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.
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. [
Garlock et al. [
Christopoulos et al. [
Chou et al. [
Kim and Christopoulos [
More recently, Chou et al. [
Chou and Chen [
Inertia force transfer mechanism in selfcentering moment frames has been studied via shake table and cyclic tests [
Wang and Filiatrault [
Several PTED connections based on different arrangement of the friction devices have been proposed and studied [
Wolski et al. [
Tsai et al. [
Lin et al. [
Finally, Dimopoulos et al. [
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 [
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 [
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.
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
Moment resisting frame with PTTC connections.
Connection details.
Exterior connection
Interior connection
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
Behavior of Tstubs.
Two bolted Tstubs
Forcedeformation relation of Tstubs
To determine the Tstub stiffness and strength parameters, two Tstubs connected by bolts are considered as shown in Figure
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 [
Mode 1, flange yielding:
Mode 2, bolt failure with flange yielding:
Mode 3, bolt failure:
The inelastic stiffness of the Tstubs is obtained from
Finally, the ultimate force of the Tstubs (
The ultimate deformation of the Tstubs (
The idealized expected momentrotation
Momentrotation behavior of posttensioned connection.
Deformation of PTTC under applied forces.
The moment to initiate this separation is called the decompression moment (
As shown in Figure
The connection moment after decompression is equal to
Event 3 marks the beginning of the unloading portion of the cycle. Assuming
Reverse yielding of the tension Tstubs occurs at an unloading moment equal to 2
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,
In this section, a stepbystep design procedure is given for design of PTTC connection.
To design the proposed PTTC connection, several limit states should be satisfied, including criteria on decompression moment (
To reduce connection permanent plastic deformation and to provide the selfcentering behavior, the decompression moment should be theoretically more than
The connection moment strength at the onset of Tstub yielding is recommended to be as follows [
To avoid Tstub fracture, this criterion is recommended:
The strands should not yield under the maximum credible earthquake (MCE) [
It is common to design the columns stronger than the beams to avoid soft story mechanism.
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) [
The following procedure is a stepbystep design procedure that should be considered to design a PT frame including PTTC connections.
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.
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 [
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.
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,
Consequently the decompression moment (
Finally, the design parameters of the Tstubs are determined based on (
Numerical simulation of the posttensioned Tstub connection (PTTC) is performed using OpenSees program, Open System for Earthquake Engineering Simulation [
Modeling of posttensioned Tstub connections in OpenSees.
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
Finally, the panel zone is modeled using a zero length rotational spring fiber element (E6) [
To model the depth of beams and columns, rigidlinks (E7) are placed between the zerolength elements and the nodes of columnbeam elements.
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 [
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. [
Test matrix (Garlock et al.) [
Specimen 
Column section  Beam section  Angle size 



20 s18 



20  1526 
20 s18 w 



20  1312 
16 s45 



16  3051 
36 s30 



36  4728 
36 s20P 



36  3194 
36 s30P 



36  4759 
Garlock’s experiments [
Connection details and
test setup
OpenSees and experimental results.
16s45 model
36s20 model
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
PTTC specimens.
Type  Beam  Column 









S1 


9946.9  3432  1.2  2265  1359  38.6  3519  30 
S2 


9946.9  3432  0.95  1793  1076  38.6  2786  30 
S3 


9946.9  3432  0.75  1416  849  38.6  2199  30 
S4 


9520.9  3284.7  1.2  2167  1300  45.6  2852  30 
S5 


9520.9  3284.7  0.95  1716  1029  45.6  2258  30 
S6 


9520.9  3284.7  0.75  1355  813  45.6  1783  20 
S7 


9520.9  3284.7  0.75  1355  813  45.6  1783  30 
S8 


10946.6  3776.5  1.2  2493  1496  45.9  3253  60 
S9 


10946.6  3776.5  0.95  1973  1184  45.9  2575  60 
S10 


10946.6  3776.5  0.75  1558  935  45.9  2033  60 
S11 


15338.3  5292  0.95  2765  1659  47.1  3522  40 
S12 


15338.3  5292  0.95  2765  1659  47.1  3522  50 
S13 


15338.3  5292  0.95  2765  1659  47.1  3522  60 
Size and geometry of Tstubs.
Type of Tstub  Flange thickness (mm)  Web thickness (mm)  Bolt diameter (mm)  Bolt material 


A  25  15  25.4  A490  345 
B  30  15  25.4  A490  345 
To investigate effects of the connection details on the behavior of the proposed connection, several parameters including beam size,
Response of analysis.
Type  Beam 


Tstub 



S1 

3519  30  B  0.39  0.46 
S2 

2786  30  B  0.31  0.35 
S3 

2199  30  B  0.24  0.28 
S4 

2852  30  A  0.39  0.36 
S5 

2258  30  A  0.31  0.29 
S6 

1783  20  A  0.24  0.34 
S7 

1783  30  A  0.24  0.22 
S8 

3253  60  B  0.39  0.21 
S9 

2575  60  B  0.31  0.16 
S10 

2033  60  B  0.24  0.13 
S11 

3522  40  B  0.31  0.33 
S12 

3522  50  B  0.31  0.27 
S13 

3522  60  B  0.31  0.22 
Effect of
Momentrelative rotation response specimens S8, S9, and S10.
According to Figure
Momentrelative rotation response specimens S4 and S5.
Momentrelative rotation response specimens S1, S2, and S3.
The axial stiffness of the strands (which is directly proportional to
Momentrelative rotation response S6 and S7.
Same results are shown in Figure
Momentrelative rotation response S11, S12, and S13.
The relationship between strand forces normalized by the strand capacity (
Strand behavior (S6, S7).
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