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Cyclic behavior of a prefabricated self-centering beam–column connection with a bolted web friction device
Engineering Structures 111 (2016) 185–198
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Cyclic behavior of a prefabricated self-centering beam–column connection with a bolted web friction device Ai-lin Zhang a,b, Yan-xia Zhang a,⇑, Rui Li c, Zong-yang Wang c a
Beijing Higher Institution Engineering Research Center of Structural Engineering and New Materials, Beijing University of Civil Engineering and Architecture, 100044, PR China Beijing Engineering Research Center of High-Rise and Large-Span Prestressed Steel Structure, Beijing University of Technology, 100124, PR China c School of Civil and Transportation Engineering, Beijing University of Civil Engineering and Architecture, 100044, PR China b
a r t i c l e
i n f o
Article history: Received 20 December 2014 Revised 11 December 2015 Accepted 17 December 2015
Keywords: Cyclic behavior Prefabricated post-tensioned self-centering beam–column connection Bolted web friction device High-rise buildings
a b s t r a c t A prefabricated post-tensioned (PT) self-centering beam–column connection using a bolted web friction device (PSC connection) has been proposed. This connection is different from a common self-centering connection using a bolted web friction device (SC connection) in that the beam of a steel frame with a PSC connection is divided into three parts connected with a vertical plate and PT strands, and the beam, including the gap opening feature, can be treated as a normal single beam on site. Eight PSC connections were designed with various combinations of design parameters, which include the initial PT forces, friction bolt forces and loading histories. Low-cycle loading experiments were conducted to study the seismic behavior of the PSC connections and to investigate the effects of the initial PT force and the friction bolt force. Additionally, relevant theoretical analyses were conducted, and the results indicated that the maximum PT force at 5% radians drift with the PSC connection did not exceed the yield force, and the average loss of the PT force was within 10%. The residual rotations of all the specimens were minimal, which indicated that the PSC connection had the same robust self-centering behavior compared to that of the SC connection. Simultaneously, the PSC connection does not require on-site aerial tension in high-rise buildings because the post tensioning can be introduced on the ground or in the factory. The theoretical double-flag models match the experimental results notably well and can be applied in the analysis and design of prefabricated self-centering steel frames. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction To achieve a good seismic performance of steel frame beam– column connections [1] and be protected from unexpected weld fractures under seismic hazards, a variety of modified connections were designed, such as widened beam section (WBS) [2] and reduced beam section (RBS) connections [3], which could effectively move the plastic hinge from the face of the column such that the ductility, as well as the energy dissipation, could be improved. However, dissipating energy under the designed earthquake can induce yielding and correlative damage in critical regions of the primary structural members, which can result in a large residual drift after the earthquake and a high cost of seismic rehabilitation. Thus, post-tensioned self-centering beam–column connections were developed. The design principle is to enable the connection
⇑ Corresponding author. E-mail addresses: [email protected] (A.-l. Zhang), zhangyanxia@bucea. edu.cn (Y.-x. Zhang), [email protected] (R. Li), [email protected] (Z.-y. Wang). http://dx.doi.org/10.1016/j.engstruct.2015.12.025 0141-0296/Ó 2015 Elsevier Ltd. All rights reserved.
to develop a gap opening at the beam–column interface, and the PT force enables the connection to self-center upon unloading. Thus, the energy dissipation occurs in special devices designed for the beam–column connection regions. The first experimental study on self-centering steel moment resistant frames (SC-MRFs) was conducted in 1997 [4]. Afterwards, SC-MRFs consisting of post-tensioned moment connections with top-and-seat angles were proposed and validated extensively by, for example, Ricles et al. [5], Ricles et al. [6] and Garlock [7], Garlock et al. [8], Garlock et al. [9], Garlock et al. [10]. Kim and Christopoulos [11] used PT friction-damped connections placed on the top and bottom beams in the SC-MRF. Iyama et al. [12] used two types of friction devices: a PT friction damped connection placed on the top and bottom of the beam flanges and a bottom flange-only friction device. In the same year, Wolski et al. [13] designed seven specimens with beam bottom flange friction devices (BFFD), and the experimental results indicated that the BFFD provided energy dissipation to the SC beam–column connection and avoided interference with the floor slab. George et al. [15] proposed a new self-centering steel post-tensioned connection which uses high-strength steel
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Fig. 1. PSC plane frame details. Fig. 3. Ideal M–hr behavior.
post-tensioned bars to provide self-centering behavior and steel energy dissipation elements that consist of cylindrical pins with hourglass shape to provide enhanced deformation capacity. Lin et al. [16,17] used web friction devices (WFDs) on beams for energy dissipation in the SC-MRF and conducted hybrid simulations and experiments to investigate the seismic performance of SC-MRFs under the design basis earthquake (DBE) and the maximum considered earthquake (MCE) [19]. Karavasilis et al. [14] conducted a parametric study on the seismic response of highly damped single-degree-of-freedom systems with self-centering flag-shaped or bilinear elastoplastic hysteresis. However, this type of structural system requires on-site aerial tension in high-rise buildings. A PSC connection with WFDs has been proposed for high-rise buildings, which is suitable for different types of columns, and the beams are post-tensioned to a short connecting element at each end. This assembly is subsequently erected similar to a traditional beam, which avoids the potential issues of aerial PT operations [18]. In this report, eight PSC connections were designed with different combinations of design parameters. These design parameters were initial PT forces and friction bolt forces as well as loading histories. The low-cycle loading experiments were presented to study the seismic behavior of the PSC connections for the life safety and
collapse prevention levels compared to that of the SC connection and investigate the effects of the initial PT forces and friction bolt forces.
2. PSC connection details 2.1. Detailed description The PSC plane frame with WFDs is illustrated in detail in Fig. 1. The beam of the steel frame designed with the PSC connection is divided into three parts: a long-beam portion and two shortbeam portions at both ends. These parts are connected with a vertical plate, and PT high-strength strands run parallel to the beam. Brass plates are sandwiched between the webs of the beam and the friction plates to achieve reliable friction and dissipate energy. The requirements for maximum beam rotation determine the size of the oversized circular bolt holes on the long-beam web. The transverse and longitudinal stiffeners are built up to strengthen the two short-beam portions. The entire assembly is connected to the column similar to a traditional beam.
Fig. 2. Schematic figure of PSC connection gap opening.
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A.-l. Zhang et al. / Engineering Structures 111 (2016) 185–198 Table 2 Material properties for rolled steel sections and plates.
Table 1 Test matrix. Specimens
Loading history (maximum amplitudes of story drift)
T0/Ty
T0/Tu
Friction bolt
Thick (mm)
3.5% 3.5% 3.5% 5% 5% 5% 5% 5%
0.20 0.25 0.35 0.15 0.20 0.35 0.2 0.25
0.18 0.23 0.32 0.14 0.18 0.32 0.18 0.23
6M20 6M20 6M20 6M20 6M20 6M20 6M24 6M24
Ultimate strength (N/mm2)
Elastic modulus ( 105 N/mm2)
PSCC1 PSCC2 PSCC3 PSCC4 PSCC5 PSCC6 PSCC7 PSCC8
Yield strength (N/mm2)
Percent elongation at fracture
14 16 18 20 22 30
384 392 381 384 388 350
561 555 555 550 574 505
2.15 2.06 2.22 2.09 2.09 2.07
27.0 23.3 25.3 25.7 26.8 26.5
2.2. Flexural conception and formula derivation A schematic diagram of the PSC connection opening gap is provided in Fig. 2. The ideal moment and gap-opening rotation (M–hr) behavior of the PSC connection under cyclic loading [13] is illustrated in Fig. 3, where M is the moment at the long beam
portion-vertical plate interface, and hr is the gap-opening rotation, as indicated in Fig. 2. The PSC connection behavior is similar to the conventional welded moment connection behavior before the gap opening, which is defined as event 0–1, as indicated in Fig. 3. Md is the decompression moment at event 7. M is the sum of the moments provided by the WFDs (Mf) and the PT force (Mpt) [21]. Because the gap opening increases the elongation of the PT strands,
Fig. 4. Details of PSC specimen.
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Table 3 PT strand material properties. Strand
Specimen
Yield PT force (kN)
Ultimate PT force (kN)
Elastic modulus ( 105 N/mm2)
1 19
1 2 3 Average value
540.8 540.4 542.2 541.1
592.8 593.2 586.8 590.9
2.03 2.05 2.00 2.03
(a) Preloaded in the stressing end
(a) Friction experiment of brass plates
(b) Adjust prestressed force Fig. 6. Prestressed tension of strands.
is the number of bolts; P is the pretension force in each bolt; and nf is the number of friction surfaces. Mpt can be expressed as follows:
(b) Force-Displacement hysteresis loop
Mpt ¼
Fig. 5. Friction experiment.
ð4Þ
i¼1
the bearing capacity increases gradually until unloading occurs at event 2. If loading continues, the PT strands will yield at event 3. Upon unloading, hr remains constant between event 2 and event 4. The connection moment decreases by 2Mf due to the direction of the friction force reversing in the WFD. Thereafter, hr reduces to zero from event 4 to event 5, and the gap opening closes at event 5. Then, M drops to 0 at event 6. The reversal of loading results in the behavior in M–hr being centrosymmetric. The moment M at the long beam portion-vertical plate interface can be expressed as follows:
M ¼ Mf þ M pt
n X T i hi
ð1Þ
where Mf and Mpt are the moment provided by the WFDs and the PT force, respectively. Mf can be expressed as follows:
Mf ¼ F f r
ð2Þ
F f ¼ nnf lp
ð3Þ
where r is the distance from the center of rotation to the centroid of the friction force, as indicated in Fig. 2; l is the friction coefficient; n
where Ti is the PT force of the ith strand; and hi is the distance from Ti to the center of rotation. Ti can be expressed as follows:
T i ¼ T 0 þ DT i
ð5Þ
where T0 is the initial PT force; and DTi is the increment of the PT force during the loading procedure. Due to the equality in the increment of the PT force and the beam axis force, the equilibrium equation can be expressed as follows: n X ½ksi ðdsi db Þ ¼ kb db
ð6Þ
i¼1
Pn P K si dsi K si ni¼1 hr hi K s h r hb ¼ ¼ db ¼ Pn i¼1 Ks þ Kb 2ð K s þ K b Þ i¼1 K si þ K b
ð7Þ
where dsi (i = 1, 2, 3 . . . , n) is the elongation of each strand as the rotation increases; and db is the compressive deformation of the beam. DTi can be expressed as follows:
DT i ¼ K si ðdsi db Þ ¼ K si hr hi
K s hb 2ðK s þ K b Þ
ð8Þ
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Fig. 7. Test set up.
Hence, Ti can be expressed as follows:
T i ¼ T 0i þ DT i ¼ T 0i þ K si ðdsi db Þ K s hb ¼ T 0i þ K si hr hi 2ðK s þ K b Þ
ð9Þ
Mpt is the moment provided by the tensile force based on the actual location of the PT strands. The expression for Mpt can be presented as follows:
K s hb hi 2ðK s þ K b Þ i¼1 X X X K si K s hb ¼ T 0i hi þ K si hi hi hr ¼ Md þ K 2h hr 2ðK s þ K b Þ
M pt ¼
n X X ðT i hi Þ ¼ T 0i þ K si hr hi
ð10Þ Fig. 8. Test photograph.
where Md is the decompression moment; and K2h is the rotational stiffness after the gap opening. M1 is the moment at the gap opening, which can be expressed as follows:
M5 ¼ M 4 K 2h h4 ¼ M 4 K 2h h2 ¼ M d M f
M 1 ¼ M IGO ¼ M f þ Md
where h4 is the gap-opening rotation at event 4 and is equal to h2.
ð11Þ
Furthermore, the M at event 2 can be given by
M 2 ¼ M 1 þ K 2h h2
ð12Þ
ð14Þ
3. Test specimens 3.1. Connection constitution
where h2 is the gap-opening rotation at event 2. The next turning point is event 4; M4 can be given by
M 4 ¼ M2 2Mf ¼ M f þ Md þ K 2h h2 2M f ¼ Md þ K 2h h2 M f
M5 can be expressed by
ð13Þ
Eight PSC specimens were designed and fabricated with different combinations of property parameters, including initial PT
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length of the long-beam (450 250 14 16 mm) is 3170 mm. The thicknesses of the transverse stiffener plate of the shortbeam and the longitudinal beam are 30 mm and 20 mm, respectively. The 16 mm thick cover plates are added to the long-beam flanges to ensure that the long-beam remains elastic. The size of the vertical plate is 500 250 30 mm, and the friction plate is welded on to the face of the column flange, whose size is 300 175 14 mm. Two brass plates of 3 mm thickness are sandwiched between the beam webs and the friction plates. The PT strands are thread and run parallel to the long beam, with a nominal diameter of 21.6 mm. The initial PT forces of the strands are different between specimens. The detailed dimensions are provided in Fig. 4. Six M20 friction bolts (10.9 property grade, nominal bolt diameter of 20 mm) are installed in Specimens 1–6, and six M24 friction bolts are installed in Specimens 7–8.
(a) Cyclic loading history 1
3.2. Material properties The steel for all specimens is Q345B, which has a nominal yielding strength of 345 MPa and an elastic modulus of elasticity of 1.98 105 MPa. The yielding stress fy, ultimate stress fu, elastic modulus, and percent elongation at fracture for different thickness steel plates used to construct the specimens are provided in Table 2. The material properties are based on tests of tension coupons, where the coupons are taken in the direction parallel to the rolling direction. Each PT strand is a high-strength stress relieved steel strand. The nominal diameter of the PT strand is 21.6 mm, which corresponds to a cross-sectional area of 312.9 mm2. The material properties for the PT strands are listed in Table 3. The coefficient of friction between the brass and steel is 0.34 based on experimental results. Fig. 5(a) depicts the friction experiment for the brass plates, and Fig. 5(b) illustrates the complete fifty cycles of force versus displacement relationships.
(b) Cyclic loading history 2 Fig. 9. Cyclic loading history.
strand forces, friction bolt forces, and loading histories, which are listed in Table 1. The section properties of the PSC specimens can be given as follows: all column sections are identical (H350 350 12 19 mm), based on strong-column weakbeam principles. The thickness of the column continuity plates is 30 mm, and two thick doubler plates with 16 mm thickness are installed in the beam–column panel zone joint. The length of the short-beam (H482 250 18 30 mm) is 450 mm, and the
3.3. Prestressed tension of strands The low retracting tension and anchor methods were used in the pre-stressing procedure for the strands. The beam with the PSC connection consists of long and short beam portions. The first step is completing the assembly of the long and short beams. The long beam is placed into the friction plates of the short beams and bolted. Then, the strands, the pressure sensor and the anchor-
Fig. 10. Arrangement of displacement meter.
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(a) Vertical view
(b) Front view
(c) Lateral view
(d) 1-1
Fig. 11. Arrangement of strain gauges and strands number.
age are installed in the anchor end. The strands are thread from the reserved holes of the short beam to those of the long beam. After the installation of the anchorage in the anchor end, a tensioning device is used to preload the strands (Fig. 6(a)). Then, the pre-stressed forces are adjusted while the acquisition instrument is monitored (Fig. 6(b)). The last step is to weld the beam and column together. The complete joint penetration weld would not give rise to the evident changes of the PT forces according to the monitored data. 3.4. Test Setup and cyclic loading history Each specimen was tested in the setup (Figs. 7 and 8) through a series of central displacement cycles by displacing actuators at both ends of the beams, which is consistent with the AISC [20]
loading protocol (shown in Fig. 9). There are two loading histories. The first maximum amplitude of the story drift is 3.5% radians corresponding to the life safety level, and the second maximum amplitude of the story drift is 5% radians corresponding to the collapse prevention level [19,22]. Additionally, their seismic performance objectives are different; the primary structure always remains elastic before the story drift of 3.5% radians. The strands remain elastic, the column and beam strain is within 2 ey without buckling, and there is no yielding in the beam web under shear force before the story drift of 5% radians. For Specimens PSCC1– 3, the cyclic loading history 1 consisted of 8 stages, and the first three stages contained 6 cycles. The fourth stage is only 4 cycles. Thereafter, the remaining four stages all have two cycles (shown in Fig. 9(a)). For Specimens PSCC4–8, the cyclic loading history 2
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(a) θ=2%, gap opening 5.12 mm (1.18%)
(a) θ=3%, gap opening 8.73 mm (2.01%)
(b) θ=3.5%, gap opening 10.28 mm (2.37%)
(b) θ=5%, gap opening 14.83 mm (3.42%)
Fig. 12. Experimental photograph of specimen PSCC1.
Fig. 13. Experimental photograph of specimen PSCC5.
is similar to Specimens PSCC1–3 and consists of 9 stages (shown in Fig. 9(b)). The two displacing actuators on the self-balancing equipment at both beam ends of the connection impose displacement cycles with increasing amplitude, as above, in the antisymmetric direction, and an axial compression force (axial compression ratio is 0.2) is imposed on the top of the column by a hydraulic jack.
served as the baseline specimens for the experimental study and are shown in Figs. 12 and 13, respectively, will be discussed first, and other specimens will be compared with them. The detailed data for all the specimens are presented in Table 4. For Specimen PSCC1, as the story drift (h) increased from 0.375% to 0.75% radians, the connection had an initial stiffness that was similar to the initial stiffness of a conventionally welded moment connection. When h reached 0.81% radians, a gap opening occurred at the long beam portion-vertical plate interface. The maximum opening width of the connection continued to increase during subsequent loading. When h was approximately 3.5% radians, the maximum opening width reached 10.28 mm. After the load-off, the opening closed due to the PT forces, and an extremely small residual opening width of 0.8 mm was found at the end of the long beam. The initial PT forces of PSCC2 and PSCC3 were greater compared to that of
3.5. Instrumentation The instrumentation is illustrated in Fig. 10. The column capital is subjected to an axial force by a 600T actuator, and an additional two 100T actuators on the beam ends apply cyclic loadings. Each strand has a force transducer to monitor the PT force. The displacement data for the beam ends is collected by two displacement meters arranged on the top flanges. Linear displacement potentiometers fixed on the junctions of the vertical plates and the long beams are used to measure the gap width of the beams. The column flanges, column stiffeners, top and bottom beam flanges, and vertical and horizontal directions of the beam webs are pasted with strain gauges that measure the strain changes during loading in each position, as indicated in Fig. 11. 4. Experimental results 4.1. General test observations The responses of Specimen PSCC1 (experiencing cyclic loading history 1) and PSCC5 (experiencing cyclic loading history 2), which
Table 4 Experimental results of connections. Specimens
Initial gap opening story drift ratio (rad)
Opening width (mm)
Maximum opening width (mm)
Maximum residual opening width (mm)
PSCC1 PSCC2 PSCC3 PSCC4 PSCC5 PSCC6 PSCC7 PSCC8
0.81% 0.86% 0.94% 0.50% 0.60% 0.81% 0.40% 0.74%
1.49 1.44 0.76 1.82 1.65 1.32 1.67 0.96
10.28 9.19 7.73 16.41 14.83 10.48 14.67 12.27
0.8 0.15 0.065 1.12 1.03 1.24 0.90 0.86
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Fig. 14. Vertical load–displacement response for specimen PSCC1. Fig. 16. Comparison of vertical load–displacement response for PSCC1–3.
slightly higher compared to that of PSCC7, and thus their deformation procedures were essentially similar. All the specimens had small residual opening widths after unloading, which indicates that all connections had excellent re-centering capacity. 4.2. Connection flexural behavior The connection behavior is characterized by a gap opening and closing in the interface between the vertical plate on the short beam and the long beam as a result of the re-centering force in the PT strands. The vertical force F versus the displacement response D and the moment M versus the gap-opening rotation hr for Specimen PSCC1 are provided in Figs. 14 and 15, respectively. D is the measured horizontal displacement at the end of the beam, where the actuator is connected to the specimen. M is the moment developed at the long beam-vertical plate interface under the applied vertical force F. The experimental results are summarized in Table 5, where hIGO is the imminent gap-opening rotation, hr0.05 is the maximum gap-opening rotation, and hres is the maximum residual rotation. MIGO is the imminent gap-opening moment, K1 is the initial stiffness, and bE is the effective energy dissipation ratio, which can be determined as follows:
Fig. 15. Moment–rotation response for specimen PSCC1.
PSCC1, thus their gap opening occurred slightly later. The maximum opening widths were 9.19 mm and 7.73 mm, respectively, which was less than the value of PSCC1. For Specimen PSCC5, when h increased to 0.60% radians, a gap opening occurred at the long beam portion-vertical plate interface. The maximum opening width of 14.83 mm occurred when h reached 5% radians. The opening closed automatically under the effect of the PT strands after unloading and left a small residual opening width of 1.03 mm. The test results indicate that the initial PT force has an effect on the time of a gap opening. A smaller initial PT force can lead to an earlier gap opening and a larger maximum opening width. Specimens PSCC7 and PSCC8 had the same property grade of friction bolts. The initial PT force of PSCC8 was
bE ¼ M f =M IGO
ð15Þ
To enable a satisfactory response for the SC-MRF under seismic loading, [23] recommend that bE P 0.25. It is observed that the hysteresis loops of the PSC connection have a double-flag shape similar to common SC connections. The vertical F D response indicates that Specimen PSCC1 had an initial stiffness of 9025.1 kN/m prior to the gap opening, and the connection stiffness decreased to 2297.5 kN/m when the gap opening occurred. The imminent gap-opening moment (MIGO) was
Table 5 Experimental results. Specimens
K1 (kN/m)
hIGO (rad) (%)
MIGO (kN m)
hr0.05 (rad) (%)
M0.05 (kN m)
F (kN)
hres (rad) (%)
bE
PSCC1 PSCC2 PSCC3 PSCC4 PSCC5 PSCC6 PSCC7 PSCC8
9025.1 9486.2 10842.9 7984.3 8530.1 9180.4 9837.3 10445.3
0.34 0.33 0.18 0.42 0.38 0.31 0.38 0.22
378.65 384.04 430.92 297.69 335.04 476.82 410.64 423.83
2.37 2.12 1.78 3.78 3.42 2.41 3.38 2.83
602.27 609.16 687.28 714.16 677.13 769.40 722.78 757.28
366.12 370.31 417.8 434.14 411.63 467.72 439.38 460.35
0.18 0.04 0.01 0.257 0.236 0.286 0.207 0.197
0.409 0.356 0.280 0.467 0.439 0.311 0.471 0.421
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(a) SL12 strand Fig. 17. Comparison of moment–rotation response for PSCC1–3.
(b) SL11 strand Fig. 20. PT force-story drift response of specimens PSCC4–6.
Fig. 18. Comparison of moment–rotation response for PSCC4–6.
378.65 kN m. When h was approximately 3.5% radians, the maximum applied force was 366.12 kN along with a 2.37% radians maximum rotation (gap opening) and a 602.27 kN m maximum moment. An extremely small residual rotation of 0.18% radians was left at the end of the long beam after the load-off. The F – D and M–hr hysteresis loops of Specimens PSCC1, PSCC2 and PSCC3 are provided in Figs. 16 and 17. Due to the initial PT force of PSCC2 being slightly less than that of PSCC1, the hysteresis loop of PSCC2 is close to that of PSCC1. Comparing the experimental results of PSCC3 and PSCC1, PSCC3, which had a higher initial PT
Fig. 19. Comparison of moment–rotation response for PSCC5 and PSCC7.
force, had the larger applied force and initial stiffness. As indicated in Fig. 17, PSCC3 had a delayed gap-opening time as well as a greater MIGO compared with that of PSCC1. The increment of the initial PT force results in an increase of the maximum moment from PSCC1 to PSCC3 and a decrease in the maximum gapopening rotation. The M–hr hysteresis loops for the different initial PT forces of PSCC4-6 are provided in Fig. 18. The initial PT force increased from 0.14Tu, to 0.18Tu to 0.32Tu,, and the corresponding initial stiffness increased from 7.50 104 kN m/rad to 1.72 105 kN m/rad to 2.24 105 kN m/rad. Additionally, the results for different specimens are shown in Table 5. The results indicate that MIGO increased because of the increment of the initial PT forces, from 297.69 kN m to 335.04 kN m to 476.82 kN m. The gap opening occurred at a story drift of 0.50%, 0.60% and 0.81% radians; however, the maximum gap-opening rotation decreased progressively from 3.78% to 3.42% to 2.41% radians, which provided further evidence that a higher PT force accompanied the delayed gap-opening times and smaller maximum gap-opening rotations. The largest values of the connection stiffness after the gap opening and maximum moment were from PSSC6: 1.278 104 kN m/rad and 769.40 kN m, respectively. Fig. 19 presents the M–hr hysteresis loops for the different friction bolt forces of Specimens PSCC5 and PSCC7. When the friction bolt force increased from M20 to M24 (the pretension force of one friction bolt ranged from 155 kN to 225 kN), the hysteresis loop for the specimen with the higher friction bolt force was fuller compared to the other loop. MIGO increased from 335.04 kN m to 410.64 kN m, and the maximum gap-opening rotation reduced from 3.42% to 3.38% radians. The maximum moment increased from 677.13 kN m to 722.78 kN m.
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A.-l. Zhang et al. / Engineering Structures 111 (2016) 185–198 Table 6 Experimental results of PT forces. Specimens
T0/Tu
Tmax/Ty
T max /Ty
T r /Ty
Tmax/Tu
T max /Tu
T r /Tu
ðT 0 T r Þ/T0 (%)
PSCC1 PSCC2 PSCC3 PSCC4 PSCC5 PSCC6 PSCC7 PSCC8
0.18 0.23 0.32 0.14 0.18 0.32 0.18 0.23
0.625 0.633 0.632 0.744 0.745 0.745 0.727 0.745
0.528 0.543 0.563 0.608 0.630 0.651 0.605 0.624
0.194 0.241 0.334 0.156 0.181 0.327 0.178 0.236
0.572 0.580 0.578 0.681 0.682 0.682 0.666 0.682
0.483 0.497 0.516 0.557 0.576 0.596 0.554 0.571
0.177 0.221 0.306 0.143 0.166 0.300 0.163 0.216
1.55 3.94 4.43 2.26 7.73 6.36 9.53 6.19
ratio decreased from 0.467 to 0.311, approximately 33.4%, which indicates that an increase in the PT force resulted in a decrease in the energy dissipation. When other conditions were identical, and the friction bolt force changed from 6M20 to 6M24 (for example PSCC5 and PSCC7), the energy dissipation ratio increased from 0.439 to 0.471. Therefore, a larger bolt force could lead to higher energy dissipation but this improvement was notably limited. 4.4. PT force
Fig. 21. Strain of different positions for PSCC1.
4.3. Energy dissipation The effective energy dissipation ratios of the specimens all satisfied the requirement that the energy dissipation ratio should be greater than 0.25 (Table 5), which indicates that the PSC connection has a good energy dissipation capacity. When the PT force increased from 0.14Tu to 0.32Tu, and other conditions remained the same (for example PSCC4 and PSCC6), the energy dissipation
The measured PT force-story drift responses for Specimens PSCC4–6 are provided in Fig. 20. The PT strands were stretched after the gap opening, and the corresponding PT forces increased gradually. The experimental PT forces for all specimens are provided in Table 6, where T0 is the initial PT force, Ty is the measured average yield PT force (here its value is 541 kN), Tu is the measured average ultimate PT force (its value is 591 kN), Tmax is the maximum PT force of all the strands at 0.05 radians drift, T max is the average maximum PT force at 0.05 radians of the drift, and Tr is the average residual force. The maximum PT force at 0.05 radians of drift for the PSC connection was 403.07 kN, which equals 74.5% of the yield force Ty and 68.2% of the ultimate capacity Tu. In fact, the length of the PT strand in the self-centering frame was longer compared to that in the beam–column connection, thus the PT force would be reduced in the self-centering frame. The increment of the initial PT force resulted in a slight increase in the maximum PT force of each strand; however, the outside strands of the three specimens had PT forces that nearly reached the maximum. Moreover, the friction bolt force is also a factor that affects the PT force. The increment of the friction bolt force reduced the maximum PT force from 0.682Tu to 0.666Tu. The average loss of the PT forces was within 10%, which indicated that the PT strands, the anchorage performance and the pre-stressing method in the experiments were reliable. 4.5. Strain condition of the element plates
Fig. 22. Comparison of strain for PSCC5.
Fig. 21 provides the yield strain and strain values of the element plates at different positions for Specimen PSCC1. From Fig. 21, we can obtain that all the plates of the column and beam remained elastic and undamaged, which indicates that the connection can remain elastic corresponding to the life safety level. The strain values from the element plates at different positions for PSCC5 are provided in Fig. 22. For Specimen PSCC5, before the story drift reached 3.5% radians, the column and beam essentially remained elastic. During the entire loading procedure, the reinforcing plates of the specimen reached the plastic stage early, at a story drift of approximately 1.75% radians, and the column web reached plasticity when the story drift ratio was equal to 3.5% radians. Then, minor yielding occurred in the column panel zones. The existence of the reinforcing plates resulted in the elastic beam flanges. Furthermore, the strain values indicated that there was no yielding
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(a) PSCC4
(b) PSCC5
(c) PSCC6
(d) PSCC7
(e) PSCC8 Fig. 23. Comparison of experimental and theoretical moment–rotation relationship for PSCC4–8.
in the beam web under the shear force, thus meeting the drift objectives of the collapse prevention level. 4.6. Comparison of the experimental and analytical moment–rotation relationship Apart from a discussion of the experimental results, the relevant theoretical analysis of a moment–rotation (M–hr) relationship for the PSC connection according to the analytical formulas (10)–(14) described earlier is also conducted in the following discussion using Specimens PSCC4–8 as examples. The experimental and analytical M-hr relationships are presented in Fig. 23, and the comparative responses of Specimens PSCC4–8 are summarized in Table 7. This table provides a comparison of the moment MfIGO at
the gap opening provided by the WFDs, the moment Md at the gap opening provided by the PT strands, the imminent gap opening moment MIGO, the moment Mf0.05 at hr0.05(h = 5%) provided by the WFDs, the maximum moment Mpt0.05 at hr0.05 provided by the PT strands, and the maximum moment Mp0.05 at hr0.05, where MIGO is equal to the sum of MfIGO and Md and Mp0.05 is equal to the sum of Mf0.05 and Mpt0.05. Mu is the normal plastic moment capacity of the beam. Additionally, the connection rotation stiffness after the gap opening is provided in Table 7. When MIGO was achieved, the contact between the vertical plate and the long beam flange plate reached a critical state in which there was neither a gap opening nor any contact. The monitoring value of the gap opening was minimal, and the analytical gap-opening rotation was zero. For example, for Specimen PSCC5, the experimental rotation at the gap
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A.-l. Zhang et al. / Engineering Structures 111 (2016) 185–198 Table 7 Comparison of experiment and theory data of specimens. Specimens
Classification
hrIGO (103 rad)
MfIGO/Mu
Md/Mu
hr0.05 (102 rad)
Mf0.05/Mu
Mpt0.05/Mu
Mp0.05/Mu
K2h (kN m/rad)
PSCC4
Experiment Theory Deviation ratio (%)
4.2 0 –
0.18 0.20 12.7
0.21 0.18 13.6
0.37 0.39 5.0
3.8 3.7 2.7
0.18 0.20 12.0
0.70 0.81 13.7
0.88 1.02 13.3
13686.9 13801.2 0.8
PSCC5
Experiment Theory Deviation ratio (%)
3.8 0 –
0.16 0.20 20.9
0.23 0.24 0.4
0.41 0.44 6.0
3.4 3.3 3.0
0.18 0.20 14.1
0.66 0.78 15.9
0.84 0.99 15.5
12907.8 13484.8 4.3
PSCC6
Experiment Theory Deviation ratio (%)
3.1 0 –
0.17 0.20 17.0
0.42 0.42 0.2
0.59 0.62 5.4
2.4 2.4 0.0
0.18 0.20 10.7
0.77 0.82 6.7
0.95 1.03 7.5
12780.0 13657.2 6.4
PSCC7
Experiment Theory Deviation ratio (%)
3.8 0 –
0.23 0.30 21.8
0.31 0.24 30.2
0.51 0.53 5.2
3.4 3.1 9.7
0.24 0.30 18.3
0.65 0.75 13.9
0.89 1.05 15.2
12405.6 13510.6 8.2
PSCC8
Experiment Theory Deviation ratio (%)
2.2 0 –
0.24 0.30 19.6
0.32 0.30 6.9
0.52 0.59 11.7
2.8 2.8 0.0
0.26 0.30 14.1
0.68 0.77 12.1
0.93 1.07 12.6
11845.7 13816.4 14.3
MIGO/Mu
opening was 0.38% radians but the analytical gap-opening rotation was zero; the experimental value of Md = 0.23Mu is close to the analytical value of 0.24Mu. The experimental value of MfIGO = 0.16Mu was less than the analytical value of 0.20Mu due to the loss of the bolt friction force during the test; the experimental value of MIGO = 0.41Mu was less than the analytical value of 0.44Mu by approximately 6%. The average difference between the experimental value and the analytical value of MIGO was approximately 6.7%. At hr0.05, Mf0.05 = 0.18Mu was less than the analytical value of 0.20Mu by 14.1%; the experimental value of Mpt0.05 = 0.66Mu was less than the analytical value of 0.78Mu by 15.9% due to the loss of strand anchorage. The experimental value of Mp0.05 = 0.84Mu is less than the analytical value of 0.99Mu by 15.5%; the average difference between the experimental and analytical values of Mp is approximately 12.8%. The experimental rotation stiffness after the gap opening of K2h = 12907.8 kN m/rad was less than the analytical value of 13484.8 kN m/rad by 4.3%; the average difference between the experimental and analytical values of K2h was 6.8%. The hysteresis loops of M–hr for the specimens summarized in Fig. 23 indicated that there was a slight difference between the experimental results and the theoretical analysis. To summarize, the theoretical results were observed to match the experimental data reasonably well.
5. Conclusions A prefabricated self-centering beam–column connection with a bolted web friction device is proposed for high-rise buildings, and eight PSC connections are designed with various combinations of design parameters. The low-cycle loading experiments and theoretical analysis are presented. The results indicate that the hysteresis loops of the PSC connection present an obvious double-flag model, which indicates that the connection has the same satisfactory self-centering capacity compared to that of the SC connection. At the same time, it does not need on-site aerial tension in high-rise buildings. Furthermore, the frame beam is connected to the column as a traditional beam and is easily accepted by structural designers. The maximum PT force of the PSC connection would not exceed the yield force. In fact, the length of the PT strand in the PSC frame would be longer than that in the beam–column connection, thus the PT force would be reduced in the PSC frame. The average loss of the PT force was within 10%. The energy dissipation capacity satisfied the requirement that the effective energy dissipation ratio should be greater than 0.25. The frame beam and column essentially remained elastic and undamaged prior to a story drift of
3.5% radians corresponding to the life safety level. After that point, minor yielding occurred in the column panel zones, and no yielding occurred in the beam web under the shear force before the story drift of 5% radians, thus meeting the drift objectives of the collapse prevention level. The residual rotations of all of the specimens were minimal, which indicated that the PSC connection had an excellent re-centering capacity, and the PT strands, the anchorage performance and the pre-stressing method in the experiments were reliable. With the increment in the initial PT force, the initial stiffness, the imminent gap opening moment, and the maximum PT force improved to different extents; the maximum gap opening rotation and the energy-dissipation capacity indicated a decreasing tendency with increasing initial PT force. Therefore, it is suggested that for the purposes of practical engineering, the degree of the initial PT force should be selected based on the performance design objectives of the structural elements. The increment in the friction bolt forces can result in an increase in the imminent moment, a decrease in the gap-opening rotation, a decrease in the PT force, and a slight increase in the energy dissipation capacity. The theoretical results of the PSC connection match the experimental data reasonably well. The results of the experiment have verified that the theoretical model can be applied to the analysis and design of prefabricated self-centering steel frames. Acknowledgments The research reported herein is supported by the National Natural Science Foundation of China under Grant No. 51278010 and the National Natural Science Foundation of China under Grant No. 51278027. Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.engstruct.2015. 12.025. References [1] Gross LJ. A connection model for the seismic analysis of welded steel moment frames. Eng Struct 1998;20(4–6):390–7. [2] Egor Paul Popov, Yang Tzong-Shuoh, Chang Shih-Po. Design of steel MRF connections before and after 1994 Northridge earthquake. Eng Struct 1998;22 (12):1030–8. [3] Shen J, Kitjasateanphun T, Srivanich W. Seismic performance of steel moment frames with reduced beam sections. Eng Struct 2000;22(8):968–83.
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[4] Garlock M, Ricles JM, Sause R, Peng SW, Zhao C, Lu LW. Post-tensioned seismic resistant connections for steel frames. In: Structural stability research council conference workshop. Rolla Missouri: Structural Stability Research Council; 1998. [5] Ricles JM, Sause R, Garlock M, Zhao C. Post-tensioned seismic-resistant connections for steel frames. J Struct Eng 2001;127(2):113–21. [6] Ricles JM, Sause R, Peng SW, Lu LW. Experimental evaluation of earthquake resistant post-tensioned steel connections. J Struct Eng 2002;128(7): 850–9. [7] Garlock M. Full-scale testing, seismic analysis, and design of post-tensioned seismic resistant connections for steel frames. Ph.D. dissertation, Civil and Environmental Engineering Dept., Lehigh Univ., Bethlehem, PA; 2002. [8] Garlock M, Ricles JM, Sause R. Cyclic load tests and analysis of bolted top-andseat angle connections. J Struct Eng 2003;129(12):1615–25. [9] Garlock MM, Ricles JM, Sause R. Experimental studies on full-scale posttensioned steel connections. J Struct Eng 2005;131(3):438–48. [10] Garlock M, Ricles JM, Sause R. Influence of design parameters on seismic response of post-tensioned steel MRF systems. Eng Struct 2008;30:1037–47. [11] Kim HJ, Christopoulos C. Friction damped post-tensioned self-centering steel moment-resisting frames. J Struct Eng 2008;134(11):1768–79. [12] Iyama J, Seo CY, Ricles JM, Sause R. Self-centering MRFs with bottom flange friction devices under earthquake loading. J Constr Steel Res 2009;65: 314–25. [13] Wolski M, Ricles JM, Sause R. Experimental study of a self-centering beam– column connection with bottom flange friction device. J Struct Eng 2009;135 (5):479–88.
[14] Karavasilis TL, Seo CY. Seismic structural and non-structural performance evaluation of highly damped self-centering and conventional systems. Eng Struct 2011;33:2248–56. [15] George V, Theodore LK, Brian U. Finite element models and cyclic behavior of self-centering steel post-tensioned connections with web hourglass pins. Eng Struct 2013;52:1–16. [16] Lin YC, Sause R, Ricles JM. Seismic performance of steel self-centering, moment-resisting frame: hybrid simulations under design basis earthquake. J Struct Eng 2013;139(11):1823–32. [17] Lin YC, Sause R, Ricles JM. Seismic performance of a large-scale steel selfcentering moment-resisting frame: MCE hybrid simulations and quasi-static pushover tests. J Struct Eng 2013;139(7):1227–36. [18] Zhang AL, Zhang YX, Liu XC. Research outlook of earthquake resilient prestressed steel structures. J Beijing Univ Technol 2013;39(4):507–14. [19] Federal Emergency Management Agency (FEMA)450. NEHRP recommended provisions for seismic regulations for new buildings and other structures. Part 1-provisions and Part 2-commentary. Washington, D.C.; 2003. [20] ANSI/AISC. Seismic provisions for structural steel buildings. Chicago (IL): American Institute of Steel Construction; 2005. [21] Khoo HH, Clifton C, Butterworth J, Macrae G, Gledhill G, Sidwell G. Development of the self-centering Sliding Hinge Joint with friction ring springs. J Constr Steel Res 2012;78(11):201–11. [22] Federal Emergency Management Agency (FEMA)273. NEHRP Guidelines for the seismic rehabilitation of buildings. Washington, D.C.; 1997. [23] Seo C, Sause R. Ductility demands on self-centering MRFs with bottom flange friction energy dissipators. ACI Struct J 2005;102(2):275–85.
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Engineering Structures journal homepage: www.elsevier.com/locate/engstruct
Cyclic behavior of a prefabricated self-centering beam–column connection with a bolted web friction device Ai-lin Zhang a,b, Yan-xia Zhang a,⇑, Rui Li c, Zong-yang Wang c a
Beijing Higher Institution Engineering Research Center of Structural Engineering and New Materials, Beijing University of Civil Engineering and Architecture, 100044, PR China Beijing Engineering Research Center of High-Rise and Large-Span Prestressed Steel Structure, Beijing University of Technology, 100124, PR China c School of Civil and Transportation Engineering, Beijing University of Civil Engineering and Architecture, 100044, PR China b
a r t i c l e
i n f o
Article history: Received 20 December 2014 Revised 11 December 2015 Accepted 17 December 2015
Keywords: Cyclic behavior Prefabricated post-tensioned self-centering beam–column connection Bolted web friction device High-rise buildings
a b s t r a c t A prefabricated post-tensioned (PT) self-centering beam–column connection using a bolted web friction device (PSC connection) has been proposed. This connection is different from a common self-centering connection using a bolted web friction device (SC connection) in that the beam of a steel frame with a PSC connection is divided into three parts connected with a vertical plate and PT strands, and the beam, including the gap opening feature, can be treated as a normal single beam on site. Eight PSC connections were designed with various combinations of design parameters, which include the initial PT forces, friction bolt forces and loading histories. Low-cycle loading experiments were conducted to study the seismic behavior of the PSC connections and to investigate the effects of the initial PT force and the friction bolt force. Additionally, relevant theoretical analyses were conducted, and the results indicated that the maximum PT force at 5% radians drift with the PSC connection did not exceed the yield force, and the average loss of the PT force was within 10%. The residual rotations of all the specimens were minimal, which indicated that the PSC connection had the same robust self-centering behavior compared to that of the SC connection. Simultaneously, the PSC connection does not require on-site aerial tension in high-rise buildings because the post tensioning can be introduced on the ground or in the factory. The theoretical double-flag models match the experimental results notably well and can be applied in the analysis and design of prefabricated self-centering steel frames. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction To achieve a good seismic performance of steel frame beam– column connections [1] and be protected from unexpected weld fractures under seismic hazards, a variety of modified connections were designed, such as widened beam section (WBS) [2] and reduced beam section (RBS) connections [3], which could effectively move the plastic hinge from the face of the column such that the ductility, as well as the energy dissipation, could be improved. However, dissipating energy under the designed earthquake can induce yielding and correlative damage in critical regions of the primary structural members, which can result in a large residual drift after the earthquake and a high cost of seismic rehabilitation. Thus, post-tensioned self-centering beam–column connections were developed. The design principle is to enable the connection
⇑ Corresponding author. E-mail addresses: [email protected] (A.-l. Zhang), zhangyanxia@bucea. edu.cn (Y.-x. Zhang), [email protected] (R. Li), [email protected] (Z.-y. Wang). http://dx.doi.org/10.1016/j.engstruct.2015.12.025 0141-0296/Ó 2015 Elsevier Ltd. All rights reserved.
to develop a gap opening at the beam–column interface, and the PT force enables the connection to self-center upon unloading. Thus, the energy dissipation occurs in special devices designed for the beam–column connection regions. The first experimental study on self-centering steel moment resistant frames (SC-MRFs) was conducted in 1997 [4]. Afterwards, SC-MRFs consisting of post-tensioned moment connections with top-and-seat angles were proposed and validated extensively by, for example, Ricles et al. [5], Ricles et al. [6] and Garlock [7], Garlock et al. [8], Garlock et al. [9], Garlock et al. [10]. Kim and Christopoulos [11] used PT friction-damped connections placed on the top and bottom beams in the SC-MRF. Iyama et al. [12] used two types of friction devices: a PT friction damped connection placed on the top and bottom of the beam flanges and a bottom flange-only friction device. In the same year, Wolski et al. [13] designed seven specimens with beam bottom flange friction devices (BFFD), and the experimental results indicated that the BFFD provided energy dissipation to the SC beam–column connection and avoided interference with the floor slab. George et al. [15] proposed a new self-centering steel post-tensioned connection which uses high-strength steel
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Fig. 1. PSC plane frame details. Fig. 3. Ideal M–hr behavior.
post-tensioned bars to provide self-centering behavior and steel energy dissipation elements that consist of cylindrical pins with hourglass shape to provide enhanced deformation capacity. Lin et al. [16,17] used web friction devices (WFDs) on beams for energy dissipation in the SC-MRF and conducted hybrid simulations and experiments to investigate the seismic performance of SC-MRFs under the design basis earthquake (DBE) and the maximum considered earthquake (MCE) [19]. Karavasilis et al. [14] conducted a parametric study on the seismic response of highly damped single-degree-of-freedom systems with self-centering flag-shaped or bilinear elastoplastic hysteresis. However, this type of structural system requires on-site aerial tension in high-rise buildings. A PSC connection with WFDs has been proposed for high-rise buildings, which is suitable for different types of columns, and the beams are post-tensioned to a short connecting element at each end. This assembly is subsequently erected similar to a traditional beam, which avoids the potential issues of aerial PT operations [18]. In this report, eight PSC connections were designed with different combinations of design parameters. These design parameters were initial PT forces and friction bolt forces as well as loading histories. The low-cycle loading experiments were presented to study the seismic behavior of the PSC connections for the life safety and
collapse prevention levels compared to that of the SC connection and investigate the effects of the initial PT forces and friction bolt forces.
2. PSC connection details 2.1. Detailed description The PSC plane frame with WFDs is illustrated in detail in Fig. 1. The beam of the steel frame designed with the PSC connection is divided into three parts: a long-beam portion and two shortbeam portions at both ends. These parts are connected with a vertical plate, and PT high-strength strands run parallel to the beam. Brass plates are sandwiched between the webs of the beam and the friction plates to achieve reliable friction and dissipate energy. The requirements for maximum beam rotation determine the size of the oversized circular bolt holes on the long-beam web. The transverse and longitudinal stiffeners are built up to strengthen the two short-beam portions. The entire assembly is connected to the column similar to a traditional beam.
Fig. 2. Schematic figure of PSC connection gap opening.
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A.-l. Zhang et al. / Engineering Structures 111 (2016) 185–198 Table 2 Material properties for rolled steel sections and plates.
Table 1 Test matrix. Specimens
Loading history (maximum amplitudes of story drift)
T0/Ty
T0/Tu
Friction bolt
Thick (mm)
3.5% 3.5% 3.5% 5% 5% 5% 5% 5%
0.20 0.25 0.35 0.15 0.20 0.35 0.2 0.25
0.18 0.23 0.32 0.14 0.18 0.32 0.18 0.23
6M20 6M20 6M20 6M20 6M20 6M20 6M24 6M24
Ultimate strength (N/mm2)
Elastic modulus ( 105 N/mm2)
PSCC1 PSCC2 PSCC3 PSCC4 PSCC5 PSCC6 PSCC7 PSCC8
Yield strength (N/mm2)
Percent elongation at fracture
14 16 18 20 22 30
384 392 381 384 388 350
561 555 555 550 574 505
2.15 2.06 2.22 2.09 2.09 2.07
27.0 23.3 25.3 25.7 26.8 26.5
2.2. Flexural conception and formula derivation A schematic diagram of the PSC connection opening gap is provided in Fig. 2. The ideal moment and gap-opening rotation (M–hr) behavior of the PSC connection under cyclic loading [13] is illustrated in Fig. 3, where M is the moment at the long beam
portion-vertical plate interface, and hr is the gap-opening rotation, as indicated in Fig. 2. The PSC connection behavior is similar to the conventional welded moment connection behavior before the gap opening, which is defined as event 0–1, as indicated in Fig. 3. Md is the decompression moment at event 7. M is the sum of the moments provided by the WFDs (Mf) and the PT force (Mpt) [21]. Because the gap opening increases the elongation of the PT strands,
Fig. 4. Details of PSC specimen.
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Table 3 PT strand material properties. Strand
Specimen
Yield PT force (kN)
Ultimate PT force (kN)
Elastic modulus ( 105 N/mm2)
1 19
1 2 3 Average value
540.8 540.4 542.2 541.1
592.8 593.2 586.8 590.9
2.03 2.05 2.00 2.03
(a) Preloaded in the stressing end
(a) Friction experiment of brass plates
(b) Adjust prestressed force Fig. 6. Prestressed tension of strands.
is the number of bolts; P is the pretension force in each bolt; and nf is the number of friction surfaces. Mpt can be expressed as follows:
(b) Force-Displacement hysteresis loop
Mpt ¼
Fig. 5. Friction experiment.
ð4Þ
i¼1
the bearing capacity increases gradually until unloading occurs at event 2. If loading continues, the PT strands will yield at event 3. Upon unloading, hr remains constant between event 2 and event 4. The connection moment decreases by 2Mf due to the direction of the friction force reversing in the WFD. Thereafter, hr reduces to zero from event 4 to event 5, and the gap opening closes at event 5. Then, M drops to 0 at event 6. The reversal of loading results in the behavior in M–hr being centrosymmetric. The moment M at the long beam portion-vertical plate interface can be expressed as follows:
M ¼ Mf þ M pt
n X T i hi
ð1Þ
where Mf and Mpt are the moment provided by the WFDs and the PT force, respectively. Mf can be expressed as follows:
Mf ¼ F f r
ð2Þ
F f ¼ nnf lp
ð3Þ
where r is the distance from the center of rotation to the centroid of the friction force, as indicated in Fig. 2; l is the friction coefficient; n
where Ti is the PT force of the ith strand; and hi is the distance from Ti to the center of rotation. Ti can be expressed as follows:
T i ¼ T 0 þ DT i
ð5Þ
where T0 is the initial PT force; and DTi is the increment of the PT force during the loading procedure. Due to the equality in the increment of the PT force and the beam axis force, the equilibrium equation can be expressed as follows: n X ½ksi ðdsi db Þ ¼ kb db
ð6Þ
i¼1
Pn P K si dsi K si ni¼1 hr hi K s h r hb ¼ ¼ db ¼ Pn i¼1 Ks þ Kb 2ð K s þ K b Þ i¼1 K si þ K b
ð7Þ
where dsi (i = 1, 2, 3 . . . , n) is the elongation of each strand as the rotation increases; and db is the compressive deformation of the beam. DTi can be expressed as follows:
DT i ¼ K si ðdsi db Þ ¼ K si hr hi
K s hb 2ðK s þ K b Þ
ð8Þ
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Fig. 7. Test set up.
Hence, Ti can be expressed as follows:
T i ¼ T 0i þ DT i ¼ T 0i þ K si ðdsi db Þ K s hb ¼ T 0i þ K si hr hi 2ðK s þ K b Þ
ð9Þ
Mpt is the moment provided by the tensile force based on the actual location of the PT strands. The expression for Mpt can be presented as follows:
K s hb hi 2ðK s þ K b Þ i¼1 X X X K si K s hb ¼ T 0i hi þ K si hi hi hr ¼ Md þ K 2h hr 2ðK s þ K b Þ
M pt ¼
n X X ðT i hi Þ ¼ T 0i þ K si hr hi
ð10Þ Fig. 8. Test photograph.
where Md is the decompression moment; and K2h is the rotational stiffness after the gap opening. M1 is the moment at the gap opening, which can be expressed as follows:
M5 ¼ M 4 K 2h h4 ¼ M 4 K 2h h2 ¼ M d M f
M 1 ¼ M IGO ¼ M f þ Md
where h4 is the gap-opening rotation at event 4 and is equal to h2.
ð11Þ
Furthermore, the M at event 2 can be given by
M 2 ¼ M 1 þ K 2h h2
ð12Þ
ð14Þ
3. Test specimens 3.1. Connection constitution
where h2 is the gap-opening rotation at event 2. The next turning point is event 4; M4 can be given by
M 4 ¼ M2 2Mf ¼ M f þ Md þ K 2h h2 2M f ¼ Md þ K 2h h2 M f
M5 can be expressed by
ð13Þ
Eight PSC specimens were designed and fabricated with different combinations of property parameters, including initial PT
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length of the long-beam (450 250 14 16 mm) is 3170 mm. The thicknesses of the transverse stiffener plate of the shortbeam and the longitudinal beam are 30 mm and 20 mm, respectively. The 16 mm thick cover plates are added to the long-beam flanges to ensure that the long-beam remains elastic. The size of the vertical plate is 500 250 30 mm, and the friction plate is welded on to the face of the column flange, whose size is 300 175 14 mm. Two brass plates of 3 mm thickness are sandwiched between the beam webs and the friction plates. The PT strands are thread and run parallel to the long beam, with a nominal diameter of 21.6 mm. The initial PT forces of the strands are different between specimens. The detailed dimensions are provided in Fig. 4. Six M20 friction bolts (10.9 property grade, nominal bolt diameter of 20 mm) are installed in Specimens 1–6, and six M24 friction bolts are installed in Specimens 7–8.
(a) Cyclic loading history 1
3.2. Material properties The steel for all specimens is Q345B, which has a nominal yielding strength of 345 MPa and an elastic modulus of elasticity of 1.98 105 MPa. The yielding stress fy, ultimate stress fu, elastic modulus, and percent elongation at fracture for different thickness steel plates used to construct the specimens are provided in Table 2. The material properties are based on tests of tension coupons, where the coupons are taken in the direction parallel to the rolling direction. Each PT strand is a high-strength stress relieved steel strand. The nominal diameter of the PT strand is 21.6 mm, which corresponds to a cross-sectional area of 312.9 mm2. The material properties for the PT strands are listed in Table 3. The coefficient of friction between the brass and steel is 0.34 based on experimental results. Fig. 5(a) depicts the friction experiment for the brass plates, and Fig. 5(b) illustrates the complete fifty cycles of force versus displacement relationships.
(b) Cyclic loading history 2 Fig. 9. Cyclic loading history.
strand forces, friction bolt forces, and loading histories, which are listed in Table 1. The section properties of the PSC specimens can be given as follows: all column sections are identical (H350 350 12 19 mm), based on strong-column weakbeam principles. The thickness of the column continuity plates is 30 mm, and two thick doubler plates with 16 mm thickness are installed in the beam–column panel zone joint. The length of the short-beam (H482 250 18 30 mm) is 450 mm, and the
3.3. Prestressed tension of strands The low retracting tension and anchor methods were used in the pre-stressing procedure for the strands. The beam with the PSC connection consists of long and short beam portions. The first step is completing the assembly of the long and short beams. The long beam is placed into the friction plates of the short beams and bolted. Then, the strands, the pressure sensor and the anchor-
Fig. 10. Arrangement of displacement meter.
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(a) Vertical view
(b) Front view
(c) Lateral view
(d) 1-1
Fig. 11. Arrangement of strain gauges and strands number.
age are installed in the anchor end. The strands are thread from the reserved holes of the short beam to those of the long beam. After the installation of the anchorage in the anchor end, a tensioning device is used to preload the strands (Fig. 6(a)). Then, the pre-stressed forces are adjusted while the acquisition instrument is monitored (Fig. 6(b)). The last step is to weld the beam and column together. The complete joint penetration weld would not give rise to the evident changes of the PT forces according to the monitored data. 3.4. Test Setup and cyclic loading history Each specimen was tested in the setup (Figs. 7 and 8) through a series of central displacement cycles by displacing actuators at both ends of the beams, which is consistent with the AISC [20]
loading protocol (shown in Fig. 9). There are two loading histories. The first maximum amplitude of the story drift is 3.5% radians corresponding to the life safety level, and the second maximum amplitude of the story drift is 5% radians corresponding to the collapse prevention level [19,22]. Additionally, their seismic performance objectives are different; the primary structure always remains elastic before the story drift of 3.5% radians. The strands remain elastic, the column and beam strain is within 2 ey without buckling, and there is no yielding in the beam web under shear force before the story drift of 5% radians. For Specimens PSCC1– 3, the cyclic loading history 1 consisted of 8 stages, and the first three stages contained 6 cycles. The fourth stage is only 4 cycles. Thereafter, the remaining four stages all have two cycles (shown in Fig. 9(a)). For Specimens PSCC4–8, the cyclic loading history 2
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(a) θ=2%, gap opening 5.12 mm (1.18%)
(a) θ=3%, gap opening 8.73 mm (2.01%)
(b) θ=3.5%, gap opening 10.28 mm (2.37%)
(b) θ=5%, gap opening 14.83 mm (3.42%)
Fig. 12. Experimental photograph of specimen PSCC1.
Fig. 13. Experimental photograph of specimen PSCC5.
is similar to Specimens PSCC1–3 and consists of 9 stages (shown in Fig. 9(b)). The two displacing actuators on the self-balancing equipment at both beam ends of the connection impose displacement cycles with increasing amplitude, as above, in the antisymmetric direction, and an axial compression force (axial compression ratio is 0.2) is imposed on the top of the column by a hydraulic jack.
served as the baseline specimens for the experimental study and are shown in Figs. 12 and 13, respectively, will be discussed first, and other specimens will be compared with them. The detailed data for all the specimens are presented in Table 4. For Specimen PSCC1, as the story drift (h) increased from 0.375% to 0.75% radians, the connection had an initial stiffness that was similar to the initial stiffness of a conventionally welded moment connection. When h reached 0.81% radians, a gap opening occurred at the long beam portion-vertical plate interface. The maximum opening width of the connection continued to increase during subsequent loading. When h was approximately 3.5% radians, the maximum opening width reached 10.28 mm. After the load-off, the opening closed due to the PT forces, and an extremely small residual opening width of 0.8 mm was found at the end of the long beam. The initial PT forces of PSCC2 and PSCC3 were greater compared to that of
3.5. Instrumentation The instrumentation is illustrated in Fig. 10. The column capital is subjected to an axial force by a 600T actuator, and an additional two 100T actuators on the beam ends apply cyclic loadings. Each strand has a force transducer to monitor the PT force. The displacement data for the beam ends is collected by two displacement meters arranged on the top flanges. Linear displacement potentiometers fixed on the junctions of the vertical plates and the long beams are used to measure the gap width of the beams. The column flanges, column stiffeners, top and bottom beam flanges, and vertical and horizontal directions of the beam webs are pasted with strain gauges that measure the strain changes during loading in each position, as indicated in Fig. 11. 4. Experimental results 4.1. General test observations The responses of Specimen PSCC1 (experiencing cyclic loading history 1) and PSCC5 (experiencing cyclic loading history 2), which
Table 4 Experimental results of connections. Specimens
Initial gap opening story drift ratio (rad)
Opening width (mm)
Maximum opening width (mm)
Maximum residual opening width (mm)
PSCC1 PSCC2 PSCC3 PSCC4 PSCC5 PSCC6 PSCC7 PSCC8
0.81% 0.86% 0.94% 0.50% 0.60% 0.81% 0.40% 0.74%
1.49 1.44 0.76 1.82 1.65 1.32 1.67 0.96
10.28 9.19 7.73 16.41 14.83 10.48 14.67 12.27
0.8 0.15 0.065 1.12 1.03 1.24 0.90 0.86
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Fig. 14. Vertical load–displacement response for specimen PSCC1. Fig. 16. Comparison of vertical load–displacement response for PSCC1–3.
slightly higher compared to that of PSCC7, and thus their deformation procedures were essentially similar. All the specimens had small residual opening widths after unloading, which indicates that all connections had excellent re-centering capacity. 4.2. Connection flexural behavior The connection behavior is characterized by a gap opening and closing in the interface between the vertical plate on the short beam and the long beam as a result of the re-centering force in the PT strands. The vertical force F versus the displacement response D and the moment M versus the gap-opening rotation hr for Specimen PSCC1 are provided in Figs. 14 and 15, respectively. D is the measured horizontal displacement at the end of the beam, where the actuator is connected to the specimen. M is the moment developed at the long beam-vertical plate interface under the applied vertical force F. The experimental results are summarized in Table 5, where hIGO is the imminent gap-opening rotation, hr0.05 is the maximum gap-opening rotation, and hres is the maximum residual rotation. MIGO is the imminent gap-opening moment, K1 is the initial stiffness, and bE is the effective energy dissipation ratio, which can be determined as follows:
Fig. 15. Moment–rotation response for specimen PSCC1.
PSCC1, thus their gap opening occurred slightly later. The maximum opening widths were 9.19 mm and 7.73 mm, respectively, which was less than the value of PSCC1. For Specimen PSCC5, when h increased to 0.60% radians, a gap opening occurred at the long beam portion-vertical plate interface. The maximum opening width of 14.83 mm occurred when h reached 5% radians. The opening closed automatically under the effect of the PT strands after unloading and left a small residual opening width of 1.03 mm. The test results indicate that the initial PT force has an effect on the time of a gap opening. A smaller initial PT force can lead to an earlier gap opening and a larger maximum opening width. Specimens PSCC7 and PSCC8 had the same property grade of friction bolts. The initial PT force of PSCC8 was
bE ¼ M f =M IGO
ð15Þ
To enable a satisfactory response for the SC-MRF under seismic loading, [23] recommend that bE P 0.25. It is observed that the hysteresis loops of the PSC connection have a double-flag shape similar to common SC connections. The vertical F D response indicates that Specimen PSCC1 had an initial stiffness of 9025.1 kN/m prior to the gap opening, and the connection stiffness decreased to 2297.5 kN/m when the gap opening occurred. The imminent gap-opening moment (MIGO) was
Table 5 Experimental results. Specimens
K1 (kN/m)
hIGO (rad) (%)
MIGO (kN m)
hr0.05 (rad) (%)
M0.05 (kN m)
F (kN)
hres (rad) (%)
bE
PSCC1 PSCC2 PSCC3 PSCC4 PSCC5 PSCC6 PSCC7 PSCC8
9025.1 9486.2 10842.9 7984.3 8530.1 9180.4 9837.3 10445.3
0.34 0.33 0.18 0.42 0.38 0.31 0.38 0.22
378.65 384.04 430.92 297.69 335.04 476.82 410.64 423.83
2.37 2.12 1.78 3.78 3.42 2.41 3.38 2.83
602.27 609.16 687.28 714.16 677.13 769.40 722.78 757.28
366.12 370.31 417.8 434.14 411.63 467.72 439.38 460.35
0.18 0.04 0.01 0.257 0.236 0.286 0.207 0.197
0.409 0.356 0.280 0.467 0.439 0.311 0.471 0.421
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(a) SL12 strand Fig. 17. Comparison of moment–rotation response for PSCC1–3.
(b) SL11 strand Fig. 20. PT force-story drift response of specimens PSCC4–6.
Fig. 18. Comparison of moment–rotation response for PSCC4–6.
378.65 kN m. When h was approximately 3.5% radians, the maximum applied force was 366.12 kN along with a 2.37% radians maximum rotation (gap opening) and a 602.27 kN m maximum moment. An extremely small residual rotation of 0.18% radians was left at the end of the long beam after the load-off. The F – D and M–hr hysteresis loops of Specimens PSCC1, PSCC2 and PSCC3 are provided in Figs. 16 and 17. Due to the initial PT force of PSCC2 being slightly less than that of PSCC1, the hysteresis loop of PSCC2 is close to that of PSCC1. Comparing the experimental results of PSCC3 and PSCC1, PSCC3, which had a higher initial PT
Fig. 19. Comparison of moment–rotation response for PSCC5 and PSCC7.
force, had the larger applied force and initial stiffness. As indicated in Fig. 17, PSCC3 had a delayed gap-opening time as well as a greater MIGO compared with that of PSCC1. The increment of the initial PT force results in an increase of the maximum moment from PSCC1 to PSCC3 and a decrease in the maximum gapopening rotation. The M–hr hysteresis loops for the different initial PT forces of PSCC4-6 are provided in Fig. 18. The initial PT force increased from 0.14Tu, to 0.18Tu to 0.32Tu,, and the corresponding initial stiffness increased from 7.50 104 kN m/rad to 1.72 105 kN m/rad to 2.24 105 kN m/rad. Additionally, the results for different specimens are shown in Table 5. The results indicate that MIGO increased because of the increment of the initial PT forces, from 297.69 kN m to 335.04 kN m to 476.82 kN m. The gap opening occurred at a story drift of 0.50%, 0.60% and 0.81% radians; however, the maximum gap-opening rotation decreased progressively from 3.78% to 3.42% to 2.41% radians, which provided further evidence that a higher PT force accompanied the delayed gap-opening times and smaller maximum gap-opening rotations. The largest values of the connection stiffness after the gap opening and maximum moment were from PSSC6: 1.278 104 kN m/rad and 769.40 kN m, respectively. Fig. 19 presents the M–hr hysteresis loops for the different friction bolt forces of Specimens PSCC5 and PSCC7. When the friction bolt force increased from M20 to M24 (the pretension force of one friction bolt ranged from 155 kN to 225 kN), the hysteresis loop for the specimen with the higher friction bolt force was fuller compared to the other loop. MIGO increased from 335.04 kN m to 410.64 kN m, and the maximum gap-opening rotation reduced from 3.42% to 3.38% radians. The maximum moment increased from 677.13 kN m to 722.78 kN m.
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T0/Tu
Tmax/Ty
T max /Ty
T r /Ty
Tmax/Tu
T max /Tu
T r /Tu
ðT 0 T r Þ/T0 (%)
PSCC1 PSCC2 PSCC3 PSCC4 PSCC5 PSCC6 PSCC7 PSCC8
0.18 0.23 0.32 0.14 0.18 0.32 0.18 0.23
0.625 0.633 0.632 0.744 0.745 0.745 0.727 0.745
0.528 0.543 0.563 0.608 0.630 0.651 0.605 0.624
0.194 0.241 0.334 0.156 0.181 0.327 0.178 0.236
0.572 0.580 0.578 0.681 0.682 0.682 0.666 0.682
0.483 0.497 0.516 0.557 0.576 0.596 0.554 0.571
0.177 0.221 0.306 0.143 0.166 0.300 0.163 0.216
1.55 3.94 4.43 2.26 7.73 6.36 9.53 6.19
ratio decreased from 0.467 to 0.311, approximately 33.4%, which indicates that an increase in the PT force resulted in a decrease in the energy dissipation. When other conditions were identical, and the friction bolt force changed from 6M20 to 6M24 (for example PSCC5 and PSCC7), the energy dissipation ratio increased from 0.439 to 0.471. Therefore, a larger bolt force could lead to higher energy dissipation but this improvement was notably limited. 4.4. PT force
Fig. 21. Strain of different positions for PSCC1.
4.3. Energy dissipation The effective energy dissipation ratios of the specimens all satisfied the requirement that the energy dissipation ratio should be greater than 0.25 (Table 5), which indicates that the PSC connection has a good energy dissipation capacity. When the PT force increased from 0.14Tu to 0.32Tu, and other conditions remained the same (for example PSCC4 and PSCC6), the energy dissipation
The measured PT force-story drift responses for Specimens PSCC4–6 are provided in Fig. 20. The PT strands were stretched after the gap opening, and the corresponding PT forces increased gradually. The experimental PT forces for all specimens are provided in Table 6, where T0 is the initial PT force, Ty is the measured average yield PT force (here its value is 541 kN), Tu is the measured average ultimate PT force (its value is 591 kN), Tmax is the maximum PT force of all the strands at 0.05 radians drift, T max is the average maximum PT force at 0.05 radians of the drift, and Tr is the average residual force. The maximum PT force at 0.05 radians of drift for the PSC connection was 403.07 kN, which equals 74.5% of the yield force Ty and 68.2% of the ultimate capacity Tu. In fact, the length of the PT strand in the self-centering frame was longer compared to that in the beam–column connection, thus the PT force would be reduced in the self-centering frame. The increment of the initial PT force resulted in a slight increase in the maximum PT force of each strand; however, the outside strands of the three specimens had PT forces that nearly reached the maximum. Moreover, the friction bolt force is also a factor that affects the PT force. The increment of the friction bolt force reduced the maximum PT force from 0.682Tu to 0.666Tu. The average loss of the PT forces was within 10%, which indicated that the PT strands, the anchorage performance and the pre-stressing method in the experiments were reliable. 4.5. Strain condition of the element plates
Fig. 22. Comparison of strain for PSCC5.
Fig. 21 provides the yield strain and strain values of the element plates at different positions for Specimen PSCC1. From Fig. 21, we can obtain that all the plates of the column and beam remained elastic and undamaged, which indicates that the connection can remain elastic corresponding to the life safety level. The strain values from the element plates at different positions for PSCC5 are provided in Fig. 22. For Specimen PSCC5, before the story drift reached 3.5% radians, the column and beam essentially remained elastic. During the entire loading procedure, the reinforcing plates of the specimen reached the plastic stage early, at a story drift of approximately 1.75% radians, and the column web reached plasticity when the story drift ratio was equal to 3.5% radians. Then, minor yielding occurred in the column panel zones. The existence of the reinforcing plates resulted in the elastic beam flanges. Furthermore, the strain values indicated that there was no yielding
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(a) PSCC4
(b) PSCC5
(c) PSCC6
(d) PSCC7
(e) PSCC8 Fig. 23. Comparison of experimental and theoretical moment–rotation relationship for PSCC4–8.
in the beam web under the shear force, thus meeting the drift objectives of the collapse prevention level. 4.6. Comparison of the experimental and analytical moment–rotation relationship Apart from a discussion of the experimental results, the relevant theoretical analysis of a moment–rotation (M–hr) relationship for the PSC connection according to the analytical formulas (10)–(14) described earlier is also conducted in the following discussion using Specimens PSCC4–8 as examples. The experimental and analytical M-hr relationships are presented in Fig. 23, and the comparative responses of Specimens PSCC4–8 are summarized in Table 7. This table provides a comparison of the moment MfIGO at
the gap opening provided by the WFDs, the moment Md at the gap opening provided by the PT strands, the imminent gap opening moment MIGO, the moment Mf0.05 at hr0.05(h = 5%) provided by the WFDs, the maximum moment Mpt0.05 at hr0.05 provided by the PT strands, and the maximum moment Mp0.05 at hr0.05, where MIGO is equal to the sum of MfIGO and Md and Mp0.05 is equal to the sum of Mf0.05 and Mpt0.05. Mu is the normal plastic moment capacity of the beam. Additionally, the connection rotation stiffness after the gap opening is provided in Table 7. When MIGO was achieved, the contact between the vertical plate and the long beam flange plate reached a critical state in which there was neither a gap opening nor any contact. The monitoring value of the gap opening was minimal, and the analytical gap-opening rotation was zero. For example, for Specimen PSCC5, the experimental rotation at the gap
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Classification
hrIGO (103 rad)
MfIGO/Mu
Md/Mu
hr0.05 (102 rad)
Mf0.05/Mu
Mpt0.05/Mu
Mp0.05/Mu
K2h (kN m/rad)
PSCC4
Experiment Theory Deviation ratio (%)
4.2 0 –
0.18 0.20 12.7
0.21 0.18 13.6
0.37 0.39 5.0
3.8 3.7 2.7
0.18 0.20 12.0
0.70 0.81 13.7
0.88 1.02 13.3
13686.9 13801.2 0.8
PSCC5
Experiment Theory Deviation ratio (%)
3.8 0 –
0.16 0.20 20.9
0.23 0.24 0.4
0.41 0.44 6.0
3.4 3.3 3.0
0.18 0.20 14.1
0.66 0.78 15.9
0.84 0.99 15.5
12907.8 13484.8 4.3
PSCC6
Experiment Theory Deviation ratio (%)
3.1 0 –
0.17 0.20 17.0
0.42 0.42 0.2
0.59 0.62 5.4
2.4 2.4 0.0
0.18 0.20 10.7
0.77 0.82 6.7
0.95 1.03 7.5
12780.0 13657.2 6.4
PSCC7
Experiment Theory Deviation ratio (%)
3.8 0 –
0.23 0.30 21.8
0.31 0.24 30.2
0.51 0.53 5.2
3.4 3.1 9.7
0.24 0.30 18.3
0.65 0.75 13.9
0.89 1.05 15.2
12405.6 13510.6 8.2
PSCC8
Experiment Theory Deviation ratio (%)
2.2 0 –
0.24 0.30 19.6
0.32 0.30 6.9
0.52 0.59 11.7
2.8 2.8 0.0
0.26 0.30 14.1
0.68 0.77 12.1
0.93 1.07 12.6
11845.7 13816.4 14.3
MIGO/Mu
opening was 0.38% radians but the analytical gap-opening rotation was zero; the experimental value of Md = 0.23Mu is close to the analytical value of 0.24Mu. The experimental value of MfIGO = 0.16Mu was less than the analytical value of 0.20Mu due to the loss of the bolt friction force during the test; the experimental value of MIGO = 0.41Mu was less than the analytical value of 0.44Mu by approximately 6%. The average difference between the experimental value and the analytical value of MIGO was approximately 6.7%. At hr0.05, Mf0.05 = 0.18Mu was less than the analytical value of 0.20Mu by 14.1%; the experimental value of Mpt0.05 = 0.66Mu was less than the analytical value of 0.78Mu by 15.9% due to the loss of strand anchorage. The experimental value of Mp0.05 = 0.84Mu is less than the analytical value of 0.99Mu by 15.5%; the average difference between the experimental and analytical values of Mp is approximately 12.8%. The experimental rotation stiffness after the gap opening of K2h = 12907.8 kN m/rad was less than the analytical value of 13484.8 kN m/rad by 4.3%; the average difference between the experimental and analytical values of K2h was 6.8%. The hysteresis loops of M–hr for the specimens summarized in Fig. 23 indicated that there was a slight difference between the experimental results and the theoretical analysis. To summarize, the theoretical results were observed to match the experimental data reasonably well.
5. Conclusions A prefabricated self-centering beam–column connection with a bolted web friction device is proposed for high-rise buildings, and eight PSC connections are designed with various combinations of design parameters. The low-cycle loading experiments and theoretical analysis are presented. The results indicate that the hysteresis loops of the PSC connection present an obvious double-flag model, which indicates that the connection has the same satisfactory self-centering capacity compared to that of the SC connection. At the same time, it does not need on-site aerial tension in high-rise buildings. Furthermore, the frame beam is connected to the column as a traditional beam and is easily accepted by structural designers. The maximum PT force of the PSC connection would not exceed the yield force. In fact, the length of the PT strand in the PSC frame would be longer than that in the beam–column connection, thus the PT force would be reduced in the PSC frame. The average loss of the PT force was within 10%. The energy dissipation capacity satisfied the requirement that the effective energy dissipation ratio should be greater than 0.25. The frame beam and column essentially remained elastic and undamaged prior to a story drift of
3.5% radians corresponding to the life safety level. After that point, minor yielding occurred in the column panel zones, and no yielding occurred in the beam web under the shear force before the story drift of 5% radians, thus meeting the drift objectives of the collapse prevention level. The residual rotations of all of the specimens were minimal, which indicated that the PSC connection had an excellent re-centering capacity, and the PT strands, the anchorage performance and the pre-stressing method in the experiments were reliable. With the increment in the initial PT force, the initial stiffness, the imminent gap opening moment, and the maximum PT force improved to different extents; the maximum gap opening rotation and the energy-dissipation capacity indicated a decreasing tendency with increasing initial PT force. Therefore, it is suggested that for the purposes of practical engineering, the degree of the initial PT force should be selected based on the performance design objectives of the structural elements. The increment in the friction bolt forces can result in an increase in the imminent moment, a decrease in the gap-opening rotation, a decrease in the PT force, and a slight increase in the energy dissipation capacity. The theoretical results of the PSC connection match the experimental data reasonably well. The results of the experiment have verified that the theoretical model can be applied to the analysis and design of prefabricated self-centering steel frames. Acknowledgments The research reported herein is supported by the National Natural Science Foundation of China under Grant No. 51278010 and the National Natural Science Foundation of China under Grant No. 51278027. Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.engstruct.2015. 12.025. References [1] Gross LJ. A connection model for the seismic analysis of welded steel moment frames. Eng Struct 1998;20(4–6):390–7. [2] Egor Paul Popov, Yang Tzong-Shuoh, Chang Shih-Po. Design of steel MRF connections before and after 1994 Northridge earthquake. Eng Struct 1998;22 (12):1030–8. [3] Shen J, Kitjasateanphun T, Srivanich W. Seismic performance of steel moment frames with reduced beam sections. Eng Struct 2000;22(8):968–83.
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