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Experimental assessment of the semi-rigid connections behavior with angles and stiffeners
Journal of Constructional Steel Research 114 (2015) 338–348
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Journal of Constructional Steel Research
Experimental assessment of the semi-rigid connections behavior with angles and stiffeners Abdulkadir Cüneyt Aydın a,⁎, Mahmut Kılıç a, Mahyar Maali a, Merve Sağıroğlu b a b
Ataturk University, Faculty of Engineering, Department of Civil Engineering, 25240 Erzurum, Turkey Erzurum Technical University, Faculty of Engineering, Department of Civil Engineering, Erzurum, Turkey
a r t i c l e
i n f o
Article history: Received 9 March 2015 Received in revised form 19 June 2015 Accepted 4 August 2015 Available online xxxx Keywords: Top-and-seat angle connections Minor column axes Experimental testing Resistance Stiffness Steel beam-to-column
a b s t r a c t Experimental investigations were done on statically loaded beam-to-column connections that were designed with top-and-seat angles in minor column axes. This study was undertaken to analyze the influence of angles with and without stiffeners on the behavior of the beam-to-column connections. The aim was to provide necessary data to improve the Eurocode 3. While the rotation stiffness and capacity of the entire stiffener used beams decreased, the resistance moment increased. Moreover, the rotation capacity increased with the increased thickness of the top-and-seat angles. © 2015 Elsevier Ltd. All rights reserved.
1. Introduction Taking into account the behavior of the connections in the analysis and the design of steel frames is important when presenting the actual behavior of such frames. Thus, the behavior of the connections must be well-understood. The connections form various moment–rotation (M–θ) curves according to the type of connection, elements of the connection, and placement of the connection. These curves are the visual expressions of the actual behavior discovered in experiments. In 1917, Wilson and Moore [1] performed the first experiment to assess the rigidity of steel frame connections at the University of Illinois. Since then, experimental testing has continued. The data banks from experiments have been obtained partially. The four most important data banks are: 1. Goverdhan data bank. The first one to be developed, in 1984 [2], has the results of 230 tests from the United States of America (USA) carried out between 1950 and 1983. 2. Nethercot data bank. The first European data bank on steel connections was developed in 1985. Nethercot [3,4] examined more than 70 experimental studies that involved collecting more than 700 individual tests by other researchers [5]. 3. Steel connection data bank. In the USA, the work of Goverdhan [2] was followed by that of Kishi and Chen [6,7], who prepared a data bank collecting experimental tests carried out from 1936 to 1986 all over the world. They compiled the results of more than 303 tests [8,9]. In 1995, Abdalla and Chen [10] added the results of 46 ⁎ Corresponding author. E-mail address: [email protected] (A.C. Aydın).
http://dx.doi.org/10.1016/j.jcsr.2015.08.017 0143-974X/© 2015 Elsevier Ltd. All rights reserved.
additional experimental tests of steel beam-to-column joints. 4. SERICON data bank. Developed by Arbed Recherches [11] and Aachen University [12], it includes only European test results [13]. These databanks have completed classification and the formation of mathematical models to express the behavior of connections. However, classification is limited to seven types of beam–column connections. The seven connection types are called: 1 — single web angle, 2 — double web angle, 3 — header plate, 4 — top-and-seat angle, 5 — end plate without column stiffeners, 6 — end plate with column stiffeners, and 7 — T-stub. These connection types were experimentally tested between 1958 and 1990 [14–33]. However, there are many different types of beam–column connections in steel structures today that aren't defined in data banks. de Lima et al. [34] investigated the experimental and mechanical models for predicting the behavior of minor axis beam-to-column semi-rigid joints. The investigation motivated the development of a mechanical model for assessing the connections structural response. The mechanical model is based upon the component method of design, in accordance with the Eurocode 3 specifications. This philosophy implies that each joint component is represented by a spring possessing a non-linear force versus displacement (F–Δ) curve. Coelho et al. [35] investigated the assessment of the behavior of bolted 32 T-stub connections made up of welded plates. Although T-stubs have been used over many years to model the tension zone of bolted joints, the research mainly focused on rolled profiles as T-stub elements. To extend this model to the case of welded plates as T-stub elements, a test program was undertaken and reported.
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Coelho et al. [36] investigated the ductility of the extended end-plate connections. An experimental investigation of eight statically loaded extended end-plate moment connections was undertaken to provide insight into the behavior of this joint type up to collapse. The specimens were designed to confine failure to the end plate and/or bolts without the development of the full plastic moment capacity of the beam. Coelho and Bijlaard [37] researched the experimental behavior of high-strength steel end-plate connections. The major contributions to this study are (i) the characterization of the nonlinear behavior, (ii) the validation of current Eurocode 3 specifications, and (iii) the ductility analysis of high-strength steel moment connections. The test results show that the tested connections satisfy the current design provisions for stiffness, resistance, and rotation demands. Cabrero and Bayo [38] researched the semi-rigid behavior of three-dimensional steel beamto-column joints subjected to proportional loading. An experimental investigation of statically loaded extended end-plate connections in both major and minor column axes was undertaken. The aim of the research was to provide insight into the behavior of these joints when a proportional load is applied to both axes (three-dimensional loading). The rotational stiffness of the joints increased in this type of three-dimensional loading. The findings also showed the increasing end-plate thickness as an increase in the connections flexural strength and stiffness and as a decrease in its rotation capacity. Shi et al. [39] investigated the experimental and theoretical analysis for the moment–rotation behavior of stiffened extended end-plate connections. A new theoretical model for evaluating the moment–rotation (M–Φ) relationship for stiffened and extended steel beam column end-plate connections was derived. Based on a specific definition of the end-plate connection rotation, the end-plate connection was broken down into several components, including the panel zone, bolt, end-plate, and column flange. The complete loading–deformation process of each component was then analyzed. Recently, Abidelah et al. [40] researched the experimental and analytical behavior of bolted end-plate connections with or without stiffeners. The experimental results of eight specimens of steel bolted beam-to-column and beam-to-beam connections with flush or extended end plates were investigated. Four of the connections had the end plates reinforced with stiffeners in the extended parts. The lowresistance column was used to observe the failure modes in the tension and compression zones. The results were analyzed on the basis of global moment–rotation curves and the evolution of the tension forces in the bolts. The main parameters observed were the failure modes, the evolution of the resistance, the stiffness, and the rotation capacity. Experimental results were used as a basis for comparison with the analytical results given by the component method of Eurocode 3, leading to code specifications that enabled the calculation of the moment–rotation characteristics of major axis beam-to-column joints, beam-to-beam joints, and column bases, as stated in the current draft version of Eurocode 3, Part 1.8 [41]. When beam-to-column joints to the column minor axis were considered, the adopted design process generally assumed these joints to be pinned; however they did not behave as though they were pinned [34]. Given that no code provisions currently exist for semi-rigid minor axis joints, a mechanical model was developed in accordance with the general principles of Eurocode 3 [41] to evaluate the connections structural behavior. Authors investigated [10] beam-to-column minor connections with or without stiffeners in top-and-seat angles and web of the beam in two groups. The conventional usage of stiffeners can be designed to present local bending, local yielding, and local buckling of the beam or column. However, the usage of stiffeners with angles is not mentioned and investigated either in Eurocode 3 or in the literature as in this research. Thus, the aim of the study was to analyze the influence on the beam and joint stiffeners and lengths (L) of top-and-seat angle joints on the behavior of connections and to provide the necessary data for improving Eurocode 3. Moment–rotation curves were used to evaluate the main parameters characterizing the behavior of the tested connections, such
339
as the stiffness, the resistance, the failure mode, and the deformation capacity of the joints. 2. Description of the experimental program 2.1. Test details Two series of 10 bolted beam-to-column connections were investigated throughout this study, the experimental program is shown in Fig. 1. The joints were fabricated from a minor axis connection, as shown in Fig. 1 and detailed in Table 1. Each of the minor axis beamto-column connections had a control specimen (without a beam stiffener) to compare its behavior within each group (A60 and A50). All stiffeners with a thickness equal to 5 mm and 10 mm were welded to the beam and to the top-and-seat angle by means of a continuous 45° fillet weld. The fillet welds were prepared for the workshop in a down-hand position. The manual metal arc welding type of procedure was involved with a consumable electrode. The chosen steel grade for the top-andseat angle, plate stiffener, and profile section was S235. The column IPE300, the beam IPE120, and hand-tightened full-threaded grade 8.8 M8 bolts in 10 mm drilled holes were kept constant for all tested specimens. 2.2. Mechanical properties The test program included one steel grade for the beam; the column and stiffeners were S235 with nominal values of yield strength fy, n and ultimate tensile strength fu, n equal to 235 MPa and 360 MPa, respectively. The coupon tension test on the structural steel material was performed according to the appropriate UNE procedures [42]. The real mechanical characteristics were obtained using tensile tests on coupons cut from the flange and web of the beam and column and from the topand-seat angles 50 and 60 and the stiffeners. For each component, three tests were performed. Table 2 gives the values for the static yield and tensile stresses, fy and fu. Each bolt was tested under tension in order to determine the mechanical properties of the bolt material, in accordance with UNE-EN 10002-1 [42]. The average properties are set out in Table 2. 2.3. Test arrangement and instrumentation The specimens were subjected to a static force applied by a 250 kN hydraulic jack with a maximum piston stroke of 200 mm. Tests were performed under displacement control with a constant speed of 0.016 mm/s up to the collapse of the specimens. The test arrangements are shown in Fig. 2. In order to prevent the lateral torsional buckling of the beam while loading, a two-column guidance device near the beam was provided. In fact, from the experiments, it was observed that lateral torsional buckling of the beam with the course of loading did not occur. The instrumentation plan is described in Fig. 2. The lengths of the beam and column (1500 mm) were chosen to ensure that a realistic stress pattern was developed at the connection, on the one hand, and that fracture of the several specimens, i.e., ultimate load, was attained with the specific testing machine. The full instrumentation plan is described below. The primary requirements of the instrumentation were the measurement of: 1. the applied load (P), which is obtained directly from the hydraulic jack; 2. the displacements (DT) of the connection, beam, top-and-seat angle, and web of the column, which are directly predicted by using linear variable displacement transducers (LVDTs); and 3. the strains at the stiffener of the beam and at the top-and-seat angle connections, which are obtained directly from the strain gauges. The results were collected using a data logging device that recorded all measurements and the load cells at one-second intervals. All of the
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Fig. 1. Top-and-seat angle geometry and proposed three-dimensional semi-rigid joint.
data were recorded for the duration of the test. Displacements were measured using linear variable displacement transducers with a maximum displacement of 100 mm (LVDTs, shown as DT in Fig. 2). Two strain gauges of TML YEFLA-5 (maximum strain of 15%–20%) were added to the top angle connection (horizontal and vertical) and to the stiffener of the beam (horizontal and vertical) as shown in Fig. 3 to observe the strain distribution. The test setup is shown in Fig. 4.
displacements of the beam or top-and-seat angle connection as well as multiplication of the distance between the load application point and beam end, bolted to column (Lload), respectively: M ¼ PLload :
The rotational deformation of the joint (θ) is equal to the connection rotation. The beam rotation is approximately given by (Fig. 2): θB ¼
3. Test results 3.1. Bending moment The moment–rotation curve is the behavior of the moment connections that describe the relationship between the applied moment (M) and the corresponding rotation (θ) between the members. The rotation and the bending moment (M) are predicted by using
ð1Þ
arctan δDT1 −δDT4 −δb:elðDT1Þ arctan δDT2 −δDT4 −δb:elðDT2Þ ¼ ð2Þ L1 L2
where δDTi and δb.el(DTi) are the vertical displacements and the beam elastic deflection, at LVDT DTi, respectively. δb.el(DTi) is evaluated as follows: ZZZ EIδb:elðDTiÞ ¼ −P
ð3Þ
Table 1 Test details. Experiment
Top-and-seat angle Length of angle (L) (mm) Stiffener thickness of top-and-seat angle (tP) (mm) Beam stiffener Stiffener thickness of beam (mm)
A60-L73-SA10-SB10 L60x60x6 A60-L64-SA5-SB10 A60-L55-SA5-SB10 A60-L73-SA5-SB10 A60-L73-SA5 A50-L73-SA5 L50x50x5 A50-L73-SA5-SB10 A50-L64-SA5-SB10 A50-L55-SA5-SB10 A50-L73-SA10-SB10
73 64 55 73 73 73 73 64 55 73
10 5
YES
10
5
–
–
5
YES
10
10
A = top-and-seat angles L50x50x5 and L60x60x6, L = length of top-and-seat angle, SA = stiffener of top-and-seat angle, SB = stiffener of beam.
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Table 2 Average characteristic values for structural steels and bolt. Stress (MPa)
Beam web
Beam flange
Column web
Column flange
Top-and-seat angle 50
Top-and-seat angle 60
Stiffener
Bolt
fy fu
338.14 446.78
348.98 477.35
341.09 445.81
339.65 438.11
308.14 448.64
311.28 450.45
334.63 453.50
789.98 871.63
ZZ EIδb:elðDTiÞ ¼ −PX þ C 1
Z EIδb:elðDTiÞ ¼
EIδb:elðDTiÞ ¼
−
−PX 2 2 PX 3 6
ð4Þ
! þ C1X þ C2
! þ
C1X2 2
ð5Þ
! þ C2 X þ C3
ð6Þ
Z EIδb:elðDTiÞ ¼ θ ¼ 0→C 2 ¼ 0
If… ::X ¼ 0;
ð7Þ
ZZ If… ::X ¼ L;
EIδb:elðDTiÞ ¼ M ¼ 0→C 1 ¼ PLload
If… ::X ¼ 0; EIδb:elðDTiÞ ¼
δb:elðDTiÞ ¼
P − EI
PX 6
3
! !! X 3 DTi LloadX 2 DTi − 6 2
✓ The plastic flexural resistance, Mj.Rd, which corresponds to the intersection point of the previous two regression lines obtained for the initial stiffness (Sj.ini) and for the post-limit stiffness (Sj.p–l) and its corresponding rotation θM.Rd; ✓ The maximum bending moment, Mj.max, and its corresponding rotation, θM.j.max; ✓ The knee-range of the M–θ curve, which is defined as the transition zone between the initial and post-limit stiffness, with its lower boundary at Mmin.k–R and rotation θmink–R, and with its upper limit at Msupk–R and rotation θsupk–R; ✓ The bending moment capacity, Mθ.Cd, and its corresponding rotation capacity, θcd.
ð8Þ
! ¼ δ ¼ 0→C 3 ¼ 0
the following characteristics were assessed for the different experimental tests [41,43,44], as drawn in Fig. 5:
ð9Þ
ð10Þ
where I is the moment of inertia and E is the Young's modulus of beam. Some differences among the results from DT3 are expected when compared to the remaining LVDTs. The results from LVDTs DT1–DT2 are identical, as expected. Therefore, all of the deformation values presented throughout the remainder of the section refer to the readings from DT1. 3.2. Moment–rotation curve
The characteristics of tests involved in this study will be explained in Section 3.3. The ductility of a joint (Ψj) is a property that reflects the length of the yield plateau of the moment–rotation response. The proposed definition of the ductility of a joint is the difference between the rotation value corresponding to the joint plastic resistance, θM.Rd, and the total rotation capacity, θCd [45,46] (Fig. 5). Thus, the ductility of a joint relates the maximum rotation of the joint, θCd, to the rotation value corresponding to the joint's plastic flexural resistance, θM.Rd [36]: Ψj ¼
θCd : θM:Rd
Also, the rotation values at the maximum load and corresponding ductility levels, Ψj.max load, can be derived from: Ψ j: max load ¼
The M–θ curve of the connection may be characterized by using the aforementioned relationships. The main features of this curve are: moment resistance, rotational stiffness, and rotation capacity. In particular,
ð11Þ
θM j: max : θM:Rd
ð12Þ
The conclusions of the ductility of a joint and the rotation values at the maximum load and corresponding ductility levels will be explained
Fig. 2. Location of the displacement transducers (DT = LVDTs).
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Fig. 3. Location of the strain gauges (ST1 = parallel of beam on top angle, ST1 = vertical of beam on top angle, ST3 = parallel of stiffener beam, ST4 = vertical of stiffener beam).
in Section 3.3. Eurocode 3 [41] gives quantitative rules for predicting the joint flexural plastic resistance and initial rotational stiffness for major beam-to-column joints of end-plate connections. These structural properties are evaluated below using the geometric and mechanical nominal properties in the Eurocode 3. 3.3. Characteristics of the tests 3.3.1. Specimens with A60 top-and-seat angle The moment–rotation and moment–strain response for the five specimens using A60 top-and-seat angle joints with a 5 mm and 10 mm stiffener thickness of the top-and-seat angle and a 10 mm stiffener thickness of the beam are reported in Fig. 6. These curves show that:
Fig. 4. System setup and hydraulic jack.
1. The moment resistance increased with the increasing lengths (L) of angles in the same character. For example, the moment resistance of the A60-L73-SA5-SB10 specimen was 18.93% greater than that of A60-L55-SA5-SB10; 2. The maximum moment increased by 20.47% with the increasing stiffener thickness of the top-and-seat angle in the lengths of the same angles; 3. The moment resistance was increased by 11.49% by using a stiffener in the beam; 4. The initial and post-limit stiffener increased with the increasing lengths of angles in the same character;
Fig. 5. Moment–rotation curve characteristics.
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Fig. 6. Moment–rotation/strain curve for A60 group tests.
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Fig. 7. Collapse models for A60 group tests.
5. The rotation stiffness increased with the increasing lengths of angles. For example, the rotation stiffness of the A60-L73-SA5-SB10 specimen was 2.78% greater than that of A60-L55-SA5-SB10; 6. The rotation stiffness and rotation capacity were decreased by using a stiffener in the beams of all joints; 7. The rotation capacity decreased with the increasing lengths of angles; and 8. The rotation capacity increased by 45.91% with the increasing stiffener thickness of the top-and-seat angle in the lengths of the same angles. The ductility of joints and the rotation values at the maximum load and corresponding ductility levels of joints increased about 45.09% and 17.86%, with the increasing stiffener thickness of angles, respectively. Furthermore, the rotation values at the maximum load and corresponding ductility levels of joints decreased with the increasing lengths of angles (Fig. 6). While the strains were in the elastic region in the beam stiffener, strains passed to the plastic region in the topangle joints as shown in the moment–strain curves (Fig. 6). Furthermore, top-angle-joint strain rates were greater than that of the beam stiffener. Energy dissipation capacity increased with the increasing lengths of angles. For example, energy dissipation of A60-L73-SA5-SB10 was
13.96% greater than that of A60-L55-SA5-SB10. The amount of energy dissipated depended on the stiffener thickness of the top and seat angles and beams. Thus, it could be increased with the increasing stiffener thickness of the angles and beams. Two collapse modes were observed during the tests: (i) the bolt being directly overloaded by the applied forces and (ii) excessive bearing stress under the nut face (Fig. 7). An examination of the fracture showed a full slant fracture surface and evidence of a shear-face tensile fracture, characteristic of an overload. The failure modes of specimens appeared after necking positions in the top-angle connections (Fig. 8). Furthermore, the maximum deflection on the web of the column after loading was 23 mm in the A60-L73-SA5 test, in which there was no stiffener beam; the minimum deflection was 15 mm in the A60-L73-SA10SB10 test, in which the stiffener was thickest in the top-and-seat angle.
3.3.2. Specimens with A50 top-and-seat angle The moment–rotation and the moment–strain response of the five A50 specimens showed a similar behavior as the previous A60 series test specimens (Fig. 9). The ductility of joints and the rotation values at the maximum load and corresponding ductility levels of joints decreased about 74.78–73.30% with the increasing stiffener thickness
Fig. 8. Deflection on web of column for A60 group tests.
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Fig. 9. Moment–rotation/strain curve for 50 group tests.
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Fig. 10. Collapse models for A50 group tests.
of angles, respectively. Furthermore, rotation values at the maximum load and corresponding ductility levels of joints increased with the increasing lengths of angles. Energy dissipation capacity increased with the increasing lengths of angles in the same character as given in Table 4. For example, energy dissipation of A50-L73-SA5-SB10 was 6.13% greater than that of A50-L55-SA5-SB10. The collapse characteristic of A50-L73-SA5-SB10 was observed with a 25 mm maximum deflection, and the collapse characteristics of A50-L73-SA5 and A50-L55-SA5SB10 were observed with a 19 mm minimum deflection on the web of the column after loading (Figs. 10 and 11). The main features of the predicted M–θ curves, assessed in Section 3.2, are summarized in Table 3. As seen in Table 3, the maximum moment resistance increased about 2.34–16.66% with the increasing thickness of angles of 5 mm to 6 mm. Furthermore, the minimum moment resistance and maximum moment resistance were obtained in the lengths of 55 mm and 64 mm, respectively. The plastic flexural resistance increased about 1.23–36.39% with the increasing thickness of angles of 5 mm to 6 mm. However, the minimum plastic flexural resistance was observed in the length of 55 mm. The bending moment capacity increased about 3.18–15.49% with the increasing thickness of angles of 5 mm to 6 mm. The minimum and maximum moment resistance were predicted in the lengths of 55 mm and 73 mm, respectively. Thus, the ideal length of the angle was observed as being equal to the length of the flange beam for moment resistance. In all of the tests, except for the L73-SA5-SB10 model test, the stiffness decreased about 52.56–8.22% with the increasing thickness of angles of 5 mm to 6 mm. The joint ductility index (Ψ j ), the rotation values at the maximum load, and the corresponding ductility levels index (Ψj.max load) are evaluated as mentioned in Section 3.2 and presented in Table 4:
i. The ductility of joints, the rotation values at the maximum load, and the corresponding ductility levels of joints decreased with the increasing thickness of angles of 5 mm to 6 mm, and ii. The ductility of joints, the rotation values at the maximum load, and the corresponding ductility levels of joints increased with the increasing stiffener thickness of top-and-seat angles of joints.
Furthermore, dissipated energy decreased with the increasing stiffener thickness of top-and-seat angles of joints and the maximum deflection on the web of the column; the maximum deflection appeared in A50-L73-SA5-SB10 and A60-L73-SA5, respectively (Table 4). Thus, the stiffener usage prevented excessive deflection in the web column (Figs. 8 and 11). 4. Conclusion The aim of this study was to analyze the influence of the beam and joint stiffeners as well as the lengths of top-and-seat angle joints on the behavior of connections and to provide necessary data for improving Eurocode 3. Stiffener usage with angles resulted not only in increasing the stiffness of the joint but also in increasing the moment transferring capability. Shear-type beam-to-column connections without angle stiffeners are discussed in Eurocode 3 as non-moment transferring joints. However, as investigated throughout this work, the observed moment transferring ability was emphasized the usability of angles with stiffener-type joints. Thus, this type of connections may be included in to the Eurocode 3. Moreover, some other conclusions that can be drawn from the work may be as follows: ➢ The moment resistance, initial stiffener, and post-limit stiffener increased with the increasing lengths of angles. ➢ The maximum moment increased with an increase in the stiffener thickness of the top-and-seat angle in the lengths of the same angles. ➢ The moment resistance was increased by using a stiffener in the beam, but the rotation stiffness and rotation capacity were decreased by using a stiffener in the beams of all test joints. ➢ The rotation stiffness increased with the increasing lengths of angles, but the rotation capacity decreased with the increasing length of the connection. ➢ The rotation capacity increased with an increase in the stiffener thickness of the top-and-seat angle in the lengths of the same angles. ➢ The ductility of joints and the rotation values for the maximum load and corresponding ductility levels of joints increased with the increasing stiffener thickness of angles in A60-type samples, conversely in A50-type samples.
Fig. 11. Deflection on web of column for A50 group tests.
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Table 3 Main characteristics of the moment–rotation curves. Experiment
A60-L73-SA10-SB10 A60-L64-SA5-SB10 A60-L55-SA5-SB10 A60-L73-SA5-SB10 A60-L73-SA5 A50-L73-SA5 A50-L73-SA5-SB10 A50-L64-SA5-SB10 A50-L55-SA5-SB10 A50-L73-SA10-SB10
Resistance (KN·m)
Stiffness (KN·m/rad)
Rotation (rad)
KR (knee-range)
Mj.Rd
Mj.max
Mθ.Cd
Sj.ini
Sj.p–l
Sj.ini/Sj.p–l
θM.Rd
θmink–R
θMsupk–R
θMj.max
θCd
4.6098–5.6945 4.3963–5.6801 3.0688–5.4856 4.3073–6.4037 3.6436–5.3738 1.4811–5.1843 2.5358–4.1528 3.3903–4.8030 2.8190–5.4854 2.9849–5.5383
5.4621 5.1744 4.4498 5.4889 4.8582 3.8141 3.4913 4.2026 4.5939 5.3945
8.4837 7.1196 6.0226 6.7468 7.2505 6.5914 5.9536 5.9332 5.8817 7.1207
8.1715 6.6138 5.9075 6.4800 7.1768 6.4063 5.9169 5.6859 5.7077 6.9049
0.812 0.8544 0.8261 0.9007 0.89156 0.88615 0.9426 0.9194 0.8293 0.9799
0.2610 0.3833 0.2578 0.3300 0.4304 0.3708 0.3576 0.2713 0.1905 0.2911
3.1106 2.2291 3.2049 2.7300 2.0716 2.3898 2.6359 3.3895 4.3533 3.3663
0.0574 0.0659 0.0559 0.0575 0.1011 0.0473 0.0432 0.0380 0.0575 0.0397
0.0525 0.0510 0.0390 0.0511 0.0547 0.0100 0.0282 0.0069 0.3808 0.0225
0.0732 0.0755 0.0922 0.0838 0.1573 0.1849 0.0641 0.0513 0.1072 0.0399
0.1172 0.1110 0.1129 0.0882 0.1704 0.1982 0.1235 0.1202 0.1301 0.0656
0.1636 0.1112 0.1138 0.0885 0.1739 0.1999 0.1292 0.1373 0.1319 0.0679
➢ The rotation values at the maximum load and corresponding ductility levels of joints decreased with the increasing lengths of angles in A50-type samples, conversely in A60-type samples. ➢ While the strains were in the elastic region, in the beam stiffener, strains passed to the plastic region in the top-angle joints. Furthermore, top-angle-joint strain rates were greater than that of the beam stiffener in all groups. ➢ The maximum moment resistance, the plastic flexural resistance, and the bending moment capacity increased with the increased thickness of angles of 5 mm to 6 mm. Thus, the ideal length of the angle is equal to the length of the flange beam for the maximum moment resistance. ➢ The stiffness decreased with the increasing thickness of angles of 5 mm to 6 mm in all tests except for the L73-SA5-SB10 model tests. ➢ The ductility of joints, the rotation values at maximum load, and corresponding ductility levels of joints decreased with the increasing thickness of angles of 5 mm to 6 mm; they increased with the increasing stiffener thickness of top-and-seat angles of joints. ➢ The observed maximum deflection on the web of the column was prevented by using stiffeners. Nomenclature ultimate or tensile stress fu yield stress fy X Cartesian axis; distance F nonlinear force δ=Δ displacement E Young's modulus I moment of inertia distance between the point I and the top-angle face Li distance between the load application point and the face of Lload the top-angle joint M bending moment
Mj.Rd joint flexural plastic (design) resistance maximum bending moment Mj.max Mmin.k–R lower resistance bound of the knee-range of the joint moment–rotation curve Msupk–R upper resistance bound of the knee-range of the joint moment–rotation curve bending moment at fracture of the joint Mθ.Cd P concentrated force initial rotational stiffness of a joint Sj.ini post-yield rotational stiffness of a joint Sj.p–1 rotation capacity of a connection θCd θMj.max rotation of the connection at maximum load connection rotation analytical value at which the moment θM.j.Rd resistance first reaches Mj.Rd θmink–R rotation between the lower bound of the knee-range of the joint moment–rotation curve and the rotation capacity rotation between the upper bound of the knee-range of the θsupk–R joint moment–rotation curve and the rotation capacity Ψj.max load joint ductility index evaluated for the rotation at maximum load joint ductility index Ψj θ rotation LVDT DTi DTi STi strain gauge STi tp stiffener thickness of top-and-seat angle
Acknowledgment The writers gratefully acknowledge the support for this work, to which financial support was given by the BAP project of Ataturk University (2014/76) and Gençler Metal steel company in making the test machine and test specimens available, and their support in conducting the tests is most appreciated.
Table 4 Experimental evaluation of the joint ductility indices Ψj and Ψj.max load. Experiment
θMR.d (rad)
θMj.max (rad)
θC.d (rad)
Ψj
Ψj.max load
Energy dissipated (kN·mm·rad)
Deflection on web of column (mm)
A60-L73-SA10-SB10 A60-L64-SA5-SB10 A60-L55-SA5-SB10 A60-L73-SA5-SB10 A60-L73-SA5 A50-L73-SA5 A50-L73-SA5-SB10 A50-L64-SA5-SB10 A50-L55-SA5-SB10 A50-L73-SA10-SB10
0.0574 0.0659 0.0559 0.0575 0.1011 0.0473 0.0432 0.0380 0.0575 0.0397
0.1072 0.1110 0.1129 0.0882 0.1704 0.1982 0.1235 0.1202 0.1301 0.0656
0.1636 0.1109 0.1138 0.0885 0.1739 0.1999 0.1292 0.1373 0.1319 0.0679
2.850 1.683 2.033 1.539 1.720 4.228 2.991 3.616 2.294 1.710
1.867 1.685 2.018 1.534 1.685 4.191 2.857 3.168 2.264 1.651
0.668417 0.455727 0.514308 0.597778 0.770692 0.72943 0.738993 0.719826 0.693685 0.584937
15 2 2 22 23 19 25 2 19 2
348
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References [1] W.M. Wilson, H.F. Moore, Tests to determine the rigidity of riveted joints in steel structures, University of Illinois. Engineering Experiment Station, Bulletin, 104, University of Illinois, Urbana (USA), 1917. [2] A.V. Goverdhan, A Collection of Experimental Moment–Rotation Curves and Valuation of Prediction Equations for Semi-rigid ConnectionsMaster thesis Vanderbilt University, Nashville (TN), 1984. [3] D.A. Nethercot, Steel beam-to-column connections: a review of test data and its applicability to the evaluation of joint behaviour in the performance of steel frames, CIRIA report1985 RP338. [4] Performance of steel frames, in: W.F. Chen (Ed.), Connection Flexibility and Steel Frames, Proc. of a Session Sponsored by the ASCE Structural Division, Detroit, 1985. [5] S.W. Jones, P.A. Kirby, D.A. Nethercot, Effect of semi-rigid connections on steel column strength, J. Constr. Steel Res. 1 (1980) 38–46. [6] N. Kishi, W.F. Chen, Steel connection data bank program, Structural Engineering, 2nd ed., Report no. CE-STR86-18School of Civil Engineering, Purdue University, West Lafayette, 1986. [7] N. Kishi, W.P. Chen, Data base of steel beam-to-column connections, Structural Engineering, Report no. CE-STR-86-26, 1/2, School of Civil Engineering, Purdue University, West Lafayette, 1986. [8] W.F. Chen, S. Toma, Advanced Analysis of Steel Frames, CRC Press, Boca Raton (FL), 1994. [9] N. Kishi, in: W.P. Chen, S. Toma (Eds.), Semi-rigid Connections. Advanced Analysis of Steel Frames, CRC Press, Boca Raton (FL), 1994. [10] K.M. Abdalla, W.F. Chen, Expanded database of semi-rigid steel connections, Comput. Struct. 56 (4) (1995) 553–564. [11] J.C. Gerardy, J.B. Schleich, Semi-rigid action in steel frame structures, Report no. 7210-SAl507. , Arbed Recherches, Luxembourg, 1991. [12] K. Weynand, SERICON I — databank on joints building frames, Proc. COST C1 First State of the Art Workshop on Semi-rigid Behaviour of Civil, Engineering Structures 1992, pp. 463–474. [13] K. Weynand, M. Huter, P.A. Kirby, Simões da Silva LAP, P.J.S. Cruz, SERICON—data bank on joint in building frames, Proceedings of the COST C1 Workshop, 1998. [14] A.K. Aggarwal, Behavior of flexible end plate beam-to-column joints, J. Constr. Steel Res. 16 (1990) 111–134. [15] A.K. Aggarwal, Behaviour of flexible beam-to-column connections, The Institution of Engineers Australia Structural Engineering Conf, 1990 (462-b67). [16] A. Azizinamini, J.H. Bradbum, J.B. Radziminski, Static and cyclic behavior of semi-rigid steel beam–column connections, Dept. of Civ. Engrg., Univ. of South Carolina, Columbia, S.C., 1985 [17] J.R. Bailey, Strength and rigidity of bolted beam-to-column connections, Conf. on Joints in Structures, 1, Univ. of Sheffield, Sheffield, England 1970, p. 4. [18] W.G. Bell, E. Chesson, W.H. Munse, Static Tests of Standard Riveted and Bolted Beam-to-Column Connections, Univ. of Illinois Engrg., Experiment Station, Urbana, 1958 111. [19] B. Bose, Moment–rotation characteristic of semi-rigid joints in steel structures, J. Inst. Eng. (India) Civ. Eng. Div. 62 (2) (1981) 128–132. [20] J. Davison, B.P. Kirby, A. Nethercot, Rotational stiffness characteristics of steel beam-to column connections, J. Construct. Steel Res. 8 (1987) 17–54. [21] R.J. Dews, Experimental Test Results on Experimental End-plate Moment Connections. Thesis Presented to Vanderbilt University, at Nashville, Tenn., in Partial Fulfillment of the Requirements for the Degree of Master of Science, 1979. [22] P. Grundy, I.R. Thomas, I.D. Bennetts, Beam-to-column moment connections, J. Struct. Div. ASCE 106 (ST1) (1980) 313–330. [23] S.A. Ioannides, Flange Behavior in Bolted End-plate Moment Connections. Thesis Presented to Vanderbilt University, at Nashville, Tenn., in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy, 1978. [24] C.W. Lewitt, E. Chesson, W.H. Munse, Restraint Characteristics of Flexible Riveted and Bolted Beam-to-Column Connections, Dept. of Civ. Engrg., Univ. of Illinois, Urbana, 1966 111.
[25] D.B. Moore, P.A.C. Sims, The influence of backing plates on the behaviour of extended end plate connections, J. Constr. Steel Res. 6 (1986) 95–122. [26] J.R. Ostrander, An Experimental Investigation of End-plate Connections. Thesis Presented to the University of Saskatchewan, at Saskatoon, Saskatchewan, in Partial Fulfillment of the Requirements for the Degree of Master of Science, 1970. [27] J.A. Packer, L.J. Morris, A limit state design method for the tension region of bolted beam–column connections, Struct. Eng. 55 (10) (1977) 446–458. [28] J. Philips, J.A. Packet, The effect of plate thickness plate connections, J. Constr. Steel Res. 6 (1986) 95–122. [29] A.N. Sherbourne, Bolted beam-to-column connections, Struct. Eng. 39 (1961) 203–210 (Jun.). [30] W.H. Sommer, Behavior of Welded-header-plate Connections. Thesis Presented to University of Toronto, at Toronto, Canada, in Partial Fulfillment of the Requirements for the Degree of Master of Applied Science, 1969. [31] J.O. Surtees, A.P. Mann, End plate connection in plastically designed structures, Conf. on Joints in Structures, 1(5), Univ. of Sheffield, Sheffield, England, 1970. [32] L.E. Thompson, R.J. McKee, D.A. Visintainer, An investigation of rotation characteristic of web shear framed connections using A-36 and A-441 steels, Dept. of Civ. Engrg., Univ. of Missouri-Rolla, Rolla, Mo, 1970. [33] R. Zandonini, P. Zanon, Experimental analysis of end plate connections, in: R. Biorhovde, J. Brozzetti, A. Colson (Eds.), Connections in Steel Structures, Behavior, Strength and Design, Elsevier Applied Science, London 1988, pp. 41–51. [34] L.R.O. de Lima, S.A.L. de Andrade, P.C.G. da Vellasco, L.S. da Silva, Experimental and mechanical model for predicting the behaviour of minor axis beam-to-column semi-rigid joints, Int. J. Mech. Sci. 44 (2002) 1047–1065. [35] Ana M. Girao Coelho, Frans S.K. Bijlaard, Nol Gresnigt, Luı's Simo˜es da Silva, Experimental assessment of the behaviour of bolted T-stub connections made up of welded plates, J. Constr. Steel Res. 60 (2004) 269–311. [36] Ana M. Girao Coelho, Frans S.K. Bijlaard, Luı's Simo˜es da Silva, Experimental assessment of the ductility of extended end plate connections, Eng. Struct. 26 (2004) 1185–1206. [37] Ana M. Girao Coelhoa, Frans S.K. Bijlaard, Experimental behaviour of high strength steel end-plate connections, J. Constr. Steel Res. 63 (2007) 1228–1240. [38] J.M. Cabrero, E. Bayo, The semi-rigid behaviour of three-dimensional steel beam-tocolumn joints subjected to proportional loading. Part I. Experimental evaluation, J. Constr. Steel Res. 63 (2007) 1241–1253. [39] Yongjiu Shi, Gang Shi, Yuanqing Wang, Experimental and theoretical analysis of the moment–rotation behaviour of stiffened extended end-plate connections, J. Constr. Steel Res. 63 (2007) 1279–1293. [40] A. Abidelah, A. Bouchaïr, D.E. Kerdal, Experimental and analytical behavior of bolted end-plate connections with or without stiffeners, J. Constr. Steel Res. 76 (2012) 13–27. [41] European Committee for Standardization (CEN), Design of Steel Structures. Part 1.8: Design of Joints, Stage 49 Draft, Brussels, 2005. [42] 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. [43] B. Bose, G.K. Youngson, Z.M. Wang, An appraisal of the design rules in Eurocode 3 for bolted end plate joints by comparison with experimental results, Proc. Inst. Civ. Eng. Struct. Build. 116 (1996) 221–234. [44] B. Bose, S. Sarkar, M. Bahrami, Finite Element Analysis of unstiffened extended end plate connections, Struct. Eng. Rev. 3 (1991) 211–224. [45] J.B. Schleich, P. Chantrain, B. Chabrolin, Y. Gal´ea, A. Bureau, J. Anza, 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. [46] B. Gil, J.M. Cabrero, R. Go˜ni, E. Bayo, An assessment of the rotation capacity required by structural hollow sections for plastic analysis, in: M.A. Jaurrieta, A. Alonso, J.A. Chica (Eds.), Tubular Structures, X. Lisse, Holland 2003, pp. 277–292 (A.A. Balkema Publishers).
Contents lists available at ScienceDirect
Journal of Constructional Steel Research
Experimental assessment of the semi-rigid connections behavior with angles and stiffeners Abdulkadir Cüneyt Aydın a,⁎, Mahmut Kılıç a, Mahyar Maali a, Merve Sağıroğlu b a b
Ataturk University, Faculty of Engineering, Department of Civil Engineering, 25240 Erzurum, Turkey Erzurum Technical University, Faculty of Engineering, Department of Civil Engineering, Erzurum, Turkey
a r t i c l e
i n f o
Article history: Received 9 March 2015 Received in revised form 19 June 2015 Accepted 4 August 2015 Available online xxxx Keywords: Top-and-seat angle connections Minor column axes Experimental testing Resistance Stiffness Steel beam-to-column
a b s t r a c t Experimental investigations were done on statically loaded beam-to-column connections that were designed with top-and-seat angles in minor column axes. This study was undertaken to analyze the influence of angles with and without stiffeners on the behavior of the beam-to-column connections. The aim was to provide necessary data to improve the Eurocode 3. While the rotation stiffness and capacity of the entire stiffener used beams decreased, the resistance moment increased. Moreover, the rotation capacity increased with the increased thickness of the top-and-seat angles. © 2015 Elsevier Ltd. All rights reserved.
1. Introduction Taking into account the behavior of the connections in the analysis and the design of steel frames is important when presenting the actual behavior of such frames. Thus, the behavior of the connections must be well-understood. The connections form various moment–rotation (M–θ) curves according to the type of connection, elements of the connection, and placement of the connection. These curves are the visual expressions of the actual behavior discovered in experiments. In 1917, Wilson and Moore [1] performed the first experiment to assess the rigidity of steel frame connections at the University of Illinois. Since then, experimental testing has continued. The data banks from experiments have been obtained partially. The four most important data banks are: 1. Goverdhan data bank. The first one to be developed, in 1984 [2], has the results of 230 tests from the United States of America (USA) carried out between 1950 and 1983. 2. Nethercot data bank. The first European data bank on steel connections was developed in 1985. Nethercot [3,4] examined more than 70 experimental studies that involved collecting more than 700 individual tests by other researchers [5]. 3. Steel connection data bank. In the USA, the work of Goverdhan [2] was followed by that of Kishi and Chen [6,7], who prepared a data bank collecting experimental tests carried out from 1936 to 1986 all over the world. They compiled the results of more than 303 tests [8,9]. In 1995, Abdalla and Chen [10] added the results of 46 ⁎ Corresponding author. E-mail address: [email protected] (A.C. Aydın).
http://dx.doi.org/10.1016/j.jcsr.2015.08.017 0143-974X/© 2015 Elsevier Ltd. All rights reserved.
additional experimental tests of steel beam-to-column joints. 4. SERICON data bank. Developed by Arbed Recherches [11] and Aachen University [12], it includes only European test results [13]. These databanks have completed classification and the formation of mathematical models to express the behavior of connections. However, classification is limited to seven types of beam–column connections. The seven connection types are called: 1 — single web angle, 2 — double web angle, 3 — header plate, 4 — top-and-seat angle, 5 — end plate without column stiffeners, 6 — end plate with column stiffeners, and 7 — T-stub. These connection types were experimentally tested between 1958 and 1990 [14–33]. However, there are many different types of beam–column connections in steel structures today that aren't defined in data banks. de Lima et al. [34] investigated the experimental and mechanical models for predicting the behavior of minor axis beam-to-column semi-rigid joints. The investigation motivated the development of a mechanical model for assessing the connections structural response. The mechanical model is based upon the component method of design, in accordance with the Eurocode 3 specifications. This philosophy implies that each joint component is represented by a spring possessing a non-linear force versus displacement (F–Δ) curve. Coelho et al. [35] investigated the assessment of the behavior of bolted 32 T-stub connections made up of welded plates. Although T-stubs have been used over many years to model the tension zone of bolted joints, the research mainly focused on rolled profiles as T-stub elements. To extend this model to the case of welded plates as T-stub elements, a test program was undertaken and reported.
A.C. Aydın et al. / Journal of Constructional Steel Research 114 (2015) 338–348
Coelho et al. [36] investigated the ductility of the extended end-plate connections. An experimental investigation of eight statically loaded extended end-plate moment connections was undertaken to provide insight into the behavior of this joint type up to collapse. The specimens were designed to confine failure to the end plate and/or bolts without the development of the full plastic moment capacity of the beam. Coelho and Bijlaard [37] researched the experimental behavior of high-strength steel end-plate connections. The major contributions to this study are (i) the characterization of the nonlinear behavior, (ii) the validation of current Eurocode 3 specifications, and (iii) the ductility analysis of high-strength steel moment connections. The test results show that the tested connections satisfy the current design provisions for stiffness, resistance, and rotation demands. Cabrero and Bayo [38] researched the semi-rigid behavior of three-dimensional steel beamto-column joints subjected to proportional loading. An experimental investigation of statically loaded extended end-plate connections in both major and minor column axes was undertaken. The aim of the research was to provide insight into the behavior of these joints when a proportional load is applied to both axes (three-dimensional loading). The rotational stiffness of the joints increased in this type of three-dimensional loading. The findings also showed the increasing end-plate thickness as an increase in the connections flexural strength and stiffness and as a decrease in its rotation capacity. Shi et al. [39] investigated the experimental and theoretical analysis for the moment–rotation behavior of stiffened extended end-plate connections. A new theoretical model for evaluating the moment–rotation (M–Φ) relationship for stiffened and extended steel beam column end-plate connections was derived. Based on a specific definition of the end-plate connection rotation, the end-plate connection was broken down into several components, including the panel zone, bolt, end-plate, and column flange. The complete loading–deformation process of each component was then analyzed. Recently, Abidelah et al. [40] researched the experimental and analytical behavior of bolted end-plate connections with or without stiffeners. The experimental results of eight specimens of steel bolted beam-to-column and beam-to-beam connections with flush or extended end plates were investigated. Four of the connections had the end plates reinforced with stiffeners in the extended parts. The lowresistance column was used to observe the failure modes in the tension and compression zones. The results were analyzed on the basis of global moment–rotation curves and the evolution of the tension forces in the bolts. The main parameters observed were the failure modes, the evolution of the resistance, the stiffness, and the rotation capacity. Experimental results were used as a basis for comparison with the analytical results given by the component method of Eurocode 3, leading to code specifications that enabled the calculation of the moment–rotation characteristics of major axis beam-to-column joints, beam-to-beam joints, and column bases, as stated in the current draft version of Eurocode 3, Part 1.8 [41]. When beam-to-column joints to the column minor axis were considered, the adopted design process generally assumed these joints to be pinned; however they did not behave as though they were pinned [34]. Given that no code provisions currently exist for semi-rigid minor axis joints, a mechanical model was developed in accordance with the general principles of Eurocode 3 [41] to evaluate the connections structural behavior. Authors investigated [10] beam-to-column minor connections with or without stiffeners in top-and-seat angles and web of the beam in two groups. The conventional usage of stiffeners can be designed to present local bending, local yielding, and local buckling of the beam or column. However, the usage of stiffeners with angles is not mentioned and investigated either in Eurocode 3 or in the literature as in this research. Thus, the aim of the study was to analyze the influence on the beam and joint stiffeners and lengths (L) of top-and-seat angle joints on the behavior of connections and to provide the necessary data for improving Eurocode 3. Moment–rotation curves were used to evaluate the main parameters characterizing the behavior of the tested connections, such
339
as the stiffness, the resistance, the failure mode, and the deformation capacity of the joints. 2. Description of the experimental program 2.1. Test details Two series of 10 bolted beam-to-column connections were investigated throughout this study, the experimental program is shown in Fig. 1. The joints were fabricated from a minor axis connection, as shown in Fig. 1 and detailed in Table 1. Each of the minor axis beamto-column connections had a control specimen (without a beam stiffener) to compare its behavior within each group (A60 and A50). All stiffeners with a thickness equal to 5 mm and 10 mm were welded to the beam and to the top-and-seat angle by means of a continuous 45° fillet weld. The fillet welds were prepared for the workshop in a down-hand position. The manual metal arc welding type of procedure was involved with a consumable electrode. The chosen steel grade for the top-andseat angle, plate stiffener, and profile section was S235. The column IPE300, the beam IPE120, and hand-tightened full-threaded grade 8.8 M8 bolts in 10 mm drilled holes were kept constant for all tested specimens. 2.2. Mechanical properties The test program included one steel grade for the beam; the column and stiffeners were S235 with nominal values of yield strength fy, n and ultimate tensile strength fu, n equal to 235 MPa and 360 MPa, respectively. The coupon tension test on the structural steel material was performed according to the appropriate UNE procedures [42]. The real mechanical characteristics were obtained using tensile tests on coupons cut from the flange and web of the beam and column and from the topand-seat angles 50 and 60 and the stiffeners. For each component, three tests were performed. Table 2 gives the values for the static yield and tensile stresses, fy and fu. Each bolt was tested under tension in order to determine the mechanical properties of the bolt material, in accordance with UNE-EN 10002-1 [42]. The average properties are set out in Table 2. 2.3. Test arrangement and instrumentation The specimens were subjected to a static force applied by a 250 kN hydraulic jack with a maximum piston stroke of 200 mm. Tests were performed under displacement control with a constant speed of 0.016 mm/s up to the collapse of the specimens. The test arrangements are shown in Fig. 2. In order to prevent the lateral torsional buckling of the beam while loading, a two-column guidance device near the beam was provided. In fact, from the experiments, it was observed that lateral torsional buckling of the beam with the course of loading did not occur. The instrumentation plan is described in Fig. 2. The lengths of the beam and column (1500 mm) were chosen to ensure that a realistic stress pattern was developed at the connection, on the one hand, and that fracture of the several specimens, i.e., ultimate load, was attained with the specific testing machine. The full instrumentation plan is described below. The primary requirements of the instrumentation were the measurement of: 1. the applied load (P), which is obtained directly from the hydraulic jack; 2. the displacements (DT) of the connection, beam, top-and-seat angle, and web of the column, which are directly predicted by using linear variable displacement transducers (LVDTs); and 3. the strains at the stiffener of the beam and at the top-and-seat angle connections, which are obtained directly from the strain gauges. The results were collected using a data logging device that recorded all measurements and the load cells at one-second intervals. All of the
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Fig. 1. Top-and-seat angle geometry and proposed three-dimensional semi-rigid joint.
data were recorded for the duration of the test. Displacements were measured using linear variable displacement transducers with a maximum displacement of 100 mm (LVDTs, shown as DT in Fig. 2). Two strain gauges of TML YEFLA-5 (maximum strain of 15%–20%) were added to the top angle connection (horizontal and vertical) and to the stiffener of the beam (horizontal and vertical) as shown in Fig. 3 to observe the strain distribution. The test setup is shown in Fig. 4.
displacements of the beam or top-and-seat angle connection as well as multiplication of the distance between the load application point and beam end, bolted to column (Lload), respectively: M ¼ PLload :
The rotational deformation of the joint (θ) is equal to the connection rotation. The beam rotation is approximately given by (Fig. 2): θB ¼
3. Test results 3.1. Bending moment The moment–rotation curve is the behavior of the moment connections that describe the relationship between the applied moment (M) and the corresponding rotation (θ) between the members. The rotation and the bending moment (M) are predicted by using
ð1Þ
arctan δDT1 −δDT4 −δb:elðDT1Þ arctan δDT2 −δDT4 −δb:elðDT2Þ ¼ ð2Þ L1 L2
where δDTi and δb.el(DTi) are the vertical displacements and the beam elastic deflection, at LVDT DTi, respectively. δb.el(DTi) is evaluated as follows: ZZZ EIδb:elðDTiÞ ¼ −P
ð3Þ
Table 1 Test details. Experiment
Top-and-seat angle Length of angle (L) (mm) Stiffener thickness of top-and-seat angle (tP) (mm) Beam stiffener Stiffener thickness of beam (mm)
A60-L73-SA10-SB10 L60x60x6 A60-L64-SA5-SB10 A60-L55-SA5-SB10 A60-L73-SA5-SB10 A60-L73-SA5 A50-L73-SA5 L50x50x5 A50-L73-SA5-SB10 A50-L64-SA5-SB10 A50-L55-SA5-SB10 A50-L73-SA10-SB10
73 64 55 73 73 73 73 64 55 73
10 5
YES
10
5
–
–
5
YES
10
10
A = top-and-seat angles L50x50x5 and L60x60x6, L = length of top-and-seat angle, SA = stiffener of top-and-seat angle, SB = stiffener of beam.
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Table 2 Average characteristic values for structural steels and bolt. Stress (MPa)
Beam web
Beam flange
Column web
Column flange
Top-and-seat angle 50
Top-and-seat angle 60
Stiffener
Bolt
fy fu
338.14 446.78
348.98 477.35
341.09 445.81
339.65 438.11
308.14 448.64
311.28 450.45
334.63 453.50
789.98 871.63
ZZ EIδb:elðDTiÞ ¼ −PX þ C 1
Z EIδb:elðDTiÞ ¼
EIδb:elðDTiÞ ¼
−
−PX 2 2 PX 3 6
ð4Þ
! þ C1X þ C2
! þ
C1X2 2
ð5Þ
! þ C2 X þ C3
ð6Þ
Z EIδb:elðDTiÞ ¼ θ ¼ 0→C 2 ¼ 0
If… ::X ¼ 0;
ð7Þ
ZZ If… ::X ¼ L;
EIδb:elðDTiÞ ¼ M ¼ 0→C 1 ¼ PLload
If… ::X ¼ 0; EIδb:elðDTiÞ ¼
δb:elðDTiÞ ¼
P − EI
PX 6
3
! !! X 3 DTi LloadX 2 DTi − 6 2
✓ The plastic flexural resistance, Mj.Rd, which corresponds to the intersection point of the previous two regression lines obtained for the initial stiffness (Sj.ini) and for the post-limit stiffness (Sj.p–l) and its corresponding rotation θM.Rd; ✓ The maximum bending moment, Mj.max, and its corresponding rotation, θM.j.max; ✓ The knee-range of the M–θ curve, which is defined as the transition zone between the initial and post-limit stiffness, with its lower boundary at Mmin.k–R and rotation θmink–R, and with its upper limit at Msupk–R and rotation θsupk–R; ✓ The bending moment capacity, Mθ.Cd, and its corresponding rotation capacity, θcd.
ð8Þ
! ¼ δ ¼ 0→C 3 ¼ 0
the following characteristics were assessed for the different experimental tests [41,43,44], as drawn in Fig. 5:
ð9Þ
ð10Þ
where I is the moment of inertia and E is the Young's modulus of beam. Some differences among the results from DT3 are expected when compared to the remaining LVDTs. The results from LVDTs DT1–DT2 are identical, as expected. Therefore, all of the deformation values presented throughout the remainder of the section refer to the readings from DT1. 3.2. Moment–rotation curve
The characteristics of tests involved in this study will be explained in Section 3.3. The ductility of a joint (Ψj) is a property that reflects the length of the yield plateau of the moment–rotation response. The proposed definition of the ductility of a joint is the difference between the rotation value corresponding to the joint plastic resistance, θM.Rd, and the total rotation capacity, θCd [45,46] (Fig. 5). Thus, the ductility of a joint relates the maximum rotation of the joint, θCd, to the rotation value corresponding to the joint's plastic flexural resistance, θM.Rd [36]: Ψj ¼
θCd : θM:Rd
Also, the rotation values at the maximum load and corresponding ductility levels, Ψj.max load, can be derived from: Ψ j: max load ¼
The M–θ curve of the connection may be characterized by using the aforementioned relationships. The main features of this curve are: moment resistance, rotational stiffness, and rotation capacity. In particular,
ð11Þ
θM j: max : θM:Rd
ð12Þ
The conclusions of the ductility of a joint and the rotation values at the maximum load and corresponding ductility levels will be explained
Fig. 2. Location of the displacement transducers (DT = LVDTs).
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Fig. 3. Location of the strain gauges (ST1 = parallel of beam on top angle, ST1 = vertical of beam on top angle, ST3 = parallel of stiffener beam, ST4 = vertical of stiffener beam).
in Section 3.3. Eurocode 3 [41] gives quantitative rules for predicting the joint flexural plastic resistance and initial rotational stiffness for major beam-to-column joints of end-plate connections. These structural properties are evaluated below using the geometric and mechanical nominal properties in the Eurocode 3. 3.3. Characteristics of the tests 3.3.1. Specimens with A60 top-and-seat angle The moment–rotation and moment–strain response for the five specimens using A60 top-and-seat angle joints with a 5 mm and 10 mm stiffener thickness of the top-and-seat angle and a 10 mm stiffener thickness of the beam are reported in Fig. 6. These curves show that:
Fig. 4. System setup and hydraulic jack.
1. The moment resistance increased with the increasing lengths (L) of angles in the same character. For example, the moment resistance of the A60-L73-SA5-SB10 specimen was 18.93% greater than that of A60-L55-SA5-SB10; 2. The maximum moment increased by 20.47% with the increasing stiffener thickness of the top-and-seat angle in the lengths of the same angles; 3. The moment resistance was increased by 11.49% by using a stiffener in the beam; 4. The initial and post-limit stiffener increased with the increasing lengths of angles in the same character;
Fig. 5. Moment–rotation curve characteristics.
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Fig. 6. Moment–rotation/strain curve for A60 group tests.
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Fig. 7. Collapse models for A60 group tests.
5. The rotation stiffness increased with the increasing lengths of angles. For example, the rotation stiffness of the A60-L73-SA5-SB10 specimen was 2.78% greater than that of A60-L55-SA5-SB10; 6. The rotation stiffness and rotation capacity were decreased by using a stiffener in the beams of all joints; 7. The rotation capacity decreased with the increasing lengths of angles; and 8. The rotation capacity increased by 45.91% with the increasing stiffener thickness of the top-and-seat angle in the lengths of the same angles. The ductility of joints and the rotation values at the maximum load and corresponding ductility levels of joints increased about 45.09% and 17.86%, with the increasing stiffener thickness of angles, respectively. Furthermore, the rotation values at the maximum load and corresponding ductility levels of joints decreased with the increasing lengths of angles (Fig. 6). While the strains were in the elastic region in the beam stiffener, strains passed to the plastic region in the topangle joints as shown in the moment–strain curves (Fig. 6). Furthermore, top-angle-joint strain rates were greater than that of the beam stiffener. Energy dissipation capacity increased with the increasing lengths of angles. For example, energy dissipation of A60-L73-SA5-SB10 was
13.96% greater than that of A60-L55-SA5-SB10. The amount of energy dissipated depended on the stiffener thickness of the top and seat angles and beams. Thus, it could be increased with the increasing stiffener thickness of the angles and beams. Two collapse modes were observed during the tests: (i) the bolt being directly overloaded by the applied forces and (ii) excessive bearing stress under the nut face (Fig. 7). An examination of the fracture showed a full slant fracture surface and evidence of a shear-face tensile fracture, characteristic of an overload. The failure modes of specimens appeared after necking positions in the top-angle connections (Fig. 8). Furthermore, the maximum deflection on the web of the column after loading was 23 mm in the A60-L73-SA5 test, in which there was no stiffener beam; the minimum deflection was 15 mm in the A60-L73-SA10SB10 test, in which the stiffener was thickest in the top-and-seat angle.
3.3.2. Specimens with A50 top-and-seat angle The moment–rotation and the moment–strain response of the five A50 specimens showed a similar behavior as the previous A60 series test specimens (Fig. 9). The ductility of joints and the rotation values at the maximum load and corresponding ductility levels of joints decreased about 74.78–73.30% with the increasing stiffener thickness
Fig. 8. Deflection on web of column for A60 group tests.
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Fig. 9. Moment–rotation/strain curve for 50 group tests.
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Fig. 10. Collapse models for A50 group tests.
of angles, respectively. Furthermore, rotation values at the maximum load and corresponding ductility levels of joints increased with the increasing lengths of angles. Energy dissipation capacity increased with the increasing lengths of angles in the same character as given in Table 4. For example, energy dissipation of A50-L73-SA5-SB10 was 6.13% greater than that of A50-L55-SA5-SB10. The collapse characteristic of A50-L73-SA5-SB10 was observed with a 25 mm maximum deflection, and the collapse characteristics of A50-L73-SA5 and A50-L55-SA5SB10 were observed with a 19 mm minimum deflection on the web of the column after loading (Figs. 10 and 11). The main features of the predicted M–θ curves, assessed in Section 3.2, are summarized in Table 3. As seen in Table 3, the maximum moment resistance increased about 2.34–16.66% with the increasing thickness of angles of 5 mm to 6 mm. Furthermore, the minimum moment resistance and maximum moment resistance were obtained in the lengths of 55 mm and 64 mm, respectively. The plastic flexural resistance increased about 1.23–36.39% with the increasing thickness of angles of 5 mm to 6 mm. However, the minimum plastic flexural resistance was observed in the length of 55 mm. The bending moment capacity increased about 3.18–15.49% with the increasing thickness of angles of 5 mm to 6 mm. The minimum and maximum moment resistance were predicted in the lengths of 55 mm and 73 mm, respectively. Thus, the ideal length of the angle was observed as being equal to the length of the flange beam for moment resistance. In all of the tests, except for the L73-SA5-SB10 model test, the stiffness decreased about 52.56–8.22% with the increasing thickness of angles of 5 mm to 6 mm. The joint ductility index (Ψ j ), the rotation values at the maximum load, and the corresponding ductility levels index (Ψj.max load) are evaluated as mentioned in Section 3.2 and presented in Table 4:
i. The ductility of joints, the rotation values at the maximum load, and the corresponding ductility levels of joints decreased with the increasing thickness of angles of 5 mm to 6 mm, and ii. The ductility of joints, the rotation values at the maximum load, and the corresponding ductility levels of joints increased with the increasing stiffener thickness of top-and-seat angles of joints.
Furthermore, dissipated energy decreased with the increasing stiffener thickness of top-and-seat angles of joints and the maximum deflection on the web of the column; the maximum deflection appeared in A50-L73-SA5-SB10 and A60-L73-SA5, respectively (Table 4). Thus, the stiffener usage prevented excessive deflection in the web column (Figs. 8 and 11). 4. Conclusion The aim of this study was to analyze the influence of the beam and joint stiffeners as well as the lengths of top-and-seat angle joints on the behavior of connections and to provide necessary data for improving Eurocode 3. Stiffener usage with angles resulted not only in increasing the stiffness of the joint but also in increasing the moment transferring capability. Shear-type beam-to-column connections without angle stiffeners are discussed in Eurocode 3 as non-moment transferring joints. However, as investigated throughout this work, the observed moment transferring ability was emphasized the usability of angles with stiffener-type joints. Thus, this type of connections may be included in to the Eurocode 3. Moreover, some other conclusions that can be drawn from the work may be as follows: ➢ The moment resistance, initial stiffener, and post-limit stiffener increased with the increasing lengths of angles. ➢ The maximum moment increased with an increase in the stiffener thickness of the top-and-seat angle in the lengths of the same angles. ➢ The moment resistance was increased by using a stiffener in the beam, but the rotation stiffness and rotation capacity were decreased by using a stiffener in the beams of all test joints. ➢ The rotation stiffness increased with the increasing lengths of angles, but the rotation capacity decreased with the increasing length of the connection. ➢ The rotation capacity increased with an increase in the stiffener thickness of the top-and-seat angle in the lengths of the same angles. ➢ The ductility of joints and the rotation values for the maximum load and corresponding ductility levels of joints increased with the increasing stiffener thickness of angles in A60-type samples, conversely in A50-type samples.
Fig. 11. Deflection on web of column for A50 group tests.
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Table 3 Main characteristics of the moment–rotation curves. Experiment
A60-L73-SA10-SB10 A60-L64-SA5-SB10 A60-L55-SA5-SB10 A60-L73-SA5-SB10 A60-L73-SA5 A50-L73-SA5 A50-L73-SA5-SB10 A50-L64-SA5-SB10 A50-L55-SA5-SB10 A50-L73-SA10-SB10
Resistance (KN·m)
Stiffness (KN·m/rad)
Rotation (rad)
KR (knee-range)
Mj.Rd
Mj.max
Mθ.Cd
Sj.ini
Sj.p–l
Sj.ini/Sj.p–l
θM.Rd
θmink–R
θMsupk–R
θMj.max
θCd
4.6098–5.6945 4.3963–5.6801 3.0688–5.4856 4.3073–6.4037 3.6436–5.3738 1.4811–5.1843 2.5358–4.1528 3.3903–4.8030 2.8190–5.4854 2.9849–5.5383
5.4621 5.1744 4.4498 5.4889 4.8582 3.8141 3.4913 4.2026 4.5939 5.3945
8.4837 7.1196 6.0226 6.7468 7.2505 6.5914 5.9536 5.9332 5.8817 7.1207
8.1715 6.6138 5.9075 6.4800 7.1768 6.4063 5.9169 5.6859 5.7077 6.9049
0.812 0.8544 0.8261 0.9007 0.89156 0.88615 0.9426 0.9194 0.8293 0.9799
0.2610 0.3833 0.2578 0.3300 0.4304 0.3708 0.3576 0.2713 0.1905 0.2911
3.1106 2.2291 3.2049 2.7300 2.0716 2.3898 2.6359 3.3895 4.3533 3.3663
0.0574 0.0659 0.0559 0.0575 0.1011 0.0473 0.0432 0.0380 0.0575 0.0397
0.0525 0.0510 0.0390 0.0511 0.0547 0.0100 0.0282 0.0069 0.3808 0.0225
0.0732 0.0755 0.0922 0.0838 0.1573 0.1849 0.0641 0.0513 0.1072 0.0399
0.1172 0.1110 0.1129 0.0882 0.1704 0.1982 0.1235 0.1202 0.1301 0.0656
0.1636 0.1112 0.1138 0.0885 0.1739 0.1999 0.1292 0.1373 0.1319 0.0679
➢ The rotation values at the maximum load and corresponding ductility levels of joints decreased with the increasing lengths of angles in A50-type samples, conversely in A60-type samples. ➢ While the strains were in the elastic region, in the beam stiffener, strains passed to the plastic region in the top-angle joints. Furthermore, top-angle-joint strain rates were greater than that of the beam stiffener in all groups. ➢ The maximum moment resistance, the plastic flexural resistance, and the bending moment capacity increased with the increased thickness of angles of 5 mm to 6 mm. Thus, the ideal length of the angle is equal to the length of the flange beam for the maximum moment resistance. ➢ The stiffness decreased with the increasing thickness of angles of 5 mm to 6 mm in all tests except for the L73-SA5-SB10 model tests. ➢ The ductility of joints, the rotation values at maximum load, and corresponding ductility levels of joints decreased with the increasing thickness of angles of 5 mm to 6 mm; they increased with the increasing stiffener thickness of top-and-seat angles of joints. ➢ The observed maximum deflection on the web of the column was prevented by using stiffeners. Nomenclature ultimate or tensile stress fu yield stress fy X Cartesian axis; distance F nonlinear force δ=Δ displacement E Young's modulus I moment of inertia distance between the point I and the top-angle face Li distance between the load application point and the face of Lload the top-angle joint M bending moment
Mj.Rd joint flexural plastic (design) resistance maximum bending moment Mj.max Mmin.k–R lower resistance bound of the knee-range of the joint moment–rotation curve Msupk–R upper resistance bound of the knee-range of the joint moment–rotation curve bending moment at fracture of the joint Mθ.Cd P concentrated force initial rotational stiffness of a joint Sj.ini post-yield rotational stiffness of a joint Sj.p–1 rotation capacity of a connection θCd θMj.max rotation of the connection at maximum load connection rotation analytical value at which the moment θM.j.Rd resistance first reaches Mj.Rd θmink–R rotation between the lower bound of the knee-range of the joint moment–rotation curve and the rotation capacity rotation between the upper bound of the knee-range of the θsupk–R joint moment–rotation curve and the rotation capacity Ψj.max load joint ductility index evaluated for the rotation at maximum load joint ductility index Ψj θ rotation LVDT DTi DTi STi strain gauge STi tp stiffener thickness of top-and-seat angle
Acknowledgment The writers gratefully acknowledge the support for this work, to which financial support was given by the BAP project of Ataturk University (2014/76) and Gençler Metal steel company in making the test machine and test specimens available, and their support in conducting the tests is most appreciated.
Table 4 Experimental evaluation of the joint ductility indices Ψj and Ψj.max load. Experiment
θMR.d (rad)
θMj.max (rad)
θC.d (rad)
Ψj
Ψj.max load
Energy dissipated (kN·mm·rad)
Deflection on web of column (mm)
A60-L73-SA10-SB10 A60-L64-SA5-SB10 A60-L55-SA5-SB10 A60-L73-SA5-SB10 A60-L73-SA5 A50-L73-SA5 A50-L73-SA5-SB10 A50-L64-SA5-SB10 A50-L55-SA5-SB10 A50-L73-SA10-SB10
0.0574 0.0659 0.0559 0.0575 0.1011 0.0473 0.0432 0.0380 0.0575 0.0397
0.1072 0.1110 0.1129 0.0882 0.1704 0.1982 0.1235 0.1202 0.1301 0.0656
0.1636 0.1109 0.1138 0.0885 0.1739 0.1999 0.1292 0.1373 0.1319 0.0679
2.850 1.683 2.033 1.539 1.720 4.228 2.991 3.616 2.294 1.710
1.867 1.685 2.018 1.534 1.685 4.191 2.857 3.168 2.264 1.651
0.668417 0.455727 0.514308 0.597778 0.770692 0.72943 0.738993 0.719826 0.693685 0.584937
15 2 2 22 23 19 25 2 19 2
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