Research Article  Open Access
Design and Analytical Evaluation of a New SelfCentering Connection with Bolted TStub Devices
Abstract
A new posttensioned Tstub connection (PTTC) for earthquake resistant steel moment resisting frames (MRFs) is introduced. The proposed connection consists of high strength posttensioned (PT) strands and bolted Tstubs. The posttensioning strands run through the column and are anchored against the flange of the exterior column. The Tstubs, providing energy dissipation, are bolted to the flange of beam and column and no field welding is required. The strands compress the Tstub against the column flange to develop the resisting moment to service loads and to provide a restoring force that returns the structure to its initial position following an earthquake. An analytical model based on fiber elements is developed in OpenSees to model PTTCs. The analytical model can predict the expected behavior of the new proposed connection under cyclic loading. PTTC provides similar characteristic behavior of the posttensioned connections. Both theoretical behavior and design methods are proposed, and the design methods are verified based on parametric studies and comparison to analytical results. The parametric studies prove the desired selfcentering behavior of PTTC and show that this connection can reduce or eliminate the plastic rotation by its selfcentering behavior as well as providing required strength and stiffness under large earthquake rotations.
1. Introduction
Posttensioned energy dissipation (PTED) beamtocolumn connections are newly proposed to be utilized as an alternative to welded connections in rigid moment frames (MRFs). They can provide required ductility and stable cyclic behavior under severe earthquakes. PTEDs main characteristics are the selfcentering behavior and explicit energy dissipation capability. Selfcentering addresses a rebounding capability that minimizes the residual deformations in the connection that finally results in minimal residual drift in the structure. Most of inelastic deformations and energy dissipation happens in energy dissipater (ED) devices, and the main structural elements such as beams and columns are supposed to remain elastic. EDs could be replaced in some cases after a major earthquake to make the structure ready for the next earthquake events.
Ricles et al. [1, 2] developed a selfcentering beamtocolumn connection system in which the PT system is based on a series of high resistance steel strands running parallel to the beams whereas the ED system is composed of bolted steel topandseat angles. The dissipative mechanism is based on the formation of plastic hinges in each angle. The experimental results showed that reinforcing plates are necessary to control the inelastic deformation of the beams. Size and geometry of the angles influence the connection moment capacity and the energy dissipation capacity. The strands must be designed to remain elastic to provide the selfcentering and load carrying capability of the system.
Garlock et al. [3, 4] experimentally investigated six steel beamcolumn joint subassemblies with PT connections similar to Ricles’s PT connection. A design procedure is also proposed for SMRFs with PT connections.
Christopoulos et al. [5] have experimentally studied a selfcentering moment connection in which the PT system is composed of a couple of high resistant steel bars and other steel bars confined in steel cylinders as the ED system.
Chou et al. [6, 7] have proposed a PTED beamtocolumn connections that consists of high resistant steel strands (PT system) and reduced flange steel plates welded to the column and bolted to the beam flanges, as ED system.
Kim and Christopoulos [8] proposed details for the gap openings accommodation along the boundaries of the slabs.
More recently, Chou et al. [9] experimentally showed that negative connection moments provided by slab reinforcements provide low residual deformations in selfcentering connections. Moreover, a detail for eliminating the slab restraining effects was proposed [10].
Chou and Chen [11] evaluated the beam compression forces and column bending stiffness by modeling column deformation which resulted from gapopenings at all stories.
Inertia force transfer mechanism in selfcentering moment frames has been studied via shake table and cyclic tests [12, 13]. A threedimensional analytical model including rotational spring has been proposed to study the effects of column bases behavior on the seismic behavior of the selfcentering frames [14]. More recently, largescale steel SC frame tests showed reasonable flagshaped hysteresis responses [15].
Wang and Filiatrault [16] performed shake table test on two onethird scale 3story, 2bay steel frames (SMRF and selfcentering posttensioned frame). By comparing displacement response, acceleration response, and the energy dissipation of the tested frames, improved detailing was suggested [16].
Several PTED connections based on different arrangement of the friction devices have been proposed and studied [17–19]. Rojas et al. [18] proposed a PTED connection made up of high resistance steel strands and friction devices at the top and bottom flange of the beam. An analytical model based on the fiber elements proved the connection performance in terms of strength, storey drift, local deformation and selfcentering capability [18].
Wolski et al. [19] introduced a PTED connection including a frictional ED system only below the beam bottom flange (BFFD). The detail was proposed to avoid interferences between the floor slab and the friction devices.
Tsai et al. [20] have proposed bolted web friction devices (WFDs) in PTED connections. The behavior of the isolated bolted web friction device as well as the fullscale tests on the connections including the proposed details was performed.
Lin et al. [21] developed largescale tests of a 0.6scale, fourstory, and twobay moment frames including web friction devices. The results showed the frame selfcentered with no damage under DBE earthquake.
Finally, Dimopoulos et al. [22] have proposed a new posttensioned connection with web hourglass shape pins (WHPs). The experimental results reveal that the connection has the selfcentering behavior without residual drift [22].
Several types of beamtocolumn connections have been proposed to reliably implement the PTED concept in steel moment resisting frames, so far. The main differences among the proposed systems are related to the technological solutions proposed for the PT and ED systems. PT systems are based on the use of high strength steel strands or bars, whereas the ED systems are to provide yielding or friction mechanisms [1–22].
In this paper, a new posttensioned bolted Tstub connection (PTTC) for earthquake resistant steel moment resisting frames (MRFs) is proposed. The proposed connection consists of high strength posttensioned strand, as PT device, and bolted Tstubs as the ED device. The PT strands provide restoring force for selfcentering behavior, while the Tstubs dissipate energy by plastic mechanisms in the Tstub flanges. The new connection requires no field welding, and the beam reinforcing plates which are common in PTED connections could be eliminated.
In the proposed PTED connection, friction devices [18–21], steel bars [5], and reduced flange steel plates [6, 7] are replaced by Tstubs as an energy dissipater device. The Tstub is much more common device in the steel construction practice compared to the other devices proposed for PTEDs. Moreover, the proposed connection can be used in retrofitting and enhancement of existing nonseismic Tstub connections. According to the common shape of the connection in the construction practice, it can be assumed that the proposed connection has an easier and more economic fabrication process. It should be noted that the proposed connection is assumed to be more similar to PTED connections with top and bottom angles rather than the other types explained herein.
According to inherent characteristic of PTED connections, it is expected that the proposed connection minimizes inelastic deformation in comparison with the TStub moment connections without posttensioning. Both theoretical and numerical analyses are conducted to evaluate the cyclic behavior of the connection. A set of design equations are also set forth for designing PTTC connections. The selfcentering behavior of PTTC is studied using the OpenSees finite element program based on fiber elements. To verify the OpenSees models, the results are compared against the existing experimental results of a similar connection. Consequently, a detailed parametric study is performed on the designed beamto column connections using the verified models to verify the design equations and study the selfcentering behavior of the connection with different parameters such as, initial posttensioning and number of strands.
2. Posttensioned Bolted TStub Connection (PTTC)
2.1. Connection Details
PTTC is composed up of Tstubs bolted to the beam flanges and column flange, along with posttensioned high strength strands running parallel to the beam and anchored outside of the connection as shown in Figure 1. When strands are posttensioned with initial posttensioning force, the beam flanges and the Tstubs are compressed against the column flanges. As shown in Figures 2(a) and 2(b), beam flange reinforcing plates may not be used because the Tstems provide enough stiffness to avoid premature flange buckling. Bolted Tstubs dissipate energy with developing plastic hinges in the Tstub flange. In this section, the behavior of the energy dissipation devices (Tstubs) and PT connection is evaluated theoretically.
(a) Exterior connection
(b) Interior connection
2.2. ForceDeformation Relation of TStubs
In order to determine the contribution of the Tstubs in the connection behavior, it is necessary to determine the forcedeformation relationship of the Tstub under applied loads. The forcedeformation behavior is assumed to be bilinear in tension (path oabcd in Figure 3(b)), and no forcedisplacement relationship is assumed in compression following the Tstub contact. Kinematic hardening role is assumed to determine the cyclic behavior of the Tstubs, and the forcedeformation relation of the Tstubs is determined according to EC3 [23]. When the applied moment overcomes the decompression moment (as defined in Section 2.3) of the connection, a gap opening occurs and the Tstub is in tension. As the moment increases, the tensile Tstub yields in tension at point (a) as shown in Figure 3(b). After yielding, point (a), the stiffness of the Tstub, decreases significantly to hardening stiffness. Unloading stiffness of the Tstubs is assumed to be equal to the elastic stiffness.
(a) Two bolted Tstubs
(b) Forcedeformation relation of Tstubs
To determine the Tstub stiffness and strength parameters, two Tstubs connected by bolts are considered as shown in Figure 3(a). The initial elastic stiffness of Tstub is obtained from the initial elastic stiffness of the two Tstubs connected by bolts () and is calculated as follows [23]: where , are initial stiffness of each Tstubs and is initial stiffness of bolts. Where a Tstub is connected to a rigid base (like most of the cases in Tstub to column flange connection), one of the Tstubs can be assumed to be rigid and the initial stiffness of the rigid Tstub is considered to be infinity (. Consider (bolt length) is defined based on EC3 [23]: where is the bolt area and , , and are the thicknesses of the bolt head, nut, and washer, respectively. and are the flange thickness of each Tstub. is the effective length. is the distance between the flangetoweb plastic hinge and the bolt axis on the flange, and is the distance between the location of the bolt axis and the tip of the flange ().
Based on EC3 Tstubs have three failure modes such as Mode 1: flange yielding, Mode 2: bolt failure with flange yielding, and Mode 3: bolt failure [23]. Accordingly, the capacity of each mode can be calculated as the following [23].
Mode 1, flange yielding:
Mode 2, bolt failure with flange yielding:
Mode 3, bolt failure: where is the plastic moment resistance of the flange in bending, is the resistance of the bolts in tension, b is the width of the Tstub, is the flange thickness of the Tstub, and is yielding stress of the Tstub flange. The yield strength of the Tstubs, , in the forcedeformation curve (point (a) in Figure 3(b)) can be estimated from (4), (7), and (8). To achieve a ductile behavior, Tstubs should be designed in Mode 1: flange yielding and higher strength should be provided for the other failure modes including bolt failure.
The inelastic stiffness of the Tstubs is obtained from where is is the strain hardening modulus and is the modulus of elasticity [24].
Finally, the ultimate force of the Tstubs () in the forcedeformation curve can be estimated from (4), (7), and (8), by replacing the plastic condition with the ultimate condition. For this purpose the in (5) can be calculated based on the ultimate strength and the bolt strength should be replaced by the ultimate capacity [24].
The ultimate deformation of the Tstubs () can be estimated from the following equation obtained from forcedeformation curve of the Tstub (Figure 3(b)):
2.3. Theoretical Analysis of the Cyclic Behavior of the PTTC
The idealized expected momentrotation behaviour of a welldesigned PT steel connection is shown in Figure 4, where is relative rotation between the beam and column (Figure 5). The behaviour of a PT connection is characterized by a gap opening, , and closing at the beamcolumn interface under cyclic loading (Figure 5).
The moment to initiate this separation is called the decompression moment (). Using Figure 5, the decompression moment, , is estimated by moment equilibrium about the point of compressive force at the compressive Tstub (point C): is the distance between the beam centerline and the center of contact force (bottom Tstub in Figure 5) and is the total initial strand force. Notably, at the point of decomposition, relative beamcolumn rotation is zero and the tensile Tstub (top Tstub in Figure 5) is about losing the contact with the column face and no force is developed in that.
As shown in Figure 2(a), there is a gap between the beam web and the column face. The gap ensures the contact of the Tstubs against the column face. As shown in Figure 5, when the bottom flange is in compression, the bottom Tstub carries the compression force. Accordingly, the Tstub center of contact is reasonably assumed at the stem of the Tstub, and therefore is defined as above.
The connection moment after decompression is equal to where , the connection stiffness between point and , is the resultant of two main components: the contribution of the tension Tstub elastic stiffness, , and the contribution of the strand axial stiffness, . Point in Figure 4 and point (a) in Figure 3 are corresponding to the , where Tstub is yielding at point 2. Therefore, where is the strand stiffness and (i.e., ) is the beam stiffness. is the length of one bay, and is the distance between center of contact force and the center of the tensile Tstub. can be obtained from (1).
Event 3 marks the beginning of the unloading portion of the cycle. Assuming is given, the moment at load reversal is , the stiffness between point and in Figure 4, is resulted from two components: the contribution of the tensile Tstub in hardening range () and the contribution of the strand axial stiffness (. Consider can be determined using (9).
Reverse yielding of the tension Tstubs occurs at an unloading moment equal to 2, where the stiffness again is changed to · Therefore,
The curve becomes vertical at event 6 where both flanges on the beam are in contact with the column and the relative angle between beam and column is zero,
3. Connection Design
In this section, a stepbystep design procedure is given for design of PTTC connection.
3.1. Design Criteria
To design the proposed PTTC connection, several limit states should be satisfied, including criteria on decompression moment (), connection strength, Tstub fracture, strands yielding, and column plastic hinge. The proposed design criteria are a set of limitstate design criteria that enable the designer to design a connection based on specific column size and the beam size. These design criteria are more based on Garlock and Ricles research work; however, a simplified approach is considered to reduce the need for performing nonlinear analyses [1, 4].
3.1.1. Decompression Moment () Criterion
To reduce connection permanent plastic deformation and to provide the selfcentering behavior, the decompression moment should be theoretically more than . However, it is experimentally showed that the decompression moment should be considered as the following for more confidence about the connection behavior [4]: where is the connection moment at the onset of Tstubs yielding. Connection moment initiating Tstub yielding, (), is
3.1.2. Connection Strength Criterion
The connection moment strength at the onset of Tstub yielding is recommended to be as follows [4]: where is nominal plastic moment capacity of the beam section and is a design parameter. Garlock suggested taken between 0.75 and 1.2 for PT connection with reasonable strength and deformation capacity [4].
3.1.3. TStub Fracture Criterion
To avoid Tstub fracture, this criterion is recommended: where is relative rotation causing the Tstub fracture, is equal to at the Tstub fracture point (10), and is relative rotation demand under the design base earthquake (DBE) demands. is estimated in accordance to the amplified codebased demands [4].
3.1.4. Strand Yielding Criteria
The strands should not yield under the maximum credible earthquake (MCE) [4]: where is relative rotation causing the strands to yield, is yield force in one strand, is initial posttensioning force in one strand, and : is relative rotation demand under the MCE. This criterion ensures that the frame carries gravity load, even if the Tstubs fractured.
3.1.5. Column Plastic Hinge Criterion
It is common to design the columns stronger than the beams to avoid soft story mechanism.
3.2. StepbyStep Design Procedure
The design of a frame that includes posttensioned connections is an iterative procedure, as well as all other design procedures. The preliminary beam and column sections of a PTTC frame are proportioned similar to a special moment frame (ignoring PTED characteristics) [4]. Accordingly, all “code based” provisions like strong columnweak beam criterion and system stiffness are checked using the applicable seismic code assuming rigid connections. After proportioning of the beam and column elements and designing the corresponding PTED connection, the behavior of the moment frame can be determined via a nonlinear analysis using the modeling parameters described in Section 4.
The following procedure is a stepbystep design procedure that should be considered to design a PT frame including PTTC connections.
Step 1 (Beam and Column Preliminary Proportioning). Beam and column sections of a PTTC frame are proportioned as a special moment frame since current codes do not have specific design provisions for PT frame. According to the code based analysis and design of the structure, the required parameters for connection design can be determined based on the preliminary assumptions for beam and column sections.
Step 2 (Check for Strong ColumnWeak Beam Design Criterion). In this step, the selected beam and column section in the previous step should be checked for the strong columnweak beam design criterion and the flange and web slenderness limits of the AISC seismic provisions [25].
Step 3 (Check for the System Stiffness). In the third step, the frame should be checked for building code story drift limit criterion. If the building code drift limits are not satisfied, the beam and column sections must be revised to fulfill the code requirements.
Step 4 (Designing the PTTC Connection). Up to now, all the beam and column sections are determined, and therefore all beams to column connection can be designed. By knowing the beam section, the beam nominal moment capacity, , can be calculated. In this step, the connection moment and the onset on Tstub yielding, , can be determined (20).
Consequently the decompression moment ( is known from (18). By knowing the decompression moment, the initial posttensioning force of the strands () can be calculated easily (11), and therefore the number of PT strands () is determined from the following equation: where is the total initial strand force, is the number of strands, and is the strand capacity. The selected and should satisfy strand yielding criteria in Section 3.1.4. is assumed to be 30% of the strand ultimate strength [4].
Finally, the design parameters of the Tstubs are determined based on (1)–(10). For designing Tstubs, according to EC3 [23] the plastic mechanism of the Tstub can be assumed to be developed at the flangetoweb connection or at the bolt axis or both. The prying forces developed in the bolts should be considered so that the bolt fracture does not occur. For designing Tstubs for the proposed posttensioned connection, only Mode 1: flange yielding is acceptable because bolt failure is a brittle failure mode and can affect the connection performance. The selection of the PT connection parameters is iterative. Notably, the connection panel zone should be designed as per conventional moment connections [4].
4. Approaches for Numerical Simulation of SelfCentering Connections with TStubs
Numerical simulation of the posttensioned Tstub connection (PTTC) is performed using OpenSees program, Open System for Earthquake Engineering Simulation [26]. Each structural member such as Tstub (dissipater), column, and beam is modeled by using various elements with specified material properties and structural behavior (see Figure 6). The connection model is made up of 6 groups of OpenSees elements. Beams and columns are modeled by linear beamcolumn elements (E1 and E2). Zerolength elements are used to model the gap (including both opening and closing) behavior, and these elements are assigned only to carry compression forces (in case of contact) without rotational stiffness (E3). Elasticnotension (ENT) material is used for modeling gap opening/closing behavior.
The energy dissipater elements, which in PTTC are Tstubs (E4), are assumed to be truss elements with an elasticplastic material. Truss element behavior is defined by an initial stiffness, hardening ratio, and yield stress consistent with the characteristic behavior and energy dissipation of the Tstubs. STEEL01 material is assigned to energy dissipater elements to simulate the Tstub behavior. The STEEL01 material is used to make up a uniaxial bilinear steel material.
The posttensioning strands (E5) distributed along the depth of the beam are all grouped at the beam centerline and anchored at the exterior columns (Figure 6). Strands are modeled with elasticperfectlyplastic (EPP) truss elements.
Finally, the panel zone is modeled using a zero length rotational spring fiber element (E6) [4]. The panel zone model used in this study was developed by Krawinkler [27]. The following equations describe the model: where and are the panel zone shear force deformation at the yield point, respectively. The ultimate panel zone shear is assumed to occur at a deformation of 4. is the yield stress of the column material, and , , , , , and are the beam depth, column depth, column web thickness, column flange thickness, total doubler plate thickness, and column width, respectively. is only a function of the material properties and not the panel zone geometry as described in (25).
To model the depth of beams and columns, rigidlinks (E7) are placed between the zerolength elements and the nodes of columnbeam elements.
5. Verification of the Connection Model
Both Tstub and angle energy dissipaters used in posttensioned connections are providing yielding mechanisms for dissipating energy through formation of plastic hinges in EDs. Three unsymmetrical plastic hinges are formed in the angles [3]: two on the angle leg connected to the column, and one on the angle leg connected to the beam. However, Tstubs form four symmetric plastic hinges: two plastic hinges in the flange plates close to bolt holes and two in the flange plates close to the stem as shown in Figure 5 [23]. Formation of four plastic hinges in Tstubs provides more energy dissipation capacity for Tstubs compared to angles. Furthermore, Tstubs can provide higher strength as an ED device where higher moment capacity is needed to connect deeper beams to column by PTED connections.
To evaluate the accuracy of the OpenSees analytical models for simulating PTTC behavior, same modeling assumptions are adopted to model posttensioned connections with angle ED devices. From modeling point of view, the difference between two systems (PT connection with angles and Tstubs) is reflected in modeling properties of E4 element and STEEL01 material. The modeling results are then compared to test results conducted by the Garlock et al. [3]. The Connection details and test setup are shown in Figure 7. All 6 test specimens were cruciformshaped beamcolumn subassemblages that simulated an interior joint in a moment resisting frame. Dimensions, sizes, and detailed properties of the test specimens are tabulated in Table 1. The momentrelative rotation response behavior predicted by OpenSees is compared with test results for PT connection (36s20P and 16s45) in Figure 8. The OpenSees numerical results are in good agreement with the experimental results. Therefore, the modeling methodology and assumptions are adopted for modeling PTTC in the following section.
 
: number of strands, : initial force in kips (per strands). 
(a) Connection details and
(b) test setup
(a) 16s45 model
(b) 36s20 model
6. Modeling Parameters for the New Connection (PTTC)
To model the new proposed connection, all modeling properties are adopted similar to the models in the previous section. The size of beams and columns is presented in Table 2. The nominal yield strength () for beams and columns is considered to be 345 MPa. Height of all columns is 3962 mm, and the combined length of the specimens including column depth and the length of the two beams is 8992 mm according to Garlock et al. test setup [3]. Size and geometry of the Tstubs designed in accordance the design procedure of with Section 3 is tabulated in Table 3. The tensile capacity and the modulus of elasticity of strands are 266 kN and 199 GPa, respectively. The yielding force of the strands is 230 kN, and the nominal area of each strand is 140 mm^{2} [4].
 
: Plastic moment capacity of the beam section. : Plastic modulus. 

7. Parametric Studies on the Designed Specimens
To investigate effects of the connection details on the behavior of the proposed connection, several parameters including beam size, , number of strands, and initial posttensioning force are considered in a numerical study on the designed PTTC connections listed in Table 2. Each model consistes of a cruciformshaped beamcolumn subassemblage that simulates an interior joint in a moment resisting frame. The SAC standard cyclic loading protocol is applied to the specimens in accordance with FEMA350 [28]. The numerically resulted decompression moment, , normalized by the nominal plastic moment capacity, is tabulated in Table 4.

7.1. Effects of Initial Posttensioning () or
Effect of on the connection behavior is illustrated in terms of versus in Figure 9, where is the moment of the east beam at the column face. Specimens (S8, S9, and S10) have different values (3253, 2575, and 2033 kN, resp.) which corresponded to different but the same number of and . The decompression moments are 0.39, 0.31, and 0.24 for PT connections S8, S9, and S10, respectively. S8 with the largest posttensioning force provides relatively larger connection moment for a given compared to S9 and S10 as shown in Figure 9.
According to Figure 10, specimen S4 () has larger moment values than S5 (). The same results are illustrated in Figure 11 for specimens S1, S2, and S3. For all of the specimens the larger posttensioning force resulted in larger moment capacity.
7.2. Effects of the Number of Strands
The axial stiffness of the strands (which is directly proportional to and ) mostly contributes to the stiffness of the connection after decompression. This can be seen by comparing the plots for S6 (with 20 strands) and S7 (with 30 strands) in Figure 12. These specimens has essentially the same value (and therefore the same ) but different number of strands (Table 4). As shown in Figure 12, after decompression the stiffness of S7 is greater than that of S6. The connection with larger number of strands (S7) has greater strength due to larger stiffness after decompression and have greater deformation capacity for a smaller initial force per strands.
Same results are shown in Figure 13 for S11, S12, and S13. These specimens have the same value but different number of strands (Table 4). Figure 13 shows that after decompression, the stiffness of specimen (S13) is greater than that of specimens (S11 and S12).
The relationship between strand forces normalized by the strand capacity () versus relative rotations is shown in Figure 14 for S6 and S7. As shown, the strands remained elastic throughout the analyses. The specimen S6 is vulnerable to fracture under cyclic loading where . Therefore, the connections with more strands may have better seismic behavior and the strands yield at high rotations.
8. Summary and Conclusions
A new posttensioned connection for seismic resistant steel frame structures that requires no field welding has been presented. Combining bolted Tstubs with high strength PT strands results in a connection with an initial stiffness that is similar to fully welded moment resisting connections. In addition, the connection has a selfcentering capability, resulting in minimal permanent story drift in a building following a severe earthquake. An analytical model based on fiber elements is developed which accurately predicts the behavior of a PTTC under cyclic loading. The model is used for parametric analytical study of the effects of connection details on the behavior of interior connection subassemblages. The details investigated include the level of posttensioning force, number of strands, and . The result showed that increasing the initial posttensioning force and increases the decompression moment and the moment capacity of the connection. However, an excessive post tensioning force results in yielding of the PT strands. It is shown that using larger number of strands in the connection prevents strand yielding criteria and increases and strength of connection.
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Copyright © 2013 Mahbobeh Mirzaie Aliabadi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.