experimental analysis and modelling of semi-rigid steel

ELSEVIER

J. Construct. Steel Res. Vol. 38, No. 2, pp. 95-123, 1996 Copyright © 1996 Elsevier Science Ltd

Printed in Great Britain. All fights reserved PII: S0143-974X(96)00013-2 0143-974X/96 $15.00 + 0.00

Experimental Analysis and Modelling of Semi-rigid Steel Joints under Cyclic Reversal Loading

C. Bernuzzi, R. Zandonini & P. Zanon

Department of Structural Mechanics and Design Automation, University of Trento, Mesiano, 38050, Trento, Italy

(Received 11 November 1994; revised version received 1 December 1995; accepted 13 February 1996)

ABSTRACT

This paper reports on the first phase of a research project aimed at developing simple design criteria for semi-rigid steel frames in seismic zones. The experimental phase comprised of two series of tests on beam-to-column joints under cyclic reversal loading. The evaluation of the test results first allowed the influence of the loading history to be investigated and the main stiffness and strength parameters to be identified, which define the cyclic response of the connection. A simple prediction model was then developed and proposed, which enables satisfactory approximation of the joint response for use in numerical analysis. Copyright © 1996 Elsevier Science Ltd.

1 INTRODUCTION

Aseismic design requires selection of energy dissipation mechanisms which combine stable cyclic response with the possibility of controlling simply, yet reliably, the key behavioural parameters. The energy dissipation capability of the whole ~ystem depends basically on the stability of the hysteretic behaviour of the individual components, such as members and joints. Therefore, in addition to material ductility the overall and local buckling as well as the low cycle fatigue phenomena are important factors affecting the system seismic performance.

Traditional design approaches concentrate energy dissipation in the bracing cantilever ,system of simple non-sway frames, or in the beam-to-column joints of rigid sway frames. In the former case the bracing system does generally possess high stiffness; however, its cyclic response is not satisfactory in terms

95

96 C. Bernuzzi, R. Zandonini, P. Zanon

of ductility and shape of the response cycles. In the latter case the higher ductility of the nodes is combined with a fairly lower overall stiffness of the frame and high fabrication costs. The semi-rigid design philosophy, which already proved its efficiency for design under static loading, 1.2 may also be a convenient option for seismic design: 3,4 i.e. the cost/effectiveness ratio and the seismic performance of steel frames can be enhanced if semi-rigid joints are part of the key dissipation system. Besides other aspects, the increased possibility of controlling the actual location and response of energy dissipative elements represents an important advantageous feature.

A research study is underway at the University of Trento, which aims at developing simple design criteria enabling the effective design of semi-rigid steel frames in seismic zones.

The knowledge of the cyclic response of semi-rigid joints, and the capability of approximating it, represents a vital precondition to any design approach. Research studies of cyclic performance of joints were traditionally related to rigid connections. The recent interest in partially restrained frames prompted investigations also of the cyclic behaviour of semi-rigid joints. T M The research work mainly focused on the performance of joints with extended endplate connections or with cleated connections. The studies of joints with extended endplate connections were aimed at the understanding of the key features of both the overall joint response and the individual contributions of the various joint components (i.e. column panel zone, end plate and bolts). On the other hand, the extensive work related to cleated connections (either top and seat 8-1° or top, seat and web angles connections H) dealt primarily with the problem of cumulative damage assessment. Knowledge of the cyclic behaviour of semi-rigid beam-to-column connections hence advanced remarkably. However, the available data cannot yet be considered to form a sufficient background for the development of a comprehensive prediction model, even for the most popular types of connections.

Therefore, the preliminary experimental phase of the research project here presented was devoted to the detailed characterization of the cyclic response of some forms of semi-rigid connections of practical interest for aseismic frames. A first series of tests was designed in order to investigate the influence of the loading history on the joint performance, and to contribute to the development of the most appropriate standard definition of this prime factor. A second series of tests was then performed with the goal of singling out the key parameters enabling full description of the connection response, including the energy dissipation capability. The measurement setup was devised so that the behaviour of the main connection components was monitored, as well as the overall response.

The evaluation of the experimental data enabled definition and validation of the criteria to develop a simple prediction numerical model, which con-

Semi-rigid steel joints 97

veniently relates the loading and unloading stiffness deterioration to the dissipated energy.

2 THE EXPERIMENTAL ANALYSIS

The use of an appropriate testing procedure is an essential requisite of experimental analysis. On the one hand, economical requirements impose that the calibration of cyclic joint behavioural models are based on a limited number of tests. On the other hand, model reliability entails test procedures simple yet complete, in order to ensure general validity.

The testing procedures for assessing the behaviour of structural components under cyclic loads have hence been extensively discussed also in recent years, aiming at the definition of standard specifications. In Europe, recommendations were approved by the European Convention for Constructional Steel- work (ECCS) in 1986,12 which have been referred to in the study. However, some aspects still need further work in order to achieve a better understanding: one of them is the proper selection of the loading history; which parameter is particularly important for a correct assessment of the ductility and energy dissipation characteristics.

A preliminary series of tests was hence designed to appraise the influence of the loading history on the cyclic response of the steel connections considered. "Fine study is based on the general prediction philosophy by components recently adopted in EC3.t3 The attention is hence focused on the connection, while., the deformation of other components of the joint (i.e. column flanges and panel zone) is disregarded. Besides the overall response of the connection, the behaviour of its constitutive elements (angles, plates and bolts) is considered. With reference to the moment-rotation curve, an operational definition of the rotation of the whole connection Con and of the rotations associated to the various components of the deformation was adopted (consistent]Ly with the authors' previous research work15), as schematically indicated in Fig. l(a).

2.1 Testing apparatus and the measurement setup

All specimens consist of a long beam stub of an IPE 300 section, attached through the., connection to be tested to a 'rigid' counterbeam, as shown in Fig. 2. The loads are applied to the free end of the specimen by means of a device that transfers horizontal forces only. Testing conditions hence approximate quite closely the case of beam-to-column joints with negligible column deformabili.ty.

The measurement set up, shown in Fig. l(b), allows both the rotation of


¢

M M

v

a)

INDUCTIVE TRANSDUCER (LVDT)

ELECTRICAL STRAIN GAGES

. ~ A

D ~ D

~/////////////////Afl~

b) Fig. 1. Connection rotation and its components.

+

El / A k

o)

the connection as a whole and the contributions of the various components to be obtained, consistently with the schematic definition of Fig. l(a). Inductive displacement transducers (LVDTs) enable determination of (1) the beam rotation %m at a distance 300 mm from the beam end equal to the beam depth (LVDTs A), (2) the total connection rotation Con (LVDTs B), (3) the contribution of bolt deformation Cb (LVDTs C), and, when relevant, (4) the additional rotation due to the slip between the beam and the connection angle Csl (LVDTs D). The rotation ~p associated with the deformation of the end plate (or Ca in the case of angles) is obtained by subtracting the bolts rotation from the overall connection rotation: % = ~cn - % (or Ca ~- ¢en -- ~ -- Csl)" Electrical strain gauges were used in order to have an appraisal of the beam strain state in the vicinity of the connection and the evolvement of the exten- sional and flexural deformation of the bolts [Fig. l(c)].


Fig. 2. Testing apparatus.

2.2 The specimens

A total of 16 specimens were tested in two series: the first aimed at investigat- ing the inlFluence of the loading history and comprised of l0 specimens, two of which were tested under monotonically increasing load. The remaining six were tested following the procedure described in Section 2.3.

The follLowing forms of connections were investigated (Fig. 3): (a) top and seat angles connection (TSC); (b) flush end plate connection (two configur- ations diftering for number and size of the bolts: FPC-1 and FPC-2); (c) end plate connection extended on both sides of the beam (two plate thickness: EPBC-1 and EPBC-2); (d) end plate connection extended only on one side of the beam (EPC).

The main geometrical dimensions are indicated in the figure. All bolts were grade 8.8 bolts. They were fully preloaded according to the

Italian cocle ~4 in the first series of tests focused on the loading history parameter. In the second series, the preloading was limited to the 40% of the actual yield strength, a condition which corresponds approximately to the pretension induced by hand tightening up to the snug tight condition, and is therefore a close representation of usual practice.

Tension coupon tests were conducted to determine the yield and ultimate strength. The results related to the end plates and angles are presented in Table 1. The m~tterial properties of the beam stubs have a very low scatter within


TSC t p = 1 2 m m

F P C - 1 tp = 12rain

F P C - 2 t p = 1 2 r a m

6oil Bolts M20 Bolts M20 Bolts M16

tp

420

120 300 120 300 3 0 0

E P B C - 1 tp=12rnm E P B C - 2 t p = 1 8 m m

• , , , ~ t p

E P C t p = l S m m

~~~ t p

Bolts M20 Bolts M20

+ !+ +i 2 +

,I t Bol I I ll8O 120 120 120 0

520 420

Fig. 3. The connections considered in the study.

the same group of specimens. Mean values can hence be adopted for the elastic and plastic moments of resistance; they are: M~,b = 144 kNm and Mp,b = 172 kNm for the first series of tests, M~,b = 244 kNm and Mp,b = 284 kNm for the second one.

Semi-rigid steel joints

TABLE 1

101

Component fy f, A tp (mm) (MPa) (MPa) (%)

First series Angles 11.8 313 459 33 End plates 12.0 309 408 34

Second series Angles 12.2 209 324 29 End plates 11-9 321 465 32 End plates 17.5 339 513 29

2.3 Tesling procedure

The loading history may be considered the most important factor affecting the significance of cyclic tests, with reference to their use in seismic analyses. Amplitu&~ and sequence of cycles in the inelastic range are, in particular, parameters affecting the experimental assessment of the capability of the tested component to dissipate energy. The ECCS drafted specific recommendations, 12 which were adopted in many recent research studies. This document: (1) assumes as the prime test control parameter a characteristic displacement component e [i.e. in the present study the horizontal displacement of the beam stub, Fig. 4(a)], (2) provides criteria for determining the force Fy and the displacement ey at the elastic limit conditions [Fig. 4(a)], and (3) defines the loading h:istory in the inelastic range as a sequence of sets of three cycles,

~=Lo.d 1~t e/ey e=Displacement 61

÷ "4 ll~ ~z~ j ~ f - ~ t / l ° 2t ~ ~

. u . I V - 2 . ~ II II IJ e~ e - - ~ -4 - . ]¢Aq ~ y

(E~c~rpCroo.) . - 8 .

, q " .

10 ,,.)

Fig. 4. The ECCS testing procedure.

2'0 b ) Time

102 C. Bernuzzi, R. Zandonini, 19. Zanon

the amplitude of which is defined by the even values of the displacement ratio e/ey [Fig. 4(b)].

Remarks were made on this procedure, which on the one side seems too severe with reference to the assessment of the level of ductility, while on the other may not allow the tested component to fully achieve its potential strength. The significance of the information obtained as to the total energy dissipation capability is a further aspect to examine.

Besides the ECCS procedure (procedure A in Fig. 4), three different loading histories were hence adopted (see Fig. 5) in the preliminary series of tests. They differ from the ECCS procedure in (1) the law of cycle amplitude increase (equal to ey in loading histories B and C), and (2) the number of cycles at the same level of displacement ratio e/ey (one cycle for the loading histories B and D, two cycles for the loading history C). Monotonic tests (TSC/M and FPC/M) were also carded out in order to (1) determine Fy and ey according to the complete testing procedure specified in Ref. 12, and (2) permit comparative assessment of performances.

On the basis of the results of the preliminary series of tests, loading history C was adopted in the second phase of the study. It should be noted that the selection of this loading procedure also implies a significant reduction in the testing work.

In the elastic range, the amplitude of the cycles was always selected so that they were small enough to ensure that the onset of the inelastic phase was detected with a satisfactory approximation. The quasi-static nature of the test procedure required a very low rate of load application: the duration of each test ranged from 3 to 4 hours.

1 0 8- 6- 4- 2 ~ oi

- 2 - 4 ~ - 6 ~ --~-

- 1 0

a

-A- C proe. "x[ I ~ 1

1'0 - 2'0 - 3 0 Time

Fig. 5. The loading histories considered.


3 THE CYCLIC RESPONSE OF THE JOINTS

3.1 The first series of tests

Besides the comparison among different loading histories, the first series of tests enabled an understanding of the main behavioural characteristics of the top and seat and flush end plate connections. Therefore, the behaviour of each specimen is first demonstrated with reference to the moment-rotation curves M-4b; the main features are singled out for both the overall and the component responses. A 'seismic' assessment of joint response is then presented.

Figure 6 shows the responses of top and seat angle connections; the M- ~b curve of the monotonic test is also plotted (dashed line) for comparison. The envelopes of the cyclic curves correlate well with the monotonic one both in the initial elastic and in the final inelastic ranges. In the intermediate range, differences are remarkable. Such a discrepancy is mainly associated with the slippage, which occurs between the beam flanges and the connection angles. Alternate loading significantly reduces bolt pretension after a limited number of cycles; as a consequence, slippage in the connections subject to cyclic loads develops less gradually and starts at lower values of the applied moment.

8O 60 M [kNm] [

TEST I 40 ; ~ 20

0 -2o I

-6oi -80 -80-60-40-20 0

. . ,°,"

_=.,ivv vvv (~cn[mrad]

20 40 60 80

M [kNm] TEsT TSC/B

-80 -60 -40 -20 ~cn[mrad]

0 20 40 60 80

80- 601 M [kNm] . "~"'~"

F'-- 40 T E S T , , ~ 20 TSC/C

-20 - 4 0 -80. I -80 . . . . . . ~ -80-60-40-20 0 20 40 60 80

80

406020 MTSc/DTEsT[kNm] ,~'.~// ....

-6C qbcn [mrad] -ac ..... : , ...........

- 8 0 - 8 0 - 4 0 - 2 0 0 20 40 60 80

Fig. 6. Responses of top and seat angle connections.


When a set of two or three cycles was performed at the same displacement, a comparative evaluation of the subsequent cycles allows the observation of: (1) a moderate reduction of the maximum value of the moment achieved, (2) an increase of the portion of the reloading branch characterised by a reduced rotational stiffness, and (3) a substantial agreement of the stiffnesses of the unloading and reloading behaviour. These general features are consistent with the findings of previous studies. 8,1°,H Failure was always attained by fracture of one bolt on the side in tension at very high connection rotation (more than 60 mrad). Point (2) is related to the increase of the plastic deformation of the angles (including hole ovalisation), which occurs at the first cycle of the set for which the maximum displacement is increased. Such a deformation increase affects significantly the relative displacements for which contact among the different connection components is attained.

The slippage of the angles relative to the beam represents an important factor affecting the inelastic response. It develops at rather low values of moment (of about 12% of the beam plastic moment capacity Me.b), and its contribution to the overall connection rotation is the predominant one from the very beginning of the inelastic range, although the component associated with the angle deformation in shear and bending tends to build up with ~cn (see Fig. 7), where the main contributions are shown to the beam rotation Cbm [Fig. 7(a)] and the connection rotation ~cn [Fig. 7(b)] for specimen TSC/A at e/ey = 12 (failure occurred at e[ey = 14).

The moment rotation behaviour of the flush endplate connections (the FPC tests) is presented in Fig. 8. In the inelastic range the envelopes of the cyclic responses differ remarkably from the monotonic curve (dashed line). The shape of the deformation of the connection (Fig. 9) provides a mechanical explanation of these differences. As a consequence of the residual bending deformation at the end plate in the vicinity of the beam flanges, the end plate

80

60

40

20

0

-20

- 4 0 ~

- 6 0 ~

-8G -80-60-40-20 0

M [ k N m ]

TSC/A cycle at 12ey

/ s "

f

. . . . tot.l((1)~) . c o n n e e U o n ( ~ ) b e ~

¢ [mrad] • , . , . , . . ,

20 40 60 80

80

60 M [ k N - , ]

40 TSC/A 20 cyc le a t 12ey

0 #, i

--20

- 4 0

- 8 0

- 8 0 . . . . . . . --80-60--40--20 0

- - eonneetton ( ~ n ) - - - .Up ( ¢ , s )

[ m r a d ]

20 40 80 80

b) F i g . 7. Components of the rotational flexibility of specimen TSC/A.


~ t M [leNto] I ,0

1TEST ' ~"" 40] T E S T ~ ~

01 ~ / . , ~ r l T I I I I I I I I I l l l l d J

o _,ot - 2 0

-40 _,=,7 vvv VVV I -,o1 ~ 1 _,,,,,[-TV- l - - - -J- ' - I , ° ° t ~ . < -60 ~°n [ m r a d ] I - 6 0 ~ - - E~"

- 8 0 1 - . " . . . . . . t . . . . . . . . 801 . . . . . . . t . . . . . . . - 8 0 - - 6 0 - 4 0 - 2 0 0 20 40 80 80 - 8 0 - 6 0 - 4 0 - 2 0 0 20 40 60 80

80]~ J ~ - r a ~ t .. t 80 t I ~

, _ , , . /

-40 -40 _.

- 6 ° 1 - . ~ ' f " I ¢o.[- ,r.dl - 6 0 _ - 8 0 1 . . . . . . . t . . . . . . . i - 8 0 / . . . . . . . I " - - t

- 8 0 - . 6 0 - 4 0 - 2 0 0 20 40 60 80 - 8 0 - 6 0 - 4 0 - 2 0 0 20 40 60 80

Fig. 8. Cyclic behaviour of flush end plate connections.

is in contact with the counterbeam only within its central part just after a few cycles in the inelastic range. This state becomes more and more significant, and affects the stiffness of an increasing part of the loading phase of a cycle. Moreover, further connection deformations cause the bolts to enter the inelastic range and the nuts not to remain in contact with the endplate for the whole response.

This type of behaviour explains the greater sensitivity to the loading history of this form of connection with respect to the TSC connection. Two main factors can be identified, which play a major role: (1) the law of increase of the amplitude of the cycles--in many instances maximum moment values closer to the monotonic curve would have clearly been achieved if higher cycle limit displacements were selected, (2) the rate of loading--a too low loading rate may affect the test results in the vicinity of the end of each loading phase.

The main contribution to the rotation of the nodal zone (i.e. at 300 mm from the beam end) is that of the connection (see Fig. 10), to which the end plate defo:rmation contributes the most (close to the 90%).

The comparative examination of the envelopes of the peak values of the


Fig. 9. Typical deformation of the end plate of a FPC connection during a loading cycle.

first cycles performed at a given displacement (Figs 11 and 12) allows some preliminary conclusions to be drawn:

(a) The scatter among the responses obtained through the different loading histories considered is limited for both types of connection. This para-


6 0 M [kNm]

40 FPC/A cycle a t 10%

20

-2(

-40 -

- 6 1 . . . . . - 60 - 4 0 - 2 0

_ - - t o t a l ( C l ~ b m )

- - comaecUoa (~o~) . . . . b e a m

¢ [mrad]

0 20 40 60

6f M [kNm]

4( FPC/A ~+ ~ / zt ~ycle at ~Oe.~. .~ ,/

(,ool -41 .... bol~, (~d

-61 . . . . . ~ [mrad] - 6 0 - 4 0 - 2 0 0 2 0 4 0 6 0

a) b)

]Fig. 10. Components of the rotational flexibility of specimen FPC/A.

80

60]

40

20

0

- 2 0

-4o2 -6o: -80

M [kNm]

f With Slip

j TSCZA ~; - _ _ TSCLB

TSCLC ~ TSC/D

-.~ ~ c n [ m r a d ]

- 8 0 - 6 0 - 4 0 - 2 0 0 20 40 60 80

80

60

40

20

0

20

4fl

60

flO

M [kNm]

.j • , , , . , ,

.

thout Slip

TSC/A TSC/B TSCZC TSC/D

C a [ m r a d ] • , . , , , ,

- 8 0 - 6 0 - 4 0 - 2 0 0 20 40 60 80

a) b)

Fig. 11. Envelopes of the cyclic responses of TSC connections: (a) overall response, (b) response without slippage.

80

60

40

20

0

- 2 0

-4o ~ -6o; - 8 0

M [kNm] ~ ' ~

--- FP( FPC FPC/D

qb~[mrad] • , . . . , .

8(

6(

4[

2(

(

-21

-4 l

-61

-81

M [kNm]

• , . , . , .

Bolts

FPC/.A FPCZB FPCZC FPC/D

- 8 0 - 6 0 - 4 0 - 2 0 0 20 40 60 80 - I ] 0 - 6 0 - 4 0 - 2 0 0 20 40 60 80

a) b)

Fig. 12. Envelopes of the cyclic responses of FPC connections (a) overall response, (b) bolt contribution.


meter affects more remarkably the maximum rotation capacity of the flush end plate connections, for which differences up to 40% of the lowest experimental value were observed. The results seem to confirm that the ECCS procedure may provide a rather conservative assessment of joint ductility.

(b) The contribution of the deformation of the cleats to the overall rotation of the TSC connection is modest, and negligible for most of the response (Fig. 11). Even in the vicinity of the ultimate condition it does not attain the 30% of %,. The moment-rotation relationships associated with angle and bolt deformation show a fairly good agreement: discrep- ancies among the overall responses appear to be related only to the slip, which occurred at different moment levels.

(c) The contribution of bolt deformation to the behaviour of FPC connections is negligible, even when bolts enter into the inelastic range [Fig. 12(b)].

The loading history affects significantly the shape of each individual cycle (see Figs 6 and 8), the dissipated energy represents a significant parameter for a quantitative comparison, with reference also to seismic design. In Fig. 13 the mean value Em of the energy dissipated per cycle during each series of cycles at the same displacement is plotted versus the partial ductility ratio e]ey.

Loading history D, which enables a larger plastic range of the behaviour to be 'included' in the hysteretic loop, allows for a higher energy dissipation per cycle. The difference with the other loading histories is greater for TSC connections, for which the cyclic response attains and follows the monotonic one.

The degrading of the behaviour at the subsequent cycle at the same displacement (more significant for the flush end plate connection), causes a noticeable decrease of the mean value of the dissipated energy. The energy absorption

7 0 0 0 -

6000 ~

5000 ~

4000 ~

3000 ~

20001

1000 ~

7000 , E m [J] Em

---*- TSC/A i,,* 5ooo~ • T S C / B ~w ~ / ' ~ TSCZC ~ .~ 4000~

y 3ooo-I rPC/A FPC/.B

2000 "t F P C / C I~C/D

e/ey X000"l e/ey 4 ~I 1'2 t 6 0{~ 4 I~ 1'2 1'8

a) b) Fig. 13. Mean dissipated energy versus partial ductility ratio.


tends to remain constant in the further cycles (load history A). This result is consistent with the outcome of previous studies of low cycle fatigue of angle connections. 1°,11

The coraparative evaluation of the experimental data with reference to the energy dissipation parameter indicates that (1) procedure D may lead to a design overestimation of the potential capacity of energy dissipation with respect to 'average' expected seismic response, (2) the other procedures may be conside, red basically equivalent to each other.

Based on these remarks, procedure C was adopted for the second series of tests. This procedure, without affecting the accuracy of the results, permits an adequa~te assessment of the influence of cyclic degrading and reduces the experimental effort compared with the ECCS recommendations.

3.2 Second series of tests

The second series of tests was aimed at the development of a better understanding of the influence of the key geometrical and mechanical parameters on the cyclic performance of TSC and FPC connections as well as at extending the study to other connection forms.

All the connection forms presented in Fig. 3 are included in this series. The main parameters considered were: (1) the steel grade of the beam (Fe 510 in lieu of Fe 360), (2) number and diameter of bolts for the FPC connection, (3) endplate thickness for the EPBC connections (tp), and (4) the dissymmetry of the connection (the EPC connection with one side extension of the end plate). The moment-rotation responses of the six joints of the second series are plotted in Fig. 14.

Comparison between the corresponding tests of the two series [i.e. tests TSC/C (Fig. 6) and TSC, and tests FPC/C (Fig. 8) and FPC-1] enables an appraisal of the influence of the steel grade of the beam on joint response. Such influence appears not to be significant for the flush end plate connection, for which both the connection deformation and the M--~ curves show only modest differences. The deformation of the cleats in the TSC specimens was fairly affected by the beam steel grade. In the first series, where the beam was made of Fe 360 steel, the interaction between the angle and the beam flange made this latter element deform plastically due to local bending [Fig. 15(a)]. The beam flange of specimen TSC (of which the steel grade was Fe 510) did not bend locally, even at the connection failure by fracture of the cleat [Fig. 15(b)]. As a consequence, the deformation of the cleat, and hence the overall response of the connection, also changed: the cyclic behaviour of connection TSC shows a lower pinching and a higher resistance (of about 14%) than the behaviour of the connections tested in the first series. These results indiicate that the relative strength of the beam and connection compo-


8 0 .

M [kNm] 6 0 -

40.

o

-40. -60. - 8 o .

- 8 0 - 6 0 - 4 0 - 2 0 0

• ~o-t=?d] 20 40 60 80

~o° /

150 1

100 1

5o 1

M [kNm]

° / I - - - . / / I ~

-100 -150 1 . , • -40 -20

I EPC ] .o:,t~:.,.] 0 20 40 0 8;r;,Z

20.40"o M [ k N ~ Z40a0 M [kNm]

-~°1 I i 1 ~ TEST - zo I l l l l l l l N " TEST -4° 1 ~ 1 ~ 1 / I / [ FPC-2 -40. I IL / ,# lW I FPC-1

_°o I. _=t I. - 8 0 - 6 0 - 4 0 - 2 0 0 ZO 40 60 80 - 8 0 - 6 0 - 4 0 - 2 0 0 20 40 60 80

100- co: M [kNm] 50~

o 2 -zo; -4o; -so:

- l O O ~ ~ - 6 o -40 -20

E P B C - 1

20 40 6 0

zoo T

,oo i., .ml I # / / / f k - '°°1 J l l Y ~

-5°1/ L ~ i - TEST -'°°1/ /Y//~//'l EPBC-Z

-30 -20 -10 0 10 20 30

Fig. 14. Responses of the connections of the second series of tests.

nents may be a rather important parameter to be considered in the assessment of cleated connection performance.

The two flush end plate connections tested differ for number and diameter of bolts (four M20 in specimen FPC-1, eight M16 in specimen FPC-2). The resulting difference in the ratio between the end plate bending stiffness and the axial stiffness of the bolts (which is higher in the FPC-2 connection) appears to be an important factor affecting connection behaviour. Connection FPC-2 (Fig. 14) showed a higher initial stiffness and resistance capacity. Bolts were, however, more strained and more significantly elongated entering the plastic range of behaviour (Fig. 16). As a result, the bolts closer to the beam flange lost contact with the plate while unloading and, which is more influen-


Fig. 15. Influence of the steel grade of the beam on the angle and beam flange deformation: (a) steel grade Fe 360 (first series of tests), (b) steel grade Fe 510 (second series of tests).


Fig. 16. Bolt inelastic elongation during test Ft~-2.

tial, in the first phase of the reloading. Hysteresis loops exhibit hence a greater pinching and a more significant stiffness deterioration than for connection FPC-1, in which axial deformation of the bolts has been lower. On the other hand, being the plastic deformation of FPC-1 basically concentrated in the end plate and the failure mode associated, in both connections, to the weld fracture in correspondence of the internal part of the beam flange, this connection showed a lower ductility. However, the partial ductility ratio e~,~x/ey remains as high as 14 (it is 21 for FPC-2). The above-mentioned difference in the main behavioural features affects also the value of the bending moment achieved in the two subsequent cycles performed at the same displacement: a non-negligible decrease of moment capacity was observed for specimen FPC-2, whilst for connection FPC-1 the resistance drop was modest.

Similar considerations can be drawn for connections EPBC with end plates extended on both sides of the beam (Fig. 14). The plate extension ensures a noticeable increase in stiffness and strength of connection EPBC-1 with respect to the corresponding flush end plate connection (test FPC-1). The key features of the behaviour are nonetheless the same, with the plate contributing the most to the response in both the elastic and the inelastic range. Connection EPBC-2, with the end plate thickness increased to 18 mm, showed a substantially different behaviour. This was remarkably affected by bolt inelastic elongation due to the higher bolt forces consequent to the increase of the plate to bolt stiffness and strength ratios. When the most stressed bolts (the ones


internal to the beam) enter the inelastic range in tension (a phenomenon which happened already in the cycle with amplitude 2er), their residual deformation prevents contact between them and the plate in the reloading branch of the next cycle. The hysteresis loops present, hence, a noticeable pinch that becomes more and more significant as the loop amplitude, and hence the bolt inelastic elongation, increases. The failure mode and the rotational capacity change as well: (1) A crack started in specimen EPBC-1 at the weld in the plate extension during the cycles at 18¢y. This crack further expanded in the following cycles until collapse was achieved by fracturing of the plate over its full width. Connection EPBC-2 failed by bolt rupture. (2) The partial ductility ratio of connection EPBC-2 is significantly lower, which is not surprising since this feature is typical of failure modes involving bolt fracture. Specimen EPBC-2, however, had significantly higher stiffness and ultimate moment capacity.

Colmection EPC, with the end plate extended only on one side of the beam, showed a response qualitatively very similar to that of the corresponding (tp = 18 mm) connection EPBC-2 (Fig. 14). Collapse was associated, also in this case, with the fracture of the internal bolts, which occurred under positive moments in the cycle performed at 4ey. The test was then continued cycling within the range of negative moments without inverting the load direc- tion, in order to assess more completely the cyclic performance of the connection. The collapse was again associated to bolt fracturing during the cycle at 6ey. The lack of symmetry of the behaviour clearly reflects the asymmetry of the connection geometry.

It is interesting to note that a comparison with the response of nominally identical extended end plate connections tested under monotonic loading 15 seem to indicate that cycling affects remarkably the moment capacity and ductility when plate deformation is the dominant component of the connection rotational response, which happens for specimen EPBC-1. Further studies on these connections are needed in order to investigate in detail this aspect.

4 EVALUATION OF THE RESULTS

The experimental responses illustrated in the previous section confirm that steel semi.-rigid connections have in general a satisfactory cyclic behaviour. Yet the significant differences observed in the tests stress the importance of an appropriate design philosophy; in particular a proper selection of the strength and stiffness of the end plate relative to the bolt group enables reduction of the pinching and improvement of the stability of the hysteresis loops and of the overall ductility.

Table 2 reports, for both series of tests, the main parameters characterizing


o

j~

I

I 6 6 6 6 6

6 o o 6 6 6

6 6 6 o o 6

- , ~ , 6 6

-8-

i


the connection performance: i.e. the initial stiffness, Ko, the moment capacity, Mm~x, the associated rotation, Cn~x and the rotation at collapse, %. The values of these parameters refer to the envelopes of the M--Cp curves in the positive and negative range. The values of the relative strength ratio MmJMp,b show that all connections are partial strength connections. Furthermore, the flush end plate connections would be classified as pinned if the Eurocode 3 classification criterion is adopted. Eurocode classification may also be referred to in order to have an assessment of the degree of 'semi-rigidity': Fig. 17(a) compares the M--dp envelopes and the Eurocode boundaries 13 assuming for the beam a span equal to 6 m. Extended end plate connections with rather thick plates (EPC and EPBC-2) lie in the upper part of the semi-rigid zone, whilst all the other connections are close to the lower boundary of this region. Connection EPBC-1 shows a fairly stiff elastic response associated to a quite low ultimate resistance. All connections possess a rotation capacity (in terms of both maximum rotation and partial ductility ratio), which seems satisfactory even for the high demand typical of seismic design. A beam line analysis [see Fig. 17(b) 16] indicates that the connection ductility is sufficient to make a plastic hinge to :form at beam midspan, even when the connection deformation is associated primarily with the bolts.

The energy dissipation capacities of the different connection forms are compared in Fig. 18 with reference to the mean energy per cycle, which is plotted against the partial ductility ratio [Fig. 18(a)] and the mean maximum connection rotation Cm attained in the positive hemicycles [Fig. 18(b)]. All forms of connection show an energy dissipation capacity which increases steadily with the connection deformation. The cleated connection TSC has a performance, in terms of energy dissipation, which is comparable, at the same value of e/ey, with the extended end plate EPBC-1, and remarkably higher than both flush end plate connections. Such an energy dissipation capability can, however, be

1.0" .__ t . 0,8: m I.~--tm :.:. zca • ---mzlzraeod

o.e~ o.4~

0.0

-0.4"

-O.62 * ~

-0.8: : /

-¢,,- ~ P B C - 2 ]gPC

.: e l~c n -1.0 ~ , . . : , . - . . . : . . ; . , ; . . . , . . . . . . ~ . . . . . . . . .

- 1 . 0 - 0 . 8 - 0 . 6 - 0 . 4 - 0 . 2 0.0 0.2 0.4 0.6 0.8 1.0

300

gO0- Lu:tm ' .----IMmm d~uln

- 1 0 0 -

- 2 0 0 -

-300 . . . . . . . - 8 0 - 6 0 - 4 0 - 2 0 0

a) b)

. . . .

--.o- TSC FPC-1

EPBC-2 E P C

dpon [farad] 20 40 60 80

Fig. 17. Assessment of connection behaviour: (a) classification according to Eurocode 3, (b) connection performance and beam ultimate limit domains.


6000

5000

4 0 0 0

3000

2000

1000

E~ [Jl

, ~ r 7 . ~ - - 4 - - l ~ c - ~ / / # ~ " . ~ ~ XPBC-I / / / / "

0 4 8 12 16 20

6000

5 0 0 0

4000

3 0 0 0

2000

1 0 0 0

0 0

E~ [J]

--.o.- TSC

. . . . . . ~.m,tm. r,ad. ] 10 20 30 40 50 60 70 80

a) b)

Fig. 18. Mean dissipated energy per cycle versus (a) the partial ductility ratio and (b) maximum connection rotation.

mobilised only in the range of high rotations (4) >20 mrad), which is usually of lower importance in seismic design. The extended end plate connection EPBC-1 shows hence the better balance between the stiffness and rotational ductility. The other forms of connection do have cyclic performances practi- cally equivalent to each other. On the other hand, the results shown in Fig. 18(a) indicate that cleated connections potentially have a response similar to ductile extended end plate connections, if their stiffness is sufficiently high. Connections where web cleats are associated with flange cleats may hence provide a rather simple form of semi-rigid connection suitable for seismic design.

5 A CYCLIC RESPONSE MODEL

The approximation of the cyclic response of a connection is a vital pre-requisite for any attempt to simulate numerically the seismic behaviour of a framing system. This aspect becomes even more important for semi-rigid partial strength framing. As a first step towards the setting up of a general prediction model, the experimental results were evaluated and used in order to enable determination of the law of deterioration of the loading and unloading stiffnesses of a connection. The dissipated energy, a parameter which can be easily computed at any stage of the loading history, was adopted as the reference variable. In this preliminary phase the attention was focused on the flush end plate connections.

As previously discussed, the main factor affecting the stiffness deterioration at each increase of the cycle amplitude is the increasing residual plate defor-


marion. This leads to the type of response shown in Fig. 19, where the FPC moment-rotation hemicycles are shifted in order to make all of them start at the origin of the axes. When the bolts are stressed in the inelastic region, two phases of the behaviour can be identified, due to the bolt deformation contribution. However, this phenomenon occurs only at rather significant rotations IIFig. 19(f)].

All responses are qualitatively very similar, and close to a linear behaviour for both loading and unloading. A linearization of the M-t~ curves is hence

80 8 0 60 M l[kNm]

40 F P C / A

20

0

- 4 0

- 6 0

- 6 0 . . . . . - 1 2 0 --80 - 4 0

80 ̧

~ [ m r a d ] t~ [mrad ] • , . , . 1 r - - - - - v - - - - - - -

0 40 80 120 80 160

60 M [kNm]

40 FPC/C 20

0

- 4 0 i

- 6 0

-6G . , . - 20 - 6 0

80

a)

[mrad]

0 60 120

6O

4 0

2 0

0

- 2 0 i i

-4o 2 -6o2 -8G

- 1 2 0 --80 - 4 0

M [ kNm]

F P C - I

~} [mrad]

c)

6 0 M [ kNm]

4 0 20. I~C/B

-20.

-40.

-60.

- 6 0 ~ - - -160 -80 O

b) 60

• , . , . . , . , .

0 40 80 120

60'

4 0

2 0

0

-20"

-40"

-60 '

M [kNm]

F P C / D

~ E m r a d ] - 80 . . . . . . . . . .

-120 - 6 0 - 4 0 0 40 80 120

d) 80' 0o. M [~m]

40.Z0. F P C - 2 [

o

-20,

- 4 0

-60.

-80 . . . . . - 1 5 0 - 1 0 0 - 5 0 0

e) f)

r 50 100 150

Fig. 19. Experimental hemicycles shifted to the axes origin.


80

60

40 20

0 -201 -4oi

- 6 0 ~

- 8 0

M [kNm]

TEST FPC/D - [ ~

Test I , inearizat ion

~) [mrad] • , , , . . , • , ,

- 1 2 0 - 8 0 - 4 0 0 40 80 120

Fig. 20. Linearization of the experimental response.

possible, and it enables determination of the stiffness parameters in a straight- forward, yet sufficiently approximate, way (see Fig. 20).

If the total energy dissipated during the test, Etot, is assumed as the reference parameter, the deterioration of the connection performance in terms of stiffness shows a fairly definite general trend. The use of normalised variables for the stiffnesses and the energies enables convenient expressions to be found (via the least square method) for the loading and unloading stiffnesses, on the basis of the data related to the linearized responses of all the specimens tested in the first series. Such expressions are reported in Fig. 21(a) together with the experimental data: K i is the stiffness at cycle i, Ko the initial value of the stiffness, and E is the cumulated dissipated energy at the onset of the considered hemicycle. A further simplification may be achieved if the unloading stiffness is considered as a function of the loading one, as shown in Fig. 21(b).

The use of these laws for approximating the response of the FPC connection to loading histories different from those considered in this study (Figs 4 and

0.30 Ki [a .,~l~.=t.1 v~.~.. ( ~ 1 0.4

0.Z5 ~ o ~ ,,~,,. (,o,d~ _11 0 . 3

0.20

, ' , Unload x, , . , -u o.z.5 ~ , , ~ ¢ = ' ~ t ~ o.z A A

~ A 4

0.I0 " " " " ~ "~%r"--~---~.-....~..$_..~__ 0.I k Load _~L=-- ,, z ~-~' .

0.05 ~ ~ = . o . ~ j V-/Etot

~ ~ - - ~ ' ~ ~ - . . . . e - - 0.00 i0 °'°°o.o o.2 0.4 o.e o.e 1.o . ' o.'2 o . ' 4 o . ' e

a ) b )

Fig. 21. Stiffness deterioration versus the dissipated energy.

K i.load K i , u n l o a d

~ . . . ,~,.,o., =o.,oT(~y °'~ K l , u n l o a d " *~ to t !

E/Etot

o.'8 1.o


te I e /e ,

- _ Cublo [ . ~ '

• 4, ~ @ @

8- ~ ~ ' 7 ( I + l Linetr apprmdmat/on=e/ey-- P,4E= +I

Cubic --e/ey-- O.~gm a - | ~ I ~ 4 - ~ = 4"I

~ J / E..lO[kJ]

4

0 o.1 o.~ o'.3 o'.4 o'.5 o'.e o.~

Fig. 22. Partial ductility ratio versus mean dissipated energy.

5) would be hampered by the requirement of an a priori knowledge of the total dissipated energy. A further evaluation of the test data indicated that a rather simple relationship exists between the partial ductility ratio and the mean dissipated energy computed for the cycles having the same amplitude. Curve fitting techniques allowed a linear and polynomial approximation law to be obtained (Fig. 22). These expressions permit calculation of the value of Etot when the loading history is known. The connection response can be then generated cycle per cycle as shown in Fig. 23 with reference to loading history D.

The complete response is then obtained, by shifting each cycle so that it starts whe, re the previous one ends (Fig. 24).

Comparison with the experimental M-~ curves indicates that the proposed model permits a satisfactory approximation for design purposes. However, the model tends to overestimate the connection maximum moment for low partial ductility ratios. This is a consequence of the lack of any strength limitation within the model; an immediate improvement can be obtained, if a boundary

8O 60 M [kNm] ~' Y . . . ~/

| I i • 2040 FPC/D ~

- • - MODEL

-60~ e !/ , ~)[mradl

- ~ . , . o - i 3 o - 4 ~ , + o '4 'o " a'o 1 2 o

Fig, 23. Approximation of the experimental hemicycles of test FI~/D.


401 FPC/,

-2°i l l I J J m r -

- 8 0 - 6 0 - 4 0 - 2 0 0 20 40 60 80

60 ~ M [kNm] r

401 FPC/B

201

_4o i .~ --,- . o ~ -6o. - , a - ~ . ~ r - ~ e ~ / / ;

-8o . . . . ¢: tmr"l - 8 0 - 6 0 - 4 0 - 2 0 0 20 40 60 80

80

60

40

20

0

- 2 0

-40,

- 6 0

-81

M [kNm] 1

- 8 0 - 8 0 - 4 0 - 2 0 0 20 40 60 80

8O 6O 2 40 20~

O -2o I -4o~ -6o~ - 8 0 '

r l . A r 1 M t,,,,mj , , p , . . .

---~-- MODI~

t~en[mrad]

0 - 6 0 - 4 0 - 2 0 0 20 40 60 60

Fig. 24. Approximation of the experimental responses of FPC connections.

to the moment capacity is included [for example, and for the cases considered, on the basis of the M--O envelopes of Fig. 12(a)].

The values of the key parameters of the model (i.e., of the stiffnesses K,.) were here determined (as in previous studies 5) via curve fitting techniques of the experimental data related to the overall connection response. The adopted measurement setup, which allows the individual contributions of the connection components to be singled out, permits development of mechanical models of the individual components. The use of these component models for the definition of the stiffness deterioration laws of the connection will enhance significantly the scope of the cyclic model.

6 CONCLUDING REMARKS

The paper highlighted the main outcomes of an experimental investigation of the cyclic behaviour of semi-rigid connections, which has been carried out as part of a research study on the aseismic design of semi-continuous steel frames. The first appraisal of the observed performance and the subsequent evaluation of the test data indicate that:

(1) As to the loading history:


• The ]Loading history affects significantly the shape of each individual cycle,, whereas the envelopes of the cyclic response depend moderately on the loading history (Figs 11 and 12).

• Two cycles at the same maximum amplitude are sufficient to quantify the resistance deterioration.

• A loetding procedure which increases the cycles amplitude too rapidly (see l~rocedure D in Fig. 5) may lead to an overestimation of the dissipat- ing energy capacity of the connection.

Loading procedure C (see Fig. 5) is therefore proposed as a cyclic testing procedure which well balances the required experimental effort and the effectiveness of the results. Nonetheless, it should be remarked that:

• The proposed procedure is based on a deformation control technique, which enables the response to be followed in the presence of softening behaviour. However, this procedure may somewhat affect the accuracy of the results.

• An experimental analysis, which combines tests where the loading history is based on deformation control with tests where the maximum load is the controlling parameter, would provide more complete and reliable information about the cyclic performance of the connection. An evaluation of the results related to the end plate connections, including a comparison with previous studies, 15 indicates that this combined analysis would be more appropriate (and efficient) for rather stiff and resistant end plate connections, which are sensitive to the deterioration of stiffness associated with the residual connection deformation.

(2) As to the connections' cyclic performance: • The CryClic response of semi-rigid connections can be generally con-

sidered quite satisfactory in terms of stiffness, strength and rotational ductility.

• If inelasticity is concentrated in the end plate (cleat), the hysteresis loops show a reduced pinching and a higher deformation capacity.

• The performance of cleated connections is substantially affected by slippage, which should be accounted for and possibly controlled at the design stage.

• The energy dissipation capacity seems adequate even for the top and seat cleated connection considered, although it becomes significant at high rotations, which can be associated with frame sways outside the range of interest in seismic design.

It should be concluded that (1) on the one hand semi-rigid connections confirm their suitability to be used as a part of a system which combines different sources of energy dissipation in order to 'optimize' the seismic performance, (2) on the other hand, connection design criteria should be


developed to appropriately balance stiffness and ductility under cyclic loading (the connections tested were designed in accordance to static design criteria).

(3) As to the prediction of the cyclic response: • When bolt contribution to connection rotation can be neglected, simple

prediction models can be used in order to approximate the M--~ cyclic response of flush end plate connections, which basically must recognize the stiffness deterioration.

• A mathematical expression is proposed for approximating the deterioration law of the loading and unloading stiffness of the considered FPC connection as a function of the dissipated energy, and an analytical expression has been developed, which relates this last parameter to the partial ductility ratio. The model permits simulation of any loading history, and can be implemented in computer programs for seismic frame analyses.

• A boundary to the maximum moment should be included in the model to avoid overestimation of connection strength, in particular at low values of the partial ductility ratio.

The study is currently continuing, aimed at developing mechanical models enabling determination of the key parameters of the proposed prediction model (connection stiffness, dissipated energy and partial ductility ratio) as a function of the connection geometry and of the material properties of its components. The range of application of the proposed model will be then extended to different forms of connections.

A subsequent implementation of the prediction model in a general purpose program will allow for a parametric study to be carried out on the seismic performance of steel frames, where the semi-rigid connections are part of the dissipative system.

ACKNOWLEDGEMENTS

This research was supported by a grant of the Italian Ministry of the University and Scientific and Technological Research (M.U.R.S.T.). The authors greatly appreciate the skilful work of the technical staff of the laboratory of the Department of Structural Mechanics and Design Automation, and express their thanks to Dr Ing. Paolo Rosa for his assistance in the evaluation of experimental data.


REFERENCES

1. European Convention for Constructional Steelwork, Analysis and Design of Steel Frames with Semi-rigid Joints. Publ. No. 67, 1992, p. 281.

2. Bjorhovde, R. & Colson, A., Economy of semi-rigid frame design. In Connec- tions hz Steel Structures II: Behaviour, Strength and Design, ed. R. Bjorhovde, A., Colson, G. Haaijer & J. W. B. Stark. American Institute of Steel Construction, 1991, pp. 418-430.

3. Nader, M. N. & Astaneh, A., Seismic design concepts for semi-rigid frames. Proc. ASCE-Structures Congress '92. San Antonio, TX, 13-15 April 1992, pp. 971-974.

4. Einashai, A. S. & Elghazouli, A. Y., Seismic behaviour of semi-rigid steel frames. J. Con,:truct. Steel Res., 29 (1994) 149-174.

5. Ballio, G., Calado, L., De Martino, A., Faella, C. & Mazzolani, F. M., Cyclic behaviour of steel beam-to-column joints, experimental research. Costruzioni Metalliche, 2 (1987) 160-181.

6. Ghobatah, A., Korol, R. M. & Osman, A., Cyclic behaviour of extended endplate joints. J. Struct. Engng Am. Soc. Civil Engng, 118 (1992) 1333-1353.

7. Tsai, K. C. & Popov, E. P., Cyclic behaviour of end-plate moment connections. J. Struct. Engng Am. Soc. Civil Engng, 116 (1990) 2917-2930.

8. Chastaneh, C. P., Fleishman, R. B. & Driscoll, G. C. L.-W., Top- and seat-angle connections and end-plate connections: behavior and strength under monotonic and cyclic loading. Proc. AISC, 1989 National Steel Construction Conf. Nash- ville, TN, 21-24 June 1989, pp. 6.3-6.32.

9. Calado, L. & Castiglioni, C., Low cycle fatigue testing of semi-rigid beam-to- column connections. Preliminary Proc. Third Int. Workshop on Connections in Steel Structures. Trento, 28-31 May 1995.

10. Mander, J. B., Chen, S. S. & Pekcan, G., Low-cycle fatigue behavior of semi- rigid top-and-seat angle connections. Engineering Journal, American Institute of Steel Construction, 3rd quarter (1994) 111-122.

11. Azizinamini, A. & Radziminski, J. B., Static and cyclic performance of semirigid steel beam-to-columns connections. J. Struct. Engng Am. Soc. Civil Engng, 115 (1989) 2979-2999.

12. European Convention for Constructional Steelwork, Recommended Testing Pro- cedures for Assessing the Behaviour of Structural Elements under Cyclic Loads. Technical Committee 1, TWG 1.3--Seismic Design, Publ. No. 45, 1986, p. 12.

13. Europe~Ln Committee for Standardization (CEN), ENV 1993-1-1 Eurocode 3: Design of Steel Structures--Part 1: General Rules and Rules for Buildings, 1992.

14. CNR-UNI 10011, Steel Structures--Recommendations for Design, Execution and Mainter~,ance (in Italian), 1985.

15. Bernuzzi, C., Zandonini, R. & Zanon, P., Rotational behaviour of end plate connections. Costruzioni Metalliche, 2 ( 1991) 74-103.

16. Zandonini, R. & Zanon, P., Analysis of beams in partially restrained non sway frames. In Semi-rigid Connections in Steel Frames, ed. W. F. Chert & R. F. Lorentz. McGraw-Hill, New York, 1992.

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experimental analysis and modelling of semi-rigid steel

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