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The semi-rigid behaviour of three-dimensional steel beam-to-column joints subjected to proportional loading. Part I. Experimental evaluation
Journal of Constructional Steel Research 63 (2007) 1241–1253 www.elsevier.com/locate/jcsr
The semi-rigid behaviour of three-dimensional steel beam-to-column joints subjected to proportional loading. Part I. Experimental evaluation J.M. Cabrero ∗ , E. Bayo Department of Structural Analysis and Design, School of Architecture, University of Navarra, 31080 Pamplona, Spain Received 29 June 2006; accepted 8 November 2006
Abstract An experimental investigation of statically loaded extended end-plate connections in both major and minor column axes was undertaken at the University of Navarra, Spain. The aim was to provide insight into the behaviour of these joints when a proportional load is applied to both axes (three-dimensional loading). The rotational stiffness of the joints increases with this type of three-dimensional loading. The findings also show that an increase in the end-plate thickness results in an increase in the connection’s flexural strength and stiffness, and a decrease in its rotation capacity. c 2006 Elsevier Ltd. All rights reserved.
Keywords: End plate connections; Major axis connections; Minor axis connections; Three-dimensional behaviour; Experimental testing; Resistance; Stiffness; Rotation capacity; Steel connections
1. Introduction It is currently recognised that a great majority of joints exhibit a rather different behaviour than that idealised as rigid or pinned. Extensive investigation of the behaviour of such semi-rigid joints in the major axis has been carried out. Works by Zoetemeijer [1], Yee and Melchers [2] and Jaspart [3] constitute the basis for the current component method proposed by Eurocode 3 [4] for the analysis of joints. Faella, Pilusso and Rizzano proposed several modifications to this method [5]. The works headed by Chen [6–9] are also a major source regarding experimental results of semirigid joints and reference advanced analysis methods for semirigid frames. Works by Aggarwal and Krishnamurthy [10, 11] are also a major reference for experimental results and analytical models for extended end-plate joints [12]. Another source for experimental results is the database compiled by Cruz, Sim˜oes da Silva, Rodrigues and Sim˜oes [13]. Less effort has been dedicated to analysing the behaviour of minoraxis joints and to proposing adequate analytical models. Lima and Andrade tested several angle joints and proposed a ∗ Corresponding author. Tel.: +34 948425600x2704; fax: +34 948425629.
E-mail addresses: [email protected] (J.M. Cabrero), [email protected] (E. Bayo). c 2006 Elsevier Ltd. All rights reserved. 0143-974X/$ - see front matter doi:10.1016/j.jcsr.2006.11.004
corresponding analytical model [14,15]; Costa Neves carried out an experimental programme on extended end-plate joints bolted to the column’s web and proposed an analytical model for both stiffness and resistance[16]. Plane joints subjected to in-plane loading have constituted the most studied configuration. Few references are available accounting for three-dimensional out-of-plane behaviour with joints in both axes. Gibbons, Kirby and Nethercot tested several type of joints in three-dimensional frames [17]. Janss, Jaspart and Maquoi also reported tests for three-dimensional and minor axis joints [18]. Recently, V´ertes and Iv´anyi [19] ran a test program on three-dimensional joints and proposed an analytical model based on the plate formula developed in Eurocode 3 [20]. This paper presents the experimental programme carried out at the University of Navarra, Spain, on a new proposal for a three-dimensional semi-rigid steel joint. Proportional loading was applied in two different arrangements: to the joint axis (bi-dimensional or in-plane loading) or to both axes (threedimensional loading). The proposed three-dimensional joint configuration is presented in Fig. 1. It consists of extended end-plate joints for both major and minor axes. The minor-axis joints are not bolted to the column web, but to an additional plate welded to the column flanges (see Fig. 2). By virtue of this additional plate, the corresponding minor-axis beams do not get into the column
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Nomenclature
S j.h
Greek letters
S j.ini S j.l
δb δc δv δh.i δl.c δl.t u y rem φ φCd φinf K −R φsup K −R Ψj Ψinf K −R
Ψsup K −R ρy θi
beam elastic displacement displacement corresponding to joint rotation beam elastic shear deformation vertical displacement measured at point i horizontal deformation of the end-plate at the compression zone horizontal deformation of the end-plate at the tension zone ultimate strain strain at the yield point remaining strain rotational deformation of the joint rotation capacity rotation at the lower resistance bound of the kneerange of the joint moment–rotation curve rotation at the upper resistance bound of the knee-range of the joint moment–rotation curve joint ductility index ductility index evaluated at the lower bound of the knee-range of the joint moment–rotation curve ductility index evaluated at the upper bound of the knee-range of the joint moment–rotation curve yield ratio joint rotation
Upper cases effective tension resistance of the end-plate of bolt-row r Hc.low clearance of the column below the end-plates Hc.mid clearance of the column between the minor-axis end-plates Hc.up clearance of the column above the end-plate Li distance between the point i and the end-plate face L beam length of the beam L c−t distance between the transducers located in the end-plate at the tension and compression zones L load distance between the load application point and the face of the end-plate M bending moment Mep.Rd flexural resistance of the end-plate Minf K −R lower resistance bound of the knee-range of the joint moment–rotation curve M j.Rd joint flexural resistance Mmax maximum bending moment Msup K −R upper resistance bound of the knee-range of the joint moment–rotation curve Q total load applied Ri reaction force at support i Fep.Rd
S j. p−l
initial joint rotational stiffness measured according to the beam vertical displacement initial joint rotational stiffness initial joint rotational stiffness measured according to the end-plate deformation post-limit joint rotational stiffness
Lower cases bb bc bep dinf K −R
dsup K −R e ex fu fy f cd hb hc hr h ep ki p p2−3 tep tfb tfc twb w z
beam section width column section width end-plate width rotation comprised between the lower bound of the knee-range of the joint moment–rotation curve and the rotation capacity rotation comprised between the upper bound of the knee-range of the joint moment–rotation curve and the rotation capacity edge distance lateral edge distance ultimate or tensile stress yield stress tensile stress at failure beam section height column section height distance from the bolt-row r to the centre of compression end-plate height stiffness coefficient for component i pitch of the tension bolts distance between the tension bolt-row 2 and the compression bolt-row 3 end-plate thickness beam flange thickness column flange thickness beam web thickness gauge of the bolts lever arm
and the joints do not hinder each other, so they may be designed individually. This plate also acts as a stiffener for the joint in the major axis. The end-plate of the proposed and tested minor-axis joints consists of two partial end-plates. The remaining gap is required for practical reasons, to access and tighten the bolts properly. These end-plates could be executed as a single end-plate extended on both sides if the column size were big enough to allow for those operations from the upper or the lower side of the joint. 2. Description of the experimental program 2.1. Test details The experimental programme essentially comprised two test details on the joint configuration shown in Fig. 1. The
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Fig. 1. Proposed three-dimensional semi-rigid joint. (a) Major-axis joint.
(b) Minor-axis joint.
Fig. 2. Additional plate welded to the column flanges.
specimens were fabricated from a set of two major- and minoraxis joints, as shown in detail in Table 1 and Fig. 3. One main parameter was varied: the end-plate thickness, tep —A series corresponds to a thick plate (tep = 16 mm), while B series to a thin plate (tep = 10 mm)—. The chosen steel grade for plates and sections was S275. Hand tightened full-threaded grade 8.8 M20 bolts in 22 mm drilled holes were used in all the sets. The column had a section profile HEB160. In addition, due to the loading procedure, the clearances above (Hc.up ) and below (Hc.low ) of the end-plate were close to 150 mm. All specimens were designed to comply with Eurocode 3 requirements [4], so that the component endplate and bolts in the tension zone were the determining factors for the failure.
(c) Complete test arrangement. Fig. 3. General test detail. Table 1 Test details Series
Column
Minor-axis beam
Major-axis beam
Bolt
tep
A B
HEB 160 HEB 160
IPE 240 IPE 240
IPE 330 IPE 330
TR 20 TR 20
16 10
2.2. Geometrical properties The actual geometry of the connection elements was recorded before starting the test. The actual dimensions of
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Table 2 Actual geometry of the connection (dimensions in mm, referred to those indicated in Fig. 3) Column profile Test ID
hc
bc
tfc
Hc.up
Hc.mid
Hc.low
A B
160.80 158.20
159.00 159.50
12.30 12.30
153.50 150.00
76.50 78.50
146.50 150.00
Test ID
hb
bb
tfb
twb
L beam
L load
Major axis
A-M B-M
329.63 329.75
161.84 161.90
11.44 11.41
7.52 7.38
1247.75 1248.75
948.00 949.50
Minor axis
A-n B-n
241.60 241.04
119.30 120.21
9.51 9.71
6.08 6.23
1248.00 1249.25
947.00 949.50
Beam profile
End-plate and connection geometry Test ID
h ep
bep
tep
e
w
ex
p
p2−3
Major axis
A-M B-M
409.75 408.50
161.50 159.50
16.55 10.10
29.65 28.83
99.04 97.98
31.79 31.81
89.66 89.21
228.41 227.81
Minor axis
A-n B-n
150.38 150.67
142.00 141.50
16.35 10.10
30.64 31.03
79.33 77.95
31.83 32.00
89.81 89.55
– –
Table 3 Average characteristic values for the structural steel
Table 4 Average characteristic values for the bolts
Specimen Steel grade
End-plate S275
Beam S275
f y (MPa) f u (MPa) f cd (MPa)
383.12 521.00 340.20
357.82 499.10 248.57
5.32 23.28 33.35 18.00
4.00 46.76 62.56 36.29
y max u rem ρ
0.735
0.717
the profiles, plates and connection geometry are summarised in Table 2. These values correspond to the average of the different measurements for each series. There was not a large scattering for geometrical measurements. Actual dimensions met the requirements according to the standard UNE-EN 10034:1994 [21]. 2.3. Mechanical properties 2.3.1. Tension tests on the structural steel The test programme included one steel grade for the endplates and sections: S275. The coupon tension test on the structural steel material was performed according to the appropriate UNE procedures [22]. The average characteristics are set out in Table 3. The Table gives the values for the static yield and tensile stresses, f y and f u , the stress at failure, f cd , the yield ratio, ρ y = f y / f u , the strain at the yield point, y , the maximum strain, max , the ultimate strain, u , and the remaining strain after the test, rem . 2.3.2. Tension tests on the bolts Two machined bolts were tested under tension in order to determine the mechanical properties of the bolt material,
Steel grade
8.8
f y (MPa) f u (MPa) f cd (MPa)
793.75 879.60 438.08
y max cd rem ρ
25.99 34.43 43.75 20.74 0.902
in accordance with UNE-EN 10002-1 [22]. The average properties are shown in Table 4. 2.4. Test arrangement and instrumentation The actual connections were rotated downwards for practical reasons. The load was applied to the upper-side of the column by a 400 kN testing machine (hydraulic jack with maximum piston stroke of 200 mm). The beams were pinned supported at a distance of 950 mm to the end-plate face. In order to prevent lateral torsional buckling of the beam while loading, a beam guidance device near the support had to be provided. The instrumentation plan is described in Figs. 4 and 5. The primary requirements of the instrumentation were measuring the applied load and the relevant displacements of the connection (e.g. the vertical displacement of the beam, the horizontal displacement of the end-plate). The displacements were measured by means of linear variable displacement transducers (LVDTs, shown as δl in Fig. 4, which accounted for total deformation of the end-plate and the column flange), and linear position transducers (δh ) located as indicated in Fig. 4 (which recorded the vertical displacements of the beams).
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Fig. 5. Joints instrumentation plan.
Fig. 4. General instrumentation plan adopted for each beam.
Strain gauges (maximum strain ±2%) were added to the endplate (front side) and to the column as shown in Fig. 5 to provide insight into the strain distribution. Total applied loads (Q) were obtained directly from the hydraulic jack. Reactions (Ri ) were measured by load-cells located at the beam supports. 2.5. Testing procedure The dimensions of the plates were recorded before installing the specimens into the testing rig. The bolts were handtightened up to a torque value of 165 N m (approximately 30% of the total torque value for preloaded bolts) to simulate the snug-tight condition. The specimens were then placed and aligned. The measurement devices and strain gauges were then connected. Electronic recording started and all the equipment was verified. The specimens were subjected to monotonic force, which was applied to the column as explained previously (load is indicated as Q in Fig. 4). The joints were tested with load applied either along one or along both axes. The aim of the tests was to characterise the joints’ behaviour, and to verify whether or not there were coupling effects between the joints in the minor and major axes when submitted to proportional loading. First, the assembly was tested with three-dimensional proportional loading (load applied to both axes). The four beams were supported at the same distance, so loads were applied to both axes in a symmetric pattern. This test is referred to from now on in this paper as three-dimensional loading. The test was only carried out in the elastic range behaviour of the joints, under force control. Initially, joints were loaded up to a small degree and partially unloaded, to suppress slipping and to allow the different parts to settle and adjust. Subsequently, joints were loaded up to the start of their non-elastic behaviour and unloaded afterwards. This complete loading cycle (comprising both loading and unloading) was repeated twice. After the three-dimensional test, different tests were conducted for both individual axes submitted to in-plane loading (bi-dimensional tests). The non-tested joints remained fastened to the column. The minor-axis joints were loaded first,
followed by the major-axis joints. In both cases, the testing procedure was the same: • Joints were loaded (after initial preloading allowing for settlement) up to 2/3M j.Rd (which corresponds to the theoretical elastic limit according to Eurocode 3 [4]), where M j.Rd is the full plastic moment resistance of the joint. After unloading, joints were loaded up again to this same load degree twice. This first part of the tests was carried out under force control. The maximum load was kept for 30 s to record quasi-static forces in the joint. • In a second phase, the joints were tested until failure occurred. The test control was changed to displacement control. 3. Test results The results presented in the following sections relate mostly to the second phase of the tests, involving controlled displacement. The first, elastic phase, only gives the elastic rotational stiffness. The plotted graphs refer to the applied load, displacement and strain direct readings and to the corresponding bending moments and deformations. 3.1. Preliminary concepts 3.1.1. Bending moment The bending moment, M, acting on the connection corresponds to the reaction force, Ri , multiplied by the distance between the load application point and the face of the end plate, L load (Fig. 4): M = Ri × L load .
(1)
3.1.2. Joint rotation The rotational deformation of the joint, φ, is quantified in three different ways, according to the measurements taken (Fig. 4): • By beam and column vertical displacements, shown as δh in Fig. 4. The total displacement at a point i, δi , is the sum of the displacement corresponding to the joint rotation δc , the beam elastic, δb , and shear, δv , deformations at that point: δi = δc,i + δb,i + δv,i .
(2)
The displacement related to the joint rotation is δc,i = δi − δb,i − δv,i ,
(3)
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The stiffness values are obtained by means of linear regression analysis of the quasi-linear branches before and after the knee-range. In particular, the corresponding final unloading portion of the M–φ curve (final step for the second complete loading cycle of the elastic-range tests) measured by the transducer located 500 mm from the end-plate face is used to determine S j.ini (as will be explained in Section 3.3). 3.1.4. Joint ductility The ductility of a joint is a property that reflects the length of the yield plateau of the M–φ response. This property can be quantified by means of an index, Ψ j , that relates the maximum rotation of the joint, φCd , to the rotation value corresponding to the joint’s plastic resistance, φ M Rd [25]:
Fig. 6. Moment–rotation curve characteristics.
Ψj =
and joint rotation is finally obtained as δc,i . (4) Li • By the same vertical displacement measurements (Fig. 4): the joint rotation may be also obtained by means of the resulting displacement difference between two of the measurement points, after suppressing both beam deformations: δi − δb,i − δv,i − (δ j − δb, j − δv, j ) . (5) θ2 = arctan Li − L j θ1 = arctan
• By the LVDTs located in the end-plate (δl , Fig. 4): θ3 = arctan
δl.t − δl.c . L c−t
(6)
Rotations θ1 and θ2 led to similar results, and were finally adopted, as will be shown in Section 3.3. The reliability of this method has been already proved in [23]. In the same section, it will be shown how the actual location of the sensors for θ3 leads to unreliable results. 3.1.3. Joint moment–rotation characteristics The M–φ curve of the connection may be characterised by using the aforementioned relationships. The main features of this curve are: moment resistance, rotational stiffness and rotation capacity. In particular, the following characteristics are assessed for the different tests [24], as drawn in Fig. 6: • the initial stiffness, S j.ini ; • the post-limit stiffness, S j. p−l ; • the plastic flexural resistance, M j.Rd , which corresponds to the intersection point of the previous two regression lines obtained for the initial (S j.ini ) and post-limit (S j. p−l ) stiffnesses; • the maximum bending moment, Mmax , and its corresponding rotation, φmax ; • the knee-range of the M–φ curve, which is defined as the transition zone between the initial and post-limit stiffnesses, with its lower boundary at Minf K −R and rotation φinf K −R , and its upper limit at Msup K −R and rotation φsup K −R ; • and the rotation capacity, φCd .
φCd . φ M Rd
(7)
Other authors [26,27] propose to define ductility as the difference between the rotation value corresponding to the joint plastic resistance, φ M Rd , and the total rotation capacity, φCd (Fig. 6). Both indexes are evaluated in this paper. Since the experimental value of the joint’s plastic resistance is not easily assessed [25], two different resistance levels are taken into account: the lower and upper boundaries for the knee-range of the M–φ curve, corresponding to φinf K −R and φsup K −R , respectively. Eurocode 3 [4] gives quantitative rules to predict joint flexural plastic resistance and initial rotational stiffness. These structural properties are evaluated below using the geometric and mechanical nominal properties. An alternative stiffness formulation presented in [5] will also be evaluated. 3.2. Moment–rotation curves As explained above, the M–φ curves for the several connections are obtained from the beam or end-plate displacement readings and the applied load. In the case of the beam readings, beam deformations are excluded through application of Eqs. (3) and (5). Results for the three vertical displacement sensors, two of which are located in the beam (250 and 500 mm away from the end-plate face respectively) and one in the column, led to similar results. Fig. 7 shows the complete rotational behaviour obtained for each of the tested joints. Both stiffness and resistance decrease when the end-plate thickness is reduced. The thickness of the end-plate also affects the joint’s ductility: the thin end-plate joints exhibit a greater rotation capacity. Fig. 8 depicts the yielding sequence detected by the strain gauges for each of the individual tests. In the case of thin plates, the bending components (mainly the end-plate in the tension zone) are the weak components. It may be observed in Fig. 6 how in the case of the A-M test (major-axis thickplate), its stiffness decreases in three sudden steps. These are due to nut stripping. Bolt cracking caused the final collapse of the joint. Both phenomena involve brittle failure. Nut stripping was reported for most of the bolts on the tension side, as shown
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J.M. Cabrero, E. Bayo / Journal of Constructional Steel Research 63 (2007) 1241–1253 Table 5 In-plane loading Test ID
S j.ini
S j. p−l
S j.h
S j.l
A-M B-M
50 782.13 31 511.77
71 478.79 27 539.31
(+10 000) (+45 000)
3023.38 1055.69
A-n B-n
29 867.85 15 157.78
27 797.87 17 457.77
(+32 000) (+1000)
875.45 713.69
Initial stiffness (values in kN m/rad).
3.3. Initial stiffness
Fig. 7. Resulting moment–rotation behaviour for the tested joints (bidimensional loading).
in Fig. 10. These phenomena were not observed in the thick plate tests for the minor-axis joints. 3.2.1. Discussion on the moment–rotation curves Fig. 9 shows the application of the Frye and Morris polynomial model [28–30] for the tested joints. The model predicts less stiffness and resistance than experimentally observed. The differences seem reasonable, since tested connections are three-dimensional, and are thus additionally stiffened by means of the joint in the other axis.
Tables 5 and 6 present the resulting rotational stiffness values for each tested joint. As previously indicated, they correspond to the last unloading path in the elastic analysis for each of the joints. Results are shown for both measuring methods, S j.h and S j.l . S j.h corresponds to the previously explained rotations θ1 (4) and θ2 (5), according to the transducers that measure the beam and column vertical displacements. Both lead to similar results. The rotational stiffness values for each joint relate to the measure of the beam’s vertical displacements (in this paper, the given values correspond to those of the transducer located 500 mm away from the end-plate face). The same Table 5 also describes post-limit stiffness values.
(a) Major-axis thick-plate (A-M).
(b) Major-axis thin-plate (B-M).
(c) Minor-axis thick-plate (A-n).
(d) Minor-axis thin-plate (B-n).
Fig. 8. Yielding sequence for each of the joints tested. The strain gauge numbering refers to Fig. 5. Corresponding component and bolt-row are given between brackets.
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S j.ini S j.h
S j.l
A-M B-M
59 408.68 35 521.46
109 534.95 64 301.99
A-n B-n
32 294.94 18 674.62
64 752.02 24 308.70
Initial stiffness (values in kN m/rad).
(a) Major-axis tests.
beam and column displacements gave similar values for both joints. The LVDTs were located as close to the beam flange as permitted by the weldings. As shown in Fig. 13, the resulting deformations in the actual locations (slightly above and below of the flanges of the beam) are less than those occurring in the beam flanges. This fact explains in part the differences in stiffness measured by these sensors. Also, the variation on the stiffness values between the two symmetrical tested joints may be due to differences in the location of the sensors because of the weldings, and also to their possible slipping on the plates during loading. As shown in Table 6, both axis joints exhibit an increase of initial stiffness when they are subjected to three-dimensional proportional loading. Increased stiffness due to coupling effects between the joints located in both axes is thus observed. The stiffness increase for the major-axis joints is about 15%. In the case of the minor-axis joints, this ranges from 8% for joint A-n (thick end-plate) up to 23% for B-n (thin end-plate).
(b) Minor-axis tests. Fig. 9. Application of the Frye–Morris model [28–30] to the tested joints subjected to in-plane loading.
3.3.1. Discussion of the stiffness results. The initial rotational stiffness of the end-plate bolted joints is given by a mechanical model [4] composed of several springs, each one representing a component of the joint, assembled as follows: z S j.ini = P 1 . (8) i
Fig. 10. Major-axis joints. Bolts after joint failure.
S j.l corresponds to the rotation θ3 (6), measured by the LVDTs located in the end-plate. In regard to these latter values, the difference in stiffness between the two tested joints (measured by the LVDTs located in the end plate) is given as an additional value between brackets. These variations are of great importance in most cases, while the results according to the
ki
The lever arm z is taken to be equal to the distance from the centre of compression to a point midway between the two bolt rows in tension and ki is the stiffness coefficient for joint component i. For the double-sided major-axis beam-to-column joints, the stiffness coefficients to be taken into account are those related to the column web in shear (kcws ) and in transverse compression (kcwc ), and an equivalent stiffness coefficient keq that represents the basic components related to the bolt rows in tension. The latter coefficient is based on the stiffness coefficients for the column web in tension, the column flange in bending, the end-plate in bending and the bolts in tension. Although all these components are given in Eurocode 3 [4], some minor modifications must be made to include the additional stiffening provided by the additional plate welded to the column flanges. Currently available analytical methods should consequently underestimate the major-axis response. Table 7 sets up the predicted values for the major-axis joints’ initial stiffness and compares them with the experiments.
J.M. Cabrero, E. Bayo / Journal of Constructional Steel Research 63 (2007) 1241–1253 Table 7 In-plane loading Test ID Experimental
A-M 50 782.13
B-M 31 511.77
Eurocode [4] Error
67 041.22 32.02%
42 065.04 33.49%
Faella et al. [5] Error
40 573.10 −20.10%
26 701.52 −15.26%
Comparison between the experimental and theoretical stiffness characteristics (values in kN m/rad). Table 8 In-plane loading Test ID
Knee-range Minf K −R
Msup K −R
A-M B-M
140.37 70.97
A-n B-n
62.20 41.65
M j.Rd
Mmax
179.22 96.49
167.77 93.24
223.08 171.50
89.65 60.66
78.49 55.23
109.77 95.78
Experimental resistance characteristics (values in kN m).
Eurocode [4] predicts stiffer joints. This overestimation has also been reported in [25] when testing joints with stiff columns. The alternative stiffness formulation proposed in [5] (which mainly changes the T-stub model for the end-plate and column flange in bending) underestimates the stiffness. However, this theoretical value seems to be more appropriate, as the analytical components still do not take into account the additional stiffening provided by the additional plate welded to both column flanges. In the case of the minor-axis beam-to-column joints, a similar spring model can be obtained. While some of the components have already been developed and presented in Eurocode [4], others are not yet available. Even though some proposals have been made [15,16,31,32] for minor-axis joints, they only apply when joints are directly bolted to the column web, so none of them may be applied in this case. No prediction for the stiffness can then be obtained for the minor-axis joints, due to the lack of required components. A new model for both major and minor axis joints, also accounting for three-dimensional loading effects, will be proposed in the second part of this paper. 3.4. Plastic flexural resistance Tests with three-dimensional loading (in both axes) were performed just in the elastic range, so the experimental values presented herein only correspond to the joints subjected to inplane loading (bi-dimensional loading). The experimental value for the moment resistance of the joint, M j.Rd , is obtained as the intersection point between the two regression lines obtained for the initial, S j.ini , and postlimit, S j. p−l , stiffnesses. Two additional resistance values are also indicated, those corresponding to the beginning (Minf K R ) and end (Msup K ) of the knee-range behaviour (Fig. 6). All R these values are given in Table 8.
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3.4.1. Discussion on resistance results Eurocode [4] lacks components to obtain the resistance of the tested joints. But as the collapse was mainly due to the end-plate failure in the tension zone, the analytical end-plate resistance can be compared to the experimental joint resistance. End-plate flexural resistance is evaluated as follows: Mep.Rd =
2 X
h r Fep.Rd
(9)
r =1
where h r is the distance of the r -th bolt-row from the centre of compression, and Fep.Rd is the effective tension resistance of the end-plate of bolt row r . The end-plate model relies on the T-stub idealisation, which can fail according to three possible plastic collapse mechanisms: Type-1 is characterised by complete flange yielding, Type-2 corresponds to bolt failure with flange yielding, and Type-3 involves only bolt failure. Applying this procedure provides the results presented in Table 9. When comparing the theoretical predictions with the experiments, they show values below the experimental values. Most of them are close to the lower limit of the knee-range. The same Table 9 also presents the results provided by the method proposed by Murray et al. [33,34]. This model predicts around 30% less resistance for the thin plate tests. Slightly better agreement is observed for the thick plate connections. Both methods also provide predictions for the type of failure of the end-plate. They lead to similar results, and show a good agreement with the experimental behaviour. Thin plate joints fail due to end-plate yielding. Thick-plate joints fail according to a mixed failure involving both end-plate yielding and bolt fracture. 3.5. Rotation capacity The experimental values for the rotation capacity and the corresponding ductility indices for the various tests are presented in Tables 10 and 11. Tests with thin plates present higher ductility. The different rotation capacity is due to the different failure mechanism type produced for the end-plate: in the case of thin plates, failure follows a Type-1 mechanism, which shows very high ductility. The tests with thick plates fail according to Type-2, which includes the brittle bolt failure. 4. Behaviour of the plates in bending 4.1. End-plate deformation behaviour One of the most significant characteristics describing the overall behaviour of the extended end-plate joints is related to the end-plate deformation. Different end-plate behaviours are observed when thin and thick end-plate joints are compared. Accordingly, their different failure mechanisms are shown in Figs. 11 and 12. The resulting deformation for the thin plates clearly relates to the theoretical yield line pattern for Type-1 mechanism. Deformations are greater for the tension side. Little deformation is noticed in the compression side, as shown
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Table 9 In-plane loading Eurocode [4] Test ID
A-M
B-M
A-n
93.24
B-n
Experimental
167.77
Eurocode [4] Type of failure
126.00 epb (m1)-epb (m2)
65.79 epb (m1)-epb (m1)
83.97 epb (m1)-epb (m2)
78.49
43.56 epb (m1)-epb (m1)
55.23
Error M j.Rd Error Minf K −R Error Msup K −R
−24.90% −10.23% −29.69%
−29.44% −7.30% −31.82%
6.98% 35.00% −6.33%
−21.13% 4.59% −28.19%
Murray et al. [33,34] Experimental
167.77
93.24
78.49
55.23
Murray et al. [33,34] Type of failure
169.47 C
62.94
39.70
A
99.54 B
A
Error M j.Rd Error Minf K −R Error Msup K −R
1.01% 20.73% −5.44%
−32.50% −11.31% −34.77%
26.82% 60.03% 11.04%
−28.12% −4.68% −34.55%
Legend for the types of failure (Eurocode): epb (m1) End plate in bending, type 1 (end plate yielding). epb (m2) End plate in bending, type 2 (mixed failure with plate yielding and fracture of the bolts). The two predictions indicated for each test account for the first and the second bolt-rows in the following way: pred. for 1st bolt row-pred. for 2nd bolt row. Legend for the types of failure (Murray et al.): A Thin plate behaviour controlled by end plate yielding (Eurocode’s Type 1). B Thin plate behaviour controlled by bolt rupture (w/prying action) (Eurocode’s Type 2). C Thick plate with behaviour controlled by bolt rupture (no prying action) (Eurocode’s Type 3). Comparison between the experimental and theoretical resistance characteristics (values in kN m). Table 10 In-plane loading Test ID
φinf K −R (m rad)
A-M B-M
3.71 3.01
A-n B-n
3.90 3.24
φ Mmax (m rad)
φCd (m rad)
8.83 8.30
25.70 96.30
41.58 96.30
11.04 11.06
31.36 68.00
33.85 68.00
φsup K −R (m rad)
to “follow” the end-plate deformation, rather than restraining it (the restriction due to this second bolt row is hardly appreciated in the end-plate deformation). This is consistent with the Type-2 mechanism reported for the thick plates. In both series, the lever arm seems to comprise the distance between the axis of the beam flange under tension (maximum deformation) and the lower bolt-row, since no deformation originates below this point.
Experimental rotations.
4.2. Additional plate deformation behaviour
Table 11 In-plane loading
The additional plate’s deformation behaviour in the tension zone was measured using a linear transducer in the minoraxis and three-dimensional tests. As pointed out in Fig. 14, its stiffness increases when both axes are loaded. This increase results in stiffer behaviour in the minor axis joints, as shown in Section 3.3. The additional plates in the tension and compression zones behave in different ways, as demonstrated by their resulting deformation (Fig. 15(a)). The plate in the tension zone behaves as a laterally pinned plate, as proved by the single curvature of its resulting deformation (Fig. 15(b)). The restraining effect of the welds may be assumed to be pinned. By contrast, in the compression zone, an additional restriction is provided by the column flanges: the plate may be assumed to act as though it was laterally clamped.
Joint
Ψinf K −R
Ψsup K −R
dinf K −R (m rad)
dsup K −R (m rad)
A-M B-M
6.93 31.97
2.91 11.60
37.87 93.28
32.75 87.99
A-n B-n
8.04 20.97
2.84 6.15
29.95 64.76
22.81 56.94
Ductility assessment.
in Fig. 13 for major-axis joints. The deformability of the end-plate increases for smaller values of tep . This effect was already noticed in the moment–rotation behaviour, since the components’ end-plate and bolts are the main sources of connection deformability. The restraining effect of the second bolt row is clear in the tension side of the thin plate (Fig. 13(a)). In the thick plates (Fig. 13(b)), bolts are submitted to greater tension forces, resulting in greater elongations. As a consequence, bolts seem
5. Conclusions This paper presented an experimental programme on extended end-plate beam-to-column symmetrically loaded
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(a) Thin plate specimen. Tension end-plate and additional plate deformation.
(b) Thick plate specimen. General view.
(c) Thin plate specimen. Tension end-plate deformation.
(a) Thin plate specimen. General view.
(b) Thick plate specimen. General view.
(c) Thin plate specimen. End-plate deformation in the tension zone.
(d) Thick plate specimen. Tension zone (notice the lower bolt cracking and the upper bolt nut stripping).
Fig. 12. Major-axis joints failure.
3.
4.
5. (d) Thick plate. Deformation of the additional plate in the tension zone. Fig. 11. Minor-axis joints’ failure.
6. joints in both major and minor axes under bi- and threedimensional proportional loading carried out at the University of Navarra, Spain. The main conclusions of this investigation are: 1. Both the moment resistance and the rotational stiffness of the joint increase when the thickness of the end-plate is also increased. 2. Eurocode 3 [4] overestimates the rotational stiffness of the tested major axis joints when compared with experimental
results. The alternative proposal in [5] seems to obtain better agreement. Eurocode 3 [4] proposals give safe approaches for predicting joint resistance. The predictions underestimate the resistance in these particular cases. Special attention should be given to the nut stripping behaviour observed in the major axis thick plate tests, as this is a brittle failure. The initial rotational stiffness results for all tests indicate that three-dimensional proportional loading (load in both axes) significantly affects the joint structural behaviour. The initial stiffness increases for this loading arrangement. In the case of the minor axis joints, additional stiffening may be related to the additional plate’s reported stiffer behaviour. Analytical models for these joints are required. Additional components to those presented in Eurocode [4] are also needed. Models should provide an effective way to include the three-dimensional reported effects.
The experimental investigation presented in this paper provides a first insight into the semi-rigid behaviour of threedimensional joints subjected to proportional loading. More experimental investigation is required to fully assess this behaviour. The second part of this paper presents appropriate analytical models that have been developed for this purpose.
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(a) Thin plate (B).
(a) General view. Column is shown downwards, so the tension zone is located below, and the compression zone above.
(b) Thick plate (A). Fig. 13. Major axis joints. Remaining deformation on end-plate.
(b) Detail of the additional plate deformation in the tension zone. Fig. 15. Additional plate deformation.
References
Fig. 14. Additional plate force–deformation behaviour.
Acknowledgements The support given to this work by the Arcelor Chair of the University of Navarra is greatly acknowledged. The Alumni Navarrenses association and the Spanish Science and Education Ministry are also gratefully acknowledged for providing sponsorship to the first author. The assistance provided by the staff at the University of Navarra School of Architecture Laboratory in making the test specimens available and their support in conducting the tests is most appreciated.
[1] Zoetemeijer P. Summary of the research on bolted beam-to-column connections (period 1978–1983). Tech. rep. 6-85-M. Delft: Steven Laboratory; 1983. [2] Yee YL, Melchers RE. Moment–rotation curves for bolted connections. Journal of Structural Engineering ASCE 1986;112(3):615–35. [3] Jaspart JP. Etude de la Semi-Rigidite des Noeuds Poutre-Colonne et son Influence sur la Resistance et la Stabilite des Ossatures in Acier. Ph.D. thesis. University of Liege; 1991. [4] CEN, Eurocode 3: Design of steel structures. Part 1.8: Design of Joints (EN 1993-1-8:2005). 2005. [5] Faella C, Piluso V, Rizzano G. Structural steel semirigid connections: Theory, design and software. In: New directions in civil engineering. Boca Raton (Florida): CRC Publishers; 2000. [6] Chen W. Practical analysis for semi-rigid frame design. Singapore: World Scientific; 2000. [7] Chen W, Goto Y, Liew JR. Stability design of semi-rigid frames. John Wiley & sons, Inc.; 1996. [8] Chen W, Toma S. Advanced analysis of steel frames: Theory, software and applications. In: New directions in civil engineering. CRC Press, Inc.; 1994. [9] Chen W, Lorens R, Kato B. Semi-rigid connections in steel frames. McGraw-Hill, Inc.; 1993. [10] Krishnamurthy N. Fresh look at bolted end-plate behaviour and design. Engineering Journal AISC 1978;2(15):39–49. [11] Krishnamurthy N, Huang H, Jeffrey P, Avery L. Analytical moment–rotation curves for end-plate connections. Journal of the Structural Division ASCE 1979;105:133–45.
J.M. Cabrero, E. Bayo / Journal of Constructional Steel Research 63 (2007) 1241–1253 [12] Aggarwal AK. Comparative tests on endplate beam-to-column connections. Journal of Constructional Steel Research 1994;30(2):151–75. [13] Cruz PJS, Sim˜oes da Silva LAP, Rodrigues DS, Sim˜oes RAD. Database for the semi-rigid behaviour of beam-to-column connections in seismic regions. Journal of Constructional Steel Research 1998;46(1–3):233–4. [14] de Lima LRO, de Andrade SAL, da S Vellasco PCG. Bolted semirigid connections in the column’s minor axis. In: Studnicka J, Wald F, Machacek J, editors. Proceedings of the Eurosteel’99 conference. Prague: Czech Technical University in Prague; 1999. p. 473–6. [15] de Lima LRO, de Andrade SAL, da S Vellasco PCG, da Silva LS. Experimental and mechanical model for predicting the behaviour of minor axis beam-to-column semi-rigid joints. International Journal of Mechanical Sciences 2002;44:1047–65. [16] da Costa Neves LF. Comportamento monot´onico e c´ıclico de ligac¸oes de exixo fraco e tubulares em estruturas met´alicas e mistas ac¸o-bet˜ao. Ph.D. thesis. Civil Engineering Department, Science and Technology Faculty, University of Coimbra; 2004. [17] Gibbons C, Kirby P, Nethercot DA. Experimental behaviour of 3-D column subassemblages with semi-rigid joints. Journal of Constructional Research 1991;19:235–46. [18] Janss J, Jaspart J-P, Maquoi R. Strength and behaviour of in plane weak axis joints and 3-D joints. In: Connections in steel structures: Behaviour, strength and design. Elsevier; 1988. p. 60–8. [19] V´ertes K, Iv´anyi M. Investigation of minor axis and 3d bolted end-plate connections – experimental and numerical analysis – load tests. Periodica Polytechnica Ser. Mechanical Engineering 2005;49(1):47–58. [20] CEN, Eurocode 3: Design of Steel Structures. Part 1.7: Strength and stability of planar plated structures to out of plane loading (prEN 1993-17). 2005. [21] UNE, UNE-EN 10034:1994. Perfiles I y H de acero estructural. Tolerancias dimensionales y de forma. (Versi´on oficial EN 10034:1993). AENOR; 1994. [22] UNE-EN 10002-1: Materiales met´alicos. Ensayos de tracci´on. Parte 1: M´etodo de ensayo a temperatura ambiente. july 2002 Edition, AENOR; 2002.
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[23] Aribert J-M, Braham M, Lachal A. Testing of simple joints and their characterisation for structural analysis. Journal of Constructional Steel Research 2004;60:659–81. [24] Gir˜ao Coelho AM, Sim˜oes da Silva L, Bijlaard FSK. Ductility analysis of bolted extended end-plate beam-to-column connections. In: The third international conference on steel & composite structures. 2004. [25] Gir˜ao Coelho AM, Bijlaard FSK, Sim˜oes da Silva L. Experimental assesment of the ductility of extended end plate connections. Engineering Structures 2004;26:1185–206. [26] Schleich JB, Chantrain P, Chabrolin B, Gal´ea Y, Bureau A, Anza J et al. Promotion of plastic design for steel and composite cross sections: New required conditions in Eurocodes 3 and 4, practical tools for designers. European commission; 1998. [27] Gil B, Cabrero JM, Go˜ni R, Bayo E. An assessment of the rotation capacity required by structural hollow sections for plastic analysis. In: Jaurrieta MA, Alonso A, Chica JA, editors. Tubular structures X. Lisse (Holland): A.A. Balkema Publishers; 2003. p. 277–92. [28] Frye J, Morris G. Analysis of flexibly connected steel frames. Canadian Journal of Civil Engineering 1975;(2):280–91. [29] Kishi N. PR connection database. In: Practical analysis for semi-rigid frame design. Singapour: World Scientific; 2000. p. 261–323. [30] Kishi N. Semi-rigid connections. In: New directions in civil engineering. Advanced analysis of steel frames, CRC Press; 1994. p. 91–138. [31] Costa Neves L, Sim˜oes da Silva L, da S Vellasco PCG. A model for predicting the stiffness of beam to concrete filled column and minor axis joints under static monotonic loading. In: Hoffmeister B, Hechler O, editors. Eurosteel 2005: 4th European conference on steel and composite structures, vol. C. Maastricht: Verlag Mainz; 2005. p. 4.10-131–4.10-138. [32] Silva LAP, Neves LFN, Gomes F. Rotational stiffness of rectangular hollow sections composite joints. Journal of Structural Engineering ASCE 2003;129(4):487–94. [33] Murray T, Shoemaker WL. Flush and extended multiple row: Moment end-plate connections. Steel design guide series, Chicago (USA): American Institute of Steel Construction; 2002. [34] Murray T, Sumner E. Extended end-plate moment connections. 2nd ed. Steel design guide, vol. 4. American Institute of Steel Construction; 2004.
The semi-rigid behaviour of three-dimensional steel beam-to-column joints subjected to proportional loading. Part I. Experimental evaluation J.M. Cabrero ∗ , E. Bayo Department of Structural Analysis and Design, School of Architecture, University of Navarra, 31080 Pamplona, Spain Received 29 June 2006; accepted 8 November 2006
Abstract An experimental investigation of statically loaded extended end-plate connections in both major and minor column axes was undertaken at the University of Navarra, Spain. The aim was to provide insight into the behaviour of these joints when a proportional load is applied to both axes (three-dimensional loading). The rotational stiffness of the joints increases with this type of three-dimensional loading. The findings also show that an increase in the end-plate thickness results in an increase in the connection’s flexural strength and stiffness, and a decrease in its rotation capacity. c 2006 Elsevier Ltd. All rights reserved.
Keywords: End plate connections; Major axis connections; Minor axis connections; Three-dimensional behaviour; Experimental testing; Resistance; Stiffness; Rotation capacity; Steel connections
1. Introduction It is currently recognised that a great majority of joints exhibit a rather different behaviour than that idealised as rigid or pinned. Extensive investigation of the behaviour of such semi-rigid joints in the major axis has been carried out. Works by Zoetemeijer [1], Yee and Melchers [2] and Jaspart [3] constitute the basis for the current component method proposed by Eurocode 3 [4] for the analysis of joints. Faella, Pilusso and Rizzano proposed several modifications to this method [5]. The works headed by Chen [6–9] are also a major source regarding experimental results of semirigid joints and reference advanced analysis methods for semirigid frames. Works by Aggarwal and Krishnamurthy [10, 11] are also a major reference for experimental results and analytical models for extended end-plate joints [12]. Another source for experimental results is the database compiled by Cruz, Sim˜oes da Silva, Rodrigues and Sim˜oes [13]. Less effort has been dedicated to analysing the behaviour of minoraxis joints and to proposing adequate analytical models. Lima and Andrade tested several angle joints and proposed a ∗ Corresponding author. Tel.: +34 948425600x2704; fax: +34 948425629.
E-mail addresses: [email protected] (J.M. Cabrero), [email protected] (E. Bayo). c 2006 Elsevier Ltd. All rights reserved. 0143-974X/$ - see front matter doi:10.1016/j.jcsr.2006.11.004
corresponding analytical model [14,15]; Costa Neves carried out an experimental programme on extended end-plate joints bolted to the column’s web and proposed an analytical model for both stiffness and resistance[16]. Plane joints subjected to in-plane loading have constituted the most studied configuration. Few references are available accounting for three-dimensional out-of-plane behaviour with joints in both axes. Gibbons, Kirby and Nethercot tested several type of joints in three-dimensional frames [17]. Janss, Jaspart and Maquoi also reported tests for three-dimensional and minor axis joints [18]. Recently, V´ertes and Iv´anyi [19] ran a test program on three-dimensional joints and proposed an analytical model based on the plate formula developed in Eurocode 3 [20]. This paper presents the experimental programme carried out at the University of Navarra, Spain, on a new proposal for a three-dimensional semi-rigid steel joint. Proportional loading was applied in two different arrangements: to the joint axis (bi-dimensional or in-plane loading) or to both axes (threedimensional loading). The proposed three-dimensional joint configuration is presented in Fig. 1. It consists of extended end-plate joints for both major and minor axes. The minor-axis joints are not bolted to the column web, but to an additional plate welded to the column flanges (see Fig. 2). By virtue of this additional plate, the corresponding minor-axis beams do not get into the column
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Nomenclature
S j.h
Greek letters
S j.ini S j.l
δb δc δv δh.i δl.c δl.t u y rem φ φCd φinf K −R φsup K −R Ψj Ψinf K −R
Ψsup K −R ρy θi
beam elastic displacement displacement corresponding to joint rotation beam elastic shear deformation vertical displacement measured at point i horizontal deformation of the end-plate at the compression zone horizontal deformation of the end-plate at the tension zone ultimate strain strain at the yield point remaining strain rotational deformation of the joint rotation capacity rotation at the lower resistance bound of the kneerange of the joint moment–rotation curve rotation at the upper resistance bound of the knee-range of the joint moment–rotation curve joint ductility index ductility index evaluated at the lower bound of the knee-range of the joint moment–rotation curve ductility index evaluated at the upper bound of the knee-range of the joint moment–rotation curve yield ratio joint rotation
Upper cases effective tension resistance of the end-plate of bolt-row r Hc.low clearance of the column below the end-plates Hc.mid clearance of the column between the minor-axis end-plates Hc.up clearance of the column above the end-plate Li distance between the point i and the end-plate face L beam length of the beam L c−t distance between the transducers located in the end-plate at the tension and compression zones L load distance between the load application point and the face of the end-plate M bending moment Mep.Rd flexural resistance of the end-plate Minf K −R lower resistance bound of the knee-range of the joint moment–rotation curve M j.Rd joint flexural resistance Mmax maximum bending moment Msup K −R upper resistance bound of the knee-range of the joint moment–rotation curve Q total load applied Ri reaction force at support i Fep.Rd
S j. p−l
initial joint rotational stiffness measured according to the beam vertical displacement initial joint rotational stiffness initial joint rotational stiffness measured according to the end-plate deformation post-limit joint rotational stiffness
Lower cases bb bc bep dinf K −R
dsup K −R e ex fu fy f cd hb hc hr h ep ki p p2−3 tep tfb tfc twb w z
beam section width column section width end-plate width rotation comprised between the lower bound of the knee-range of the joint moment–rotation curve and the rotation capacity rotation comprised between the upper bound of the knee-range of the joint moment–rotation curve and the rotation capacity edge distance lateral edge distance ultimate or tensile stress yield stress tensile stress at failure beam section height column section height distance from the bolt-row r to the centre of compression end-plate height stiffness coefficient for component i pitch of the tension bolts distance between the tension bolt-row 2 and the compression bolt-row 3 end-plate thickness beam flange thickness column flange thickness beam web thickness gauge of the bolts lever arm
and the joints do not hinder each other, so they may be designed individually. This plate also acts as a stiffener for the joint in the major axis. The end-plate of the proposed and tested minor-axis joints consists of two partial end-plates. The remaining gap is required for practical reasons, to access and tighten the bolts properly. These end-plates could be executed as a single end-plate extended on both sides if the column size were big enough to allow for those operations from the upper or the lower side of the joint. 2. Description of the experimental program 2.1. Test details The experimental programme essentially comprised two test details on the joint configuration shown in Fig. 1. The
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Fig. 1. Proposed three-dimensional semi-rigid joint. (a) Major-axis joint.
(b) Minor-axis joint.
Fig. 2. Additional plate welded to the column flanges.
specimens were fabricated from a set of two major- and minoraxis joints, as shown in detail in Table 1 and Fig. 3. One main parameter was varied: the end-plate thickness, tep —A series corresponds to a thick plate (tep = 16 mm), while B series to a thin plate (tep = 10 mm)—. The chosen steel grade for plates and sections was S275. Hand tightened full-threaded grade 8.8 M20 bolts in 22 mm drilled holes were used in all the sets. The column had a section profile HEB160. In addition, due to the loading procedure, the clearances above (Hc.up ) and below (Hc.low ) of the end-plate were close to 150 mm. All specimens were designed to comply with Eurocode 3 requirements [4], so that the component endplate and bolts in the tension zone were the determining factors for the failure.
(c) Complete test arrangement. Fig. 3. General test detail. Table 1 Test details Series
Column
Minor-axis beam
Major-axis beam
Bolt
tep
A B
HEB 160 HEB 160
IPE 240 IPE 240
IPE 330 IPE 330
TR 20 TR 20
16 10
2.2. Geometrical properties The actual geometry of the connection elements was recorded before starting the test. The actual dimensions of
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Table 2 Actual geometry of the connection (dimensions in mm, referred to those indicated in Fig. 3) Column profile Test ID
hc
bc
tfc
Hc.up
Hc.mid
Hc.low
A B
160.80 158.20
159.00 159.50
12.30 12.30
153.50 150.00
76.50 78.50
146.50 150.00
Test ID
hb
bb
tfb
twb
L beam
L load
Major axis
A-M B-M
329.63 329.75
161.84 161.90
11.44 11.41
7.52 7.38
1247.75 1248.75
948.00 949.50
Minor axis
A-n B-n
241.60 241.04
119.30 120.21
9.51 9.71
6.08 6.23
1248.00 1249.25
947.00 949.50
Beam profile
End-plate and connection geometry Test ID
h ep
bep
tep
e
w
ex
p
p2−3
Major axis
A-M B-M
409.75 408.50
161.50 159.50
16.55 10.10
29.65 28.83
99.04 97.98
31.79 31.81
89.66 89.21
228.41 227.81
Minor axis
A-n B-n
150.38 150.67
142.00 141.50
16.35 10.10
30.64 31.03
79.33 77.95
31.83 32.00
89.81 89.55
– –
Table 3 Average characteristic values for the structural steel
Table 4 Average characteristic values for the bolts
Specimen Steel grade
End-plate S275
Beam S275
f y (MPa) f u (MPa) f cd (MPa)
383.12 521.00 340.20
357.82 499.10 248.57
5.32 23.28 33.35 18.00
4.00 46.76 62.56 36.29
y max u rem ρ
0.735
0.717
the profiles, plates and connection geometry are summarised in Table 2. These values correspond to the average of the different measurements for each series. There was not a large scattering for geometrical measurements. Actual dimensions met the requirements according to the standard UNE-EN 10034:1994 [21]. 2.3. Mechanical properties 2.3.1. Tension tests on the structural steel The test programme included one steel grade for the endplates and sections: S275. The coupon tension test on the structural steel material was performed according to the appropriate UNE procedures [22]. The average characteristics are set out in Table 3. The Table gives the values for the static yield and tensile stresses, f y and f u , the stress at failure, f cd , the yield ratio, ρ y = f y / f u , the strain at the yield point, y , the maximum strain, max , the ultimate strain, u , and the remaining strain after the test, rem . 2.3.2. Tension tests on the bolts Two machined bolts were tested under tension in order to determine the mechanical properties of the bolt material,
Steel grade
8.8
f y (MPa) f u (MPa) f cd (MPa)
793.75 879.60 438.08
y max cd rem ρ
25.99 34.43 43.75 20.74 0.902
in accordance with UNE-EN 10002-1 [22]. The average properties are shown in Table 4. 2.4. Test arrangement and instrumentation The actual connections were rotated downwards for practical reasons. The load was applied to the upper-side of the column by a 400 kN testing machine (hydraulic jack with maximum piston stroke of 200 mm). The beams were pinned supported at a distance of 950 mm to the end-plate face. In order to prevent lateral torsional buckling of the beam while loading, a beam guidance device near the support had to be provided. The instrumentation plan is described in Figs. 4 and 5. The primary requirements of the instrumentation were measuring the applied load and the relevant displacements of the connection (e.g. the vertical displacement of the beam, the horizontal displacement of the end-plate). The displacements were measured by means of linear variable displacement transducers (LVDTs, shown as δl in Fig. 4, which accounted for total deformation of the end-plate and the column flange), and linear position transducers (δh ) located as indicated in Fig. 4 (which recorded the vertical displacements of the beams).
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Fig. 5. Joints instrumentation plan.
Fig. 4. General instrumentation plan adopted for each beam.
Strain gauges (maximum strain ±2%) were added to the endplate (front side) and to the column as shown in Fig. 5 to provide insight into the strain distribution. Total applied loads (Q) were obtained directly from the hydraulic jack. Reactions (Ri ) were measured by load-cells located at the beam supports. 2.5. Testing procedure The dimensions of the plates were recorded before installing the specimens into the testing rig. The bolts were handtightened up to a torque value of 165 N m (approximately 30% of the total torque value for preloaded bolts) to simulate the snug-tight condition. The specimens were then placed and aligned. The measurement devices and strain gauges were then connected. Electronic recording started and all the equipment was verified. The specimens were subjected to monotonic force, which was applied to the column as explained previously (load is indicated as Q in Fig. 4). The joints were tested with load applied either along one or along both axes. The aim of the tests was to characterise the joints’ behaviour, and to verify whether or not there were coupling effects between the joints in the minor and major axes when submitted to proportional loading. First, the assembly was tested with three-dimensional proportional loading (load applied to both axes). The four beams were supported at the same distance, so loads were applied to both axes in a symmetric pattern. This test is referred to from now on in this paper as three-dimensional loading. The test was only carried out in the elastic range behaviour of the joints, under force control. Initially, joints were loaded up to a small degree and partially unloaded, to suppress slipping and to allow the different parts to settle and adjust. Subsequently, joints were loaded up to the start of their non-elastic behaviour and unloaded afterwards. This complete loading cycle (comprising both loading and unloading) was repeated twice. After the three-dimensional test, different tests were conducted for both individual axes submitted to in-plane loading (bi-dimensional tests). The non-tested joints remained fastened to the column. The minor-axis joints were loaded first,
followed by the major-axis joints. In both cases, the testing procedure was the same: • Joints were loaded (after initial preloading allowing for settlement) up to 2/3M j.Rd (which corresponds to the theoretical elastic limit according to Eurocode 3 [4]), where M j.Rd is the full plastic moment resistance of the joint. After unloading, joints were loaded up again to this same load degree twice. This first part of the tests was carried out under force control. The maximum load was kept for 30 s to record quasi-static forces in the joint. • In a second phase, the joints were tested until failure occurred. The test control was changed to displacement control. 3. Test results The results presented in the following sections relate mostly to the second phase of the tests, involving controlled displacement. The first, elastic phase, only gives the elastic rotational stiffness. The plotted graphs refer to the applied load, displacement and strain direct readings and to the corresponding bending moments and deformations. 3.1. Preliminary concepts 3.1.1. Bending moment The bending moment, M, acting on the connection corresponds to the reaction force, Ri , multiplied by the distance between the load application point and the face of the end plate, L load (Fig. 4): M = Ri × L load .
(1)
3.1.2. Joint rotation The rotational deformation of the joint, φ, is quantified in three different ways, according to the measurements taken (Fig. 4): • By beam and column vertical displacements, shown as δh in Fig. 4. The total displacement at a point i, δi , is the sum of the displacement corresponding to the joint rotation δc , the beam elastic, δb , and shear, δv , deformations at that point: δi = δc,i + δb,i + δv,i .
(2)
The displacement related to the joint rotation is δc,i = δi − δb,i − δv,i ,
(3)
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The stiffness values are obtained by means of linear regression analysis of the quasi-linear branches before and after the knee-range. In particular, the corresponding final unloading portion of the M–φ curve (final step for the second complete loading cycle of the elastic-range tests) measured by the transducer located 500 mm from the end-plate face is used to determine S j.ini (as will be explained in Section 3.3). 3.1.4. Joint ductility The ductility of a joint is a property that reflects the length of the yield plateau of the M–φ response. This property can be quantified by means of an index, Ψ j , that relates the maximum rotation of the joint, φCd , to the rotation value corresponding to the joint’s plastic resistance, φ M Rd [25]:
Fig. 6. Moment–rotation curve characteristics.
Ψj =
and joint rotation is finally obtained as δc,i . (4) Li • By the same vertical displacement measurements (Fig. 4): the joint rotation may be also obtained by means of the resulting displacement difference between two of the measurement points, after suppressing both beam deformations: δi − δb,i − δv,i − (δ j − δb, j − δv, j ) . (5) θ2 = arctan Li − L j θ1 = arctan
• By the LVDTs located in the end-plate (δl , Fig. 4): θ3 = arctan
δl.t − δl.c . L c−t
(6)
Rotations θ1 and θ2 led to similar results, and were finally adopted, as will be shown in Section 3.3. The reliability of this method has been already proved in [23]. In the same section, it will be shown how the actual location of the sensors for θ3 leads to unreliable results. 3.1.3. Joint moment–rotation characteristics The M–φ curve of the connection may be characterised by using the aforementioned relationships. The main features of this curve are: moment resistance, rotational stiffness and rotation capacity. In particular, the following characteristics are assessed for the different tests [24], as drawn in Fig. 6: • the initial stiffness, S j.ini ; • the post-limit stiffness, S j. p−l ; • the plastic flexural resistance, M j.Rd , which corresponds to the intersection point of the previous two regression lines obtained for the initial (S j.ini ) and post-limit (S j. p−l ) stiffnesses; • the maximum bending moment, Mmax , and its corresponding rotation, φmax ; • the knee-range of the M–φ curve, which is defined as the transition zone between the initial and post-limit stiffnesses, with its lower boundary at Minf K −R and rotation φinf K −R , and its upper limit at Msup K −R and rotation φsup K −R ; • and the rotation capacity, φCd .
φCd . φ M Rd
(7)
Other authors [26,27] propose to define ductility as the difference between the rotation value corresponding to the joint plastic resistance, φ M Rd , and the total rotation capacity, φCd (Fig. 6). Both indexes are evaluated in this paper. Since the experimental value of the joint’s plastic resistance is not easily assessed [25], two different resistance levels are taken into account: the lower and upper boundaries for the knee-range of the M–φ curve, corresponding to φinf K −R and φsup K −R , respectively. Eurocode 3 [4] gives quantitative rules to predict joint flexural plastic resistance and initial rotational stiffness. These structural properties are evaluated below using the geometric and mechanical nominal properties. An alternative stiffness formulation presented in [5] will also be evaluated. 3.2. Moment–rotation curves As explained above, the M–φ curves for the several connections are obtained from the beam or end-plate displacement readings and the applied load. In the case of the beam readings, beam deformations are excluded through application of Eqs. (3) and (5). Results for the three vertical displacement sensors, two of which are located in the beam (250 and 500 mm away from the end-plate face respectively) and one in the column, led to similar results. Fig. 7 shows the complete rotational behaviour obtained for each of the tested joints. Both stiffness and resistance decrease when the end-plate thickness is reduced. The thickness of the end-plate also affects the joint’s ductility: the thin end-plate joints exhibit a greater rotation capacity. Fig. 8 depicts the yielding sequence detected by the strain gauges for each of the individual tests. In the case of thin plates, the bending components (mainly the end-plate in the tension zone) are the weak components. It may be observed in Fig. 6 how in the case of the A-M test (major-axis thickplate), its stiffness decreases in three sudden steps. These are due to nut stripping. Bolt cracking caused the final collapse of the joint. Both phenomena involve brittle failure. Nut stripping was reported for most of the bolts on the tension side, as shown
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J.M. Cabrero, E. Bayo / Journal of Constructional Steel Research 63 (2007) 1241–1253 Table 5 In-plane loading Test ID
S j.ini
S j. p−l
S j.h
S j.l
A-M B-M
50 782.13 31 511.77
71 478.79 27 539.31
(+10 000) (+45 000)
3023.38 1055.69
A-n B-n
29 867.85 15 157.78
27 797.87 17 457.77
(+32 000) (+1000)
875.45 713.69
Initial stiffness (values in kN m/rad).
3.3. Initial stiffness
Fig. 7. Resulting moment–rotation behaviour for the tested joints (bidimensional loading).
in Fig. 10. These phenomena were not observed in the thick plate tests for the minor-axis joints. 3.2.1. Discussion on the moment–rotation curves Fig. 9 shows the application of the Frye and Morris polynomial model [28–30] for the tested joints. The model predicts less stiffness and resistance than experimentally observed. The differences seem reasonable, since tested connections are three-dimensional, and are thus additionally stiffened by means of the joint in the other axis.
Tables 5 and 6 present the resulting rotational stiffness values for each tested joint. As previously indicated, they correspond to the last unloading path in the elastic analysis for each of the joints. Results are shown for both measuring methods, S j.h and S j.l . S j.h corresponds to the previously explained rotations θ1 (4) and θ2 (5), according to the transducers that measure the beam and column vertical displacements. Both lead to similar results. The rotational stiffness values for each joint relate to the measure of the beam’s vertical displacements (in this paper, the given values correspond to those of the transducer located 500 mm away from the end-plate face). The same Table 5 also describes post-limit stiffness values.
(a) Major-axis thick-plate (A-M).
(b) Major-axis thin-plate (B-M).
(c) Minor-axis thick-plate (A-n).
(d) Minor-axis thin-plate (B-n).
Fig. 8. Yielding sequence for each of the joints tested. The strain gauge numbering refers to Fig. 5. Corresponding component and bolt-row are given between brackets.
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J.M. Cabrero, E. Bayo / Journal of Constructional Steel Research 63 (2007) 1241–1253 Table 6 Three-dimensional loading Test ID
S j.ini S j.h
S j.l
A-M B-M
59 408.68 35 521.46
109 534.95 64 301.99
A-n B-n
32 294.94 18 674.62
64 752.02 24 308.70
Initial stiffness (values in kN m/rad).
(a) Major-axis tests.
beam and column displacements gave similar values for both joints. The LVDTs were located as close to the beam flange as permitted by the weldings. As shown in Fig. 13, the resulting deformations in the actual locations (slightly above and below of the flanges of the beam) are less than those occurring in the beam flanges. This fact explains in part the differences in stiffness measured by these sensors. Also, the variation on the stiffness values between the two symmetrical tested joints may be due to differences in the location of the sensors because of the weldings, and also to their possible slipping on the plates during loading. As shown in Table 6, both axis joints exhibit an increase of initial stiffness when they are subjected to three-dimensional proportional loading. Increased stiffness due to coupling effects between the joints located in both axes is thus observed. The stiffness increase for the major-axis joints is about 15%. In the case of the minor-axis joints, this ranges from 8% for joint A-n (thick end-plate) up to 23% for B-n (thin end-plate).
(b) Minor-axis tests. Fig. 9. Application of the Frye–Morris model [28–30] to the tested joints subjected to in-plane loading.
3.3.1. Discussion of the stiffness results. The initial rotational stiffness of the end-plate bolted joints is given by a mechanical model [4] composed of several springs, each one representing a component of the joint, assembled as follows: z S j.ini = P 1 . (8) i
Fig. 10. Major-axis joints. Bolts after joint failure.
S j.l corresponds to the rotation θ3 (6), measured by the LVDTs located in the end-plate. In regard to these latter values, the difference in stiffness between the two tested joints (measured by the LVDTs located in the end plate) is given as an additional value between brackets. These variations are of great importance in most cases, while the results according to the
ki
The lever arm z is taken to be equal to the distance from the centre of compression to a point midway between the two bolt rows in tension and ki is the stiffness coefficient for joint component i. For the double-sided major-axis beam-to-column joints, the stiffness coefficients to be taken into account are those related to the column web in shear (kcws ) and in transverse compression (kcwc ), and an equivalent stiffness coefficient keq that represents the basic components related to the bolt rows in tension. The latter coefficient is based on the stiffness coefficients for the column web in tension, the column flange in bending, the end-plate in bending and the bolts in tension. Although all these components are given in Eurocode 3 [4], some minor modifications must be made to include the additional stiffening provided by the additional plate welded to the column flanges. Currently available analytical methods should consequently underestimate the major-axis response. Table 7 sets up the predicted values for the major-axis joints’ initial stiffness and compares them with the experiments.
J.M. Cabrero, E. Bayo / Journal of Constructional Steel Research 63 (2007) 1241–1253 Table 7 In-plane loading Test ID Experimental
A-M 50 782.13
B-M 31 511.77
Eurocode [4] Error
67 041.22 32.02%
42 065.04 33.49%
Faella et al. [5] Error
40 573.10 −20.10%
26 701.52 −15.26%
Comparison between the experimental and theoretical stiffness characteristics (values in kN m/rad). Table 8 In-plane loading Test ID
Knee-range Minf K −R
Msup K −R
A-M B-M
140.37 70.97
A-n B-n
62.20 41.65
M j.Rd
Mmax
179.22 96.49
167.77 93.24
223.08 171.50
89.65 60.66
78.49 55.23
109.77 95.78
Experimental resistance characteristics (values in kN m).
Eurocode [4] predicts stiffer joints. This overestimation has also been reported in [25] when testing joints with stiff columns. The alternative stiffness formulation proposed in [5] (which mainly changes the T-stub model for the end-plate and column flange in bending) underestimates the stiffness. However, this theoretical value seems to be more appropriate, as the analytical components still do not take into account the additional stiffening provided by the additional plate welded to both column flanges. In the case of the minor-axis beam-to-column joints, a similar spring model can be obtained. While some of the components have already been developed and presented in Eurocode [4], others are not yet available. Even though some proposals have been made [15,16,31,32] for minor-axis joints, they only apply when joints are directly bolted to the column web, so none of them may be applied in this case. No prediction for the stiffness can then be obtained for the minor-axis joints, due to the lack of required components. A new model for both major and minor axis joints, also accounting for three-dimensional loading effects, will be proposed in the second part of this paper. 3.4. Plastic flexural resistance Tests with three-dimensional loading (in both axes) were performed just in the elastic range, so the experimental values presented herein only correspond to the joints subjected to inplane loading (bi-dimensional loading). The experimental value for the moment resistance of the joint, M j.Rd , is obtained as the intersection point between the two regression lines obtained for the initial, S j.ini , and postlimit, S j. p−l , stiffnesses. Two additional resistance values are also indicated, those corresponding to the beginning (Minf K R ) and end (Msup K ) of the knee-range behaviour (Fig. 6). All R these values are given in Table 8.
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3.4.1. Discussion on resistance results Eurocode [4] lacks components to obtain the resistance of the tested joints. But as the collapse was mainly due to the end-plate failure in the tension zone, the analytical end-plate resistance can be compared to the experimental joint resistance. End-plate flexural resistance is evaluated as follows: Mep.Rd =
2 X
h r Fep.Rd
(9)
r =1
where h r is the distance of the r -th bolt-row from the centre of compression, and Fep.Rd is the effective tension resistance of the end-plate of bolt row r . The end-plate model relies on the T-stub idealisation, which can fail according to three possible plastic collapse mechanisms: Type-1 is characterised by complete flange yielding, Type-2 corresponds to bolt failure with flange yielding, and Type-3 involves only bolt failure. Applying this procedure provides the results presented in Table 9. When comparing the theoretical predictions with the experiments, they show values below the experimental values. Most of them are close to the lower limit of the knee-range. The same Table 9 also presents the results provided by the method proposed by Murray et al. [33,34]. This model predicts around 30% less resistance for the thin plate tests. Slightly better agreement is observed for the thick plate connections. Both methods also provide predictions for the type of failure of the end-plate. They lead to similar results, and show a good agreement with the experimental behaviour. Thin plate joints fail due to end-plate yielding. Thick-plate joints fail according to a mixed failure involving both end-plate yielding and bolt fracture. 3.5. Rotation capacity The experimental values for the rotation capacity and the corresponding ductility indices for the various tests are presented in Tables 10 and 11. Tests with thin plates present higher ductility. The different rotation capacity is due to the different failure mechanism type produced for the end-plate: in the case of thin plates, failure follows a Type-1 mechanism, which shows very high ductility. The tests with thick plates fail according to Type-2, which includes the brittle bolt failure. 4. Behaviour of the plates in bending 4.1. End-plate deformation behaviour One of the most significant characteristics describing the overall behaviour of the extended end-plate joints is related to the end-plate deformation. Different end-plate behaviours are observed when thin and thick end-plate joints are compared. Accordingly, their different failure mechanisms are shown in Figs. 11 and 12. The resulting deformation for the thin plates clearly relates to the theoretical yield line pattern for Type-1 mechanism. Deformations are greater for the tension side. Little deformation is noticed in the compression side, as shown
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Table 9 In-plane loading Eurocode [4] Test ID
A-M
B-M
A-n
93.24
B-n
Experimental
167.77
Eurocode [4] Type of failure
126.00 epb (m1)-epb (m2)
65.79 epb (m1)-epb (m1)
83.97 epb (m1)-epb (m2)
78.49
43.56 epb (m1)-epb (m1)
55.23
Error M j.Rd Error Minf K −R Error Msup K −R
−24.90% −10.23% −29.69%
−29.44% −7.30% −31.82%
6.98% 35.00% −6.33%
−21.13% 4.59% −28.19%
Murray et al. [33,34] Experimental
167.77
93.24
78.49
55.23
Murray et al. [33,34] Type of failure
169.47 C
62.94
39.70
A
99.54 B
A
Error M j.Rd Error Minf K −R Error Msup K −R
1.01% 20.73% −5.44%
−32.50% −11.31% −34.77%
26.82% 60.03% 11.04%
−28.12% −4.68% −34.55%
Legend for the types of failure (Eurocode): epb (m1) End plate in bending, type 1 (end plate yielding). epb (m2) End plate in bending, type 2 (mixed failure with plate yielding and fracture of the bolts). The two predictions indicated for each test account for the first and the second bolt-rows in the following way: pred. for 1st bolt row-pred. for 2nd bolt row. Legend for the types of failure (Murray et al.): A Thin plate behaviour controlled by end plate yielding (Eurocode’s Type 1). B Thin plate behaviour controlled by bolt rupture (w/prying action) (Eurocode’s Type 2). C Thick plate with behaviour controlled by bolt rupture (no prying action) (Eurocode’s Type 3). Comparison between the experimental and theoretical resistance characteristics (values in kN m). Table 10 In-plane loading Test ID
φinf K −R (m rad)
A-M B-M
3.71 3.01
A-n B-n
3.90 3.24
φ Mmax (m rad)
φCd (m rad)
8.83 8.30
25.70 96.30
41.58 96.30
11.04 11.06
31.36 68.00
33.85 68.00
φsup K −R (m rad)
to “follow” the end-plate deformation, rather than restraining it (the restriction due to this second bolt row is hardly appreciated in the end-plate deformation). This is consistent with the Type-2 mechanism reported for the thick plates. In both series, the lever arm seems to comprise the distance between the axis of the beam flange under tension (maximum deformation) and the lower bolt-row, since no deformation originates below this point.
Experimental rotations.
4.2. Additional plate deformation behaviour
Table 11 In-plane loading
The additional plate’s deformation behaviour in the tension zone was measured using a linear transducer in the minoraxis and three-dimensional tests. As pointed out in Fig. 14, its stiffness increases when both axes are loaded. This increase results in stiffer behaviour in the minor axis joints, as shown in Section 3.3. The additional plates in the tension and compression zones behave in different ways, as demonstrated by their resulting deformation (Fig. 15(a)). The plate in the tension zone behaves as a laterally pinned plate, as proved by the single curvature of its resulting deformation (Fig. 15(b)). The restraining effect of the welds may be assumed to be pinned. By contrast, in the compression zone, an additional restriction is provided by the column flanges: the plate may be assumed to act as though it was laterally clamped.
Joint
Ψinf K −R
Ψsup K −R
dinf K −R (m rad)
dsup K −R (m rad)
A-M B-M
6.93 31.97
2.91 11.60
37.87 93.28
32.75 87.99
A-n B-n
8.04 20.97
2.84 6.15
29.95 64.76
22.81 56.94
Ductility assessment.
in Fig. 13 for major-axis joints. The deformability of the end-plate increases for smaller values of tep . This effect was already noticed in the moment–rotation behaviour, since the components’ end-plate and bolts are the main sources of connection deformability. The restraining effect of the second bolt row is clear in the tension side of the thin plate (Fig. 13(a)). In the thick plates (Fig. 13(b)), bolts are submitted to greater tension forces, resulting in greater elongations. As a consequence, bolts seem
5. Conclusions This paper presented an experimental programme on extended end-plate beam-to-column symmetrically loaded
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(a) Thin plate specimen. Tension end-plate and additional plate deformation.
(b) Thick plate specimen. General view.
(c) Thin plate specimen. Tension end-plate deformation.
(a) Thin plate specimen. General view.
(b) Thick plate specimen. General view.
(c) Thin plate specimen. End-plate deformation in the tension zone.
(d) Thick plate specimen. Tension zone (notice the lower bolt cracking and the upper bolt nut stripping).
Fig. 12. Major-axis joints failure.
3.
4.
5. (d) Thick plate. Deformation of the additional plate in the tension zone. Fig. 11. Minor-axis joints’ failure.
6. joints in both major and minor axes under bi- and threedimensional proportional loading carried out at the University of Navarra, Spain. The main conclusions of this investigation are: 1. Both the moment resistance and the rotational stiffness of the joint increase when the thickness of the end-plate is also increased. 2. Eurocode 3 [4] overestimates the rotational stiffness of the tested major axis joints when compared with experimental
results. The alternative proposal in [5] seems to obtain better agreement. Eurocode 3 [4] proposals give safe approaches for predicting joint resistance. The predictions underestimate the resistance in these particular cases. Special attention should be given to the nut stripping behaviour observed in the major axis thick plate tests, as this is a brittle failure. The initial rotational stiffness results for all tests indicate that three-dimensional proportional loading (load in both axes) significantly affects the joint structural behaviour. The initial stiffness increases for this loading arrangement. In the case of the minor axis joints, additional stiffening may be related to the additional plate’s reported stiffer behaviour. Analytical models for these joints are required. Additional components to those presented in Eurocode [4] are also needed. Models should provide an effective way to include the three-dimensional reported effects.
The experimental investigation presented in this paper provides a first insight into the semi-rigid behaviour of threedimensional joints subjected to proportional loading. More experimental investigation is required to fully assess this behaviour. The second part of this paper presents appropriate analytical models that have been developed for this purpose.
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(a) Thin plate (B).
(a) General view. Column is shown downwards, so the tension zone is located below, and the compression zone above.
(b) Thick plate (A). Fig. 13. Major axis joints. Remaining deformation on end-plate.
(b) Detail of the additional plate deformation in the tension zone. Fig. 15. Additional plate deformation.
References
Fig. 14. Additional plate force–deformation behaviour.
Acknowledgements The support given to this work by the Arcelor Chair of the University of Navarra is greatly acknowledged. The Alumni Navarrenses association and the Spanish Science and Education Ministry are also gratefully acknowledged for providing sponsorship to the first author. The assistance provided by the staff at the University of Navarra School of Architecture Laboratory in making the test specimens available and their support in conducting the tests is most appreciated.
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