Experimental study of the restoring force mechanism in the self-centering beam (SCB)

Abstract

In the past, several self-centering (SC) seismic systems have been developed. However, examples of self-centering systems used in practice are limited due to unusual field construction practices, high initial cost premiums and deformation incompatibility with the gravity framing. A self centering beam moment frame (SCB-MF) has been developed that mitigates several of these issues while adding to the advantages of a typical SC system. The self-centering beam (SCB) is a shop-fabricated, self-contained structural component that when implemented in a moment resisting frame can bring a building back to plumb after an earthquake. This paper describes the SCB concepts and experimental program on five SCB specimens at two-third scale relative to a prototype building. Experimental results are presented including the global force-deformation behavior. The SCBs are shown to undergo 5%–6% story drift without any observable damage to the SCB body and columns. Strength equations developed for the SCB predict the moment capacity well, with a mean difference of 6% between experimental and predicted capacities. The behavior of the restoring force mechanism is described. The limit states that cause a loss in system's restoring force which lead to a decrease in the self-centering capacity of the SCB-MF, are presented.

Keywords

self-centering seismic system / seismic design / hysteretic behavior / restoring force / resilient structural system

Introduction and background

Although conventional earthquake-resisting structural systems are generally deemed adequate in providing protection against collapse, they may experience significant structural damage during strong ground shaking. Damage to the structure may include yielding, buckling or fracture of structural elements and permanent horizontal displacements after the earthquake, referred to as residual drift. Repairing structural damage is expensive and time-consuming because the damage is often distributed throughout the structure in non-replaceable elements. If the damage is too severe, or if there is significant residual drift, the structure may be demolished.

For that reason, the development of systems that can return to their initial position following an earthquake is required to minimize business downtime and structural repair cost. Self-centering (SC) seismic force resisting systems aim at reducing residual drifts after ground shaking. This results in reduced damage, since SC systems can be designed to resist the design basis earthquake without significant damage to the main structural elements of the building. In addition, they are often also designed to dissipate seismic energy using easily replaceable components which in turn reduces damage to the main structural components (beams, columns, etc).

Self-centering moment resisting frame (SC-MRF) systems with horizontal post-tensioned elements have been studied for concrete MRFs (e.g., Ref. [ 1]), coupled shear walls (e.g., Ref. [ 2]), and for steel MRFs (e.g., Ref. [ 3]). In a SC-MRF system, the horizontal post-tensioning elements clamp the beams to the columns as shown in Fig. 1. During an earthquake, the post-tensioned connections decompress and develop a gap-opening that leads to effective softening of the system without structural damage. The SC capability (i.e., the restoring force mechanism) is provided by the post-tensioning elements acting to close the gap. Energy dissipation in these systems is often accomplished by using supplemental energy dissipating elements, such as yielding angles or friction dampers [ 3, 4]. Numerous tests of steel self-centering moment resisting frame have been conducted and they show reliable self-centering behavior of the system. An example of steel SC-MRF is the system developed and tested on post-tensioned beam-to column connections known as PTED connection [ 5]. This connection incorporated post-tensioned high-strength bars to provide the restoring force along with energy dissipating bars that are able to yield in axial tension and compression. A large-scale PTED connection specimen was designed and subjected to a maximum interstory drift of 4%. At 4% drift level, no noticeable damage was observed in the PTED connection other than the replaceable ED bars. The beam compression flanges did not buckle, no inelastic deformations occurred in the column panel zone or the column flanges, and no slip was observed across the beam-to-column interface. Furthermore, at the end of the test, no residual drift was observed. A similar beam-column interior connection subassembly of post-tensioned wide flange beam-to-column moment connections were subjected to inelastic cyclic loading up to 4% story drift to simulate earthquake loading effects [ 6, 7]. These connections, however, used a different kind of energy dissipation device (yielding top-and-seat angles) to dissipate seismic energy. Another system which employs the post-tensioned beam-column connections is the self-centering steel plate shear wall (SC-SPSW) [ 8] which consists of replaceable thin steel web panels as the primary lateral load resistance and energy dissipation elements. Quasi-static and pseudo-dynamic testing on one-third scale single-bay three-story SC-SPSW specimens showed the specimens fully re-centered with less than 0.2% residual drifts at the end of the test.

One of the key aspects of self-centering systems is the restoring force mechanism. The most common approach for creating a restoring force mechanism in SC systems involves gap formation between two elements precompressed together. There are three categories of restoring-force mechanism which use this gap-opening behavior. The first category includes rocking precast concrete walls and braced frames where the gap-formation occurs at the base of the frame or wall (e.g., Refs. [ 9, 10]). The second category includes self-centering moment resisting frames, where the gap-opening occurs at the beam-column joints (e.g., Refs. [ 11]). The last category of restoring force mechanism includes self-centering braces in which a gap forms between telescoping concentric tubes and anchorage plates (e.g., Ref. [ 12]). Although the restoring force mechanism in some SC systems use shape memory alloys (SMA) (e.g., Refs. [ 12, 13]) or depend on gravity loads (e.g., Ref. [ 14]), the restoring-force mechanism in most of these self-centering systems is created by steel post-tensioning strands or bars.

As described above, the restoring force component of the SC systems often utilizes a gap opening mechanism. Specifically in SC-MRFs, the gap opening can create deformation incompatibility with the diaphragm system. The horizontal displacement of the beam relative to the face of the column, labeled as D_g in Fig. 1, has the cumulative effect of increasing the width of the moment frame by D_g*N_conn, where N_conn is the number of beam-to-column connections. If the diaphragm is connected across these beams, it hinders the self-centering capability of the system by restricting the gap opening and causes damage to the floor slab.

Although schemes for accommodating the expansion of the floor plate have been devised [ 15], they require the diaphragm to be disconnected along large lengths of the moment resisting frame, and special detailing to allow horizontal frame expansion. Schemes for accommodating SC moment frame expansion have been further developed, built and tested [ 16]. In this case, one of the SC moment frame beams is rigidly attached to the diaphragm while the other SC moment frame beams and the associated columns are allowed to move laterally (and experience frame expansion) relative to the floor system through the use of slotted and sliding connections. Cyclic [ 16] and shake table tests [ 17] show that these diaphragm connection schemes can limit the amount of restraint the diaphragm imposes on the self-centering beam-to-column connection and reduce the amount of floor slab damage. Alternatively, a moment connection that has gap opening at the bottom flange only was developed to eliminate frame expansion, but may have less self-centering capability [ 18].

Although there have been significant advances in the development of SC seismic force resisting systems, the examples of their use in practice are limited. The factors hindering the implementation of self-centering systems in practice include complex field construction and challenges associated with deformation incompatibility between the SC system and gravity framing of the structure (e.g., the diaphragm vs. gap-opening issue described in the previous paragraph). Additionally, self-centering systems require field construction methods that are uncommon in steel buildings including setting post-tensioning strands and anchorage, field fit-up of sensitive bearing surfaces, and post-tensioning procedures.

A new self-centering beam (SCB) moment frame has been developed [ 19] which builds on the advantages of a typical SC system while mitigating several of the challenges. This system possesses the type of resilient performance during large earthquakes characteristic of SC systems: virtually eliminating residual drifts and concentrating structural damage in replaceable elements. The SCB also eliminates deformation incompatibility with the gravity framing, thereby mitigating damage to the floors. The SCB is shop fabricated, making it more accessible to the construction industry by allowing for conventional field construction methods. This system also allows design flexibility such that the strength and stiffness of the moment frame can be separately tuned, thereby allowing more efficient use of steel, such as smaller columns.

Concept of SCB-MF

The SCB consists of a typical W-section beam augmented with a restoring force mechanism at its lower flange as shown in Fig. 2. The restoring force mechanism consists of two concentric HSS sections at the bottom chord of the SCB that are encouraged to stay aligned by post-tensioning strands. The events which describe the behavior of a SCB are listed below.

1) The outer tube that is welded to the bottom flange of the W-section but not connected directly to the columns, moves laterally in unison with the W-section as the frame is subjected to lateral drift.

2) The inner tube that is connected directly to the columns moves laterally relative to the outer tube (telescoping) as the columns rotate associated with story drift.

3) The post-tensioning (PT) strands located inside the concentric tubes that were subjected to initial post-tensioning stress before the SCB was installed, act to bring the inner and outer tubes back into alignment after lateral earthquake forces cease.

4) Free floating anchorage plates (at the two ends of the concentric tubes) slide over the end connections, and are held in place by the post-tensioning force. During lateral loading, the inner tube bears on the anchorage plate at one end (left end in Fig. 2), while the outer tube bears on the anchorage plate at the other end (the right end in Fig. 2) creating gap openings between the tubes and anchorage plates at both ends and further elongating the PT strands.

5) Energy dissipation (ED) fuses dissipate seismic energy through plastic axial deformations. One end of the ED fuse is connected to the inner tube and the other end is connected to the outer tube. The telescopic movement between the two tubes cause the fuses to deform axially and dissipate energy.

Since the distance between the columns remains constant and the gap openings related to the restoring force mechanism are internal (at the bottom chord), there is no deformation incompatibility between the SCB and the diaphragm. This system, therefore eliminates the need for special diaphragm detailing because there is no horizontal frame expansion.

The expected behavior of the SCB (along with the component behavior of the post-tensioned beam and ED fuses) when subjected to cyclic loading is shown in Fig. 3. The key events that define the response of the system are described in the following paragraphs. After the loading begins at point A, the SCB body (W-section and the concentric tubes) contribute to the stiffness of the system as the tubes decompress. Once the lateral force becomes large enough to overcome the pre-compression force provided by the PT strands, gap opening occurs between the anchorage plates and the tubes which is marked as point B in Fig. 3. An equation to predict the applied moment associated with this event will be presented in the next section.

The gap opening causes a softening of the system load-deformation response which is evident from the decrease in the stiffness of the SCB-MF as shown in Fig. 3. This reduction in stiffness is desirable because it limits the forces that can develop in SCB-MF (i.e., softening occurs without structural damage). The telescopic movement of the tubes after the gap opening causes axial deformation of the ED fuses and eventually leads to their yielding (marked as point C in Fig. 3).

The moment capacity (associated with point C in Fig. 3) depends on the initial post-tensioning force and fuse yield strength whereas the initial stiffness is associated primarily with geometric properties of the section. Thus, it is possible to separately adjust initial stiffness and moment capacity. The design of most moment resisting frames is controlled by lateral drift resulting in conventional beams that have substantially more strength than needed and large columns that have to be designed to be stronger than the beams to prevent story mechanisms. Conversely, the ability to reduce SCB moment capacity separately from its stiffness allows reduction in column, connection and foundation demands (see Ref. [ 19] for more details).

The stiffness of the system after gap opening is controlled by the axial stiffness of the PT strands, post-yield stiffness of the ED fuses, and their location with respect to the point of rotation of the SCB. Depending on the amount of initial stress applied to the PT strands and the amount of lateral loading, the PT strands may yield and eventually fracture. However, these limit states are not shown in Fig. 3, but will be discussed later in the paper. After the load reversal (point D), the fuse yields in the opposite direction (point F) and the gap closes at point G. Finally, at the end of the loading cycle (point H) the SCB returns its original position with near-zero drift.

SCB design equations

Equations that define the moment capacities of a SCB at different stages during the loading and other important parameters related to the design of the SCB, are presented in this section. Additionally, the post gap-opening stiffness which is associated with the restoring force mechanism has also been derived for comparison with experimental results in a subsequent section.

Moment demand, M_u, is calculated as the sum of the applied moments at both ends of the SCB, M_u1 and M_u2, because the moment capacities of the two ends are not independent.

(1) M_{\mathrm{u}}=M_{\mathrm{u}\mathrm{1}}+M_{\mathrm{u}\mathrm{2}}.

The moment capacities of the two ends of the SCB are not independent because the restoring force mechanism and the ED fuses work as one SCB unit and not separately for each end. The equations presented in the following paragraphs for gap opening moment capacity and fuse yield moment capacity are total moment (sum of the two end moments) for direct comparison to the applied moment demand, M_u.

The behavior of a SCB-moment frame subjected to lateral loading, can be characterized by moments associated with two key events. The first is the moment associated with gap opening between the anchorage plate and the two concentric tubes, M_PTi and is given by,

(2) M_{PTi}=A_{PT}{f}_{PTi}{d}_{SCB},

where, A_PT = total cross-section area of the post-tensioning strands; f_PTi = initial post-tensioning stress,

d_{SCB}

= SCB depth measured from the center of the top flange of the W-section to the centroid of the post-tensioning strands as shown in Fig. 2.

After gap opening, further telescoping of the concentric tubes causes axial deformation of the ED fuses and eventually leads to ED fuse yielding. The design moment of the SCB is defined as moment associated with the ED fuse yield, M_fuse, added to the gap opening moment, M_PTi, as given by the following equations. It is noted that the additional force in the PT strands past M_PTi is neglected in the following equation.

(3) M_n=M_{PTi}+M_{fuse},

(4) M_{fuse}=A_{ED}{f}_{yED}{d}_{SCB},

where, A_{ED}^{ } = total cross-sectional area of the ED fuses, f_yED = yield stress of the ED fuse material.

The ratio of initial post-tensioning force in the PT strands to the ultimate tensile strength of the strands, PT_i, affects the deformation capacity of the SCB. Larger levels of initial post-tensioning stress leave less strain capacity in the PT strands before yield and fracture and will thus limit the deformation capacity of the entire system. To ensure that the SCB-MF has enough deformation capacity, the SCB specimens were designed such that the PT strands would not yield before 2% story drift. The story drift ratio associated with PT strand yield, drift_PT,y, was estimated assuming rigid body rotation as follows,

(5) drif{t}_{PT,y}=\mathrm{100}\times [{\epsilon }_{PT,y}-{\displaystyle \frac{f_{pTi}}{E_{PT}}}]{\displaystyle \frac{L_{PT}}{d_{SCB}}},

where, E_{PT} = modulus of elasticity for PT strand material taken as 199 GPa, L_{PT} = length of PT strands taken as 4694 mm for experimental specimens, {\epsilon }_{PT,y} = yield strain of the PT strands taken as 0.01 mm/mm

The ratio of restoring moment provided by the PT to the moment associated with yielding the energy dissipating fuses, SC is given by;

(6) SC={\displaystyle \frac{M_{PTi}}{M_{fuse}}}={\displaystyle \frac{A_{PT}{f}_{PTi}}{A_{ED}{f}_{yED}}}.

In the tested configuration, both the fuses and the PT strands act along the same line of force (the centroid of the concentric tubes) and thus SC simplifies to the ratio of the initial PT force to the axial yield force of the energy dissipation fuses. SCBs with SC higher that 1 implies that the restoring force (provided by the PT strands) is higher than the ED fuse yield force which means that the beam will return to its original shape when the end moments are removed thus leaving negligible permanent drifts. Conversely, SCBs with the SC ratio less than 1 have restoring force mechanism that cannot overcome the fuse yield force and thus can display permanent residual drifts when end moments are removed.

The SC ratio is defined for the initial configuration and may reduce during displacement cycles due to several factors. After the system is subjected to lateral loading, the PT strands experience a loss in the initial post-tensioning stress due to seating losses and strand inelasticity. Additionally, upon yielding, the ED fuses experience strain hardening resulting in subsequent yield forces higher than initial yield force. Due to the combined effect of loss in post-tensioning stress in the PT strands and fuse hardening, the SC ratio of SCBs tend to reduce during large displacement cycles. This idea is further explored in a later section. For design purposes, self-centering capability of the SCB, as characterized by the SC ratio, can be adjusted by tuning the relative magnitudes of the initial PT force and the yield capacity of the energy dissipation elements.

The post gap-opening stiffness of the SCB, K_PT, is dominated by the stiffness contribution of the post-tensioning strands and is given by Eq. (7), neglecting the strain hardening of the ED fuses. K_PT, as calculated using Eq. (7) is compared to the experimental stiffness later in the paper.

(7) {{\displaystyle K}}_{PT}={\displaystyle \frac{{{\displaystyle M}}_{PTi}}{{{\displaystyle Ø}}_{SCB}}}={\displaystyle \frac{{{\displaystyle F}}_{PT}{{\displaystyle d}}_{SCB}}{{{\displaystyle Ø}}_{SCB}}}={\displaystyle \frac{{\displaystyle \frac{{{\displaystyle A}}_{PT}}{{{\displaystyle L}}_{PT}}}{{\displaystyle \Delta }}_{gap}{{\displaystyle d}}_{SCB}}{{\displaystyle \frac{{{\displaystyle \Delta }}_{gap}}{{{\displaystyle d}}_{SCB}}}}}={\displaystyle \frac{{{\displaystyle A}}_{PT}{{\displaystyle E}}_{PT}}{{{\displaystyle L}}_{PT}}}{{{\displaystyle d}}_{SCB}}^{\mathrm{2}},

where,

{Ø}_{SCB}

is the rotation of the SCB with respect to the column.

A free-body diagram of the self-centering beam body (i.e., beam and outer tube) drawn with the peak fuse and PT forces shows that the weld between the outer tube and the beam section should be designed for the maximum forces the fuse and post-tensioning can produce. However, since there is a long interface length, even intermittent welds are sufficient [ 19].

Description of experimental program

To investigate and validate the concept of the SCB, a large-scale testing program was conducted at the Thomas M. Murray Structures Laboratory at Virginia Tech. The test matrix for the experimental program is presented in Table 1. The SCB depth was varied between d_SCB = 432 mm to d_SCB = 622 mm because depth affects the strength and stiffness of the SCB. The SC ratio was varied from SC = 1.00 to SC = 1.82 to investigate the range of self-centering ability and how it changes during testing. The initial post-tensioning force ratio to ultimate was varied from PT_i = 0.33 to PT_i = 0.69 to explore PT behavior and limit states including seating losses, yielding, and fracture. A range of moment capacity, M_n = 264 kN-m to M_n = 509 kN-m was used to represent a range of applications such as beams at the upper floors and lower floors of a building. The results are presented in the next section and will primarily focus on behavior of the restoring force mechanism.

The test setup for the experimental program is shown in Fig. 4(a). The specimen includes one entire bay rather than just a portion of the beam like typical moment connection tests which include the beam from inflection point to the column. To investigate the restoring force and gap-opening mechanism it is necessary to test a full beam since the SCB acts as a unit. The total frame width between column centerlines is 6096 mm and the height of the frame (from the pinned base of the column to the height of loading, is h = 2643 mm. The base of the columns are connected to the foundation blocks with a true pin connection. Lateral load was applied at the top of the column by a 979 kN capacity actuator with displacement capacity of 508 mm. A gravity load simulator, that is capable of applying vertical gravity load while undergoing large lateral displacements was used to apply constant gravity load to the specimen at one-third points. The gravity load was consistent with perpendicular gravity beams framing into the SCB. The SCB was braced against out-of-plane translation at approximately one-third points by a steel frame. The specimen columns were also braced against out-of-plane movement at the loading height using diagonal threaded rods anchored to the strong floor. A pin-ended compression strut was placed between the two specimen columns to allow distribution of the actuator force to both columns. The loading protocol, as shown in Fig. 4(b), was adopted from the special moment-resisting frame connection qualification protocol outlined in Chapter K of AISC 341-10 [ 20].

Discussion of experimental results

This section presents some of the key results from the large-scale experiments conducted on SCB. The main focus of the section is behavior of the restoring force mechanism of the SCB, but global behavior is explained for necessary context.

Global force-deformation behavior

The global behavior of the SCBs is presented in Fig. 5 in the form of moment ratio vs story drift ratio plots. The moment ratio of the SCB is defined as the ratio of the applied global moment (actuator force, F_act, multiplied by height, h) to the design moment capacity of the SCB as defined in Eq. (3) and given in Table 2.

As shown in the plots, even after being subjected to 6% story drift, SCB-2, with higher SC ratio of 1.82, exhibits smaller displacements when the moment is removed as compared to SCB-1 and 3. SCB-1 and 3 had a near 1.0 SC ratio at the beginning of the test. Due to the combined effect of losses in post-tensioning stress (decrease in f_PTi in Eq. (6)) and fuse hardening (increase in f_yED in Eq. (6)), the SC ratio for these beams became less than 1.0 during cyclic loading at large drifts. These SCBs did not have full self-centering as characterized by small drifts at zero moment. For example, SCB-1 and 3 displayed 0.25% and 0.74% drift at zero force at the end of 4% drift cycle. However, previous studies [ 21] have found that SC systems with less than full self-centering hysteretic shape such as demonstrated by SCB-1 and SCB-3, still result in negligible residual drifts after earthquake ground motions. Even though the drift at zero force is non-negligible, the restoring force in the SC systems leads to an increased probability that the system will experience inelastic deformations in the direction toward zero displacement rather than away from zero displacement which leads to probabilistic self-centering and negligible residual drifts [ 21].

All the SCBs displayed adequate initial stiffness. The measured initial stiffness of SCB-1, SCB-2 and SCB-3 were 37,897 kN-m, 58,680 kN-m and 95,355 kN-m respectively. The SCB-MF also displayed high deformation capacity. All the SCBs were subjected to 6% story drift without causing any observable damage to the SCB, columns or beam-end connections. All the damages were limited to the ED fuses and PT strands.

The strength equation presented in the earlier section (refer to Eq. (3)) predicts the moment capacity of the SCBs within reasonable tolerances. Table 2 presents a comparison between the predicted and experimental moment capacity of the SCBs where the experimental capacity was determined using the intersection of two lines fit to the initial and post-yield curves. On average, the experimental moment capacity of the SCB-MF was found to be 6% greater than the predicted capacity.

Restoring-force mechanism

The restoring force mechanism in the SCB is provided by low-relaxation PT strands with 1860 MPa nominal tensile strength which are post-tensioned to a target initial stress level before SCB installation in the moment frame. As described earlier in the paper, the gap opening occurs when the applied overturning moment divided by the beam depth, d_SCB, exceeds the post-tensioning force resulting in the formation of gap opening between the concentric tubes and the anchorage plate as shown in Fig. 6. The PT force acts to close this gap and thus produces restoring force, bringing the SCB back to center.

For each SCB specimen, four strands (12.7 mm diameter for SCB-1 and SCB-4 and 15.2 mm diameter for others) were post-tensioned using a hydraulic jack applicable for prestressed/post-tensioned concrete construction. A reusable mono-strand chuck anchorage system (wedge and barrel) was used. The PT force was continuously measured using load cells on each of the four strands while the gap opening was measured using linear potentiometers (LP) attached between the concentric tubes and the anchorage plate at both ends of the beam.

Figure 7 shows the post-tensioning moment vs gap opening response of the SCB excluding the response of the ED fuses to investigate the nonlinear elastic behavior provided by the PT force alone. The gap opening ratio is defined as the ratio of the gap opening, D_gap, to the depth of the SCB, d_SCB. As evident from Fig. 7, gap formation in a SCB occurs when the overturning moment exceeds M_PTi (refer to Eq. (2)). The gap opening moment, M_PTi calculated using Eq. (2) is compared to the measured values in Table 3. On average, the experiment produced 7% larger moment capacity at gap opening than predicted by the equations.

The contribution of the post-tensioning strands to the SCB stiffness, K_PT after gap-opening was calculated from the data shown in Fig. 7 and compared with the predicted stiffness (refer to Eq. (6) and Table 3). The measured post gap-stiffness, calculated as an average of positive and negative stiffnesses, was on average 6% greater than the predicted value.

Figure 8 shows the plot of gap-opening ratio (at each end of the concentric tubes) with respect to the story drift. As shown in the plot, the gap opening starts occurring in a SCB-MF after a certain story drift. The story drift at which the gap-opening occurs is governed by the initial stiffness of the SCB-MF system and is an important parameter because it marks the initiation of softening in the system response which is desirable because it limits the forces applied to the rest of the system. Due to the nature of the ED fuse attachment, the energy dissipation in the SCB also begins only after the gap-opening occurs. In the tests performed on SCB specimens, the story drift ratio at gap-opening ranged from 0.3% – 0.5%.

Gap formation in a SCB also results in additional elongation of the PT strands. Figure 9 shows PT force-gap opening response of the SCB. The PT strands in SCB-2, which were post-tensioned to a higher level of initial PT stress, yielded during the 3% drift cycle as compared to SCB-1 which experienced yielding during the 6% story drift cycles. Due to higher inelastic deformations in the PT strands, the loss of PT stress was more significant in SCB-2. Quantitatively, the loss in the PT stress after unloading was approximately 33% in SCB-2 as compared to 13% in SCB-1. While designing the SCB test specimens, the story drift at PT strand yield was analytically predicted (refer to Eq. (6)) to ensure that the strands do not yield prior to 2% story drift displacement levels. This was done to limit significant loss in initial post-tensioning stress leading to a decrease in self-centering capacity of the SCB.

Subjecting the PT strands to large inelastic strains may also result in fracture of individual wires of PT strands which results in sudden, albeit small, drops in the restoring force. It should be noted that each PT strand is made up of seven separate wires and the wires typically fracture one at a time. Figure 10(a) shows the PT stress-strain behavior of SCB-4 for which a single wire fracture occurred in two of the four strands. In the plot shown in Fig. 10, the PT stress ratio is the total force in the PT strands normalized to the ultimate tensile stress of the PT strands, F_u,PT = 1860 MPa and the PT strain is the measured elongation of the PT strands normalized by the total length of the strands, L_PT = 4694 mm.

The PT strands were stressed to 69% of the ultimate tensile stress of the strands before testing. At the peak displacement in the 4% story drift cycle, one of the wires in one of the strands fractured at a strain of 1.13% and peak stress of 0.996 F_u,PT. This led to a drop of approximately 5% in the total PT stress. Following this fracture, another wire fractured in the first cycle of 5% drift cycle. At the time of fracture, the PT strand was subjected to a total of 1.19% strain and peak stress of 0.94 F_u,PT. This lead to another 5% drop in the total PT stress. As expected, the wire fractures were found to occur at the location of chucks as indicated by the teeth marks formed by the chuck wedges near the fracture location (see Fig. 10(b)). Due to the yielding of all the strands and fracture of a wire in two strands, the total loss in PT stress was approximately 56% which resulted in severe loss in the SC capability of the SCB leading to larger story drifts of 1.5% at zero-force toward the end of the test.

Another source of loss in the PT stress during the tests is due to seating losses. Seating losses occur when the wedges slide further into the chuck body as the strand force increases past its previous maximum value. To accurately estimate restoring force, seating losses that occur within PT strand systems during cyclic loading should be considered. A study was performed at Virginia Tech to predict the seating losses as a function of the initial post-tensioning stress level and peak PT stress [ 22]. Prior to the yielding of the PT strands, all the loss in the PT stress is likely due to the seating losses. Despite the inevitable loss in the SC capacity, all the SCBs showed good self-centering capability during 4% drift cycles.

Summary and conclusions

Based on the work presented in this paper, several observations and conclusions can be made.

1) The SCB moment frame is a high-performance self-centering lateral force resisting system which reduces residual drifts and prevents inelastic damage to the main structural components of the system.

2) In addition to the advantages associated with a typical SC system, the SCB can be shop fabricated which allows for conventional field construction methods. The design of a SCB also eliminates deformation incompatibility with the gravity framing system.

3) One of the limitations of the SCB is that it is not currently in production for use in practice. The prototype specimens were not designed or detailed for economy and thus would have a cost premium compared to conventional moment resisting frames. The cost premium is expected to reduce substantially if the SCB was redesigned for production.

4) Based on the experimental behavior, the SCB was shown to have a large deformation capacity. All three SCBs were successfully tested up to a story drift of 6% without causing any damage to the end connections, SCB body or columns.

5) The strength equations developed for the SCB predicted the moment capacity well, with a mean difference of 6% between experimental and predicted capacities.

6) The results obtained from equations developed to predict beam moment at gap opening, M_PTi and post-gap opening stiffness, K_PT were found to be in good agreement with the experimental results 7% and 6% greater than the predicted respectively.

7) The behavior of PT strands were examined with respect to the gap opening ratio. Depending on the initial post-tensioning stress, the PT strands were shown to lose some of the PT stress due to seating losses and inelastic deformations. This loss in PT stress leads to a decrease in self-centering capability of the SCB that can be controlled in design.

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