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An experimental and numerical study of a semi-rigid bolted-plate connections (BPC)
Thin-Walled Structures 88 (2015) 82–89
Contents lists available at ScienceDirect
Thin-Walled Structures journal homepage: www.elsevier.com/locate/tws
An experimental and numerical study of a semi-rigid bolted-plate connections (BPC) Hui-Huan Ma a,n, Ali Mohamed Issa b, Feng Fan c, Guy Oyeniran Adeoti d a
School of Civil Engineering, Harbin Institute of Technology, Harbin 150090, PR China Civil Engineering Department, University of Kordofan, El Obeid, Sudan c School of Civil Engineering, Harbin Institute of Technology, Harbin 150090, PR China d School of Civil Engineering, Harbin Institute of Technology, Harbin 150090, PR China b
art ic l e i nf o
a b s t r a c t
Article history: Received 27 February 2014 Received in revised form 11 November 2014 Accepted 11 November 2014
The aim of this paper is to evaluate the bending stiffness of a new bolted-plate joint for single-layer or double-layer reticulated shells. In order to investigate the performance of the joint, experimental tests and numerical simulations were undertaken. ANSYS was used for the numerical study, with contact elements (target 170 and contact 174) and solid elements (solid 187), used to establish bending stiffness curves for the bolted-plate joints. The good agreement between numerical simulation and experiment indicated that the simulation is an accurate and effective way of evaluating the mechanical properties of the bolted-plate joint system. In addition, using nonlinear beam elements (beam 189 element) with end spring elements (combin39), the single-layer reticulated cylindrical shell with bolted-plate joints was analyzed for different rise to width ratios. The analyses determined the load-bearing capacity of the shell. It is concluded that the bolted-plate joint system is a good choice for space structures with small or medium spans. & 2014 Elsevier Ltd. All rights reserved.
Keywords: Bolted connections Experimental analysis Reticulated shell Semi-rigid connections Numerical simulation
1. Introduction The ultimate strength of all types of space frame (single, double or triple-layer space structures) is controlled by the joint rigidity, the geometric shape and the material properties of the members. The joint rigidity appears to have the most significant influence [1–4]. The rigidity of connections has been investigated in experimental tests, which show non-linear behavior. The MERO joint system is one of the most popular semi-rigid joint systems. It was developed by Dr. Ing. Max. Mengeringhausen in 1942. The MERO system is widely used for double-layered roof structures, with either flat or curved surfaces [5]. The joint consists of a spherical node forged with flat facets and tapped holes. Members are circular hollow sections with cone-shaped steel forgings welded at the two ends. The ends accommodate bolts for connection with the joint. The bolts are tightened by means of a hexagonal sleeve and dowel pin arrangement, resulting in a completed joint such as that shown in Fig. 1. In the original version, up to 18 tubular members can be connected at a joint with no eccentricity.
n Correspondence to: Lecturer, School of Civil Engineering, Harbin Institute of Technology, 202 Haihe Road, Nangang District, Harbin 150090, PR China. E-mail addresses: [email protected] (H.-H. Ma), [email protected] (A.M. Issa), [email protected] (G.O. Adeoti).
http://dx.doi.org/10.1016/j.tws.2014.11.011 0263-8231/& 2014 Elsevier Ltd. All rights reserved.
Many researchers have studied the mechanical behavior of joint systems and developed new systems. Works by Landesmann et al. [6] led to the implementation of a model for structural analysis with semi-rigid connections. López et al. [7] obtained the rigidity of one semi-rigid joint in both experimental and numerical studies. Lee et al. [8] and Swaddiwudhipong et al. [9] experimentally investigated two special frame connections up to failure and obtained their bending stiffnesses. The experimental study conducted by Shibata et al. [10] established moment–rotation curves for some semi-rigid joints. EI-Sheikh obtained experimentally, the bending stiffness of one kind of bolt-ball joint system [11]. Feng Fan, Ma et al. [12] investigated the moment–rotation characteristics of bolt-ball joints using experiments and numerical analysis, and revealed significant non-linearity of the joint response, even at an early stage of loading. Based on the bending–rotation curves of the bolt-ball joints obtained through numerical simulation, a finite element model of single-layer reticulated domes with boltball joints was developed, using nonlinear beam elements with end spring elements using ANSYS software. Aitziber et al. [13,7], Ma et al. [14] and Kato et al. [15] verified that the rigidity of the joints is an important factor that influences the behavior of single layer latticed domes. El-Sheikh [16], Chenaghlou and Nooshin [17] found out that the overall behavior, and the failure mode of a structure, are influenced by the bending stiffness of the connections. From all of these studies, it can be concluded that the
H.-H. Ma et al. / Thin-Walled Structures 88 (2015) 82–89
bending stiffness and strength of connections needs to be considered when analyzing spatial structures, and the behaviour of joints plays a key role in the behavior of spatial structures. Also, most of these systems have bolted connections, since welded connections can be expensive with more constructive difficulties, and therefore are practically uneconomical. Joints are crucial elements in structures. Nowadays, one of the main concerns of structural designers is to develop an appropriate joint system which can provide the structure with enough stiffness and meet, at the same time, other important requirements such as easy to be prefabricated, ease of erection and economic advantages. In view of these merits, this paper is focused on the assessment of the behavior of a new semi-rigid assemble joint-system for space trusses and reticulated shells (Fig. 2). A series of tests on the new joints were conducted in the School of Civil Engineering, Harbin Institute of Technology, China. The dimensions and sizes are in accord with the Chinese Code for design of steel structures (GB50017-2003) [18]. The
83
bolted-plate connection used for this experiment can be fabricated and erected easily. This connection can be used for medium and short-span space structures. The bolted-plate connection is a semi-rigid joint system that includes a base gusset plate, bolts with nuts and washers and tubular members with end plates. Fig. 3. shows various configuration diagrams. It can be easily used in single-layer or double-layer reticulated shells.
2. The test program 2.1. Test setup and material properties The experimental set-up is shown in Fig. 4. It was designed to obtain moment–rotation curves for the connection. This test
Sleeve Slot Dowel pin Steel tuble
Sleeve
Bolt Ball
End cone End cone
Ball node Pipe
Fig. 1. MERO joint. (a) Overview. (b) Sectional view.
Fig. 2. New type of semi-rigid bolted plate connections. (a) For double-layer grid structures. (b) For single-layer reticulated shell structures.
Fig. 3. Pictures and configuration diagrams of bolted plate connections.
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2.2. Test procedure
specimen was simply supported on concrete columns and subjected to a vertical load at its centre. The loading system was a screw jack with a load cell. The lengths of the specimen beams were about 1200 mm. The displacement at different points (points 1 to 6) and the central load were measured by displacement transducers and a load cell, as shown in Fig. 4. The distances, l1, l2, l3 and l4, between the displacement transducers, were recorded before the test. The strains at different positions in the specimen were measured using strain gauges, and the specific location were recorded before loading. The gauge arrangement and numbering scheme is shown in Fig. 5. 1/2, 7/11, 8/12, 9/13, and 10/14 in the figure indicate two gauge numbers; the first number is for the gauge on the top side of the plate, and the second is for the gauge on the bottom side.
To investigate the mechanical behavior of the bolted plate connection, the specimen set-up in Fig. 6 was adopted. The bending stiffnesses of the connection under bending moment and shear force, for both of the major and minor axes, were obtained. The vertical load acting at the centre of the connection was gradually increased, and at the same time the displacement transducer measurements were recorded, to allow the joint rotation to be calculated. In addition, the strain gauges recorded the stresses at different parts of the specimen. The mechanical properties of the material components of the test specimens are presented in Table 1. The specimens’ dimensions are shown in Table 2.
Fig. 4. Test setup.
3
4
5
6
7/11
1/2
8/12
L
10/14 9/13
L3
L2
L1 L
Fig. 5. Numbering and arrangement of the strain gauges.
Fig. 6. Testing setup of the specimen. (a) Major axis. (b) Minor axis.
H.-H. Ma et al. / Thin-Walled Structures 88 (2015) 82–89
The loading process was controlled as follows. At first, the joint specimens were subject to a small load and unloaded in order to ensure the loading apparatus and the displacement gauges were working properly and to allow the different parts of the specimen to work as a whole. Then, the test was carried out under force control in the elastic range of the joints. At this stage, the centre displacement of the specimen increased continuously with increasing force. Subsequently, when the joints were loaded up to their nonlinear region, the test control was changed to displacement control
Table 1 Test specimens’ material properties. Component
Material Yield strength standard/grate Fy (MPa)
Poisson ratio
Modulus of elasticity (GPa)
Central plate Tubular member Bolts
Q235 Q235 High tensile steel/10.9
0.3 0.3 0.3
206 206 223
235 235 900
Table 2 Test specimen dimension. Test no.
Loading axis
Bolt
T1 T2 T3 T4
BPC300 major BPC300 minor BPC350 major BPC350 minor
until failure of the joint occurred. In this phase, the moment– rotation curve of the joint moves from the stiff part to the soft part. The load force increased slowly, however, the centre displacement increased sharply. Figs. 7 and 8 show pictures of the specimens at the initial stage and after the test. During the test, each load increment lasted for at least 10 min to make the transformation stable.
3. Comparison of test and numerical results The mechanical behavior of the connections can be represented by M–Φ curves that describe the relationship between the applied bending moment M and the corresponding rotation Φ of the joint. In this experimental study, the M–Φ curves were established indirectly, as the values of M and Φ were calculated based on the readings of the displacement transducers and load cells. The bending moment, M, acting on the connection, is equal to the product of the applied load F and the distance between the load application point and the connection point, L, as shown in Fig. 9. The rotational deformation, Φ, in Fig. 9, is the sum of the elastic deformation of the steel pipe and the rotational deformation of the connection φ. In these tests, the elastic deformation of the steel pipe can be neglected as it is quite small in comparison with the
Dimensions in (mm) l
l1
l2
l3
Gusset thickness
End plate thickness
Gusset flange height
M12 300 25 40 75 10
8
90
M12 300 25 40 75 10
8
90
M16 350 30 40 75 15
10
90
M16 350 30 40 80 15
10
90
85
Fig. 8. The specimens after testing.
Fig. 7. Failure modes of the specimens. (a) Failure mode in the major axis direction. (b) Failure mode about the minor axis.
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connection deformation. Therefore, Φ is approximately equal The rotation deformation Φ is calculated as follows:
Φ¼
∑nk ¼ 1 Φij n
Φij ¼ arctan
φ. ð1Þ
δi δj
ð2Þ
lij
where δi and δj are the displacements measured by the displacement transducers at the points i and j (Points 1–3 or 4–6 in Fig. 4), and lij is the distance between the two points. To get more accurate data, all the values of lij were recorded after the specimens and measurement devices were installed. For the four bolted plate connections which were tested, Finite Element Analysis (FEA) was undertaken using ANSYS, Inc.’s mechanical APDL Software release 14.5. The dimensions were the same as the tested connections BPC300 and BPC350. Since the geometry of the BPC joint under pure bending moment (Fig. 6) is symmetric, only half of the specimen was modeled to save the analysis time. The boundary condition of the joints was the same; i.e. the node area is fixed and the forces act on the end of the pipe. The numerical solid models were established with element type SOLID187 and used the properties of the actual material, as shown in Fig. 10. For the contact algorithm, the Lagrange method with higher order contact elements CONTA174 and TARG170 was used. The surface names and the element chosen for different surface are listed in Table 3. The experimental and non-linear numerical results are plotted in Figs. 11 and 12, and the maximum bending moments are listed in Table 4.
4. Discussion Fig. 11(a), presents a graphical result of the experimental and numerical analysis of the moment–rotation curves for BPC300 bending about the minor axis. From this graph, it can be observed that the experimental and numerical results are close when the rotation is smaller than 0.04 rad; then there is a slight variation between experimental and numerical results. This variation may be due to imperfections of geometry and material uniformity of
the mass distribution. The non-linear zone, for both numerical and experiment results, corresponds to bending moments greater than 0.4 kN m. Failure occurred for the test specimen at a bending moment of about 0.5 kN m, and at about 0.55 kN m for the numerical analysis. Fig. 12(a), presents moment–rotation curves for the connection BPC350 bending about the minor axis. Both experimental and numerical non-linear analysis results agree for bending moments up to a rotation of 0.03 rad. The elastic zones for the test specimen and the numerical non-linear analysis are the same between 0.0 and 0.6 kN m, before the non-linear behavior occurs. Failure occurred for the test specimen at a bending moment of about 0.68 kN m, and for the numerical it occurred at about 0.8 kN m. Figs. 11(b) and 12(b), show graphical results for the test specimens BPC300 and BPC350 and numerical non-linear analysis results, and moment–rotation curves about the major axes. Similar to the results about the minor axes, the experiment and numerical results agree in bending moments in the elastic zone (from 0 to 1.5 kN m for BPC300; from 0 to 3.0 kN m for BPC350), but there are slight variations in the non-linear zone. In general, the four experimental results showed close agreement with the nonlinear numerical analysis results within the linear elastic zone, but slight variations in the non-linear zone. The ratios of the experimental results to the corresponding numerical results are between 0.88 and 0.90, as shown in Table 4. Fig. 13. shows the stress at different parts of the connections due to bending moments about the major and minor axes. During the tests, for all the specimens, the largest deformations occur at the end plate of the tubular member when the connections experience excessive deformation, and the stresses in the end plate of the tubular member are bigger. Therefore, strain gauges 1, 2, 3 and 5 are high. From the results, it can be seen that the mechanical performance of the connection can be improved effectively by: (i). increasing the cross section area of the end plate; and (ii). using tube with a double end plate or higher yield strength materials.
Table 3 Contact surfaces in the model. Number
F
M=F·L/2 L
D
L
1 2 3 4 5 6 7
Contact surface pairs Simulated by element TARGE170
Simulated by element CONTA174
Bolt shank Bolt shank washers washers Nut Screw nut Center plate
End plate Center plate End plate Center plate End plate washers End plate
Fig. 9. Definition of bending moment and rotation of joint.
Fig. 10. Numerical models of the bolted plate connection. (a) Model about minor axes. (b) Model about major axes.
0.6
3.0
0.5
2.5
0.4
2.0
M (kN m)
M (kN m)
H.-H. Ma et al. / Thin-Walled Structures 88 (2015) 82–89
0.3 0.2
87
1.5 1.0
Experiment
0.1
Experiment
0.5
FE Modeling
FE Modeling 0.0 0.0
0.1
0.2
0.3
0.0 0.0
0.4
0.1
0.2
Φ (rad)
0.3
0.4
0.5
Φ (rad)
1.0
5
0.8
4
M (kN m)
M (kN m)
Fig. 11. Comparison of moment–rotation curves for BPC300 joint. (a) BPC300-T1 about minor axes. (b) BPC300-T2 about major axes.
0.6
0.4
0.2
3
2
1
Experiment
Experiment FE Modeling
FE Modeling 0.0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0 0.0
Φ (rad)
0.1
0.2
0.3
0.4
0.5
Φ (rad)
Fig. 12. Comparison of moment–rotation curves for BPC350 joint. (a) BPC350-T3 about minor axes. (b) BPC350-T4 about major axes.
is 235 MPa, and the member cross sections are
Table 4 Comparison of experimental and numerical results. Specimen Test no. BPC300 BPC350
T1 T2 T3 T4
Φ76 6.3.
Loading axis
Experiment (kN m)
FEM (kN m)
M Experiment =M FEM
Minor Major Minor Major
0.495 2.250 0.680 3.60
0.556 2.510 0.770 4.000
0.89 0.90 0.88 0.90
where M Experiment =M FEM indicate the ratios of the experimental maximum bending moments to the numerical maximum bending moments.
5. Critical buckling load of a single-layer reticulated cylindrical shell with BPC joint systems 5.1. Configuration and material properties of the single-layer reticulated cylindrical shell Single-layer reticulated cylindrical shells, with bolted plate joints BPC350 and three different rise to width ratios, were considered in the analysis. The shell is supported simply along its four boundary lines with pin joint supports. The overall dimensions are 15 10 m, with three different rise to width ratios (f/B ¼1/5, 1/4 and 1/3); as shown in Fig. 14(a) and (b). The material properties for all the members are the same— Modulus of elasticity is 2.06 MPa, Poison’s ratio is 0.3, Yield strength
Φ38 3.5 and
5.2. Method and results of the analysis The study identifies a structural member as the basic element for establishing the numerical model of the lattice shells using ANSYS [12], as shown in Fig. 15. The member model is composed of: (i) an elasto-plastic beam element; with (ii) node areas at both ends; and (iii) non-linear spring elements connecting the beam and ball nodes. The non-linear spring element COMBIN39, with unidirectional freedom and non-linear characteristics, is used to simulate the bending stiffness and moment capacity of the flexible joints. Both the tube and the node area in the model are simulated using elasto-plastic beam elements BEAM189; the section of the node area being greater than that of the tube due to its higher stiffness. Non-linear numerical analyses were performed to estimate the buckling load of the cylindrical reticulated shell with the bolted plate connection. The buckling loads for the shells with different rise to width ratios (f/B) were obtained, and the results are shown in Figs. 16 and 17. Fig. 16 represents the load-deflection curves of the numerical non-linear analysis for all three rise-width ratios. The critical loads of the shells are presented in Fig. 17. From these figures it can be seen that: (i) a single-layer reticulated dome with a bolted plate joint system has a certain load-bearing capacity; (ii) the critical load increases with an increase of f/B.
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that the single-layer reticulated dome with a bolted plate joint system, can be a good solution for a space structure with a small or medium span.
6. Conclusion The analytical results obtained with the model for four bolted plate joints, using ANSYS simulation with SOLID187, CONTACT174 and TARGET170 elements, fits well with the experimental results. This indicates that the actual bending stiffness of a bolted plate joint system can be correctly predicted using the model. The high stresses were concentrated in the end plate of the tubular member, both in the numerical analysis and the test specimen. This indicated that the end plate is the weaker part of the connection, and the mechanical behavior of the connection can be improved by increasing the thickness of the end plate. Although it is generally accepted that the connections of a single-layer reticulated dome should be rigid, the study of a singlelayer reticulated dome with a bolted plate connection indicates that it has a certain load-bearing capacity. It is therefore concluded
Fig. 15. Member model of single-layer latticed domes.
300
300 1 2 3 4 5 6 7 8 9 10 11 12 13 14
100 0 -100 -200 -300
0.0
0.1
0.2
0.3
0.4
0.5
1 2 3 4 5 6 7 8 9 10 11 12 13 14
200
Stress (Mpa)
Stress (Mpa)
200
100 0 -100 -200 -300 0.0
0.6
0.2
Bending Moment (kN m)
300
0.8
1.0
100 0 -100 -200
0.0
0.5
1.0
1.5
2.0
Bending Moment (kN m)
2.5
3.0
1 2 3 4 5 6 7 8 9 10 11 12 13 14
200
Stress (Mpa)
Stresses (Mpa)
0.6
300
1 2 3 4 5 6 7 8 9 10 11 12 13 14
200
-300
0.4
Bending Moment (kN m)
100 0 -100 -200 -300 0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
Bending Moment (kN m)
Fig. 13. Stress distribution at different parts of the four specimens. (a) Stress distribution of BPC300 about the minor axis. (b) Stress distribution of BPC350 about the minor axis. (c) Stress distribution of BPC300 about the major axis. (d) Stress distribution of BPC350 about the major axis.
Fig. 14. Single-layer cylindrical reticulated shell. (a) Geometry of the cylindrical reticulated shell. (b) Supports along the boundary.
H.-H. Ma et al. / Thin-Walled Structures 88 (2015) 82–89
References
Buckling Load (kN/m2)
6 f/B=1/5 f/B=1/4 f/B=1/3
5 4 3 2 1 0 0
50
100
150
200
250
300
Deflection(mm) Fig. 16. Load-deflection curves for different f/B values.
Buckling Load (kN/m2)
7
6
5
4
3
2
1/5
1/4
1/3
89
1/2
f/B Fig. 17. Buckling load vs f/B values.
Acknowledgement This research is supported by grants from the Natural Science Foundation of China under Grant no. 51308153; China Postdoctoral Science Foundation funded project no. 2013M531020; the Fundamental Research Funds for the Central Universities Grant no. HIT. NSRIF. 2014099.
[1] Tagiguchi Y, Saka T, Shuku Y. Buckling behavior of space trusses constructed by a bolted jointing system, space structures 4. In: Proceedings of the fourth international conference on space structures. Guildford, UK: 1993. p.89-98. [2] Ueki T, Matsushita F, Shibata R, Kato S. Design procedure for single-layer latticed domes, space structures 4. In: Proceedings of the fourth international conference on space structures. Guildford, UK; 1993. p.237-246. [3] Kato S, Mutoh I, Shomura M. Effect of joint rigidity on buckling strength of single layer lattice domes, spatial, lattice and tension structures. In: Proceeding of IASS-ASCE international symposium. Georgia, USA; 1994. p.468-477. [4] Hiyam Y, Iijima T, Takashima H, Taniguchi N. Buckling behavior of ball joined single layer reticular domes using aluminum alloys, shells and spatial structures. In: 40th Anniversary congress of the international association for shell and spatial structures, vol. 1. Madrid, Spain; 1999. p. B2.13–B2.20. [5] Makowski ZS. Analysis, design and construction of braced domes. London, UK: GRANADA; 1984. [6] Landesmann, A. et al. (2001). Implementação de modelo avançado para análise estrutural com ligações semi-rígidas. Anais do IV Seminário Internacional “O Uso de Estruturas Metálicas na Construção Civil” e I Congresso Internacional da Construção Metálica – I CICOM. São Paulo – SP. [7] López Aitziber, Puente Iñigo, Serna Miguel A. Numerical model and experimental tests on single-layer latticed domes with semi-rigid joints. Comput Struct 2007;85:360–74. [8] Lee SL, See T, Swaddiwudhipong S. Development and testing of a universal space frame connector. Int J Space Struct 1990;5(2):130–8. [9] Swaddiwudhipong S, Koh CG, Lee SL. Development and experimental investigation of a space frame connector. Int J Space Struct 1994;9(2):99–106. [10] Shibata R Kato S, Yamada S. Experimental study on the ultimate strength of single-layer reticular domes. In: Proceedings of the fourth international conference of space structures. University of Surry, UK; 1993. p.387–395. [11] EI-Sheikh AI. Numerical analysis of space trusses with flexible member-end joints. Int J Space Struct 1993;8(3):189–97. [12] Ma Huihuan, Fan Feng, Shen Shizhao. Numerical parametric investigation of single-layer latticed domes with semi-rigid joints. J Int Assoc Shell Spatial Struct 2008;49(2):99–110. [13] López Aitziber, Iñigo Puente, Serna Miguel A. Direct evaluation of the buckling loads of semi-rigidly jointed single-layer latticed domes under symmetric loading. Eng Struct 2007;29:101–9. [14] Huihuan Ma, Feng Fan, Zhenggang Cao, Shizhao Shen. Direct estimation of critical load for single-layer reticulated domes with semi-rigid joints. Int J Space Struct 2010;25(1):15–24. [15] Kato S, Mutoh I, Shomura M. Collapse of semi-rigidly jointed reticulated domes with initial geometric imperfections. J Constr Steel Res 1998;48:145–68. [16] EI-Sheikh AI. Numerical analysis of space trusses with flexible member-end joints Int J Space Struct 1993;8(3):189–97. [17] Chenaghlou MR, Nooshin H. Response of semi-rigidly jointed space structures, space structures, vol. 5. London: Thomas Telford; 2002. [18] Chinese Code for design of steel structures (GB50017-2003).
Contents lists available at ScienceDirect
Thin-Walled Structures journal homepage: www.elsevier.com/locate/tws
An experimental and numerical study of a semi-rigid bolted-plate connections (BPC) Hui-Huan Ma a,n, Ali Mohamed Issa b, Feng Fan c, Guy Oyeniran Adeoti d a
School of Civil Engineering, Harbin Institute of Technology, Harbin 150090, PR China Civil Engineering Department, University of Kordofan, El Obeid, Sudan c School of Civil Engineering, Harbin Institute of Technology, Harbin 150090, PR China d School of Civil Engineering, Harbin Institute of Technology, Harbin 150090, PR China b
art ic l e i nf o
a b s t r a c t
Article history: Received 27 February 2014 Received in revised form 11 November 2014 Accepted 11 November 2014
The aim of this paper is to evaluate the bending stiffness of a new bolted-plate joint for single-layer or double-layer reticulated shells. In order to investigate the performance of the joint, experimental tests and numerical simulations were undertaken. ANSYS was used for the numerical study, with contact elements (target 170 and contact 174) and solid elements (solid 187), used to establish bending stiffness curves for the bolted-plate joints. The good agreement between numerical simulation and experiment indicated that the simulation is an accurate and effective way of evaluating the mechanical properties of the bolted-plate joint system. In addition, using nonlinear beam elements (beam 189 element) with end spring elements (combin39), the single-layer reticulated cylindrical shell with bolted-plate joints was analyzed for different rise to width ratios. The analyses determined the load-bearing capacity of the shell. It is concluded that the bolted-plate joint system is a good choice for space structures with small or medium spans. & 2014 Elsevier Ltd. All rights reserved.
Keywords: Bolted connections Experimental analysis Reticulated shell Semi-rigid connections Numerical simulation
1. Introduction The ultimate strength of all types of space frame (single, double or triple-layer space structures) is controlled by the joint rigidity, the geometric shape and the material properties of the members. The joint rigidity appears to have the most significant influence [1–4]. The rigidity of connections has been investigated in experimental tests, which show non-linear behavior. The MERO joint system is one of the most popular semi-rigid joint systems. It was developed by Dr. Ing. Max. Mengeringhausen in 1942. The MERO system is widely used for double-layered roof structures, with either flat or curved surfaces [5]. The joint consists of a spherical node forged with flat facets and tapped holes. Members are circular hollow sections with cone-shaped steel forgings welded at the two ends. The ends accommodate bolts for connection with the joint. The bolts are tightened by means of a hexagonal sleeve and dowel pin arrangement, resulting in a completed joint such as that shown in Fig. 1. In the original version, up to 18 tubular members can be connected at a joint with no eccentricity.
n Correspondence to: Lecturer, School of Civil Engineering, Harbin Institute of Technology, 202 Haihe Road, Nangang District, Harbin 150090, PR China. E-mail addresses: [email protected] (H.-H. Ma), [email protected] (A.M. Issa), [email protected] (G.O. Adeoti).
http://dx.doi.org/10.1016/j.tws.2014.11.011 0263-8231/& 2014 Elsevier Ltd. All rights reserved.
Many researchers have studied the mechanical behavior of joint systems and developed new systems. Works by Landesmann et al. [6] led to the implementation of a model for structural analysis with semi-rigid connections. López et al. [7] obtained the rigidity of one semi-rigid joint in both experimental and numerical studies. Lee et al. [8] and Swaddiwudhipong et al. [9] experimentally investigated two special frame connections up to failure and obtained their bending stiffnesses. The experimental study conducted by Shibata et al. [10] established moment–rotation curves for some semi-rigid joints. EI-Sheikh obtained experimentally, the bending stiffness of one kind of bolt-ball joint system [11]. Feng Fan, Ma et al. [12] investigated the moment–rotation characteristics of bolt-ball joints using experiments and numerical analysis, and revealed significant non-linearity of the joint response, even at an early stage of loading. Based on the bending–rotation curves of the bolt-ball joints obtained through numerical simulation, a finite element model of single-layer reticulated domes with boltball joints was developed, using nonlinear beam elements with end spring elements using ANSYS software. Aitziber et al. [13,7], Ma et al. [14] and Kato et al. [15] verified that the rigidity of the joints is an important factor that influences the behavior of single layer latticed domes. El-Sheikh [16], Chenaghlou and Nooshin [17] found out that the overall behavior, and the failure mode of a structure, are influenced by the bending stiffness of the connections. From all of these studies, it can be concluded that the
H.-H. Ma et al. / Thin-Walled Structures 88 (2015) 82–89
bending stiffness and strength of connections needs to be considered when analyzing spatial structures, and the behaviour of joints plays a key role in the behavior of spatial structures. Also, most of these systems have bolted connections, since welded connections can be expensive with more constructive difficulties, and therefore are practically uneconomical. Joints are crucial elements in structures. Nowadays, one of the main concerns of structural designers is to develop an appropriate joint system which can provide the structure with enough stiffness and meet, at the same time, other important requirements such as easy to be prefabricated, ease of erection and economic advantages. In view of these merits, this paper is focused on the assessment of the behavior of a new semi-rigid assemble joint-system for space trusses and reticulated shells (Fig. 2). A series of tests on the new joints were conducted in the School of Civil Engineering, Harbin Institute of Technology, China. The dimensions and sizes are in accord with the Chinese Code for design of steel structures (GB50017-2003) [18]. The
83
bolted-plate connection used for this experiment can be fabricated and erected easily. This connection can be used for medium and short-span space structures. The bolted-plate connection is a semi-rigid joint system that includes a base gusset plate, bolts with nuts and washers and tubular members with end plates. Fig. 3. shows various configuration diagrams. It can be easily used in single-layer or double-layer reticulated shells.
2. The test program 2.1. Test setup and material properties The experimental set-up is shown in Fig. 4. It was designed to obtain moment–rotation curves for the connection. This test
Sleeve Slot Dowel pin Steel tuble
Sleeve
Bolt Ball
End cone End cone
Ball node Pipe
Fig. 1. MERO joint. (a) Overview. (b) Sectional view.
Fig. 2. New type of semi-rigid bolted plate connections. (a) For double-layer grid structures. (b) For single-layer reticulated shell structures.
Fig. 3. Pictures and configuration diagrams of bolted plate connections.
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2.2. Test procedure
specimen was simply supported on concrete columns and subjected to a vertical load at its centre. The loading system was a screw jack with a load cell. The lengths of the specimen beams were about 1200 mm. The displacement at different points (points 1 to 6) and the central load were measured by displacement transducers and a load cell, as shown in Fig. 4. The distances, l1, l2, l3 and l4, between the displacement transducers, were recorded before the test. The strains at different positions in the specimen were measured using strain gauges, and the specific location were recorded before loading. The gauge arrangement and numbering scheme is shown in Fig. 5. 1/2, 7/11, 8/12, 9/13, and 10/14 in the figure indicate two gauge numbers; the first number is for the gauge on the top side of the plate, and the second is for the gauge on the bottom side.
To investigate the mechanical behavior of the bolted plate connection, the specimen set-up in Fig. 6 was adopted. The bending stiffnesses of the connection under bending moment and shear force, for both of the major and minor axes, were obtained. The vertical load acting at the centre of the connection was gradually increased, and at the same time the displacement transducer measurements were recorded, to allow the joint rotation to be calculated. In addition, the strain gauges recorded the stresses at different parts of the specimen. The mechanical properties of the material components of the test specimens are presented in Table 1. The specimens’ dimensions are shown in Table 2.
Fig. 4. Test setup.
3
4
5
6
7/11
1/2
8/12
L
10/14 9/13
L3
L2
L1 L
Fig. 5. Numbering and arrangement of the strain gauges.
Fig. 6. Testing setup of the specimen. (a) Major axis. (b) Minor axis.
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The loading process was controlled as follows. At first, the joint specimens were subject to a small load and unloaded in order to ensure the loading apparatus and the displacement gauges were working properly and to allow the different parts of the specimen to work as a whole. Then, the test was carried out under force control in the elastic range of the joints. At this stage, the centre displacement of the specimen increased continuously with increasing force. Subsequently, when the joints were loaded up to their nonlinear region, the test control was changed to displacement control
Table 1 Test specimens’ material properties. Component
Material Yield strength standard/grate Fy (MPa)
Poisson ratio
Modulus of elasticity (GPa)
Central plate Tubular member Bolts
Q235 Q235 High tensile steel/10.9
0.3 0.3 0.3
206 206 223
235 235 900
Table 2 Test specimen dimension. Test no.
Loading axis
Bolt
T1 T2 T3 T4
BPC300 major BPC300 minor BPC350 major BPC350 minor
until failure of the joint occurred. In this phase, the moment– rotation curve of the joint moves from the stiff part to the soft part. The load force increased slowly, however, the centre displacement increased sharply. Figs. 7 and 8 show pictures of the specimens at the initial stage and after the test. During the test, each load increment lasted for at least 10 min to make the transformation stable.
3. Comparison of test and numerical results The mechanical behavior of the connections can be represented by M–Φ curves that describe the relationship between the applied bending moment M and the corresponding rotation Φ of the joint. In this experimental study, the M–Φ curves were established indirectly, as the values of M and Φ were calculated based on the readings of the displacement transducers and load cells. The bending moment, M, acting on the connection, is equal to the product of the applied load F and the distance between the load application point and the connection point, L, as shown in Fig. 9. The rotational deformation, Φ, in Fig. 9, is the sum of the elastic deformation of the steel pipe and the rotational deformation of the connection φ. In these tests, the elastic deformation of the steel pipe can be neglected as it is quite small in comparison with the
Dimensions in (mm) l
l1
l2
l3
Gusset thickness
End plate thickness
Gusset flange height
M12 300 25 40 75 10
8
90
M12 300 25 40 75 10
8
90
M16 350 30 40 75 15
10
90
M16 350 30 40 80 15
10
90
85
Fig. 8. The specimens after testing.
Fig. 7. Failure modes of the specimens. (a) Failure mode in the major axis direction. (b) Failure mode about the minor axis.
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connection deformation. Therefore, Φ is approximately equal The rotation deformation Φ is calculated as follows:
Φ¼
∑nk ¼ 1 Φij n
Φij ¼ arctan
φ. ð1Þ
δi δj
ð2Þ
lij
where δi and δj are the displacements measured by the displacement transducers at the points i and j (Points 1–3 or 4–6 in Fig. 4), and lij is the distance between the two points. To get more accurate data, all the values of lij were recorded after the specimens and measurement devices were installed. For the four bolted plate connections which were tested, Finite Element Analysis (FEA) was undertaken using ANSYS, Inc.’s mechanical APDL Software release 14.5. The dimensions were the same as the tested connections BPC300 and BPC350. Since the geometry of the BPC joint under pure bending moment (Fig. 6) is symmetric, only half of the specimen was modeled to save the analysis time. The boundary condition of the joints was the same; i.e. the node area is fixed and the forces act on the end of the pipe. The numerical solid models were established with element type SOLID187 and used the properties of the actual material, as shown in Fig. 10. For the contact algorithm, the Lagrange method with higher order contact elements CONTA174 and TARG170 was used. The surface names and the element chosen for different surface are listed in Table 3. The experimental and non-linear numerical results are plotted in Figs. 11 and 12, and the maximum bending moments are listed in Table 4.
4. Discussion Fig. 11(a), presents a graphical result of the experimental and numerical analysis of the moment–rotation curves for BPC300 bending about the minor axis. From this graph, it can be observed that the experimental and numerical results are close when the rotation is smaller than 0.04 rad; then there is a slight variation between experimental and numerical results. This variation may be due to imperfections of geometry and material uniformity of
the mass distribution. The non-linear zone, for both numerical and experiment results, corresponds to bending moments greater than 0.4 kN m. Failure occurred for the test specimen at a bending moment of about 0.5 kN m, and at about 0.55 kN m for the numerical analysis. Fig. 12(a), presents moment–rotation curves for the connection BPC350 bending about the minor axis. Both experimental and numerical non-linear analysis results agree for bending moments up to a rotation of 0.03 rad. The elastic zones for the test specimen and the numerical non-linear analysis are the same between 0.0 and 0.6 kN m, before the non-linear behavior occurs. Failure occurred for the test specimen at a bending moment of about 0.68 kN m, and for the numerical it occurred at about 0.8 kN m. Figs. 11(b) and 12(b), show graphical results for the test specimens BPC300 and BPC350 and numerical non-linear analysis results, and moment–rotation curves about the major axes. Similar to the results about the minor axes, the experiment and numerical results agree in bending moments in the elastic zone (from 0 to 1.5 kN m for BPC300; from 0 to 3.0 kN m for BPC350), but there are slight variations in the non-linear zone. In general, the four experimental results showed close agreement with the nonlinear numerical analysis results within the linear elastic zone, but slight variations in the non-linear zone. The ratios of the experimental results to the corresponding numerical results are between 0.88 and 0.90, as shown in Table 4. Fig. 13. shows the stress at different parts of the connections due to bending moments about the major and minor axes. During the tests, for all the specimens, the largest deformations occur at the end plate of the tubular member when the connections experience excessive deformation, and the stresses in the end plate of the tubular member are bigger. Therefore, strain gauges 1, 2, 3 and 5 are high. From the results, it can be seen that the mechanical performance of the connection can be improved effectively by: (i). increasing the cross section area of the end plate; and (ii). using tube with a double end plate or higher yield strength materials.
Table 3 Contact surfaces in the model. Number
F
M=F·L/2 L
D
L
1 2 3 4 5 6 7
Contact surface pairs Simulated by element TARGE170
Simulated by element CONTA174
Bolt shank Bolt shank washers washers Nut Screw nut Center plate
End plate Center plate End plate Center plate End plate washers End plate
Fig. 9. Definition of bending moment and rotation of joint.
Fig. 10. Numerical models of the bolted plate connection. (a) Model about minor axes. (b) Model about major axes.
0.6
3.0
0.5
2.5
0.4
2.0
M (kN m)
M (kN m)
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0.3 0.2
87
1.5 1.0
Experiment
0.1
Experiment
0.5
FE Modeling
FE Modeling 0.0 0.0
0.1
0.2
0.3
0.0 0.0
0.4
0.1
0.2
Φ (rad)
0.3
0.4
0.5
Φ (rad)
1.0
5
0.8
4
M (kN m)
M (kN m)
Fig. 11. Comparison of moment–rotation curves for BPC300 joint. (a) BPC300-T1 about minor axes. (b) BPC300-T2 about major axes.
0.6
0.4
0.2
3
2
1
Experiment
Experiment FE Modeling
FE Modeling 0.0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0 0.0
Φ (rad)
0.1
0.2
0.3
0.4
0.5
Φ (rad)
Fig. 12. Comparison of moment–rotation curves for BPC350 joint. (a) BPC350-T3 about minor axes. (b) BPC350-T4 about major axes.
is 235 MPa, and the member cross sections are
Table 4 Comparison of experimental and numerical results. Specimen Test no. BPC300 BPC350
T1 T2 T3 T4
Φ76 6.3.
Loading axis
Experiment (kN m)
FEM (kN m)
M Experiment =M FEM
Minor Major Minor Major
0.495 2.250 0.680 3.60
0.556 2.510 0.770 4.000
0.89 0.90 0.88 0.90
where M Experiment =M FEM indicate the ratios of the experimental maximum bending moments to the numerical maximum bending moments.
5. Critical buckling load of a single-layer reticulated cylindrical shell with BPC joint systems 5.1. Configuration and material properties of the single-layer reticulated cylindrical shell Single-layer reticulated cylindrical shells, with bolted plate joints BPC350 and three different rise to width ratios, were considered in the analysis. The shell is supported simply along its four boundary lines with pin joint supports. The overall dimensions are 15 10 m, with three different rise to width ratios (f/B ¼1/5, 1/4 and 1/3); as shown in Fig. 14(a) and (b). The material properties for all the members are the same— Modulus of elasticity is 2.06 MPa, Poison’s ratio is 0.3, Yield strength
Φ38 3.5 and
5.2. Method and results of the analysis The study identifies a structural member as the basic element for establishing the numerical model of the lattice shells using ANSYS [12], as shown in Fig. 15. The member model is composed of: (i) an elasto-plastic beam element; with (ii) node areas at both ends; and (iii) non-linear spring elements connecting the beam and ball nodes. The non-linear spring element COMBIN39, with unidirectional freedom and non-linear characteristics, is used to simulate the bending stiffness and moment capacity of the flexible joints. Both the tube and the node area in the model are simulated using elasto-plastic beam elements BEAM189; the section of the node area being greater than that of the tube due to its higher stiffness. Non-linear numerical analyses were performed to estimate the buckling load of the cylindrical reticulated shell with the bolted plate connection. The buckling loads for the shells with different rise to width ratios (f/B) were obtained, and the results are shown in Figs. 16 and 17. Fig. 16 represents the load-deflection curves of the numerical non-linear analysis for all three rise-width ratios. The critical loads of the shells are presented in Fig. 17. From these figures it can be seen that: (i) a single-layer reticulated dome with a bolted plate joint system has a certain load-bearing capacity; (ii) the critical load increases with an increase of f/B.
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that the single-layer reticulated dome with a bolted plate joint system, can be a good solution for a space structure with a small or medium span.
6. Conclusion The analytical results obtained with the model for four bolted plate joints, using ANSYS simulation with SOLID187, CONTACT174 and TARGET170 elements, fits well with the experimental results. This indicates that the actual bending stiffness of a bolted plate joint system can be correctly predicted using the model. The high stresses were concentrated in the end plate of the tubular member, both in the numerical analysis and the test specimen. This indicated that the end plate is the weaker part of the connection, and the mechanical behavior of the connection can be improved by increasing the thickness of the end plate. Although it is generally accepted that the connections of a single-layer reticulated dome should be rigid, the study of a singlelayer reticulated dome with a bolted plate connection indicates that it has a certain load-bearing capacity. It is therefore concluded
Fig. 15. Member model of single-layer latticed domes.
300
300 1 2 3 4 5 6 7 8 9 10 11 12 13 14
100 0 -100 -200 -300
0.0
0.1
0.2
0.3
0.4
0.5
1 2 3 4 5 6 7 8 9 10 11 12 13 14
200
Stress (Mpa)
Stress (Mpa)
200
100 0 -100 -200 -300 0.0
0.6
0.2
Bending Moment (kN m)
300
0.8
1.0
100 0 -100 -200
0.0
0.5
1.0
1.5
2.0
Bending Moment (kN m)
2.5
3.0
1 2 3 4 5 6 7 8 9 10 11 12 13 14
200
Stress (Mpa)
Stresses (Mpa)
0.6
300
1 2 3 4 5 6 7 8 9 10 11 12 13 14
200
-300
0.4
Bending Moment (kN m)
100 0 -100 -200 -300 0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
Bending Moment (kN m)
Fig. 13. Stress distribution at different parts of the four specimens. (a) Stress distribution of BPC300 about the minor axis. (b) Stress distribution of BPC350 about the minor axis. (c) Stress distribution of BPC300 about the major axis. (d) Stress distribution of BPC350 about the major axis.
Fig. 14. Single-layer cylindrical reticulated shell. (a) Geometry of the cylindrical reticulated shell. (b) Supports along the boundary.
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References
Buckling Load (kN/m2)
6 f/B=1/5 f/B=1/4 f/B=1/3
5 4 3 2 1 0 0
50
100
150
200
250
300
Deflection(mm) Fig. 16. Load-deflection curves for different f/B values.
Buckling Load (kN/m2)
7
6
5
4
3
2
1/5
1/4
1/3
89
1/2
f/B Fig. 17. Buckling load vs f/B values.
Acknowledgement This research is supported by grants from the Natural Science Foundation of China under Grant no. 51308153; China Postdoctoral Science Foundation funded project no. 2013M531020; the Fundamental Research Funds for the Central Universities Grant no. HIT. NSRIF. 2014099.
[1] Tagiguchi Y, Saka T, Shuku Y. Buckling behavior of space trusses constructed by a bolted jointing system, space structures 4. In: Proceedings of the fourth international conference on space structures. Guildford, UK: 1993. p.89-98. [2] Ueki T, Matsushita F, Shibata R, Kato S. Design procedure for single-layer latticed domes, space structures 4. In: Proceedings of the fourth international conference on space structures. Guildford, UK; 1993. p.237-246. [3] Kato S, Mutoh I, Shomura M. Effect of joint rigidity on buckling strength of single layer lattice domes, spatial, lattice and tension structures. In: Proceeding of IASS-ASCE international symposium. Georgia, USA; 1994. p.468-477. [4] Hiyam Y, Iijima T, Takashima H, Taniguchi N. Buckling behavior of ball joined single layer reticular domes using aluminum alloys, shells and spatial structures. In: 40th Anniversary congress of the international association for shell and spatial structures, vol. 1. Madrid, Spain; 1999. p. B2.13–B2.20. [5] Makowski ZS. Analysis, design and construction of braced domes. London, UK: GRANADA; 1984. [6] Landesmann, A. et al. (2001). Implementação de modelo avançado para análise estrutural com ligações semi-rígidas. Anais do IV Seminário Internacional “O Uso de Estruturas Metálicas na Construção Civil” e I Congresso Internacional da Construção Metálica – I CICOM. São Paulo – SP. [7] López Aitziber, Puente Iñigo, Serna Miguel A. Numerical model and experimental tests on single-layer latticed domes with semi-rigid joints. Comput Struct 2007;85:360–74. [8] Lee SL, See T, Swaddiwudhipong S. Development and testing of a universal space frame connector. Int J Space Struct 1990;5(2):130–8. [9] Swaddiwudhipong S, Koh CG, Lee SL. Development and experimental investigation of a space frame connector. Int J Space Struct 1994;9(2):99–106. [10] Shibata R Kato S, Yamada S. Experimental study on the ultimate strength of single-layer reticular domes. In: Proceedings of the fourth international conference of space structures. University of Surry, UK; 1993. p.387–395. [11] EI-Sheikh AI. Numerical analysis of space trusses with flexible member-end joints. Int J Space Struct 1993;8(3):189–97. [12] Ma Huihuan, Fan Feng, Shen Shizhao. Numerical parametric investigation of single-layer latticed domes with semi-rigid joints. J Int Assoc Shell Spatial Struct 2008;49(2):99–110. [13] López Aitziber, Iñigo Puente, Serna Miguel A. Direct evaluation of the buckling loads of semi-rigidly jointed single-layer latticed domes under symmetric loading. Eng Struct 2007;29:101–9. [14] Huihuan Ma, Feng Fan, Zhenggang Cao, Shizhao Shen. Direct estimation of critical load for single-layer reticulated domes with semi-rigid joints. Int J Space Struct 2010;25(1):15–24. [15] Kato S, Mutoh I, Shomura M. Collapse of semi-rigidly jointed reticulated domes with initial geometric imperfections. J Constr Steel Res 1998;48:145–68. [16] EI-Sheikh AI. Numerical analysis of space trusses with flexible member-end joints Int J Space Struct 1993;8(3):189–97. [17] Chenaghlou MR, Nooshin H. Response of semi-rigidly jointed space structures, space structures, vol. 5. London: Thomas Telford; 2002. [18] Chinese Code for design of steel structures (GB50017-2003).