The design of structural steel frames under consideration of the nonlinear behaviour of joints

J. Construct. Steel Research 1i (1988) 73-103

The Design of Structural Steel Frames under Consideration of the Nonlinear Behaviour of Joints Ferdinand Tschemmernegg Head of the Institute for Steel and Timber Construction, University of lnnsbruck, Technikerstrasse 13, 6020 Innsbruck, Austria

& Christian H u m e r Riedgasse 3, 6020 InnsbruclC Austria (Received 16 June 1987;revised version received 5 January 1988;accepted 6 January 1988) A BSTRA CT This paper introduces a method to determine analytically the nonlinear moment-rotation relationship for joints in structural steel frames. This method was developed on the basis of extensive test series performed at the Institute of Steel and Timber Construction, University of lnnsbruck, Austria. The most important features of this development were: the joint was divided into the panel zone and the connection; a nonlinear spring model for the panel zone was established and also the connection was simulated by a nonlinear spring. The necessary parameters to define the springs were evaluated from the test series. The field of application includes welded joints as well as bolted joints. The examples at the end of this paper demonstrate how to incorporate practically the influence of nonlinear joint rigidity into the design of unbraced frames.

1 INTRODUCTION The layout of joints in framed steel structures has great influence on the b e h a v i o u r and hence the design of the frame. Further, the overall frame costs are mainly determined by the layout of joints. For these reasons the use of plastic reserves in joint design may lead to considerable economic benefit, which should not be omitted. F o r the plastic design of steel frames, problems are mainly encountered in 73 J. Construct. Steel Research 0143-974X/88/$03.50 © 1988 Elsevier Science Publishers Ltd, England. Printed in Great Britain

F. Tschemmernegg, C. Humer

74

the design of the joints, as their elastic-plastic behaviour has not yet been clarified. Therefore several recent research programmes have concentrated on this field. Two central groups of problems should be distinguished: - - t h e elastic-plastic behaviour of joints - - t h e influence of joint behaviour on system behaviour as was already highlighted in Ref. 1 by the author. These two problems have special relevance for semi-rigid constructions. At the Institute for Steel and Timber Construction, University of Innsbruck, numerous test series have been performed to obtain information on load--deformation behaviour of semi-rigid joints and the results have been published during the last few years. 2-5 The following gives a brief review of the findings and reports on the theory developed for the determination of moment-rotation curves based on the test results.

2 DEFINITIONS AND B A C K G R O U N D Structural steel frames consist in general of beams (B) and columns (C) connected to each other by joints (J) (see Fig. 1). The normal approach in static calculation is to assume that the joint, which has defined dimensions, is contracted to a point at the intersection of the m e m b e r centrelines. This assumption is not valid in the case where stiffeners in the joints are omitted. The basic approach for obtaining more knowledge on deformation behaviour of the joint is to look at the joint in a macroscopic view. Figure 1 gives an example of a joint designed in one case as a welded joint (Fig. l(a)) and in the other case as a bolted joint (Fig. l(b)). At these joints a basic distinction has to be made between the flexibility of - - t h e panel zone, and - - t h e connection. This distinction combined with the macroscopic aspect of the joint represents a development over known approaches. This new approach allows for separating the differentinfluencing factors on joint behaviour at tests as well as in the model to be established. 2.1 Panel z o n e

The panel zone consists of the column web and the two flanges of the column for the height of the connected beam profiles. The load--deformation behaviour of this part is independent of the behaviour of the connection.

Nonlinear behaviour of joints in structural steel frames

75

r ELEMENTBEAM(B)( IELEMENTJOINT("T) - ELEMENTCOLUMN(C)

COLUMN

CON

CO I BEAM

(a)

(b) BOLTED CONNECTION

WELDED CONNECTION CONNECTION MEANS: -WELDS

CONNECTION MEANS: -WELDS -END PLATE -BOLTS -COLUMN FLANGE

Fig. 1. Structural steel frames.

2.2 Connection The load--deformation behaviour of the connection is very strongly dependent on the connection means chosen (compare Fig. l(a) and l(b)). For the design of the connection there exists a large variety of connection types, a selection of which is given in Fig. 2(a)-)h).

F. Tschemmernegg, C. Humer

76

(a)

(b)

(c)

(d)

l

H (*)

'(f)

I

(Q)

(h)

Fig. 2. Connections.

Nonlinear behaviour of joints in structural steel frames

77

2.3 Overall behaviour of the joint

Describing the overall behaviour of the joint--including the panel zone and the connection---classification can take place using the M--O diagram, where 0 is the total rotation of the joint; this diagram is given in Fig. 3. According to this diagram three groups of joints have to be distinguished: --rigid joints --semi-rigid joints --hinged joints. At the rigid joint the moment increases strongly with rotation and reaches at least 80% of the moment capacity MpB of the connected beam. This capacity of the joint is still usable at the rotation Op (sufficient rotation capacity). Semi-rigid joints have less stiffness and moment capacity and--in some cases--also lower rotation capacity. The moment capacity is from 20% to 80% of MpB. A hinged joint is defined as a joint with a moment capacity lower than 20% of Mpn. It can be concluded that stiffness, moment capacity and rotation capacity have to be regarded as the determining factors for the behaviour of joints. M

MpB 1.0-I

RIGID JOINTS

0.B

exampleforseml-rigid joint SEMI-RIGID JOINTS

0.2 HINGED JOINTS

¢ Fig. 3. M-O diagram.

78

F. Tschemmernegg, C. Humer

The target of the test series described in the following section was to analyze separately the different contributions of panel zone and connections to the overall behaviour of the joint and by this approach to find some answers to the still pending questions. The tests were performed on beams and columns fabricated from European profiles or profiles HD of the company A R B E D .

3 TESTS 3.1 Tests on joints

Figure 4 gives a summary of the test series performed to analyze joint behaviour. Test series 1 served to isolate the forces introduced into the panel zone by the beam flange and to study this effect separately

(a)

(b) Fig. 4. Test series welded joints.

Nonlinear behaviour of joints in structural steel frames

79

Test series 2--performed under symmetrical load---allowed for studying the additional effect of the beam web on load introduction Test series 3--representing an unsymmetrically loaded joint--was performed to study the combined effect of load introduction and shear acting on the panel zone Test series 4 basically conducted in the same configuration as series 3--was undertaken to deliver information on the additional influence of axial forces acting in the column.

All tests were performed on welded joints. Hence the influence of the connection was prevented and the pure panel zone behaviour could be analyzed separately.

(c)

(d) Fig. g---contd.

(a)

(b)

I

(c) Fig. 5. Test series bolted joints.

Nonlinear behaviour or joints in structural steel frames

81

3.2 Tests on connections

Out of the variety of possible connections a very popular connection type-the extended end-plate connection---was selected due to its high stiffness and moment capacity. On this connection type three test series were performed (Fig. 5). Test series 1 served to isolate the tension side of the connection Test series 2 investigated deformation behaviour on a full joint under symmetrical loading Test series 3 investigated deformation behaviour on a full joint under unsymmetric loading. 3.3 Measurements

Details of the test procedures are reported in Refs 3, 4 and 5. Figure 6 shows schematically the test specimen and the arrangement of the measuring equipment. The tests revealed that the arrangement selected made it possible to record separately the deformations due to the different influences of load introduction and shear. In addition a special photogrammetric procedure was developed to analyze the shear behaviour of panel zones under unsymmetrical load. A fine grid was applied on the panel zone and the neighbouring zones of the test specimen. At defined load stages photos of the grid were taken and the slides were projected on to a digitizer. The coordinates of the grid were evaluated by a computer program. By this method, the intensity and distribution of the deformation could be analyzed. A finite element analysis using the ADINA finite element program--performed parallel to the test program~was adjusted by the test results. Figure 7 shows a test specimen with the applied grid, the results of the optical analysis at specified load stages and the deformed finite element grid. The density of the dots in Fig. 7 represents the intensity of shear deformation over the surface of the panel zone. This test program resulted in a separate evaluation of spring curves for the load introduction spring and for the shear spring, as explained in the following section. Figure 8 describes in general such an elastic-plastic spring curve with its four characteristic values: ---elastic --plastic ---elastic --plastic

limit moment Me limit moment Mp limit of rotation ~ge limit of rotation ~p

The plastic limit of rotation was defined as the rotation at which the applied

82

F. Tschemmernegg, C. Humer

t e s t load

test~series

bolted

I: w e l d e d test load

q[

-Q-

. . . . . . .

Ti"

II

',,

',,

I i

iI

II

& test series

2: w e l d e d

and bolted

N test series test series

i

3: N = 0 4: N # 0

test load

I

-[] ..... II

iWi iI ii

I i

I

II ,

test series

3 ÷ 4: w e l d e d

.J

.~

i

II

i I

0

and b o l t e d

Fig. 6. Test specimen and measuring equipment.

APPLIED GRID

TEST SPECIMEN WITH

...'•

Fig. 7. Sheer panel•

ANALYSIS

MeQ
PHOTOOPTICAL

M
-.

,•.i:ii•

.

,'..'.••.

.","i'."."

M ~ MpQ

• ",'" ".

.,'.-.•

FE

-

GRID

e~

2

84

F. Tschemmernegg, C. Humer

b,1

Me

D

Fig. 8. Elastic plastic spring.

load--with the test being performed under controlled deformation--started decreasing. For most of the test specimens the decreasing load was accompanied by plastic buckling of the column web. Hence collapse due to elastic instability of the web can be excluded for the tested profiles until they reach tgp or Mp respectively. A n o t h e r consequence is that the load introduction spring has equal characteristics for the tension and compression sides. The tests were performed with controlled deformation at a low strain rate and the tests were stopped at certain load stages for several minutes to obtain the static load. Evaluation was done according to Ref. 7, i.e. geometrical and material properties were taken for all test specimens and the tests were evaluated on a statistical basis using actual material and geometrical data.

4 T H E SPRING M O D E L On the basis of the measurements and the following systematic evaluation, a model for the joint was developed in a step-by-step method with the result that this model describes the behaviour of the joint in an appropriate and consistent way (Fig. 9 (a) and (b)). The symmetrical load (Fig: 9(a)) only activates the load introduction spring causing the rotation BE. The unsymmetrical load activates the load introduction spring as well as the shear spring (Fig. 9(b)). These two springs

(b) UNSYMMETRICAL JOINT - -

I

r

.

.

.

.

.

.

.

I ! I I ! I I

|

., iS"

DEFORMATION DUE TO LOAD INTRODUCTION (~E)

Pip

N ~ "~l,

PHOTO

Fig. 9. Deformation of a joint.

DEFORMATION DUE TO LOAD INTRODUCTION ('u£E) AND SHEAR (~Q)

(a) SYMMETRICAL JOINT - -

C

~'&

PHOIO

86

F. Tschenimernegg, C. Humer

Z ' ~ L - ~

l

i

i

t

Mx( i !

i

!

v~

LOAD INTRODUCTION SPRING SHEAR SPRING CONNECTION SPRING

J D

SUPERPOSITION FOR MR= 0

I,E,

=.M=M~.,.,.~-

MA

+

LOAD INTRODUCTION SPRING

MA

Xo SHEAR SPRING

AM=MA

C +

MA

Mp

=

CONNECTION SPRING

OVERALL SPRING

Fig. 10. Spring model.

are assembled in series, so the total rotation of the joint is the sum of the rotation tgE and the rotation Oo due to shear deformation of the panel zone. In the case given in Fig. 9 the connection between the beam and the column is welded and therefore the connection spring may be assumed infinitely rigid. With the developed model there is no problem to simulate any connection type by means of an additional elastic-plastic spring. The generally valid spring model---presented in Fig. lO---incorporates the following springs: - - l o a d introduction spring - - s h e a r spring ---connection spring. MA and MA, shall be the applied moments on both sides of the joint. The connection spring and load introduction spring react on the applied moments MA and MA, respectively, whereas the shear spring only reacts on

Nonlinear behaviour of joints in structural steel frames load intoductlon spring

87

joint spring (overall spring)

shear spring

M

2o

(a)

load introduction spring ~M

joint spring (overall spring)

shear spring

-

0

~Co (b) Fig. 11. Collapse of joints: (a) collapsedue to load introduction(columnsHEA and HEB): and (b) collapsedue to shear (columnsHEM and HD).

the difference of applied moments, AM = M A - M A , . All these springs are assembled in series. Therefore the overall carrying capacity of a joint is determined by its weakest spring, while the overall joint deformation is the sum of the deformations of the springs. The connection should be designed in a way to deliver an appropriate capacity--in accordance with the capacity of the panel zone--as there is no sense in designing the connection to be stronger than the panel zone itself. The welded connection in Fig. ll(a) and (b) is designed according to the panel zone capacity. The flexibility of the connection may be neglected in this case. Figure 1l(a) and (b) further shows the overall spring curve consisting of three segments. In the first part, both load introduction spring and shear spring behave elastically (ee), in the second, one of the springs is already plastic (ep). In the last segment both springs behave plastically (pp). The following section summarizes the characteristic values for each spring.

F. Tschemmernegg, C. Humer

88

5 C H A R A C T E R I S T I C V A L U E S F O R T H E SPRINGS The research project delivered all the necessary data to establish the m o m e n t - r o t a t i o n curves of unstiffened joints; provision is also made to incorporate horizontal and/or diagonal stiffeners. All the equations to determine the characteristic values were then developed on the basis of test results. A detailed description of the procedure including all the equations developed is beyond the scope of this paper, but reference may be made in this connection to Ref. 6, where the established theory is presented in detail; in Ref. 6 are described the design methods for braced and unbraced frames with the necessary examples and for practical use tables, with the characteristic values of beam-column combinations out of the European profiles and profiles HD, are provided.

5.1 Load introduction spring Basically distinction has to be made between the elastic and plastic range of the spring. The graph can be simplified as a bilinear curve. The elastic range can be defined either by the elastic limit moment and the elastic limit of rotation or by the elastic limit moment and the original stiffness. For the definition of the plastic range, the plastic limit m o m e n t and the plastic limit of rotation are necessary. Equations for all characteristic values were established; the plastic limit m o m e n t determined by the compressive capacity of the column web was defined in coincidence with the plastic load-distribution 1:2,5 according to Ref. 7, as the tests proved this to be an appropriate approach; additionally the rotational capacity of the load introduction spring was defined. Tables giving the real values for any realistic combination of beams and columns are provided in Ref. 6.

5.2 Shear spring Based on the findings in Ref. 2, the shear behaviour of the panel zone was investigated by Klein 3 and Braun. 4 The characteristic values to determine the elastic and the plastic range of the shear spring were defined by equations which are presented in Ref. 6. As to the plastic capacity of the shear spring, a new approach was made, because the test results showed that the use of the von Mises criterion in the panel zone does not reflect the real behaviour of the panel zone under unsymmetrical loading. As for the load introduction spring, the characteristic plastic values for the shear spring are listed in the respective tables in Ref. 6.

Nonlinear behaviour of joints in structural steel frames

89

5.3 Connection spring The research project concentrated on the connection type shown in Fig. 2(b) and (c). This connection is an extended end plate connected to a column without stiffeners. In cases where the capacity of the column flange is not sufficient, the connection has to be designed according to Fig. 2c with backing plates. The target of the investigation was to define the capacity of the tension side with limited deformations and to find a possible way to introduce at the tension side a load equal to that introduced at the compression side. In this way the capacity of the connection is adapted to the capacity of the panel zone. Therefore, the test program concentrated mainly on the tension side of the connection. The load-deformation curve had in all tests performed a similar and very typical aspect (Fig. 12). The first part of the curve (very steep, practically linear gradient) reveals very high stiffness and the second part drastically reduced stiffness (gradient also almost linear). As soon as the column flange starts to deform visibly, the deformations of the connection drastically increase. This deformation increase is assumed to take place due to the plastic hinges having formed in the column flange along the bolt line. The load level at which deformations at the column flange start to increase can be influenced very effectively by inserting backing plates, so that the tensile capacity can be adjusted to the compressive capacity of the panel zone (compare Fig. 13). In this case the joint without stiffeners will collapse--analogously to the welded joint--at the compression side due to plastic buckling. The connection deformations being negligible, the end plate connection behaves as a fully welded connection. The test program as well as the model for the column flange is described in detail by Humer. 5Based on this model, tables for standardized connections were developed using a computer program--also given in Ref. 5--for any realistic beam-column combination out of the European profiles. Those tables and a brief summary of the model is incorporated in Ref. 6.

5.4 Examples With the joint model being consistent and the characteristic values available, frame calculations for steel with consideration of semi-rigid joint action has become less complicated. All necessary data are evaluated and published in Ref. 6. Tables 1 and 2 give samples of the tables established for plastic limit moment and plastic limit of rotation with regard to load introduction and shear.

F. Tschernmernegg, C. Humer

°A)

backing p ates

,

Zl

~ZI with backing plates Zt without backing plates

ZI ~

with backing plates Zz

without backing plates e

Photo 1

Photo 2

Fig. 12. Tension side of a c o n n e c t i o n

An example, given in Fig. 14, demonstrates how the moment-rotation curves for the combination HEB180-IPE270 can be established without difficulties, using Ref. 6, for the following cases: --unstiffened joint (Fig. 14(a)) --joint with horizontal stiffeners only (Fig. 14(b)) --fully stiffened joint (Fig. 14(c)).

Nonlinear behaviour or joints in structural steel frames

91

Fig. 13. Tensile capacitance---compressive capacitance.

All characteristic values to define the bilinear spring curves can either be taken directly from the tables (this applies to the plastic values--the values corresponding to this example are marked in Tables 1 and 2) or evaluated by using the equations given in Ref. 6. Figure 15 shows a comparison of these three moment-rotation curves. The curves are the result of the combined moment-rotation curves for load introduction and shear. Further tables in Ref. 6 give all the necessary data for the design of unstiffened joints with extended end-plate connections. The standardized end-plate connections were evaluated by a computer program in such a way that they fit exactly to the required stiffness of the respective welded connection. From Table 3 the appropriate end-plate connection can be taken.

6 IMPLICATIONS ON F R A M E RESPONSE The design of braced frames may be performed as traditional design or as a c o m p u t e r calculation. The design m e t h o d for hand calculation is described in detail in Ref. 6 and simplified procedures are developed for the user. For unbraced frames, computer calculation ought to be favoured due to the complexity of the systems and amount of calculation steps. Hand calculation would turn out to be uneconomic.

92

F. Tschemmernegg, C. Humer

HEB 180

IPE 270 LOAD INTRODUCTION SPRING

SHEAR SPRING

ME

N0

j

Mpo=7500kNcm

[~,.°-" 1959.25,95 = 5066 k Ncm / Eq.5 from/6/

Eq. 2-.. from/6/ Eq.3 /

m 25gB2 6 C,E=I2(X)0'~ =/,.0510 kNcmlrod

I

A,=7.A8cm2

~t= ~,'1.15'16'

~l),: 17,6.10'rad

E

-%

~T,~"1.73.1(33 .,Tpo=10,2.163 tad constant

NO STIFFENERS ME

M°

t4p[ = ,8900 + 2t,,O.5.025,98 = 12017 kNCm

I ~q. 4,, / from/ 6 / Eq. 2

{b)

AM

~

MeE=/.66&÷ 24Di&(~25,98 = 7781 kNcm /.-/ /~ "4g/.5

as°

0.

Ast =5.0cm 1

HORIZONTAL STIFFENERS

~,£ a s °

MQ

M~

/ f

Eq.7 from/6/ R MpQ=7500+1289 259B= I0949kNcm

r"~,°=5056 ÷ 1289259B = 8A14kNcm ~M

as b

I l~q-.5 ~rom161 i>%I

i"

as a

Ast =10.0 cmz

HORIZONTAL AND DIAGONAL STIFFENERS

~'L~s o/4O Fig. 14. Example.

Nonlinear behaviour of joints in structural steel frames ,M

93

[kNem3

8000 7600

6000

o~

10

,

2O

,

La'o

Fig. 15. Moment rotation curves.

The following shows an example of computerized flame calculation (Fig. 16). In the first step the program establishes for the selected profiles the m o m e n t - r o t a t i o n curves for load introduction and shear. Then, internal forces and deformations are calculated considering the flexibility of joints defined by these moment-rotation curves. For comparison purposes the calculation in this example was performed additionally for rigid joints. A n o t h e r example will demonstrate the effectiveness of the presented approach. This example of computer calculation was performed on a single-storey flame tested in the laboratory. Two specimens were tested, one with horizontal stiffeners only, the other without stiffeners. Figure 17 gives a sketch of the test specimen. The horizontal deformation was measured and practically no difference in deformation behaviour between the stiffened and unstiffened flame could be detected.

85

115

154

198

253

307

367

448

180

200

220

240

260

280

300

Mpc (kNm)

160

Support column (HEB hot rolled section)

46 50 50 61 60 80 65 95 76 120 82 143 87 160 99 195

30

160

Characteristic Values for

52 52 57 64 68 83 74 98 86 124 93 148 99 166 113 201

40

180

MpEand

TABLE 1

59 54 64 66 76 86 83 102 96 128 104 153 1ll 171 126 207

53

200

65 57 71 69 85 90 92 106 107 133 116 157 123 176 140 213

69

220

72 59 79 72 93 93 101 lI0 117 137 127 162 135 182 153 219

88

240

81 63 89 76 106 98 114 116 133 144 144 169 153 190 174 229

116 91 66 100 81 118 103 128 122 149 151 161 177 171 198 194 238

102 70 111 85 131 108 142 128 165 157 179 184 190 207 215 247

(kNm) 151 193

mpB

113 74 123 90 145 114 157 134 182 164 197 192 209 215 237 257

245

(1PE hot rolled sections) 270 300 330 360

Beam

127 79 139 96 163 121 177 142 205 174 221 202 234 227 266 270

314

400

145 86 158 104 186 130 202 152 233 186 252 215 267 241 303 286

488

450

164 93 179 112 211 139 228 163 263 198 283 228 300 256 340 302

527

5(X)

183 100 200 120 235 149 254 174 293 210 315 241 334 271 379 319

669

550

Mpo in kNm where Yield Stress = 24.0 kN/cm 2 for Beam and Support Column

204 107 223 128 261 158 282 185 325 223 350 255 371 287 419 336

843

600

e~ e~

515

577

644

777

956

1155

1342

1542

320

340

360

400

450

500

550

600

107 216 114 23l 121 248 134 276 144 311 155 347 163 373 171 399

121 222 129 239 137 256 152 286 164 322 175 360 185 387 194 416

136 229 144 246 153 264 170 295 183 333 196 373 206 402 217 433

150 235 160 253 170 272 188 305 203 345 217 386 228 417 240 449

165 242 176 261 186 280 207 315 222 356 238 399 250 432 263 466

187 252 199 272 211 292 234 330 252 373 270 419 284 454 298 492

209 263 222 284 236 305 262 345 281 391 301 439 317 477 333 517

232 273 246 295 261 318 290 360 312 408 334 459 351 500 369 543

255 283 271 306 288 330 319 375 343 426 367 479 386 523 405 568

286 298 304 322 323 347 358 395 384 449 411 506 432 554 454 ~)3

325 316 346 342 367 369 407 421 436 479 467 540 491 593 515 647

366 334 389 362 412 391 457 448 490 510 524 575 551 632 579 692

407 352 432 382 458 413 508 474 544 541 582 610 612 672 642 737

450 371 478 403 507 436 561 5(11 602 571 643 645 676 712 7(~ 782

e~

5"

e~

320

300

280

260

240

220

200

1811

160

Support column (HEB hot rolled section)

50-8 7.8 62.6 7-5 66-8 7.6 66.8 7.3 66.8 7-5 66.8 7.8 66.8 7-6 66,8 7.8 66.8 7.5

160

38-3 8.3 47.2 7.9 59-3 7.9 59.3 7.6 59.3 7-6 59.3 7-9 59.3 7-7 59-3 7.8 59.3 7.5

180 29.7 8.8 36-6 8-4 48.3 8.2 53.3 7-9 53-3 7.9 53.3 8-1 53.3 7.9 53.3 8.0 53-3 7.6

200 23.7 9.3 29.2 8.9 38-5 8.7 46.0 8-3 48-4 8.2 48.4 8.4 48-4 8.2 48-4 8-2 48-4 7.7

220 19-3 9-9 23.8 9.4 31.3 9.1 37.4 8.7 44-3 8-6 44.3 8.7 44.3 8.5 44-3 8,4 44.3 8-0

240 14.5 10-8 17-8 10-2 23.5 9-8 28.0 9.4 35.4 9.2 39-3 9,2 39.3 9-1) 39.3 8.8 39.3 8.3

11.2 11.8 13-8 11-1 18-2 10.6 21.6 10.1 27.4 9.8 32.1 9-8 35.3 9,5 35-3 9.3 35.3 8,8

9-1/ 12-7 11.0 11.9 14-5 1 I-4 17.3 10-8 21-9 111-5 25-6 10.4 29-3 10.1 32.0 9.9 32.11 9-3

7-4 13.7 9.1 12.8 11-9 12.2 14-2 11.6 17.9 11-1 2141 11.1/ 24-1/ 111.8 29.2 111.5 29.4 9.8

Beam (I P E hot rolled section) 270 31X) 330 360 5-7 15.11 7.1 14.1 9.3 13.3 11-11 12-6 13.9 12-1 16-3 12.0 18.6 11,6 22.6 11.3 25.0 111.5

400 4.4 16-7 5-4 15-6 7.11 14.8 8.4 13.9 111.5 13.3 12.3 13.1 14.1 12.8 17. I 12-3 19.6 11.5

450 3-4 18-4 4.2 17-2 5-5 16.2 6-6 15-3 8.3 14-6 9-6 14-3 11,11 13.9 13-4 13-4 15-3 12,5

51X)

2-8 211-2 3.4 18.8 4-4 17.7 5.3 16-7 6.6 15-8 7.7 15-5 8-8 15- 1 111-7 14-5 12,3 13-5

550

TABLE 2 C h a r a c t e r i s t i c Values for OpE = Op and OpO in 10 -3 rad where Yield Stress = 24-0 kN/cm 2 for B e a m a n d S u p p o r t C o l u m n

2-3 21-9 2.8 211-4 3-7 19-2 4-3 18.11 5.5 17-1 6-4 16.8 7.3 16.3 8.8 15-6 111-1 14-5

600

e~

e~

550

500

~50

J,O0

360

340

66-8 7.1 66.8 6-8 66.8 6-3 66.8 5.9 66.8 5.6 66-8 5"2 66.8 4.9

59.3 7.1 59-3 6.8 59.3 6.3 59.3 5.9 59-3 5-6 59.3 5.2 59.3 5-0

53.3 7-2 53-3 6-9 53-3 6.4 53.3 6.0 53.3 5.6 53.3 5.3 53-3 5" 1

48.4 7-4 48.4 7.1 48.4 6-5 48.4 6.1 48.4 5.7 48.4 5.4 48.4 5.2

44.3 7-6 44"3 7.3 44'3 6.7 44.3 6.3 44'3 5.9 44.3 5-6 44.3 5"3

39.3 8-0 39.3 7.6 39.3 7.1 39-3 6.6 39.3 6.2 39.3 5.9 39.3 5.6

35.3 8.4 35.3 8.0 35.3 7.5 35-3 6.9 35.3 6.5 35-3 6-2 35"3 5.9

32.0 8.9 32.0 8"5 32.0 7.9 32.0 7.3 32.0 6-8 32.0 6.5 32-0 6-3

29.4 9.3 29-4 8-9 29.4 8-3 29.4 7.7 29-4 7.2 29.4 6.9 29.4 6.6

26.4 10"0 26-4 9.6 26.4 9.0 26.4 8.3 26.4 7.7 26.4 7.4 26.4 7.1

22. l 11 "0 23-4 10.5 23.4 9.8 23.4 9.1 23.4 8-4 23-4 8-1 23-4 7.8

17.3 11.9 19.4 11.0 21.1 10.6 21.1 9.8 21.1 9.2 21.1 8.8 21-1 8-5

13.8 12.9 15.5 12.3 19.1 11 "5 19' 1 10.6 19.1 9.9 19.1 9.5 19.1 9.2

11 "4 13"9 12-8 13"2 17"7 12-4 17-6 11-5 17.6 10.7 17.6 10"3 17-6 9"9

---I

t'.,

160 110 130 140 160 170 180 180 180 180 180 180 180

M20 M12 M16 M20 M20 M20 M20 M20 M20 M20 M20 M20 M20

141

IPE 400 30 4O 53 68 88 100 112 124 137 153 174 195

130 130 150 160 160 161) 160 160 160

M16 M16 M20 M20 M20 M20 M20 M20 M20

30 40 53 68 31 92 103 114 125

IPE 160 IPE 180 IPE 200 IPE 220 IPE 240 IPE 270 IPE 300 IPE 330 IPE 360

HEBI~

IPE 160 IPE 180 IPE 200 1PE 220 IPE 240 IPE 270 IPE 300 IPE 330 IPE 360 IPE 400 IPE 450 IPE 500

130 130 140 140 140 140 140

M16 M16 M20 M20 M20 M20 M20

30 48 52 37 83 72 8O

IPE 160 IPE 180 IPE 200 IPE 220 IPE 240 IPE 270 IPE 300

HEBI40

HEB 180

bp

Beam

Support column

2(1 20 25 25 25 25 25 25 25 25 25 25

25

20 20 25 25 25 25 25 25 25

20 20 25 25 25 25 25

tp

220 250 280 300 320 35(1 380 41(I 440 480 531) 50(1

488

230 250 280 300 320 350 38(1 410 440

230 250 280 300 320 350 380

hp

End-plate Bolts (10.9)

Mp = rain ( M pE, MpB ) (kNm)

St 360

TABLE 3

20 25 30 30 30 3(1 30 3(I 311 30 30 30

3(I

25 25 30 30 311 30 30 30 38

25 25 30 30 30 30 38

el

70 90 105 125 145 170 20() 230 255

70 90 105 125 145 170 200

e3

55 55 60 6(I 60 60 60 60 65

55 55 60 60 60 60 61)

e4

70 80 8(1 90 85 105 85 125 85 145 911 170 911 20() 90 23(1 91) 255 9(1 295 911 345 95 391)

50 55 6(I 61) 61) 611 611 6(I 65 65 65 65

911 295 65

80 80 85 85 85 90 90 91) 90

80 80 85 85 85 90 90

e2

30 35 40 41) 40 411 411 411 411 4(I 4(/ 411

411

35 35 40 40 4(I 4(I 40 4(1 40

35 35 40 40 41) 40 41)

e5

25 25 35 40 40 40 40 4(I 441

25 25 30 30 30 30 30

w3

71) 81) 81) 81) 8(1 80 80 80 81) 81) 80 9(I

2(1 25 311 41) 45 50 5(I 50 5(1 50 50 45

80 4(1

80 80 80 8(1 80 8(1 80 8(I 80

80 80 80 80 80 80 80

wl

Bolt geometry

10 10 10 10 11) 10 1(1 10 10 I0 111 11)

10

10 10 I0 1(I I0 I0 10 10 10

13 13 10 10 10 10 10

u

4 4 4 5 5 5 5 5 5 5 5 5

4

4 4 4 5 5 5 5 5 5

4 4 4 4 4 4 4

3 3 3 3 3 3 4 4 4 4 5 5

4

3 3 3 3 3 3 4 4 4

3 3 3 3 3 3 4

aF aw

WeMs

153

158

145 158 158 158 158

145 145 145 151) 158

Iv

E x t e n d e d E n d - p l a t e C o n n e c t i o n with High T e n s i o n Bolts ( m e a s u r e m e n t s given in c m )

8

8

8 8 8 8 8

8 8 8 8 8

tv

43

48

48 48 48 48 48

3(1 38 38 38 38

~'l

Backing plates

25

20

2(I 211 20 211 211

25 25 25 25 25

v2

"~

•

u=l==

hp

IPE 160 IPE 180 IPE 200 IPE 220 IPE 240 IPE 270 1PE 300 IPE 330 IPE 360 IPE 400 IPE 450 IPE 500 IPE 550 IPE 600

HEB 220

,31

IPE 160 IPE 180 IPE 200 IPE 220 IPE 240 IPE 270 IPE 300 IPE 330 IPE 360 IPE 400 IPE 450 IPE 500 IPE 550 IPE 600

HEB2~

30 40 33 68 68 116 143 159 175 196 223 250 277 306

30 40 53 60 88 116 138 147 162 182 207 232 257 283 II0 120 150 150 170 190 200 200 200 200 200 200 200 200

110 120 150 150 170 180 200 210 220 220 220 220 220 220

M12 M12 M20 M20 M20 M24 M24 M24 M24 M24 M24 M24 M24 M24

M12 M12 M20 M20 M20 M20 M24 M24 M24 M24 M24 M24 M24 M24

20 20 25 25 25 25 30 30 30 30 30 30 30 30

20 20 25 25 25 30 30 30 30 30 38 30 30 38

220 240 280 300 320 350 400 430 460 500 550 600 650 700

220 240 200 300 320 370 400 430 460 500 550 600 650 700

20 20 30 30 30 30 40 40 40 40 40 40 40 40

20 20 30 30 30 40 41) 41) 40 41) 40 40 40 40

70 70 85 85 85 90 105 105 105 105 105 110 110 110

70 70 85 85 85 105 105 105 105 105 105 110 110 110

80 100 105 125 145 170 165 215 245 285 335 375 425 475

50 50 60 61) 60 60 70 70 70 70 70 75 75 75

80 5(1 I(}0 511 105 6(I 125 6(1 145 60 155 70 185 70 215 70 245 70 285 70 335 70 375 75 425 75 475 75

~) 7(1 20 30 70 25 40 90 30 4(1 90 30 40 90 40 40 90 45 50 90 55 50 90 60 50 90 65 50 90 65 50 90 65 50 100 60 50 100 60 50 100 60

30 7(1 20 30 70 25 40 90 30 40 90 30 40 90 40 50 90 50 50 91) 55 50 90 55 50 91) 55 51) 90 55 50 90 55 50 100 50 50 100 50 50 100 50

10 10 10 10 10 10 I0 10 I0 10 10 10 10 10

I0 I0 10 10 I0 10 10 10 10 10 10 10 10 10

4 4 4 5 5 5 5 5 5 5 5 5 5 5

4 4 4 5 5 5 5 5 5 5 5 5 5 5

3 3 3 3 3 3 4 4 4 4 5 5 6 6

3 3 3 3 3 3 4 4 4 4 5 5 6 6

190 190 190

150 185 185 185 185 183 198 198 lth)

8 8 8

8 8 8 8 8 8 8 8 8

60 60 68

50 53 53 55 53 53 58 58 58

25 25 25

20 20 20 21) 20 20 25 25 25

e~

e~

e~

'+++°

8

I-6

I

-I

32

q

~-,7;;°°~-

31

F=O-OS-q-L

L:5000

Fe 360 q = 40 kNIm

Jr

-r

.2

-r

IPE "~00

,.=,

•4

,=.,

_

Z2

!

~4

1.5

17

+

[

~

,8 _,

19

21

r 1° -q t '3 I IIIIilIUJI~III! llllllllllllll

t+

tUm.UUt~'~ Um"l" ml ~ ,3 3? +,4__~_

,,I])--30

,,

l,~,,mm~,u~ L_,.,,~ =,r--aa 29__

F

F

curve

0

d

10

20

30

40

50

0.02

0-04 0.06 Rotation (tad)

0'06

0"10

Fig. 16. Computer calculation.

o,

O-

0.~

0.4

0.6

0-8

1-0

70

~

1-2

80

60

1-4

1-6

1-8

2.0

I

!

J

!

I

I

i

I

I

0.04 O , O O 0.12 0.16 0.20 0.24 H o r i z o n t a l d e f l e c t i o n of j o i n t 26 ( m )

|

• S i m p l i f i e d m e t h o d of 161

X Comp, p r o g r a m o f / 6 1 - s e m i - r i g i d - j o i n t

• Comp, p r o g r a m of 161- r i g i d j o i n t

90

100

110

120

130 ,

B e a m : IPE 3 0 0 F Y = 2 3 5 N I m m -2 Column : HEB 200 FY = 235 N l m m -2

Moment-rotation

+

Nonlinear behaviour or joints in structural steel frames 0,388 Fz

IPE220

•

0.612 Fz

I 1-I1

fy=36GNImm

L I

900

101

z

400

MEASUREMENT

180. 320 11

= TEST LOAD IJ =

--

U~DIT~MTAI

~

~1 ~ C T T ~ N

Xp

~z

1700 Fig. 17. Test frame.

This frame was also analyzed using the program of Ref. 6 and the result of the calculation is compared with the measured deformation in Fig. 18. As can be seen, the calculation gives very good correlation with the test measurements.

7 CONCLUSION The test program performed at the Institute of Steel and Timber Construction, University of Innsbruck, resulted in a mass of new information on semi-rigid joints, especially with regard to stiffness and rotational capacity. On this basis a new joint model was developed. The advantage of this model is the fact that the single contributions to load deformation behaviour of the joint can be evaluated separately. Furthermore, new approaches were developed for the different influencing factors e.g. shear or end-plate connections. Finally, new calculation procedures were developed on the basis of these findings. All these new developments are summarized in Ref. 6.

E

¢:

Z v

4C

"~ 60

80

100

t

a

I

(:>020

t-

0

v

50C

0

100

200

300

400

I

I

5.0

I

10-0 Horizontal

I

I

I

0

I

I

5.0

I

10.0 Horizontal

I

I

I

I

I

15-0 deflection

t

20.0 (mm)

|

15.0 20-0 deflection (mm)

o Comp, p r o g r a m of 161- rigid j o i n t n Comp, p r o g r a m o f 161- s e m i - rigid- j o i n t A S e m i - r i g i d joint - Von m i s e s c r i t e r i o n

0_~ 0

Fig. 18. Results of test frame. *Deflection forces = load-introduction and shear stresses according to yon Mises criterion.

I I i I t I I 0.016 0.004 0-008 0-012 R o t a t i o n (tad)

OE

Beam : IPE 22{).FY : 3 6 0 N I m m -2 C o l u m n : HEB 140 FY : 2 6 8 N / m m -2

I00

200

300

i

4O0

500

•

25-0

l

25-0

J

i:Z. n

l

eb

t~

Nonlinear behaviour or joints in structural steel frames

103

REFERENCES 1. Tschemmernegg, F., Zur Entwicklung der steifenlosen Stahlbauweise. Der Stahlbau 7 (1982) Seite 201 ft. 2. Tautschnig, A., Entwicklung eines neuen, makromechanischen Knotenmodelles und Erstellung eines darauf aufbauenden EDV-Programmes zur Berechnung von Stahlskeletttragwerken unter Beriicksichtigung nichtlinearer Nachgiebigkeiten der Verbindungselemente insbesondere bei "steifenloser" Bauweise. Dissertation, Universit~it Innsbruck, Austria, 1983. 3. Klein, H., Das elastisch.-plastische Last-Verformungsverhalten M- steifenloser, geschweiBter Knoten fur die Berechnung von Stahlrahmen mit HEB-Stfitzen. Dissertation, Universit~it Innsbruck, Austria, 1985. 4. Braun, Ch., Das Momenten-Rotationsverhalten von geschweiBten, steifenlosen Rahmenknoten bei Querkraftbeanspruchung. Dissertation, Universit~it lnnsbruck, Austria, 1987. 5. Humer, Ch., Das Momenten-Rotationsverhalten von steifenlosen Rahmenknoten mit Kopfplattenanschliissen. Dissertation, Universit~it Innsbruck, Austria, 1987. 6. Rahmentragwerke in Stahl unter besonderer Berficksichtigung der steifenlosen Bauweise. Theoretische Grundlagen--Beispiele .-7-Bemessungstabellen. Herausgeber: Osterreichischer Stahlbauverband (OSTV), 1130 Wien, Larochegasse 28, und Schweizerische Zentralstelle ffir Stahlbau (SZS), 8034 Z/.irich, Postfach, 1987. 7. Eurocode 3, Gemeinsame einheitliche Regeln ffir Stahlbauten. Deutsche Ausgabe: Deutscher Stahlbau-Verband, K61n, 1984.