### Behaviour, strength and design

### Behaviour, strength and design

Edited ByR. Bjorhovde, J. Brozzetti, A. Colson

Edition 1st Edition

First Published 19 February 1988

eBook Published 19 February 1988

Pub. location London

Imprint CRC Press

eBook ISBN 9781482286427

SubjectsEngineering & Technology

Get Citation

#### Get Citation

Bjorhovde, R. (Ed.), Brozzetti, J. (Ed.), Colson, A. (Ed.). (1988). Connections in Steel Structures. London: CRC Press.

ABOUT THIS BOOK

TABLE OF CONTENTS

realistically possible to abreast of all substantially from one locale to the next, result that interpretation of the findings and how they may to a particular case will be a dubious undertaking. Finally, with carried out in universities, research laboratories and

parts, mechanical fasteners, welds, and so on. Such studies essential for the understanding of the failure mechanisms of the identifying the main load and deformation controlling parameters. The three primary characteristics of non-linear identified, namely, stiffness, ultimate strength, establish familiarity with the types of connections that are used in actual structures around the world, and facilitate correlation efforts. of connection strength and behaviour, of load-deflection behaviour into two sub-sessions. Their topics of coverage and anticipated outcome

effects for the connections, the structural entire frame, but that establish exactly what the individual solutions can accomplish, and correlate with tests (if other analytical solutions. anticipated outcome of the frame analysis session was the of a repertory of computer programs, including definitions

of the various technical sessions, the final session was intended as the outlet for two primary groups of presentations, namely, (1) a discussion and evaluation of a potential of the session reporters and reporters. Th• former subject was of significant interest, that a proper organizational structure would facilitate future of information, as well as of work. The research reporters and their function crucial to the workshop, as these reports would focus that needs to be undertaken, to remove current deficiencies of available data and to add to data bases as well as

definition the stress area of. the bolt is the sectional area of smooth cylinder which, subjected to tension, has failure load as the threaded part of bolt from the in tension in Fig. 2, is internationally is evident that, based on the definition of As' the strength function for bolt in tension will be taken as: is the ultimate tensile strength of the bolt material. jointuso called prying forces occur due to flexibility of the parts. This is illustrated in Fig. 3.

draft the edge distance is therefore limited to a minimum of 1.5 d. section fully stressed upto the tensile material strength fu. So the strength of the member, also the mean stress in cross-section at ultimate load should be less than the yield of unsymmetrical or unsymmetrically

this line of mean values is then multiplied coefficient ok to find the characteristic line fractile). value of calculated with the statistical data of the population [8]. factor can be calculated: all test reports provide the data actual material geometric properties of test as required for the straight procedure additional cases can be distinguished: of the material strengths in the sample are given, but 0.6'------'--'---....._

bolts the ultimate shear strength of 0.7 fu' as assumed in the strength function (Table 1). will be followed in evaluation of test results. the about test results are available is the tensile force the connection, is the of the

greater than The reason for true fracture stress in a tensile fact is also in fig for a structural steel, designated 1, and a cold finished steel, plates in bending the contraction of the tensile zone restrained by the compressive zone. Therefore the potential factor of

local •lreee alraln elre•• Slraln this a view on actual t•st is details in tension, bendinQ, tension • bendinQ, and in included, Dltt:alls 1 n i:lll"'si an

failed, in brittle fracture at 2.1 times of the other details to 2.6 times without fracture. investi;ation with thick plate in bendin; showed an stress of 2.1 times YS, ••• fig4.

the different magnitude of strain at the two yield lines. details loaded in tension or bending according to fig 3 were later straightened, machined flush, and bolted together as and-plate stresses at failure of the connections were calculated, conservatively assuming equal compressive and tensile stress stress in the tension member and at the bolt line, with minor

plate, fig 6. In spite of the great mean tensile stress, also fig 6the maximum stresses are of the magnitude of 3 - stresses in pure bending. fracture and the magnitude of the ultimate stress, a correction for shear stresses Boll

ather Juet auteide the wide campreeeian member welde varieble a: 3.5 variable test canpr•••ian details in pure gr•ater strength was found for small welds, in an to d•cide acc•ptable lack of fit in pressur•· Th• test r•sults ive member. With guid• anol•s, as indicated in fig 7, the load was possibl• to increa•• to levels corr•sponding to on th• the compression member. Without any visibl• sign of fractur•, th• compressiv• m•mb•r was th•n mor• or less liquidiz•d, "floating out" around the guid• bolts a coupl• of These stresses to about 3 tim•• of th• mild st••l compr•ssion members.

initial stiffness of tests is not affected the level of that the ultimate strength is quasi of this level. However, the slip is initiated earlier for test (test 01:2), the initial stiffness not significantly ; so for the overall shape of the curve.

early in the loading sequence. at each toe of the in the vicinity of the bolt line on the leg of the flange angle attached to the column, together with

is of the same order as the this expression should not be significantly stiffer seat angles only.

significantly affect moment- rotation behavior are: the depth of the beam section to which the effective gage in the leg of the flange angles attached to the column. test results, a parametric model was developed to predict the

rotation (four ~O~Q~~~ trans at 300 from Bin fig. 4a); the rotation to bolt deformation (four transdu- ject to a plied to

tests. A comparison between the curves related to the corresponding of the two series shows that the presence of the extension of plate on the compression side has a limited influence on the significant strains in the beam stub, within the hardening range, the inelastic buckling of the compressive flange (and of the of the web for the specimens with thicker end plate) before of the connection was achieved. rotation capacity 'u,cnis at the contrary adversely affected by the principally is affected by plate relatively thin, the connection rotation in the nonlinear range is to the elastic-

plate, characteristics in a zone were important plastic strains should develop. The contribution of the bolts becomes more significant {up to about 35\ for the plate thickness. The limited ductility, typical of related to the average deformation histories of the bolts external and internal to the beam stub respectively for the

bolts in the specimen EP1-1 experienced remarkable plastic deformations, their behaviour in the specimen EP1-5 shows a limited nonlinearity, of the connection in the bolt by relating the deformation measured during the connection results that, in rotation flexibility

internal part. The former part can be simply modelled as cantilever element clamped to the possible prying • to be considered as a plate with restraints. A first is given the results related to the ....... its tensile strength. further

ki,red and kst determined for the tested are reported in table 1, where also the contributions of the end plate and of the bolts are also to define the values of the elastic limit moment and of the plastic moment M . The latter defini- tion is not clear-cut, based

of the whole connection, was verified to be in very the two component "in series". Values of ki are mean values related to the the elastic limit moment. bolt preloading and by that: bolt contribution depends on plate stiffness and increases with this parameter; b) the increment of the plate contribution is less sig- nificant than expected on the basis of the variation in thickness, in- of the plate restraint conditions, which

plastische Last-Verformungsverhalten steifenloser, geschweisster Knoten fur die Berechnung von Stahlrahmen P., Semi-Rigid and Flexible Connections: an Int. Conf. Steel Structures; to Design, Part

Technical University Lyngby have been studied results obtained in these investigations. In an analytical investi- gation of end-plate connections in beam sections, a design method was developed, and the basic equations of method are given in paper. Special attention was paid to studying the effect of prying action in the connection. Also T-stub connections and end-plate connections in circular sections were studied to clarify the strength stiffness characteristics. For experimental investigations were carried out to verify the analytical

have been combined in a single diagram, shown in Fig. 5. The curves give the prying connection with speci- fied values of b/a and r • The curves have been drawn for values of are of no practical interest. For = 1.00. lnyestiqation In the experimental part of the investigation of end-plate

Byr 0.25. smaller values of r r 2.85, no prying appears in the connection, and P

In the permits the analysis of bolted end-plate connections in sections, including determination of the tion, bolt forces, the effect of prying action, etc. ·In the experimental part of the study, a bolt forces were determined by means of strain gages. of the results obtained from this test series with those obtained by means of the suggested design method shows difference between the values obtained, the maximum deviation in bolt forces being only about yield load for the connection, as defined in the suggested design method, is also in this case c·onsidered to be the load the reduced yield moment is in the end-plate at the toe also that heavy plastic deformations of the end-plate will be avoi- In the connections with thin end-plates, the ultimate load was found to be more than greater than the theoretical yield load. the connections with heavier end-plates, the difference was found to be 25-75%.

gations includes consideration of the deformations of the individual fatigue. were determined, as well as proposed design methods provide sufficient accuracy for practical purposes. The experimental results obtained concerning connection deformations may contribute to a data base of load-deflection curves, established. 1. Agerskov, H., High-Strength Bolted Connections Subject to Prying,

bolts (quality 10.9) were used. All the mechanical set of test specimens are summarized in joint, four beam-to-column stiffness ratios are that allows also to change the slenderness ratio h /a of the co- inertia, while a very dif- stiffness (fig. 2) test specimens with weak axis connections test arrangement is illustrated in figure 3. The load is applied at the cantilever beam and is increased progressively either up to collapse limiting vertical deflection (40 of the cantilever due to requirements of the testing facilities. of the

elastic and exhibits an will be unloadea and then loaded again, whichever the loading level rea- is last strain hardening range, the stiffness K of which is quasi

(serie A). For a test specimen, both sets of results give two limiting interaction curve (fig. 12), the aim of which is to show the in a 3-D joint. Any other point interaction curve would require tests on the associated 3-D specimen.

this interaction curve and to joints ; therefore additional tests will be in order to implement the information. I. Rentschler, G.P. and Chen, W.F., Tests of Beam-to-Column Moment Jaspart, J.P., Essais sur poutre-colonne d'axe faible et C.R.I.F., Bruxelles (in preparation). J., Jaspart, J.P. R., of the Joints, Proceedings, Workshop

for Hollow Section statically loaded - Steel Structures,

of an IPE 330 beam welded to a 160 for NR4, and of a 500 beam welded to a 300 column for (Fig.l). The ratio of shear is generally less important; for comparison pur- @ 500 @ 300 M/2 -

.Li...l ...... ! ) ) . 2ll.j( ·-r······-·T········ train hardening begins

of the connections happens mainly by total plastification of that part of the column web which is adjacent to the rather complex, the two main causes of flexibility [1] are clearly visible local deformation near points B and C, i.e. at the flanges detailed results be found in Ref. [5].

-y have been derived from the numerical plotted in Fig. 8. They can be used in a T-sping model of

Int. Rep. 86/6, July 1986. in mechanical and cross-sectional properties steel. Int. Conf. on Planning and Design of Tall Buildings, Stability of Steel Structures, Publ. 22, Bruxelles, results are in good agreement with the work presented here, in that range of small relative node rotations which is of practical interest. about this subject should appear in further steifen-

stress design stress of 1,5 times the ultimate value ; this has recently been reduced to 1,2, due to large hole deformations in the plate or member material stress. European stress value of 3,0 times the yield stress ; this will likely be clear that numerous and highly advanced finite element solution of one-, two- local analyses. Material and geometric properties are of yielding, stability effects, It that investigations of this will of the most important factors for the behaviour

is believed possible. To come up with acceptable models, however, task and requires several years of research and development. specific due to the limited length of the paper the large variety of subjects to cover, we will limit ourselves, in the next sections, to a condensed presentation of the computer programs we brief descriptions of some elements and techniques of resolution

res, Vol. 17, no 1, 1983, pp. 51-59. the angle of loading. Structural Engineering Report 133, calcul automatique des configurations pre lineaires en calcul des structures. a paraitre civil, Universite Laval,

plastic hinge concept rather than the pro- plastification of the bar. correlation with and interpretation of experimental results clearly defined in order to arrive tests. is proposed to use the initial stiffness Kand the ultimate load Fui in order to describe the non linearity. In a general way,

that the initial stiffness in a forseeable way, perties of the components of the connection. This means that for in- dustrial practice,

theoreti- cal results, for a cyclic hardening case is given in the figure 11. -+"'· +-'-

to o l is expressed f+ + n)=R(n) , Rtt\) ( M+- 4 "R simulate different unloading conditions (see fig. lc).

By1 1 I I are of

the upper bound of the quasi- ela- stic behaviour. are c6nveXtionally defined the intersection of the lines shown in fig. to interpret the results

cyclic behaviour of 14 beams-to-column specimens has been experi- in [ 5 ] • They have been designed following the current in rigid and semirigid connections for steel structures. In fig. the are in four

characterization of the hysteretic loops

with Double Web-Angle Connections Kishi angle with double web-angle tions stiffness the ultimate carrying capacity the con- nection are determined using simple analytical procedure for modeling the top-, seat-, web-angles of the semi-rigid con- nections. connection stiffness the ultimate

angle with double web-angle connections as shown in Fig. 1. This connection type has the inherent ural deformation of both flange and angles in the legs attached to the column. In this paper, an developed to predict the moment-rotation ultimate capacity. three-parameter power model is used here to represent the whole moment-rotation behavior of the con- nections. experimental results reported et al (1982) and Azizinamini et al (1985) are used here to verify the proposed procedure.

between M and 3(Elt) (d (12) connection stiffness the value; (Eit) (Ela) (d (ta) (13) 0.78(tt) 2.2 Ultimate Moment the experimental results reported et al (1982) and Azizinamini al (1985), the collapse for the top- seat- angle connection and of web-angle connection as shown in Figs. and 6, respectively.

Kishi web-angle and double web-angle beam-to-column connections developed. In this development, the connection stiffness is determined using the simple bending torsion theory and the ultimate capacity the simple plastic complete moment-rotation relationship of the connections is represented three-parameter model. analytical

ByN. KISHI, W. F. CHEN, K. G. MATSUOKA and S. G. NOMACHI

general deformation pattern of the web-angle connections is in Fig. 2. experimental results reported Bell, (1958) and by Lewitt, Chesson and (1966) double web-angle connections showed the following behavior: 1. The center of rotation of the connection near the mid- in which uniform torsional constant warping constant

shear has a parabolic distribution along the angle height value V at the upper edge of the angle (y • 1 ) and the maximum V = vat the lower edge analytical the variation of is to linear distribution in Fig. 6. resultant plastic shear force is

(1958), Static Tests of Standard Riveted and Bolted Beam-To-Column Connections, Progress Report of an Investigation Conducted the University Illinois Engineering Experiment Station. Kishi, (1987), Moment-Rotation Relation of Top- Seat-Angle Connection, CE-STR-87-4, School of Civil Engineer- nois. Lipson, S.L. (1968), Single-Angle and Single-Plate Framing Connections, Canadian Structural Engineering Conference, Toronto, Ontario, 141-162. (1969), Behavior of Welded Header Plate Connections,

bolts, the baseplate in in compression. They used a model based on the yield-line patterns in [1] were not yet in evidence, nor was there consideration of the axial loads increased the stiffness for small deformations, as also might prediction, that this was relative to experimentally observed stiffness properties of connections in steel frames are of importance deflection prediction, and for stability calculations [4, 5]. is therefore surprising that for connections, for

that there is evidence of dissipation, also, at higher that reversal from positive rotation to negative rotation can occur under (close to) zero applied moment. that for bases with sufficiently thin baseplates the connection will indeed behave as a "pin", provided sufficiently high previous loading is not feasible to test all possible design it is theoretical relationships between applied moment axial force P and connection rotation 8. A previous attempt [8) to do so for beam-column connections that a relationship between moment capacity and connection rotation

details have been given elsewhere [10] results. relative contributions of the bolts to the connection strength.

that such connections always have strength and stiffness in in cases of thick baseplates and adequate bolts, these factors significant. However, deformation of the baseplate at higher loads will render the "pinned" design assumption true for subsequent relatively rotation. The present work did not address the possible

force/elongation- behaviour the control element diagram. The diagram as a polygon, and values be taken from test results or are derived previous calculation for the shear panel. The differential in the joint = h•N where is the axial force in the control element, the angle of the shear deformation is y = Al/h. for the symmetrical loading and for antimetrical

and Design Centre "f-1ostostal Krucza This :paper -oroblem of stepped (unequal width) girders. First of modes elastic formulae being established. Then shown how those haracteristics can be extended into non-linear range of behaviour. Some comparison with test results is also given. Having known (calculated) joint flexibility one can take into account in the structural analysis by using so-called micro-bar model of a joint. last years a ll!'rge e!"mmt of research, stimulated co-ordinated mainly by and IIW, has been done in the domain of P?S joints (1]. Also in Poland, in Centre,

indicated [6], that se- cond order system adequate calculation model for girders particularly for Flexibility formulae and calculation model presented can be directly used in the analysis and design of Struc. Div., ASCE, vol. 108, ST 9, Sept., 1982. 6. Czechowskl, A., Investigation into the statics strength lattice girders, In Weldinf of Tubular Structures, Proceedings the Second Interne tonal Conference held in Boston, Massachusetts, USA, 16 - July 1984, Pergamon

will have significant impact on the moment-rotation characteristics, least following the first load reversal or after bolt slip has taken that have been developed excellent promise for general applications to

is confronted directly with the fact that for a better insight into topics such as the of members and connections, understanding of the behaviour of is essential. of course essential that designers are able to determine characteristics, preferably in the form of a mathematical model. The this point will be reviewed in an IABSE-report that is under preparation now [1]. is drafted in liaison with of steel frames.

structural properties of both members and connections. The relevant properties of these elements are strenzth, stiffness and deformation (ductility). Assuming for the present that bending is dominant, of the type illustrated qualitatively in Fig. 2.

Bijlaard, F.S.K., Nethercot, D.A., Stark, J.W.B., Tschemmernegg, F., P., Structural properties of semi-rigid joints in steel

relative rotation within each joint. Such an arrangement could not, of this rotation due to the different flexibility within the joint, merely the overall effect. light column and beam sections featured in all joint tests in the subassemblage and frame tests. A total of 25

bolts for the bottom cleats and six bolts for the web cleat connection. self straining rig was constructed of steel channels and a 100 x 90 plate was bolted on the vertical members to which the to apply the out-of- torsional loading at the free end of the beam via a load

investigate different conditions,one for interior columns and one for exterior identical joint conditions. results of torsion tests on two web cleat and one flange cleat in Figures 7 and 8, from which

torsionally very infinitely this is not the case. restrained warping distortions of the top and bottom flanges of the beam for web cleat and cleat connections. For theoretical analyses there is a need to

results. This also holds true for stability analyses of individual part of subassemblages. Again, the importance of stiffness stressed by discussers and alike.

proportionality during the loading evolution. This leads to the definition of a parameter a , representing a multiplier of t}{e loading data of the programme. non-linearity in the structural response to the applied loads, resulting from the occurence of either plastic hinges or second order

of the equivalent springs are modified at each step of the step-by-step" procedure, according to the evolution of the that have an influence over these stiffnesses (for instance, the is then •attached" to stiffness integrates K

Bye . connection is therefore

in compression). rotation of the member as of the member between ends i and inertia of the member cross section. of the member cross section. =1+-+--

By-.j£1

of the structure has been drawn as a function of the loads that increase factor and this for the three plastic analysis + rigid connections (curve B) plastic analysis + semi-rigid connections (curve of the loading step was limited by the most severe condition, i.e. or A D - that resulted in 48 steps before reaching the collapse and 4 20 seconds of behaviour depending on whether the semi-rigid into account should be noted. instability in the elasto-

described here includes models for beam-to-column connections having nonlinear moment-rota- tion curves (including unloading composite steel !-shaped treats the cross-secti- as three rectangular elements. All cross-section effects are computed as analytic expressions relative to these rectangular elements and then in terms of overall section sections along the length will experience plastic strains in the presence of axial load and moment. In the regions where plastification predicted, the length of the plastic region as the distance from the point where elastic behavior ceases to the point of moment. the point of

in frame analysis. Second-Order Geometric Effects formulating the stiffness matrix of in the frame, classical used for reducing the flexural stiffness coefficients to the presence axial thrust. Overall P-Delta effects are accounted elastic unloading. tails the development can be found in references and Initial Loading Curves initial loading curves for the connection models can be represented as either Frye-and-Morris polynomial

are parts of frames consists of preprocessing step of under gravity loads and frame analysis that utilizes stiffness data generated in the preproceseing step. the preprocessing step, the desired gravity loads are specified on simply-supported composite girder with the given cross-section, This girder then analyzed could start with a large positive at the face of attached result in tapered to "necking of the effective slab width the usual effective width along the span to the width of the column flange (under positive bending), an equivalent prismatic region in the

By1, 1978. 2. Ackroyd, M.H., "Nonlinear Flexibly-Connected Plane Steel Frames", University of Colorado, Boulder, Colorado, 1979. 3. Connolly, R., and Fisher, "Shear Strength of Stud Connectors in Concrete", Engineering Journal, Vol. 8, No. 2, April, 1971. 7. Yam, L.C.P. and Chapman, J.C., Inelastic Behavior of Simply-Supported Composite Beams of Steel and Concrete", Proceedings of Institution of Civil Engineers,

different solving strategies were adopted in order to optimize the to the cases of proportional and to available experimental results are also reported of the proposed method drawn. I 1 11

{Fig.lb). plastic zones that the distribution of plastic strains {p{x,z)) be controlled at large points. This would produce a lack of compatibility between plastic and total strain distributions that causes self equilibrated stresses in the isolated element subject to plastic strains only. The

Byin [3] is adopted to avoid the presence of these

(8c,f) is a vector of plastic multipliers ; is a vector of plastic potentials is a vector of positive constants, K is

in figure 3 where also the mesh adopted in the analysis plotted. The moment rotation curves determined in Sheffield in a previous series of connection tests were adopted. table of figure 3a gathers the values of the ultimate axial load N in to predict the ultimate column that substantial for the top and seat angle connections used in the test. results seem to confirm that the assumed joint law, though simple, may be sufficiently accurate also for cyclic analysis.

Byis severe the stiffness degrading is particularly

is also clear that further research work of the increased connection stiffness that results slab continuity is achieved (through the use steel bars). In the way, that of composite connection effects have shown that

in length, hinged rotation of the footing on the soil. By means of a centrally located roller and calibrated springs placed to simulate the rotation of the footing on loose is considered as soil condition. variable of the tests the differential displacement of axis.

of the axial compression load on the value of ~ obtained from (1). Since the buckling elastically when buckling occurs, the moment-rotation curves were in the elastic range. Each column was tested eight axial load levels and was bent successively about both principal that 0.517 s s 0.873 for 0.24 s C s 0.45 Cy• is the axial load in the is the axial plastic capacity of the column (Cy = is the yield stress). __ _

that case the rotational flexibility factor fixity factor (y) are not constant. With an axial com- in the column the measured moment-rotation curves were linear

also be used if the ultimate strength of the the condi- tions at failure are to determined. In this latter case, three diffe- rent nonlinear effects should be considered: connection nonlinearity, plastification and geometric nonlinearity leading to member and instability.

into design standards around the world [ 1,2,3,4 that although the of the actual support of the member should be accounted for. At the outset felt that the restraining effects of the connections the of the surrounding structure would be likely to raise

that even significant additional buckling strength to end- restrained columns [ 5,6 ~"''" d

of the concepts into design code potential for utilizing in the design standards that reflected specific levels of end restraint, rather than having curves that were based on the traditional will continue to be the focal point. This has been done that although is recognized that true pinned-end exist in real structures, such a model reflects accurately of the member itself, is not the factors that are related to the overall structure. There are obvious advantages to this approach, especially when it is that stability that reflect the restraint conditions between the

restraining member or assembly. The higher the value of G, the more moment will be asked to carry. In the most extreme case the columns infinitely that the beams will transfer no moment to the column. This, in turn, is an expression of the fact that the beam in this case cannot offer any distribution factor, G, for a realistic should replaced Gr, end-restraint stiffness distribution factor. Equation (2) therefore in the effective length solution procedure, rather than Eq. Gras is noted that a single is used for each column end. this can be explained as follows: interior columns: In the general frame certain amount prior to column buckling. The connect-

Stability of Steel Structures, Budapest, Faella, of semirigid frames. Annual Technical Session on Stability of

is only possible to calculate their strength and stiffness with relatively modest accuracy. It is, stiffness of if reliable structural response of the frame. .-f-·

ByI ~ /

H.t than in the case of the non-linear curve at the same value for F.t. 2(g)). In that case, using the bi-linear approximation leads to a lower value F.t than using the non-linear curve

that they do not collapse prior to the columns. The same holds for the interaction formulae have been presented for pin-ended beam-colomns axial compression and bending. To obtain the magnitude of that the use of the system length as buckling length in many cases [6]. Therefore, checks on column stability in elastic effective length. elastic effective length as buckling length in the interaction formulae,

practice for steel structures", International Colloquium on Stability.

finite element techniques", Heron, Vol. (1985)

at midheight. Loading then occurred in two stages. In the levels indicated in Table 1 and axial column load P was applied to failure. After the subassemblage tests, material yield stresses were that the analysis was terminated prematurely to numerical divergence. typical load deflection plot is in Fig 2 together with the at the University of in ref 6. The close correspondence is apparent. results of some 'design' calculations ,which

that these ratios, taken as unity for the previous calculation, surprisingly short, the columns were initially very straight and contained minimal stresses. --Top

create pattern loading. distribution around frames 1 and 2 after full design load had been applied to the beams. These distributions

the structure strength by plastic analysis. If that acts nearly linearly-elastic at working levels, and possesses sufficient ductility at ultimate, then simple, well-known methods will be available for the design of flexibly-connected steel frames. typical beam-column connections in steel frames can

resulting load-deformation curves will be compared with similar curves their behavior at working and will be studied in order to evaluate the elastic, and plastic, analysis at these two levels.

plotted in Fig. 7 Lastly, in order to establish the relation of analysis and tested by Stelmack [10] and shown

to give expressions for the three rotations, 01, 02, These rotations then back-substituted into rotational spring at each of the girder to obtain expressions for the "flexible (as contrasted to "fixed end moments") to be used in the frame coefficients "flexible end"

drift limits will to revised. This suitable topic for major research effort. substantial agreement on the characteristics and controlling parameters for and limit states are well defined, the solutions are less

based on determined from linear ratio of the bolt dis- tance from the 4. R and the moments for statics for the group is checked. 5. The location of the assuming that the bolt receives additional tension. In reality, the additional load is probably combination of tension bending. Fig. 6 diagrams the procedure as formulated first extreme is the plate is very thin 0(

weld groups. However, the welded case more complicated because the strength deformation curve for welds depends on the angle to which the weld loaded. seen in Fig. assumed that the ultimate strength value straight line equaled the specified value of 0.6 the deformation on a particular weld segment was small the computer program followed load- deformation curve the

written in terms of the resistances are given for complete and partial joint penetration strength of the weld metal and the base metal, at the joint. special simple construction, and resist gravity loads the basis of simple construction lateral loads distributing the to lateral loads selected

bolt. joints in shear must meet the shear and bearing requirements and slip requirements. However, slip-resistant joints are to be the exception rather than the rule. Installation of high strength bolts is restricted to turn-of-nut method or tensile strength of the weld its electrode classification, the ratio tensile strength of the weld metal. for the weld group in a to use an ultimate strength analysis method to determine the

joint to minimize the risk of lamellar tearing. bolts and welds are permitted in the same shear plane, the number bolts are to be determined based on resistance of the connection is limited to the greater of that of is Qssential to ensure that are both economical and reliable. In the past few years a projeets hava been undertaken in Canada which deepen reliability. This portion of the will touch on some of their Partial Joint Penetration Groove (PJPG) Welds

tested in pairs the ratio was 1.17 with a of 11.2%. that their results were consistent with those the following 3]. Although Standards Sl6.1 and [6] permit an ultimate strength is given. In 1971, Butler and Kulak [7] proposed that ultimate

s, tests [8], Holtz and Harre, Swannell and Skewes [9], and Biggs et al contributed to the experimental data while, to develop mathematical models. carefully designed and instrumented test involving is concluded that the fillet ductility is essentially of the that the deformations are proportional to the gauge length". Plate Connections plates have been used for decades, a rational design method fully developed. Since Whitmore's [14] effective width concept

in reduced fabrication costs and improved ability to compete with structures, but also in reduced shrinkage and distortions in the residual stresses. Steel Structures For States Design), Canadian Standards Association, Rexdale, direction of load, Welding Research Supplement, Welding Reasearch Institute,

connection restraint, not gravity loads. In the writer's designs, drift the If one follows that procedure, a safe t-uilding design

the late steel, using built-up-columns and I-beam sections in simple construction. resistance was accomplished either thru shear action of the late 40's and early SO's most of steel framed multistory buil-- in riveted construction. Welded-moment connection in the 60's and high-strength bolded connections in the 70's.

sistance of the steel buildings in the 40's without the need of also used riveted construction and A-7 Steel. This type large result of large joint rotations. either buckled or in tension, and some of the buildings lateral deflections which condemned them like the City Hall building com- at the Central in City, fared very well typical of the ductility levels exhibited by these connections overcame the large demands of overloading produced by the extreme earthquake suffe-

tion used in moment-resistant. built - resistant space frame in which one of the three 23-story towers

structures inspected after the earthquake (i.e. actual strengths of the constructed buildings at the that such an earthquake occurred), in order to better understand the actual

stren- that the enormous elastic strength and the demanded elastic strength was furnisheo in great part by the many incursions of the steel - large ductility values - stable hysteresis cycles. to assess the elastic rotations of the connec- tions and consequently the deformational behaviour of such connections. -- flexibility the panel- of which were indeed responsible in a good part of drifts in frames, but scarce energy dissipation. is now under consideration, to ig

to several cycles of extreme earthquake loading? this type of construction develops in -- lateral loading? ..• should the required strenght plates, as in the case of the Pino Suarez building complex?

California, Berke Distrito FEderal. "Reglamento para las Construcio el Distrito Federal, Edici6n 1987". (to be released

joints between circular hollow sections axial force(s) in the brace member(s) due to the design to the in Table 1. joints with square or circular hollow section brace mem- failure (yielding or instability) failure iv. chord punching shear failure failure with reduced effective width to: "Design recom- joints", IIW-document

in the safety assessment. Hence the q -factor performs a correction factor for the linear dynamic model and this paper the influence of semi-rigid connections to the -fac- tor will treated. 2. Method for the calculative determination of the q -factors rational procedure for the determination of q -factors has been Ballio, Perotti, Rampazzo, Setti /2/.

to the physical limits caused effects and represent safe side values in view of other limit state as lowcycle-fatigue or fracture of connections, fig. 4. limits of course have to be checked separately, unless their

that restrict the data collection effort to beam-to-column connections and column footing connections part of the collection, nor would fatigue characteristics. Although both of the latter are the limitations are necessary to the task

is clear that is currently available regarding the strength and behaviour of types of beam-to-column connections. It is unified basic format, in order that several primary objectives can be attained, as follows basis, to obtain data base of

~f/Jp Fiiure 1 Definition of Beam that the initial slope of the as in Figure 1, is function of the length of the element. Figure

Bycurve for beam= f({}

stiffness of rigid, semi-rigid and flexible §earn-to-column connections, respectively. that is regarded as the most suitable. It is that stiffer shorter length, in order to arrive that is used to non-dimensionalize the is plotted dimensionally first, to get _____ this figure the term indicates the ultimate connection (in case of the of clear plateau, is necessary of the required

their connections. of semi-rigid connections. of bolt pretension to produce specific forms of Stability and Simplified Methods

TABLE OF CONTENTS

realistically possible to abreast of all substantially from one locale to the next, result that interpretation of the findings and how they may to a particular case will be a dubious undertaking. Finally, with carried out in universities, research laboratories and

parts, mechanical fasteners, welds, and so on. Such studies essential for the understanding of the failure mechanisms of the identifying the main load and deformation controlling parameters. The three primary characteristics of non-linear identified, namely, stiffness, ultimate strength, establish familiarity with the types of connections that are used in actual structures around the world, and facilitate correlation efforts. of connection strength and behaviour, of load-deflection behaviour into two sub-sessions. Their topics of coverage and anticipated outcome

effects for the connections, the structural entire frame, but that establish exactly what the individual solutions can accomplish, and correlate with tests (if other analytical solutions. anticipated outcome of the frame analysis session was the of a repertory of computer programs, including definitions

of the various technical sessions, the final session was intended as the outlet for two primary groups of presentations, namely, (1) a discussion and evaluation of a potential of the session reporters and reporters. Th• former subject was of significant interest, that a proper organizational structure would facilitate future of information, as well as of work. The research reporters and their function crucial to the workshop, as these reports would focus that needs to be undertaken, to remove current deficiencies of available data and to add to data bases as well as

definition the stress area of. the bolt is the sectional area of smooth cylinder which, subjected to tension, has failure load as the threaded part of bolt from the in tension in Fig. 2, is internationally is evident that, based on the definition of As' the strength function for bolt in tension will be taken as: is the ultimate tensile strength of the bolt material. jointuso called prying forces occur due to flexibility of the parts. This is illustrated in Fig. 3.

draft the edge distance is therefore limited to a minimum of 1.5 d. section fully stressed upto the tensile material strength fu. So the strength of the member, also the mean stress in cross-section at ultimate load should be less than the yield of unsymmetrical or unsymmetrically

this line of mean values is then multiplied coefficient ok to find the characteristic line fractile). value of calculated with the statistical data of the population [8]. factor can be calculated: all test reports provide the data actual material geometric properties of test as required for the straight procedure additional cases can be distinguished: of the material strengths in the sample are given, but 0.6'------'--'---....._

bolts the ultimate shear strength of 0.7 fu' as assumed in the strength function (Table 1). will be followed in evaluation of test results. the about test results are available is the tensile force the connection, is the of the

greater than The reason for true fracture stress in a tensile fact is also in fig for a structural steel, designated 1, and a cold finished steel, plates in bending the contraction of the tensile zone restrained by the compressive zone. Therefore the potential factor of

local •lreee alraln elre•• Slraln this a view on actual t•st is details in tension, bendinQ, tension • bendinQ, and in included, Dltt:alls 1 n i:lll"'si an

failed, in brittle fracture at 2.1 times of the other details to 2.6 times without fracture. investi;ation with thick plate in bendin; showed an stress of 2.1 times YS, ••• fig4.

the different magnitude of strain at the two yield lines. details loaded in tension or bending according to fig 3 were later straightened, machined flush, and bolted together as and-plate stresses at failure of the connections were calculated, conservatively assuming equal compressive and tensile stress stress in the tension member and at the bolt line, with minor

plate, fig 6. In spite of the great mean tensile stress, also fig 6the maximum stresses are of the magnitude of 3 - stresses in pure bending. fracture and the magnitude of the ultimate stress, a correction for shear stresses Boll

ather Juet auteide the wide campreeeian member welde varieble a: 3.5 variable test canpr•••ian details in pure gr•ater strength was found for small welds, in an to d•cide acc•ptable lack of fit in pressur•· Th• test r•sults ive member. With guid• anol•s, as indicated in fig 7, the load was possibl• to increa•• to levels corr•sponding to on th• the compression member. Without any visibl• sign of fractur•, th• compressiv• m•mb•r was th•n mor• or less liquidiz•d, "floating out" around the guid• bolts a coupl• of These stresses to about 3 tim•• of th• mild st••l compr•ssion members.

initial stiffness of tests is not affected the level of that the ultimate strength is quasi of this level. However, the slip is initiated earlier for test (test 01:2), the initial stiffness not significantly ; so for the overall shape of the curve.

early in the loading sequence. at each toe of the in the vicinity of the bolt line on the leg of the flange angle attached to the column, together with

is of the same order as the this expression should not be significantly stiffer seat angles only.

significantly affect moment- rotation behavior are: the depth of the beam section to which the effective gage in the leg of the flange angles attached to the column. test results, a parametric model was developed to predict the

rotation (four ~O~Q~~~ trans at 300 from Bin fig. 4a); the rotation to bolt deformation (four transdu- ject to a plied to

tests. A comparison between the curves related to the corresponding of the two series shows that the presence of the extension of plate on the compression side has a limited influence on the significant strains in the beam stub, within the hardening range, the inelastic buckling of the compressive flange (and of the of the web for the specimens with thicker end plate) before of the connection was achieved. rotation capacity 'u,cnis at the contrary adversely affected by the principally is affected by plate relatively thin, the connection rotation in the nonlinear range is to the elastic-

plate, characteristics in a zone were important plastic strains should develop. The contribution of the bolts becomes more significant {up to about 35\ for the plate thickness. The limited ductility, typical of related to the average deformation histories of the bolts external and internal to the beam stub respectively for the

bolts in the specimen EP1-1 experienced remarkable plastic deformations, their behaviour in the specimen EP1-5 shows a limited nonlinearity, of the connection in the bolt by relating the deformation measured during the connection results that, in rotation flexibility

internal part. The former part can be simply modelled as cantilever element clamped to the possible prying • to be considered as a plate with restraints. A first is given the results related to the ....... its tensile strength. further

ki,red and kst determined for the tested are reported in table 1, where also the contributions of the end plate and of the bolts are also to define the values of the elastic limit moment and of the plastic moment M . The latter defini- tion is not clear-cut, based

of the whole connection, was verified to be in very the two component "in series". Values of ki are mean values related to the the elastic limit moment. bolt preloading and by that: bolt contribution depends on plate stiffness and increases with this parameter; b) the increment of the plate contribution is less sig- nificant than expected on the basis of the variation in thickness, in- of the plate restraint conditions, which

plastische Last-Verformungsverhalten steifenloser, geschweisster Knoten fur die Berechnung von Stahlrahmen P., Semi-Rigid and Flexible Connections: an Int. Conf. Steel Structures; to Design, Part

Technical University Lyngby have been studied results obtained in these investigations. In an analytical investi- gation of end-plate connections in beam sections, a design method was developed, and the basic equations of method are given in paper. Special attention was paid to studying the effect of prying action in the connection. Also T-stub connections and end-plate connections in circular sections were studied to clarify the strength stiffness characteristics. For experimental investigations were carried out to verify the analytical

have been combined in a single diagram, shown in Fig. 5. The curves give the prying connection with speci- fied values of b/a and r • The curves have been drawn for values of are of no practical interest. For = 1.00. lnyestiqation In the experimental part of the investigation of end-plate

Byr 0.25. smaller values of r r 2.85, no prying appears in the connection, and P

In the permits the analysis of bolted end-plate connections in sections, including determination of the tion, bolt forces, the effect of prying action, etc. ·In the experimental part of the study, a bolt forces were determined by means of strain gages. of the results obtained from this test series with those obtained by means of the suggested design method shows difference between the values obtained, the maximum deviation in bolt forces being only about yield load for the connection, as defined in the suggested design method, is also in this case c·onsidered to be the load the reduced yield moment is in the end-plate at the toe also that heavy plastic deformations of the end-plate will be avoi- In the connections with thin end-plates, the ultimate load was found to be more than greater than the theoretical yield load. the connections with heavier end-plates, the difference was found to be 25-75%.

gations includes consideration of the deformations of the individual fatigue. were determined, as well as proposed design methods provide sufficient accuracy for practical purposes. The experimental results obtained concerning connection deformations may contribute to a data base of load-deflection curves, established. 1. Agerskov, H., High-Strength Bolted Connections Subject to Prying,

bolts (quality 10.9) were used. All the mechanical set of test specimens are summarized in joint, four beam-to-column stiffness ratios are that allows also to change the slenderness ratio h /a of the co- inertia, while a very dif- stiffness (fig. 2) test specimens with weak axis connections test arrangement is illustrated in figure 3. The load is applied at the cantilever beam and is increased progressively either up to collapse limiting vertical deflection (40 of the cantilever due to requirements of the testing facilities. of the

elastic and exhibits an will be unloadea and then loaded again, whichever the loading level rea- is last strain hardening range, the stiffness K of which is quasi

(serie A). For a test specimen, both sets of results give two limiting interaction curve (fig. 12), the aim of which is to show the in a 3-D joint. Any other point interaction curve would require tests on the associated 3-D specimen.

this interaction curve and to joints ; therefore additional tests will be in order to implement the information. I. Rentschler, G.P. and Chen, W.F., Tests of Beam-to-Column Moment Jaspart, J.P., Essais sur poutre-colonne d'axe faible et C.R.I.F., Bruxelles (in preparation). J., Jaspart, J.P. R., of the Joints, Proceedings, Workshop

for Hollow Section statically loaded - Steel Structures,

of an IPE 330 beam welded to a 160 for NR4, and of a 500 beam welded to a 300 column for (Fig.l). The ratio of shear is generally less important; for comparison pur- @ 500 @ 300 M/2 -

.Li...l ...... ! ) ) . 2ll.j( ·-r······-·T········ train hardening begins

of the connections happens mainly by total plastification of that part of the column web which is adjacent to the rather complex, the two main causes of flexibility [1] are clearly visible local deformation near points B and C, i.e. at the flanges detailed results be found in Ref. [5].

-y have been derived from the numerical plotted in Fig. 8. They can be used in a T-sping model of

Int. Rep. 86/6, July 1986. in mechanical and cross-sectional properties steel. Int. Conf. on Planning and Design of Tall Buildings, Stability of Steel Structures, Publ. 22, Bruxelles, results are in good agreement with the work presented here, in that range of small relative node rotations which is of practical interest. about this subject should appear in further steifen-

stress design stress of 1,5 times the ultimate value ; this has recently been reduced to 1,2, due to large hole deformations in the plate or member material stress. European stress value of 3,0 times the yield stress ; this will likely be clear that numerous and highly advanced finite element solution of one-, two- local analyses. Material and geometric properties are of yielding, stability effects, It that investigations of this will of the most important factors for the behaviour

is believed possible. To come up with acceptable models, however, task and requires several years of research and development. specific due to the limited length of the paper the large variety of subjects to cover, we will limit ourselves, in the next sections, to a condensed presentation of the computer programs we brief descriptions of some elements and techniques of resolution

res, Vol. 17, no 1, 1983, pp. 51-59. the angle of loading. Structural Engineering Report 133, calcul automatique des configurations pre lineaires en calcul des structures. a paraitre civil, Universite Laval,

plastic hinge concept rather than the pro- plastification of the bar. correlation with and interpretation of experimental results clearly defined in order to arrive tests. is proposed to use the initial stiffness Kand the ultimate load Fui in order to describe the non linearity. In a general way,

that the initial stiffness in a forseeable way, perties of the components of the connection. This means that for in- dustrial practice,

theoreti- cal results, for a cyclic hardening case is given in the figure 11. -+"'· +-'-

to o l is expressed f+ + n)=R(n) , Rtt\) ( M+- 4 "R simulate different unloading conditions (see fig. lc).

By1 1 I I are of

the upper bound of the quasi- ela- stic behaviour. are c6nveXtionally defined the intersection of the lines shown in fig. to interpret the results

cyclic behaviour of 14 beams-to-column specimens has been experi- in [ 5 ] • They have been designed following the current in rigid and semirigid connections for steel structures. In fig. the are in four

characterization of the hysteretic loops

with Double Web-Angle Connections Kishi angle with double web-angle tions stiffness the ultimate carrying capacity the con- nection are determined using simple analytical procedure for modeling the top-, seat-, web-angles of the semi-rigid con- nections. connection stiffness the ultimate

angle with double web-angle connections as shown in Fig. 1. This connection type has the inherent ural deformation of both flange and angles in the legs attached to the column. In this paper, an developed to predict the moment-rotation ultimate capacity. three-parameter power model is used here to represent the whole moment-rotation behavior of the con- nections. experimental results reported et al (1982) and Azizinamini et al (1985) are used here to verify the proposed procedure.

between M and 3(Elt) (d (12) connection stiffness the value; (Eit) (Ela) (d (ta) (13) 0.78(tt) 2.2 Ultimate Moment the experimental results reported et al (1982) and Azizinamini al (1985), the collapse for the top- seat- angle connection and of web-angle connection as shown in Figs. and 6, respectively.

Kishi web-angle and double web-angle beam-to-column connections developed. In this development, the connection stiffness is determined using the simple bending torsion theory and the ultimate capacity the simple plastic complete moment-rotation relationship of the connections is represented three-parameter model. analytical

ByN. KISHI, W. F. CHEN, K. G. MATSUOKA and S. G. NOMACHI

general deformation pattern of the web-angle connections is in Fig. 2. experimental results reported Bell, (1958) and by Lewitt, Chesson and (1966) double web-angle connections showed the following behavior: 1. The center of rotation of the connection near the mid- in which uniform torsional constant warping constant

shear has a parabolic distribution along the angle height value V at the upper edge of the angle (y • 1 ) and the maximum V = vat the lower edge analytical the variation of is to linear distribution in Fig. 6. resultant plastic shear force is

(1958), Static Tests of Standard Riveted and Bolted Beam-To-Column Connections, Progress Report of an Investigation Conducted the University Illinois Engineering Experiment Station. Kishi, (1987), Moment-Rotation Relation of Top- Seat-Angle Connection, CE-STR-87-4, School of Civil Engineer- nois. Lipson, S.L. (1968), Single-Angle and Single-Plate Framing Connections, Canadian Structural Engineering Conference, Toronto, Ontario, 141-162. (1969), Behavior of Welded Header Plate Connections,

bolts, the baseplate in in compression. They used a model based on the yield-line patterns in [1] were not yet in evidence, nor was there consideration of the axial loads increased the stiffness for small deformations, as also might prediction, that this was relative to experimentally observed stiffness properties of connections in steel frames are of importance deflection prediction, and for stability calculations [4, 5]. is therefore surprising that for connections, for

that there is evidence of dissipation, also, at higher that reversal from positive rotation to negative rotation can occur under (close to) zero applied moment. that for bases with sufficiently thin baseplates the connection will indeed behave as a "pin", provided sufficiently high previous loading is not feasible to test all possible design it is theoretical relationships between applied moment axial force P and connection rotation 8. A previous attempt [8) to do so for beam-column connections that a relationship between moment capacity and connection rotation

details have been given elsewhere [10] results. relative contributions of the bolts to the connection strength.

that such connections always have strength and stiffness in in cases of thick baseplates and adequate bolts, these factors significant. However, deformation of the baseplate at higher loads will render the "pinned" design assumption true for subsequent relatively rotation. The present work did not address the possible

force/elongation- behaviour the control element diagram. The diagram as a polygon, and values be taken from test results or are derived previous calculation for the shear panel. The differential in the joint = h•N where is the axial force in the control element, the angle of the shear deformation is y = Al/h. for the symmetrical loading and for antimetrical

and Design Centre "f-1ostostal Krucza This :paper -oroblem of stepped (unequal width) girders. First of modes elastic formulae being established. Then shown how those haracteristics can be extended into non-linear range of behaviour. Some comparison with test results is also given. Having known (calculated) joint flexibility one can take into account in the structural analysis by using so-called micro-bar model of a joint. last years a ll!'rge e!"mmt of research, stimulated co-ordinated mainly by and IIW, has been done in the domain of P?S joints (1]. Also in Poland, in Centre,

indicated [6], that se- cond order system adequate calculation model for girders particularly for Flexibility formulae and calculation model presented can be directly used in the analysis and design of Struc. Div., ASCE, vol. 108, ST 9, Sept., 1982. 6. Czechowskl, A., Investigation into the statics strength lattice girders, In Weldinf of Tubular Structures, Proceedings the Second Interne tonal Conference held in Boston, Massachusetts, USA, 16 - July 1984, Pergamon

will have significant impact on the moment-rotation characteristics, least following the first load reversal or after bolt slip has taken that have been developed excellent promise for general applications to

is confronted directly with the fact that for a better insight into topics such as the of members and connections, understanding of the behaviour of is essential. of course essential that designers are able to determine characteristics, preferably in the form of a mathematical model. The this point will be reviewed in an IABSE-report that is under preparation now [1]. is drafted in liaison with of steel frames.

structural properties of both members and connections. The relevant properties of these elements are strenzth, stiffness and deformation (ductility). Assuming for the present that bending is dominant, of the type illustrated qualitatively in Fig. 2.

Bijlaard, F.S.K., Nethercot, D.A., Stark, J.W.B., Tschemmernegg, F., P., Structural properties of semi-rigid joints in steel

relative rotation within each joint. Such an arrangement could not, of this rotation due to the different flexibility within the joint, merely the overall effect. light column and beam sections featured in all joint tests in the subassemblage and frame tests. A total of 25

bolts for the bottom cleats and six bolts for the web cleat connection. self straining rig was constructed of steel channels and a 100 x 90 plate was bolted on the vertical members to which the to apply the out-of- torsional loading at the free end of the beam via a load

investigate different conditions,one for interior columns and one for exterior identical joint conditions. results of torsion tests on two web cleat and one flange cleat in Figures 7 and 8, from which

torsionally very infinitely this is not the case. restrained warping distortions of the top and bottom flanges of the beam for web cleat and cleat connections. For theoretical analyses there is a need to

results. This also holds true for stability analyses of individual part of subassemblages. Again, the importance of stiffness stressed by discussers and alike.

proportionality during the loading evolution. This leads to the definition of a parameter a , representing a multiplier of t}{e loading data of the programme. non-linearity in the structural response to the applied loads, resulting from the occurence of either plastic hinges or second order

of the equivalent springs are modified at each step of the step-by-step" procedure, according to the evolution of the that have an influence over these stiffnesses (for instance, the is then •attached" to stiffness integrates K

Bye . connection is therefore

in compression). rotation of the member as of the member between ends i and inertia of the member cross section. of the member cross section. =1+-+--

By-.j£1

of the structure has been drawn as a function of the loads that increase factor and this for the three plastic analysis + rigid connections (curve B) plastic analysis + semi-rigid connections (curve of the loading step was limited by the most severe condition, i.e. or A D - that resulted in 48 steps before reaching the collapse and 4 20 seconds of behaviour depending on whether the semi-rigid into account should be noted. instability in the elasto-

described here includes models for beam-to-column connections having nonlinear moment-rota- tion curves (including unloading composite steel !-shaped treats the cross-secti- as three rectangular elements. All cross-section effects are computed as analytic expressions relative to these rectangular elements and then in terms of overall section sections along the length will experience plastic strains in the presence of axial load and moment. In the regions where plastification predicted, the length of the plastic region as the distance from the point where elastic behavior ceases to the point of moment. the point of

in frame analysis. Second-Order Geometric Effects formulating the stiffness matrix of in the frame, classical used for reducing the flexural stiffness coefficients to the presence axial thrust. Overall P-Delta effects are accounted elastic unloading. tails the development can be found in references and Initial Loading Curves initial loading curves for the connection models can be represented as either Frye-and-Morris polynomial

are parts of frames consists of preprocessing step of under gravity loads and frame analysis that utilizes stiffness data generated in the preproceseing step. the preprocessing step, the desired gravity loads are specified on simply-supported composite girder with the given cross-section, This girder then analyzed could start with a large positive at the face of attached result in tapered to "necking of the effective slab width the usual effective width along the span to the width of the column flange (under positive bending), an equivalent prismatic region in the

By1, 1978. 2. Ackroyd, M.H., "Nonlinear Flexibly-Connected Plane Steel Frames", University of Colorado, Boulder, Colorado, 1979. 3. Connolly, R., and Fisher, "Shear Strength of Stud Connectors in Concrete", Engineering Journal, Vol. 8, No. 2, April, 1971. 7. Yam, L.C.P. and Chapman, J.C., Inelastic Behavior of Simply-Supported Composite Beams of Steel and Concrete", Proceedings of Institution of Civil Engineers,

different solving strategies were adopted in order to optimize the to the cases of proportional and to available experimental results are also reported of the proposed method drawn. I 1 11

{Fig.lb). plastic zones that the distribution of plastic strains {p{x,z)) be controlled at large points. This would produce a lack of compatibility between plastic and total strain distributions that causes self equilibrated stresses in the isolated element subject to plastic strains only. The

Byin [3] is adopted to avoid the presence of these

(8c,f) is a vector of plastic multipliers ; is a vector of plastic potentials is a vector of positive constants, K is

in figure 3 where also the mesh adopted in the analysis plotted. The moment rotation curves determined in Sheffield in a previous series of connection tests were adopted. table of figure 3a gathers the values of the ultimate axial load N in to predict the ultimate column that substantial for the top and seat angle connections used in the test. results seem to confirm that the assumed joint law, though simple, may be sufficiently accurate also for cyclic analysis.

Byis severe the stiffness degrading is particularly

is also clear that further research work of the increased connection stiffness that results slab continuity is achieved (through the use steel bars). In the way, that of composite connection effects have shown that

in length, hinged rotation of the footing on the soil. By means of a centrally located roller and calibrated springs placed to simulate the rotation of the footing on loose is considered as soil condition. variable of the tests the differential displacement of axis.

of the axial compression load on the value of ~ obtained from (1). Since the buckling elastically when buckling occurs, the moment-rotation curves were in the elastic range. Each column was tested eight axial load levels and was bent successively about both principal that 0.517 s s 0.873 for 0.24 s C s 0.45 Cy• is the axial load in the is the axial plastic capacity of the column (Cy = is the yield stress). __ _

that case the rotational flexibility factor fixity factor (y) are not constant. With an axial com- in the column the measured moment-rotation curves were linear

also be used if the ultimate strength of the the condi- tions at failure are to determined. In this latter case, three diffe- rent nonlinear effects should be considered: connection nonlinearity, plastification and geometric nonlinearity leading to member and instability.

into design standards around the world [ 1,2,3,4 that although the of the actual support of the member should be accounted for. At the outset felt that the restraining effects of the connections the of the surrounding structure would be likely to raise

that even significant additional buckling strength to end- restrained columns [ 5,6 ~"''" d

of the concepts into design code potential for utilizing in the design standards that reflected specific levels of end restraint, rather than having curves that were based on the traditional will continue to be the focal point. This has been done that although is recognized that true pinned-end exist in real structures, such a model reflects accurately of the member itself, is not the factors that are related to the overall structure. There are obvious advantages to this approach, especially when it is that stability that reflect the restraint conditions between the

restraining member or assembly. The higher the value of G, the more moment will be asked to carry. In the most extreme case the columns infinitely that the beams will transfer no moment to the column. This, in turn, is an expression of the fact that the beam in this case cannot offer any distribution factor, G, for a realistic should replaced Gr, end-restraint stiffness distribution factor. Equation (2) therefore in the effective length solution procedure, rather than Eq. Gras is noted that a single is used for each column end. this can be explained as follows: interior columns: In the general frame certain amount prior to column buckling. The connect-

Stability of Steel Structures, Budapest, Faella, of semirigid frames. Annual Technical Session on Stability of

is only possible to calculate their strength and stiffness with relatively modest accuracy. It is, stiffness of if reliable structural response of the frame. .-f-·

ByI ~ /

H.t than in the case of the non-linear curve at the same value for F.t. 2(g)). In that case, using the bi-linear approximation leads to a lower value F.t than using the non-linear curve

that they do not collapse prior to the columns. The same holds for the interaction formulae have been presented for pin-ended beam-colomns axial compression and bending. To obtain the magnitude of that the use of the system length as buckling length in many cases [6]. Therefore, checks on column stability in elastic effective length. elastic effective length as buckling length in the interaction formulae,

practice for steel structures", International Colloquium on Stability.

finite element techniques", Heron, Vol. (1985)

at midheight. Loading then occurred in two stages. In the levels indicated in Table 1 and axial column load P was applied to failure. After the subassemblage tests, material yield stresses were that the analysis was terminated prematurely to numerical divergence. typical load deflection plot is in Fig 2 together with the at the University of in ref 6. The close correspondence is apparent. results of some 'design' calculations ,which

that these ratios, taken as unity for the previous calculation, surprisingly short, the columns were initially very straight and contained minimal stresses. --Top

create pattern loading. distribution around frames 1 and 2 after full design load had been applied to the beams. These distributions

the structure strength by plastic analysis. If that acts nearly linearly-elastic at working levels, and possesses sufficient ductility at ultimate, then simple, well-known methods will be available for the design of flexibly-connected steel frames. typical beam-column connections in steel frames can

resulting load-deformation curves will be compared with similar curves their behavior at working and will be studied in order to evaluate the elastic, and plastic, analysis at these two levels.

plotted in Fig. 7 Lastly, in order to establish the relation of analysis and tested by Stelmack [10] and shown

to give expressions for the three rotations, 01, 02, These rotations then back-substituted into rotational spring at each of the girder to obtain expressions for the "flexible (as contrasted to "fixed end moments") to be used in the frame coefficients "flexible end"

drift limits will to revised. This suitable topic for major research effort. substantial agreement on the characteristics and controlling parameters for and limit states are well defined, the solutions are less

based on determined from linear ratio of the bolt dis- tance from the 4. R and the moments for statics for the group is checked. 5. The location of the assuming that the bolt receives additional tension. In reality, the additional load is probably combination of tension bending. Fig. 6 diagrams the procedure as formulated first extreme is the plate is very thin 0(

weld groups. However, the welded case more complicated because the strength deformation curve for welds depends on the angle to which the weld loaded. seen in Fig. assumed that the ultimate strength value straight line equaled the specified value of 0.6 the deformation on a particular weld segment was small the computer program followed load- deformation curve the

written in terms of the resistances are given for complete and partial joint penetration strength of the weld metal and the base metal, at the joint. special simple construction, and resist gravity loads the basis of simple construction lateral loads distributing the to lateral loads selected

bolt. joints in shear must meet the shear and bearing requirements and slip requirements. However, slip-resistant joints are to be the exception rather than the rule. Installation of high strength bolts is restricted to turn-of-nut method or tensile strength of the weld its electrode classification, the ratio tensile strength of the weld metal. for the weld group in a to use an ultimate strength analysis method to determine the

joint to minimize the risk of lamellar tearing. bolts and welds are permitted in the same shear plane, the number bolts are to be determined based on resistance of the connection is limited to the greater of that of is Qssential to ensure that are both economical and reliable. In the past few years a projeets hava been undertaken in Canada which deepen reliability. This portion of the will touch on some of their Partial Joint Penetration Groove (PJPG) Welds

tested in pairs the ratio was 1.17 with a of 11.2%. that their results were consistent with those the following 3]. Although Standards Sl6.1 and [6] permit an ultimate strength is given. In 1971, Butler and Kulak [7] proposed that ultimate

s, tests [8], Holtz and Harre, Swannell and Skewes [9], and Biggs et al contributed to the experimental data while, to develop mathematical models. carefully designed and instrumented test involving is concluded that the fillet ductility is essentially of the that the deformations are proportional to the gauge length". Plate Connections plates have been used for decades, a rational design method fully developed. Since Whitmore's [14] effective width concept

in reduced fabrication costs and improved ability to compete with structures, but also in reduced shrinkage and distortions in the residual stresses. Steel Structures For States Design), Canadian Standards Association, Rexdale, direction of load, Welding Research Supplement, Welding Reasearch Institute,

connection restraint, not gravity loads. In the writer's designs, drift the If one follows that procedure, a safe t-uilding design

the late steel, using built-up-columns and I-beam sections in simple construction. resistance was accomplished either thru shear action of the late 40's and early SO's most of steel framed multistory buil-- in riveted construction. Welded-moment connection in the 60's and high-strength bolded connections in the 70's.

sistance of the steel buildings in the 40's without the need of also used riveted construction and A-7 Steel. This type large result of large joint rotations. either buckled or in tension, and some of the buildings lateral deflections which condemned them like the City Hall building com- at the Central in City, fared very well typical of the ductility levels exhibited by these connections overcame the large demands of overloading produced by the extreme earthquake suffe-

tion used in moment-resistant. built - resistant space frame in which one of the three 23-story towers

structures inspected after the earthquake (i.e. actual strengths of the constructed buildings at the that such an earthquake occurred), in order to better understand the actual

stren- that the enormous elastic strength and the demanded elastic strength was furnisheo in great part by the many incursions of the steel - large ductility values - stable hysteresis cycles. to assess the elastic rotations of the connec- tions and consequently the deformational behaviour of such connections. -- flexibility the panel- of which were indeed responsible in a good part of drifts in frames, but scarce energy dissipation. is now under consideration, to ig

to several cycles of extreme earthquake loading? this type of construction develops in -- lateral loading? ..• should the required strenght plates, as in the case of the Pino Suarez building complex?

California, Berke Distrito FEderal. "Reglamento para las Construcio el Distrito Federal, Edici6n 1987". (to be released

joints between circular hollow sections axial force(s) in the brace member(s) due to the design to the in Table 1. joints with square or circular hollow section brace mem- failure (yielding or instability) failure iv. chord punching shear failure failure with reduced effective width to: "Design recom- joints", IIW-document

in the safety assessment. Hence the q -factor performs a correction factor for the linear dynamic model and this paper the influence of semi-rigid connections to the -fac- tor will treated. 2. Method for the calculative determination of the q -factors rational procedure for the determination of q -factors has been Ballio, Perotti, Rampazzo, Setti /2/.

to the physical limits caused effects and represent safe side values in view of other limit state as lowcycle-fatigue or fracture of connections, fig. 4. limits of course have to be checked separately, unless their

that restrict the data collection effort to beam-to-column connections and column footing connections part of the collection, nor would fatigue characteristics. Although both of the latter are the limitations are necessary to the task

is clear that is currently available regarding the strength and behaviour of types of beam-to-column connections. It is unified basic format, in order that several primary objectives can be attained, as follows basis, to obtain data base of

~f/Jp Fiiure 1 Definition of Beam that the initial slope of the as in Figure 1, is function of the length of the element. Figure

Bycurve for beam= f({}

stiffness of rigid, semi-rigid and flexible §earn-to-column connections, respectively. that is regarded as the most suitable. It is that stiffer shorter length, in order to arrive that is used to non-dimensionalize the is plotted dimensionally first, to get _____ this figure the term indicates the ultimate connection (in case of the of clear plateau, is necessary of the required

their connections. of semi-rigid connections. of bolt pretension to produce specific forms of Stability and Simplified Methods

CONTENTS

ABOUT THIS BOOK

TABLE OF CONTENTS

realistically possible to abreast of all substantially from one locale to the next, result that interpretation of the findings and how they may to a particular case will be a dubious undertaking. Finally, with carried out in universities, research laboratories and

parts, mechanical fasteners, welds, and so on. Such studies essential for the understanding of the failure mechanisms of the identifying the main load and deformation controlling parameters. The three primary characteristics of non-linear identified, namely, stiffness, ultimate strength, establish familiarity with the types of connections that are used in actual structures around the world, and facilitate correlation efforts. of connection strength and behaviour, of load-deflection behaviour into two sub-sessions. Their topics of coverage and anticipated outcome

effects for the connections, the structural entire frame, but that establish exactly what the individual solutions can accomplish, and correlate with tests (if other analytical solutions. anticipated outcome of the frame analysis session was the of a repertory of computer programs, including definitions

of the various technical sessions, the final session was intended as the outlet for two primary groups of presentations, namely, (1) a discussion and evaluation of a potential of the session reporters and reporters. Th• former subject was of significant interest, that a proper organizational structure would facilitate future of information, as well as of work. The research reporters and their function crucial to the workshop, as these reports would focus that needs to be undertaken, to remove current deficiencies of available data and to add to data bases as well as

definition the stress area of. the bolt is the sectional area of smooth cylinder which, subjected to tension, has failure load as the threaded part of bolt from the in tension in Fig. 2, is internationally is evident that, based on the definition of As' the strength function for bolt in tension will be taken as: is the ultimate tensile strength of the bolt material. jointuso called prying forces occur due to flexibility of the parts. This is illustrated in Fig. 3.

draft the edge distance is therefore limited to a minimum of 1.5 d. section fully stressed upto the tensile material strength fu. So the strength of the member, also the mean stress in cross-section at ultimate load should be less than the yield of unsymmetrical or unsymmetrically

this line of mean values is then multiplied coefficient ok to find the characteristic line fractile). value of calculated with the statistical data of the population [8]. factor can be calculated: all test reports provide the data actual material geometric properties of test as required for the straight procedure additional cases can be distinguished: of the material strengths in the sample are given, but 0.6'------'--'---....._

bolts the ultimate shear strength of 0.7 fu' as assumed in the strength function (Table 1). will be followed in evaluation of test results. the about test results are available is the tensile force the connection, is the of the

greater than The reason for true fracture stress in a tensile fact is also in fig for a structural steel, designated 1, and a cold finished steel, plates in bending the contraction of the tensile zone restrained by the compressive zone. Therefore the potential factor of

local •lreee alraln elre•• Slraln this a view on actual t•st is details in tension, bendinQ, tension • bendinQ, and in included, Dltt:alls 1 n i:lll"'si an

failed, in brittle fracture at 2.1 times of the other details to 2.6 times without fracture. investi;ation with thick plate in bendin; showed an stress of 2.1 times YS, ••• fig4.

the different magnitude of strain at the two yield lines. details loaded in tension or bending according to fig 3 were later straightened, machined flush, and bolted together as and-plate stresses at failure of the connections were calculated, conservatively assuming equal compressive and tensile stress stress in the tension member and at the bolt line, with minor

plate, fig 6. In spite of the great mean tensile stress, also fig 6the maximum stresses are of the magnitude of 3 - stresses in pure bending. fracture and the magnitude of the ultimate stress, a correction for shear stresses Boll

ather Juet auteide the wide campreeeian member welde varieble a: 3.5 variable test canpr•••ian details in pure gr•ater strength was found for small welds, in an to d•cide acc•ptable lack of fit in pressur•· Th• test r•sults ive member. With guid• anol•s, as indicated in fig 7, the load was possibl• to increa•• to levels corr•sponding to on th• the compression member. Without any visibl• sign of fractur•, th• compressiv• m•mb•r was th•n mor• or less liquidiz•d, "floating out" around the guid• bolts a coupl• of These stresses to about 3 tim•• of th• mild st••l compr•ssion members.

initial stiffness of tests is not affected the level of that the ultimate strength is quasi of this level. However, the slip is initiated earlier for test (test 01:2), the initial stiffness not significantly ; so for the overall shape of the curve.

early in the loading sequence. at each toe of the in the vicinity of the bolt line on the leg of the flange angle attached to the column, together with

is of the same order as the this expression should not be significantly stiffer seat angles only.

significantly affect moment- rotation behavior are: the depth of the beam section to which the effective gage in the leg of the flange angles attached to the column. test results, a parametric model was developed to predict the

rotation (four ~O~Q~~~ trans at 300 from Bin fig. 4a); the rotation to bolt deformation (four transdu- ject to a plied to

tests. A comparison between the curves related to the corresponding of the two series shows that the presence of the extension of plate on the compression side has a limited influence on the significant strains in the beam stub, within the hardening range, the inelastic buckling of the compressive flange (and of the of the web for the specimens with thicker end plate) before of the connection was achieved. rotation capacity 'u,cnis at the contrary adversely affected by the principally is affected by plate relatively thin, the connection rotation in the nonlinear range is to the elastic-

plate, characteristics in a zone were important plastic strains should develop. The contribution of the bolts becomes more significant {up to about 35\ for the plate thickness. The limited ductility, typical of related to the average deformation histories of the bolts external and internal to the beam stub respectively for the

bolts in the specimen EP1-1 experienced remarkable plastic deformations, their behaviour in the specimen EP1-5 shows a limited nonlinearity, of the connection in the bolt by relating the deformation measured during the connection results that, in rotation flexibility

internal part. The former part can be simply modelled as cantilever element clamped to the possible prying • to be considered as a plate with restraints. A first is given the results related to the ....... its tensile strength. further

ki,red and kst determined for the tested are reported in table 1, where also the contributions of the end plate and of the bolts are also to define the values of the elastic limit moment and of the plastic moment M . The latter defini- tion is not clear-cut, based

of the whole connection, was verified to be in very the two component "in series". Values of ki are mean values related to the the elastic limit moment. bolt preloading and by that: bolt contribution depends on plate stiffness and increases with this parameter; b) the increment of the plate contribution is less sig- nificant than expected on the basis of the variation in thickness, in- of the plate restraint conditions, which

plastische Last-Verformungsverhalten steifenloser, geschweisster Knoten fur die Berechnung von Stahlrahmen P., Semi-Rigid and Flexible Connections: an Int. Conf. Steel Structures; to Design, Part

Technical University Lyngby have been studied results obtained in these investigations. In an analytical investi- gation of end-plate connections in beam sections, a design method was developed, and the basic equations of method are given in paper. Special attention was paid to studying the effect of prying action in the connection. Also T-stub connections and end-plate connections in circular sections were studied to clarify the strength stiffness characteristics. For experimental investigations were carried out to verify the analytical

have been combined in a single diagram, shown in Fig. 5. The curves give the prying connection with speci- fied values of b/a and r • The curves have been drawn for values of are of no practical interest. For = 1.00. lnyestiqation In the experimental part of the investigation of end-plate

Byr 0.25. smaller values of r r 2.85, no prying appears in the connection, and P

In the permits the analysis of bolted end-plate connections in sections, including determination of the tion, bolt forces, the effect of prying action, etc. ·In the experimental part of the study, a bolt forces were determined by means of strain gages. of the results obtained from this test series with those obtained by means of the suggested design method shows difference between the values obtained, the maximum deviation in bolt forces being only about yield load for the connection, as defined in the suggested design method, is also in this case c·onsidered to be the load the reduced yield moment is in the end-plate at the toe also that heavy plastic deformations of the end-plate will be avoi- In the connections with thin end-plates, the ultimate load was found to be more than greater than the theoretical yield load. the connections with heavier end-plates, the difference was found to be 25-75%.

gations includes consideration of the deformations of the individual fatigue. were determined, as well as proposed design methods provide sufficient accuracy for practical purposes. The experimental results obtained concerning connection deformations may contribute to a data base of load-deflection curves, established. 1. Agerskov, H., High-Strength Bolted Connections Subject to Prying,

bolts (quality 10.9) were used. All the mechanical set of test specimens are summarized in joint, four beam-to-column stiffness ratios are that allows also to change the slenderness ratio h /a of the co- inertia, while a very dif- stiffness (fig. 2) test specimens with weak axis connections test arrangement is illustrated in figure 3. The load is applied at the cantilever beam and is increased progressively either up to collapse limiting vertical deflection (40 of the cantilever due to requirements of the testing facilities. of the

elastic and exhibits an will be unloadea and then loaded again, whichever the loading level rea- is last strain hardening range, the stiffness K of which is quasi

(serie A). For a test specimen, both sets of results give two limiting interaction curve (fig. 12), the aim of which is to show the in a 3-D joint. Any other point interaction curve would require tests on the associated 3-D specimen.

this interaction curve and to joints ; therefore additional tests will be in order to implement the information. I. Rentschler, G.P. and Chen, W.F., Tests of Beam-to-Column Moment Jaspart, J.P., Essais sur poutre-colonne d'axe faible et C.R.I.F., Bruxelles (in preparation). J., Jaspart, J.P. R., of the Joints, Proceedings, Workshop

for Hollow Section statically loaded - Steel Structures,

of an IPE 330 beam welded to a 160 for NR4, and of a 500 beam welded to a 300 column for (Fig.l). The ratio of shear is generally less important; for comparison pur- @ 500 @ 300 M/2 -

.Li...l ...... ! ) ) . 2ll.j( ·-r······-·T········ train hardening begins

of the connections happens mainly by total plastification of that part of the column web which is adjacent to the rather complex, the two main causes of flexibility [1] are clearly visible local deformation near points B and C, i.e. at the flanges detailed results be found in Ref. [5].

-y have been derived from the numerical plotted in Fig. 8. They can be used in a T-sping model of

Int. Rep. 86/6, July 1986. in mechanical and cross-sectional properties steel. Int. Conf. on Planning and Design of Tall Buildings, Stability of Steel Structures, Publ. 22, Bruxelles, results are in good agreement with the work presented here, in that range of small relative node rotations which is of practical interest. about this subject should appear in further steifen-

stress design stress of 1,5 times the ultimate value ; this has recently been reduced to 1,2, due to large hole deformations in the plate or member material stress. European stress value of 3,0 times the yield stress ; this will likely be clear that numerous and highly advanced finite element solution of one-, two- local analyses. Material and geometric properties are of yielding, stability effects, It that investigations of this will of the most important factors for the behaviour

is believed possible. To come up with acceptable models, however, task and requires several years of research and development. specific due to the limited length of the paper the large variety of subjects to cover, we will limit ourselves, in the next sections, to a condensed presentation of the computer programs we brief descriptions of some elements and techniques of resolution

res, Vol. 17, no 1, 1983, pp. 51-59. the angle of loading. Structural Engineering Report 133, calcul automatique des configurations pre lineaires en calcul des structures. a paraitre civil, Universite Laval,

plastic hinge concept rather than the pro- plastification of the bar. correlation with and interpretation of experimental results clearly defined in order to arrive tests. is proposed to use the initial stiffness Kand the ultimate load Fui in order to describe the non linearity. In a general way,

that the initial stiffness in a forseeable way, perties of the components of the connection. This means that for in- dustrial practice,

theoreti- cal results, for a cyclic hardening case is given in the figure 11. -+"'· +-'-

to o l is expressed f+ + n)=R(n) , Rtt\) ( M+- 4 "R simulate different unloading conditions (see fig. lc).

By1 1 I I are of

the upper bound of the quasi- ela- stic behaviour. are c6nveXtionally defined the intersection of the lines shown in fig. to interpret the results

cyclic behaviour of 14 beams-to-column specimens has been experi- in [ 5 ] • They have been designed following the current in rigid and semirigid connections for steel structures. In fig. the are in four

characterization of the hysteretic loops

with Double Web-Angle Connections Kishi angle with double web-angle tions stiffness the ultimate carrying capacity the con- nection are determined using simple analytical procedure for modeling the top-, seat-, web-angles of the semi-rigid con- nections. connection stiffness the ultimate

angle with double web-angle connections as shown in Fig. 1. This connection type has the inherent ural deformation of both flange and angles in the legs attached to the column. In this paper, an developed to predict the moment-rotation ultimate capacity. three-parameter power model is used here to represent the whole moment-rotation behavior of the con- nections. experimental results reported et al (1982) and Azizinamini et al (1985) are used here to verify the proposed procedure.

between M and 3(Elt) (d (12) connection stiffness the value; (Eit) (Ela) (d (ta) (13) 0.78(tt) 2.2 Ultimate Moment the experimental results reported et al (1982) and Azizinamini al (1985), the collapse for the top- seat- angle connection and of web-angle connection as shown in Figs. and 6, respectively.

Kishi web-angle and double web-angle beam-to-column connections developed. In this development, the connection stiffness is determined using the simple bending torsion theory and the ultimate capacity the simple plastic complete moment-rotation relationship of the connections is represented three-parameter model. analytical

ByN. KISHI, W. F. CHEN, K. G. MATSUOKA and S. G. NOMACHI

general deformation pattern of the web-angle connections is in Fig. 2. experimental results reported Bell, (1958) and by Lewitt, Chesson and (1966) double web-angle connections showed the following behavior: 1. The center of rotation of the connection near the mid- in which uniform torsional constant warping constant

shear has a parabolic distribution along the angle height value V at the upper edge of the angle (y • 1 ) and the maximum V = vat the lower edge analytical the variation of is to linear distribution in Fig. 6. resultant plastic shear force is

(1958), Static Tests of Standard Riveted and Bolted Beam-To-Column Connections, Progress Report of an Investigation Conducted the University Illinois Engineering Experiment Station. Kishi, (1987), Moment-Rotation Relation of Top- Seat-Angle Connection, CE-STR-87-4, School of Civil Engineer- nois. Lipson, S.L. (1968), Single-Angle and Single-Plate Framing Connections, Canadian Structural Engineering Conference, Toronto, Ontario, 141-162. (1969), Behavior of Welded Header Plate Connections,

bolts, the baseplate in in compression. They used a model based on the yield-line patterns in [1] were not yet in evidence, nor was there consideration of the axial loads increased the stiffness for small deformations, as also might prediction, that this was relative to experimentally observed stiffness properties of connections in steel frames are of importance deflection prediction, and for stability calculations [4, 5]. is therefore surprising that for connections, for

that there is evidence of dissipation, also, at higher that reversal from positive rotation to negative rotation can occur under (close to) zero applied moment. that for bases with sufficiently thin baseplates the connection will indeed behave as a "pin", provided sufficiently high previous loading is not feasible to test all possible design it is theoretical relationships between applied moment axial force P and connection rotation 8. A previous attempt [8) to do so for beam-column connections that a relationship between moment capacity and connection rotation

details have been given elsewhere [10] results. relative contributions of the bolts to the connection strength.

that such connections always have strength and stiffness in in cases of thick baseplates and adequate bolts, these factors significant. However, deformation of the baseplate at higher loads will render the "pinned" design assumption true for subsequent relatively rotation. The present work did not address the possible

force/elongation- behaviour the control element diagram. The diagram as a polygon, and values be taken from test results or are derived previous calculation for the shear panel. The differential in the joint = h•N where is the axial force in the control element, the angle of the shear deformation is y = Al/h. for the symmetrical loading and for antimetrical

and Design Centre "f-1ostostal Krucza This :paper -oroblem of stepped (unequal width) girders. First of modes elastic formulae being established. Then shown how those haracteristics can be extended into non-linear range of behaviour. Some comparison with test results is also given. Having known (calculated) joint flexibility one can take into account in the structural analysis by using so-called micro-bar model of a joint. last years a ll!'rge e!"mmt of research, stimulated co-ordinated mainly by and IIW, has been done in the domain of P?S joints (1]. Also in Poland, in Centre,

indicated [6], that se- cond order system adequate calculation model for girders particularly for Flexibility formulae and calculation model presented can be directly used in the analysis and design of Struc. Div., ASCE, vol. 108, ST 9, Sept., 1982. 6. Czechowskl, A., Investigation into the statics strength lattice girders, In Weldinf of Tubular Structures, Proceedings the Second Interne tonal Conference held in Boston, Massachusetts, USA, 16 - July 1984, Pergamon

will have significant impact on the moment-rotation characteristics, least following the first load reversal or after bolt slip has taken that have been developed excellent promise for general applications to

is confronted directly with the fact that for a better insight into topics such as the of members and connections, understanding of the behaviour of is essential. of course essential that designers are able to determine characteristics, preferably in the form of a mathematical model. The this point will be reviewed in an IABSE-report that is under preparation now [1]. is drafted in liaison with of steel frames.

structural properties of both members and connections. The relevant properties of these elements are strenzth, stiffness and deformation (ductility). Assuming for the present that bending is dominant, of the type illustrated qualitatively in Fig. 2.

Bijlaard, F.S.K., Nethercot, D.A., Stark, J.W.B., Tschemmernegg, F., P., Structural properties of semi-rigid joints in steel

relative rotation within each joint. Such an arrangement could not, of this rotation due to the different flexibility within the joint, merely the overall effect. light column and beam sections featured in all joint tests in the subassemblage and frame tests. A total of 25

bolts for the bottom cleats and six bolts for the web cleat connection. self straining rig was constructed of steel channels and a 100 x 90 plate was bolted on the vertical members to which the to apply the out-of- torsional loading at the free end of the beam via a load

investigate different conditions,one for interior columns and one for exterior identical joint conditions. results of torsion tests on two web cleat and one flange cleat in Figures 7 and 8, from which

torsionally very infinitely this is not the case. restrained warping distortions of the top and bottom flanges of the beam for web cleat and cleat connections. For theoretical analyses there is a need to

results. This also holds true for stability analyses of individual part of subassemblages. Again, the importance of stiffness stressed by discussers and alike.

proportionality during the loading evolution. This leads to the definition of a parameter a , representing a multiplier of t}{e loading data of the programme. non-linearity in the structural response to the applied loads, resulting from the occurence of either plastic hinges or second order

of the equivalent springs are modified at each step of the step-by-step" procedure, according to the evolution of the that have an influence over these stiffnesses (for instance, the is then •attached" to stiffness integrates K

Bye . connection is therefore

in compression). rotation of the member as of the member between ends i and inertia of the member cross section. of the member cross section. =1+-+--

By-.j£1

of the structure has been drawn as a function of the loads that increase factor and this for the three plastic analysis + rigid connections (curve B) plastic analysis + semi-rigid connections (curve of the loading step was limited by the most severe condition, i.e. or A D - that resulted in 48 steps before reaching the collapse and 4 20 seconds of behaviour depending on whether the semi-rigid into account should be noted. instability in the elasto-

described here includes models for beam-to-column connections having nonlinear moment-rota- tion curves (including unloading composite steel !-shaped treats the cross-secti- as three rectangular elements. All cross-section effects are computed as analytic expressions relative to these rectangular elements and then in terms of overall section sections along the length will experience plastic strains in the presence of axial load and moment. In the regions where plastification predicted, the length of the plastic region as the distance from the point where elastic behavior ceases to the point of moment. the point of

in frame analysis. Second-Order Geometric Effects formulating the stiffness matrix of in the frame, classical used for reducing the flexural stiffness coefficients to the presence axial thrust. Overall P-Delta effects are accounted elastic unloading. tails the development can be found in references and Initial Loading Curves initial loading curves for the connection models can be represented as either Frye-and-Morris polynomial

are parts of frames consists of preprocessing step of under gravity loads and frame analysis that utilizes stiffness data generated in the preproceseing step. the preprocessing step, the desired gravity loads are specified on simply-supported composite girder with the given cross-section, This girder then analyzed could start with a large positive at the face of attached result in tapered to "necking of the effective slab width the usual effective width along the span to the width of the column flange (under positive bending), an equivalent prismatic region in the

By1, 1978. 2. Ackroyd, M.H., "Nonlinear Flexibly-Connected Plane Steel Frames", University of Colorado, Boulder, Colorado, 1979. 3. Connolly, R., and Fisher, "Shear Strength of Stud Connectors in Concrete", Engineering Journal, Vol. 8, No. 2, April, 1971. 7. Yam, L.C.P. and Chapman, J.C., Inelastic Behavior of Simply-Supported Composite Beams of Steel and Concrete", Proceedings of Institution of Civil Engineers,

different solving strategies were adopted in order to optimize the to the cases of proportional and to available experimental results are also reported of the proposed method drawn. I 1 11

{Fig.lb). plastic zones that the distribution of plastic strains {p{x,z)) be controlled at large points. This would produce a lack of compatibility between plastic and total strain distributions that causes self equilibrated stresses in the isolated element subject to plastic strains only. The

Byin [3] is adopted to avoid the presence of these

(8c,f) is a vector of plastic multipliers ; is a vector of plastic potentials is a vector of positive constants, K is

in figure 3 where also the mesh adopted in the analysis plotted. The moment rotation curves determined in Sheffield in a previous series of connection tests were adopted. table of figure 3a gathers the values of the ultimate axial load N in to predict the ultimate column that substantial for the top and seat angle connections used in the test. results seem to confirm that the assumed joint law, though simple, may be sufficiently accurate also for cyclic analysis.

Byis severe the stiffness degrading is particularly

is also clear that further research work of the increased connection stiffness that results slab continuity is achieved (through the use steel bars). In the way, that of composite connection effects have shown that

in length, hinged rotation of the footing on the soil. By means of a centrally located roller and calibrated springs placed to simulate the rotation of the footing on loose is considered as soil condition. variable of the tests the differential displacement of axis.

of the axial compression load on the value of ~ obtained from (1). Since the buckling elastically when buckling occurs, the moment-rotation curves were in the elastic range. Each column was tested eight axial load levels and was bent successively about both principal that 0.517 s s 0.873 for 0.24 s C s 0.45 Cy• is the axial load in the is the axial plastic capacity of the column (Cy = is the yield stress). __ _

that case the rotational flexibility factor fixity factor (y) are not constant. With an axial com- in the column the measured moment-rotation curves were linear

also be used if the ultimate strength of the the condi- tions at failure are to determined. In this latter case, three diffe- rent nonlinear effects should be considered: connection nonlinearity, plastification and geometric nonlinearity leading to member and instability.

into design standards around the world [ 1,2,3,4 that although the of the actual support of the member should be accounted for. At the outset felt that the restraining effects of the connections the of the surrounding structure would be likely to raise

that even significant additional buckling strength to end- restrained columns [ 5,6 ~"''" d

of the concepts into design code potential for utilizing in the design standards that reflected specific levels of end restraint, rather than having curves that were based on the traditional will continue to be the focal point. This has been done that although is recognized that true pinned-end exist in real structures, such a model reflects accurately of the member itself, is not the factors that are related to the overall structure. There are obvious advantages to this approach, especially when it is that stability that reflect the restraint conditions between the

restraining member or assembly. The higher the value of G, the more moment will be asked to carry. In the most extreme case the columns infinitely that the beams will transfer no moment to the column. This, in turn, is an expression of the fact that the beam in this case cannot offer any distribution factor, G, for a realistic should replaced Gr, end-restraint stiffness distribution factor. Equation (2) therefore in the effective length solution procedure, rather than Eq. Gras is noted that a single is used for each column end. this can be explained as follows: interior columns: In the general frame certain amount prior to column buckling. The connect-

Stability of Steel Structures, Budapest, Faella, of semirigid frames. Annual Technical Session on Stability of

is only possible to calculate their strength and stiffness with relatively modest accuracy. It is, stiffness of if reliable structural response of the frame. .-f-·

ByI ~ /

H.t than in the case of the non-linear curve at the same value for F.t. 2(g)). In that case, using the bi-linear approximation leads to a lower value F.t than using the non-linear curve

that they do not collapse prior to the columns. The same holds for the interaction formulae have been presented for pin-ended beam-colomns axial compression and bending. To obtain the magnitude of that the use of the system length as buckling length in many cases [6]. Therefore, checks on column stability in elastic effective length. elastic effective length as buckling length in the interaction formulae,

practice for steel structures", International Colloquium on Stability.

finite element techniques", Heron, Vol. (1985)

at midheight. Loading then occurred in two stages. In the levels indicated in Table 1 and axial column load P was applied to failure. After the subassemblage tests, material yield stresses were that the analysis was terminated prematurely to numerical divergence. typical load deflection plot is in Fig 2 together with the at the University of in ref 6. The close correspondence is apparent. results of some 'design' calculations ,which

that these ratios, taken as unity for the previous calculation, surprisingly short, the columns were initially very straight and contained minimal stresses. --Top

create pattern loading. distribution around frames 1 and 2 after full design load had been applied to the beams. These distributions

the structure strength by plastic analysis. If that acts nearly linearly-elastic at working levels, and possesses sufficient ductility at ultimate, then simple, well-known methods will be available for the design of flexibly-connected steel frames. typical beam-column connections in steel frames can

resulting load-deformation curves will be compared with similar curves their behavior at working and will be studied in order to evaluate the elastic, and plastic, analysis at these two levels.

plotted in Fig. 7 Lastly, in order to establish the relation of analysis and tested by Stelmack [10] and shown

to give expressions for the three rotations, 01, 02, These rotations then back-substituted into rotational spring at each of the girder to obtain expressions for the "flexible (as contrasted to "fixed end moments") to be used in the frame coefficients "flexible end"

drift limits will to revised. This suitable topic for major research effort. substantial agreement on the characteristics and controlling parameters for and limit states are well defined, the solutions are less

based on determined from linear ratio of the bolt dis- tance from the 4. R and the moments for statics for the group is checked. 5. The location of the assuming that the bolt receives additional tension. In reality, the additional load is probably combination of tension bending. Fig. 6 diagrams the procedure as formulated first extreme is the plate is very thin 0(

weld groups. However, the welded case more complicated because the strength deformation curve for welds depends on the angle to which the weld loaded. seen in Fig. assumed that the ultimate strength value straight line equaled the specified value of 0.6 the deformation on a particular weld segment was small the computer program followed load- deformation curve the

written in terms of the resistances are given for complete and partial joint penetration strength of the weld metal and the base metal, at the joint. special simple construction, and resist gravity loads the basis of simple construction lateral loads distributing the to lateral loads selected

bolt. joints in shear must meet the shear and bearing requirements and slip requirements. However, slip-resistant joints are to be the exception rather than the rule. Installation of high strength bolts is restricted to turn-of-nut method or tensile strength of the weld its electrode classification, the ratio tensile strength of the weld metal. for the weld group in a to use an ultimate strength analysis method to determine the

joint to minimize the risk of lamellar tearing. bolts and welds are permitted in the same shear plane, the number bolts are to be determined based on resistance of the connection is limited to the greater of that of is Qssential to ensure that are both economical and reliable. In the past few years a projeets hava been undertaken in Canada which deepen reliability. This portion of the will touch on some of their Partial Joint Penetration Groove (PJPG) Welds

tested in pairs the ratio was 1.17 with a of 11.2%. that their results were consistent with those the following 3]. Although Standards Sl6.1 and [6] permit an ultimate strength is given. In 1971, Butler and Kulak [7] proposed that ultimate

s, tests [8], Holtz and Harre, Swannell and Skewes [9], and Biggs et al contributed to the experimental data while, to develop mathematical models. carefully designed and instrumented test involving is concluded that the fillet ductility is essentially of the that the deformations are proportional to the gauge length". Plate Connections plates have been used for decades, a rational design method fully developed. Since Whitmore's [14] effective width concept

in reduced fabrication costs and improved ability to compete with structures, but also in reduced shrinkage and distortions in the residual stresses. Steel Structures For States Design), Canadian Standards Association, Rexdale, direction of load, Welding Research Supplement, Welding Reasearch Institute,

connection restraint, not gravity loads. In the writer's designs, drift the If one follows that procedure, a safe t-uilding design

the late steel, using built-up-columns and I-beam sections in simple construction. resistance was accomplished either thru shear action of the late 40's and early SO's most of steel framed multistory buil-- in riveted construction. Welded-moment connection in the 60's and high-strength bolded connections in the 70's.

sistance of the steel buildings in the 40's without the need of also used riveted construction and A-7 Steel. This type large result of large joint rotations. either buckled or in tension, and some of the buildings lateral deflections which condemned them like the City Hall building com- at the Central in City, fared very well typical of the ductility levels exhibited by these connections overcame the large demands of overloading produced by the extreme earthquake suffe-

tion used in moment-resistant. built - resistant space frame in which one of the three 23-story towers

structures inspected after the earthquake (i.e. actual strengths of the constructed buildings at the that such an earthquake occurred), in order to better understand the actual

stren- that the enormous elastic strength and the demanded elastic strength was furnisheo in great part by the many incursions of the steel - large ductility values - stable hysteresis cycles. to assess the elastic rotations of the connec- tions and consequently the deformational behaviour of such connections. -- flexibility the panel- of which were indeed responsible in a good part of drifts in frames, but scarce energy dissipation. is now under consideration, to ig

to several cycles of extreme earthquake loading? this type of construction develops in -- lateral loading? ..• should the required strenght plates, as in the case of the Pino Suarez building complex?

California, Berke Distrito FEderal. "Reglamento para las Construcio el Distrito Federal, Edici6n 1987". (to be released

joints between circular hollow sections axial force(s) in the brace member(s) due to the design to the in Table 1. joints with square or circular hollow section brace mem- failure (yielding or instability) failure iv. chord punching shear failure failure with reduced effective width to: "Design recom- joints", IIW-document

in the safety assessment. Hence the q -factor performs a correction factor for the linear dynamic model and this paper the influence of semi-rigid connections to the -fac- tor will treated. 2. Method for the calculative determination of the q -factors rational procedure for the determination of q -factors has been Ballio, Perotti, Rampazzo, Setti /2/.

to the physical limits caused effects and represent safe side values in view of other limit state as lowcycle-fatigue or fracture of connections, fig. 4. limits of course have to be checked separately, unless their

that restrict the data collection effort to beam-to-column connections and column footing connections part of the collection, nor would fatigue characteristics. Although both of the latter are the limitations are necessary to the task

is clear that is currently available regarding the strength and behaviour of types of beam-to-column connections. It is unified basic format, in order that several primary objectives can be attained, as follows basis, to obtain data base of

~f/Jp Fiiure 1 Definition of Beam that the initial slope of the as in Figure 1, is function of the length of the element. Figure

Bycurve for beam= f({}

stiffness of rigid, semi-rigid and flexible §earn-to-column connections, respectively. that is regarded as the most suitable. It is that stiffer shorter length, in order to arrive that is used to non-dimensionalize the is plotted dimensionally first, to get _____ this figure the term indicates the ultimate connection (in case of the of clear plateau, is necessary of the required

their connections. of semi-rigid connections. of bolt pretension to produce specific forms of Stability and Simplified Methods

TABLE OF CONTENTS

is of the same order as the this expression should not be significantly stiffer seat angles only.

Byr 0.25. smaller values of r r 2.85, no prying appears in the connection, and P

for Hollow Section statically loaded - Steel Structures,

.Li...l ...... ! ) ) . 2ll.j( ·-r······-·T········ train hardening begins

-y have been derived from the numerical plotted in Fig. 8. They can be used in a T-sping model of

theoreti- cal results, for a cyclic hardening case is given in the figure 11. -+"'· +-'-

By1 1 I I are of

characterization of the hysteretic loops

ByN. KISHI, W. F. CHEN, K. G. MATSUOKA and S. G. NOMACHI

Bye . connection is therefore

By-.j£1

Byin [3] is adopted to avoid the presence of these

Byis severe the stiffness degrading is particularly

that even significant additional buckling strength to end- restrained columns [ 5,6 ~"''" d

ByI ~ /

practice for steel structures", International Colloquium on Stability.

finite element techniques", Heron, Vol. (1985)

Bycurve for beam= f({}