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Experimental investigation of sinus beams with end-plate connections
Thin-Walled Structures 97 (2015) 35–43
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Thin-Walled Structures journal homepage: www.elsevier.com/locate/tws
Experimental investigation of sinus beams with end-plate connections Abdulkadir Cüneyt Aydın a,n, Mahyar Maali a, Mahmut Kılıç a, Merve Sağıroğlu b a b
Ataturk University, Department of Civil Engineering, Faculty of Engineering, 25240 Erzurum, Turkey Erzurum Technical University, Department of Civil Engineering, Faculty of Engineering, Erzurum, Turkey
art ic l e i nf o
a b s t r a c t
Article history: Received 19 June 2015 Received in revised form 4 September 2015 Accepted 5 September 2015
Using high-strength steel with reduced weight in buildings and industry is important because, as the weight of the buildings is reduced, the behavior of steel in various situations becomes important. In this study, moment–rotation curves of sinusoidal beams were investigated using fixed end-plate connections. Use of a new sinusoidal beam model is proposed. Results were compared with experiments performed not only with IPE profile but also with similar manufactured profile. In the result, weight was reduced for sinusoidal 70° beams, showing improvements in terms of moment resistance. & 2015 Elsevier Ltd. All rights reserved.
Keywords: Sinusoidal beams Experiment Moment–rotation
1. Introduction
2. Specimens and test procedure
In engineering buildings, selecting optimum dimensions is very important. It is important to use bearing elements with optimum dimensions and low weights for engineering considerations. For this reason, many studies are performed to provide optimum dimensions and to reduce weight. In some studies, researchers have tried to increase moment resistance by making changes not only to the structure, but also to the shape of the beams. Lee et al. 2015 [1] investigated the structural performance of pre-stressed composite girders with corrugated steel plate webs. In this investigation, Lee et al. conducted various composite experiments by changing the web shape of girders and obtained measured results. In another method, optimum conditions may be obtained by using high-strength steels in elements [2]. In this research, end-plate connections are used in beam-tocolumn joints, and connection dimensions are selected from the research of Coelho et al. [2]. This study aims to investigate the effect of the sinus angles in the web of I-beam with end-plate connection to the moment–rotation curves. Accordingly, moment– rotation curves are drawn for four end-plate optimum connections. The purpose of these experiments is to understand the effects of sinus beam connections on the end-plates. Among these four models, two models using sinus beams, one simple (manufactured) model, and one IPE beam model are prepared. The moment–rotation curves are compared and the effects of sinus beams are examined at end-plate connections.
The experimental test models were selected considering various issues; primarily, selection was limited by laboratory equipment and fabrication capabilities. The selected plate should be capable of easily creating all common sinusoidal angles without introducing geometrical defects that change the bearing capacity. Finally, for better realism, plates were selected from widely used materials, and sinus beams should be selected to allow comparison not only with IPE profile but also with similar manufactured profile. In this research, a total of four specimens were manufactured and tested. Among these four models, labeled “sinusoidal”, “simple” (manufactured; made of three plates by welding), and “IPE standard profile” were tested. The experimental program is shown in Figs. 1 and 2, and Table 1. The details of the beam and column are shown in Table 1. Hand-tightened fully threaded grade 8.8 M10 bolts in 12-mm drilled holes are kept constant for all the tested specimens. The test program included a single steel grade for the beam; the column and plate are of S235 with nominal values of yield strength fy (235 MPa) and ultimate tensile strength fu (360 MPa). The coupon tension test on the structural steel material was performed according to the appropriate UNE procedures [3]. 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 plates. For each component, three tests were performed. Table 2 gives the values for the static yield and tensile stresses fy and fu. Three bolts were tested under tension in order to determine the mechanical properties of the bolt material in accordance with UNE-EN 10002-1 [3]. The average properties are set out in Table 2.
n
Corresponding author. E-mail address: [email protected] (A. Cüneyt Aydın).
http://dx.doi.org/10.1016/j.tws.2015.09.003 0263-8231/& 2015 Elsevier Ltd. All rights reserved.
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Nomenclature Fu Ultimate or tensile stress Fy Yield stress X Cartesian axis; distance tp Stiffener thickness of end-plate connection E Young’s modulus I Moment of inertia M Bending moment Mj.Rd Joint flexural plastic (design) resistance Mj.max Maximum bending moment Mmin.K-R Lower resistance bound of the knee-range of the joint moment–rotation curve Msup.K-R Upper resistance bound of the knee-range of the joint moment–rotation curve Mϴ.Cd Bending moment at fracture of the joint P Concentrated force Sj.ini Initial rotational stiffness of a joint
Sj.p-1
Post-yield rotational stiffness of a joint
ϴCd Rotation capacity of a connection ϴMj.max Rotation of the connection at maximum load ϴM.j.Rd Connection rotation analytical value at which the moment resistance first reaches Mj.Rd
ϴmin K-R Rotation between the lower bound of the kneerange of the joint moment–rotation curve and the rotation capacity ϴsup K-R Rotation between the upper bound of the knee-range of the joint moment–rotation curve and the rotation capacity Ψj.max load Joint ductility index evaluated for rotation at maximum load Ψj Joint ductility index ϴ Rotation DTi LVDT DTi STi Strain gauge STi
Fig.1. Shapes of beam models. (a) Sinus shape. (b) Sinusoidal Angle. (c) Manufactured (simple) beam. (d) Standard IPE profile.
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37
models after completion.
3. Test machine and instrumentation
Fig.2. Shape of end-plates: (a) sinusoidal and (b) IPE160.
Because the web and flange of the sinusoidal beam have 2.5mm and 4-mm thicknesses, respectively, sheets with dimensions of 1500 6000 mm2 were first prepared. Next, these sheets were divided into ten and eighteen parts for the web and flange, respectively, using a cutting device. The cylindrical device was then prepared as shown in Fig. 3. This device works with three cylinders. To run 30°- and 70°-angles, the upper cylinder and two lower cylinders were made with diameters of 269.1 mm and 238.85 mm, respectively. After making the cylinders, the sheets were made into a sinusoidal shape inside this device. These sinusoidal sheets are shown in Fig. 4. To realize all planned lengths, because the sheet length was 1500 mm, sheets were welded by using arc welding with a continuous 45° fillet weld. The fillet welds were made in the down-hand position. The procedure involves manual metal arc welding using a consumable electrode. Three main zones could be identified after the welding process: weld metal (WM), the heat-affected zone (HAZ), and base metal (BM) which is the part of the parent plate that was not influenced by the heat input. The HAZ is the portion of the plate on either side of the weld that is affected by heat, because of which the metal suffers thermal disturbances and structural modifications that may include recrystallization, refining, and grain growth. The hot WM causes the plate to bend upward owing to shrinkage during cooling and, therefore, considerable force is exerted toward this end. The residual stresses can then be expected in the HAZ. Obviously, this influences the overall behavior of the connection. The composition of the WM deposited with the electrode compared to that of the BM is of great importance because this will naturally alter the properties of the steel at and near the weld toe. For each steel quality there are often a large number of electrode types to choose from [4–7]. After making sinusoidal sheets, wing sheets of 4-mm thickness and 180-mm width and 2.5-mm thickness and 160-mm width are made; these sheets are cut using the cutting device. Next, wing sheets are carefully welded to web sheets by arc welding. Because of the sinusoidal shape of the web, its vibration is also sinusoidal. The sinusoidal sheets are shown in Fig. 4. These sheets are easy to weld and, as a result, the precision of the operation is increased. Fig. 4 shows the shape of the sinusoidal 70°
The specimens are subjected to a static force applied by a 900kN hydraulic jack with a maximum stroke of 300 mm. Tests are performed under displacement control with a constant speed of 0.01 mm/s up to the collapse of the specimens. The test arrangements are shown in Fig. 5. In order to prevent the lateral torsional buckling of the beam while loading, a two-column guidance device near the beam is provided. From the experiments, it is observed that lateral torsional buckling of the beam in the course of loading did not occur. The instrumentation plan is described in Fig. 5 [8–11]. The lengths of the beam and column (1500 mm) are chosen on one hand to ensure that a realistic stress pattern is developed at the connection, and on the other hand so that fracture of the several specimens, i.e., ultimate load, is attained with the specific testing machine. The full instrumentation plan is described below. The primary requirements of the instrumentation are the measurement of applied load (P), displacements (DT) of the beam, and strains (ST) at the end-plate connections. The results are collected using a data-logging device that records all measurements for the load cells at one-second intervals. All the data are recorded for the duration of the tests. Displacements are measured using linear variable displacement transducers with a maximum displacement of 100 mm (LVDTs are shown as DT in Fig. 5). TML YEFLA-5 (maximum strain of 15–20%) strain gauges are added to the system to provide insight into the strain distribution, as shown in Fig. 5.
4. Test results The moment–rotation curve shows 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 displacements of the beam or the top-and-seat angle connection as well as multiplication of the distance between the load application point and beam end bolted to the column (Lload), respectively:
M = PL load
(1)
The rotational deformation of the joint (ϴ) is equal to the connection rotation. The beam rotation is approximately given by (Fig. 5.)
θ=
arctan(δDT 1 − δDT 5 − δb. el(DT 1)) L1
(2)
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:
Table 1 Experimental models. Name of model Simple (manufactured) Sinusoidal 30° Sinusoidal 70° IPE160 tp ¼ thickness of end-plate.
h (mm)
b (mm)
t (mm)
s (mm)
160
150
4
2.5
160
82
7.4
5
L (mm)
Weight (kg/m)
tp (mm)
– 85.8 200.2 –
15.68 12.7 16.57 15.8
8 8 8 8
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Table 2 Average characteristics of structural steels and bolts. Stress (MPa)
Beam web
Beam flange
Column web
Column flange
Plate (4 mm)
Plate (2.5 mm)
Bolt (M10, grade 8.8)
fy
358.74
378. 8
349.19
351
324.08
351.11
789.98
fu
454.918
457.6
485.31
439
465.14
448.12
871.63
Fig. 3. Sinusoidal sheet manufacturing system.
δb. el(DTi) = ( −
P ⎛ X3DTi LloadX2DTi ⎞ )⎜( )−( )⎟ 2 EI ⎝ 6 ⎠
(3)
where i is the moment of inertia and E is Young's modulus for the 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 this section refer to the readings from DT1. 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, the following characteristics are assessed for the different experimental tests [8, 12–14], as illustrated in Fig. 6: In Fig. 6, the plastic flexural resistance Mj.Rd 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 is Mj.max and its corresponding rotation is ϴM.j.max. The knee-range of the M–ϴ curve is defined as the transition zone between the initial and post-limit stiffness, with its lower boundary at Mmink R
and rotation ϴmink R, and with its upper limit at Msupk R and rotation ϴsupk R. The bending moment capacity is Mϴ.Cd and its corresponding rotation capacity is ϴcd. Table 3 and Figs. 7 and 8 are obtained from the moment–rotation curves of the tested systems. As seen from Table 3, the kneerange is observed for the simple (manufactured) model. the kneerange values of the simple (manufactured) model is higher than the sinusoidal 30°, sinusoidal 70°, and IPE160 models by 44.68%, 17.33%, and 59.23%, respectively. The knee-range values of the sinusoidal 70° model is higher than the sinusoidal 30° and IPE160 models by 33.48% and 50.07%, respectively. In addition, the kneerange value of the sinusoidal 30° model is higher than the IPE160 model by 25.85%. As a result, it is observed that the moment resistance is increased with the increasing sinus degree of the web. Furthermore, it is observed that the knee-range is increased with the increasing sinus degree of the web from 30° to 70°. In addition, as seen from Table 3, the maximum bending capacity is observed for the sinusoidal 70° model. Moreover, MjRd (plastic flexural resistance) and Mjmax (maximum bending moment) values of the sinusoidal 70° model are higher than for the simple (manufactured), sinusoidal 30°, and IPE160 models by 1.64%, 22.16%, and 39.57%, and by 11.3%, 25.12%, and 44.87%, respectively. Moreover, MjRd (plastic flexural resistance) and Mjmax (maximum bending moment) values for the simple (manufactured) model are higher than the IPE160 model by 38.63% and 37.73%, respectively, while MjRd (plastic flexural resistance) and Mjmax (maximum bending moment) values for the sinusoidal 30° model are higher than the IPE160 model by 22.80% and 26.26%, respectively. When the Mϴcd (bending moment capacity) values are taken into consideration, for the sinusoidal 70° and simple (manufactured) models, sinusoidal 30° and IPE160 beam, it is observed that the bending moment capacity of sinusoidal 70° beam is higher in values by 28.43%, 28.95%, 60.50%, respectively. Mϴcd (bending moment capacity) values for the simple (manufactured) model are higher than for the IPE160 and sinusoidal 30° models by 44.77% and 0.72%, respectively, while Mϴcd (bending moment capacity) values for the sinusoidal 30° model are higher than the IPE160 model by 44.37%. As a result, it is observed that the moment resistance is increased with the increasing sinus degree of the web. In the experiments, the highest stiffness is observed in the
Fig. 4. Sinusoidal 70° sheets.
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39
Fig. 5. Location of the displacement transducers (DT¼ LVDTs) and the strain gauges: ST1 and ST2 are parallel to the column web while ST3 and ST4 are vertical to the column web (L1 ¼ 770 mm, Lload ¼1415 mm).
Fig. 6. Moment–rotation curve characteristics. Table 3 Main characteristics of the moment–rotation curves. Experiment
Simple (manufactured) Sinusoidal 30° Sinusoidal 70° IPE 160
Resistance (KN.m) KR (knee-range)
Mj.Rd
Mj.
1.56–9.58 3.45–7.86 4.8–11.43 2.87–6.14
8.88 7.06 9.03 5.45
10.55 8.91 11.90 6.57
max
Stiffness (KN m/rad)
Rotation (rad)
MϴCd
Sj.ini
Sj.p l
Sj.ini/Sj.p l
ϴM.Rd
ϴMin.K.R
ϴMsup.k.R
ϴMj.
8.28 8.22 11.57 4.573
1.60 1.73 1.21 3.09
0.36 0.45 0.59 0.43
4.44 3.84 2.05 7.18
0.14 0.09 0.18 0.08
0.02 0.05 0.09 0.04
0.16 0.14 0.24 0.15
0.23 0.25 0.27 0.22
max
ϴCd 0.36 0.30 0.30 0.39
40
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Fig. 7. Moment–rotation and strain curves for all model tests.
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Therefore, the ductility of a joint (Ψj) is related to the maximum rotation of the joint (ϴCd) and the rotation value corresponding to the joint's plastic resistance, ϴMRd[6]:
Ψj =
θCd θMRd
(4)
The rotation values at the maximum load and corresponding ductility levels, Ψj.max.load are also related by
Ψj.maxload =
Fig. 8. Moment–rotation curves.
IPE160 specimen and the least is observed in the sinusoidal 70° specimen. The rate of rise of the initial stiffness to the post-limit stiffness values for the simple (manufactured) model is higher than the for sinusoidal 30° and sinusoidal 70° models by 13.51% and 53.83%, respectively, and the rate of rise of the initial stiffness to the post-limit stiffness values for the IPE160 model is higher than for the sinusoidal 30°, sinusoidal 70°, and simple (manufactured) models. Additionally, the rate of rise of the initial stiffness to the post-limit stiffness values for the sinusoidal 30° model is higher than for the sinusoidal 70° model by 46.61%. In the results, it is observed that the moment resistance is increased with the increasing sinus degree of the web. The rotation for all specimens is shown in Table 3. The rotation at the maximum bending moment (ϴMjmax) has the highest value for the sinusoidal 70° model. When the other models are compared with the sinusoidal 70° model, it is observed that the rotation capability of the sinusoidal 70° model at the maximum bending moment is higher than for the IPE160, sinusoidal 30°, and simple (manufactured) models by 18.5%, 7.4%, and 14.8%, respectively. Moreover, the ϴMjmax value of the sinusoidal 30° model is 12% greater than for the IPE 160 model and the ϴMjmax value of the simple (manufactured) model is 4.35% greater than for the IPE 160 model. As seen in Table 3 and Fig. 7, the rotation plastic flexural resistance (Mj.Rd) of the sinusoidal 70° model is 2.25, 2, and 1.2 times greater than those of the IPE160, sinusoidal 30°, and simple (manufactured) models, respectively. As a result, it is observed that the rotation plastic flexural resistance is increased with the increasing sinus degree of the web. In Fig. 7, the moment–rotation curves of 4 models are compared. According to the comparisons, it is observed that the moment resistance of sinusoidal 70° model is greater than all of the other models. Thus, it is suggested to use various sinus beams with end-plate connections, while the equal weight design phenomenon is thought for mentioned models, namely the moment resistance, the stiffness, and the rotation, etc. In this study, the ductility of a joint (Ψj) is a property that reflects the length of the yield plateau of the moment–rotation response. The purpose here is to define ductility as the difference between the rotation value corresponding to the joint plastic resistance (ϴMRd) and the total rotation capacity (ϴCd) [9–10].
θMj. max θMRd
(5)
Eurocode 3 [12] gives quantitative rules to predict joint flexural plastic resistance and initial rotational stiffness for major beam-tocolumn joints of end-plate connections. These structural properties are evaluated below using the geometric and mechanical nominal properties in Eurocode 3. The Ψj and Ψj.max.load values of the sinusoidal 30° model are higher than for the simple (manufactured) and sinusoidal 70° simple (manufactured) models by 22.82% and 50.15% and by 40.79% and 45.85%, respectively (Table 4). Moreover, it is observed that Ψj in the IPE160 model is greater than in the simple (manufactured), sinusoidal 30°, and sinusoidal 70° specimens by 47.22%, 31.62%, and 65.91%, respectively. The Ψj.maxload values of the IPE160 beam are greater than those of the sinusoidal 70° and simple (manufactured) models by 45.45% and 40.36%, respectively. Table 4 shows that energy dissipation capacity values of the simple (manufactured) model are higher than for the sinusoidal 30°, sinusoidal 70°, and IPE160 models. Moreover, energy dissipation capacity values of the sinusoidal 70° model are higher than for the sinusoidal 30° and IPE160 models. As a result, the sinusoidal 70° model has less ductility capacity and higher energy dissipated compared with the other models. It seems that the improved knee-range (plastic flexural resistance) and maximum bending moment are increased with the increasing sinus degree of the web. However, the ductility of a joint and the rate of rise of the initial stiffness to the post-limit stiffness is decreased with increasing sinus degree of the web. Moreover, the ductility of a joint for the sinusoidal 30° model is greater than for the simple and sinusoidal 70°models. However, for a flexural member, the ductility of a joint is most important and is essential to performance in terms of the moment strength capacity. Therefore, despite the fact that the ductility of a sinus beam joint is lower than in other models, the energy dissipated by sinus models are greater than in other models; as a result, the sinus models are better than other models for use in industry. The similar performance of moment–strain curves for the models are shown in Fig. 8 for both horizontal and vertical strain gauges. The observed values from strain gauges 1 and 3 are approximately two times greater than the values from strain gauges 2 and 4. Although vertically connected strain gauges have been exposed to plastic deformation in some regions, horizontally connected strain gauges have been exposed to elastic deformation. The observed collapse modes of the models are presented in Fig. 9. All of the bolts used in the models show similar failure patterns with 45° angles. However, the number of broken bolts is four, except for the sinusoidal 70° model, which have three broken
Table 4 Joint ductility indices Ψj and Ψj.max.load. Experiment
ϴMR.d (rad)
ϴ.Mj.max (rad)
ϴC.d (rad)
Simple Sinusoidal 30° Sinusoidal 70° IPE 160
0.14 0.09 0.18 0.08
0.23 0.25 0.27 0.22
0.36 0.30 0.30 0.39
Ψj = 2.57 3.33 1.66 4.87
θCd θMRd
Ψj . max . load = 1.64 2.77 1.5 2.75
θMj . max θMRd
Energy dissipated (kN m rad)
1.90 1.34 1.79 1.28
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Fig. 9. Collapse of all models.
bolts. The failures of the bolts are obtained from the top down, as expected.
5. Conclusion The purpose of these experiments is to understand the effects of sinus-type beam composites on end-plates and to provide data necessary to improve Eurocode 3. The main conclusions that can be drawn from the test program are as follows. The knee-range is observed for the simple (manufactured) model. The knee-range values of the simple (manufactured) model are higher than for other models. Therefore, the knee-range is increased with the increasing sinus degree of the web from 30° to 70°. The plastic flexural resistance, maximum bending moment, and bending moment capacity are increased with the increasing sinus degree of the web. Therefore, the rotation plastic flexural resistance is increased with the increasing sinus degree of the web. The rate of rise of the initial stiffness to the post-limit stiffness values of the I profile is higher than in the sinus and simple (manufactured) models. The rotation at the maximum bending moment and the rotation plastic flexural resistance is increased with the increasing sinus degree of the web. The Ψj and Ψj.max.load values of the sinusoidal 30° model are higher than for the simple (manufactured)
and sinusoidal 70° simple (manufactured) models. Moreover, it is observed that Ψj in the IPE160 model is greater than in the simple (manufactured), sinusoidal 30°, and sinusoidal 70° specimens. The Ψj.maxload values of the IPE160 beam are greater than those of the sinusoidal 70° and simple (manufactured) models. The energy dissipation capacity values of the simple (manufactured) model are higher than for other models. Moreover, energy dissipation capacity values of the sinusoidal 70° model are higher than for the sinusoidal 30° and IPE160 models. Therefore, despite the fact that the ductility of a sinus beam joint is lower than for other models, the energy dissipated in sinus models is greater than in other models. As a result, the sinus models are better than other models for use in industry. The similar performance of moment–strain curves for the models are obtained for both horizontal and vertical strain gauges. The observed values from strain gauges 1 and 3 are approximately two times greater than the values from strain gauges 2 and 4. Although vertically connected strain gauges have been exposed to plastic deformation in some regions, horizontally connected strain gauges have been exposed to elastic deformation. All of the bolts used in the models show similar failure patterns with 45° angles. However, the number of broken bolts is four, except for the sinusoidal 70° models, which have three broken bolts. The failures of the bolts were obtained from the top down, as expected.
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Acknowledgments The writers gratefully acknowledge support for this work; financial support was provided by the Gençler Metal steel company in building the test machine and making test specimens available. Their support in conducting the tests is most appreciated.
[7]
[8]
[9]
References [10] [1] D.H. Lee, J.Y. Oh, H. Kang, S.K. Kim, J.K. Kim, H.Y. Kim, Structural performance of prestressed composite girders with corrugated steel plate webs, J. Constr. Steel Res. 104 (2015) 9–21. [2] A.M.G. Coelho, F.S.K. Bijlaaed, Experimental behaviour of high steel end-plate connection, J. Constr. Steel Res. 63 (2007) 1228–1240. [3] UNE-EN 10002-1, Materiales met´alicos. Ensayos de tracci´on. Parte 1: M ´etodo de ensayo a temperatura ambiente. july 2002 Edition, AENOR. [4] D.M. Rodrigues, L.F. Menezes, A. Loureiro, J.V. Fernandes, Numerical study of the plastic behavior in tension of welds in high strength steels, J. Plast. 20 (2004) 1–18. [5] A.C. Davies, The Science and Practice Of Welding—Welding Science and Technology, Cambridge University Press, Cambridge, 1992. [6] A.M.G. Coelho, Bijlaard FSK, S.N. Gresnigt, da L. Simões, Experimental
[11]
[12] [13]
[14]
43
assessment of the behaviour of bolted T-stub connections made up of welded plates, J. Constr. Steel Res. 60 (2004) 269–311. M. Maali, A.C. Aydın, M. Sağıroğlu, Investigation of innovative steel runway beam in industrial building, Sadhana-Academy Proceedings in Engineering Science, 2015, in press. A.C. Aydın, M. Kılıç, M. Maali, M. Sağıroğlu, Experimental Assessment of the Semi-rigid Connections Behavior with Angles and Stiffeners, J. Constr. Steel Res. 114 (2015) 338–348. J.B. Schleich, P. Chantrain, B. Chabrolin, Y. Gal´ea, A. Bureau, J. Anza, 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. M. Sagiroglu, A.C. Aydin, Design and analysis of non-linear space frames with semi-rigid connections, Steel Compos. Struct. 18 (6) (2015) 1405–1421. 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, A.A. Balkema Publishers, Lisse (Holland), 2003, pp. 277–292. European Committee for Standardization (CEN)., Design of steel structures, Part 1.8: Design of joints”, 2005, Stage 49 draft, Brussels. B. Bose , G.K. Youngson, Z.M. Wang , An appraisal of the design rules in Eurocode 3 for bolted end plate joints btcomparison with experimental results, in: Proceedings from the Institute of Civil Engineers Structures and Buildings, 1996. B. Bose, S. Sarkar, M. Bahrami, Finite element analysis of unstiffened extended end plate connections, Struct. Eng. Rev. 3 (1991) 211–224.
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Thin-Walled Structures journal homepage: www.elsevier.com/locate/tws
Experimental investigation of sinus beams with end-plate connections Abdulkadir Cüneyt Aydın a,n, Mahyar Maali a, Mahmut Kılıç a, Merve Sağıroğlu b a b
Ataturk University, Department of Civil Engineering, Faculty of Engineering, 25240 Erzurum, Turkey Erzurum Technical University, Department of Civil Engineering, Faculty of Engineering, Erzurum, Turkey
art ic l e i nf o
a b s t r a c t
Article history: Received 19 June 2015 Received in revised form 4 September 2015 Accepted 5 September 2015
Using high-strength steel with reduced weight in buildings and industry is important because, as the weight of the buildings is reduced, the behavior of steel in various situations becomes important. In this study, moment–rotation curves of sinusoidal beams were investigated using fixed end-plate connections. Use of a new sinusoidal beam model is proposed. Results were compared with experiments performed not only with IPE profile but also with similar manufactured profile. In the result, weight was reduced for sinusoidal 70° beams, showing improvements in terms of moment resistance. & 2015 Elsevier Ltd. All rights reserved.
Keywords: Sinusoidal beams Experiment Moment–rotation
1. Introduction
2. Specimens and test procedure
In engineering buildings, selecting optimum dimensions is very important. It is important to use bearing elements with optimum dimensions and low weights for engineering considerations. For this reason, many studies are performed to provide optimum dimensions and to reduce weight. In some studies, researchers have tried to increase moment resistance by making changes not only to the structure, but also to the shape of the beams. Lee et al. 2015 [1] investigated the structural performance of pre-stressed composite girders with corrugated steel plate webs. In this investigation, Lee et al. conducted various composite experiments by changing the web shape of girders and obtained measured results. In another method, optimum conditions may be obtained by using high-strength steels in elements [2]. In this research, end-plate connections are used in beam-tocolumn joints, and connection dimensions are selected from the research of Coelho et al. [2]. This study aims to investigate the effect of the sinus angles in the web of I-beam with end-plate connection to the moment–rotation curves. Accordingly, moment– rotation curves are drawn for four end-plate optimum connections. The purpose of these experiments is to understand the effects of sinus beam connections on the end-plates. Among these four models, two models using sinus beams, one simple (manufactured) model, and one IPE beam model are prepared. The moment–rotation curves are compared and the effects of sinus beams are examined at end-plate connections.
The experimental test models were selected considering various issues; primarily, selection was limited by laboratory equipment and fabrication capabilities. The selected plate should be capable of easily creating all common sinusoidal angles without introducing geometrical defects that change the bearing capacity. Finally, for better realism, plates were selected from widely used materials, and sinus beams should be selected to allow comparison not only with IPE profile but also with similar manufactured profile. In this research, a total of four specimens were manufactured and tested. Among these four models, labeled “sinusoidal”, “simple” (manufactured; made of three plates by welding), and “IPE standard profile” were tested. The experimental program is shown in Figs. 1 and 2, and Table 1. The details of the beam and column are shown in Table 1. Hand-tightened fully threaded grade 8.8 M10 bolts in 12-mm drilled holes are kept constant for all the tested specimens. The test program included a single steel grade for the beam; the column and plate are of S235 with nominal values of yield strength fy (235 MPa) and ultimate tensile strength fu (360 MPa). The coupon tension test on the structural steel material was performed according to the appropriate UNE procedures [3]. 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 plates. For each component, three tests were performed. Table 2 gives the values for the static yield and tensile stresses fy and fu. Three bolts were tested under tension in order to determine the mechanical properties of the bolt material in accordance with UNE-EN 10002-1 [3]. The average properties are set out in Table 2.
n
Corresponding author. E-mail address: [email protected] (A. Cüneyt Aydın).
http://dx.doi.org/10.1016/j.tws.2015.09.003 0263-8231/& 2015 Elsevier Ltd. All rights reserved.
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Nomenclature Fu Ultimate or tensile stress Fy Yield stress X Cartesian axis; distance tp Stiffener thickness of end-plate connection E Young’s modulus I Moment of inertia M Bending moment Mj.Rd Joint flexural plastic (design) resistance Mj.max Maximum bending moment Mmin.K-R Lower resistance bound of the knee-range of the joint moment–rotation curve Msup.K-R Upper resistance bound of the knee-range of the joint moment–rotation curve Mϴ.Cd Bending moment at fracture of the joint P Concentrated force Sj.ini Initial rotational stiffness of a joint
Sj.p-1
Post-yield rotational stiffness of a joint
ϴCd Rotation capacity of a connection ϴMj.max Rotation of the connection at maximum load ϴM.j.Rd Connection rotation analytical value at which the moment resistance first reaches Mj.Rd
ϴmin K-R Rotation between the lower bound of the kneerange of the joint moment–rotation curve and the rotation capacity ϴsup K-R Rotation between the upper bound of the knee-range of the joint moment–rotation curve and the rotation capacity Ψj.max load Joint ductility index evaluated for rotation at maximum load Ψj Joint ductility index ϴ Rotation DTi LVDT DTi STi Strain gauge STi
Fig.1. Shapes of beam models. (a) Sinus shape. (b) Sinusoidal Angle. (c) Manufactured (simple) beam. (d) Standard IPE profile.
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models after completion.
3. Test machine and instrumentation
Fig.2. Shape of end-plates: (a) sinusoidal and (b) IPE160.
Because the web and flange of the sinusoidal beam have 2.5mm and 4-mm thicknesses, respectively, sheets with dimensions of 1500 6000 mm2 were first prepared. Next, these sheets were divided into ten and eighteen parts for the web and flange, respectively, using a cutting device. The cylindrical device was then prepared as shown in Fig. 3. This device works with three cylinders. To run 30°- and 70°-angles, the upper cylinder and two lower cylinders were made with diameters of 269.1 mm and 238.85 mm, respectively. After making the cylinders, the sheets were made into a sinusoidal shape inside this device. These sinusoidal sheets are shown in Fig. 4. To realize all planned lengths, because the sheet length was 1500 mm, sheets were welded by using arc welding with a continuous 45° fillet weld. The fillet welds were made in the down-hand position. The procedure involves manual metal arc welding using a consumable electrode. Three main zones could be identified after the welding process: weld metal (WM), the heat-affected zone (HAZ), and base metal (BM) which is the part of the parent plate that was not influenced by the heat input. The HAZ is the portion of the plate on either side of the weld that is affected by heat, because of which the metal suffers thermal disturbances and structural modifications that may include recrystallization, refining, and grain growth. The hot WM causes the plate to bend upward owing to shrinkage during cooling and, therefore, considerable force is exerted toward this end. The residual stresses can then be expected in the HAZ. Obviously, this influences the overall behavior of the connection. The composition of the WM deposited with the electrode compared to that of the BM is of great importance because this will naturally alter the properties of the steel at and near the weld toe. For each steel quality there are often a large number of electrode types to choose from [4–7]. After making sinusoidal sheets, wing sheets of 4-mm thickness and 180-mm width and 2.5-mm thickness and 160-mm width are made; these sheets are cut using the cutting device. Next, wing sheets are carefully welded to web sheets by arc welding. Because of the sinusoidal shape of the web, its vibration is also sinusoidal. The sinusoidal sheets are shown in Fig. 4. These sheets are easy to weld and, as a result, the precision of the operation is increased. Fig. 4 shows the shape of the sinusoidal 70°
The specimens are subjected to a static force applied by a 900kN hydraulic jack with a maximum stroke of 300 mm. Tests are performed under displacement control with a constant speed of 0.01 mm/s up to the collapse of the specimens. The test arrangements are shown in Fig. 5. In order to prevent the lateral torsional buckling of the beam while loading, a two-column guidance device near the beam is provided. From the experiments, it is observed that lateral torsional buckling of the beam in the course of loading did not occur. The instrumentation plan is described in Fig. 5 [8–11]. The lengths of the beam and column (1500 mm) are chosen on one hand to ensure that a realistic stress pattern is developed at the connection, and on the other hand so that fracture of the several specimens, i.e., ultimate load, is attained with the specific testing machine. The full instrumentation plan is described below. The primary requirements of the instrumentation are the measurement of applied load (P), displacements (DT) of the beam, and strains (ST) at the end-plate connections. The results are collected using a data-logging device that records all measurements for the load cells at one-second intervals. All the data are recorded for the duration of the tests. Displacements are measured using linear variable displacement transducers with a maximum displacement of 100 mm (LVDTs are shown as DT in Fig. 5). TML YEFLA-5 (maximum strain of 15–20%) strain gauges are added to the system to provide insight into the strain distribution, as shown in Fig. 5.
4. Test results The moment–rotation curve shows 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 displacements of the beam or the top-and-seat angle connection as well as multiplication of the distance between the load application point and beam end bolted to the column (Lload), respectively:
M = PL load
(1)
The rotational deformation of the joint (ϴ) is equal to the connection rotation. The beam rotation is approximately given by (Fig. 5.)
θ=
arctan(δDT 1 − δDT 5 − δb. el(DT 1)) L1
(2)
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:
Table 1 Experimental models. Name of model Simple (manufactured) Sinusoidal 30° Sinusoidal 70° IPE160 tp ¼ thickness of end-plate.
h (mm)
b (mm)
t (mm)
s (mm)
160
150
4
2.5
160
82
7.4
5
L (mm)
Weight (kg/m)
tp (mm)
– 85.8 200.2 –
15.68 12.7 16.57 15.8
8 8 8 8
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Table 2 Average characteristics of structural steels and bolts. Stress (MPa)
Beam web
Beam flange
Column web
Column flange
Plate (4 mm)
Plate (2.5 mm)
Bolt (M10, grade 8.8)
fy
358.74
378. 8
349.19
351
324.08
351.11
789.98
fu
454.918
457.6
485.31
439
465.14
448.12
871.63
Fig. 3. Sinusoidal sheet manufacturing system.
δb. el(DTi) = ( −
P ⎛ X3DTi LloadX2DTi ⎞ )⎜( )−( )⎟ 2 EI ⎝ 6 ⎠
(3)
where i is the moment of inertia and E is Young's modulus for the 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 this section refer to the readings from DT1. 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, the following characteristics are assessed for the different experimental tests [8, 12–14], as illustrated in Fig. 6: In Fig. 6, the plastic flexural resistance Mj.Rd 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 is Mj.max and its corresponding rotation is ϴM.j.max. The knee-range of the M–ϴ curve is defined as the transition zone between the initial and post-limit stiffness, with its lower boundary at Mmink R
and rotation ϴmink R, and with its upper limit at Msupk R and rotation ϴsupk R. The bending moment capacity is Mϴ.Cd and its corresponding rotation capacity is ϴcd. Table 3 and Figs. 7 and 8 are obtained from the moment–rotation curves of the tested systems. As seen from Table 3, the kneerange is observed for the simple (manufactured) model. the kneerange values of the simple (manufactured) model is higher than the sinusoidal 30°, sinusoidal 70°, and IPE160 models by 44.68%, 17.33%, and 59.23%, respectively. The knee-range values of the sinusoidal 70° model is higher than the sinusoidal 30° and IPE160 models by 33.48% and 50.07%, respectively. In addition, the kneerange value of the sinusoidal 30° model is higher than the IPE160 model by 25.85%. As a result, it is observed that the moment resistance is increased with the increasing sinus degree of the web. Furthermore, it is observed that the knee-range is increased with the increasing sinus degree of the web from 30° to 70°. In addition, as seen from Table 3, the maximum bending capacity is observed for the sinusoidal 70° model. Moreover, MjRd (plastic flexural resistance) and Mjmax (maximum bending moment) values of the sinusoidal 70° model are higher than for the simple (manufactured), sinusoidal 30°, and IPE160 models by 1.64%, 22.16%, and 39.57%, and by 11.3%, 25.12%, and 44.87%, respectively. Moreover, MjRd (plastic flexural resistance) and Mjmax (maximum bending moment) values for the simple (manufactured) model are higher than the IPE160 model by 38.63% and 37.73%, respectively, while MjRd (plastic flexural resistance) and Mjmax (maximum bending moment) values for the sinusoidal 30° model are higher than the IPE160 model by 22.80% and 26.26%, respectively. When the Mϴcd (bending moment capacity) values are taken into consideration, for the sinusoidal 70° and simple (manufactured) models, sinusoidal 30° and IPE160 beam, it is observed that the bending moment capacity of sinusoidal 70° beam is higher in values by 28.43%, 28.95%, 60.50%, respectively. Mϴcd (bending moment capacity) values for the simple (manufactured) model are higher than for the IPE160 and sinusoidal 30° models by 44.77% and 0.72%, respectively, while Mϴcd (bending moment capacity) values for the sinusoidal 30° model are higher than the IPE160 model by 44.37%. As a result, it is observed that the moment resistance is increased with the increasing sinus degree of the web. In the experiments, the highest stiffness is observed in the
Fig. 4. Sinusoidal 70° sheets.
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39
Fig. 5. Location of the displacement transducers (DT¼ LVDTs) and the strain gauges: ST1 and ST2 are parallel to the column web while ST3 and ST4 are vertical to the column web (L1 ¼ 770 mm, Lload ¼1415 mm).
Fig. 6. Moment–rotation curve characteristics. Table 3 Main characteristics of the moment–rotation curves. Experiment
Simple (manufactured) Sinusoidal 30° Sinusoidal 70° IPE 160
Resistance (KN.m) KR (knee-range)
Mj.Rd
Mj.
1.56–9.58 3.45–7.86 4.8–11.43 2.87–6.14
8.88 7.06 9.03 5.45
10.55 8.91 11.90 6.57
max
Stiffness (KN m/rad)
Rotation (rad)
MϴCd
Sj.ini
Sj.p l
Sj.ini/Sj.p l
ϴM.Rd
ϴMin.K.R
ϴMsup.k.R
ϴMj.
8.28 8.22 11.57 4.573
1.60 1.73 1.21 3.09
0.36 0.45 0.59 0.43
4.44 3.84 2.05 7.18
0.14 0.09 0.18 0.08
0.02 0.05 0.09 0.04
0.16 0.14 0.24 0.15
0.23 0.25 0.27 0.22
max
ϴCd 0.36 0.30 0.30 0.39
40
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Fig. 7. Moment–rotation and strain curves for all model tests.
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Therefore, the ductility of a joint (Ψj) is related to the maximum rotation of the joint (ϴCd) and the rotation value corresponding to the joint's plastic resistance, ϴMRd[6]:
Ψj =
θCd θMRd
(4)
The rotation values at the maximum load and corresponding ductility levels, Ψj.max.load are also related by
Ψj.maxload =
Fig. 8. Moment–rotation curves.
IPE160 specimen and the least is observed in the sinusoidal 70° specimen. The rate of rise of the initial stiffness to the post-limit stiffness values for the simple (manufactured) model is higher than the for sinusoidal 30° and sinusoidal 70° models by 13.51% and 53.83%, respectively, and the rate of rise of the initial stiffness to the post-limit stiffness values for the IPE160 model is higher than for the sinusoidal 30°, sinusoidal 70°, and simple (manufactured) models. Additionally, the rate of rise of the initial stiffness to the post-limit stiffness values for the sinusoidal 30° model is higher than for the sinusoidal 70° model by 46.61%. In the results, it is observed that the moment resistance is increased with the increasing sinus degree of the web. The rotation for all specimens is shown in Table 3. The rotation at the maximum bending moment (ϴMjmax) has the highest value for the sinusoidal 70° model. When the other models are compared with the sinusoidal 70° model, it is observed that the rotation capability of the sinusoidal 70° model at the maximum bending moment is higher than for the IPE160, sinusoidal 30°, and simple (manufactured) models by 18.5%, 7.4%, and 14.8%, respectively. Moreover, the ϴMjmax value of the sinusoidal 30° model is 12% greater than for the IPE 160 model and the ϴMjmax value of the simple (manufactured) model is 4.35% greater than for the IPE 160 model. As seen in Table 3 and Fig. 7, the rotation plastic flexural resistance (Mj.Rd) of the sinusoidal 70° model is 2.25, 2, and 1.2 times greater than those of the IPE160, sinusoidal 30°, and simple (manufactured) models, respectively. As a result, it is observed that the rotation plastic flexural resistance is increased with the increasing sinus degree of the web. In Fig. 7, the moment–rotation curves of 4 models are compared. According to the comparisons, it is observed that the moment resistance of sinusoidal 70° model is greater than all of the other models. Thus, it is suggested to use various sinus beams with end-plate connections, while the equal weight design phenomenon is thought for mentioned models, namely the moment resistance, the stiffness, and the rotation, etc. In this study, the ductility of a joint (Ψj) is a property that reflects the length of the yield plateau of the moment–rotation response. The purpose here is to define ductility as the difference between the rotation value corresponding to the joint plastic resistance (ϴMRd) and the total rotation capacity (ϴCd) [9–10].
θMj. max θMRd
(5)
Eurocode 3 [12] gives quantitative rules to predict joint flexural plastic resistance and initial rotational stiffness for major beam-tocolumn joints of end-plate connections. These structural properties are evaluated below using the geometric and mechanical nominal properties in Eurocode 3. The Ψj and Ψj.max.load values of the sinusoidal 30° model are higher than for the simple (manufactured) and sinusoidal 70° simple (manufactured) models by 22.82% and 50.15% and by 40.79% and 45.85%, respectively (Table 4). Moreover, it is observed that Ψj in the IPE160 model is greater than in the simple (manufactured), sinusoidal 30°, and sinusoidal 70° specimens by 47.22%, 31.62%, and 65.91%, respectively. The Ψj.maxload values of the IPE160 beam are greater than those of the sinusoidal 70° and simple (manufactured) models by 45.45% and 40.36%, respectively. Table 4 shows that energy dissipation capacity values of the simple (manufactured) model are higher than for the sinusoidal 30°, sinusoidal 70°, and IPE160 models. Moreover, energy dissipation capacity values of the sinusoidal 70° model are higher than for the sinusoidal 30° and IPE160 models. As a result, the sinusoidal 70° model has less ductility capacity and higher energy dissipated compared with the other models. It seems that the improved knee-range (plastic flexural resistance) and maximum bending moment are increased with the increasing sinus degree of the web. However, the ductility of a joint and the rate of rise of the initial stiffness to the post-limit stiffness is decreased with increasing sinus degree of the web. Moreover, the ductility of a joint for the sinusoidal 30° model is greater than for the simple and sinusoidal 70°models. However, for a flexural member, the ductility of a joint is most important and is essential to performance in terms of the moment strength capacity. Therefore, despite the fact that the ductility of a sinus beam joint is lower than in other models, the energy dissipated by sinus models are greater than in other models; as a result, the sinus models are better than other models for use in industry. The similar performance of moment–strain curves for the models are shown in Fig. 8 for both horizontal and vertical strain gauges. The observed values from strain gauges 1 and 3 are approximately two times greater than the values from strain gauges 2 and 4. Although vertically connected strain gauges have been exposed to plastic deformation in some regions, horizontally connected strain gauges have been exposed to elastic deformation. The observed collapse modes of the models are presented in Fig. 9. All of the bolts used in the models show similar failure patterns with 45° angles. However, the number of broken bolts is four, except for the sinusoidal 70° model, which have three broken
Table 4 Joint ductility indices Ψj and Ψj.max.load. Experiment
ϴMR.d (rad)
ϴ.Mj.max (rad)
ϴC.d (rad)
Simple Sinusoidal 30° Sinusoidal 70° IPE 160
0.14 0.09 0.18 0.08
0.23 0.25 0.27 0.22
0.36 0.30 0.30 0.39
Ψj = 2.57 3.33 1.66 4.87
θCd θMRd
Ψj . max . load = 1.64 2.77 1.5 2.75
θMj . max θMRd
Energy dissipated (kN m rad)
1.90 1.34 1.79 1.28
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Fig. 9. Collapse of all models.
bolts. The failures of the bolts are obtained from the top down, as expected.
5. Conclusion The purpose of these experiments is to understand the effects of sinus-type beam composites on end-plates and to provide data necessary to improve Eurocode 3. The main conclusions that can be drawn from the test program are as follows. The knee-range is observed for the simple (manufactured) model. The knee-range values of the simple (manufactured) model are higher than for other models. Therefore, the knee-range is increased with the increasing sinus degree of the web from 30° to 70°. The plastic flexural resistance, maximum bending moment, and bending moment capacity are increased with the increasing sinus degree of the web. Therefore, the rotation plastic flexural resistance is increased with the increasing sinus degree of the web. The rate of rise of the initial stiffness to the post-limit stiffness values of the I profile is higher than in the sinus and simple (manufactured) models. The rotation at the maximum bending moment and the rotation plastic flexural resistance is increased with the increasing sinus degree of the web. The Ψj and Ψj.max.load values of the sinusoidal 30° model are higher than for the simple (manufactured)
and sinusoidal 70° simple (manufactured) models. Moreover, it is observed that Ψj in the IPE160 model is greater than in the simple (manufactured), sinusoidal 30°, and sinusoidal 70° specimens. The Ψj.maxload values of the IPE160 beam are greater than those of the sinusoidal 70° and simple (manufactured) models. The energy dissipation capacity values of the simple (manufactured) model are higher than for other models. Moreover, energy dissipation capacity values of the sinusoidal 70° model are higher than for the sinusoidal 30° and IPE160 models. Therefore, despite the fact that the ductility of a sinus beam joint is lower than for other models, the energy dissipated in sinus models is greater than in other models. As a result, the sinus models are better than other models for use in industry. The similar performance of moment–strain curves for the models are obtained for both horizontal and vertical strain gauges. The observed values from strain gauges 1 and 3 are approximately two times greater than the values from strain gauges 2 and 4. Although vertically connected strain gauges have been exposed to plastic deformation in some regions, horizontally connected strain gauges have been exposed to elastic deformation. All of the bolts used in the models show similar failure patterns with 45° angles. However, the number of broken bolts is four, except for the sinusoidal 70° models, which have three broken bolts. The failures of the bolts were obtained from the top down, as expected.
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Acknowledgments The writers gratefully acknowledge support for this work; financial support was provided by the Gençler Metal steel company in building the test machine and making test specimens available. Their support in conducting the tests is most appreciated.
[7]
[8]
[9]
References [10] [1] D.H. Lee, J.Y. Oh, H. Kang, S.K. Kim, J.K. Kim, H.Y. Kim, Structural performance of prestressed composite girders with corrugated steel plate webs, J. Constr. Steel Res. 104 (2015) 9–21. [2] A.M.G. Coelho, F.S.K. Bijlaaed, Experimental behaviour of high steel end-plate connection, J. Constr. Steel Res. 63 (2007) 1228–1240. [3] UNE-EN 10002-1, Materiales met´alicos. Ensayos de tracci´on. Parte 1: M ´etodo de ensayo a temperatura ambiente. july 2002 Edition, AENOR. [4] D.M. Rodrigues, L.F. Menezes, A. Loureiro, J.V. Fernandes, Numerical study of the plastic behavior in tension of welds in high strength steels, J. Plast. 20 (2004) 1–18. [5] A.C. Davies, The Science and Practice Of Welding—Welding Science and Technology, Cambridge University Press, Cambridge, 1992. [6] A.M.G. Coelho, Bijlaard FSK, S.N. Gresnigt, da L. Simões, Experimental
[11]
[12] [13]
[14]
43
assessment of the behaviour of bolted T-stub connections made up of welded plates, J. Constr. Steel Res. 60 (2004) 269–311. M. Maali, A.C. Aydın, M. Sağıroğlu, Investigation of innovative steel runway beam in industrial building, Sadhana-Academy Proceedings in Engineering Science, 2015, in press. A.C. Aydın, M. Kılıç, M. Maali, M. Sağıroğlu, Experimental Assessment of the Semi-rigid Connections Behavior with Angles and Stiffeners, J. Constr. Steel Res. 114 (2015) 338–348. J.B. Schleich, P. Chantrain, B. Chabrolin, Y. Gal´ea, A. Bureau, J. Anza, 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. M. Sagiroglu, A.C. Aydin, Design and analysis of non-linear space frames with semi-rigid connections, Steel Compos. Struct. 18 (6) (2015) 1405–1421. 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, A.A. Balkema Publishers, Lisse (Holland), 2003, pp. 277–292. European Committee for Standardization (CEN)., Design of steel structures, Part 1.8: Design of joints”, 2005, Stage 49 draft, Brussels. B. Bose , G.K. Youngson, Z.M. Wang , An appraisal of the design rules in Eurocode 3 for bolted end plate joints btcomparison with experimental results, in: Proceedings from the Institute of Civil Engineers Structures and Buildings, 1996. B. Bose, S. Sarkar, M. Bahrami, Finite element analysis of unstiffened extended end plate connections, Struct. Eng. Rev. 3 (1991) 211–224.