al (10) conducted numerical analyses on a single gap K-joint geometry using different boundary conditions for chord and braces. Variations in capacities of up to 10 % were observed while the post-peak load-deformation responses also varied significantly among the cases considered. However, Bolt reported that confidential research on K-joint configurations with different sets of geometric parameters suggested an even much greater dependency of boundary conditions. As part of a larger study into the behaviour of overlapped K-joints, Healy (11) performed various numerical simulations to assess the effect of chord and brace end restraints on the axial capacity. Healy evaluated two sets of boundary conditions often used in experiments.

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(a) “single” restraints (b) “double” restraints

Figure 2. “Single” and “double” boundary conditions for K-joints. Figure 2a illustrates “single” boundary conditions : one chord end is left free, while one brace end reacts the load applied to the other. Figure 2b depicts the “double” set of boundary conditions where both chord ends are restrained. Healy concluded that, when lateral movements of the braces are restricted, the differences between both sets of boundary conditions are negligible for the joints considered. On the other hand, Healy mentioned that experiments carried out by Bjornoy (12) revealed a strong dependency of boundary conditions on the ultimate strength of K-joints, especially for eccentric overlapped joints. Bjornoy’s conclusion was supported by preliminary research on overlapped K-joints carried out by Dexter et al (13). “Single” type restraints were found to give significantly higher capacities compared to exactly balanced loading conditions, especially for the more heavily overlapped joints. In 1998, Liu et al (14, 15) investigated the effect of boundary conditions and chord load on the capacity of selected uniplanar and multiplanar RHS gap K-joints. Similar to the findings of the previous researchers, the authors concluded that boundary conditions have a significant influence on the ultimate strength of RHS K-joints.

Figure 3. Dimensions and non-dimensional geometric parameters for uniplanar K-joints. SCOPE OF NUMERICAL RESEARCH The configuration of uniplanar K-joints and the definition of the geometric parameters are shown in figure 3. The geometric parameters β and 2γ analysed in van der Vegte’s numerical study (7) are summarized in Table 1. Although the programme of twelve K-joints considered two values of the brace angle θ (45˚ and 60˚), only the six configurations referring to θ = 45˚ are presented in Table 1. The current study focuses on the following four K-joint geometries shown in Table 1 : β = 0.48 and 0.67, 2γ = 25.4 and 63.5 (joints K3 to K6). The K-joints with β = 0.25 are not further studied, as the influence of the horizontal reaction forces on the ultimate load is not as pronounced as for the other configurations due to the relatively small failure loads of K-joints

d0

l0

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t1t2 d2

e

g θ1 θ2

α = 2l0/d0 β = d1/d0 2γ = d0/t0 ξ = g/d0

+Nop

N2 N1

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with small β values. Since the current programme is limited to K-joints with positive gap-values, for some configurations, eccentricities have been introduced to avoid overlapped joints. For each of the K-joints with eccentricities, the gap size g was taken as 32 mm, corresponding to t1 + t2 for the thick walled joints. The values of the gap ratio ξ (= g/d0), g/t0 and e/d0 are also presented in Table 1. The non-dimensional chord length parameter α (= 2l0/d0) is held at 16, whereas d0 = 406.4 mm. The length of the braces is set to 5d1. The steel grade used for the tubular members is S355 with fy = 355 N/mm2 and fu = 510 N/mm2. The boundary conditions investigated are summarized in figure 4. These boundary conditions are commonly used in experiments and numerical analyses. In model 1, loads have been applied to the compression brace end only. This force is primarily reacted by the pinned end of the tension brace whereas the resulting horizontal forces are reacted at the pinned end of the chord. However, because of geometric non-linear effects, this arrangement may lead to unequal forces in the compression and tension braces. In models 2 to 4, equal, opposite loads have been applied to both the compression and tension braces, using the Riks algorithm. In models 1 and 2, the horizontal component of the brace forces causes compressive stresses in the left side of the chord, while in model 4, tensile stresses occur in the right side of the chord. In model 3, the horizontal components of the brace loads are distributed between both chord ends. Model 1 Model 2 Model 3 Model 4

Figure 4. K-joint models with different boundary conditions. In line with the analyses of the parametric study on K-joints, for each of the configurations considered, nine values of the external chord pre-load N0p have been analysed, giving the following chord pre-load ratios N0p/A0fy0 : +0.9, +0.8, +0.6, +0.3 , 0.0, -0.3, -0.6, -0.8, -0.9 (positive values refer to tensile pre-load). Table 1. Geometric parameters of the four K-joints analysed (K3 to K6).

joint t0 (mm) 2γ ξ g/t0 e/d0

K1 16 25.4 0.65 16.4 0.0 β = 0.25 (d1 = 101.6 mm) K2 6.4 63.5 0.65 41.0 0.0

K3 16 25.4 0.33 8.3 0.0 β = 0.48 (d1 = 193.7 mm) K4 6.4 63.5 0.33 20.7 0.0

K5 16 25.4 0.079 2.0 0.015

θ = 45˚

β = 0.67 (d1 = 273.1 mm) K6 6.4 63.5 0.079 5.0 0.015

Remarks : - for all joints, d0 = 406.4 mm - the numerical analyses of K-joints K1 and K2, modelled with boundary

conditions 2 are reported by van der Vegte et al (7)

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FINITE ELEMENT ANALYSES FE modelling aspects The numerical analyses were carried out with the finite element package ABAQUS (8). The joints are modelled using twenty noded solid elements employing reduced integration (ABAQUS element C3D20R). Two layers of elements are modelled through the thickness of each member. Due to symmetry in geometry and loading, only one half of each joint has been analysed. The appropriate boundary conditions are applied to the nodes located in the plane of symmetry. For all joints, the geometry of the welds at the brace-chord intersection has been modelled. The dimensions of the welds in the numerical model are in accordance with the specifications recommended by the AWS (16). Both ends of the braces and the chord ends have rigid diaphragms. The length of the members is considered to be sufficient to exclude any influence of the end caps on the static response of the joints. Since the incorporation of material- and geometric non-linearity in ABAQUS requires the use of true stress-true strain relationships, the engineering stress-strain curve is modelled as a multi-linear relationship and subsequently converted into a true stress-true strain relationship. The hardening rule proposed by Ramberg-Osgood has been used to describe the true stress-true strain behaviour after the peak stress in the engineering stress strain curve is reached. In order to validate the numerical model, comparisons were made with experimental evidence. In 1981, de Koning and Wardenier (3) conducted a series of static tests on uniplanar CHS K-joints. Out of this programme, two thin walled gap K-joints (β = 0.33 and 0.65, 2γ ≈ 56, θ = 45˚, e = 0) were chosen to serve as a basis for validation of the current FE model. As described by van der Vegte et al (7), for both geometries good agreement was observed between the numerical and experimental load-deformation responses, not only for the initial stiffness but also for the peak load and the post-peak behaviour. Loading and boundary conditions of the K-joints In the first step of the numerical analyses, the chord end is pre-loaded with uniformly distributed axial forces using the load-control method. During this first step, the chord ends are roller supported i.e. free to move laterally. In the second step of the loading procedure, the appropriate boundary conditions are applied to the chord ends whereas axial brace loads are applied to the nodes of the brace tip. Meanwhile, the axial forces at the chord ends are maintained at the same level as at the end of the first step. In the second step of the joints modelled with the boundary conditions of model 1, the displacement of the tip of the compression-loaded brace is prescribed, i.e. the joint is loaded employing the displacement-control method. In the second step of the loading history of models 2 to 4, equal but opposite loads are applied to both the compression and tension braces, using the Riks algorithm, enabling to monitor the load-indentation behaviour for declining brace loads.

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NUMERICAL RESULTS AND DISCUSSION Failure criteria Ultimate load is defined as the force on the compression brace first exceeding one of the following four failure criteria : (1) peak load in the load-displacement diagram. (2) for the joints which load-displacement curves do not show a clear peak load, the value

at Lu’s deformation limit (= indentation of 0.03d0) is taken as the “ultimate” load (17). (3) for joints with small gaps, large tensile strains are observed in the chord wall at the weld

toe of the tension brace. Although the load-indentation curves can be extended well beyond this point, it is assumed that cracks initiate if the strain at the integration point of the chord element closest to the weld toe of the tension brace, exceeds 20 %. While the value of 20 % is arbitrary, the use of such a “crack initiation” criterion enables a comparison among the different K-joints and to identify those joints which are vulnerable for fracture.

(4) early termination of the numerical analysis, indicating member failure (i.e. reaching squash load) or the onset of chord buckling.

Effect of boundary conditions Figure 5 shows the chord stress contours obtained for K-joints K5 and K6 (β = 0.67) modelled with various boundary conditions. Although not presented, the contours for joints K3 and K4 with β = 0.48 look very similar. For each joint, the ultimate load is normalized by the corresponding capacity for N0p = 0, where N0p refers to the externally applied chord pre-load. The diagrams shown in figure 5a display the normalized capacities versus the chord pre-stress ratio n’ = N0p/A0fy0, while the contours in figure 5b are based on the actual chord stress ratio n, including the horizontal brace load components. Depending on the boundary conditions shown in figure 4, n is defined as n’-2N1,u cos θ /A0fy0 for models 1 and 2 (left side of the chord), while n = n’+2N1,u cos θ /A0fy0 for model 4 (right side of the chord). Since the K-joints modelled with boundary conditions 3 are statically indeterminate, the chord stresses can not be captured by a formula and are obtained from the FE analyses. For these joints, figure 5b presents the chord stress contours for both sides of the chord. As presented in the section hereafter, the differences between the ultimate capacities of models 1 and 2 are small. To avoid overlap of the chord stress contours and to enhance clarity of the diagrams, the curves for model 1 are not shown in the diagrams of figure 5b. Comparison between models 1 and 2. Comparing the chord stress contours of the joints modelled with boundary conditions 1 and 2, displayed in the graphs of figure 5a, it becomes clear that the differences are small. A better understanding of the effects of chord stress for the joints modelled with boundary conditions 2 is gained after examining the diagrams of figure 5b, where the horizontal axis depicts the actual chord stress ratio. Because of the applied boundary conditions, each contour is shifted in horizontal direction towards the compression side, whereas the amount of transition is determined by the magnitude of the equilibrium loads. From these diagrams it becomes clear that the joints of model 2 subjected to large compressive pre-loads fail by chord member failure. Although not shown in these chord stress contours, the joints of model 1 exhibit similar failure behaviour.

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(a) based on chord pre-stress ratio n’ (b) based on actual chord stress ratio n

Figure 5. Chord stress contours for K-joints K5 and K6 modelled with various boundary conditions.

Comparison between models 2 and 4. Comparing the chord stress contours of the joins modelled with boundary conditions 2 and 4, it is found that for the joints under large tensile chord pre-loads, the ultimate capacities of the joints of model 4 are significantly lower, caused by member failure of the chord. Chord member failures are easily detected from the chord stress contours with the actual chord stress being displayed on the horizontal axis (diagrams displayed in figure 5b). For the K-joints modelled with boundary conditions 4 and pre-loaded by compression or under zero pre-load, the ultimate capacities of the joints are higher than for the corresponding joints of model 2. The unfavourable combination of compression pre-load and compressive reaction forces leading to member failure (i.e. chord buckling or reaching the squash load) observed for the joints of model 2, does not occur in the joints of model 4 under compression pre-load. For the joints under zero pre-load and modelled with boundary conditions 4, the gap area is still subjected to tensile stresses, giving a higher ultimate strength in comparison with the joints where the gap area is loaded in compression, as is the case for the joints of model 2.

0

0.2

0.4

0.6

0.8

1

1.2

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1n'

f(n'

) Model 4 CHS K-jointsModel 3 β = 0.67 Model 2 2γ = 25.4 Model 1 θ = 45

0

0.2

0.4

0.6

0.8

1

1.2

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1n

f(n)

Model 4 CHS K-jointsModel 3 - right side β = 0.67 Model 3 - left side 2γ = 25.4 Model 2 θ = 45

0

0.2

0.4

0.6

0.8

1

1.2

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1n'

f(n'

)

Model 4 CHS K-jointsModel 3 β = 0.67 Model 2 2γ = 63.5 Model 1 θ = 45

0

0.2

0.4

0.6

0.8

1

1.2

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1n

f(n)

Model 4 CHS K-jointsModel 3 - right side β = 0.67 Model 3 - left side 2γ = 63.5 Model 2 θ = 45

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Discussion of results for model 3. The chord stress contours for the joints of model 3, based on the pre-load ratio n’, show that the effect of chord pre-load on the ultimate capacity is much smaller than for the other models. Especially for the joints pre-loaded by compression, the reduction in strength is much less pronounced. This may be explained by considering the chord stress distribution as a result of both chord pre-load and reaction forces. For this purpose, K-joint K5 (θ = 45˚, β = 0.67 and 2γ = 25.4) is examined in detail.

K-joint K5 under compressive pre-load (n’ = -0.9)

K-joint K5 under tensile pre-load (n’ = 0.9)

Step 1 : Chord pre-load

Step 2a : Small brace loads

Step 2b : Reversal of left or right chord reaction force

Step 2c : Ultimate load

Remarks : - The length of each arrow is proportional to the magnitude of the force - Open block arrow : chord pre-load - Black arrow : brace loads and chord reaction forces

Figure 6. External pre-load, brace loads and chord reaction forces of K-joint K5 modelled with boundary conditions 3.

In figure 6, the external chord pre-load and the reaction forces of K-joint K5 modelled with boundary conditions model 3 are schematically illustrated for large compressive (n’ = -0.9) and tensile (n’ = 0.9) chord pre-stress. In each of the diagrams, the length of the arrows is proportional to the magnitude of the forces. The loading procedure considers two steps. In the first step, the chord pre-load is applied while the chord ends are free to move horizontally. The first row of figure 6 illustrates the external forces applied to both chord ends. At the start of the second load step, in which the brace loads are applied, the chord is restrained in horizontal direction, causing reaction

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forces to develop as soon as the braces are loaded. For the two load cases considered (n’ = -0.9 and 0.9), the second step is also visualized in figure 7, displaying the non-dimensional chord load at either side of the K-joint as a function of the brace load. For both chord pre-load cases, the following three stages can be distinguished when the braces are loaded up to failure : STEP 2A : For small brace loads, the chord reaction forces at either side of the K-joint are almost equal in magnitude, pointing in the direction opposite to the brace loads (see second row of figure 6). For the K-joint under pre-compression, this leads to a further increase of compressive chord stress at the left side of the chord, while the chord stress in the right side reduces. For the K-joint under pre-tension, the tensile stress in the right side of the chord becomes larger. This trend continues until the left chord side of the K-joint under pre-compression and the right side of the K-joint under pre-tension come close to yield, resulting in the initiation of load-redistribution. STEP 2B : For the K-joint subjected to n’ = -0.9, further loading of the braces causes the chord reaction force at the left end to decrease and reverse. For the K-joint subjected to n’ = 0.9, a similar remark can be made for the chord reaction force at the right chord end. The reversal of the chord reaction forces is illustrated by step 2b in figure 6. STEP 2C : Continuous loading of the braces up to failure will then increase all chord reaction forces. Failure of the K-joints is visualized by the “ultimate load” data points in figure 7, which are also part of the chord stress contours displayed in figure 5b.

Figure 7. Chord load at either side of the chord for K-joint K5 under compressive (n’ = -0.9)

or tensile (n’ = 0.9) pre-load as a function of brace load.

For the thick walled K-joint (2γ = 25.4) under pre-compression, the chord is subjected to such large reaction forces at failure that the resulting chord stress in the right side of the chord has turned tensile. For the pre-tensioned joint, a similar redistribution is observed. These aspects also become clear from the chord stress contours based on the actual chord stress, shown in figure 5b. While the initial chord stresses due to the external loads vary between -0.9 fy0 and +0.9 fy0, at failure, the actual chord stresses at both sides of the chord are significantly less, thus explaining the less pronounced effect of external chord pre-load.

-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 0

1000

2000

3000

4000

Small brace load

Reversal of chord reaction force

Ultimate load

Left chord side (under tension brace) Right chord side (under compression brace)

N1 [

kN]

chord load / A0 fy0

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For the thin walled joints (2γ = 63.5), a similar redistribution is found although less significant. For these joints, the non-dimensional chord reaction forces (i.e. made non-dimensional after dividing by A0fy0) are much smaller than for thick walled joints. A comparison between the contours based on the chord pre-load ratio n’, shown in figure 5a, reveals no relation between the curves of model 3 and the contours of models 2 and 4. However, after looking at the diagrams in figure 5b based on the actual chord stress, it becomes clear that the stress contours of the “compression” (left) side of the chord of model 3 are slightly below the contours obtained for model 2, while the chord stress contours of the “tension” (right) side of the chord of model 3 are in good agreement with the stress contours of model 4. This means that, when the actual chord stress is considered, the contours for boundary conditions 3 are closely related to the contours of the two other models. This clearly confirms the need to describe the chord stress effects as a function of the actual chord stress rather than the stress due to externally applied chord loads. CONCLUSIONS Numerical analyses have been carried out into the strength of four axially loaded uniplanar CHS gap K-joints subjected to axial chord pre-loading, with the main variables being the geometric parameters β and 2γ and various sets of boundary conditions. Based on the results of this selected set of K-joints, the following conclusions can be drawn : a. In line with the data obtained for uniplanar X-joints, it is found that compressive chord

stresses have a detrimental effect on the ultimate capacity of axially loaded uniplanar K-joints. For K-joints under tensile chord pre-load, the capacity of the joints either increases or decreases compared to the ultimate strength of the corresponding joints under zero pre-load, dependent on the value of β and 2γ, the amount of pre-load and the boundary conditions.

b. The influence of boundary conditions on the ultimate capacity of K-joints can be significant. The differences between the chord stress contours obtained for the joints with the tensile brace end being pinned (model 1) and the joints where the tensile brace is roller-supported to enable equal brace loads (model 2) are negligible. For K-joints with both chord ends being pinned (model 3), the reduction in strength due to chord pre-load diminishes, contrary to the behaviour exhibited by the joints modelled with the other sets of boundary conditions, for which the strength reducing effects due to chord pre-load are more pronounced.

c. The chord stress contours generated for K-joints clearly show that a better understanding of the effects of chord pre-load is attained by considering the maximum chord stress as the governing variable, rather than the chord stress due to external pre-loads.

d. In future publications, the FE data generated in this study will be combined with available data on other types of CHS and RHS joints and proposals for new chord stress functions will be made.

ACKNOWLEDGEMENT The first author would like to thank the Centennial Anniversary Foundation of the Faculty of Engineering, Kumamoto University, Japan for the opportunity to carry out the research reported herein.

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REFERENCES (1) Vegte, G.J. van der and Makino, Y., (2001). The Effect of Chord Stresses on the Static

Strength of CHS X-Joints. Memoirs of the Faculty of Engineering, Kumamoto University, Vol. 46, No. 1.

(2) Kurobane, Y. and Makino, Y., (1965). Local Stress in Tubular Truss Joints. Research Report, Kyushu Branch of Architectural Institute of Japan, No. 4, pp. 75-80 (in Japanese).

(3) Koning, C.H.M. de and Wardenier, J., (1981). The Static Strength of Welded CHS K-Joints. TNO-IBBC Report BI-81-35/63.5.5470, Stevin Report 6-81-13, Delft, The Netherlands.

(4) Dier, A.F. and Lalani, M., (1998). New Code Formulations for Tubular Joint Static Strength. Proc. 8th International Symposium on Tubular Structures, Singapore, pp. 107-116.

(5) Pecknold, D.A., Ha, C.C. and Mohr, W.C., (2000). Ultimate Strength of DT Tubular Joints with Chord Preloads. Proc. 19th International Conference on Offshore Mechanics and Arctic Engineering, New Orleans, U.S.A.

(6) Pecknold, D.A., Park, J.B. and Koppenhoefer, K.C., (2001). Ultimate Strength of Gap K Tubular Joints with Chord Preloads. Proc. 20th International Conference on Offshore Mechanics and Arctic Engineering, Rio de Janeiro, Brazil.

(7) Vegte, G.J. van der, Makino, Y. and Wardenier, J., (2002). The Effect of Chord Pre-load on the Static Strength of Uniplanar Tubular K-joints. Proc. 12th International Offshore and Polar Engineering Conference, Kitakyushu, Japan, Vol. IV, pp. 1-10.

(8) ABAQUS/Standard, (2000). Version 6.1, Hibbitt, Karlsson & Sorensen, U.S.A. (9) Connelly, L.M. and Zettlemoyer, N., (1989). Frame Behaviour Effects on Tubular Joint

Capacity. Proc. 3rd International Symposium on Tubular Structures, Lappeenranta, Finland, pp. 81-89.

(10) Bolt, H.M., Seyed-Kebari, H. and Ward, J.K., (1992). The Influence of Chord Length and Boundary Conditions on K-Joint Capacity. Proc. 2nd International Offshore and Polar Engineering Conference, San Francisco, U.S.A., Vol. IV, pp. 347-354.

(11) Healy, B.E., (1994). A Numerical Investigation into the Capacity of Overlapped Circular K-joints. Proc. 6th International Symposium on Tubular Structures, Melbourne, Australia, pp. 563-571.

(12) Bjornoy, O.H., (1993). Static Strength of Tubular Joints, Phase II, Analyses and Tests of Gap and Overlap K-Joints. Veritec Report No 91-3393, AS Veritec.

(13) Dexter, E.M., Lee, M.M.K. and Kirkwood, M.G., (1994). Effect of Overlap on Strength of K-joints in CHS Tubular Members. Proc. 6th International Symposium on Tubular Structures, Melbourne, Australia, pp. 581-588.

(14) Liu, D.K., Yu, Y. and Wardenier, J., (1998). Effect of Boundary Conditions and Chord Preload on the Strength of RHS Uniplanar Gap K-Joints. Proc. 8th International Symposium on Tubular Structures, Singapore, pp. 223-230.

(15) Liu, D.K., Yu, Y. and Wardenier, J., (1998). Effect of Boundary Conditions and Chord Preload on the Strength of RHS Multiplanar Gap K-Joints. Proc. 8th International Symposium on Tubular Structures, Singapore, pp. 231-238.

(16) AWS American Welding Society, (1992). Structural Welding Code. AWS D1.1-92. (17) Lu, L.H., Winkel, G.D. de, Yu, Y. and Wardenier, J., (1994). Deformation Limit for the

Ultimate Strength of Hollow Section Joints. Proc. 6th International Symposium on Tubular Structures, Melbourne, Australia, pp. 341-347.

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SHEAR LAG IN SLOTTED GUSSET PLATE CONNECTIONS TO TUBES

S. Willibald, University of Toronto, Canada J.A. Packer, University of Toronto, Canada

G. Martinez Saucedo, University of Toronto, Canada R.S. Puthli, Universität Karlsruhe, Germany

INTRODUCTION Gusset plates can be found in almost any type of steel building. As hollow sections have become more popular due to their exceptional properties in compression and torsion, the combination of both gusset plates and hollow sections can be found in numerous applications. These gusset plate connections can be used to splice hollow section members or to connect web members to the chords in roof trusses (see Figure 1). Three possible fabrication details are shown in Figure 2. Slotting the hollow section (Figures 2 (b) and (c)) is the most common version of this connection type. Various failure modes are possible under tension loading with shear lag being one of them. Shear lag of the hollow section can occur as the circumference of the hollow section is connected to the gusset plate only at two points on opposing sides. The unconnected circumference of the hollow section is not fully engaged and contributes only in part to the resistance of the member. In addition, local stress peaks at the slot ends can cause initiating cracks that may result in an early failure. The presented study focused on shear lag failure for round hollow sections. An experimental study on six connections under tensile loading has been carried out, followed by a numerical analysis, which will be used to substitute for further experimental work. Additionally, recent research and international specifications on this topic are evaluated and "best practice" recommendations are made for application to round hollow section members.

ABSTRACT Hollow Structural Sections (HSS) are commonly used as bracing members insteel-framed buildings or as web members in roof trusses. The tubes arefrequently slotted onto gusset plates to simplify fabrication and avoid profiling.Under tension loading, these gusset plate connections can be susceptible toshear lag failure of the HSS since only a part of the tube cross-section is connected to the plate. This paper compares current design proposals foundin research, design guides and specifications against recent experimental and numerical work by the Authors, which comprised of gusset plateconnections for round hollow sections with varying fabrication details.

Figure 1. Metro Toronto Convention Centre.

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(a) (b) (c)

Figure 2. Fabrication details of tested gusset plate connections. LITERATURE STUDY Of the failure modes that can occur in gusset plate connections, shear lag is one of the most ill-defined. Shear lag fracture of the hollow section takes place due to the uneven stress distribution around the circumference of the hollow section. The stresses peak at the points where the hollow section is connected to the plate or weld and become less as the distance to the weld increases (see Figure 3). Therefore, the uncon-nected circumference only contributes in part to the capacity of the member. International specifications and design guides For tension loaded connections, Eurocode 3 (1) provides shear lag provisions that are only applicable for bolted connections. For connections with welds, no specific design method is provided in the Eurocode. Otherwise, shear lag is mentioned only in connection with locally introduced shear loads causing bending moments in longitudinally stiffened plated structures. The North American specifications address shear lag for welded connections under tension loading. Unfortunately, the American and Canadian specifications (AISC 2, CSA 3) differ in their design methods for this limit state. In addition, changing formulae in old and new specifications (e.g. AISC 4 versus AISC 5) indicate a lack of certainty with this connection type. The Japanese specification (6) excludes shear lag by providing minimum connection lengths. The following paragraphs briefly introduce the different design methods of the various specifications.

0

10000

20000

30000

40000

0 22.5 45 67.5 90 112.5 135 157.5 180Angle θ [ ]

Stra

in [

µm]

500 kN750 kN1000 kN1032 kN

o

0

90

180

θ

Figure 3. Strain distribution around circumference of theround hollow section (specimen 1, slotted HSS, noweld return).

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The current American Specification for Hollow Structural Sections (AISC 2) uses the concept of "effective net area". The design method provided is based on research carried out by Chesson and Munse (7). An eccentricity factor U is calculated from the connection eccentricity (see Figure 4) and the connection length Lw:

U = 1- wLx

≤ 0.9 (1)

with: x = πD for round hollow sections (2)

The effective net area is then calculated as:

Ae = An · U (3)

Lw

centre of gravityof top half

wxtsl

tp t

D

wp

Figure 4. Parameters of the experimental and numerical study. The current LRFD Specification (AISC 4, Equation B3-2) uses the gross area Ag of the member to calculate the effective net area Ae (Ae = Ag · U) which can result in considerably different design strengths for gusset plate connections where the hollow section is slotted (An = Ag - 2tp·t). In practice, the slot width tsl is usually greater than tp to allow ease of fabrication, and in such cases An = Ag - 2tsl·t. Recently, a general examination of the AISC LRFD shear lag design provisions has been made by Kirkham and Miller (8). Based on recent studies, it was concluded that the existing design approaches are overly conservative and further research was necessary. The draft version (5) of the upcoming AISC Specification in 2005 now uses the net area of the member, An, in its formula but no longer has an upper limit of 0.9 for the eccentricity factor U (see Equation 1). For round HSS with Lw ≥ 1.3D, the factor U becomes equal to unity. Connection lengths Lw less than D are not covered. The current Canadian Standard (CSA 3) addresses shear lag in elements connected by a pair of welds parallel to the load by calculating the "effective net area" (Clause 12.3.3) based on an efficiency factor that depends on the ratio of the distance between the welds around the hollow section perimeter, w, and the connection length, Lw (see Figure 4). The efficiency factor given is:

1.0 for Lw/w ≥ 2.0; 0.5 + 0.25 Lw/w for 2.0 > Lw/w ≥ 1.0; 0.75 Lw/w for Lw/w < 1.0.

A similar approach based on the former Canadian standard CAN/CSA-S16.1-94 (CSA 9), as well as research done by Korol et al. (10), is given in the design guide for hollow structural sections by Packer and Henderson (11). The recommended efficiency factor there is:

1.0 for Lw/w ≥ 2.0; 0.87 for 2.0 > Lw/w ≥ 1.5; 0.75 for 1.5 > Lw/w ≥ 1.0; 0.62 for 1.0 > Lw/w ≥ 0.6.

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For values smaller than Lw/w = 0.6 shear rupture of the base metal along the weld line is supposed to govern. As the experimental study by Korol et al. (10) was done with gusset plate connections for square hollow sections, it is possible that the results might not be fully applicable for shear lag in round hollow sections. The Japanese recommendations for the design and fabrication of tubular truss structures in steel (6) exclude shear lag by providing a minimum connection length of Lw ≥ 1.2D for gusset plate connections. To account for uncertainties in fabrication of these connections, the connection capacity is restricted to 90% of the unslotted (gross) member strength. Also, AIJ avoid use of the net area of the slotted tube by means of a specific fabrication detail. Table 1 gives an overview of all the above shear lag provisions. Table 1. Shear lag design provisions for round hollow sections.

Specification or design guide

Effective net area Shear lag coefficients Range of

validity AISC (4) Ae = Ag · U

AISC (2) U = 1-

wLx

≤ 0.9 with x = πD no

restrictions

AISC (5) Ae = An · U U = 1-

wLx

U = 1 for Lw ≥ 1.3D Lw ≥ D

AIJ (6) Ae = Ag · U U = 0.9* Lw ≥ 1.2D

CSA (3) U = 1.0 for Lw/w ≥ 2.0 U = 0.5 + 0.25 Lw/w for 2.0 > Lw/w ≥ 1.0 U = 0.75 Lw/w for Lw/w < 1.0

no restrictions

Packer and Henderson (11)

Ae = An · U U = 1.0 for Lw/w ≥ 2.0 U = 0.87 for 2.0 > Lw/w ≥ 1.5 U = 0.75 for 1.5 > Lw/w ≥ 1.0 U = 0.62 for 1.0 > Lw/w ≥ 0.6

shear lag not critical for Lw < 0.6w

Korol (17) Ae = An· α ·U

α = 1.0 for Lw/w ≥ 1.2 α = 0.4 + 0.5 Lw/w for 1.2 > Lw/w ≥ 0.6

U = 1 – 0.4 wLx

shear lag not critical for Lw < 0.6w

*) The factor 0.9 accounts for uncertainties in fabrication. Recent research on shear lag in HSS A number of studies on gusset plate connections have been carried out in the last few years. The latest study, on a special type of gusset plate connection, the so-called hidden joint connection, by Willibald (12) showed that shear lag was not critical for square HSS in this specific connection type but can become critical for rectangular HSS. The results of the parametric study supported the use of the American specifications (2, 4, 5) but indicated a generally overly conservative approach in all current design methods. In an experimental study by British Steel (Swinden Laboratories 13) on slotted end plate connections for circular, square and rectangular hollow sections, 13 of the 24 specimens failed by shear lag. The results of an experimental as well as numerical investigation on shear lag failure for slotted circular hollow sections were given by Cheng et al. (14). Nine tests on gusset plate connections to CHS tension members were performed, but none of the specimens failed by shear lag. However, the experimental and numerical investigations showed that considerable stress concentrations occur at the slot ends. Comparing the results of the study with the then current Canadian (Cheng et al. 15) as well as American specifications (Cheng and Kulak 16), it was shown that neither code accurately represented the behaviour of slotted circular hollow section connections. In contrast to the specifications, Cheng and Kulak (16) concluded that shear lag failure was not critical for round HSS if the connection

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length was longer than 1.3 times the diameter of the circular hollow section (U = 1.0), however all their tests but one were performed with the slot end welded. The results of this research will be incorporated in the upcoming AISC (5) specification (see Table 1). A study on shear lag in slotted square and rectangular hollow sections has been performed by Korol et al. (10). A total of 18 specimens was tested under tensile loading with seven specimens failing by shear lag. The authors concluded that for six of the seven specimens that failed by shear lag, all with Lw/w ≈ 1.0, the connection capacity was nearly equal to the tensile capacity of the hollow section, Nu = An · Fu. One specimen, where Lw/w = 0.61, failed very prematurely due to shear lag. For specimens with Lw/w-ratios smaller than 0.6, base metal shear failure of the hollow section governed. The influence of the eccentricity x on the connection capacity was found to be only minor. Based on the results of the earlier study, Korol (17) proposed a slightly modified approach for the calculation of the effective shear lag net section area. Instead of using the efficiency factors as given in the Canadian or American specifications, less conservative formulae were provided:

α = 1.0 for Lw/w ≥ 1.2 (net/gross section failure governs) (4a) α = 0.4 + 0.5 Lw/w for 1.2 > Lw/w ≥ 0.6 (shear lag failure governs) (4b) non-applicable for Lw/w < 0.6 (block shear tear-out governs).

The eccentricity factor U was then calculated by:

U = 1.0 – 0.4 wLx

(5)

The effective shear lag net section was then given by:

Ae = An · α · U (6)

EXPERIMENTAL STUDY Scope of testing The experimental study comprised of six gusset plate connections for round hollow sections. The specimens had varying fabrication details (see Figure 2): slotted versus unslotted HSS, slot end welded versus no weld return. A further parameter in the test series was the weld or connection length Lw with the Lw/w-ratio varying between 0.66 and 0.88 (with w = 0.5 · π · D - tsl or w = 0.5 · π · D – tp). Standard cold-formed 168 x 4.8 mm Class C hollow sections with a specified yield stress of 350 MPa (CSA 18) were used. The gusset plate was made out of 1" (25.4 mm) Grade 300W steel. Table 2 shows the dimensional, and Table 3 the material, properties of the tested specimens. The welds connecting the hollow section and the gusset plate were standard 10 mm fillet welds using E480XX electrodes (CSA 19). Each specimen was equipped with 10 linear strain gauges measuring the longitudinal strain distribution on the hollow section (see Figure 5). The displacement of the connection was measured by four LVDTs (Linear Variable Differential Transformers). The results of these measurements were later on used to verify the numerical models of the tested specimens.

50

22.5o22.5o

22.5o22.5o

50 50

12

34

567

8

910

Figure 5. Strain gauge locations on tested specimens.

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Table 2. Measured dimensional properties of test specimens.

Specimen HSS tsl [mm]

w [mm]

Lw [mm]

tp [mm] wp [mm] Connection type

1 156 197 Slotted tube, slot end not filled

2 169 197 3 208 198

Slotted tube, slot end filled

4

27.0 238

192 198 Slotted tube, slot end not filled

10 162 2 x 74.3 11

168.5 x 4.9 Ag = 2513 mm2

with x = 53.6 mm

- 239 195

25.7

2 x 75.5 Slotted plate

Table 3. Measured material properties of test specimens.

E [MPa] Fy [MPa] Fu [MPa] εu [%] HSS 196000 498* 540 25.9 Plate 201000 358 482 28.0

*) Using the 0.2% offset method, as material was cold-formed. Test results Failure of all six specimens was caused by either shear lag (specimens 3, 4, 10, 11)), tear-out of the HSS base material along the weld (specimen 2) or both failures taking place at the same time (specimen 1, see Figure 6). Shear lag failure causes the HSS to fail circum-ferentially while block shear tear-out happens along the weld. Table 4 shows the ultimate connection strength, the failure mode as well as the predicted failure loads according to current design methods. Generally, the specimens with the shorter connection lengths (specimens 1, 2 and 10) had a reduced connection capacity. Before failure, all specimens showed ovalization in the hollow section, especially pronounced in the specimens with the unslotted tube and the slotted plate (see Figure 2 (a)). In all specimens, the strain gauge readings showed very high stresses at the strain gauges closest to the weld at the beginning of the connection (strain gauge 5, see Figures 3 and 5). The strain gauge furthest away from the weld (strain gauge 8) reported either negligible or even negative strains (specimens 10 and 11) at ultimate load. The strain distribution along the weld and beyond could be

0

200

400

600

800

1000

1200

1400

0 5 10 15 20 25Displacement [mm]

Con

nect

ion

Load

[kN

]

Sp. 11Sp. 10Sp. 4

Sp. 1Sp. 2

Sp. 3

Figure 7. Load versus Displacement curves of the tested specimens.

Figure 6. Specimen 1 at failure.

Shear lag

Tear-out

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observed by comparing strain gauges 1, 3, 5 and 10. Again, strain gauge 5 had the highest strain levels in each specimen. Considerable displacement took place in all tested specimens (see Figure 7). The specimens having an unslotted tube and a slotted plate showed the largest deformation before reaching their ultimate loads. Considering these sizable displacements, it might be necessary to define a deformation limit which, for some connections, will then govern their capacity. Having comparable connection lengths, specimens 1,2 and 10 as well as specimens 3, 4 and 11 have only slightly different capacities. This indicates that the fabrication detail only has a little influence on the connection strength. Currently most codes do not specify the use of a certain detail but provide one design method to cover all three cases. However, with increasing gusset plate thickness, the difference in connection strength between the various fabrication details might be more pronounced. Generally, the design methods found in the American specifications (AISC 4,5) show the best agreement with the tests but further research seems necessary. Table 4. Actual and predicted connection strength of test specimens.

Specimen Test Failure Mode* Nux/AnFu Nux/AgFu

AISC (4)

AISC (5)

CSA (3)

Packer and Henderson

(11)

Korol (17)

Nux or Nu [kN] 1032 890 796 597 754 762 1 Nux/Nu - SL, TO 0.85 0.76 1.16 1.30 1.73 1.37 1.35

Nux or Nu [kN] 1087 881 829 647 754 801 2 Nux/Nu - TO 0.89** 0.80 1.17 1.31 1.68 1.44 1.36 Nux or Nu [kN] 1211 973 902 798 754 913 3 Nux/Nu - SL 1.00** 0.89 1.20 1.34 1.52 1.61 1.33 Nux or Nu [kN] 1154 979 876 737 754 868 4 Nux/Nu - SL 0.95 0.85 1.18 1.32 1.57 1.53 1.33 Nux or Nu [kN] 1107 907 907 688 842 869 10 Nux/Nu - SL 0.81 1.22 1.22 1.61 1.31 1.27 Nux or Nu [kN] 1196 984 984 829 842 975 11 Nux/Nu - SL 0.88 1.22 1.22 1.44 1.42 1.23

*) SL stands for shear lag failure and TO stands for block shear tear-out failure along the weld; **) As slot end was welded, it might be also appropriate to assume An = Ag; Nu = Ae · Fu. NUMERICAL STUDY For further study of gusset plate connections, a numerical study has been started. The final goal of this numerical study will be a parametric study concentrating on the influences of several variables: weld length, hollow section diameter, hollow section wall thickness, the eccentricity of the top or bottom part of the HSS, and fabrication details. The Finite Element program ANSYS 5.7 (Swanson Analysis System Inc. 20) has been used for the numerical study. A geometric and material non-linear analysis was performed for all specimens. 8-noded, large strain solid elements (solid45) with reduced integration and hourglass control were used throughout. The material properties were input as a multi-linear curve with the engineering stress and strain converted to the true stress and strain values. To simulate cracking in the models, a maximum equivalent plastic strain limit was used. The so-called "birth and death" elements allow the user to significantly reduce the stiffness of the elements, or "kill them", if an equivalent plastic strain is reached. Due to the symmetry of the connection it was only necessary to model an eighth of the connection (see Figure 8). The welds were fully modelled. A gap between the gusset plate

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and the hollow section was modelled to prohibit any direct stress transfer between the plate and the hollow section thus forcing load transfer to occur only via the welds. Symmetry boundary conditions were employed along the planes of symmetry (translations normal to the plane of symmetry were fixed) and the nodes at the HSS end were fixed. The finite element models were then loaded by displacing the nodes at the end of the gusset plate. Specimens 2 and 3, which have a slotted HSS with the slot end welded (fabrication detail (c), see Figure 2) have been numerically modelled and show very good agreement with the tests. The predicted ultimate loads for these two specimens are both within 2% of the actual ultimate loads for each test (see Table 5). Figure 9a compares the load-displacement curves for specimens 2 and 3 with the respective results of the numerical models. For both specimens the agreement is very good up to peak load. Unfortunately, the numerical models had problems converging beyond a certain point. At this load step, a high number of elements are “killed” which causes a sudden change in stiffness thus causing severe convergence problems. Yet, due to the high number of lost elements it is safe to assume that the ultimate load of the FE-model has been reached and subsequent calculation steps would result in a lower connection load. The comparison of the most critical strain gauge (strain gauge 5, see Figure 5) also shows good agreement between test and FE model (see

Figure 8. Numerical model of specimen 2.

Table 5. Comparison between test and numerical results.

Specimen Nux [kN] NFE [kN] Nux/ NFE 2 1087 1073 1.01 3 1211 1190 1.02

0

200

400

600

800

1000

1200

1400

0 2 4 6 8 10 12 14 16Displacement [mm]

Con

nect

ion

Load

[kN

]

Spec. 2FE Spec. 2Spec. 3FE Spec. 3

0

200

400

600

800

1000

1200

1400

0 5000 10000 15000 20000 25000 30000

Strain [µm]

Con

nect

ion

Load

[kN

]

Spec. 2FE Spec. 2Spec. 3FE Spec. 3

Strain Gauge 5

Figures 9a and 9b. Comparison between test and numerical results.

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Figure 9b). For the future, it is planned to have comparable models for the other two fabrication details and to use these finite element models in a parametric study. CONCLUSIONS An experimental, numerical as well as literature study on shear lag in round hollow section gusset plate connections under tension loading has been carried out. The experimental study showed that shear lag can indeed become critical in gusset plate connections. The connection length had the largest effect on the connection capacity, whereas the fabrication detail of the connection (see Figure 2) only had a minor influence on the capacity. For some specimens, large displacements could be observed before failure, which could become critical if deformations are restricted by a deformation limit. The numerical study showed that it is possible to generate very good finite element models of these connections. The numerical study will soon be extended to do further parametric studies to finally provide suitable design methods against shear lag failure. The design methods that can be found in current international specifications have been introduced in the literature study and have been evaluated against the experimental research carried out. At present, the American specification (AISC 5) seems to be best suited to design against shear lag failure under quasi-static tension loading, but all design methods are overly conservative and additional research is still necessary. For the future, further research is currently planned on shear lag in gusset plate connections under cyclic loading, as can be found in earthquake situations. With these connections, special attention will be paid to the fabrication and refined connection details will be considered. ACKNOWLEDGEMENTS Financial support for this project has been provided by CIDECT (Comité International pour le Développement et l’Etude de la Construction Tubulaire) Programme 8G and NSERC (Natural Sciences and Engineering Research Council of Canada). IPSCO Inc. and Walters Inc. (Hamilton, Canada) generously donated steel material and fabrication services, respectively. NOTATION Ag = gross cross-sectional area of hollow section Ae = effective net cross-sectional area of hollow section An = net cross-sectional area of hollow section D = outside diameter of round hollow section E = modulus of elasticity Fy = yield tensile stress Fu = ultimate tensile stress Lw = weld length NFE = connection strength as predicted by numerical model Nu = calculated connection strength Nux = measured connection strength U = coefficient for shear lag net section fracture calculation t = wall thickness of hollow section tp = thickness of gusset plate tsl = width of slot in hollow section

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wp = width of gusset plate w = distance between the welds, measured around the perimeter of the HSS x = eccentricity ratio α = coefficient for shear lag net section failure calculation εu = ultimate strain at rupture θ = angle between gusset plate centre line and radial line of hollow section REFERENCES (1) Eurocode 3, (1993). Design of steel structures - General rules - Part 1-8: Design of

joints. Draft version. British Standards Institute, London, England. (2) AISC, (2000). Load and Resistance Factor Design Specification for Steel Hollow

Structural Sections. American Institute of Steel Construction, Chicago, USA. (3) CSA, (2001). Limit States Design of Steel Structures. CAN/CSA-S16-01. Canadian

Standards Association, Toronto, Canada. (4) AISC, (1999). Load and Resistance Factor Design Specification for Structural Steel

Buildings. American Institute of Steel Construction, Chicago, USA. (5) AISC, (2003). Specification for Structural Steel Buildings. Draft (December 1, 2003)

version of the forthcoming (2005) Specification. American Institute of Steel Construction, Chicago, USA.

(6) AIJ, (2002). Recommendations for the Design and Fabrication of Tubular Truss Structures in Steel. (in Japanese) Architectural Institute of Japan, Japan.

(7) Chesson E., Jr., and Munse, W.H. (1963). Riveted and bolted joints: Truss type tensile connections. Journal of the Structural Division, ASCE, 89(1), 67-106.

(8) Kirkham, W.J., and Miller, T.H. (2000). Examination of AISC LRFD shear lag design provisions. Engineering. Journal, AISC, 3rd Quarter, 83-98.

(9) CSA, (1994). Limit States Design of Steel Structures. CAN/CSA-S16.1-94. Canadian Standards Association, Toronto, Canada.

(10) Korol, R.M., Mirza, F.A., and Mirza, M.Y. (1994). Investigation of shear lag in slotted HSS tension members. Proceedings, 6th International Symposium on Tubular Structures, Melbourne, Australia, 473-482.

(11) Packer, J. A., and Henderson, J. E. (1997). Hollow structural section connections and trusses - A design guide. 2nd Ed., Canadian Institute of Steel Construction, Toronto, Canada. ISBN: 0-88811-086-3.

(12) Willibald, S. (2003). Bolted Connections for rectangular hollow sections under tensile loading. PhD thesis, University of Karlsruhe, Germany.

(13) Swinden Laboratories, (1992). Slotted end plate connections. Report No. SL/HED/TN/22/-/92/D. British Steel Technical, Rotherham, England.

(14) Cheng, J.J.R., Kulak, G.L., and Khoo, H. (1996). Shear lag effect in slotted tubular tension members. Proceedings, 1st CSCE Structural Specialty Conference, Edmonton, Alberta, Canada, 1103-1114.

(15) Cheng, J.J.R., Kulak, G.L., and Khoo, H. (1998). Strength of slotted tubular tension members. Canadian Journal of Civil Engineering, Vol. 25, 982-991.

(16) Cheng, J.J.R., and Kulak, G.L. (2000). Gusset plate connection to round HSS tension members. Engineering Journal, AISC, 4th Quarter, 133-139.

(17) Korol, R.M. (1996). Shear lag in slotted HSS tension members. Canadian Journal of Civil Engineering, Vol. 23, 1350-1354.

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(18) CSA, (1998). General Requirements for Rolled or Welded Structural Quality Steel/ Structural Quality Steel. CAN/CSA-G40.20/G40.21-98. Canadian Standards Association, Toronto, Canada.

(19) CSA, (2003). Welded Steel Construction (Metal Arc Welding). CAN/CSA-W59-03. Canadian Standards Association, Toronto, Canada.

(20) ANSYS Release 5.7. (2000). Swanson Analysis System Inc., Houston, USA.

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REVIEW OF TUBULAR JOINT CRITERIA

P.W. Marshall, Moonshine Hill Proprietary, Texas

ABSTRACT This note reviews and compares four sets of tubular connection design criteria for axially loaded circular tubes. The four criteria are AWS D1.1, API RP2A, ISO/WD 15-1.2, and ANSI/AISC 360-05.

INTRODUCTION The existing American design codes for welded tubular connections are AWS D1.1 Structural Welding Code (1990 thru 2002) and the substantially identical AISC Specification for the Design of Steel HSS (1997), the basis of which is documented in the author’s book (1). Three new sets of design criteria are in the works. They are: (1) Proposed update to API RP2A, Design... of Fixed Offshore Platforms, based on research conducted by Prof. Pecknold at the University of Illinois, and sponsored the API Offshore Tubular Joint Research Consortium. A lengthy Commentary is included to self-document these criteria. Extensive nonlinear finite element analyses were used to extend the experimental data base, particularly in the areas of overlapped K-joints, a moment-free baseline for T-joints, and chord stress interaction for a wide variety of joint types and loadings. In view of reduced scatter compared to existing criteria, a reduced WSD safety factor of 1.6 is proposed. This update has been approved for publication in the 22nd edition of RP2A, and is in the final stages of editing. (2) Static Strength Procedure for Welded Hollow Section Joints, IIW doc XV-E-03-279, based on CIDECT research. This is also on the fast track to becoming an international standard as ISO/WD 15-1.2, with IIW commission XV as secretariat. The immediate purpose of this note was to provide comments for a Sept. 2003 meeting of IIW s/c XV-E. (3) ANSI/AISC 360-05, Standard Specification for Structural Steel Buildings (draft of August 20, 2003), Chapter K, HSS Connections, being prepared by an ad hoc task group under the direction of Larry Kloiber. This is essentially the same as the CIDECT-based IIW document, except that it gives the characteristic ultimate strength without hiding a partial safety factor therein. Separate safety factors are then given for LRFD and ASD. COMPARISON OF THE DESIGN EQUATIONS Principal results of this review are shown in the Tables and Figures. Table 1 gives a side-by-side tabulation of the design criteria for different types of circular joints. The square bracket term is Qu in API, and simply written out in IIW and AISC. AWS criteria have been converted to this format for comparison.

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Table 1. Design equations.

CIRCULAR TUBE JOINTS -- AXIAL LOAD

AWS D1.1-92 and AISC ‘97 HSS Connection Manual

API RP 2A-WSD Offshore Platforms 22nd edition

CIDECT IIW-XV-E-03-279 ISO/WD 15-1.2

AISC 360-05 Chapter K Kloiber draft 8/03

General format Pu sin θ = to2 Fyo [*] Qf [*] defined below FS Pa sin θ = T2 Fyo [*] Qf Pn sin θ = to2 Fyo [*] Kp Pu sin θ = t2 Fyo [*] Qf

T & Y joint [*] = (18.8β + 3.4) √Qβ [*] = 2.8 + (20 + 0.8γ) β1.6

but ≤ 2.8 + 36β1.6 [*] = (2.8 + 14.2β2) γ0.2 [*] = (3.1 + 15.6β2) γ0.2

K & N gap [*] = 32β/α + 3.4 with α = 1.0 + 0.7 g/di ≤ 1.7

[*] = (16 +1.2γ) β1.2 Qg ≤ 40 β1.2 Qg Qg = 1+ 0.2(1-2.8g/D)3 **

K & N overlap ( )

)(2.3

)(4.332[*]

2

1

qfF

Fqf

y

EXXτβγ

β

+

+=

[*] as for gap with Qg = 0.13 + 0.65 φ √γ ∗∗ and φ = (tb/Fyb) / (toFyo)

[*] = (1.8 + 10.2β) Kg

( )⎥⎥⎦⎤

⎢⎢⎣

−++=

33.1g/t5.0exp1024.01

0

2.12.0 γγgK

[*] = (2.0 + 11.33β) Qg with Qg same as CIDECT Kg and g negative for overlap

X joint [*] = (13.3β + 3.4) Qβ

Also can length effect [*] = [2.8 + (12 + 0.1γ) β] Qβ

Stronger alternate for tension [ ]

β81.012.5*

−= [ ]

β81.017.5*

−=

K-T joint See general multiplanar

Use gap between loaded diagonals

As for K with eff. β = ∑ βi / 3 Special combo rules & missing cases

Not covered

K-K joint (delta truss)

See general multiplanar (no increase over K joint) Not covered Check chord gap for shear + axial

(no increase over K joint) Not covered

General multiplanar

[*] = (32β/α +3.4) Qβ0.7(α -1)

with α per Annex L Commentary reference To AWS method

X-X joints covered General case not covered Not covered

Chord load effect Qf or Kp

Tension or compression Qf = 1 - 0.03 λ γ Ū2

Ū2 = [(P/Py)2 +(M/My)

2]

Comp.(+), tens.(-) at footprint 2

yyf U

MM

PPQ 3211 CCC −−−=

Compression only Kp = 1 – 0.3 Ū (1+ Ū)

Ū = P/Py + M/My

Same as CIDECT

Other terms ( ) 6.0833.13.0

>−

= βββ

forQβ

** Qg not defined for 0.05 > g/D > -0.05 Pn includes resistance factor Pu is characteristic

ultimate

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0.0 0.5 1.0q

0.5

1.0

0.0

f 2(q)

Details of the AWS conversion to international format for overlap K&N joints are given below, where q = percent overlap as a fraction. In the existing Code, vp is the allowable punching shear and the allowable capacity normal to the chord is given by... Allowable Pn sin θ = vp to L1 + 2 vw tw L2 For conversion, the following substitutions are made...

L1 = π β D f1(q) (partial footprint arc) vw = 0.3 FEXX (allowable) L2 = β D f2(q) (lap weld ┴ to chord) vw = 0.8 FEXX (ultimate) with the resulting international format given by...

Ultimate Pu sin θ = to2 Fyo [*] Qf with ( ) )(2.3)(4.332[*] 21 qfF

Fqfy

EXXτβγβ ++=

In Figure 1, f1 and f2 shown for 45º N-joint with β < 0.5. These values were obtained graphically from a scale layout of joints with varying degrees of overlap.

Figure 1. Layout and functions f1 and f2 for overlapping 45º N-joints with β=0.5. It may be noted from Table 1 that the AWS criteria cover a wider variety of design situations than the others, with particular reference to the general multi-planar case. The proposed AISC criteria cover the least, in a deliberate effort to minimize complexity.

0.0 0.5 1.0

0.5

1.0

0.0

q

f 1(q)

q(βD)

L2

L1

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RESULTS Figures 2-5 show parametric comparison of the criteria for T&Y joints and X joints, which was performed on an Excel spreadsheet. The base case is beta of 0.5, tau of 0.5, and gamma of 20. The upper plots show the effect of varying beta, with the other parameters kept at the base case. The author’s 1969 and 1975 criteria were subsequently shown to be un-conservative for X-joints, but they are very close to the latest OTJRC results for T&Y joints. The lower plots show the effect of varying gamma; there is no effect if the T2Fy format tells the whole story. There was no effect of varying tau in any of these cases.

Figure 2. Effect of β for X-joints with γ=20.

Figure 3. Effect of γ for X-joints with β=0.5.

variations for X joints

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Qu

AWS & AISC Hdbk API proposal AISC proposal

variations for X joints

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γ

Qu

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Figure 4. Effect of β for T & Y joints with γ=20.

Figure 5. Effect of γ for T & Y joints with β=0.5.

variations for T & Y joints

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40

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Qu

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variations for T & Y joints

0

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0 5 10 15 20 25 30 35

γ

Qu

AWS & AISC Hdbk API proposal AISC proposal

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Figures 6-8 plot plots results for K&N joints. The large-scale plot in Figure 6 shows the effect of gap or overlap for base case beta, tau, and gamma. The single expression in the CIDECT-based AISC proposal, covering both gap and overlap, matches AWS in the gap range, and matches API finite element results in the overlap range, at least for the base case parameters.

Figure 6. Effect of gap/overlap for 45º N-joint with β=0.5, τ=0.5, and γ=20. Figures 7 and 8 show the effect of varying the parameters β, γ, and τ at 60% overlap and 0.1D gap, respectively. Here we see that the proposed AISC (and IIW/CIDECT) criteria completely miss the strong effect of tau in the overlap region, as predicted by the AWS strength-of-materials approach and confirmed by the API finite element studies. They also appear to under-predict the beneficial effect of large beta.

K & N joints

0

10

20

30

40

-1 -0.5 0 0.5 1

(overlap) g/D (gap)

Qu

AWS & AISC Hdbk API proposal AISC proposal

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Figure 7. Effects of β, γ, and τ for overlap N-joints with g/D = -0.3.

overlap joints

0

20

40

60

80

0 0.2 0.4 0.6 0.8 1 1.2

β

Qu

AWS & AISC Hdbk API proposal AISC proposal

overlap joints

01020304050

0 5 10 15 20 25 30 35

γ

Qu

AWS & AISC Hdbk API proposal AISC proposal

overlap joints

0

10

20

30

40

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

τ

Qu

AWS & AISC Hdbk API proposal AISC proposal

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Figure 8. Effect of β, γ, and τ for gapped N-joints with g/D = 0.1.

gap joints

0

20

40

60

80

0 0.2 0.4 0.6 0.8 1 1.2

β

Qu

overlap joints API proposal AISC proposal

gap joints

0

10

20

30

0 5 10 15 20 25 30 35

γ

Qu

AWS & AISC Hdbk API proposal AISC proposal

gap joints

0

10

20

30

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

τ

Qu

AWS & AISC Hdbk API proposal AISC proposal

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Finally, Figure 9 shows the chord load effect, with the reduction factor called Qf in US specs and kp internationally. All criteria pass through unity at zero chord load. Based on Yura’s tests, AWS criteria show the effect of chord buckling tendencies at large gamma, a feature which is missing from the other criteria. The API-OTJRC finite element parameter studies show quite different results for different brace types and loadings, and are represented in the criteria by a quadratic expression with tabulated coefficients; linear terms tilt the parabolas. AISC and IIW proposals simplify this to a single line, which is reasonable representation of the effect on joint strength at chord service loads, for most joint types. The notable exception is equal diameter X joints with compression in the branches, where biaxial membrane stresses at the saddle position make tensile chord loads detrimental and compressive chord loads slightly beneficial.

Figure 9. Reduction factor (kp or Qf) versus chord utilization. DISCUSSION Q. What are conclusions of the comparison? A. When comparing existing AWS-AISC criteria for circular tubular connections to CIDECT, both in 1992 and today, neither criteria appear to have significantly different errors on the unsafe side. Thus, one may ask the following questions: “Why churn the Code by adopting essentially similar criteria but in a different format?” “Why not look at new API results having a more significant impact on reliability?” The issue is not simply whether or not to maintain the American status quo. It is important to keep the Codes evergreen in the sense that they reflect the latest data, with researchers still

0

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new API K-axial axial new API K-axial IPBnew API T/Y axial axial new API T/Y comp IPBnew API X <.9 axial new API X =1 com ax ialnew API bending axial new API bending IPBAWS = 20 axial combined AWS = 20 IPB combinedAWS = 20 OPB combined new AISC all cases all cases

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new API K-axial axial new API K-axial IPBnew API T/Y axial axial new API T/Y comp IPBnew API X <.9 axial new API X =1 com ax ialnew API bending axial new API bending IPBAWS = 20 axial combined AWS = 20 IPB combinedAWS = 20 OPB combined new AISC all cases all cases

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active into the future who remember where it all comes from. Q. There are obviously parameters that are treated very differently (tau overlapped and overlap) and others that vary much less between the standards. Why? A. Tau: All the criteria capture the effect of tau (t/T) in the same way, but without explicit expression in point load criteria for T, Y, and X connections. This is not to say that tau is unimportant; indeed, its primary importance was more obvious to the user in the old AWS punching shear format. When one gets called in after the fact on structural failures and tubular projects in trouble, one of the first things to look for is excessive tau ratios. Tau effect in overlapped connections: In the old AWS-API-AISC criteria, this is captured by mechanistic consideration of both punching at the partial footprint (L1) and shear in the overlap weld (L2). In Pecknold’s new API criteria, this is based on an extensive inelastic finite element parameter study, with totally separate Qg expressions for gap and overlap joints. Pecknold’s indicated higher strength for large beta and large tau is also consistent with the unexpectedly good performance of same-size overlapped K-bracing in Hurricane Andrew. In CIDECT-IIW-ISO criteria, overlap is treated as an extension of the behaviour of gap connections in which tau has no effect; a single Kg expression for both is curve-fit to the smaller empirical test data base. This makes computerized design easier, but gives the designer no insight into the physical mechanism of load transfer. Effect of overlap amount: Both Pecknold (new API) and CIDECT agree that there is a significant, but nearly constant, beneficial effect beyond g/D of -0.1. The old AWS-API approach (dating back to 1975) was apparently intuitively appealing but wrong, while remaining on the safe side for moderate amounts of overlap. Pecknold gives no equations for |g/D| smaller than 0.05, and suggests interpolation in this region. In older codes, this was a prohibited zone, due to concern over creating a weak hard spot and awkward welding conditions. The smooth transition shown in the CIDECT strength criteria (and in Efthymiou’s SCF criteria) may simply be an artefact of curve-fitting. This issue needs to be re-examined, seeking data in the prohibited zone. Welded connections with tensile strains over 2% in inelastic finite element solutions may be considered vulnerable to fracture. Effect of chord loading: The 1972 AWS Code included a modest Qf penalty for compressive chord loads, based on Japanese data. Existing AWS-AISC criteria reflect further effects of gamma and chord load type, based on Yura’s X-joint data. CIDECT criteria are simpler, with Kp close to being on the safe side of Yura. Pecknold’s criteria, based on extended finite element results, reflect effects of both chord and brace load type (but not gamma). This is reasonably consistent with CIDECT for K and N connections, but its better prediction for other types of connections has a significant effect on reliability, prompting a modest reduction in working stress design safety factor in API. One common design case in which both CIDECT and AWS-AISC are significantly on the unsafe side is equal size X-braces with equal but opposite loads and no joint can. A caveat for this case is urgently needed. Q. Do we need more data to choose the right direction for the parameters that vary widely? A. Pecknold’s API data base includes both the CIDECT physical tests and his extended finite element results. It could be readily compared to CIDECT-IIW-ISO criteria, to quantify the reliability consequences of adopting these into AISC. Gathering additional research data must be left to the future. In order to meet its ambitious publication schedule, AISC should select one set of criteria and stick with it – no mix-and-match. For circular connections at this point in time, Pecknold’s criteria have not been as widely vetted as CIDECT, while CIDECT does not have the extensive set of worked examples and familiarity to American designers as the existing AWS-AISC criteria.

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Q. Are the difference due to the wide difference in the type of structures the standards are based on and do these variances really show variances due to exceeding testing limits i.e. do the API people test 48 dia 1 inch connections while the CIDECT people test 4 in x 1.4 tube? A. The differences are not always that great. D/t of 48 is quite typical for offshore structures, so punching at the material shear strength rarely governs. Most CIDECT tests are in the D/t range of standard weight structural tubing, which ranges from 6 to 34. European bridge designers seem to favor the 3 to 13 D/t range of double extra strong. American designers use D/t up to 120 for fabricated large diameter chord members, with much thicker joint cans at the nodes. None of the design criteria show an adverse size or thickness effect on static strength, although fracture mechanics and some of the tension test data suggest one. AWS criteria give no bonus for tension. Q. What is the effect on joints designed and built routinely? A. People generally want to know the impact on cost and safety before they change a design code. AISC should get a feel for this while re-working all the example problems and tabulated results in the HSS manual. Bridges and offshore structures are also influenced by fatigue, so the impact of a static strength change is muted. CONCLUSION Although this paper may be regarded as a “stream of consciousness” examination of ongoing design code developments, it is already drawing worthwhile discussion. ACKNOWLEDGEMENTS The foregoing Q&A discussion was prompted by thoughtful review of an earlier draft of this note from Tom Schlafly at AISC. Drafting of the figures has been performed by Dakang Liu at TU Delft. The author is grateful to the conference organizers for accommodating this paper. REFERENCE (1) P. W. Marshall, Design of Welded Tubular Connections, Developments in Civil

Engineering #37, Elsevier Science Publishers, Amsterdam, 1992 (limited availability at civilbooks.com)

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