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Performance analysis and design of bolted connections in modularized prefabricated steel structures
Journal of Constructional Steel Research 133 (2017) 360–373
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Journal of Constructional Steel Research
Performance analysis and design of bolted connections in modularized prefabricated steel structures X.C. Liu a,b,⁎, S.H. Pu a, A.L. Zhang a,b, X.X. Zhan a a b
Beijing Engineering Research Center of High-rise and Large-span Prestressed Steel Structures, Beijing University of Technology, Beijing 100124, China Beijing Key Laboratory of Earthquake Engineering and Structural Retrofit, Beijing University of Technology, Beijing 100124, China
a r t i c l e
i n f o
Article history: Received 4 March 2016 Received in revised form 14 February 2017 Accepted 26 February 2017 Available online xxxx Keywords: Prefabricated steel structure Truss-to-column connection Column-to-column connection Slip on contact surface Energy dissipation from slips Simplified calculation
a b s t r a c t The present study proposes a new-type all-bolted connection that can be used to connect trusses to columns and columns to columns on site in modularized prefabricated multi-rise and high-rise steel structures. The proposed connection connects columns through flanges, connects trusses to columns through cover plates that extend from the flanges and through vertical connecting plates and joint flitches. The stiffness of the connection can be controlled by adjusting the number or size of the bolts and undergoes step-like change as the load changes. Therefore, the connection can be rigid during weak earthquake, while the cover plates can slip relative to the chord members during strong earthquake, thereby dissipating energy. The FEA results was compared with experimental results and showed good agreement at all stages of loading, then the static performance of six connections with different friction coefficient or size of components were studied by FEA. The FEA results were used to determine mechanical properties of the connections that were difficult to obtain from the tests, such as the changing rule of the bolt tension, the stress distribution of bolt, the contact force on various contact surface, and the pressure on the wall of bolt hole, as well as the effects of friction coefficient on the performance of the connections. The mechanical model of the connection was established and the mechanical mechanism of the connection was got. Furthermore, simplified calculating formulas for the connection under slip state, yield state and ultimate state were proposed respectively. © 2017 Elsevier Ltd. All rights reserved.
1. Introduction During the Northridge earthquake in 1994 and the Hanshin earthquake in 1995, the beam-to-column connections of many steel structures suffered brittle failure, some even resulting in failure of entire building. The plastic deformation capacity of the structures was not fully developed. Later, shifting the plastic hinge outwardly to avoid weld seams became the major direction on improving seismic performance of beam-to-column connections [1–4]. Zhang et al. [5] conducted monotonic loading tests on prefabricated truss-to-column connections. They analyzed the stiffness, bearing capacity and ductile performance, and studied the effects of the thickness of the connecting plate and size of the members of the truss on the bearing capacity and failure mode of the connection. The results showed that the thickness of the connecting plate had a large impact on the bearing capacity and the stiffness of the connection, and the size of members of the truss had a large impact on the bearing capacity of the connection. Ma et al. [6] conducted cyclic loading tests on a kind of all-bolted beam-to-column connection with slotted bolt holes, and compared with conventional ⁎ Corresponding author at: Beijing University of Technology, Beijing 100124, China. E-mail address: [email protected] (X.C. Liu).
http://dx.doi.org/10.1016/j.jcsr.2017.02.025 0143-974X/© 2017 Elsevier Ltd. All rights reserved.
welded connections. They found that the bolts slipped inside the bolt holes, resulting in a significant increase in the ductile deformation capacity. Dessouki et al. [7] and Bai et al. [8] conducted FEA on the performance of extended end-plate beam-to-column connections and proposed simplified formulas respectively. Rahnavard et al. [9] and Kulkarni et al. [10] conducted tests and FEA on connection with holes on beam web and investigated the effect of the form of the holes on the seismic performance, respectively. Aydin et al. [11] conducted experiments to study the influence of angles with and without stiffeners on the static performance of beam-to-column connections that were designed with top-and-seat angles in minor column axes. Tests can better reflect the mechanical performance of connections and can simultaneously consider the effects of material defects, geometric defects, welding defects, and the initial stress. However, tests require large amounts of manpower, materials, and time. In addition, test results only show the combined effect of the aforementioned factors instead of the independent effect of each individual factor [12–15]. The FEA can better facilitate the establishment of many models for parameter analysis [16–19]. Nguyen et al. [20] conducted FEA of semi-rigid connections in spatial steel frames, and compared the FEA results with the test results, which verified the finite element model. The cyclic behavior of connections is captured by the independent hardening model.
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Reference [21] presents numerical study on high-strength steel endplate connections under fire conditions using ABAQUS finite element software, which revealed additional information on the behavior of high-strength steel endplate connections. It has been demonstrated that FEA gives reasonable accuracy compared with experimental results, providing an efficient, economical, and accurate tool for studying the performance of connections. In addition, due to the limitation of factors such as economy and test equipment, it is very difficult to accurately monitor the tension of high-strength bolts, the contact force and slipping rule of contact surfaces in actual engineering or tests, thus FEA become the best selection. Previous studies have mainly focused on the stress losses of high-strength bolts under shear and have not monitor and analyze the tension of the high-strength bolts and the slipping rule of the contact surfaces under actual working conditions [22–25], which can be monitored by the finite element analysis conveniently. The object of this study is to get the changing rule of bolt tension of the connection under complex loading conditions as well as the slipping rule of the contact surfaces. In the present study, ABAQUS finite element software was employed to conduct monotonic loading and cyclic loading simulation of two connections series with variable size of components (S3 and S4). The static bearing capacity, seismic capacity and failure mechanism of the connections were determined. In addition, the tension of the high-strength bolts as well as the friction on the contact surfaces were monitored to identify the changing rule in the tension of the high-strength bolts and the friction on the contact surfaces of this
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type of connection under actual working conditions, and to explore the effects of the bolt tension and the friction on the stress and failure mode of the connections. To study the effects of friction coefficient on the mechanic and seismic performance of the connection, friction coefficients of 0.303, 0.35 and 0.40 were selected for parametric analysis on specimens S3 and S4 series. Based on the test and FEA results, simplified formulas for this type of truss-to-column connection were proposed.
2. Finite element model 2.1. Specimen design To study the truss-to-column connection instead of the whole trussto-column joint, we designed S3-N and S4-N with the material Q235B steel. Fig. 1 shows the geometric dimensions of the all-bolted connection specimens. Table 1 lists the sectional parameters of the specimens. The distance from inflection point (where the moment is zero) to the intersection of truss and column is about 1/4 truss span under vertical load, the distance from inflection point to the intersection of truss and column is about 1/2 truss span under horizontal load. To study the performance of the connection under the combined action of vertical load and horizontal load, the beam length is between 1/4 and 1/2 truss span instead 1/2 truss span. Based on the mechanical characteristics of the connection under horizontal and vertical loading conditions in the
Fig. 1. Details for test specimens S3-N and S4-N. (a) Elevation drawing. (b) Planar drawing.
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Table 1 Dimensions of the components. Specimen number
Chord members
Web members
Test type
Number of bolts on each chord
S3-N S4-N
2L75X6 2L75X8
2L45X5 2L45X6
Quasi-static 4 Quasi-static 4
structure system, the two ends of the square HSS column were fixed, and the load was applied to the end of the truss [27]. 2.2. Finite element model The FEA was conducted on specimens S3-N and S4-N using the ABAQUS finite element software. The high-strength bolts were established in this finite element model because slipping on the contact surfaces in the tests. A dumbbell-shaped solid model was used to simulate the shank, nut and washer of the high-strength bolt. Additionally, the cylinder on each end of the bolt model had the same area as the washer of the actual high-strength bolt assembly. Furthermore, the middle cylinder of the bolt model had the same nominal diameter as bolt shank of each high-strength bolt. The bolt pretension was applied at the middle section of the bolt shank model. Based on the test results, the friction coefficient of the contact surface was 0.303, which is the average of three friction test models (0.29, 0.30 and 0.32), according to the technical specifications [26]. A hexagonal C3D8R element, which is an 8node linear brick with reduced integration and hourglass control (Fig. 2(a)), was used for meshing the bolt assembly. The tetrahedral C3D10 element, which is a 10-node quadratic tetrahedron, was used for meshing the truss due to its irregular shape. The hexagonal C3D8R element was used for meshing the other parts with regular shapes.
Contact relationships between the flange of upper column and the upper flange of column base, between the flange of lower column and the lower flange of column base were established, using the Coulomb friction model to simulate the contact pressure and friction on the contact surfaces of the flanges. The pressure contact and frictional contact between the lower surface of the upper cover plate and the upper surface of the upper chord member of the truss were established. In the same way, the contact relationship was established between the upper surface of the lower cover plate and the lower surface of the lower chord member of the truss. The pressure contact and frictional contact between the joint flitch and vertical connecting plate 1 were established. Similarly, the pressure contact and frictional contact between the joint flitch and vertical connecting plate 2 were also established. The friction coefficient of above-mentioned contact surfaces was 0.303. For each high-strength bolt, the pressure contact and frictional contact between the surface of the nut and the contact surface were established. The friction coefficient was 0.05. Additionally, a potential pressure contact between the side surface of the bolt shank and the wall of the bolt hole was established. When the bolt shank touched the wall of bolt hole, the bolt shank and the wall of bolt hole bore pressure; when the bolt shank didn't touch the wall of bolt hole, the contact force was zero. Each bolt was aligned with the center of the bolt hole. The effects of deviation in the location and size of bolt hole caused by installation and fabrication were not considered. The elastic modulus of an 160 × 162 × 20 mm rectangular rigid plate is ten times the steel material and the ultimate strength is unlimited. The rigid plate was fixed onto the loading end of the truss using tie constraint. The load was applied to each specimen by a reference point to simulate the concentrated force. Fixed constraints were applied to the square HSS as same locations as the test model. The global model of the specimens is shown in Fig. 2(b). Three material property tests were conducted on each type of component, thus five sets of material property tests were conducted on 15 specimens. The average value of all of the material tests were used as material constitutive relations for the FEA and test. Accordingly, the yield strength of the steel was 294 MPa, and the elastic modulus was 2.06 × 105 MPa. According to the certificate of quality assurance provided by the supplier, the yield strength of high-strength bolts was 975 MPa, the tensile strength was 1188 MPa, and the elastic modulus was 2.06 × 105 MPa. The materials of steel and bolt were simulated based on the bilinear kinematic hardening rule and von Mises yield criteria. The loading scheme in the finite element simulation was as the same as the tests. 2.3. Numbering system for high-strength bolts and contact surfaces The high-strength bolts and contact surfaces on the cover plates, joint flitch and column base flanges were numbered using an alphanumeric numbering system (Fig. 3). Each high-strength bolt on chord member B was numbered as Un. Each high-strength bolt on chord member A was numbered as Dn. Each high-strength bolt on the vertical connecting plates was numbered as Tn, only the numbers n are shown in Fig. 3, the letters are ignored. The contact surface between the upper cover plate and chord member B was numbered as UGX. The contact surface between the lower cover plate and chord member A was numbered as DGX. Each contact surface on the joint flitch was numbered as TBn. The contact surface between the flange of upper column and the upper flange of column base was numbered as UFF. The contact surface between the flange of lower column and the lower flange of column base was numbered as DFF. 3. Verification of FEA model 3.1. Hysteretic loop comparison
Fig. 2. Finite element model. (a) High-strength bolt model. (b) Overall model.
As shown in Fig. 4, the hysteretic curves of the two specimens were got by FEA and tests. Fig. 4 shows that the hysteretic loops obtained from the FEA closely match the tests: both hysteretic loops consisted
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Fig. 4. Hysteretic curves of the models. (a) Comparison of the hysteretic curves of specimen S3-N. (b) Comparison of the hysteretic curves of specimen S4-N.
of elastic stage, slip stage, elastic-plastic stage, and bearing capacity degradation stage. Moreover, the simulated ultimate bearing capacity was almost equal to that obtained from the test. Therefore, the finite element model was verified and further study on the connections could be performed by the finite element models. 3.2. Failure mode and comparison Fig. 5 summarizes the failure modes of the connections. The failure modes obtained from the FEA were almost same as that in the tests. These failure modes include the outward bending and torsional deformation of chord member B, the concave local buckling deformation of chord member A, the bending and torsional deformation of web members A and B, the elongation of the bolt holes, and significant slips between the cover plates and the chord members. The comparison of the failure models got from the FEA and test showed that the FEA could accurately simulate the phenomena that occurred during the test, thereby verifying the finite element model again. 4. Effect of friction coefficient
Fig. 3. Numbering system for high-strength bolts and interfaces. (a) Numbers of the contact surfaces and bolts on the cover plates. (b) Numbers of the contact surfaces and bolts on the flitch. (c) Numbers of the flange contact surfaces.
A comparative analysis of the hysteretic curves and failure modes of the connections showed that the finite element models are correct. Therefore, based on the finite element models, it is possible to investigate the effects of various parameters on the performance of the connections by changing the parameters, such as friction coefficient. The static analysis can show the changing rule of the tension of the highstrength bolts, the friction on the contact surfaces and the pressure on the wall of bolt hole more clearly. Therefore, static finite element analyses were conducted using friction coefficients of 0.303, 0.35, and 0.40
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respectively. The load-displacement curves at the loading point of the six models were obtained using ABAQUS finite element software (Fig. 6). It can be observed from Fig. 6 that the load-displacement curves of the six models had similar shapes: all the curves consisted of linear ascending stage (elastic stage), notable slip stage, curved ascending stage (elastic-plastic stage), and bearing capacity degradation stage. The friction coefficient of the contact surfaces had insignificant effect on the ultimate bearing capacity of the truss-to-column connections. When the friction coefficient decreased by 0.05, the ultimate bearing capacity were almost the same, indicating that the ultimate bearing capacity of each connection was not affected by friction coefficient. While, it was determined by the new connection system established after the slip completed, at which time the wall of bolt hole on the upper flange of the truss began to bear pressure. The friction coefficient had large impact on the slip load of this connection. The greater the friction coefficient was, the greater the slip load was. The slip loads of connection with different-size components of truss but with the same friction coefficient were essentially the same. However, the greater the component size of the truss was, the greater the ultimate bearing capacity was. Each of the six models has sufficient elastic-plastic deformation capacity and large ultimate displacement. 5. Changing rule of tension and stress distribution of high-strength bolts 5.1. Changing rule of tension of high-strength bolts A tracking analysis was conducted on the tension of 12 highstrength bolts on the upper and lower cover plates and the joint flitch of each model. The curves of the tension of the high-strength bolts with the displacement of the loading point were generated (Figs. 7 and 8). Figs. 7 and 8 show that the tension of the high-strength bolts on the chord and web members of the truss all decreased during the loading process. In all cases, the tension of the first-row of high-strength bolts on the upper cover plate (U1 and U2) showed the greatest decrease. For model S3, the tension of high-strength bolts U1 and U2 decreased by as much as 68%. For model S4, the tension of high-strength bolts U1 and U2 decreased by as much as 57%. A comparison of the tension of the bolts on connections S3 and S4 showed that the thinner the connecting plates was, the more the tension of the high-strength bolts decreased with increase of load. The decrease in the tension of the high-strength bolts resulted in decrease in the contact friction between the cover plates and the chord members of the truss as well as decrease in the slip load of the connection. For each specimen, the changes in the tension of the high-strength bolts underwent two stages during the entire loading process. In the elastic stage and notable slip stage, the tension of the first-row of high-strength bolts changed rapidly. During the elastic-plastic stage, the effect of the load on the tension of the high-strength bolts decreased, and the curves of the tension of the high-strength bolts became almost horizontal. A comparison of the connections with different friction coefficients showed that the friction coefficient had slight impact on the tension of the bolts. The smaller the friction coefficient was, the smaller the changes in the tension of the first-row of bolts on the upper cover plate were. For each of the six models, compared to the changes in the tension of the first-row of high-strength bolts, the decrease in the tension of the second-row of high-strength bolts (U3 and U4) was small (the tension of bolts U3 and U4 decreased by approximately 29% in all cases), which should be considered in the design of the connection. In all cases, the tension of the high-strength bolts on the lower cover plate decreased by small extent (approximately 8–25%). In addition, the
tension of the second-row of high-strength bolts (D3 and D4) decreased by slightly greater extent than that of the first-row high-strength bolts (D1 and D2). The plate thickness and the friction coefficient had an insignificant impact on the tension of the high-strength bolts on the lower cover plate. The tension of the high-strength bolts on the joint flitch decreased by the least extent (approximately 4–23%). The curves of the tension of the four bolts on the joint flitch of model S4 were more discrete than those of model S3, primarily because the shear force borne by the joint flitch of model S4 was greater than that of model S3. The shear force had an impact on the tension of the high-strength bolts, and the connecting plates were abrasion during the slipping process. 5.2. Stress distribution of high-strength bolts The tension of high-strength bolt is the axial force of the middle cross-section of the bolt along the axis of the bolt. The stress distribution of bolt under the combined effects of the tension, shear and pressure on the sidewall of bolt shank is relatively complicated. In contrast to the curves of the tension of the high-strength bolts, the stress distributions of the high-strength bolts can reflect the overall stress distribution of the high-strength bolts under certain load. For each model, stress contour plots were generated for all the high-strength bolts after all the bolts were tightened according to specification [26], when the model was in the ultimate bearing capacity state, and when the model was in the ultimate displacement state (Fig. 9). From Fig. 9(a), after the high-strength bolts was tightened, the stress was evenly distributed on the bolt shank and the values of the stresses were equal in each bolt with same size, which verifying the method used for applying pretension to the bolts. The stress conditions shown in Fig. 9(a) correspond to the starting point of each curve in Figs. 7 and 8. It can be seen from Fig. 9(a)–(m) that the stress of the high-strength bolts on the column base flanges did not change significantly during the entire loading process, the tension of these high-strength bolts almost did not change, and the column base flange did not slip relative to the upper or lower column flanges because there were enough highstrength bolts on the flanges. When the components of the truss underwent significant elastic-plastic deformation, the force produced on the contact surfaces between the column base flanges and the column flanges was not sufficient to overcome the maximum static friction, i.e., the high-strength bolt on the column base flanges belong to friction-type connection at all times during the loading process. Because there are two joint flitches, the contact pressure and friction between each bolt nut and the flitch were symmetrical about the cross-section vertical to the bolt shank. Thus, the friction between each bolt nut and the flitch was zero, and the pressure stress was evenly distributed, and there was no shear force in bolt shank. Therefore, the axial force was the main force in each bolt shank and the stress of each bolt was symmetrical about the cross-section vertical to the bolt shank. Load had largest impact on the stress distribution of the high-strength bolts on the upper cover plate. The closer to the column the body on each row of high-strength bolts on the upper cover plate was, the greater the stress in the body was. This phenomenon became more prominent with the increase of the displacement at loading point, which was mainly because the upper cover plate was connected to chord member of the truss via single contacting surface. As a result, for each bolt, friction was produced between the bolt nut and the cover plate and between the bolt cap and the corresponding chord member, which lead to unsymmetrical compressive stress between the nut and the cover plate and between the cap and the chord. In addition, this friction generated shear force in the bolt shank. The unsymmetrical pressure generated bending
Fig. 5. Typical modes of deformation failure. (a) Outward expansion deformation of chord member B. (b) Concave deformation of one end of chord member A. (c) Bending and torsional deformation of web member A. (d) Extension of a bolt hole and fracture of the plate material. (e) Relative slip on contact surface A. (f) Relative slip on contact surface B. (g) Bending and torsional deformation of web member B.
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moment in the bolt, which was in balance with the bending moment generated by the friction, thus, the bolts were bent and tensioned. The bending moment and tension generated oblique tension stress in the bolt shank, which made the maximum tensile stress in the bolt shank larger than the average tensile stress on the cross-section of the bolt shank, which was detrimental to the bearing capacity of the bolt. Furthermore, as the load increased, rigid slip occurred between the upper cover plate and chord member B. The bolt shank connected with the wall of bolt hole and began to bear pressure. The stress of each bolt increased under the combined effects of tension, shear, uneven pressure and friction on the nut and cap, and the side pressure on the sidewall of bolt shank. The pressure borne by the sidewall of each bolt continuously increased with increasing load, resulting in the increase in the stress of the bolt, which should be considered in the design of bolt. The first-row of high-strength bolts on the lower cover plate had even stress distribution. For the second-row of high-strength bolts, the closer to the column the body on the bolt was, the greater the stress in the body was. However, this uneven stress distribution was much less significant than that of bolts on the upper cover plate, which was mainly because chord member A was subjected to pressure and it was in contact with edge of the column base flanges in initial state, thus, the slip of chord member A relative to the lower cover plate was almost zero. As a result, for each bolt, the shear of the bolt shank, the pressure borne by the sidewall of the bolt shank, and the friction on the bolt nut were almost zero. The bolt mainly bore the axial tension in bolt shank and the normal pressure on bolt nut and cap from the contact surface. A comparison of the stress contour plotted in Fig. 9 shows that although the component size of truss had significant impact on the magnitude of the tension of the high-strength bolts, the component size had little impact on the stress distribution pattern of the high-strength bolt groups. In addition, the friction coefficient of the contact surfaces almost had no impact on the stress distribution pattern of the high-strength bolt group, but it had little impact on the magnitude of the tension and stress of the high-strength bolts. 6. Anti-slip capacity of contact surfaces To determine whether slip occurred on contact surface, the curves of the relative displacements between the contact surfaces with load at the loading point were extracted (Fig. 10). The point where the relative displacement is greater than zero corresponds to the time when the slip occurred. It can be observed from Fig. 10 that for each model, because the upper chord member of the truss was subjected to tension during the unidirectional loading process, the slip occurred between the upper cover plate and the upper chord member. The lower chord member was subjected to pressure, and the left end of the lower chord member was in contact with the edge of the column base flange, thus no slip occurred between the lower cover plate and the lower chord member. The curve of the slip distance was horizontal when the slip started. The maximum slip distance was the gap between the bolt hole and the bolt shank in slip stage. When the slip was completed, the load increased significantly with less displacement at truss end. Subsequently, the curve once again kinked, and the slip distance increased slowly. At the elastic-plastic stage, the slip distance was far greater than the gap between the bolt hole and the bolt shank, indicating that the deformation of the walls of the bolt holes due to the pressure by the bolt shank and the elastic-plastic deformation of the cross-sections of the chord members at the location of bolt hole, which resulted in elongation of the bolt holes. For the models with the same-size component of the truss, the smaller the friction coefficient was, the smaller the slip load was. Slips occurred between the joint flitch and the vertical connecting plates. However, the distances of the slips were less than 2 mm, which occurred mainly because the slip occurred on the contact surface between the upper cover plate and the upper chord member, and then the truss rotated around the axis close to the lower chord member.
Fig. 6. Load-displacement curves at the truss end of the models.
But, the slip distances were small because the bolts on the web member were much closer to the rotational axis than upper cover plate. Hence, the high-strength bolts on the joint flitch and the vertical connecting plates belong to friction-type connection at all times and had no pressure on the sidewall of bolt shank and wall of the bolt hole. The slip distances between the column flanges and the column base flanges were approximately zero, indicating that no slip occurred between them. The curves of the friction between the upper cover plate and the upper chord member as well as the curves of the pressure borne by the wall of bolt hole with load at the loading point of the six models were extracted (Fig. 11). In Fig. 11, UF represents the friction of the upper cover plate, UN represents the pressure borne by the wall of bolt hole on the upper cover plate, and UP represents the resultant of the friction and the pressure. Fig. 11 shows that for models S3 series and models S4 series, the slip occurred between the upper cover plate and the upper chord member, and the pressure occurred on the walls of the bolt holes in both the upper cover plate and the upper chord member. When the load applied to the truss end was not large enough to overcome the maximum static friction between the upper cover plate and the upper chord member, no slip occurred between them, and the wall of bolt hole bore no pressure. The friction between them gradually increased with the load at the truss end increasing. When the friction exceeded the maximum static friction, the slip occurred. Until the slip distance reached 2 mm, the wall of bolt hole began to bear pressure. Before the load at the truss end reached the ultimate load, the pressure borne by the wall of bolt hole gradually increased with the load at the truss end increasing, whereas the friction gradually decreased. However, the resultant force of the pressure and the friction increased. The end of the lower chord member was in contacted with the column base flange before loading, no slip between the lower cover plate and the lower chord member occurred, thus there was no pressure on the bolt shank and the wall of bolt hole. The displacement and load corresponding to the slip and bearing pressure of the wall of bolt hole of the six models were determined based on Fig. 10 and Fig. 11, and the results were listed in Table 2. Δs refers to the vertical displacement of the loading point when slip occurred. Ps refers to the load when slip occurred. Δn refers to the vertical displacement of the loading point when the wall of bolt hole began to bear pressure. Pn refers to the load when the wall of bolt hole began to bear pressure. It can be seen from Table 2 that the size of components of truss had some impact on the Δs and Δn. The stronger the truss was, the smaller the Δs and Δn were, which was mainly because the stronger the truss was, the greater the bending stiffness of the truss and the rotational stiffness of the connection were. However, the size of components of truss had no impact on the Ps and Pn. For the connection with the same-size component of truss, the greater the friction
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Fig. 7. Tension of high-strength bolts in S3-J. (a) Changes in the tension of the high-strength bolts on the upper cover plate. (b) Changes in the tension of the high-strength bolts on the lower cover plate. (c) Changes in the tension of the high-strength bolts on the joint flitch.
coefficient of the contact surface was, the greater the Δs and Δn were, and the greater the Ps and Pn were. 7. Simplified calculation
small; therefore, it was neglected in the calculation diagram. Four of Grade S10.9 M24 bolts were placed on each chord member, and two of Grade S10.9 M20 bolts were placed on the vertical connecting plate and joint flitches. The friction resisting capacity of one bolt is calculated as:
7.1. Simplified calculation for connection in slip state The truss was taken separate from the connection, the calculation diagram of which was shown in Fig. 12. It was assumed that the bending moment was carried by the bolts on the chord members, and the shear was carried by the bolts on the vertical connecting plate. The mechanical and finite element analyses showed that the prying action by the cover plate on the chord surface was very
Nbv ¼ ðμ 1 þ μ 2 Þp
ð1Þ
Here the friction coefficient is the sum of friction coefficient μ1 on the contact surface between the cover plate and chord member and the μ2 on contact surface between the bolt nut and the cover plate.
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Fig. 8. Tension of high-strength bolts in S4-J. (a) Changes in the tension of the high-strength bolts on the upper cover plate. (b) Changes in the tension of the high-strength bolts on the lower cover plate. (c) Changes in the tension of the high-strength bolts on the joint flitch.
The friction resisting bearing capacity at the end of the truss supported by four bolts is calculated as: P ¼ 4Nbv h=l1
ð2Þ
The shearing capacity of two Grade S10.9 M20 bolts is calculated as: V ¼ 2n f μ 1 P
ð3Þ
Then the load at the truss end when slip occurred between the upper chord member and the upper cover plate is: P s ¼ minðP; V Þ
ð4Þ
The results calculated using the above formulas were listed in Table 3. As shown in Table 3, the calculated values by the proposed formula get along well with the FEA and test result, which verifies the proposed formula. 7.2. Simplified calculation for connection in yield state
Here μ1 is the friction coefficient on the contact surface between the joint flitch and vertical connecting plate. nf is the amount of contact surfaces. P is the pretension of bolts.
When the connection yielded, slip had already occurred, and the bolt shanks were in contact with the wall of bolt hole. The connection
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Fig. 9. Stress contour plots of the high-strength bolts. (a) Stress contour plot of the bolts after the final tightening was completed. (b) Ultimate bearing capacity state of model S3-0303. (c) Ultimate displacement state of model S3-0303. (d) Ultimate bearing capacity state of model S3-035. (e) Ultimate displacement state of model S3-035. (f) Ultimate bearing capacity state of model S3-040. (g) Ultimate displacement state of model S3-040. (h) Ultimate bearing capacity state of model S4-0303. (i) Ultimate displacement state of model S4-0303. (j) Ultimate bearing capacity state of model S4-035. (k) Ultimate displacement state of model S4-035. (l) Ultimate bearing capacity state of model S4-040. (m) Ultimate displacement state of model S4-040.
yielded because either the material at the cross-section of the upper chord member yielded or the material at the cross-section of the web member yielded. Through analysis, we know that the cross-section at the center of the first-row of bolt holes on the upper chord member
was the weakest cross-section of the truss and bore relatively large moment. Thus, the load at the truss end when the stress at the cross section of the chord, shown on the Section 1-1 in the Fig. 12, reaches yielding
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Fig. 9 (continued).
strength is calculated as: P 1 ¼ W 1n f y =l
ð5Þ
W1n is the elastic section modulus of Section 1-1. fy is the yielding strength of steel material of chord member. According to literature [28,29], the web member will not loss stability before yields, then, the load at the truss end when the web member yields is calculated as: P 2 ¼ Aw f y sin45 °
ð6Þ
Aw is the area of web member. The yielding bearing capacity at the loading point of truss end is calculated as: P y1 ¼ minðP 1 ; P 2 Þ
ð7Þ
The bolt holes may also yield due to pressure on the wall of bolt hole, resulting in an increase in the rotation angle of the connection. The yield load of the local bearing pressure on the wall of bolt hole is calculated as follows: Nbcy ¼ d∑tf cy ¼ d∑t αf y
ð8Þ
P cy ¼ 4Nbcy h=l
ð9Þ
t is the thickness of chord member. Based on the FEA, we know that the yield load of the wall of bolt hole of specimen S3 and S4 were 145.46 kN and 156.04 kN. Based on these FEA results, the enhancement coefficient α of local yield bearing capacity in formula (8) could be deduced. For specimen S3, α = 1.60. For specimen S4, α = 1.29. Because the thickness of chord member of specimen S3 was thinner than that of specimen 4, the tension of the bolts had larger constraining effect on the wall of bolt hole and larger
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Fig. 10. Slip curves of the models. (a) Slip curves of upper chord members of model S3. (b) Slip curves of upper chord members of model S4. (c) Slip curves of web members of model S3. (d) Slip curves of web members of model S4.
enhancing the yield strength of the wall of bolt hole of specimen S3 compared to specimen S4. The smallest of the aforementioned three yield loads was selected as the yield load. Then, the yield bearing capacity of the connection is calculated as: P y ¼ min P 1 ; P 2 ; P cy
ð10Þ
The results from the proposed formula, the FEA and the test were listed in Table 4. It can be seen from Table 4 that the results from the three methods get along well with each other, which verifies the proposed formula. But more specimens or FE models with different thickness of chord members and different bolts will be needed to study the reasonable value of the enhancement coefficient α of local yield bearing capacity for different truss in the future study. 7.3. Simplified calculation for connection in ultimate state The tests and FEA showed that the cross section of chord members where the first row of bolt hole were located fractured by excessive tensile stress, no failure of the wall of bolt hole due to pressure was found. Therefore, for angle with small thickness, the wall of bolt hole may not fail because the wall is constrained by the out-of-plane pressure on both surfaces of the angle produced by high-strength bolt washer and contact surface, only yield could occur. Based on the test and FEA results, the pressure borne by the wall of bolt hole does not need to be checked for ultimate load bearing capacity. Considering that the high-strength bolts had a certain beneficial effect on the yield of the cross-sections of the chord members, the cross-section with holes possible may not deform significantly and fail when the gross cross-section near it yielded. Therefore, 0.7 times of the ultimate strength was selected as the strength of the material of
the cross-section. Hence, the yield of the gross cross-section and the cross-section at the holes should be checked at the same time. Then, the ultimate load bearing capacity at the loading point of truss end is calculated as: P 1u ¼ 0:7W p1n f u =l2
ð11Þ
P 2u ¼ W p1 f y =l2
ð12Þ
P u ¼ min P 1u ; P 2u
ð13Þ
Wp1n is the plastic net section modulus of Section 1-1. fu is the ultimate strength of steel material of chord member. Wp1 is the plastic gross section modulus of Section 1-1 neglecting the effect of bolt holes. The results from the proposed formula, the FEA and the test of the six connections were listed in Table 5. It can be seen from Table 5 that the results obtained using the simplified formulas were consistent with the test and FEA, which verifies the proposed formulas. 8. Conclusions The FEA was used to study the static and hysteretic performance of a new-type bolted truss-to-column connection with slipping contact surfaces, which is used in prefabricated multi-rise and high-rise steel structures. The following main conclusions were obtained: (1) The FEA correctly reflected the mechanical performance of the connection and were generally consistent with the test results, verifying the finite element model and the FEA method. The finite element model could be used to conduct parameter analysis on the performance of the connection by changing the parameters of the model.
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Fig. 11. Curves of friction and pressure borne by the wall of bolt hole between the upper cover plate and upper chord member. (a) Curves of model S3-J. (b) Curves of model S4-J.
(2) Each loading process of this kind of truss-to-column connection underwent the linear ascending stage (elastic stage), notable slip stage, curved ascending stage (elastic-plastic stage), and
bearing capacity degradation stage. The friction coefficient had small impact on the ultimate load of this connection, but it had large impact on the slip load. The greater the friction coefficient was, the greater the slip load was.
Table 2 Displacement and load corresponding to slip and bearing pressure. Model number
Δs/mm
Ps/kN
Δn/mm
Pn/kN
S3-0303 S3-035 S3-040 S4-0303 S4-035 S4-040
6.46 7.63 9.32 5.47 6.94 7.78
137.10 155.49 174.67 137.88 155.57 174.21
10.30 11.15 13.26 9.11 9.58 10.11
148.48 161.08 178.58 145.93 160.23 175.10
Table 3 Friction resisting bearing capacity from simplified calculation and simulation. Model number
Calculated P/kN
Calculated V/kN
Calculated PS/kN
Simulated PS/kN
Test PS/kN
S3-0303 S3-035 S3-040 S4-0303 S4-035 S4-040
137.14 155.40 174.82 137.14 155.40 174.82
187.86 217.00 248.00 187.86 217.00 248.00
137.14 155.40 174.82 137.14 155.40 174.82
137.10 155.49 174.67 137.88 155.57 174.21
134.42 – – 136.34 – –
Table 4 Yielding bearing capacity from simplified calculation and simulation.
Fig. 12. Diagram of connection calculations.
Model number
P1/kN
P2/kN
Calculated Pcy/kN
Calculated Py/kN
Simulated Py/kN
Test Py/kN
S3-0303 S3-035 S3-040 S4-0303 S4-035 S4-040
158.81 158.81 158.81 204.72 204.72 204.72
214.72 214.72 214.72 253.97 253.97 253.97
145.15 145.15 145.15 156.04 156.04 156.04
145.15 145.15 145.15 156.04 156.04 156.04
145.46 146.89 146.92 156.04 156.31 156.40
140.54 – – 156.25 – –
X.C. Liu et al. / Journal of Constructional Steel Research 133 (2017) 360–373 Table 5 Ultimate bearing capacity from simplified calculation and simulation. Model number P1u/kN
P2u/kN
Calculated Pu/kN Simulated Pu/kN Test Pu/kN
S3-0303 S3-035 S3-040 S4-0303 S4-035 S4-040
234.60 234.60 234.60 306.55 306.55 306.55
185.97 185.97 185.97 247.98 247.98 247.98
195.32 195.32 195.32 254.33 254.33 254.33
188.34 188.68 189.28 246.98 247.16 247.65
198.77 – – 250.41 – –
(3) The tension of the high-strength bolts on the cover plates and on the joint flitch all decreased. The tension of the first-row of highstrength bolts on the cover plates on the tensile side decreased the most, and the extent of the decrease reduced with the increase of the thickness of chord member. The tension of other bolts decreased by smaller extent than that of the first-row of high-strength bolts on the cover plates on the tensile side. The decrease in the tension of the high-strength bolts on the cover plates was not significantly affected by the friction coefficient. (4) During the static loading process, when the tangential force on the contact surface was smaller than the maximum static friction between the cover plates and the chord members, this highstrength bolt connection belongs to friction-type connection. There was no slip on the contact surface, and the friction between the cover plates and the chord members increased with increasing load. (5) When the tangential force on the contact surface was greater than the maximum static friction between the cover plates and the chord members, slips occurred between them. The bolt shank were in contact with the wall of bolt hole, causing the bolt shank to bear shear and the wall of bolt hole to bear pressure. Before the load reached the ultimate load, the friction gradually decreased with increasing load. In contrast, the pressure borne by the wall of bolt hole increased with increasing load sharply, as well as the sum of friction and pressure. After the load reached the ultimate load, the friction as well as the pressure decreased with decreasing load. (6) The results of the simplified formulas proposed in this paper agree well with the results of the test and FEA. These formulas can be used to describe the strength of the connection under static load and cyclic load. Acknowledgements The writers gratefully acknowledge the support for this work, which was funded by the National Natural Science Foundation of China (51678010), the Beijing Natural Science Foundation (8172009) and the Science and Technology Plan of Beijing Municipal Commission of Education (KM201610005012). References [1] T. Kim, J. Kim, Collapse analysis of steel moment frames with various seismic connection, J. Constr. Steel Res. 65 (16) (2009) 1316–1322. [2] D.K. Miller, Lessons learned from the Northridge earthquake, Eng. Struct. 20 (4) (1998) 249–260.
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Contents lists available at ScienceDirect
Journal of Constructional Steel Research
Performance analysis and design of bolted connections in modularized prefabricated steel structures X.C. Liu a,b,⁎, S.H. Pu a, A.L. Zhang a,b, X.X. Zhan a a b
Beijing Engineering Research Center of High-rise and Large-span Prestressed Steel Structures, Beijing University of Technology, Beijing 100124, China Beijing Key Laboratory of Earthquake Engineering and Structural Retrofit, Beijing University of Technology, Beijing 100124, China
a r t i c l e
i n f o
Article history: Received 4 March 2016 Received in revised form 14 February 2017 Accepted 26 February 2017 Available online xxxx Keywords: Prefabricated steel structure Truss-to-column connection Column-to-column connection Slip on contact surface Energy dissipation from slips Simplified calculation
a b s t r a c t The present study proposes a new-type all-bolted connection that can be used to connect trusses to columns and columns to columns on site in modularized prefabricated multi-rise and high-rise steel structures. The proposed connection connects columns through flanges, connects trusses to columns through cover plates that extend from the flanges and through vertical connecting plates and joint flitches. The stiffness of the connection can be controlled by adjusting the number or size of the bolts and undergoes step-like change as the load changes. Therefore, the connection can be rigid during weak earthquake, while the cover plates can slip relative to the chord members during strong earthquake, thereby dissipating energy. The FEA results was compared with experimental results and showed good agreement at all stages of loading, then the static performance of six connections with different friction coefficient or size of components were studied by FEA. The FEA results were used to determine mechanical properties of the connections that were difficult to obtain from the tests, such as the changing rule of the bolt tension, the stress distribution of bolt, the contact force on various contact surface, and the pressure on the wall of bolt hole, as well as the effects of friction coefficient on the performance of the connections. The mechanical model of the connection was established and the mechanical mechanism of the connection was got. Furthermore, simplified calculating formulas for the connection under slip state, yield state and ultimate state were proposed respectively. © 2017 Elsevier Ltd. All rights reserved.
1. Introduction During the Northridge earthquake in 1994 and the Hanshin earthquake in 1995, the beam-to-column connections of many steel structures suffered brittle failure, some even resulting in failure of entire building. The plastic deformation capacity of the structures was not fully developed. Later, shifting the plastic hinge outwardly to avoid weld seams became the major direction on improving seismic performance of beam-to-column connections [1–4]. Zhang et al. [5] conducted monotonic loading tests on prefabricated truss-to-column connections. They analyzed the stiffness, bearing capacity and ductile performance, and studied the effects of the thickness of the connecting plate and size of the members of the truss on the bearing capacity and failure mode of the connection. The results showed that the thickness of the connecting plate had a large impact on the bearing capacity and the stiffness of the connection, and the size of members of the truss had a large impact on the bearing capacity of the connection. Ma et al. [6] conducted cyclic loading tests on a kind of all-bolted beam-to-column connection with slotted bolt holes, and compared with conventional ⁎ Corresponding author at: Beijing University of Technology, Beijing 100124, China. E-mail address: [email protected] (X.C. Liu).
http://dx.doi.org/10.1016/j.jcsr.2017.02.025 0143-974X/© 2017 Elsevier Ltd. All rights reserved.
welded connections. They found that the bolts slipped inside the bolt holes, resulting in a significant increase in the ductile deformation capacity. Dessouki et al. [7] and Bai et al. [8] conducted FEA on the performance of extended end-plate beam-to-column connections and proposed simplified formulas respectively. Rahnavard et al. [9] and Kulkarni et al. [10] conducted tests and FEA on connection with holes on beam web and investigated the effect of the form of the holes on the seismic performance, respectively. Aydin et al. [11] conducted experiments to study the influence of angles with and without stiffeners on the static performance of beam-to-column connections that were designed with top-and-seat angles in minor column axes. Tests can better reflect the mechanical performance of connections and can simultaneously consider the effects of material defects, geometric defects, welding defects, and the initial stress. However, tests require large amounts of manpower, materials, and time. In addition, test results only show the combined effect of the aforementioned factors instead of the independent effect of each individual factor [12–15]. The FEA can better facilitate the establishment of many models for parameter analysis [16–19]. Nguyen et al. [20] conducted FEA of semi-rigid connections in spatial steel frames, and compared the FEA results with the test results, which verified the finite element model. The cyclic behavior of connections is captured by the independent hardening model.
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Reference [21] presents numerical study on high-strength steel endplate connections under fire conditions using ABAQUS finite element software, which revealed additional information on the behavior of high-strength steel endplate connections. It has been demonstrated that FEA gives reasonable accuracy compared with experimental results, providing an efficient, economical, and accurate tool for studying the performance of connections. In addition, due to the limitation of factors such as economy and test equipment, it is very difficult to accurately monitor the tension of high-strength bolts, the contact force and slipping rule of contact surfaces in actual engineering or tests, thus FEA become the best selection. Previous studies have mainly focused on the stress losses of high-strength bolts under shear and have not monitor and analyze the tension of the high-strength bolts and the slipping rule of the contact surfaces under actual working conditions [22–25], which can be monitored by the finite element analysis conveniently. The object of this study is to get the changing rule of bolt tension of the connection under complex loading conditions as well as the slipping rule of the contact surfaces. In the present study, ABAQUS finite element software was employed to conduct monotonic loading and cyclic loading simulation of two connections series with variable size of components (S3 and S4). The static bearing capacity, seismic capacity and failure mechanism of the connections were determined. In addition, the tension of the high-strength bolts as well as the friction on the contact surfaces were monitored to identify the changing rule in the tension of the high-strength bolts and the friction on the contact surfaces of this
361
type of connection under actual working conditions, and to explore the effects of the bolt tension and the friction on the stress and failure mode of the connections. To study the effects of friction coefficient on the mechanic and seismic performance of the connection, friction coefficients of 0.303, 0.35 and 0.40 were selected for parametric analysis on specimens S3 and S4 series. Based on the test and FEA results, simplified formulas for this type of truss-to-column connection were proposed.
2. Finite element model 2.1. Specimen design To study the truss-to-column connection instead of the whole trussto-column joint, we designed S3-N and S4-N with the material Q235B steel. Fig. 1 shows the geometric dimensions of the all-bolted connection specimens. Table 1 lists the sectional parameters of the specimens. The distance from inflection point (where the moment is zero) to the intersection of truss and column is about 1/4 truss span under vertical load, the distance from inflection point to the intersection of truss and column is about 1/2 truss span under horizontal load. To study the performance of the connection under the combined action of vertical load and horizontal load, the beam length is between 1/4 and 1/2 truss span instead 1/2 truss span. Based on the mechanical characteristics of the connection under horizontal and vertical loading conditions in the
Fig. 1. Details for test specimens S3-N and S4-N. (a) Elevation drawing. (b) Planar drawing.
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Table 1 Dimensions of the components. Specimen number
Chord members
Web members
Test type
Number of bolts on each chord
S3-N S4-N
2L75X6 2L75X8
2L45X5 2L45X6
Quasi-static 4 Quasi-static 4
structure system, the two ends of the square HSS column were fixed, and the load was applied to the end of the truss [27]. 2.2. Finite element model The FEA was conducted on specimens S3-N and S4-N using the ABAQUS finite element software. The high-strength bolts were established in this finite element model because slipping on the contact surfaces in the tests. A dumbbell-shaped solid model was used to simulate the shank, nut and washer of the high-strength bolt. Additionally, the cylinder on each end of the bolt model had the same area as the washer of the actual high-strength bolt assembly. Furthermore, the middle cylinder of the bolt model had the same nominal diameter as bolt shank of each high-strength bolt. The bolt pretension was applied at the middle section of the bolt shank model. Based on the test results, the friction coefficient of the contact surface was 0.303, which is the average of three friction test models (0.29, 0.30 and 0.32), according to the technical specifications [26]. A hexagonal C3D8R element, which is an 8node linear brick with reduced integration and hourglass control (Fig. 2(a)), was used for meshing the bolt assembly. The tetrahedral C3D10 element, which is a 10-node quadratic tetrahedron, was used for meshing the truss due to its irregular shape. The hexagonal C3D8R element was used for meshing the other parts with regular shapes.
Contact relationships between the flange of upper column and the upper flange of column base, between the flange of lower column and the lower flange of column base were established, using the Coulomb friction model to simulate the contact pressure and friction on the contact surfaces of the flanges. The pressure contact and frictional contact between the lower surface of the upper cover plate and the upper surface of the upper chord member of the truss were established. In the same way, the contact relationship was established between the upper surface of the lower cover plate and the lower surface of the lower chord member of the truss. The pressure contact and frictional contact between the joint flitch and vertical connecting plate 1 were established. Similarly, the pressure contact and frictional contact between the joint flitch and vertical connecting plate 2 were also established. The friction coefficient of above-mentioned contact surfaces was 0.303. For each high-strength bolt, the pressure contact and frictional contact between the surface of the nut and the contact surface were established. The friction coefficient was 0.05. Additionally, a potential pressure contact between the side surface of the bolt shank and the wall of the bolt hole was established. When the bolt shank touched the wall of bolt hole, the bolt shank and the wall of bolt hole bore pressure; when the bolt shank didn't touch the wall of bolt hole, the contact force was zero. Each bolt was aligned with the center of the bolt hole. The effects of deviation in the location and size of bolt hole caused by installation and fabrication were not considered. The elastic modulus of an 160 × 162 × 20 mm rectangular rigid plate is ten times the steel material and the ultimate strength is unlimited. The rigid plate was fixed onto the loading end of the truss using tie constraint. The load was applied to each specimen by a reference point to simulate the concentrated force. Fixed constraints were applied to the square HSS as same locations as the test model. The global model of the specimens is shown in Fig. 2(b). Three material property tests were conducted on each type of component, thus five sets of material property tests were conducted on 15 specimens. The average value of all of the material tests were used as material constitutive relations for the FEA and test. Accordingly, the yield strength of the steel was 294 MPa, and the elastic modulus was 2.06 × 105 MPa. According to the certificate of quality assurance provided by the supplier, the yield strength of high-strength bolts was 975 MPa, the tensile strength was 1188 MPa, and the elastic modulus was 2.06 × 105 MPa. The materials of steel and bolt were simulated based on the bilinear kinematic hardening rule and von Mises yield criteria. The loading scheme in the finite element simulation was as the same as the tests. 2.3. Numbering system for high-strength bolts and contact surfaces The high-strength bolts and contact surfaces on the cover plates, joint flitch and column base flanges were numbered using an alphanumeric numbering system (Fig. 3). Each high-strength bolt on chord member B was numbered as Un. Each high-strength bolt on chord member A was numbered as Dn. Each high-strength bolt on the vertical connecting plates was numbered as Tn, only the numbers n are shown in Fig. 3, the letters are ignored. The contact surface between the upper cover plate and chord member B was numbered as UGX. The contact surface between the lower cover plate and chord member A was numbered as DGX. Each contact surface on the joint flitch was numbered as TBn. The contact surface between the flange of upper column and the upper flange of column base was numbered as UFF. The contact surface between the flange of lower column and the lower flange of column base was numbered as DFF. 3. Verification of FEA model 3.1. Hysteretic loop comparison
Fig. 2. Finite element model. (a) High-strength bolt model. (b) Overall model.
As shown in Fig. 4, the hysteretic curves of the two specimens were got by FEA and tests. Fig. 4 shows that the hysteretic loops obtained from the FEA closely match the tests: both hysteretic loops consisted
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Fig. 4. Hysteretic curves of the models. (a) Comparison of the hysteretic curves of specimen S3-N. (b) Comparison of the hysteretic curves of specimen S4-N.
of elastic stage, slip stage, elastic-plastic stage, and bearing capacity degradation stage. Moreover, the simulated ultimate bearing capacity was almost equal to that obtained from the test. Therefore, the finite element model was verified and further study on the connections could be performed by the finite element models. 3.2. Failure mode and comparison Fig. 5 summarizes the failure modes of the connections. The failure modes obtained from the FEA were almost same as that in the tests. These failure modes include the outward bending and torsional deformation of chord member B, the concave local buckling deformation of chord member A, the bending and torsional deformation of web members A and B, the elongation of the bolt holes, and significant slips between the cover plates and the chord members. The comparison of the failure models got from the FEA and test showed that the FEA could accurately simulate the phenomena that occurred during the test, thereby verifying the finite element model again. 4. Effect of friction coefficient
Fig. 3. Numbering system for high-strength bolts and interfaces. (a) Numbers of the contact surfaces and bolts on the cover plates. (b) Numbers of the contact surfaces and bolts on the flitch. (c) Numbers of the flange contact surfaces.
A comparative analysis of the hysteretic curves and failure modes of the connections showed that the finite element models are correct. Therefore, based on the finite element models, it is possible to investigate the effects of various parameters on the performance of the connections by changing the parameters, such as friction coefficient. The static analysis can show the changing rule of the tension of the highstrength bolts, the friction on the contact surfaces and the pressure on the wall of bolt hole more clearly. Therefore, static finite element analyses were conducted using friction coefficients of 0.303, 0.35, and 0.40
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respectively. The load-displacement curves at the loading point of the six models were obtained using ABAQUS finite element software (Fig. 6). It can be observed from Fig. 6 that the load-displacement curves of the six models had similar shapes: all the curves consisted of linear ascending stage (elastic stage), notable slip stage, curved ascending stage (elastic-plastic stage), and bearing capacity degradation stage. The friction coefficient of the contact surfaces had insignificant effect on the ultimate bearing capacity of the truss-to-column connections. When the friction coefficient decreased by 0.05, the ultimate bearing capacity were almost the same, indicating that the ultimate bearing capacity of each connection was not affected by friction coefficient. While, it was determined by the new connection system established after the slip completed, at which time the wall of bolt hole on the upper flange of the truss began to bear pressure. The friction coefficient had large impact on the slip load of this connection. The greater the friction coefficient was, the greater the slip load was. The slip loads of connection with different-size components of truss but with the same friction coefficient were essentially the same. However, the greater the component size of the truss was, the greater the ultimate bearing capacity was. Each of the six models has sufficient elastic-plastic deformation capacity and large ultimate displacement. 5. Changing rule of tension and stress distribution of high-strength bolts 5.1. Changing rule of tension of high-strength bolts A tracking analysis was conducted on the tension of 12 highstrength bolts on the upper and lower cover plates and the joint flitch of each model. The curves of the tension of the high-strength bolts with the displacement of the loading point were generated (Figs. 7 and 8). Figs. 7 and 8 show that the tension of the high-strength bolts on the chord and web members of the truss all decreased during the loading process. In all cases, the tension of the first-row of high-strength bolts on the upper cover plate (U1 and U2) showed the greatest decrease. For model S3, the tension of high-strength bolts U1 and U2 decreased by as much as 68%. For model S4, the tension of high-strength bolts U1 and U2 decreased by as much as 57%. A comparison of the tension of the bolts on connections S3 and S4 showed that the thinner the connecting plates was, the more the tension of the high-strength bolts decreased with increase of load. The decrease in the tension of the high-strength bolts resulted in decrease in the contact friction between the cover plates and the chord members of the truss as well as decrease in the slip load of the connection. For each specimen, the changes in the tension of the high-strength bolts underwent two stages during the entire loading process. In the elastic stage and notable slip stage, the tension of the first-row of high-strength bolts changed rapidly. During the elastic-plastic stage, the effect of the load on the tension of the high-strength bolts decreased, and the curves of the tension of the high-strength bolts became almost horizontal. A comparison of the connections with different friction coefficients showed that the friction coefficient had slight impact on the tension of the bolts. The smaller the friction coefficient was, the smaller the changes in the tension of the first-row of bolts on the upper cover plate were. For each of the six models, compared to the changes in the tension of the first-row of high-strength bolts, the decrease in the tension of the second-row of high-strength bolts (U3 and U4) was small (the tension of bolts U3 and U4 decreased by approximately 29% in all cases), which should be considered in the design of the connection. In all cases, the tension of the high-strength bolts on the lower cover plate decreased by small extent (approximately 8–25%). In addition, the
tension of the second-row of high-strength bolts (D3 and D4) decreased by slightly greater extent than that of the first-row high-strength bolts (D1 and D2). The plate thickness and the friction coefficient had an insignificant impact on the tension of the high-strength bolts on the lower cover plate. The tension of the high-strength bolts on the joint flitch decreased by the least extent (approximately 4–23%). The curves of the tension of the four bolts on the joint flitch of model S4 were more discrete than those of model S3, primarily because the shear force borne by the joint flitch of model S4 was greater than that of model S3. The shear force had an impact on the tension of the high-strength bolts, and the connecting plates were abrasion during the slipping process. 5.2. Stress distribution of high-strength bolts The tension of high-strength bolt is the axial force of the middle cross-section of the bolt along the axis of the bolt. The stress distribution of bolt under the combined effects of the tension, shear and pressure on the sidewall of bolt shank is relatively complicated. In contrast to the curves of the tension of the high-strength bolts, the stress distributions of the high-strength bolts can reflect the overall stress distribution of the high-strength bolts under certain load. For each model, stress contour plots were generated for all the high-strength bolts after all the bolts were tightened according to specification [26], when the model was in the ultimate bearing capacity state, and when the model was in the ultimate displacement state (Fig. 9). From Fig. 9(a), after the high-strength bolts was tightened, the stress was evenly distributed on the bolt shank and the values of the stresses were equal in each bolt with same size, which verifying the method used for applying pretension to the bolts. The stress conditions shown in Fig. 9(a) correspond to the starting point of each curve in Figs. 7 and 8. It can be seen from Fig. 9(a)–(m) that the stress of the high-strength bolts on the column base flanges did not change significantly during the entire loading process, the tension of these high-strength bolts almost did not change, and the column base flange did not slip relative to the upper or lower column flanges because there were enough highstrength bolts on the flanges. When the components of the truss underwent significant elastic-plastic deformation, the force produced on the contact surfaces between the column base flanges and the column flanges was not sufficient to overcome the maximum static friction, i.e., the high-strength bolt on the column base flanges belong to friction-type connection at all times during the loading process. Because there are two joint flitches, the contact pressure and friction between each bolt nut and the flitch were symmetrical about the cross-section vertical to the bolt shank. Thus, the friction between each bolt nut and the flitch was zero, and the pressure stress was evenly distributed, and there was no shear force in bolt shank. Therefore, the axial force was the main force in each bolt shank and the stress of each bolt was symmetrical about the cross-section vertical to the bolt shank. Load had largest impact on the stress distribution of the high-strength bolts on the upper cover plate. The closer to the column the body on each row of high-strength bolts on the upper cover plate was, the greater the stress in the body was. This phenomenon became more prominent with the increase of the displacement at loading point, which was mainly because the upper cover plate was connected to chord member of the truss via single contacting surface. As a result, for each bolt, friction was produced between the bolt nut and the cover plate and between the bolt cap and the corresponding chord member, which lead to unsymmetrical compressive stress between the nut and the cover plate and between the cap and the chord. In addition, this friction generated shear force in the bolt shank. The unsymmetrical pressure generated bending
Fig. 5. Typical modes of deformation failure. (a) Outward expansion deformation of chord member B. (b) Concave deformation of one end of chord member A. (c) Bending and torsional deformation of web member A. (d) Extension of a bolt hole and fracture of the plate material. (e) Relative slip on contact surface A. (f) Relative slip on contact surface B. (g) Bending and torsional deformation of web member B.
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moment in the bolt, which was in balance with the bending moment generated by the friction, thus, the bolts were bent and tensioned. The bending moment and tension generated oblique tension stress in the bolt shank, which made the maximum tensile stress in the bolt shank larger than the average tensile stress on the cross-section of the bolt shank, which was detrimental to the bearing capacity of the bolt. Furthermore, as the load increased, rigid slip occurred between the upper cover plate and chord member B. The bolt shank connected with the wall of bolt hole and began to bear pressure. The stress of each bolt increased under the combined effects of tension, shear, uneven pressure and friction on the nut and cap, and the side pressure on the sidewall of bolt shank. The pressure borne by the sidewall of each bolt continuously increased with increasing load, resulting in the increase in the stress of the bolt, which should be considered in the design of bolt. The first-row of high-strength bolts on the lower cover plate had even stress distribution. For the second-row of high-strength bolts, the closer to the column the body on the bolt was, the greater the stress in the body was. However, this uneven stress distribution was much less significant than that of bolts on the upper cover plate, which was mainly because chord member A was subjected to pressure and it was in contact with edge of the column base flanges in initial state, thus, the slip of chord member A relative to the lower cover plate was almost zero. As a result, for each bolt, the shear of the bolt shank, the pressure borne by the sidewall of the bolt shank, and the friction on the bolt nut were almost zero. The bolt mainly bore the axial tension in bolt shank and the normal pressure on bolt nut and cap from the contact surface. A comparison of the stress contour plotted in Fig. 9 shows that although the component size of truss had significant impact on the magnitude of the tension of the high-strength bolts, the component size had little impact on the stress distribution pattern of the high-strength bolt groups. In addition, the friction coefficient of the contact surfaces almost had no impact on the stress distribution pattern of the high-strength bolt group, but it had little impact on the magnitude of the tension and stress of the high-strength bolts. 6. Anti-slip capacity of contact surfaces To determine whether slip occurred on contact surface, the curves of the relative displacements between the contact surfaces with load at the loading point were extracted (Fig. 10). The point where the relative displacement is greater than zero corresponds to the time when the slip occurred. It can be observed from Fig. 10 that for each model, because the upper chord member of the truss was subjected to tension during the unidirectional loading process, the slip occurred between the upper cover plate and the upper chord member. The lower chord member was subjected to pressure, and the left end of the lower chord member was in contact with the edge of the column base flange, thus no slip occurred between the lower cover plate and the lower chord member. The curve of the slip distance was horizontal when the slip started. The maximum slip distance was the gap between the bolt hole and the bolt shank in slip stage. When the slip was completed, the load increased significantly with less displacement at truss end. Subsequently, the curve once again kinked, and the slip distance increased slowly. At the elastic-plastic stage, the slip distance was far greater than the gap between the bolt hole and the bolt shank, indicating that the deformation of the walls of the bolt holes due to the pressure by the bolt shank and the elastic-plastic deformation of the cross-sections of the chord members at the location of bolt hole, which resulted in elongation of the bolt holes. For the models with the same-size component of the truss, the smaller the friction coefficient was, the smaller the slip load was. Slips occurred between the joint flitch and the vertical connecting plates. However, the distances of the slips were less than 2 mm, which occurred mainly because the slip occurred on the contact surface between the upper cover plate and the upper chord member, and then the truss rotated around the axis close to the lower chord member.
Fig. 6. Load-displacement curves at the truss end of the models.
But, the slip distances were small because the bolts on the web member were much closer to the rotational axis than upper cover plate. Hence, the high-strength bolts on the joint flitch and the vertical connecting plates belong to friction-type connection at all times and had no pressure on the sidewall of bolt shank and wall of the bolt hole. The slip distances between the column flanges and the column base flanges were approximately zero, indicating that no slip occurred between them. The curves of the friction between the upper cover plate and the upper chord member as well as the curves of the pressure borne by the wall of bolt hole with load at the loading point of the six models were extracted (Fig. 11). In Fig. 11, UF represents the friction of the upper cover plate, UN represents the pressure borne by the wall of bolt hole on the upper cover plate, and UP represents the resultant of the friction and the pressure. Fig. 11 shows that for models S3 series and models S4 series, the slip occurred between the upper cover plate and the upper chord member, and the pressure occurred on the walls of the bolt holes in both the upper cover plate and the upper chord member. When the load applied to the truss end was not large enough to overcome the maximum static friction between the upper cover plate and the upper chord member, no slip occurred between them, and the wall of bolt hole bore no pressure. The friction between them gradually increased with the load at the truss end increasing. When the friction exceeded the maximum static friction, the slip occurred. Until the slip distance reached 2 mm, the wall of bolt hole began to bear pressure. Before the load at the truss end reached the ultimate load, the pressure borne by the wall of bolt hole gradually increased with the load at the truss end increasing, whereas the friction gradually decreased. However, the resultant force of the pressure and the friction increased. The end of the lower chord member was in contacted with the column base flange before loading, no slip between the lower cover plate and the lower chord member occurred, thus there was no pressure on the bolt shank and the wall of bolt hole. The displacement and load corresponding to the slip and bearing pressure of the wall of bolt hole of the six models were determined based on Fig. 10 and Fig. 11, and the results were listed in Table 2. Δs refers to the vertical displacement of the loading point when slip occurred. Ps refers to the load when slip occurred. Δn refers to the vertical displacement of the loading point when the wall of bolt hole began to bear pressure. Pn refers to the load when the wall of bolt hole began to bear pressure. It can be seen from Table 2 that the size of components of truss had some impact on the Δs and Δn. The stronger the truss was, the smaller the Δs and Δn were, which was mainly because the stronger the truss was, the greater the bending stiffness of the truss and the rotational stiffness of the connection were. However, the size of components of truss had no impact on the Ps and Pn. For the connection with the same-size component of truss, the greater the friction
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Fig. 7. Tension of high-strength bolts in S3-J. (a) Changes in the tension of the high-strength bolts on the upper cover plate. (b) Changes in the tension of the high-strength bolts on the lower cover plate. (c) Changes in the tension of the high-strength bolts on the joint flitch.
coefficient of the contact surface was, the greater the Δs and Δn were, and the greater the Ps and Pn were. 7. Simplified calculation
small; therefore, it was neglected in the calculation diagram. Four of Grade S10.9 M24 bolts were placed on each chord member, and two of Grade S10.9 M20 bolts were placed on the vertical connecting plate and joint flitches. The friction resisting capacity of one bolt is calculated as:
7.1. Simplified calculation for connection in slip state The truss was taken separate from the connection, the calculation diagram of which was shown in Fig. 12. It was assumed that the bending moment was carried by the bolts on the chord members, and the shear was carried by the bolts on the vertical connecting plate. The mechanical and finite element analyses showed that the prying action by the cover plate on the chord surface was very
Nbv ¼ ðμ 1 þ μ 2 Þp
ð1Þ
Here the friction coefficient is the sum of friction coefficient μ1 on the contact surface between the cover plate and chord member and the μ2 on contact surface between the bolt nut and the cover plate.
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Fig. 8. Tension of high-strength bolts in S4-J. (a) Changes in the tension of the high-strength bolts on the upper cover plate. (b) Changes in the tension of the high-strength bolts on the lower cover plate. (c) Changes in the tension of the high-strength bolts on the joint flitch.
The friction resisting bearing capacity at the end of the truss supported by four bolts is calculated as: P ¼ 4Nbv h=l1
ð2Þ
The shearing capacity of two Grade S10.9 M20 bolts is calculated as: V ¼ 2n f μ 1 P
ð3Þ
Then the load at the truss end when slip occurred between the upper chord member and the upper cover plate is: P s ¼ minðP; V Þ
ð4Þ
The results calculated using the above formulas were listed in Table 3. As shown in Table 3, the calculated values by the proposed formula get along well with the FEA and test result, which verifies the proposed formula. 7.2. Simplified calculation for connection in yield state
Here μ1 is the friction coefficient on the contact surface between the joint flitch and vertical connecting plate. nf is the amount of contact surfaces. P is the pretension of bolts.
When the connection yielded, slip had already occurred, and the bolt shanks were in contact with the wall of bolt hole. The connection
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Fig. 9. Stress contour plots of the high-strength bolts. (a) Stress contour plot of the bolts after the final tightening was completed. (b) Ultimate bearing capacity state of model S3-0303. (c) Ultimate displacement state of model S3-0303. (d) Ultimate bearing capacity state of model S3-035. (e) Ultimate displacement state of model S3-035. (f) Ultimate bearing capacity state of model S3-040. (g) Ultimate displacement state of model S3-040. (h) Ultimate bearing capacity state of model S4-0303. (i) Ultimate displacement state of model S4-0303. (j) Ultimate bearing capacity state of model S4-035. (k) Ultimate displacement state of model S4-035. (l) Ultimate bearing capacity state of model S4-040. (m) Ultimate displacement state of model S4-040.
yielded because either the material at the cross-section of the upper chord member yielded or the material at the cross-section of the web member yielded. Through analysis, we know that the cross-section at the center of the first-row of bolt holes on the upper chord member
was the weakest cross-section of the truss and bore relatively large moment. Thus, the load at the truss end when the stress at the cross section of the chord, shown on the Section 1-1 in the Fig. 12, reaches yielding
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Fig. 9 (continued).
strength is calculated as: P 1 ¼ W 1n f y =l
ð5Þ
W1n is the elastic section modulus of Section 1-1. fy is the yielding strength of steel material of chord member. According to literature [28,29], the web member will not loss stability before yields, then, the load at the truss end when the web member yields is calculated as: P 2 ¼ Aw f y sin45 °
ð6Þ
Aw is the area of web member. The yielding bearing capacity at the loading point of truss end is calculated as: P y1 ¼ minðP 1 ; P 2 Þ
ð7Þ
The bolt holes may also yield due to pressure on the wall of bolt hole, resulting in an increase in the rotation angle of the connection. The yield load of the local bearing pressure on the wall of bolt hole is calculated as follows: Nbcy ¼ d∑tf cy ¼ d∑t αf y
ð8Þ
P cy ¼ 4Nbcy h=l
ð9Þ
t is the thickness of chord member. Based on the FEA, we know that the yield load of the wall of bolt hole of specimen S3 and S4 were 145.46 kN and 156.04 kN. Based on these FEA results, the enhancement coefficient α of local yield bearing capacity in formula (8) could be deduced. For specimen S3, α = 1.60. For specimen S4, α = 1.29. Because the thickness of chord member of specimen S3 was thinner than that of specimen 4, the tension of the bolts had larger constraining effect on the wall of bolt hole and larger
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Fig. 10. Slip curves of the models. (a) Slip curves of upper chord members of model S3. (b) Slip curves of upper chord members of model S4. (c) Slip curves of web members of model S3. (d) Slip curves of web members of model S4.
enhancing the yield strength of the wall of bolt hole of specimen S3 compared to specimen S4. The smallest of the aforementioned three yield loads was selected as the yield load. Then, the yield bearing capacity of the connection is calculated as: P y ¼ min P 1 ; P 2 ; P cy
ð10Þ
The results from the proposed formula, the FEA and the test were listed in Table 4. It can be seen from Table 4 that the results from the three methods get along well with each other, which verifies the proposed formula. But more specimens or FE models with different thickness of chord members and different bolts will be needed to study the reasonable value of the enhancement coefficient α of local yield bearing capacity for different truss in the future study. 7.3. Simplified calculation for connection in ultimate state The tests and FEA showed that the cross section of chord members where the first row of bolt hole were located fractured by excessive tensile stress, no failure of the wall of bolt hole due to pressure was found. Therefore, for angle with small thickness, the wall of bolt hole may not fail because the wall is constrained by the out-of-plane pressure on both surfaces of the angle produced by high-strength bolt washer and contact surface, only yield could occur. Based on the test and FEA results, the pressure borne by the wall of bolt hole does not need to be checked for ultimate load bearing capacity. Considering that the high-strength bolts had a certain beneficial effect on the yield of the cross-sections of the chord members, the cross-section with holes possible may not deform significantly and fail when the gross cross-section near it yielded. Therefore, 0.7 times of the ultimate strength was selected as the strength of the material of
the cross-section. Hence, the yield of the gross cross-section and the cross-section at the holes should be checked at the same time. Then, the ultimate load bearing capacity at the loading point of truss end is calculated as: P 1u ¼ 0:7W p1n f u =l2
ð11Þ
P 2u ¼ W p1 f y =l2
ð12Þ
P u ¼ min P 1u ; P 2u
ð13Þ
Wp1n is the plastic net section modulus of Section 1-1. fu is the ultimate strength of steel material of chord member. Wp1 is the plastic gross section modulus of Section 1-1 neglecting the effect of bolt holes. The results from the proposed formula, the FEA and the test of the six connections were listed in Table 5. It can be seen from Table 5 that the results obtained using the simplified formulas were consistent with the test and FEA, which verifies the proposed formulas. 8. Conclusions The FEA was used to study the static and hysteretic performance of a new-type bolted truss-to-column connection with slipping contact surfaces, which is used in prefabricated multi-rise and high-rise steel structures. The following main conclusions were obtained: (1) The FEA correctly reflected the mechanical performance of the connection and were generally consistent with the test results, verifying the finite element model and the FEA method. The finite element model could be used to conduct parameter analysis on the performance of the connection by changing the parameters of the model.
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Fig. 11. Curves of friction and pressure borne by the wall of bolt hole between the upper cover plate and upper chord member. (a) Curves of model S3-J. (b) Curves of model S4-J.
(2) Each loading process of this kind of truss-to-column connection underwent the linear ascending stage (elastic stage), notable slip stage, curved ascending stage (elastic-plastic stage), and
bearing capacity degradation stage. The friction coefficient had small impact on the ultimate load of this connection, but it had large impact on the slip load. The greater the friction coefficient was, the greater the slip load was.
Table 2 Displacement and load corresponding to slip and bearing pressure. Model number
Δs/mm
Ps/kN
Δn/mm
Pn/kN
S3-0303 S3-035 S3-040 S4-0303 S4-035 S4-040
6.46 7.63 9.32 5.47 6.94 7.78
137.10 155.49 174.67 137.88 155.57 174.21
10.30 11.15 13.26 9.11 9.58 10.11
148.48 161.08 178.58 145.93 160.23 175.10
Table 3 Friction resisting bearing capacity from simplified calculation and simulation. Model number
Calculated P/kN
Calculated V/kN
Calculated PS/kN
Simulated PS/kN
Test PS/kN
S3-0303 S3-035 S3-040 S4-0303 S4-035 S4-040
137.14 155.40 174.82 137.14 155.40 174.82
187.86 217.00 248.00 187.86 217.00 248.00
137.14 155.40 174.82 137.14 155.40 174.82
137.10 155.49 174.67 137.88 155.57 174.21
134.42 – – 136.34 – –
Table 4 Yielding bearing capacity from simplified calculation and simulation.
Fig. 12. Diagram of connection calculations.
Model number
P1/kN
P2/kN
Calculated Pcy/kN
Calculated Py/kN
Simulated Py/kN
Test Py/kN
S3-0303 S3-035 S3-040 S4-0303 S4-035 S4-040
158.81 158.81 158.81 204.72 204.72 204.72
214.72 214.72 214.72 253.97 253.97 253.97
145.15 145.15 145.15 156.04 156.04 156.04
145.15 145.15 145.15 156.04 156.04 156.04
145.46 146.89 146.92 156.04 156.31 156.40
140.54 – – 156.25 – –
X.C. Liu et al. / Journal of Constructional Steel Research 133 (2017) 360–373 Table 5 Ultimate bearing capacity from simplified calculation and simulation. Model number P1u/kN
P2u/kN
Calculated Pu/kN Simulated Pu/kN Test Pu/kN
S3-0303 S3-035 S3-040 S4-0303 S4-035 S4-040
234.60 234.60 234.60 306.55 306.55 306.55
185.97 185.97 185.97 247.98 247.98 247.98
195.32 195.32 195.32 254.33 254.33 254.33
188.34 188.68 189.28 246.98 247.16 247.65
198.77 – – 250.41 – –
(3) The tension of the high-strength bolts on the cover plates and on the joint flitch all decreased. The tension of the first-row of highstrength bolts on the cover plates on the tensile side decreased the most, and the extent of the decrease reduced with the increase of the thickness of chord member. The tension of other bolts decreased by smaller extent than that of the first-row of high-strength bolts on the cover plates on the tensile side. The decrease in the tension of the high-strength bolts on the cover plates was not significantly affected by the friction coefficient. (4) During the static loading process, when the tangential force on the contact surface was smaller than the maximum static friction between the cover plates and the chord members, this highstrength bolt connection belongs to friction-type connection. There was no slip on the contact surface, and the friction between the cover plates and the chord members increased with increasing load. (5) When the tangential force on the contact surface was greater than the maximum static friction between the cover plates and the chord members, slips occurred between them. The bolt shank were in contact with the wall of bolt hole, causing the bolt shank to bear shear and the wall of bolt hole to bear pressure. Before the load reached the ultimate load, the friction gradually decreased with increasing load. In contrast, the pressure borne by the wall of bolt hole increased with increasing load sharply, as well as the sum of friction and pressure. After the load reached the ultimate load, the friction as well as the pressure decreased with decreasing load. (6) The results of the simplified formulas proposed in this paper agree well with the results of the test and FEA. These formulas can be used to describe the strength of the connection under static load and cyclic load. Acknowledgements The writers gratefully acknowledge the support for this work, which was funded by the National Natural Science Foundation of China (51678010), the Beijing Natural Science Foundation (8172009) and the Science and Technology Plan of Beijing Municipal Commission of Education (KM201610005012). References [1] T. Kim, J. Kim, Collapse analysis of steel moment frames with various seismic connection, J. Constr. Steel Res. 65 (16) (2009) 1316–1322. [2] D.K. Miller, Lessons learned from the Northridge earthquake, Eng. Struct. 20 (4) (1998) 249–260.
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