Behaviour of Steel Beam-to-Column Joints Under Cyclic Reversal Loading: An Experimental Study

BEHAVIOUR OF STEEL BEAM-TO-COLUMN JOINTS UNDER CYCLIC REVERSAL LOADING: AN EXPERIMENTAL STUDY L. Calado ', C. A. Castiglioni ^and C. Bemuzzi ' Department of Civil Engineering - Technical University of Lisbon, Portugal ^ Department of Structural Engineering - Technical University of Milan, Italy Department of Mechanical and Structural Engineering - University of Trento, Italy

ABSTRACT An experimental study was carried out to investigate the low-cycle fatigue behaviour of beam-to-column joints. Several full-scale specimens were tested, in a multi-specimen testing program, using constant amplitude displacement histories, to develop a cumulative damage model. This model is based on S-N line approach and, although proposed here for low-cycle fatigue, was derived and is valid also for high cycle fatigue. Possible definitions of parameter S, as well as, failure criteria for the definition of A^, are compared. The influence of the definition of parameter S on the value of the slope of the S-N line is discussed. A statistical method for the assessment of the S-N lines, based on a given probability of failure with reference to suitable levels of safety and reliability of the structural joints, is also presented.

KEYWORDS Joints, connections, experimental behaviour, fatigue, damage, failure, design codes, S-N curves.

1. INTRODUCTION Selection of the energy dissipation mechanisms appears to be a fundamental requisite for aseimic design of steel structures as it allows the combination of the stable hysteretic response of the whole system, with the possibility to control reliably the main behavioural parameters influencing the structural behaviour under seismic input. Hysteretic behaviour of individual frame components (i.e, members and joints) plays a relevant role in the definition of the global response of the structure. Therefore, in addition to material ductility, overall and local buckling as well as low cycle fatigue phenomena are important factors which can significantly affect the seismic performance of the structural system. Traditional design approaches for steel structures, based on simple and rigid frame models, concentrate the dissipation of the energy associated with the earthquake, respectively in bracing cantilever systems or in beam-to-columns joints, GEN (1994). Moreover, the semi-continuous frame model, which already proved its efficiency under static loading, Bjorhovde et al (1991), may also be a convenient options for seismic design if joints are considered part of the dissipation systems, Nader et a/ (1991), Elnashai et al (1994). 279

280

L. C A L A D O £7-/11.

The paper presents the main results of a jointed research project, between the Universities of Lisbon (Portugal), Milan (Italy) and Trento (Italy) with the general scope to define suitable and accurate criteria for low-cyclic fatigue design (i.e., fracture resistant seismic design) of rigid as well as semi-continuous steel frames. A limited number of structural steel joints were identified and they were fabricated and tested in a multi-specimen program in order to establish classes of low-cycle fatigue resistance for connections, similar to those existing for structural details under high cycle fatigue, CEN (1992).

2. DAMAGE ASSESSMENT MODELS It is the author's opinion that a modem methodology to assess the low-cycle fatigue endurance of civil engineering structures should adopt parameters related to the global structural behaviour, such as displacements, rotations, bending moments, etc. Taking this into account, the S-N line approach may be adopted, considering as S, parameters related with the global structural ductility (e.g., interstorey drifts or joint rotations). The fatigue failure prediction ftinction, used by the S-N line approach, can be expressed by the following equation: N.S'"=^K (1) where N is the number of cycles to failure at the constant stress (strain) range S. The non-dimensional constant m and the dimensional parameter K depend on both the typology and the mechanical properties of the considered steel component. In the Log-Log domain Eqn. (1) can be re-written as: Log(N) =

(2)

Log(K)-mLog(S)

Eqn. (2) represents a straight line (so called S-N line) with a slope equal to -J/m called fatigue resistance line, which identify the safe and unsafe regions (Figure 1). Log(S)

Log(N)

Log(K)

Figure I: Fatigue resistance line in the Log(S)-Log(N) scale. In order to apply Eqn. (1), both parameters S and the number of cycles to failure (N) should be defined, by a consistent re-elaboration of test data in accordance with the basic assumption of the selected damage model. The number of cycles to failure iV can be identified on the basis of the adopted failure criterion, while S can be defined with reference to the definitions given in the literature by various authors. By statistical reanalisis of such data plotted in a Log(S) - Log(N) scale, is than possible to define both the slope (-1/m) of the S-N line and the constant K. Of course such value migth be different for various definitions of parameters S and A^.

BEHAVIOUR OF STEEL BEAM-TO-COLUMN JOINTS

281

2J Definition of the Strain Range (S) Some of the most relevant proposals available in literature for the definition of the strain range S are shortly presented. Krawinkler & Zohrei proposal The concept to connect the parameter (S) of the fatigue failure prediction functions with the global structural ductility was originally proposed by Krawinkler et al (1983). They proposed a relationship between the fatigue endurance and the plastic portion of the generalised displacement component, which can be expressed as: N{^5,)"'-^K,,

(3)

where zl<^/represents the plastic portion of the deformation range. Ballio & Castiglioni proposal Ballio et al (1995) proposed an unified approach for the design of steel structures under low- and/or highcycle fatigue, which is based on global displacement parameters instead of local deformation parameters. The fundamental hypothesis is the validity of the following equation: A^ Av did — = — = --^ ^y

^y

(4)

^y

where s represents the strain, v the displacement, (p the rotation (or the curvature), A the range of variation in a cycle and the subscript y identifies the yielding of the material (Sy) as well as the conventional yielding with reference to the generalised displacement (Vy„ ^^ assumed as the test control parameter. The following parameter can be defined:

The term Acf^ represents the effective stress range, associated with the real strain range Ae in an ideal member made of an indefinitely linear elastic material, 5 is the generalised displacement and E is the Young's modulus. In the case of high-cycle fatigue (i.e. under cycles in the elastic range), zlcj* coincides with the actual stress range AG. Using the S-N curves and assuming the effective stress range zlcr* as 5, Eqn. (1) can be re-written as:

A^i

= K,^.

(6)

Feldmann, Sedlacek, Weynand& Kuck proposal On the basis of an extensive finite element analysis, Feldmann (1994), Sedlacek et al (1995) and Kuck (1994) investigated the behaviour of beam-to-column joints under constant amplitude cyclic loading. It

282

L. CALADO

ET AL.

appeared that the relationship between the plastic strain, £pi, at the hot spot (strain at the relevant place where first crack occurs) and the plastic rotation ((/>pi) is linear, i.e.: ^2,pi

^

^2,pi

where subscripts J and 2 refer to two different loading steps. This linear relationship, that is somehow similar to Eqn. (4), can be re-written in terms of the plastic portion Spi of the generalized displacement component S and, when plotted in a Log-Log scale, plots as a "Wohler" line. Hence, it is possible to define an effective plastic stress range AcXpi*:

that can be assumed as parameter S and Eqn. (1) can be re-written as: 'AS„ M\ : ^ < T ( F , )

=K,,^,

(9)

Bernuzzi, Castiglioni & Calado proposal Based on the re-elaboration of an extensive experimental data of beam-to-column joints as well as of beams and beam-columns, Castiglioni et al (1996) and Bernuzzi et al (1997), they proposed to use the total interstorey drift (i.e., the total displacement range) Av as parameter 5, and consequently Eqn. (1) can be rewritten, in the form: N.AS"--' =K,,.,

(10)

2,2 Definition of the Fatigue Endurance (N) For the prediction of the low-cycle fatigue endurance of steel structural components, it seems convenient to adopt a failure criterion based on parameters associated with the response of the component (i.e. stiffness, strength or dissipated energy). Two failure criteria, which have been proposed, Castiglioni et al (1996), are in the following reviewed. Calado, Azevedo d Castiglioni criterion (Na=o.s) These authors, Calado et al (1989, 1995, 1996), developed a failure criterion of general validity for structural steel components under both constant and variable amplitude loading histories that can be written in the following form: -^
(11)

In this equation T/^ represents the ratio between the absorbed energy of the considered component at the last cycle before collapse and the energy that might be absorbed in the same cycle if it had an elastic-perfectly plastic behaviour while 7^ represents the same ratio but with reference to the first cycle in plastic range. The value of a, which depends on several factors (such as type of the joint and the steel grade of the component)

BEHAVIOUR OF STEEL BEAM-TO-COLUMN JOINTS

283

should be determined by fitting the experimental results. As it is particularly interesting to identify a a priori, in order to define a unified failure criterion, a value of a=0.5 is recommended for a satisfactory and conservative appraisal of the fatigue life. In the case of variable amplitude loading histories the same criterion remains valid but should be applied on semi-cycles, v^hich can be defined in plastic range as the part of the hysteresis loop under positive or negative loads or as two subsequent load reversal points. Bernuzzi, Calado & Castiglioni criterion (N^wr) In this criterion, valid only for constant amplitude loading, Bernuzzi et al (1997), it is assumed that the drop of the hysteretic energy dissipation is the main parameter for the definition of the low-cycle fatigue endurance. In particular, focusing attention only on the cycles performed at the displacement range ziv,, the relative energy drop, AW^ can be defined as:

(w.. -w.\ V

'^^ inn

^

where V/^^^f represents the dissipated energy in the first cycle at the assumed displacement range while V/^ is the energy associated with the i.th cycle at the same displacement range. Failure is assumed to occur when the energy drop is evident, i.e. the generic point of co-ordinates %, AW^j,, is not on the straight line. 2,3 Definition ofm The parameter m identifies the slope of the line interpreting, in a Log-Log scale, the relationship between number of cycles to failure (N) and the stress (strain) range (S). Focusing the attention on w, some discrepancies can be found in the literature among the proposal of various authors. In particular it can be noticed that Ballio & Castiglioni suggested to adopt a value of mgc^S like Bernuzzi et al m^cc^^; on the contrary, Krawinkler & Zohrei proposed an exponent rn]^2=2. The Feldmann approach tried to re-write the Coffin-Mason equation in terms of global deformation parameters, proposing a value mpswK^^ i^^ agreement with Krawinkler & Zohrei. However, both Feldmann and Krawinkler adopted the plastic range of the assumed parameters, while Ballio adopted the total cyclic excursion (i.e. elastic and plastic). Hence, it seems that the value of the exponent m depends on the definition of S. In order to clarify the influence of the definition of parameter S on the value of the exponent m, this last parameter was assessed for possible definitions ofS. In order to assess the exponent w, the data obtained in tests with cycles of constant amplitude should be plotted in terms of number of cycles to failure (N) and stress (strain) range (S) in a Log-Log diagram and fitted by a straight line. The slope m of the best fitting line can be considered the exponent to be adopted in Eqn.(I).

3. DEFINITION OF THE DESIGN S-N LINES According to the limit state design method, the parameter governing the design should be defined on the basis of a statistical analysis, allowing to make reference to a value associated with a given probability of failure / / ( o r of survival, 1- Pj). Such a probability should be defined with reference to suitable levels of safety and reliability of the structure and its components. Hence, the S-N lines should be defined with reference to a given probability of failure Pf. In this research, the procedure proposed in the JWG XIII-XV Fatigue Recommendations (1994) was used and is briefly summarised herein.

284

L. ChLMyO ET AL.

Scope of the procedure is the definition of the value Log(Kf) such that the line with a slope (-l/m), and intersecting the x-axis at Log(K), is associated with a probability of 5% that test data plot below it. In the following, reference is made to the set of values Log(K) representing the intersections with the A^ axis of the S'N lines, each one having a constant slope (-l/m), and passing for every single test data point. The basic formula to determine the design value of the random variable X=Log(K) can be assumed as: X, = ,Li-il>-\a)
(13)

where X^ is the design value, fj. is the mean value oiX, cris the standard deviation ofX, ^ is the normal law of probability and a is the probability of survival. Generally it is assumed that /i is distributed according to the t-Student model and the standard deviation G follows the chi-square law (x)- As a and // are unknown values, their estimated vales from tests, // e cr respectively, should be associated with p, confidence level. The design value of ^ can be expressed as:

t(P,n-\)

X,^^-a

\n

n-l

r'(a)-

(14)

According to Eurocode 3, CEN (1992), the confidence range should be 75% of 95% probability of survival on the Log(N) axis. Hence, by assuming a and /? respectively equal to 0.95 and 0.75, Eqn (14) can be rewritten as: X,=

(15)

^-cry

where, in the case of limited amount of data, the value of y can be obtained directly from Table 1 on the basis of the number of available data (n).

TABLE 1 COEFFICIENTS FOR STATISTICAL EVALUATION

n

2

3

4

5

6

7

8

9

10

11

12

13

14

15

Y

12.16

5.42

4.13

3.58

3.26

3.06

2.91

2.80

2.71

2.64

2.58

2.53

2.48

2.45

4. THE EXPERIMENTAL PROGRAMME AND THE TESTS An experimental study was recently carried out at the Technical University of Lisbon on steel beam-tocolumn joints, Calado et al (1996). In order to minimise size effects, specimens were as close as possible to full size. They consisted of a beam attached to a column by means of different connection details, representing frequent solutions adopted in the European steel construction practice for beam-to-column joints. Figure 2. The following typologies of beam-to-column joints were considered and tested: bolted web and flanges cleats (BCCl), extended end plate (BCC2), bolted flange plates (welded to the column) with web cleats (BCC3), welded flanges with bolted web cleats (BCC4) and welded joints (BCC5 and BCC6). Bolts used in all specimens were Ml6 grade 8.8; in the case of flange plates with web cleats specimens and for extended end plate connections, bolts were preloaded according to EC3 provisions, CEN (1992). All welds were full

285

BEHAVIOUR OF STEEL BEAM-TO-COLUMN JOINTS

penetration butt welds. Several specimens were fabricated and tested for each joint, according to a multispecimen testing program, consisting of different cyclic loading histories with both constant and variable amplitudes i F

s

I

BCC1

supporting beom

BCC1 BCC2 BCC3 BCC4 BCC5 BCC6

beam

column

HEA120 HEM 20 HEA120 HEA120 IPE300 IPE300

HEAT 2 0 HEA120 HEA120 HEA120 HEB160 HEB200

d

(rnm) 1476 1476 1476 1476 1800 1800

h

(mm) 943 943 943 943 862 862

' BCC3

BCC5

'BCC4'

BCC6

connection — web

connection-flanges L100X100K10 end plate e = 20 m m bolted plotes e = 1 0 mm butt welds butt welds butt welds

2L100X100X10

—

2 bolted plates e = 5 2 bolted plates e = 5 butt welds butt welds

mm mm

Figure 2: Schematic of beam-to-column connections specimens. In Table 2 are presented the relevant parameters of each specimen (j^ Fy and 5^, the values of the various definition of (S) (AS, A5pi, Aa^i* and Aa*) and the values of the fatigue endurance (N) (N-poT' ^mr and Na=o.5)- Ir^ the same table is also mentioned the failure mode, according to the simbology introduced. TABLE 2 TESTS ON BEAM-TO-COLUMN JOINTS: RELEVANT PARAMETERS TESTS

BCCl

BCC2

a b c d e c d e

f BCC3

BCC4

BCCS

BCC6

a b c a c d e a b d a b d

fy

P.

,v,„„-y

..

295 295 295 295 295 274 274 274 274 303 303 303 391 391 391 391 271 271 271 278 278 278

20 20 18 22 23 36 38 40 38 21 20 20 32 31 30 27 143 138 152 164 175 178

^v

30 25 23 16 16 14 15 16 13 11 10 9 13 13 14 13 7 8 8 6 6 6

Av

Av,,;

'-"'

'"'"'

200 300 150 300 200 150 180 200 200 200 150 250 200 150 100 130 100 150 75 100 150 75

139 250 104 267 169 121 150 169 173 178 131 231 173 123 73 103 85 134 59 89 139 64

Aa*

'--"' 1941 3506 1940 5374 3751 2850 3290 3512 4132 5458 4770 8185 5841 4419 2879 3776 3655 5186 2564 4888 7295 3751

AaV

1\ i(y,-

Va=.5

'^ AW'r

24 6 55 6 6 44 32 19 20 16 31 6 5 9 29 25 17 6 24 16 12 19

19 5 26 5 5 38 31 18 18 15 29 6 4 J

24 5 50 5 5 37 31 18 18 15 29 5 4 7 28 24 15 5 21 14 10 16

,v...v

1351 2916 1350 4784 3161 2302 2742 2964 3584 4852 4164 7579 5059 3637 2097 2994 3112 4644 2022 4331 6739 3194

28 25 16 5 22 14 8 18

FAILURE MODE

JF

JF

BBM

WF

WF+PM

fVF+PM

BBM

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L. C\L\DO

ET AL.

Four types of failure were observed during the tests: joint failure (JF), failure in the base material of the beam (BBM), weld failure (WF) and panel mechanism (PM). The behaviour of web and flange cleats connections (Figure 3) is characterised by large slippage between the beam flange and the angle leg due to the ovalization of holes, which increases with the number of cycles although the displacement amplitude is constant. BCC1C 25

20

41

15

''JV-

K)

' Jmt-^

,1,1 ^ r---^->-"'-

'2 -100

M

J^..

JJ •<>

J!^^ 50

100

s -15 -20 -25

j

-30

rot (radx lOe-3)

1 Figure 3: Hysteresis loops and failure mode of a web and flange cleats connection. Extended end plate connections (Figure 4) are characterised by regular histeresis loops without any slippage and with regular deterioration of both the absorbed energy and the maximum moment at the end of each cycle.

Figure 4: Hysteresis loops and failure mode of an extended end plate connection. Bolted flange plates with web cleats connections (Figure 5) exhibit slippage between flange plates and the beam flange due to the ovalization of the holes, but this phenomena has less importance when compared with web and flanges cleats connections.

BEHAVIOUR OF STEEL BEAM-TO-COLUMN JOINTS

287

Figure 5: Hysteresis loops and failure mode of a bolted flange plates with web cleats connection. The cyclic behaviour of specimens with v/elded flanges and web cleats (Figure 6) is characterised by high elasticity and great regularity in the shape of the loops with gradual deterioration of energy absorption capacity. Large plastic deformations developed in the panel zone of the column. In most cases, failure was due to cracking at toe of welds connecting the beam flanges to the column ones. BCC4E 50 40

1

/v

,''f "^ ' -100

100

f

-20 -

1

-30

// ^^

-50

rot (radx lOe- 3)

Figure 6: Hysteresis loops and failure mode of a welded flanges and web cleats connection. The welded connections (Figure 7) are characterised by regular hysteresis loops and a very good capacity for energy dissipation; note that deterioration in terms of strength, stiffness and energy absorption capacity is very limited and stable up to collapse.

288

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CALAIX)£7'/IL.

Figure 7: Hysteresis loops and failure mode of a welded connection.

5. LOW-CYCLE FATIGUE PERFORMANCE The previously mentioned test data were statisticaly re-elaborated, in accordance with the described procedures for the assessment of the stress (strain) range (S) and the number of cycles to failure (N). Concerning the fatigue endurance, assessed by the two mentioned methodologies (Na=oj and NA^VJ' (Table 2), a good accuracy was observed between the values obtained with the proposed criterion and the actual number of cycles to complete failure (NJQJ). For all the specimens tested, the Bemuzzi et al criterion (N^iy^) exhibits a mean value error of P% while the Calado et al criterion (Na^o.s) shows 12%, allowing to conclude that both criteria are valid for the assessment of the fatigue endurance of steel components under constant amplitude loading. However, it should be noticed that the Calado et al criterion has a general validity in both cyclic and random loading conditions; furthermore, the value of a=0.50 represents a unified failure parameter, independently of the structural detail. In order to assess the slope m of the S-N lines in the Log-Log scale for each typology of beam-to-column connections, and to investigate the influence of the fatigue endurance definition (Na^o.s ^^^ ^Awr) on such slope, all experimental data were re-elaborated according to the previously mentioned proposals of definition of 5. Their values are presented in Table 3. It can be noticed that the definition of the fatigue endurance (Na=o.5 ^ ^ ^^wr) has a limited influence on the variation of the slope m and on Log(K). However, these two parameters are very dependent of the definition of 5. Values of Log(K) and m parameters obtained with Krawinkler et al and Feldmann et al approaches are very similar to each other. Also the results obtained with the Ballio et al and Bemuzzi et al approaches give values for the previous mentioned parameters, very similar to each other, although different from those obtained by means of Krawinkler et al and Feldmann et al methods. In fact, the slope m of the line best fitting in a Log(S)-Log(N) plot the test data, if assessed with Krawinkler et al and Feldmann et al methods is nearly 2 while a value of approximately 3 is obtained with Ballio et al

289

BEHAVIOUR OF STEEL BEAM-TO-COLUMN JOINTS

and Bemuzzi et al approach. This is due to the fact that both Krawinkler et al and Feldmann et al approaches adopted plastic range of S, while Ballio et al and Bernuzzi et al adopted the total cyclic excursion (i.e. elastic and plastic). Figure 8 shows S-N lines for one typology of beam-to-column connections presented in Table 3. TABLE 3 LOG(K) AND m COEFFICIENTS FOR BEAM-TO-COLUMN CONNECTIONS

^Awr TESTS

A

C

B

^

a^.5

B

A

D

D

C

m

Log(K.)

m

Log(K)

m

LOB(K)

m

LogCK)

m

Log(K)

m

Log{K)

m

Log(K)

m

^.27

2J4

14.07

3.79

10.72

2.91

12.66

4.97

5.49

1.99

9.92

2.61

7.62

2.00

9.84

3.80

1.66

0.40

2.59

0.51

2.32

0.44

1.82

0.45

0.70

0.39

0."0

0.30

O.'O

0.43

0~0

0.45

6.73

2.45

11.11

2.75

9.37

2.31

7.78

2.83

6.63

2.49

11.32

2.81

9.53

2.53

7.91

2.89

7.54

2.65

11.52

2.74

11.00

2.64

8.52

3.22

^.42

2.80

11.28

2.68

10.78

2.58

8.39

3.16

6.98

2.88

13.67

3.49

10.9^

2.82

8.5^

3.49

6.98

2.88

13.67

3.49

10.9-

2.82

8.5-^

3.49

4.-^]

1.88

9.02

2.23

7.W

1.90

5.56

2.22

4.89

1.96

9.40

2 33

8.02

1.99

5.~~

2.32 I

2.49

0.69

4.10

0.80

3.74

0.-^2

2.7(7

0. ^8

3.22

1.08

5.72

1.25

5.17

1 jj

3.55

1.21

Log(lC) a b

\BCCI

c d e c d

BCC2

e

f a BCC3

b c a c

BCC4

d e a

BCC5

b d a

BCC6

b d

CRITERION FOR THE STRAIN RANGE DEFINITION : KRAWINKLER&ZOHREI BALLIO&CASTIGLIONI FELDMANN ETAL BERNUZZI ET AL

This evidence can be considered to be a general conclusion, as it can be seen directly from Table 3, which summarises the results in terms of slope m and Log(K) for all test data. In order to define S-N lines to be adopted for design and damage assessment, for the types of connections considered in this study, the statistical procedure previously presented in section 3 was applied. This is done hereafter, assuming a slope m=2 in the case of definition of S according to Krawinkler and Feldmann approaches, while m=3 is assumed in the case of Ballio and Bemuzzi definition ofS. Table 4 and Figure 9 summarises the results of such a statistical re-analysis of the test data, and give the expressions for the design ^-A^ lines for the considered structural details.

290

L. CALADO ET AL. KRAWINKLER&ZOHREI

BERNUZZI et ai.

LogAVp,

LogAv ft

tests BCCS 1 Linear Fit

Linear Fit 1

|log N,.=„3 = -1.96 log Avp, +4.89

1

|loBN„=„5 = -2,32 1ogAv*5.77

1

1

LogN„=os 1

Log Na=o 5 1

FELDMANN ct al.

BALLIO&CASTIGLIONI

LogAa'p,

LogAa* r> t&iisBCf5 1 Linear Fit 1

Linear Fit 1

|logN,.=„., = -1.99logAa%, + 8.02

1 log N,..„ 5 -= -2.33 log Aa* - 9 40

|

1

Log N„=o 5 1

Log N^.0 5

Figure 8: Evaluation of the S-N line of beam-to-column connections on the basis of Na^o 30 and considering S defined by Krawinkler, Ballio, Feldmann and Bemuzzi proposals. BERNUZZI et ai.

KRAWINKLER&ZOHREI LogAVpi

LogAv OtestsBCCS

logH.,„ = -2 1ogAVp,.4.45

2

-t--_ - o |logN„.„.'< = -3logAv*6.35

lLogN„=0 5

1

Log N„.„, 1

2.5

BALLIO&CASTIGLIONI

FELDMANN et al. LogAa'f

log N,,^, 5 =-2 log Aa%, - 7.2

1

LogAa'

flog H.^,, =-3 log ACT* - 10.65

LogN„

Log N„=o s

Figure 9: Evaluation of the S-N line of beam-to-column connections on the basis of Na=o 50 and considering S defined by (a) Krawinkler with w=2, (b) Ballio with m=3, (c) Feldmann with m=2 and (d) Bemuzzi with m=3 approaches.

BEHAVIOUR OF STEEL BEAM-TO-COLUMN JOINTS

291

TABLE 4 LOG(K) COEFFICIENTS FOR BEAM-TO-COLUMN CONNECTIONS WITH m=2 OR m = i

^

^AM>r

a^.5

D B C B A C A D Log(K) Log(K) Log(K) Log(K) Log(K) Log(K) Log(K) Log(K)

TESTS a b BCCl

4.93

10.28

6.59

A 9/

5.r

10." 5

".31

".40

1.86

''.11

4.39

3.32

1.86

"11

4.39

3.32

5.51

11.60

".98

-".91

5.50

11.58

".9"

".89

5.06

12.08

8.09

".T;

4.^9

12.14

".90

".48

4.44

11.2-:

^.39

6.86

4.4"

11.30

".42

6.89

4.46

10.64

^.22

6.30

4.45

10.65

".20

6.35

4.16

10.83

--.61

5.65

3."^

1044

".22

5.26

c d

1

^ c

d BCC2

e

f a BCC3 1

b <-' a c

BCC4

d e a

BCC5

b d a

BCC6

b d

CRITERION FOR THE STRAIN RANGE DEFINITION : KRAWINKLER&ZOHREI {in=2) BALLiO&CASTlGLlONl (m=3) FELDMANN ET AL. (m=2) BERNUZZI ET AL. (in=3)

6. CONCLUSIONS A major issue of this research is the assessment of fatigue strength category of steel connections, i.e., the appropriate 5-iV curve to be associated with each type of structural detail. These categories can be developed by means of extensive experimental research or by numerical modeling. Such models should, however, be calibrated using tests results. One of the scopes of the research was also to investigate the cause of the discrepancies that were found in the proposed values for exponent m, presented by various authors in the literature. The re-elaboration of the experimental data allows to conclude that the assessment of the slope m of the S-N lines is very dependent on the definition of the parameter S. In fact, if the parameter S is based on the plastic range, like in Krawinkler et al and Feldmann et al, a value ofm=2 applies, while a value ofm=3 is assessed if the total excursion (i.e. elastic and plastic) is used, as proposed by Ballio et al and Bemuzzi et al.

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7. ACKNOWLEDGEMENTS This research was supported by grants from the Junta Nacional de Investiga9ao Cientifica e Tecnologica (JNICT), from the Ministero dell'Universita e della Ricerca Scientifica e Tecnologia (M.U.R.S.T), and from the Consiglio Nazionale della Ricerca (C.N.R.).

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