Seismic performance of precast prestressed concrete frame joints with buckle mechanical connection of reinforcing bars

The concrete used in the specimens was divided into two batches. The first batch included the cast-in-place joint, precast columns, and the precast portion of the composite beam, while the second batch was used for the cast-in-place portion of the composite beam and the core region. The C40 concrete, a standard concrete grade with a characteristic cube compressive strength of 40 MPa at 28 days, classified according to GB 50010-2010 Code for Design of Concrete Structures, was used. The concrete mix used ordinary Portland cement with a water–binder ratio of 0.42. The mix proportions by mass were cement:sand:gravel = 1.0:1.64:2.67. The coarse aggregate was gravel with a particle size range of 5–20 mm.

Moist curing was applied immediately after casting by covering the concrete with wet burlap and plastic sheeting to maintain surface hydration. Curing was carried out under standard laboratory conditions at (20 ± 2)°C and relative humidity ≥95%, with precast components cured for 14 days. After moist curing for 14 days, the precast parts were assembled, and the joint regions were cast with in-situ concrete. The cast-in-place concrete was also cured for an additional 14 days under the same conditions. Prestressing was applied after the full 28-day curing period to ensure sufficient concrete strength and bond development. The tendons were tensioned slightly beyond the design force to compensate for relaxation losses. Strain gauges and load sensors were installed to monitor the actual prestress levels.

Both batches utilized HRB400 grade steel for reinforcement, and the prestressing steel strands were 7φ_s 15.2 mm. The HRB400 bars conform to the Chinese standard GB/T 1499.2-2018, Steel for the Reinforcement of Concrete – Part 2: Hot Rolled Ribbed Bars [33]. This standard specifies mechanical properties, chemical composition, and rib geometry requirements for hot-rolled ribbed steel bars used in reinforced concrete structures. Concrete mix proportions followed standard methods, with material properties tested according to the Standard for Test Methods of Mechanical Properties of Ordinary Concrete (GB/T 50081-2019) [34]. The mechanical properties, including compressive strength, axial strength, tensile strength, and elastic modulus, were calculated as per established formulas. These values are summarized in Table 2.

Steel reinforcement used in this experiment is of type HRB400, with diameter specifications of 8, 18, and 20 mm, with three samples reserved for material property testing. The steel strands used are 7φ_s 15.2 mm. The testing procedure follows the Method for Tensile Testing of Metallic Materials (GB228.1-2010) [35], as shown in Figure 4, along with the mechanical properties of the steel materials that are presented in Table 3.

Figure 4

Mechanical properties testing of steel reinforcements and mechanical connectors. (a) Tensile test of steel bar, (b) fracture of steel bar, (c) tensile test of mechanical connection steel reinforcement, (d) fracture of mechanical connection steel reinforcement, and (e) comparison of uniaxial tensile stress–strain curves for rebar and mechanical connector.

Additionally, Figure 4(e) shows the uniaxial tensile stress–strain curves of 18 mm diameter reinforcing bars with and without buckle mechanical connections. The reinforcement bars exhibit a rapid stress increase and stabilize near a strain of 0.02, demonstrating high yield strength and tensile capacity. The connectors show a more gradual stress increase between strains 0.02 and 0.05, indicating excellent plastic deformation and ductility. This allows connectors to better accommodate deformation under load and adapt to stress variations, reducing the risk of premature failure at connection points.

The loading procedure for Specimen S1 began with a 343.8 kN axial load. When the horizontal displacement reached 5 mm, two minor cracks appeared on the right beam. By 10 mm, four cracks formed on the left beam, while the right beam’s cracks extended and three new minor cracks appeared. A 4 cm horizontal crack (0.08 mm wide) developed in the core. At 20 mm, diagonal cracks emerged on the left beam, and additional cracks appeared in the right beam and core. By 30 mm, horizontal and vertical cracks developed, and at 45 mm, a major crack (0.79 mm) appeared on the left beam. At 60 mm, concrete crushing occurred at the left beam’s top right corner and beam-column connection. At 75 mm, surface concrete continued to crush and the main crack widened to 1.6 mm, with additional cracks in the right beam and core. By 90 mm, no new cracks formed, but existing ones reopened, and concrete spalling continued. The reverse load capacity dropped to 85% of the peak load, signaling failure, and loading was terminated. Figure 8 illustrates the cracking patterns, failure zones, and concrete crushing observed in cast-in-place specimen S1.

Figure 8

Crack distribution and failure features of cast-in-place specimen S1. (a) Cracks at the left beam of specimen S1, (b) cracks at the right beam of specimen S1, (c) cracks at the joint core of specimen S1, (d) failure at the left beam end of specimen S1, and (e) concrete crushing in the right beam of specimen S1.

Specimen S1 exhibited typical flexural failure at both beam ends, consistent with monolithic cast-in-place behavior. Cracks were symmetrically distributed, with plastic hinges forming approximately 15 cm from the column face. Concrete crushing and spalling at the plastic hinge zones accompanied reinforcement yielding. As seen in Figure 8d, flexural cracking is evident at the left beam end, while Figure 8e shows extensive concrete crushing at the right beam. No signs of shear failure were observed in the joint core. This failure morphology confirms that the cast-in-place joint followed the expected strong-joint, weak-member behavior.

The loading process for Specimen S2 began with a 343.8 kN axial load. At 3 mm displacement, an 18 cm crack appeared on the left beam near the connection. By 6 mm, the crack widened and a new one formed. At 9 mm, the original crack on the left beam extended vertically, and a new crack appeared on the right beam connection. By 12 mm, no new cracks formed, but the load–displacement curve showed a slope change. At 18 mm, new cracks appeared, including one on the right beam connection. At 27 mm, several cracks extended further, including horizontal cracks at the left beam connection and new cracks on the right beam and in the core. By 36 mm, cracks in the left beam and core widened, and new diagonal cracks formed. At 45 mm, the right beam’s connection crack widened to 2.1 mm and diagonal core cracks appeared. By 54 mm, localized concrete crushing, approximately 11 cm², occurred at the right beam’s top-right corner. At 63 mm, concrete in the left beam’s upper-right corner crushed and fell off. By 72 mm, concrete spalling occurred on the left beam, and the right beam connection crack widened to 7.4 mm. The load dropped below 85% of peak load, indicating failure, and loading was terminated. Figure 9 illustrates the overall failure mode, crack distribution, and core damage in precast non-prestressed specimen S2.

Figure 9

Crack development and failure characteristics of precast non-prestressed specimen S2. (a) Overall failure mode of specimen S2, (b) cracks in the left beam of specimen S2, (c) cracks in the right beam of specimen S2, and (d) cracks in the joint core of specimen S2.

Specimen S2’s failure mode was characterized by earlier crack initiation compared to S1 due to weaker mechanical connections. Cracks tended to initiate at beam–column interfaces and extended into the beam ends and core, with prominent concrete crushing and spalling occurring at the beam ends. Plastic hinge regions shifted slightly outward relative to the column face. Figure 9(a) and (b) illustrates the overall failure pattern and crack distribution on the left beam, while Figure 9(c) and (d) shows the cracking on the right beam and the joint core. No full shear failure was observed in the core region, consistent with a “strong joint–weak member” failure mechanism.

The loading process for Specimen S2 began with a constant axial load of 343.8 kN. At 4 mm displacement, two cracks appeared on the left beam. By 6 mm, the cracks widened to 0.38 mm. At 8 mm, a new crack emerged near the connection that later widened to 0.6 mm, exceeding the 0.4 mm threshold. By 16 mm, additional cracks formed on the left beam, and a 19 cm crack (0.6 mm wide) developed on the right beam connection. At 24 mm, a diagonal crack appeared at the left beam end, and by 32 mm, the right beam connection crack widened to 2.22 mm, with a small horizontal crack forming in the core. At 48 mm, local crushing and spalling occurred at the left beam bottom, and stirrups were exposed at the right beam connection. At 52 mm, new cracks appeared, and existing ones widened. By 68 mm, the left beam top corner was crushed, and a diagonal crack formed at the connection. At 72 mm, heavy spalling occurred at the left beam near the connection (∼42 cm²), and the right beam’s main crack widened to 6.6 mm with stirrups exposed. The forward load dropped below 85% of peak load, indicating failure, and loading was terminated. Figure 10 illustrates the crack development, joint core damage, and reinforcement and connector exposure in specimen S3.

Figure 10

Crack development and failure characteristics of precast prestressed specimen S3. (a) Cracks in the left beam of specimen S3, (b) cracks in the core joint of specimen S3, (c) cracks in the right beam of specimen S3, (d) overall failure mode of specimen S3, (e) reinforcement exposure in the left beam of specimen S3, and (f) connector exposure in specimen S3.

Specimen S3 exhibited typical prestressed joint behavior, with initial cracks concentrated near the connections. The failure mode was dominated by beam-end flexural failure with visible concrete crushing and reinforcement exposure. Connector exposure was also evident, reflecting the interaction between the prestressing tendons and the concrete. The plastic hinge formation was consistent with the “strong column, weak beam” principle.

The loading process for Specimen S4 began with a 343.8 kN axial load. No cracks formed in the first three stages. At 8 mm displacement, a 14 cm crack (0.1 mm wide) appeared on the left beam 12 cm from the beam-column connection. By 12 mm, it widened and extended diagonally. At 16 mm, two new cracks formed on the left beam and three on the right beam (max width 0.24 mm). At 28 mm, five more cracks formed on the left beam, while the right beam developed multiple cracks, including a 21 cm root crack and new cracks at five positions, with the connection crack opening to 1.74 mm, thereby exceeding the 0.4 mm serviceability threshold. A 6 cm horizontal crack (0.06 mm wide) formed in the core. At 36 mm, existing cracks widened and six new cracks appeared on the right beam, accompanied by a popping sound. At 44 mm, the left beam connection crack widened to 2 mm, and a diagonal core crack (8 cm, 0.13 mm wide) formed. At 52 mm, concrete spalling occurred at the right beam connection, where the crack width reached 5.7 mm. At 60 mm, spalling and bottom crushing intensified at the left beam, and the right beam’s main crack reached 1.06 mm. By 68 mm, severe spalling exposed stirrups at the left beam connection, indicating failure. So, the loading was terminated. Figure 11 illustrates the crack propagation, concrete spalling, and reinforcement exposure at the beam ends of specimen S4.

Figure 11

Crack propagation and beam-end damage in precast prestressed specimen S4. (a) Cracks in the left beam of specimen S4, (b) cracks in the joint core of specimen S4, (c) cracks in the right beam of specimen S4, (d) concrete spalling at the bottom of the beam in specimen S4, and (e) reinforcement exposure in the right beam of specimen S4.

Specimen S4’s failure mode was governed by flexural failure at the beam ends, with cracking initiating near the beam–column connections and gradually spreading along both beams. Compared to S3, S4 experienced reduced cracking in the core region, attributed to increased axial load and improved confinement from prestressing. The damage progressed with concrete crushing and reinforcement exposure near the plastic hinge zones, which developed approximately 15 cm from the column face. No shear failure was observed in the joint core, and the failure mode remained consistent with the “strong joint–weak member” mechanism.

To begin the loading process, specimen S5 was subjected to a vertical axial load of 515.7 kN using a hydraulic jack. No cracks were visible during pre-loading. At 6 mm, a 19 cm high crack (0.35 mm) appeared at the left beam connection, widening to 0.73 mm at 8 mm, clearly exceeding the 0.4 mm serviceability threshold. By 12 mm, it reached 1 mm. At 16 mm, five new cracks (max 0.1 mm) formed on the left beam, and two on the right (max 0.2 mm). At 20 mm, the left beam saw four more cracks (widest 0.1 mm), and seven new right beam cracks (max 0.7 mm). At 28 mm, five new cracks on the left and two on the right appeared (widest 0.4 mm). At 36 mm, the connection crack expanded to 3 mm, with three new cracks on the left and five on the right. A 24 cm diagonal crack (0.08 mm) formed in the core, and local spalling (∼14 cm²) was observed at the support. At 44 mm, additional left and right beam cracks developed (widest 0.4 mm), and the connection crack reached 2 mm. At 52 mm, it widened to 4.8 mm with crushing at the upper-right corner of the right beam and diagonal cracks in the core. At 60 mm, the left connection cracking reached 5.6 mm, accompanied by new diagonal and horizontal cracks. At 68 mm, cracking worsened on both sides, with severe bottom spalling at the left beam revealing reinforcement. This indicated failure, and the test was stopped. Figure 12 illustrates the overall damage progression in specimen S5, including beam-end cracks, connector exposure, and concrete crushing.

Figure 12

Cracking, connector exposure, and spalling in precast prestressed specimen S5. (a) Cracks in the left beam of specimen S5, (b) cracks in the joint core of specimen S5, (c) cracks in the right beam of specimen S5, (d) overall failure mode of specimen S5, (e) concrete spalling at the bottom of the beam in specimen S5, (f) connector exposure at the bottom of the beam in specimen S5, and (g) concrete crushing at the upper end of the beam in specimen S5.

Specimen S5 exhibited a clear beam-end flexural failure, initiated by an early connector crack that exceeded 0.4 mm at only 8 mm displacement. Cracks continued to spread and widen symmetrically on both beams, with concrete crushing, connector exposure, and visible reinforcement confirming plastic hinge formation at beam ends. Although minor diagonal cracking was observed in the joint core, no full shear failure occurred. This behavior aligns with the “strong column–weak beam” and “strong joint–weak member” principles.

To begin the loading process, specimen S6 was loaded with 687.6 kN, while S6 showed no cracks initially. At 2 mm, three left beam cracks formed, including a 20 cm long, 0.48 mm wide connection crack, already exceeding the 0.4 mm serviceability threshold. By 4 mm, it widened to 0.6 mm, with a small crack (3.8 cm) on the right beam. At 6 mm, a 14 cm long, 0.14 mm wide crack formed at the right joint. At 9 mm, the left crack widened to 1.3 mm and spread along the bottom; the right beam developed three new minor cracks, and the joint crack reached 0.5 mm. By 12 mm, the left bottom crack connected fully, with two side cracks (≤0.1 mm). At 15 mm, two short cracks (3–5 cm) appeared at 34 and 47 cm. No new cracks at 18 mm, but the right joint crack widened to 2.2 mm. At 21 mm, a minor crack formed at 45 cm, and cracking appeared at the right root; the joint crack widened to 3.8 mm. No new cracks at 27 mm. At 33 mm, the first core crack appeared (8 cm, 0.07 mm). By 39 mm, 14 cm² spalling occurred at the left upper corner, six new right beam cracks formed (widest 0.12 mm), and a 25 cm diagonal core crack (0.14 mm) developed. At 45 mm, cracks widened, and bottom spalling began on the right beam. At 51 mm, 57 cm² spalling occurred at the left beam top, and core cracks extended. At 57 mm, the left base crack widened with crushing and spalling, and 73 cm² spalling appeared on the column face. At 63 mm, the base crack fully connected; the joint crack reached 6.5 mm. Reinforcement was exposed at both beam ends. By 72 mm, extensive spalling and reduced load capacity (<85% of peak) marked failure and ended the test. Figure 13 illustrates severe cracking, spalling, and reinforcement exposure in specimen S6, particularly around the beam–column connection zones.

Figure 13

Severe cracking and reinforcement exposure in precast prestressed specimen S6. (a) Cracks in the left beam of specimen S6, (b) cracks in the joint core of specimen S6, (c) cracks in the right beam of specimen S6, (d) overall failure mode of specimen S6, (e) concrete crushing at the upper part of the left beam in specimen S6, (f) reinforcement exposure in the right beam of specimen S6, and (g) exposure of connectors and stirrups at the bottom of the beam in specimen S6.

Specimen S6 demonstrated a pronounced beam-end flexural failure with early crack formation at the connector zone, where the first crack exceeded 0.4 mm at only 2 mm displacement – the earliest such case among all specimens. Crack propagation was consistent and severe, with both beams experiencing concrete crushing, extensive spalling, and reinforcement exposure. The diagonal cracking in the joint core remained minor and did not result in shear failure. The overall failure mechanism complied with the “strong column–weak beam” and “strong joint–weak member” principles.

Hysteretic curve, a crucial indicator for evaluating and analyzing the seismic performance of structures, comprehensively reflects key characteristics of the specimens such as load-bearing capacity, energy dissipation ability, stiffness degradation, ductility, and restoring force behavior. Based on the cyclic loading results, the load-displacement curves of the specimens are shown in Figure 14, where Δ represents the column-end displacement and P denotes the column-end load.

Figure 14

Comparison of the hysteresis curves. (a) S1, (b) S2, (c) S3, (d) S4, (e) S5, and (f) S6.

Comparative analysis of the load–displacement curves reveals the following key findings: (1)

All specimens initially showed linear, overlapping curves with minimal enclosed area. With increasing displacement, plasticity developed, leading to pinched loops (anti-S), then horizontal slips (Z shape).

The skeleton curves were obtained by connecting the peak load points at each displacement level of the hysteresis curves. These curves provide essential parameters such as yield load, peak load, ultimate load, yield displacement, and ultimate displacement. The skeleton curve comparison of each specimen is shown in Figure 15.

Figure 15

Comparison of the skeleton curves.

Comparative analysis of the skeleton curves reveals that, except for specimens S5 and S6, all curves generally display center symmetry, indicating similar load-bearing capacities under positive and negative displacements. In the early loading stages, all specimens exhibit linear relationships, gradually transitioning to nonlinear forms as displacement increases, accompanied by a reduction in curve slope. A slight drop followed by an increase in slope is observed during early loading, likely due to increased friction as hinge supports rotate. In the mid-to-late stages, specimen S3 shows an extended horizontal segment, implying significant damage accumulation. Compared to S2, specimens S3 and S4 demonstrate load capacity increases of 7.87 and 12.03%, respectively, confirming that prestressing enhances performance. However, both show steeper post-peak declines. Specimens S5 and S6 improve peak loads by 5.36 and 12.15% over S4, suggesting that increased axial compression effectively boosts load-bearing capacity. After peak loads, the decline rate under positive loading is similar among S4–S6, though S6 shows a faster drop under negative loading. S4 and S5 behave similarly under positive loading, while S5 outperforms S4 in the reverse direction.

The characteristic values of load capacity for each specimen are summarized in Table 4, demonstrating that specimens S3–S6 have higher strength ratios compared to specimens S1 and S2, indicating better safety reserve performance.

Strength degradation refers to the phenomenon where the load-bearing capacity of a specimen decreases with an increasing number of loading cycles at the same displacement level [39]. This section introduces the strength degradation coefficient λ to quantify changes in strength, defined as the ratio of the peak load during a given cycle to the first peak load at that displacement level, as expressed in equation (1): (1) λ = P i j P i 1 , \lambda =\frac{{P}_{ij}}{{P}_{i1}}, where P represents the peak load, i denotes the displacement level, and j indicates the cycle number.

The relationship between the strength degradation coefficient λ and displacement levels for specimens S1–S6 is illustrated in Figure 16. Here, the horizontal axis represents the displacement level (i), ranging from negative to positive values to reflect the reversed cyclic loading directions. Positive values correspond to forward loading cycles, while negative values correspond to reverse loading cycles. The two curves represent the strength degradation coefficient λ for the second (j = 2) and third (j = 3) loading cycles at each displacement level, as defined in equation (1).

Figure 16

Comparison of the strength degradation. (a) Strength degradation of S1, (b) strength degradation of S2, (c) strength degradation of S3, (d) strength degradation of S4, (e) strength degradation of S5, and (f) strength degradation of S6.

Comparison of the strength degradation versus displacement level for each specimen reveals the following. (1)

Except for specimen S1, the remaining specimens did not exhibit significant strength degradation. As displacement increased, all specimens showed varying degrees of degradation. For the same displacement level, strength degradation during the third cycle was consistently greater than that of the second, indicating cumulative damage effects.

In this experiment, factors such as reduced bond between steel reinforcement and concrete, yielding of the reinforcement, and cracking of the concrete collectively contribute to irreversible damage that accumulates over time, leading to reduced stiffness. The chord stiffness K _i [36,40] is introduced to quantify the changes in stiffness, calculated according to equation (2): (2) K i = ∣ + P i ∣ + ∣ − P i ∣ ∣ + Δ i ∣ + ∣ − Δ i ∣ , {K}_{i}=\frac{| +{P}_{i}| +| -{P}_{i}| }{| +{\Delta }_{i}| +| -{\Delta }_{i}| }, where P represents the peak load values (kN) at the ith positive and negative peaks and Δ denotes the corresponding displacement values (mm). The relationship between the stiffness coefficients of each specimen and displacement is illustrated in Figure 17.

Figure 17

Comparison of the stiffness degradation.

A comparative analysis of the stiffness–displacement relationships of all specimens reveals several key trends: (1)

All specimens exhibited a similar pattern of stiffness degradation under cyclic loading. In the early loading stages, stiffness declined rapidly, followed by a more gradual reduction during the mid-stages. In the later stages, stiffness tended to stabilize around 1.0, indicating significant accumulation of plastic damage.

To evaluate ductility, the ductility ratio μ was adopted, defined as the ratio of ultimate displacement (Δ _u) to yield displacement (Δ _y), with higher values indicating better seismic energy dissipation capacity [41]. Yield displacement was determined using the equivalent elastoplastic energy method [36,42], as illustrated in Figure 18.

Figure 18

Equivalent elastic-plastic energy method.

A secant line OC originating from point O intersects the envelope curve at point B. A horizontal line is drawn through the ultimate point U to form area BCU. By rotating line OC such that area OAB equals area BCU, the vertical from point C intersects the envelope curve at point Y, identifying the yield point. The corresponding load and displacement at Y are defined as the yield load and yield displacement, respectively. The ultimate displacement corresponds to the displacement when the load drops to 85% of the peak value, i.e., the final loading stage.

From the data in Table 5, the following observations can be made: (1)

With the exception of S1, all specimens showed comparable yield displacements in both loading directions.

To evaluate the energy dissipation performance of the joints, two indicators were introduced: the energy dissipation coefficient (E) and the equivalent viscous damping ratio (hₑ), as defined in equations (3) and (4). These follow the hysteresis loop analysis principles described by Paulay and Priestley [43], where the energy dissipation coefficient E is equivalent to the ratio of dissipated energy to elastic strain energy. The schematic used for calculating these parameters is shown in Figure 19. (3) E = S ABCD S OBG + ODF , E=\frac{{S}_{\text{ABCD}}}{{S}_{\text{OBG}+\text{ODF}}}, (4) h e = S ABCD 2 π · ( S OBG + ODF ) , {h}_{\text{e}}=\frac{{S}_{\text{ABCD}}}{\text{2}\pi \text{&#x00B7;}({S}_{\text{OBG}+\text{ODF}})}, where S _ABCD represents the total energy dissipated during one cycle and S _OBE and S _ODF represent the energy dissipated during the elastic phase of a cycle. The ratio of these areas indicates the relative energy dissipation compared to an equivalent elastic body at the same displacement; a larger ratio indicates a fuller hysteresis curve and greater energy dissipation capacity. The energy dissipation coefficients E and viscous damping coefficients (h _e) for each specimen during the last loading cycle are summarized in Table 6 and illustrated in Figure 20.

Figure 19

Energy dissipation coefficient calculation diagram.

Figure 20

Comparison of energy dissipation coefficient.

The variation of energy dissipation coefficients across specimens revealed the following. (1)

All specimens exhibited a similar trend – low energy dissipation during the early elastic stage due to minimal plastic deformation, followed by a rise, a dip, and a subsequent increase as displacement progressed.

The residual deformation rate is the ratio of residual deformation to the ultimate displacement, and the calculation formula is given by equation (5), with the results shown in Table 7, where μ _r represents the residual deformation rate, Δ _r is the residual deformation displacement (mm), and Δ _u is the ultimate displacement when the specimen fails. (5) μ r = Δ r Δ u . {\mu }_{\text{r}}=\frac{{\Delta }_{\text{r}}}{{\Delta }_{\text{u}}}.

Analysis of residual deformation and deformation ratios reveals that specimens S2–S4 exhibit a negative correlation between residual deformation and prestressing force. As initial prestress increases, residual displacement decreases by 3.05 and 15.2%, indicating enhanced self-centering capacity. In contrast, residual displacements in S4–S6 increase by 12.52 and 20.73%, suggesting that axial compression negatively impacts deformation recovery.