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Final Report5BF-10/98

Title of the Project: Analysis of Existing and ForthcomingData for Multi-Planar KK-Joints withCircular Hollow Sections

Sponsors: CIDECT

Ministry of Education, Science, Sports and Culture, Japan

Research Program: CIDECT 5BF

Application for research by: Nippon Steel Metal Products

Research carried out by: Sojo University

Kumamoto University

Date: July 1998

Period covered: January 1995-December 1996

Research team: Prof. Yoshiaki Kurobane

Sojo University

Department of Architecture

Ikeda 4-22-1, Kumamoto 860-0082, Japan

Phone: +81-96-326-3111

Fax: +81-96-325-8321E-mail: [email protected]

Prof. Yuji Makino

Kumamoto University

Department of Architecture and Civil Engineering

Kurokami 2-39-1, Kumamoto 860-8555, Japan

Phone: +81-96-342-3593

Fax: +81-96-342-3569

E-mail: [email protected]

KK

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1. INTRODUCTION

Makino et al. (1984) reported the earliest experimental study on circular tubular KK-jointsunder symmetrical axial brace loading. The design formula for multi-planar KK-joints recom-mended in the current Cidect design guide (Wardenier et al. 1991) was based on these test results.Paul et al. (1992, 1994) succeeded Makinos research and proposed ultimate strength formulae forKK-joints under symmetrical loads. Mouty and Rondal (1992) also conducted a series of tests onKK-joints. However, the latter test results showed KK-joint capacities significantly lower thanthose predicted by Pauls formulae. This fact motivated the Cidect working groups to initiateResearch Program 5BF on Analysis of existing and forthcoming data for multi-planar KK-jointswith circular hollow sections. Subsequently Lee and Wilmshurst (1996) completed an extensiveseries of numerical analyses of KK-joints under symmetrical loads and proposed new ultimatestrength formulae using both numerical and experimental results. KK-joints under anti-symmetri-cal axial loads have also been studied extensively by Makino et al. (1994), Yonemura et al. (1996),Lee et al (1996) and Wilmshurst et al. (1997). The total number of joints studied as of May 1998reached 156 for joints under symmetrical loads and 112 for joints under anti-symmetrical loads.

This report proposes those further revised new ultimate strength equations for KK-jointsunder both symmetrical and anti-symmetrical axial loads, which are developed based on all the

existing test and numerical results. These formulae are applicable only to joints whose failures aregoverned by chord wall plastification. The new prediction formulae are compared with the Moutyand Rondal test results and with the AWS equation.

2. DATABASE

The screened database was constructed, by omitting the Mouty and Rondal test results aswell as the test and numerical results for specimens that failed in failure modes other than the chordwall plastification, from the database of Makinoet al. (1996) (accessible at the web site http://www.arch.kumamoto-u.ac . jp/maki_lab/ database.html). The other failure modes men-tioned above include flexural and local bucklingof compression braces, cracking at points wherestresses concentrate, and plastic deformation ofbraces. The screened database is summarized inTables 1 and 2, respectively, for joints under sym-metrical and anti-symmetrical axial loads. Thenumber designating each data set in Tables 1 and2 is identical to the serial number in Makinos da-tabase. The values of d0, t0, d1, t1,Fy,Fu, and

N1u,KKfor test specimens shown in these tables

and the values of gand gtfor test specimens inTable 1 are measured ones. The other geometricalvariables are given in nominal values. The defi-nition of symbols is shown in Appendix.

3. DERIVATION OF ULTIMATESTRENGTH EQUATIONS

3.1 Format of Ultimate Strength Equations

The ultimate strength equations proposedhere have a format of uni-planar K-joint strengthmultiplied by a correction factor. The strength of

UNIPLANAR JOINTS MULTI-PLANAR JOINTS

X

T

K

XX

TT

TX

KK

N1

N1

N1

N2

N2

N1

N1 N1

N1

N2

N2

N1

N1N2

N1

N1

N2

N2

X-JOINTS

T-JOINT

S

K-JOINTS

Fig. 1 Classification of multi-planar joints.

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Table 1 Screened database for KK-joints under symmetrical loads.

Data No. d0 t 0 d1 t 1 g g t 1 2 n 0 F y F u N 1u,KK Prediction

(mm) (mm) (mm) (mm) (mm) (mm) (deg) (deg) (deg) (MPa) (MPa) (kN) (kN)

DKS-1 216.1 7.90 76.3 6.60 85.8 36.0 49.1 49.1 30.0 0 404 460 398 346

DKS-2 216.1 7.90 76.3 6.60 58.5 89.0 54.7 54.7 45.0 0 404 460 385 344DKS-3 190.8 5.21 89.0 5.66 72.8 8.0 49.1 49.1 30.0 0 379 441 224 205

DKS-4 190.8 5.21 89.0 5.66 51.3 9.0 49.1 49.1 30.0 0 379 441 230 210

DKS-5 190.8 5.21 89.0 5.66 31.0 8.0 49.1 49.1 30.0 0 379 441 240 236

DKS-6 190.8 5.21 89.0 5.66 9.5 9.0 49.1 49.1 30.0 0 379 441 285 311

DKS-7 190.8 5.21 60.5 5.66 52.0 37.0 49.1 49.1 30.0 0 379 441 188 161

DKS-8 190.8 5.21 60.5 5.66 31.0 40.0 49.1 49.1 30.0 0 379 441 204 181

DKS-9 190.8 5.21 60.5 5.66 11.0 38.5 49.1 49.1 30.0 0 379 441 228 235

DKS-10 190.8 5.21 42.8 5.46 30.0 55.0 49.1 49.1 30.0 0 379 441 156 134

DKS-11 190.8 5.21 42.8 5.46 11.5 55.0 49.1 49.1 30.0 0 379 441 175 171

DKS-12 190.8 5.21 89.0 5.66 73.0 56.0 54.7 54.7 45.0 0 379 441 242 207

DKS-13 190.8 5.21 89.0 5.66 52.0 56.0 54.7 54.7 45.0 0 379 441 252 212

DKS-14 190.8 5.21 89.0 5.66 31.0 56.0 54.7 54.7 45.0 0 379 441 263 239

DKS-15 190.8 5.21 89.0 5.66 11.3 55.0 54.7 54.7 45.0 0 379 441 291 310

DKS-16 190.8 5.21 60.5 5.66 53.0 84.0 54.7 54.7 45.0 0 379 441 155 140

DKS-17 190.8 5.21 60.5 5.66 31.0 83.0 54.7 54.7 45.0 0 379 441 162 158

DKS-18 190.8 5.21 60.5 5.66 10.5 83.0 54.7 54.7 45.0 0 379 441 182 206

DKS-19 190.8 5.21 42.8 5.46 31.0 100.0 54.7 54.7 45.0 0 379 441 122 116

DKS-20 190.8 5.21 42.8 5.46 11.5 100.0 54.7 54.7 45.0 0 379 441 162 150

DKS-21 217.1 4.41 48.9 3.20 54.0 63.3 63.4 63.4 30.0 0 352 472 83 89

DKS-22 217.2 4.41 60.7 4.00 40.9 51.6 63.4 63.4 30.0 0 352 472 108 112

DKS-23 217.1 4.41 76.6 4.00 23.0 35.1 63.4 63.4 30.0 0 352 472 149 180DKS-25 217.0 4.45 60.1 4.00 75.0 87.1 63.4 63.4 30.0 0 432 556 114 120

DKS-26 165.3 4.39 48.9 3.20 28.4 36.9 63.4 63.4 30.0 0 385 490 136 119

DKS-27 165.0 4.29 48.3 3.20 3.5 9.3 63.4 63.4 30.0 0 278 402 127 137

DKS-28 165.0 4.21 48.5 3.20 62.2 76.5 63.4 63.4 30.0 0 278 402 71 71

DKS-29 165.2 4.21 60.2 4.00 41.5 56.4 63.4 63.4 30.0 0 278 402 97 92

DKS-30 139.8 4.37 48.4 3.20 16.2 24.2 63.4 63.4 30.0 0 386 475 136 139

DKS-31 216.2 4.48 60.7 3.80 74.9 103.9 90.0 50.6 30.0 0 472 521 106 112

DKS-32 216.2 4.54 76.5 4.00 47.2 72.2 90.0 50.6 30.0 0 472 521 139 151

DKS-33 216.0 4.49 76.6 4.00 60.0 90.0 90.0 50.6 30.0 0 472 521 131 141

DKS-34 165.4 4.32 60.7 3.80 21.6 52.9 90.0 49.1 30.0 0 409 483 139 145

DKS-35 165.4 4.42 60.6 3.80 30.3 66.3 90.0 49.1 30.0 0 409 483 126 130

DKS-36 165.4 4.32 76.4 4.00 11.6 50.4 90.0 49.1 30.0 0 409 483 198 215

DKS-37 165.3 4.41 76.3 4.00 12.0 51.1 90.0 49.1 30.0 0 409 483 179 220

DKS-38 139.9 4.12 60.7 3.80 7.4 36.2 90.0 49.1 30.0 0 371 469 165 171

DKS-39 140.5 4.08 60.6 3.80 12.1 42.2 90.0 49.1 30.0 0 371 469 163 155

DKS-40 140.1 4.05 60.6 3.80 15.2 46.5 90.0 49.1 30.0 0 371 469 152 144

DKS-41 215.9 4.36 101.7 5.24 52.8 7.9 49.1 49.1 30.0 0 388 470 179 183

DKS-42 215.9 4.36 101.7 5.24 52.8 7.9 49.1 49.1 30.0 0 388 470 189 183

DKS-82 139.7 4.00 48.3 3.20 71.4 23.7 45.0 45.0 30.0 0 322 451 112 96

DKS-86 88.9 4.00 33.7 2.60 41.2 11.9 45.0 45.0 30.0 0 320 448 80 79

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Table 1 continued



DKS-87 120.0 5.00 28.8 4.00 18.0 33.4 60.0 60.0 30.0 0 355 510 109 118

DKS-88 120.0 5.00 28.8 4.00 28.0 33.4 60.0 60.0 30.0 0 355 510 104 108

DKS-90 120.0 5.00 28.8 4.00 38.0 33.4 60.0 60.0 30.0 0 355 510 100 102

DKS-91 120.0 4.00 28.8 4.00 38.0 33.4 60.0 60.0 30.0 0 355 510 71 70

DKS-92 120.0 2.86 28.8 2.86 38.0 33.4 60.0 60.0 30.0 0 355 510 41 40

DKS-93 120.0 2.40 28.8 2.40 38.0 33.4 60.0 60.0 30.0 0 355 510 31 30

DKS-94 120.0 2.00 28.8 2.00 38.0 33.4 60.0 60.0 30.0 0 355 510 23 22

DKS-95 120.0 1.71 28.8 1.71 38.0 33.4 60.0 60.0 30.0 0 355 510 17 17

DKS-96 120.0 1.50 28.8 1.50 38.0 33.4 60.0 60.0 30.0 0 355 510 14 14

DKS-97 120.0 5.00 28.8 4.00 48.0 33.4 60.0 60.0 30.0 0 355 510 99 99

DKS-98 120.0 5.00 28.8 4.00 58.0 33.4 60.0 60.0 30.0 0 355 510 99 98

DKS-99 120.0 5.00 28.8 4.00 68.0 33.4 60.0 60.0 30.0 0 355 510 99 97

DKS-100 120.0 6.67 38.4 6.67 18.0 23.6 60.0 60.0 30.0 0 355 510 206 207DKS-101 120.0 5.00 38.4 4.00 18.0 23.6 60.0 60.0 30.0 0 355 510 138 141

DKS-102 120.0 4.00 38.4 4.00 18.0 23.6 60.0 60.0 30.0 0 355 510 104 104

DKS-103 120.0 2.86 38.4 2.86 18.0 23.6 60.0 60.0 30.0 0 355 510 60 63

DKS-104 120.0 2.40 38.4 2.40 18.0 23.6 60.0 60.0 30.0 0 355 510 45 48

DKS-105 120.0 2.00 38.4 2.00 18.0 23.6 60.0 60.0 30.0 0 355 510 34 36

DKS-106 120.0 1.71 38.4 1.71 18.0 23.6 60.0 60.0 30.0 0 355 510 27 27

DKS-107 120.0 1.50 38.4 1.50 18.0 23.6 60.0 60.0 30.0 0 355 510 22 22

DKS-108 120.0 5.00 38.4 4.00 28.0 23.6 60.0 60.0 30.0 0 355 510 126 129

DKS-111 120.0 6.67 38.4 6.67 38.0 23.6 60.0 60.0 30.0 0 355 510 182 187

DKS-112 120.0 6.67 38.4 9.34 38.0 23.6 60.0 60.0 30.0 0 355 510 181 187

DKS-113 120.0 5.00 38.4 4.00 38.0 23.6 60.0 60.0 30.0 0 355 510 120 122

DKS-115 120.0 5.00 38.4 6.00 38.0 23.6 60.0 60.0 30.0 0 355 510 120 122

DKS-116 120.0 4.00 38.4 2.40 38.0 23.6 60.0 60.0 30.0 0 355 510 86 87

DKS-117 120.0 4.00 38.4 4.00 38.0 23.6 60.0 60.0 30.0 0 355 510 87 87

DKS-118 120.0 3.33 38.4 4.00 38.0 23.6 60.0 60.0 30.0 0 355 510 66 67

DKS-119 120.0 3.33 38.4 2.00 38.0 23.6 60.0 60.0 30.0 0 355 510 67 67

DKS-120 120.0 2.86 38.4 2.29 38.0 23.6 60.0 60.0 30.0 0 355 510 53 53

DKS-121 120.0 2.86 38.4 4.00 38.0 23.6 60.0 60.0 30.0 0 355 510 53 53

DKS-122 120.0 2.40 38.4 2.40 38.0 23.6 60.0 60.0 30.0 0 355 510 42 41

DKS-123 120.0 2.00 38.4 2.00 38.0 23.6 60.0 60.0 30.0 0 355 510 32 32

DKS-124 120.0 1.71 38.4 1.71 38.0 23.6 60.0 60.0 30.0 0 355 510 26 26

DKS-125 120.0 1.50 38.4 1.50 38.0 23.6 60.0 60.0 30.0 0 355 510 21 21

DKS-126 120.0 5.00 38.4 4.00 48.0 23.6 60.0 60.0 30.0 0 355 510 119 119

DKS-127 120.0 5.00 38.4 4.00 58.0 23.6 60.0 60.0 30.0 0 355 510 118 117

DKS-128 120.0 5.00 48.0 4.00 18.0 13.4 60.0 60.0 30.0 0 355 510 159 164

DKS-129 120.0 5.00 48.0 4.00 28.0 13.4 60.0 60.0 30.0 0 355 510 144 150

DKS-130 120.0 6.67 48.0 6.67 38.0 13.4 60.0 60.0 30.0 0 355 510 203 218

DKS-131 120.0 5.00 48.0 4.00 38.0 13.4 60.0 60.0 30.0 0 355 510 135 142

DKS-132 120.0 4.00 48.0 4.00 38.0 13.4 60.0 60.0 30.0 0 355 510 98 101

DKS-133 120.0 3.33 48.0 3.33 38.0 13.4 60.0 60.0 30.0 0 355 510 76 77

DKS-134 120.0 2.86 48.0 2.86 38.0 13.4 60.0 60.0 30.0 0 355 510 61 62

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Table 1 continued

Note: Numerical results are distinguished from test results by showing them on halftone backgrounds.



DKS-135 120.0 2.40 48.0 2.40 38.0 13.4 60.0 60.0 30.0 0 355 510 48 48

DKS-136 120.0 2.00 48.0 2.00 38.0 13.4 60.0 60.0 30.0 0 355 510 37 37

DKS-137 120.0 1.71 48.0 1.71 38.0 13.4 60.0 60.0 30.0 0 355 510 30 30

DKS-138 120.0 1.50 48.0 1.50 38.0 13.4 60.0 60.0 30.0 0 355 510 25 25

DKS-139 120.0 5.00 48.0 4.00 48.0 13.4 60.0 60.0 30.0 0 355 510 133 138

DKS-140 120.0 4.00 38.4 4.00 29.7 12.0 60.0 60.0 30.0 0 355 510 83 91

DKS-141 120.0 4.00 38.4 4.00 29.7 18.0 60.0 60.0 30.0 0 355 510 87 91

DKS-142 120.0 4.00 38.4 4.00 29.7 24.0 60.0 60.0 30.0 0 355 510 90 91

DKS-143 120.0 4.00 38.4 4.00 29.7 30.0 60.0 60.0 30.0 0 355 510 92 92

DKS-144 120.0 4.00 38.4 4.00 29.7 36.0 60.0 60.0 30.0 0 355 510 89 90

DKS-145 120.0 4.00 38.4 4.00 29.7 42.0 60.0 60.0 30.0 0 355 510 87 89

DKS-146 120.0 4.00 38.4 4.00 29.7 24.0 60.0 60.0 33.8 0 355 510 92 91

DKS-147 120.0 4.00 38.4 4.00 29.7 24.0 60.0 60.0 37.5 0 355 510 95 91DKS-148 120.0 4.00 38.4 4.00 29.7 24.0 60.0 60.0 41.3 0 355 510 99 91

DKS-149 120.0 4.00 38.4 4.00 29.7 24.0 60.0 60.0 45.0 0 355 510 103 91

DKS-150 120.0 4.00 38.4 4.00 29.7 31.2 60.0 60.0 33.8 0 355 510 90 92

DKS-151 120.0 4.00 38.4 4.00 29.7 38.8 60.0 60.0 37.5 0 355 510 87 90

DKS-152 120.0 4.00 38.4 4.00 29.7 46.1 60.0 60.0 41.3 0 355 510 85 88

DKS-153 120.0 4.00 38.4 4.00 29.7 53.3 60.0 60.0 45.0 0 355 510 81 85

DKS-154 120.0 5.00 33.6 4.00 18.0 28.6 60.0 60.0 30.0 0 355 510 127 134

DKS-155 120.0 5.00 33.6 4.00 28.0 28.6 60.0 60.0 30.0 0 355 510 117 123

DKS-156 120.0 5.00 33.6 4.00 38.0 28.6 60.0 60.0 30.0 0 355 510 112 116

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Table 2 Screened database for KK-joints under anti-symmetrical loads.



DKA-1 216.6 4.30 77.7 3.90 84.8 33.8 49.1 49.1 30.0 0 404 515 -119 122

DKA-2 217.0 5.80 77.7 3.90 85.1 34.0 49.1 49.1 30.0 0 387 474 -186 194DKA-6 216.6 4.30 77.0 4.00 58.8 88.7 54.7 54.7 45.0 0 404 515 -126 121

DKA-7 216.1 5.80 77.0 4.00 58.5 88.3 54.7 54.7 45.0 0 374 472 -189 187

DKA-8 216.1 7.90 76.2 7.00 59.5 89.1 54.7 54.7 45.0 0 404 460 -311 320

DKA-10 215.9 4.40 101.7 5.20 52.4 7.1 49.1 49.1 30.0 0 388 470 -212 194

DKA-14 318.2 4.50 60.5 3.20 232.6 312.4 45.0 45.0 90.0 0 413 528 -108 108

DKA-15 318.2 4.50 139.8 4.50 120.5 285.8 45.0 45.0 90.0 0 413 528 -235 218

DKA-16 216.3 6.30 89.1 5.40 69.4 21.4 49.1 49.1 30.0 0 387 472 -270 289

DKA-17 216.3 6.30 75.7 5.40 71.4 41.9 49.1 49.1 30.0 0 387 472 -220 200

DKA-21 120.0 5.00 28.8 4.00 48.0 33.4 60.0 60.0 30.0 0 355 510 -78 85

DKA-22 120.0 5.00 28.8 4.00 58.0 33.4 60.0 60.0 30.0 0 355 510 -77 84

DKA-23 120.0 5.00 28.8 4.00 68.0 33.4 60.0 60.0 30.0 0 355 510 -76 83

DKA-25 120.0 2.86 38.4 2.86 18.0 23.6 60.0 60.0 30.0 0 355 510 -50 46

DKA-26 120.0 2.40 38.4 2.40 18.0 23.6 60.0 60.0 30.0 0 355 510 -35 33

DKA-27 120.0 2.00 38.4 2.00 18.0 23.6 60.0 60.0 30.0 0 355 510 -25 23

DKA-28 120.0 1.71 38.4 1.71 18.0 23.6 60.0 60.0 30.0 0 355 510 -19 17

DKA-29 120.0 1.50 38.4 1.50 18.0 23.6 60.0 60.0 30.0 0 355 510 -15 13

DKA-30 120.0 5.00 38.4 4.00 28.0 23.6 60.0 60.0 30.0 0 355 510 -113 116

DKA-31 120.0 5.00 38.4 4.00 38.0 23.6 60.0 60.0 30.0 0 355 510 -105 110

DKA-33 120.0 4.00 38.4 4.00 38.0 23.6 60.0 60.0 30.0 0 355 510 -70 72

DKA-34 120.0 2.86 38.4 4.00 38.0 23.6 60.0 60.0 30.0 0 355 510 -38 39

DKA-35 120.0 2.40 38.4 2.40 38.0 23.6 60.0 60.0 30.0 0 355 510 -28 28

DKA-36 120.0 2.00 38.4 2.00 38.0 23.6 60.0 60.0 30.0 0 355 510 -20 20

DKA-37 120.0 1.71 38.4 1.71 38.0 23.6 60.0 60.0 30.0 0 355 510 -16 15

DKA-38 120.0 1.50 38.4 1.50 38.0 23.6 60.0 60.0 30.0 0 355 510 -13 12

DKA-39 120.0 5.00 38.4 4.00 48.0 23.6 60.0 60.0 30.0 0 355 510 -101 107

DKA-40 120.0 5.00 38.4 4.00 58.0 23.6 60.0 60.0 30.0 0 355 510 -98 106

DKA-44 120.0 3.33 48.0 3.33 38.0 13.4 60.0 60.0 30.0 0 355 510 -74 76

DKA-45 120.0 2.86 48.0 2.86 38.0 13.4 60.0 60.0 30.0 0 355 510 -57 57

DKA-46 120.0 2.40 48.0 2.40 38.0 13.4 60.0 60.0 30.0 0 355 510 -42 42

DKA-47 120.0 2.00 48.0 2.00 38.0 13.4 60.0 60.0 30.0 0 355 510 -30 30

DKA-48 120.0 1.71 48.0 1.71 38.0 13.4 60.0 60.0 30.0 0 355 510 -23 23

DKA-49 120.0 1.50 48.0 1.50 38.0 13.4 60.0 60.0 30.0 0 355 510 -18 18DKA-51 120.0 4.00 38.4 4.00 29.7 24.0 60.0 60.0 30.0 0 355 510 -75 75

DKA-52 120.0 4.00 38.4 4.00 29.7 38.8 60.0 60.0 37.5 0 355 510 -77 79

DKA-53 120.0 4.00 38.4 4.00 29.7 53.3 60.0 60.0 45.0 0 355 510 -80 81

DKA-54 120.0 2.86 48.0 2.86 18.0 13.4 60.0 60.0 30.0 0 355 510 -68 68

DKA-55 120.0 2.86 48.0 2.86 28.0 13.4 60.0 60.0 30.0 0 355 510 -59 59

DKA-56 120.0 2.86 48.0 2.86 48.0 13.4 60.0 60.0 30.0 0 355 510 -55 57

DKA-58 216.8 5.52 76.9 3.98 108.1 202.7 45.0 45.0 90.0 0 330 436 -223 181

DKA-59 216.3 5.84 114.4 4.49 54.5 183.5 45.0 45.0 90.0 0 367 474 -385 333

DKA-62 216.5 5.39 76.9 3.98 36.2 202.4 60.0 60.0 90.0 0 332 432 -190 178

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Table 2 continued



DKA-63 216.5 6.32 76.3 4.03 36.9 202.6 60.0 60.0 90.0 0 369 504 -224 270

DKA-65 216.5 9.02 52.0 10.82 75.8 111.9 45.0 45.0 45.0 0 389 540 -364 343

DKA-66 216.5 9.02 75.8 10.82 75.8 89.8 45.0 45.0 45.0 0 389 540 -483 464

DKA-67 216.5 9.02 97.4 10.82 75.8 67.8 45.0 45.0 45.0 0 389 540 -669 582

DKA-68 216.5 9.02 75.8 10.82 108.3 89.8 45.0 45.0 45.0 0 389 540 -455 453

DKA-69 216.5 9.02 75.8 10.82 75.8 158.4 45.0 45.0 67.5 0 389 540 -520 493

DKA-70 216.5 9.02 75.8 10.82 32.5 202.8 45.0 45.0 90.0 0 389 540 -584 596

DKA-71 216.5 9.02 52.0 10.82 75.8 210.2 45.0 45.0 90.0 0 389 540 -383 374

DKA-72 216.5 9.02 75.8 10.82 75.8 202.8 45.0 45.0 90.0 0 389 540 -515 513

DKA-73 216.5 9.02 97.4 10.82 75.8 193.3 45.0 45.0 90.0 0 389 540 -641 652

DKA-74 216.5 9.02 75.8 10.82 108.3 202.8 45.0 45.0 90.0 0 389 540 -505 501

DKA-75 216.5 9.02 97.4 10.82 108.3 193.3 45.0 45.0 90.0 0 389 540 -627 637

DKA-76 216.5 4.33 75.8 5.20 32.5 89.8 45.0 45.0 45.0 0 389 540 -150 148DKA-77 216.5 4.33 52.0 5.20 75.8 111.9 45.0 45.0 45.0 0 389 540 -98 97

DKA-78 216.5 4.33 75.8 5.20 75.8 89.8 45.0 45.0 45.0 0 389 540 -130 132

DKA-79 216.5 4.33 97.4 5.20 75.8 67.8 45.0 45.0 45.0 0 389 540 -172 165

DKA-80 216.5 4.33 75.8 5.20 108.3 89.8 45.0 45.0 45.0 0 389 540 -127 132

DKA-81 216.5 4.33 75.8 5.20 32.5 158.4 45.0 45.0 67.5 0 389 540 -157 157

DKA-82 216.5 4.33 52.0 5.20 75.8 174.3 45.0 45.0 67.5 0 389 540 -103 103

DKA-83 216.5 4.33 75.8 5.20 75.8 158.4 45.0 45.0 67.5 0 389 540 -145 140

DKA-84 216.5 4.33 97.4 5.20 75.8 141.3 45.0 45.0 67.5 0 389 540 -182 177

DKA-85 216.5 4.33 75.8 5.20 108.3 158.4 45.0 45.0 67.5 0 389 540 -141 140

DKA-86 216.5 4.33 75.8 5.20 32.5 202.8 45.0 45.0 90.0 0 389 540 -155 163

DKA-87 216.5 4.33 52.0 5.20 75.8 210.2 45.0 45.0 90.0 0 389 540 -103 106

DKA-88 216.5 4.33 75.8 5.20 75.8 202.8 45.0 45.0 90.0 0 389 540 -144 146

DKA-89 216.5 4.33 97.4 5.20 75.8 193.3 45.0 45.0 90.0 0 389 540 -184 185

DKA-90 216.5 4.33 75.8 5.20 108.3 202.8 45.0 45.0 90.0 0 389 540 -140 146

DKA-91 216.5 2.71 75.8 3.25 32.5 89.8 45.0 45.0 45.0 0 389 540 -66 62

DKA-92 216.5 2.71 52.0 3.25 75.8 111.9 45.0 45.0 45.0 0 389 540 -44 44

DKA-93 216.5 2.71 75.8 3.25 75.8 89.8 45.0 45.0 45.0 0 389 540 -61 60

DKA-94 216.5 2.71 97.4 3.25 75.8 67.8 45.0 45.0 45.0 0 389 540 -72 75

DKA-95 216.5 2.71 75.8 3.25 108.3 89.8 45.0 45.0 45.0 0 389 540 -59 60

DKA-96 216.5 2.71 75.8 3.25 75.8 158.4 45.0 45.0 67.5 0 389 540 -64 64

DKA-97 216.5 2.71 75.8 3.25 32.5 158.4 45.0 45.0 67.5 0 389 540 -69 66

DKA-98 216.5 2.71 52.0 3.25 75.8 210.2 45.0 45.0 90.0 0 389 540 -44 48

DKA-99 216.5 2.71 75.8 3.25 75.8 202.8 45.0 45.0 90.0 0 389 540 -65 66

DKA-100 216.5 2.71 97.4 3.25 75.8 193.3 45.0 45.0 90.0 0 389 540 -84 84

DKA-101 216.5 2.71 75.8 3.25 108.3 158.4 45.0 45.0 67.5 0 389 540 -62 64

DKA-102 216.5 9.02 75.8 10.82 75.8 35.8 45.0 45.0 30.0 0 389 540 -453 480

DKA-103 216.5 9.02 75.8 10.82 75.8 126.5 45.0 45.0 56.3 0 389 540 -513 480

DKA-104 216.5 9.02 75.8 10.82 75.8 184.1 45.0 45.0 78.8 0 389 540 -515 505

DKA-105 216.5 4.33 75.8 5.20 75.8 35.8 45.0 45.0 30.0 0 389 540 -113 126

DKA-106 216.5 4.33 75.8 5.20 75.8 126.5 45.0 45.0 56.3 0 389 540 -141 136

DKA-107 216.5 4.33 75.8 5.20 75.8 184.1 45.0 45.0 78.8 0 389 540 -144 143

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K-joints is given by Kurobanes formula (1984), which afforded the basis for the Cidect designequation. The Cidect design guide also utilizes the same format for design equations for multi-planar joints. Although Lee and Wilmshurst (1996, 1997) have already derived accurate strength

prediction equations for KK-joints independently of K-joint strength, the new formulae were de-vised following the above format. The reason for this is that one of the easiest ways to providedesign formulae for various multi-planar joints is to classify them into 3 large groups of uni-planarX, T and K-joints as shown in Fig. 1 (Vegtevan der 1996). The behavior of each multi-planar joint is similar to that of the uni-planarcounterpart and thus relatively simple correc-tion factors suffice for accurate prediction ofstrength of multi-planar joints. Furthermore,with this format, one can derive the most reli-able prediction equations from the smallest da-tabase.

3.2 KK-Joints under Symmetrical Axial Brace Loading

KK-joints under symmetrical loads dem-onstrate two types of failure mode dependingon the out-of-plane angle , as shown in Fig.2. Paul (1992) distinguished between thesetwo failure modes and devised two differentultimate strength equations for the two fail-ure modes. The first failure pattern, which is

called the failure Type 1, shows no local de-flection in the chord wall in the region be-tween the two compression braces. Namely,the two compression braces act as one mem-ber and penetrate the chord wall together. Thesecond failure pattern, which is called the fail-ure Type 2, shows radial deflection of thechord wall in the region between the compres-sion braces, eventually creating a fold betweenthem. The Type 1 failure mode occurs whenis small. As soon as the failure mode

changes from Type 1 to Type 2, the capacityof KK-joints suddenly changes.Finite element analysis results were

Fig. 2 Failure modes for KK-joints under symmetrical axial loads.

(b) Failure Type 2

(a) Failure Type 1

Table 2 continued

Note: Numerical results are distinguished from test results by showing them on halftone backgrounds.



DKA-108 216.5 2.71 75.8 3.25 75.8 35.8 45.0 45.0 30.0 0 389 540 -50 54

DKA-109 216.5 2.71 75.8 3.25 75.8 126.5 45.0 45.0 56.3 0 389 540 -65 62DKA-110 216.5 2.71 75.8 3.25 75.8 184.1 45.0 45.0 78.8 0 389 540 -64 65

DKA-111 216.1 6.40 140.3 4.60 16.5 165.1 45.0 45.0 90.0 0 342 485 -560 655

DKA-112 216.8 4.30 165.2 5.60 -17.0 140.1 45.0 45.0 90.0 0 379 474 -543 618

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found to reproduce well the behavior ofKK-joints observed in tests. Accurate ul-timate capacity prediction equations haverecently been developed for KK-joints bycombining both test and FEA results (Leeet al. 1996, Kurobane et al. 1996) Of these,the following two equations are selectedand proposed herein.

When a Type 1 failure occurs(gt/d00.215), the ultimate strength of KK-

joints is predicted by

(1)

where

COV=0.0613.

When a Type 2 failure occurs (g t/d0>0.215), the capacity prediction equationis:

(2)where

COV=0.0752.

In the above equationsN1u,KandN1u,KKdenotesultimate strength of K and KK-joints, respec-tively, given in terms of the maximum load inthe compression brace. The right-hand sidesof these equations signify the correction fac-tors.

The border between Type 1 and 2 failuremodes is at gt/d0=0.215 according to Lee et al.(1996). The correction factors given by Eqs. 1

and 2 become discontinuous at the border. Thecorrection factors when 2=20, 40 and 80 areplotted against gt/d0in Fig. 3. Numerical re-sults, classified into 2 groups according to 2,are compared with the correction factors asshown in Fig. 3. Test results are not includedhere because they scatter more than numericalresults, although both have about the samemean values. Figure 3 shows how abruptlythe capacity changes when failure mode var-ies from Type 1 to Type 2. Predicted ultimate

strengths are shown in Table 1. Ratios of testand analysis results to predictions are plottedagainst 2in Fig. 4. In the same figure are

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0 20 40 60 80

2

test/prediction

AWSFORMULA

Eqs. 1 & 2

AWS MEAN

N1u,KKN1u,K

= 0.254 (2)0.376

N1u,KKN1u,K

= 0.438 (1 +0.833) (10.340gtd0

) (2)0.176

Fig. 4 Ratios of Test and analysis results to predictions plotted against 2 (symmetrical axial loading).

Fig. 3 Correction factors plotted against gt/d0 (symmetrical axial loading).

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0 0.2 0.4 0.6

gt/d0

correctionf

actor

2=18-362=42-80

2=80

2=40

2=20

0.215

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also plotted the predictions according to theAWS formula, which will be discussed inlater part of this report.

3.3 KK-Joints under Anti-Symmetrical Axial Brace Loading

KK-joints under anti-symmetricalloads also show two failure types. When gt/d0is small, the axial loads in the braces aretransmitted directly through the transversegap regions of the chord walls. When gt/d0becomes large, KK-joints behave moreclearly as two independent K-joints (See Fig.5). These two failure types are designated asTypes 3 and 4 respectively. The ultimatestrength equations for KK-joints under anti-symmetrical axial loads were derived following thesame procedures as those for KK-joints under symmetrical axial loads. The two simple prediction

equations shown by Eqs. 3 and 4 are herein proposed.When a Type 3 failure occurs (gt/d00.215), the ultimate strength of KK-joints is predicted

by

(3)

where

COV=0.0622.

N1u,KKN1u,K

= 1.222.36gtd0

Fig. 6 Correction factors plotted against gt/d0(anti-symmetrical axial loading).

Fig. 5 Failure modes for KK-joints under anti- symmetrical axial loads.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0.0 0.2 0.4 0.6 0.8 1.0

corr

ection

factor

2=24-30

2=50-80

2=80

2=40

2=20

2=24-80

0.215

gt/d0

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When a Type 4 failure occurs (gt/d0>0.215), the capacity prediction equation is:

(4)

where

COV=0.0663.

The correction factors are again com-pared with numerical results in Fig. 6. Pre-dicted ultimate strengths are shown in Table2. Ratios of test and analysis results to pre-dictions are plotted against 2in Fig. 7.

3.4 Further Assessment of Prediction Equa- tions

The ranges of variation of importantgeometrical variables included in the screeneddatabase are:

0.22 0.4718 280

0.03 gt/d00.9945190

602180

The COVs of observed strengths aboutthe mean strength equations (Eqs. 1, 2, 3 and4) are even smaller than COV=0.101 foundin K-joints. Therefore, resistance factors to be used for the design of KK-joints may not need to besmaller than that used for design equations for K-joints.

All the test and finite element analysis results (both under symmetrical and anti-symmetricalloading) are plotted overall against corresponding predictions in Fig. 8. Correlation between thetwo looks excellent. The test or analysis result to prediction ratios give the following statistics:

Data Source Mean Sample Standard Deviation

Test 1.016 0.099FE Analysis 0.997 0.047

No significant difference exists between the means of test and analysis results, while the standarddeviation of analysis to prediction ratios is significantly smaller than that of test to prediction ra-tios.

Test and numerical results divided simply by corresponding K-joint capacities give the fol-lowing statistics.

Data Source Mean Sample Standard DeviationKK-Joint under symmetrical axial loads 0.955 0.137

KK-Joint under anti-symmetrical axial loads 0.887 0.115

The above results demonstrate that the current Cidect design equations for KK-joints, which speci-

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0 20 40 60 80

2

test/prediction

AWSFORMULA

Eqs. 3 & 4

AWS MEAN

N1u,KKN1u,K

= 0.376 (1 +1.05) (1 + 0.221gtd0

) (2)0.112

Fig. 7 Ratios of Test and analysis results to predictions plotted against 2(anti- symmetrical axial loading).

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fies a constant value of 0.9 as the correc-tion factor, are found still reasonable, al-though less accurate than Eqs. 1, 2, 3 and4.

4. KK-JOINTS IN TRIANGULAR TRUSSES

Lets assume a triangular truss (aninverted delta truss) with 3 chords asshown in Fig. 9. Under the vertical shearload V, the KK-joint sustains axial braceloads symmetrical about the vertical sys-tem plane. Under the horizontal shear load

Hthe KK-joint sustains axial brace loadsanti-symmetrical about the vertical systemplane. The strength of KK-joints under the

shear load Qwith an inclination of canbe predicted by using the following inter-polation technique. When=, the bracesin one plane carry the shear load and thebraces in the other plane are free from anyaxial load. The strength of KK-joints with =can be given as that of planar K-joints. Thestrength of general KK-joints can be represented by straight lines linking the points at =0(sym-metrical load), =(uni-planar K-joint) and =90(anti-symmetrical load).

An example calculation is made in the following. Assume KK-joints with d0=300mm,t0=10mm, d1=d2=100mm, and 1=2=60. All the member axes are assumed to meet at one point(no eccentricity in the joint). Then the longitudinal gap is calculated as g=57.7 mm. The materialproperties of the chord is assumed asF

y=350 kN/mm2andF

u=500 kN/mm2. The ultimate strength

of a uni-planar K-joint included in these KK-joints is calculated asN1u,K=656 kN from Kurobanesformula. Now, the out-of-plane angle 2of KK-joints is varied as 30, 60, 90, 120and 180.The nondimensionalized transverse gap gt/d0is calculated by:

(5)

The above equation is valid when the eccentricity et=0 (See Makino et al. 1996). Although, insome of the joints included in Tables 1 and 2, etis not equal to zero, it is better to design joints withet=0 in practice. This is to avoid complicating fabrication processes.

The strengths of example KK-joints can be calculated by Eqs. 1. 2, 3 and 4 as follows:

2 (degrees) gt/d0 2 Failure Type Correction Factor Ultimate Strength (kN)

30 0.33 -0.08 30 1 0.912 599

Symmetrical 60 0.33 0.18 30 1 0.912 599

Loads 90 0.33 0.43 30 2 0.869 570

120 0.33 0.65 30 2 0.793 521

180 0.33 0.94 30 2 0.692 454

30 0.33 -0.08 30 3 1.404 921

Anti-Symmetrical 60 0.33 0.18 30 3 0.789 518

Loads 90 0.33 0.43 30 4 0.814 534120 0.33 0.65 30 4 0.850 557

180 0.33 0.94 30 4 0.898 589

gtd0

= sin (sin1)

Fig. 8 Test and analysis results compared with predictions for all KK-joints.

TEST AND FEA RESULTS(KN)

PREDICTION(KN)

10

100

1000

10 100 1000

FEA

TEST

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The ultimate shear loads can be calcu-

lated by the following equations:Under a symmetrical shear load,

(6)

When =,

(7)

Under an anti-symmetrical shear load,

(8)

Figure 10 illustrates how ultimateshear loads vary with the direction ofshear load.

5. COMPARISON WITH MOUTY AND RONDALS TEST RESULTS

Results of the test by Mouty

and Rondal (1992) and predictedstrengths are shown in Table 3. Thespecimens that failed by chord wallplastification only are selected. Testto prediction ratios are plotted againstgt/d0and compared with the databaseincluded in Table 1. As seen in thisfigure the Mouty and Rondal test re-sults show not only significantlylower strengths than the other test andnumerical results but also a tendency

to decrease the strength as gt/d0in-creases.It is suspected that in the tests

CL

V

H

Q

0.0

0.2

0.4

0.6

0.8

1.0

1.2

-0.2 0.0 0.2 0.4 0.6

gt/ d0

test/p

rediction

Mouty and Rondal

Database in Table 1

Fig. 9 Cross section of triangular truss.

Fig. 11 Mouty and Rondals test results compared with database included in Table 1.

Fig. 10 Strength of KK-joints under shear load in general.

V= 2N1u,KKsin 1cos

H= 2N1u,KK

sin 1

sin

Qmax

(kN)

(degree)

0

200

400

600

800

1000

1200

0 20 40 60 80 100

2=30

2=60

2=90

2=120

2=180

Q=N1u,Ksin 1

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by Mouty and Rondal the whole loading system became instable as local stiffness of joints decayeddue to plastification of the tube walls. If this was the case, ultimate loads were determined by thestiffness of joints rather than by plastic shell bending capacity of the chord wall. Further, jointssustained not only axial loads but also primary bending moments due to eccentricity in joints in-duced by rigid body rotations of the chords. Thus, strengths of joints could have been lower thanthose observed in the tests conducted under axial brace loading conditions (See also Kurobane1993).

6. COMPARISON WITH AWS EQUATIONS

The AWS code (1996) is one code that shows definite design criteria for multi-planar tubularjoints. The AWS design equation is the only exception that proposes general design criteria appli-cable to any type of non-overlapping multi-planar joints without a need of joint classification. It isworth while comparing the AWS equation with the present database.

The AWS equation in ultimate strength format is shown as :

(9)

with

Pu = 61.7 +

0.18

Q0.7(1)

Q fyt0

2

sin

= 1 + 0.7

Psincos 2exp ( z0.6

)all bracesat a joint

Psin reference brace forwhichapplies



DKS-43 139.7 6 .30 48.3 3.20 71.4 23.7 45.0 45.0 30.0 0 .00 322 451 151 183

DKS-48 139.7 6 .30 48.3 3.20 24.9 58.5 60.0 60.0 45.0 0 .00 353 494 131 217DKS-55 139.7 6 .30 76.1 4.00 32.1 -7.3 45.0 45.0 30.0 0 .00 342 479 279 297

DKS-56 139.7 6 .30 76.1 4.00 32.1 29.0 45.0 45.0 45.0 0 .00 323 452 215 280

DKS-59 139.7 6.30 76.1 4.00 -7.2 -7.3 60.0 60.0 30.0 0.00 341 477 285 334

DKS-60 139.7 6 .30 76.1 4.00 -7.2 29.0 60.0 60.0 45.0 0 .00 341 477 258 334

DKS-61 139.7 4.00 48.3 3.20 71.4 23.7 45.0 45.0 30.0 0.00 322 451 80 96

DKS-62 139.7 4.00 33.7 2.60 92.0 38.6 45.0 45.0 30.0 0.00 322 451 50 71

DKS-63 139.7 4 .00 76.1 4.00 32.1 -7.3 45.0 45.0 30.0 0 .00 320 448 110 140

DKS-67 88.9 4.00 33.7 2.60 41.2 11.9 45.0 45.0 30.0 0.00 320 448 68 79

DKS-68 219.1 6 .30 76.1 4.00 111.5 36.8 45.0 45.0 30.0 0 .00 331 463 170 244

DKS-69 139.7 6 .30 48.3 3.20 71.4 23.7 45.0 45.0 30.0 -0.11 322 451 152 176

DKS-71 139.7 6 .30 48.3 3.20 71.4 23.7 45.0 45.0 30.0 -0.19 322 451 117 171DKS-72 139.7 6 .30 48.3 3.20 71.4 58.5 45.0 45.0 45.0 -0.11 367 514 121 206

DKS-73 139.7 6 .30 48.3 3.20 71.4 58.5 45.0 45.0 45.0 -0.15 367 514 123 202

DKS-74 139.7 6 .30 48.3 3.20 71.4 58.5 45.0 45.0 45.0 -0.19 367 514 117 199

Table 3 Summary of test by Mouty and Rondal (1992).

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where

The parameter in the above equation plays a role of incorporating not only a multi-planar effectdue to chord wall overlizing (circumferential bending) but also a membrane shell effect due toloads at positionsLdistant from the reference brace. The value of is evaluated separately foreach brace for which the ultimate limit state capacity is checked (the reference brace), with thesummation being taken over all braces present at the node for each load case. The spacingLismeasured longitudinally between the centers of foot prints of two braces. The symbols and inthe above equation, respectively, are equivalent to 2and according to the definition in Appen-dix.

Multiple regression analyses on both numerical and test results showed that: the multi-planareffect due to chord ovalizing was strongly correlated with geometrical variable gt/d0; and it wasdifficult to relate the multi-planar effect with only. Therefore, the AWS equations involve sig-nificant errors in the evaluation of the multi-planar effects, especially when 2=180in anti-sym-metrical loading. However, these errors due to inappropriate modeling of multi-planar effects areeven less influential as compared with systematic errors due to thickness squared strength formula-

tion in the AWS equations.Test and numerical results divided by AWS predictions are plotted against 2in Figs. 4 and 7.

These figures reveal that AWS predictions not only scatter widely but also shows a systematiccomponent erring on the unsafe side as 2decreases. Note that the AWS formula give lower boundpredictions, with the mean equal to 1/0.74 (See AWS D1.1 Commentary 2.40.1.1). The systematiccomponent is even steeper for KK-joints than for K-joints (See Kurobane et al. 1997); the capacityof KK-connections actually varies as the 1.3 to 1.7 power of thickness.

7. SUMMARY AND CONCLUSIONS

Ultimate strength equations for KK-joints under both symmetrical and anti-symmetrical axialbrace loading were derived from a large database consisting of experimental and numerical results.These equations have a format of ultimate strength of planar K-joints multiplied by a correctionfactor. The correction factors proposed herein are simple functions of geometrical variables butenable prediction of ultimate strength with good accuracy (COV=0.06-0.08). The database coversa wide range of geometrical variables. These equations therefore are considered to be readilyapplicable to design. The resistance factor and range of application to be assumed for design,however, should be decided with some other engineering judgments. For example, KK-joints witha too small transverse gap size may sustain premature development of cracks at the weld toes underanti-symmetrical loading (See Makino et al. 1997).

Mouty and Rondals test results showed significantly lower strengths than the other experi-mental and numerical results, probably because their loading system allowed a rigid body motion

of the chord. Since in actual trusses the chord ends are restrained by neighboring braces, Moutyand Rondals test results are not considered to be reproducing the behavior of KK-joints in a truss.Although the AWS design formula is unique in its capability to automatically evaluate the strengthof any multi-planar joints, accuracy in prediction was found to be insufficient (COV=0.28). Espe-cially the AWS formula errs on the unsafe side as the chord becomes heavier.

REFERENCES

AWS (1996) Structural welding code/steel. ANSI/AWS D1.1, American Welding Society, Miami,Fla., USA

Kurobane, Y., Makino, Y. & Ochi, K. (1984) Ultimate resistance of unstiffened tubular joints.J.Struct. Engrg., ASCE, 110(2), 385-400Kurobane, Y. (1993) Assessment of double K-joint tests by Mouty and Rondal.IIW Doc. XV-E-93-

z=L/ d0t0/2

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194, Kumamoto Univ., Kumamoto, JapanKurobane, Y., Makino, Y. & Ochi, K. (1996) Analysis of existing and forth coming data for multi-

planar KK-joints with Circular hollow sections. Cidect Report 5BF-11-96Kurobane, Y. & Ochi, K (1997) AWS vs international design rules for circular tubular K-connec-

tions.Engineering Structures, 19(3), 259-266Lee, M.M.K. & Wilmshurst, S.R. (1996) A parametric study of strength of tubular multiplanar KK-

joints.J. Struct. Engrg., ASCE, 122(8), 893-904.Lee, M.M.K. & Wilmshurst, S.R. (1997) Strength of multiplanar KK-joint under anti-symmetrical

loading.J. Struct. Engrg., ASCE, 123(6), 755-764.Makino, Y., Kurobane, Y. & Ochi, K. (1984) Ultimate capacity of tubular double K-joints.Proc.

Int. Conf. IIW on Welding of Tubular Structures, Pergamon, New York, N.Y., 451-458Makino, Y., & Kurobane, Y. (1994) Tests on CHS KK-joints under anti-symmetrical loads. Tubu-

lar Structures VI, Grundy, Holgate and Wong eds., A.A. Balkema, Rotterdam, Netherlands,449-456

Makino, Y., Kurobane, Y., Ochi, K., Vegte van der, G.J, & Wilmshurst, S. (1996), Database of Testand numerical analysis results for unstiffened tubular joints.IIW Doc. XV-E-96-220, KumamotoUniv., Kumamoto

Makino, Y., Wilmshurst, S., Lee, M.M.K. & Kurobane, Y. (1997) Test and numerical analysis re-

sults for CHS KK-joints under anti-symmetrical axial brace loads. Memoirs, Fac. Eng.,Kumamoto Univ., Kumamoto, Japan

Mouty, J & Rondal, J. (1992) Study of the behaviour under static loads of welded triangular andrectangular lattice girders made with circular hollow sections. Cidect Report 5AS-92/1

Paul, J.C. (1992), The ultimate behavior of multiplanar TT and KK-joints made of circular hollowsections. Ph. D. Thesis, Kumamoto Univ., Kumamoto, Japan

Paul, J.C., Y. Makino & Y. Kurobane (1994), Ultimate resistance of unstiffened multi-planar tubu-

lar TT and KK-joints.J. Struct. Engrg., ASCE, 120(10), 2853-2870Vegte van der, J.G. (1995) The static strength of uniplanar and multiplanar tubular T- and X-joints,

Ph. D. Thesis, 1995, Delft University Press, Delft, NetherlandsWardenier, J., Kurobane, Y., Packer, J.A., Dutta, D. & Yoemans, N. (1991)Design guide for circu-

lar hollow section (CHS) joints under predominantly static loading, Cidect ed., Verlag TVRheinland GmbH, Kln, GermanyWilmshurst, S.R., Makino, Y. & Kurobane, Y., (1997), Further numerical analyses of KK-joints

under anti-symmetrical axial loading,Proc. 7th Int. Offshore and Polar Eng. Conf.Hawaii,USA, pp. 58-64

Yonemura, H., Makino, Y., Kurobane, Y. & Vegte van der, G.J. (1996) Tests on CHS Plane KK-joints under anti-symmetrical loads. Tubular Structures VII, Farkas and Karoly, eds., A.A.Balkema, Rotterdam, Netherlands, 189-195

APPENDIX Notation

0,1,2 = subscripts signifying chord, compression brace and tension brace respectivelyCOV = coefficient of variationd = outside diameter of tubeset = eccentricity between intersection of brace axes and chord center

Fy = yield strength of chord materialFu = ultimate tensile strength of chord materialg = longitudinal gap in K or KK-jointgt = transverse gap in KK-joint

H = horizontal shear load applied to KK-joint

L = longitudinal distance between foot prints of two bracesN1u,K = ultimate strength of K-joint given in terms of axial load on compression brace

N1u,KK = ultimate strength of KK-joint given in terms of axial load on compression bracen0 = axial to yield stress ratio in chord

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Pu = ultimate strength of tubular joints according to AWS CodeQ = shear load applied to KK-jointQf, Q = functions of explaining variables in AWS equationst = wall thickness of tubesV = vertical shear load applied to KK-joint = chord ovalizing parameter = d1/d0: diameter ratio = d0/(2t0): chord thinness ratio = inplane angle between chord and braces = out-of-plane angle between planes in which braces lie = angle between direction of shear load and vertical plane

SYSTEMPLANE

d1

t1

1

gtg

L

d0t0

N1

gtet

cidect 5bf-10_98.pdf

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