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Structural Performance of PC Double Beam–Column Connection Under Gravity and Seismic Loading

Abstract

Recently, as a new precast concrete (PC) construction method for increasing economy and constructability, the PC double-beam system has been developed for factories or logistic centers, where construction duration is particularly important. In this study, half-scaled PC double beam–column connection was tested under gravity loading and cyclic lateral loading. The major test parameters included the use of the spliced PC column and the addition of reinforcement at the beam–column joint. In the gravity loading test, the flexural behavior of the PC double beam was investigated. The test results showed satisfactory flexural capacity at the PC double-beam section, validating the composite action between the PC and RC members. In the cyclic lateral loading test, the seismic performance of the PC double beam–column connection was investigated. Based on the test results, the failure mode, load-carrying capacity, deformation capacity, energy dissipation capacity, secant stiffness, and shear strength of the PC double-beam system were evaluated and compared with those of a conventional RC double beam–column connection. According to the test results, the structural performance of the PC double beam–column connection was comparable to that of the RC double beam–column connection and satisfied the acceptance criteria of moment frame in the ACI 374.1-05 provision.

Introduction

In recent years, various precast concrete (PC) construction methods have been developed to cope with the extensive construction demands of factories and logistics centers, where a shortening of construction duration is a particular concern for reducing the construction cost of buildings. In PC construction, the PC slab constitutes the majority of all PC members. Thus, to reduce construction costs, new PC slab construction methods have been developed. However, the concept and shape of these methods (developed in the worldwide construction markets) are similar, where the use of prestressed tendons, hollow core sections, or T-shaped sections is common practice (Girhammar and Pajari 2008; Han et al. 2010; Hassan and Rizkalla 2002; Hsu 1989; Kim et al. 2012; Lee et al. 2016; Park et al. 2019; Ren et al. 2015). Thus, an innovative construction method is required for further reducing the construction cost of PC structural systems.

For a typical duration-shortening-type PC system, which is commonly used in factories or logistics centers (Fig. 1a and b), PC beams are constructed first. Then, on top of these, PC slabs are placed (Fig. 1b). Finally, by placing reinforcement and cast-in-place (CIP) concrete, the structural integrity among the PC beam, PC slab, and PC column is secured (Fig. 1c).

Fig. 1
figure 1

Construction of typical PC beam–concrete column connection.

Recently, as a new PC construction method for improving economy and constructability, a PC double-beam system has been developed. For factories or logistics centers, a PC beam is typically divided into two beams that are parallel to each other (Fig. 2a), because a single PC beam is generally too heavy to be carried due to its large self-weight of the members. In the PC double beam–column connection, by increasing the spacing of the two parallel double beams, the span length of the PC slab can be decreased (Fig. 2b).

Fig. 2
figure 2

Comparison of existing PC system and double-beam PC system.

In the PC double beam–column connection, a PC column module, including a PC column for the current floor, a wide bracket, and a spliced PC column for the upper floor, is used (Figs. 3a and 4a). The wide bracket of the PC column module is designed to support the widely spaced PC beams, whereas the spliced PC column on the bracket enables the upper column for the next floor to be continuously constructed without placement and/or curing of CIP concrete for topping and the beam–column joint. After placing post-installed anchors on the footing (Fig. 3b), they are connected with the PC column module (Fig. 3c). On the bracket, two paralleled double beams are placed (Fig. 3d). PC or RC slabs are constructed between the PC double beams (Fig. 3e), while another PC column module is prepared and repeated for the upper floor, by using the spliced PC column with splicing sleeves (Fig. 3f and g). Finally, CIP concrete is cast for the topping and beam–column joint at each floor (Fig. 3h).

Fig. 3
figure 3

Construction of PC double beam–PC column connection.

Fig. 4
figure 4

Design of PC double beam–column connection.

The proposed PC double beam–column connection has the following economic and structural advantages:

  1. 1)

    For conventional PC systems using the beam–column ramen structure, the net span length required for the design of PC slabs is typically greater than 10 m, which requires a relatively large cross section to sustain greater member force and displacement (Fig. 2a). In contrast, in the proposed double-beam PC system, by widening the spacings of the two paralleled beams, the net span length of the PC slab can be decreased to approximately 9 m, which amounts to a 10% reduction in materials (Fig. 2b).

  2. 2)

    Because of the shorter span length, the member forces are decreased; in particular, the flexural moment is decreased by approximately 20%, which can directly decrease the required thickness of the PC slabs (Fig. 2b).

  3. 3)

    The upper column for the next floor can be continuously constructed prior to the placement and/or curing of CIP concrete for the topping and beam–column joint, by simply connecting to the lower PC column using splice sleeves in the spliced PC column (Fig. 3f). Thus, the construction speed of the building can be enhanced, unaffected by the CIP concrete placement of the topping, beam–column joint, and/or slab.

However, in the PC double-beam system, the bracket of the PC column and the ends of the two parallel PC beams should be eventually integrated by the CIP beam–column joint. Thus, the integrity at the PC beam–PC column connection may affect the safety of the overall system. Therefore, the integrity and structural capacity for the proposed PC double beam–column connection need to be verified.

In the present study, three specimens of PC double beams under gravity loading and three specimens of beam–column connection under cyclic lateral loading were tested, to investigate the integrity and seismic performance of the PC double beam–column connection. The test parameters included the presence of the spliced PC column and the use of an additional reinforcement at the beam–column joint. An RC specimen was also tested under cyclic lateral loading for direct comparison with PC specimens. From the results of the gravity loading test, the failure mode, flexural capacity, and integrity of the PC double-beam connection were evaluated. From the results of cyclic lateral loading test, the failure mode, strength, deformation capacity, and energy dissipation capacity of the PC double-beam specimens were compared with those of the RC double-beam specimen. Further, the seismic performances of the PC double-beam specimens were evaluated based on the acceptance criteria of moment frame in the ACI 374.1-05 (ACI Committee 374 2005) provision.

Design of PC Double Beam–Column Connection

Design of PC Double Beam

Figure 4a shows a PC double beam–column joint under concentrated load at both ends. To simplify the test setup, concentrated loading was used for the gravity load. Under gravity loading, the largest flexural moment typically occurs at the beam–column joint (Fig. 4a). At the beam critical section of the joint, a constant shear force was applied due to the concentrated loading (Fig. 4a). To avoid the brittle failure mode and to induce the ductile behavior of the beam, the specimens were designed to fail in flexure prior to shear failure at the beam–column joints. In other words, the nominal shear strength Vn of the PC beam was greater than the shear force Vm at the beam critical section, which causes flexural failure of the beam, i.e., Vn > Vm = Mn / ls, where ls = shear span length of the beam (Fig. 4a). The flexural strength of the PC double beam, Mn, specified in ACI 318 (ACI Committee 318 2019) and KCI 2012 (Korea Concrete Institute 2012) can be calculated as follows:

$$M_{n} = A_{s} f_{y} \left( {d - a/2} \right),$$
(1)

where As = area of longitudinal tension reinforcement, fy = specified yield strength for longitudinal reinforcement, d = distance from extreme compression fiber to centroid of longitudinal tension reinforcement, a = depth of equivalent rectangular stress block.

The nominal shear strength Vn of PC beams can be calculated according to ACI 318–19 (ACI Committee 318 2019) or KCI 2012 (Korea Concrete Institute 2012) as follows:

$$V_{n} = V_{c} + V_{s} ,$$
$$V_{c} = \sqrt {f_{c}^{^{\prime}} } bd/6,$$
$$V_{s} = A_{s} f_{yt} d/s,$$

where Vc = nominal shear strength provided by the concrete, Vs = nominal shear strength provided by transverse reinforcement, fc = specified compressive strength of the concrete, fyt = specified yield strength of transverse reinforcement, and s = spacing of transverse reinforcement. As indicated by previous tests (Hirosawa 1977; Meinheit and Jirsa 1977), shear strength was not as sensitive to joint shear reinforcement. Thus, as required in ACI 318 (ACI Committee 318 2019) and KCI 2012 (Korea Concrete Institute, 2012), a minimum shear reinforcement was used in the specimens.

On the other hand, on the top surface of the PC double beams, topping concrete was cast during the construction and a construction joint was formed between the PC concrete and CIP topping concrete. Thus, under the applied shear Vu, a horizontal shear force Vhv occurs at the interface, which can be calculated using the force equilibrium shown in Fig. 5.

Fig. 5
figure 5

Horizontal shear of PC beam.

The nominal horizontal shear strength Vnh at the PC and topping concrete interface, which is intentionally roughened to a full amplitude of approximately 6 mm in general practice, can be calculated according to ACI 318–19 (ACI Committee 318 2019) or KCI 2012 (Korea Concrete Institute, 2012), as follows:

$$V_{nh} = \left( {1.8 + 0.6\frac{{A_{v} f_{yv} }}{{b_{v} s}}} \right)b_{v} d \le 3.5b_{v} d,$$
(5)

where Av = area of shear reinforcement within spacing s, fyv = specified yield strength of shear reinforcement, bv = width of cross section at constant surface being investigated for horizontal shear (mm), and d = distance from extreme compression fiber to centroid of longitudinal tension reinforcement. To prevent the horizontal shear failure in all specimens, the horizontal shear capacity Vnh was designed to be greater than the horizontal shear force Vhv.

Design of PC Double Beam–Column Connection

In case of an earthquake, an additional shear design of the beam–column connection should be considered (Fig. 4b). In accordance with the seismic provision of ACI 318 (ACI Committee 318 2019) and ACI-ASCE 352 (Joint ACI‐ASCE Committee 352 2002), the nominal shear strength of the beam–column connections can be defined as follows:

$$V_{jn} = \gamma \sqrt {f_{c}^{^{\prime}} } A_{j} \le 1.7\sqrt {f_{c}^{^{\prime}} } A_{j} ,$$
(6)

where fc = specified compressive strength of concrete, Aj = bj(hc2 s) = effective joint shear area reduced by the seating length s of the PC beam, bj = min{0.5(bb + bc), bb + hc, bc} or min{bb + 2x, bb + hc, bc}, where bb = width of the beam cross section, bc = width of the column cross section, hc = column depth, and x = smaller perpendicular distance from the longitudinal axis of the beam to the column side. Term γ is a coefficient addressing the confinement effect of the beams framed into the joint (ACI 318 (ACI Committee 318 2019) and ACI-ASCE 352 (Joint ACI‐ASCE Committee 352 2002)), and γ = 1.2 is used for the cruciform beam–column connections.

Based on the strong-column-and-weak-beam concept, assuming flexural yielding at the critical section of the beam (Fig. 4b), the joint shear demand Vju at the end of the PC beam–column connection can be calculated using the flexural moment demands, Muj (= Mn) and Muj (= Mn), which are developed by the beam moment capacity at the critical sections (Eq. 1). The joint shear demand Vju is calculated as follows (ACI Committee 374, 2005; Eom et al. 2015):

$$V_{ju} = \alpha \left( {C + T^{^{\prime}} } \right) - V_{col} \simeq \alpha \left( {M_{uj} + M_{uj}^{^{\prime}} } \right)\frac{1}{{h_{s} }} - V_{col} ,$$
(7)

where C and T' = resultant compression and tension forces of the beam cross sections, respectively, at the end of the PC beam; α = coefficient addressing the effects of material overstrength and cyclic strain-hardening [= 1.25; ACI 318 (ACI Committee 318 2019); ACI-ASCE 352 (Joint ACI‐ASCE Committee 352 2002)]; Vcol = shear force of the column; and hs = distance between the top and bottom flexural bars in the beam cross section (Fig. 5).

Major Test Parameters

In the specimen names, the first letters G and S indicate specimens designed for gravity loading and seismic loading (i.e., cyclic lateral loading), respectively. Two PC double-beam systems were used for the specimens: PC system I, which had a spliced PC column at the joint prior to the placement of CIP concrete (Fig. 6a), to further reduce construction duration (PC1 series specimens), and PC system II (Fig. 6b), where the joint was cast with CIP concrete without the spliced PC column (PC2 series specimens), intended to increase structural integrity. PC1 and PC2, following the first letter, indicate PC system I and PC system II, respectively, i.e., the presence and absence of the spliced PC column at the joint. In PC system I with a PC column at the joint, constructability can be further increased and construction duration can be reduced by continuously constructing the upper PC columns connected to the spliced column prior to the CIP concrete placement at the joint. On the other hand, in the presence of the spliced PC column at the panel zone of the beam–column joint, the connection integrity may be degraded. Thus, PC system II, without the spliced PC column at the joint, was also investigated. The AF following—(dash) indicates the use of additional flexural rebars at the beam–column joint. Local failure may degrade the integrity in the proposed beam–column connection. The use of additional reinforcement at the joint was considered to relocate the plastic hinge to the beam’s inner section and to prevent local failure.

Fig. 6
figure 6

Two PC double systems used in specimens.

Gravity Loading Test for PC Double Beam

In the gravity loading test, the flexural behavior of the PC double beam with PC1 and PC2 types (Fig. 6a and b, respectively) was investigated, focusing on the composite action at the PC-beam critical section. In the calculation of Eq. (1) for the PC double beam, it was assumed for (1) a fully composite action between the PC beams and topping concrete of the beam cross section and (2) the yielding of the longitudinal reinforcement. These assumptions were validated under gravity loading by investigating the actual tested strength and strain of the longitudinal rebar. The effect of additional reinforcement at the beam–column joint to relocate a plastic hinge to the inner beam section was also investigated.

Test Specimens

Table 1 shows the major parameters of the specimens. Three specimens were prepared for half-scaled PC double beam under gravity loading. Figure 7 shows the details of the joint, dimensions, and reinforcement of the specimens. The dimensions of the column section were 420 mm × 420 mm (Fig. 7a). The shaded and void areas in Fig. 7 indicate the PC concrete and CIP concrete, respectively.

Table 1 Properties of test specimens.
Fig. 7
figure 7

Configuration and reinforcement details of test specimen under gravity loading.

In GPC1, PC double beams and a spliced PC column at the joint were integrated by CIP concrete placement of the topping and beam–column joint (Figs. 6a and 7a). 14-D13 bars and 8-D19 bars were used for the upper and lower (i.e., tension and compression) longitudinal reinforcement in CIP topping concrete and PC double beams, respectively (Fig. 7 b and c); thus, the nominal flexural moment of the beam section, Mn, was calculated as 432.8 kN·m using Eq. (1). On the other hand, in the PC beam–column joint, it is difficult to satisfy the required development length of the lower (compression) longitudinal rebars in seismic provisions of the design codes (ACI Committee 318 2014; ACI Committee 374 2005; Korea Concrete Institute 2012), because of the rebar interference at the joint (Fig. 7d). Thus, for specimens under gravity loading, the development length ld of the lower flexural rebars was 210 mm, which was shorter than the design development length of Type 2 beam–column connection (Joint ACI‐ASCE Committee 352 2002): αfydb/(6.2√fc) = 370 mm, where α is a stress amplifier (= 1.25). For transverse reinforcement of the beams, D10 bars were used. The spacing was 75 mm near the joint and 100 mm at the beam center (Fig. 7 a). Thus, the nominal shear strength of the beam section, Vn, was calculated as 1,206 kN using Eqs. (2) to (4). On the other hand, the nominal horizontal shear strength at the PC concrete–CIP concrete interface of the beam section, Vnh, was calculated as 4,431 kN using Eq. (5), which was significantly higher than the expected horizontal shear demand (≈Asfy = 908 kN).

In GPC1-AF, a plastic hinge relocation method (Dalalbashi et al. 2012; Eom et al. 2015; Joh et al. 1991; Juette 1996; Yamamoto et al. 2008) was used to prevent a local failure, which is expected to degrade the integrity near the beam–column joint. In addition, 4-D10 flexural rebars and 2-D13 stirrups enclosing the flexural reinforcement were placed (Fig. 7e). Thus, the nominal flexural moment of the beam critical section, Mn, was increased to 492.3 kN·m through the additional flexural rebars. However, considering the constructability of the PC system, the lengths of the additional flexural rebars and stirrups were limited to 1400 and 1650 mm, respectively (Fig. 7e). The other details of GPC1-AF are identical to those of GPC1.

In GPC2-AF, to investigate the effect of the non-spliced PC column at the joint on joint integrity, no spliced PC column was used at the joint. Instead, the CIP topping concrete was directly filled in the beam–column joint (Figs. 6b and 7f). The reinforcement details of GPC2-AF are identical to those of GPC1-AF, except for two additional stirrups (4-D13) enclosing the flexural reinforcement (Fig. 7f).

The material tests were performed on the day of testing. Three concrete cylinders each were tested for the PC members cast with the same concrete, including the bracket, PC beam, and spliced PC column at the joint (if present), and for the CIP concrete at the topping and beam–column joint. Table 1 presents the average values of the compressive strength. The concrete compressive strength was 34.8 and 27.7 MPa for the PC members and CIP concrete, respectively. Three coupons each were tested for the rebar used in the specimens. The average values of yield strength and tensile strength are presented in Table 2. For D10, D13, and D19 bars used for the specimens under gravity loading, the yield strength was 551.9, 512, and 509.7 MPa, respectively (Table 2).

Table 2 Properties of reinforcement.

Construction Sequence

Figure 8 shows the construction of the PC double-beam system. Each PC member was fabricated prior to the assembly (Fig. 8a). In case of GPC1 and GPC1-AF, on top of the bracket, PC double beams and a spliced PC column were located and the CIP concrete covering the upper part of the PC double beams and the beam–column joint was cast (Fig. 8b). Owing to the pre-occupied spliced PC column, the upper PC column could splice to the longitudinal rebars of the lower column using the splice sleeves prior to the placement of the CIP concrete (Fig. 7a). In case of GPC2-AF without splicing, the PC column at the joint, only PC double beams were located and CIP concrete was filled in the upper part of the PC double beams and the beam–column joint, including the void, due to the absence of the PC column (Fig. 8c). Because of the absence of the spliced PC column at the joint, the upper PC column was spliced after the placement of the CIP concrete.

Fig. 8
figure 8

Construction of test specimen under gravity loading.

Test Methods

A monotonic loading was applied to the specimens (Fig. 9a), which were turned upside down for convenience of loading. Simply supported by the beam ends, the beam was subjected to a concentrated loading at the bottom of the bracket. Figure 9a shows the location of the linear variable differential transducers (LVDTs) for measuring each displacement of the specimens.

Fig. 9
figure 9

Test setup and loading protocol.

Failure Mode

Figure 10 shows the crack pattern and failure mode of the specimens under gravity loading at the end of the test. Regardless of the parameters, the crack patterns and failure modes were similar to each other. Typical flexural cracks were dominant at the tension zone throughout the tests. At the end of the test, the concrete crushing at the compression zone occurred near the section of the beam–bracket contact surface (Fig. 10), which indicates that the critical section was the interface of the PC beam and PC bracket. Other failures, such as local bearing failure, anchorage failure, and/or horizontal shear failure, did not occur.

Fig. 10
figure 10

Damage modes of specimens under gravity loading at the end of the test.

Load–Displacement Relations

Figure 11 shows the load–displacement relation of the specimens under gravity loading. The vertical load was measured at the actuator mounted on the bracket, while the displacement was measured at the upper column of the specimen by LVDTs 1 and 2 located at the center (Fig. 9a). The figures also shows the nominal flexural strength Pn based on the actual material strength in Tables 1 and 2, which was calculated as two times the nominal sectional flexural moment at the beam near the joint divided by the span length ls: Pn = 2Mn/ls (Fig. 6a). Note that the nominal flexural moment, Mn, was calculated by ACI 318 (ACI Committee 318 2019) under the assumptions of (1) the composite action of the PC double-beam sections (the PC double beams and topping concrete and (2) the yielding of the tension longitudinal reinforcement.

Fig. 11
figure 11

Loaddrift relations of specimens under gravity loading.

In GPC1, with the PC double beams, spliced PC column, and CIP concrete (Fig. 11a), the peak strength Ptest was 501 kN, which was 21% greater than the predicted flexural strength Pn (= 414 kN). This indicated that the composite action assumed for the PC double beam is valid, and that the moment capacity can be predicted by the current design prediction. At the yielding displacement δy of 15 mm, the load-carrying capacity Py was 375 kN. With an increase in the vertical displacement, the load-carrying capacity was further increased after yielding, which is attributable to strain-hardening of the rebars. The load-carrying capacity was decreased to 75% of the peak strength at an ultimate displacement of δu = 170 mm. Thus, the ductility ratio μ was 11.3 (= δuy). The definitions of yield displacement δy, ultimate displacement δu, and ductility ratio μ are presented in Fig. 11d.

In GPC1-AF (Fig. 11b) with additional reinforcement at the beam–column joint (Fig. 7e), the peak strength was increased to 523 kN, which was 11% greater than the predicted flexural strength Pn (= 471 kN). The peak strength was only 4% greater and the strength ratio was 10% smaller than that of GPC1 without additional reinforcement at the beam–column joint. Further, unlike GPC1, as the displacement increased after yielding, the load-carrying capacity was not increased. This is because the development length of the additional flexural rebars is insufficient, and therefore, they are limited to experience strain-hardening, which increases the flexural strength. The ductility ratio was μ = 11.7 (= [δuy] = [158.7 mm/13.6 mm]), which was comparable to that of GPC1.

In GPC2-AF (Fig. 11c), without the PC double column at the joint and with the additional reinforcement at the beam–column joint (Fig. 7f), the load-carrying capacity was similar to that of GPC1-AF with the PC column at the joint. This result indicates that the PC column at the beam–column joint does not significantly affect the structural performance under gravity loading.

Strain of Reinforcing Bars

Figure 12a shows the locations of strain gauges for measuring the strains of the tension longitudinal rebars. For GPC1-AF and GPC2-AF, locations of strain gauges for the additional flexural rebars are also presented.

Fig. 12
figure 12

Strain of flexural reinforcing bar in beams of specimens under gravity loading.

Figure 12b shows the rebar strain–central displacement relations for GPC1, with the PC double beams, spliced PC column, and CIP topping concrete. The strains of the longitudinal rebars were the largest at the bracket–beam interfaces (FC, FE), reaching the yield strain at approximately 15 mm, which coincided with the yield displacement δ y estimated through the definition in Fig. 11d. As the measured location was farther away from the beam–column interface, the strain was decreased (FB, FF). At the locations of FB and FF, 500 mm away from the critical section, yielding of the flexural rebars occurred. In contrast, at the location of FA and FG, 1000 mm away from the critical section, yielding of the flexural rebars did not occur throughout the test. This result indicates that the plastic hinge length lp of the PC double beam was greater than the effective depth of the beam, d (= 500 mm) (Bae and Bayrak 2008; Corley 1966; Panagiotakos and Fardis 2001; Paulay and Priestley 1992). The rebar strains in GPC1-AF and GPC2-AF were close to those in GPC1.

In GPC1-AF and GPC2-AF with additional flexural rebars (Fig. 12c), similar to the other flexural rebars, as the measured location was farther away from the critical section, the strain was decreased (AFB). Although the yielding of the flexural rebars occurred at the center of the rebar (AFD), the flexural rebar strain continuously decreased with a further increase in displacement (approximately after 70 mm). This result indicates that the effect of additional flexural rebars within the inelastic range was limited due to the lack of the bar development length engaged in the plastic hinge location.

In summary, regardless of the presence of the spliced PC column at the beam–column joint, the current design flexural strength, Mn (Eq. 1), was achieved, showing the composite action assumed for the PC double beam. On the other hand, the effect of additional reinforcement was negligible due to insufficient anchorage length. To reinforce the PC double beam–column joint, it is necessary to secure a sufficient anchorage length of the additional reinforcement outside the plastic hinge length.

Cyclic Loading Test for PC Double Beam

In the cyclic lateral loading test, the seismic capacities of two types of PC beam–column connections (PC1 and PC2 series (Fig. 6)) were evaluated on the basis of the acceptance criteria of moment frame in the ACI 374.1–05 (ACI Committee 374 2005) provision, and compared with that of a conventional RC double beam–column connection.

Test Specimens

Table 1 shows the major parameters of the specimens, and Fig. 13 shows the details of the joint, dimensions, and reinforcement of the specimens. Three specimens of half-scaled PC double beam–column connection were prepared for testing under cyclic lateral loading: one specimen for the RC double beam–column connection (SRC) and two specimens for the PC double beam–column connection (SPC1 and SPC2): for specimen names, refer to Major test parameter. Using the strong-column-and-weak-beam concept, flexural yielding was designed at the beams in all specimens. For SPC1, similar to GPC1, GPC1-AF, and GPC2-AF, a spliced column was used to splice the upper PC column. The dimensions of the column section were increased from 420 mm × 420 mm to 500 mm × 500 mm to prevent an early failure of the PC columns (Fig. 13).

Fig. 13
figure 13

Configuration and reinforcement details of test specimen under cyclic lateral loading.

In SRC (Fig. 13a), conventional RC was used for the double beam–column connection. Then, 9-D13 and 6-D19 bars were used for the upper and lower longitudinal reinforcement, respectively (Fig. 13b and c); thus, the positive and negative values of Mn were calculated as 302 and 292 kN·m, respectively (Table 1). For transverse reinforcement of the beams, D10 bars were used, with spacings of 75 mm near the joint and 100 mm at the beam center (Fig. 13b and c).

In SPC1 (Fig. 13d), similar to GPC1 (or GPC1-AF) (Fig. 7a–e), PC double beams, a spliced PC column at the joint, and CIP concrete for topping at the upper part of the double beam and beam–column joint were used. As shown in Fig. 7d for test specimens under gravity loading, 4-D16 bars among 6-D16 bars for lower reinforcement were anchored into cast-in topping concrete at beam–column joint; therefore the positive and negative values of Mn were calculated as 210 and 292 kN·m, respectively (Table 1). To satisfy the required development length of the lower longitudinal rebars in seismic provisions of ACI 318 (ACI Committee 318 2019) and KCI 2012 (Korea Concrete Institute 2012), as well as to avoid the rebar interference at the joint, alternative placement was used (Fig. 13d). Thus, the development length ld of the lower longitudinal rebars was 380 mm, which was greater than the design development length of Type 2 beam–column connection (Joint ACI‐ASCE Committee 352 2002): αfydb/(6.2√fc) = 255 mm, where α is a stress amplifier (= 1.25). The other details of SPC1 are identical to those of SRC. The nominal shear strength at the PC concrete–CIP concrete interface of the beam section, Vn, was calculated as 1,340 kN using Eqs. (2) to (4). On the other hand, the nominal horizontal shear strength of the beam section, Vnh, was calculated as 3,195 kN using Eq. (5), which was significantly greater than the expected horizontal shear demand (= Asfy = 397.9–636 kN).

In SPC2 (Fig. 13e), similar to GPC1-AF (Fig. 7e), the PC double beams and CIP concrete for the topping and beam–column joint were used without any spliced PC column at the joint. The other details of SPC2 are identical to those of SPC1.

According to the similar construction sequences of GPC1 (or GPC1-AF) and GPC2-AF, the upper PC column was spliced to the longitudinal rebars of the lower PC column prior to and after the CIP concrete placement in SPC1 with the spliced PC column at the joint and SPC2 without the spliced PC column at the joint (Fig. 13d and e).

The material tests were performed on the day of testing. Three concrete cylinders each were tested for the lower column, double beams, and CIP concrete for the upper part of the PC double beam and beam–column joint. The average values of the compressive strength are presented in Table 1. In SRC with a conventional RC double beam–column connection, the concrete for the lower column and beam was cast simultaneously (= 40.3 MPa in Table 1), followed by concrete placement for the upper column (= 40.5 MPa in Table 1). The concrete compressive strength ranged from 38.4 to 41.8 MPa. Three coupons each were tested for the rebar used in the specimens. The average values of the yield strength and tensile strength are presented in Table 2. The yield strengths of D10, D13, D16, D22 (Grade 400 MPa), and D22 (Grade 600 MPa) bars were 574, 521, 521, 506, 552, and 649 MPa, respectively (Table 2).

Test Setup

A cyclic lateral loading was applied to the specimens, as shown in Fig. 9b. The lower part of the column was hinge-supported, while both beam ends were roller-supported. The upper part of the column was hinge-connected with the actuator, which moved in the horizontal direction under displacement control. Figure 9b also shows the linear variable displacement transducers (LVDTs) for measuring lateral displacements (LVDT 1), slip at the column hinge (LVDT 2), and vertical extension and contraction of the roller supports measured at the hinges at both beam ends (LVDTs 7 and 8). The loading protocol was planned as shown in Fig. 9c; at initial loading, the story drift ratio was 0.25% and the following drift ratio was 1.5 times the previous one until a maximum drift ratio of 6.0% was achieved, with three cycle repetition at each drift ratio (ACI Committee 374 2005). Axial force generally increases the shear strength of the joint (Masi et al. 2013; Paulay and Priestley 1992a, b). However, axial load was not applied to the columns in this study to simplify the tests and to create severe loading condition for the joint (Fenwick and Irvine 1977).

Failure Mode

Figure 14 shows the crack pattern and failure mode of the specimens under cyclic lateral loading at the end of the test.

Fig. 14
figure 14

Damage modes of specimens under gravity loading at the end of the test.

In SRC with a conventional RC double beam–column connection (Fig. 13a to c), initial cracks occurred at the beam–column joint and column. As the drift ratio increased, the cracks at the joint and horizontal cracks between the upper bracket and joint were propagated (Fig. 14a).

In SPC1 and SPC2 with a PC double beam–column connection (Fig. 13(d) and (e)), cracks occurred at the beam–column joint and columns at the initial loading (Fig. 14b and c). As the drift ratio increased, the extensive cracks occurred at the interfaces between the PC beams and CIP concrete. The drift ratio at failure was 5.6%–5.9% in SPC1, which was slightly smaller than that of SRC with RC double beam–column connection (6.0%–6.2%). The failure mode was not affected by the presence (SPC1) and absence (SPC2) of the PC column at the joint.

Load–Displacement Relationships

Figure 15 shows the lateral load–displacement (drift ratio) relationships of the specimens under cyclic lateral loading. The lateral displacement indicates the net displacement, excluding slip at the column hinge (LVDT 2 in Fig. 9b) and extension and contraction of the roller supports (LVDTs 7 and 8 in Fig. 9b). The lateral drift ratio was divided by the net column height (h = 3060 mm).

Fig. 15
figure 15

Loaddrift relations of specimens under cyclic lateral loading.

Table 3 presents the maximum strength Ptest, yield drift ratio δy, yield stiffness ky, and maximum drift ratio δu. In Fig. 15d, ky is defined as the pre-peak secant stiffness corresponding to 0.75Ptest. The yield drift ratio was calculated as (Ptest/ky)/h. The maximum drift ratio δu is defined as a post-peak drift ratio corresponding to 0.75Ptest (Park 1988).

Table 3 Summary of test results and predictions.

In SPC1 (Fig. 15b) with a PC double beam–PC column connection, the overall behavior was similar to that of SRC (Fig. 15a) with the conventional RC double beam–column connection. After yielding, the load-carrying capacities of both SRC and SPC1 gradually increased. The peak strength of SPC1 with the PC double beam–column connection was + 218 kN and -254 kN in the positive and negative loading directions, respectively, which were 22% and 9% smaller than those of SRC with the RC double beam–PC column connection. The maximum drift ratio of SRCu = 6.0%–6.2%) was slightly greater than that of SPC1u = 5.6%–5.9%).

In SPC2 (Fig. 15c) with the PC double beam–column connection but without the spliced PC column at the joint, the load-carrying capacity was similar to that of SPC1 with the spliced PC column at the joint, which indicates that the PC column at the joint had negligible effect.

The disparity of the load-carrying capacity between SRC and SPC is discussed in Evaluation of Structural Performance in detail.

Rebar Strain

Figure 16 compares the normalized strains (ε/εy) of the flexural bars in SRC with the RC double beam–column connection and SPC2 with the PC double beam–RC column connection, where normalized strains were obtained based on the material test results (i.e., εy = fy/Es). Figure 16 also shows the locations of strain gauges FC (top bar) and BFC (bottom bar) within the joint, and those of strain gauges FB (top bar) and BFB (bottom bar) outside the joint.

Fig. 16
figure 16

Strain of flexural reinforcing bars in beams of specimens under cyclic lateral loading.

In the top bars of SRC with the RC double beam–column connection (left-hand side of Fig. 16a), the strain of FC within the joint was six times the yield strain, while that of FB outside the connection was maintained in the elastic range at the initial stage. As the drift ratio increased, the bar-yielding occurred both within and outside the joint.

In the top bars of SPC2 with the PC double beam–RC column connection (left-hand side of Fig. 16b), similar to SRC with the RC double beam–column connection, the strain of FC within the joint was significantly greater than the yield strain. However, the strain of FB outside the joint was smaller than that of SRC with the RC double beam–column connection, indicating that the damage was concentrated on the PC and CIP concrete interface of the connection and the plastic hinge length was limited due to the PC–RC interface (Fig. 14c). On the other hand, the strains in the bottom bars of SRC and SPC2 (right-hand sides of Fig. 16a and b) were relatively smaller than those in the top bars. This tendency was also found in SPC1 with the PC double beam–PC column connection (Fig. 14b).

Evaluation of Structural Performance

Load-Carrying Capacity and Deformation Capacity

The theoretical load-carrying capacity of the beam–column connection designed based on the strong-column-and-weak-beam concept can be predicted by assuming yielding of flexural rebars at the critical section, as follows (Im et al. 2010) (i.e., the interface between the PC beam and CIP concrete; Fig. 4b):

$$P_{n} = \left( {P_{bp} + P_{bn} } \right)\frac{l}{2h},$$
(8a)

where Pn = the load-carrying capacity of the beam–column connection, Pbp and Pbn = vertical reactions at the beam supports, l = net beam length between the left and right beam hinge supports [= 4,760 mm], and h = net column height between the top and bottom hinges [= 3,060 mm]. The vertical reactions, Pbp and Pbn, were calculated by dividing the nominal flexural positive and negative moments, Mbp and Mbn, respectively, of the beam critical section by the shear span length ls = [l—(hc—2 s)]/2 (i.e., distance from the roller support to the critical section), where hc = bracket depth and s = seating length of the PC beams. Thus, the load-carrying capacity of the PC double beam–column connection can be calculated as follows:

$$P_{n} = \left( {M_{bp} + M_{bn} } \right)\frac{l}{h}/\left( {l - h_{c} + 2s} \right)\quad \quad \quad {\text{for pc beam}}{.}$$
(8b)

On the other hand, in the case of the RC double beam–column connection, the critical section crossed the side surface of the bracket. Thus, the load-carrying capacity for RC specimens can be calculated by excluding the seating length s of the PC beams, as follows (Im et al. 2010):

$$P_{n} = \left( {M_{bp} + M_{bn} } \right)\frac{l}{h}/\left( {l - h_{c} } \right)\quad \quad \quad {\text{for rc beam}}{.}$$
(8c)

Table 3 and Fig. 15 show the theoretical load-carrying capacity Pn of the specimens calculated by Eq. (8). The flexural strength Mn of the beam critical section was calculated using the actual material strengths and rectangular concrete stress block of ACI 318 (ACI Committee 318, 2019) and KCI 2012 (Korea Concrete Institute 2012). Table 3 also presents the tested peak strength Ptest, predicted strength Pn, strength ratio Ptest/Pn, yield drift ratio δy, maximum drift ratio δu, and ductility μ = (δuy). As presented in Table 3 and Fig. 15, The Ptest/Pn ratios of SPC1 and SPC2 with the PC double beam–column connection (1.17–1.35) were greater than 1.0, using Eq. (8b), which addresses the increased shear span length, ls, due to the seating length s of the PC beams. This result indicates that the load-carrying capacity of the PC double beam–column connection can be conservatively predicted by the theoretical load-carrying strength. On the other hand, by using Eq. (8c) for addressing the smaller shear span length ls than that of the SPC specimens, the Ptest/Pn value of SRC with the RC double beam–column connection (1.16–1.18) was close to or smaller than that of the SPC specimens. The overstrength may be due to the increasing plastic hinge length of the RC specimen with uniformly distributed cracks at the beam–column joint (Fig. 14a).

As shown in Table 3, SPC1 and SPC2 with the PC double beam–column connection exhibited maximum drift ratios of δ = 5.59%–5.98%, satisfying the requirement for the maximum drift ratios of beam–column connections (= 3.5%) in ACI 374.1–05 (ACI Committee 374, 2005 The displacement ductility ratios ranged from 4.35 to 5.81, which was close to that of SRC with the RC double beam–column connection (= 5.09–5.24), on average. This result indicates that the deformation capacity is identical to that for the RC double beam–column connection.

Energy Dissipation Capacity and Secant Stiffness

Figure 17 shows the variation in the hysteretic energy dissipation per cycle of the specimens with respect to the lateral drift ratio δ. The hysteretic energy dissipation ED per cycle was calculated as the area enclosed by the third load cycle at each drift level. In Fig. 17a, the value of ED for SRC with the RC double beam–column connection was smaller than those for SPC1 and SPC2 with the PC double beam–column connection before δ = 2.5%. However, after δ = 2.5%, the value of ED for SRC with the RC double beam–column connection significantly increased and was greater than those for the PC double beam SPC1 and SPC2. This was because SRC with more distributed cracks at the beam–column joint (Fig. 14a) dissipated energy faster than SPC1 and SPC2 with concentrated cracks at the PC-CIP concrete (Fig. 14b and c). However, by further increasing δ to 6.0%, the ED of the PC double beam SPC1 and SPC2 was close to that of SRC with the RC double beam–column connection.

Fig. 17
figure 17

Energy dissipation capacity of specimens under cyclic lateral loading.

ACI 374.1-05 (ACI Committee 374 2005) recommends that at a drift level of no less than 3.5%, the energy dissipation ratio κ (= ED/Eep) by the third load cycle should be no less than 0.125, where Eep denotes the energy dissipation per cycle attributable to the idealized elastic perfectly plastic behavior (Fig. 17b). As shown in Fig. 17b, regardless of the specimens, the energy dissipation capacity ratio κ was greater than 0.125 at a lateral drift ratio of 3.5%, satisfying the ACI 374.1–05 requirement.

ACI 374.1–05 also requires that, for the third load cycle at a drift level of no less than 3.5%, the secant stiffness for ks ranging from –0.35% to + 0.35% should not be less than 0.05 times the initial stiffness ki. Table 3 summarizes the initial stiffness ki, secant stiffness ks, and ratio ks/ki. In SPC1 and SPC2, with the PC double beam–column connection, the ks/ki ratios were 0.17 to 0.20, which were greater than the ACI 374.1-05 requirement (= 0.05). The ks/ki ratios of SPC1 and SPC2 were not significantly inferior to that of SRC with the RC double beam–column connection (= 0.20).

Shear Strength of Beam–Column Joints

Table 4 presents the joint shear strength and demand, Vjn and Vju, of the specimens evaluated using Eqs. (6) and (7), respectively. The joint shear strength Vjn of SRC with the conventional RC beam–column connection was calculated using γ = 1.2, and the effective joint shear area Aj = 0.5(bb + bc)hc. The joint shear demand Vju for SRC with RC double beam–column connection at the column face was calculated from Eq. (7) using α = 1.25; (C + T') = Astfy (Ast = total area of beam flexural bars at the critical section) and Vcol = the tested peak strength Ptest. On the other hand, in the case of specimens with PC double beam–column connection (SPC1 and SPC2), Vjn was Aj =0.5(bb + bc)(hc-2 s), considering the seating length s = 150 mm. The value of Vju for SPC1 and SPC2 at the end of the PC double beam was calculated from Eq. (7) using α = 1.25; (C + T') = Astfy; Vcol = Ptest.

Table 4 Joint shear strength of test specimens.

Table 4 compares the joint shear demand Vju and capacity Vjn of the specimens. For all specimens, Vjn/Vju was greater than 1.0. This result agrees with the test results showing that joint shear failure did not occur (Fig. 14d–f).

Conclusion

Recently, as a new PC construction method for increasing economy and constructability, a PC double-beam system has been developed. This paper presents the test results of specimens with half-scaled beam–column connection with PC double beams under gravity loading or cyclic lateral loading, to investigate the integrity and structural capacity of the PC double beam–column connection. The major test parameters included the presence of a spliced column and the use of an additional flexural reinforcement at the beam–column joint.

The major findings of the gravity loading test are summarized as follows:

  1. 1.

    All specimens failed in flexural compression at the PC bracket–PC double-beam interface. The plastic hinge length lp of the PC double beam was greater than the effective depth of beam d.

  2. 2.

    In the PC double beam under gravity load, the peak strength was 11%–21% greater than the predicted strength, by the current design code, which indicates that the composite action at the beam–column connection assumed for the PC members was valid for the PC double beam–column under gravity loading.

  3. 3.

    By using additional flexural rebars with a short anchorage length, the load-carrying capacity was increased at the initial loading, but gradually decreased due to the insufficient anchorage length. Thus, it is necessary to secure sufficient anchorage length considering a plastic hinge length.

  4. 4.

    The load-carrying capacity of specimens without the spliced PC column at the joint was comparable to that of specimens with the spliced PC column at the joint, which indicates that the spliced PC column at the joint had negligible effect on structural integrity.

The major findings of the cyclic lateral loading test are summarized as follows:

  1. 1.

    In the RC specimen, initial cracks occurred at the beam section adjacent to the end of the bracket, and gradually propagated toward the beams. In contrast, in the PC specimens, cracks were concentrated on the PC beam–CIP concrete.

  2. 2.

    In the RC specimen, bar-yielding occurred at the beam section adjacent to the end of the bracket and the yield penetration gradually propagated toward the beams. In contrast, in the PC specimens, yielding was concentrated on the top rebars across the RC–PC interface.

  3. 3.

    The peak strength of the PC specimens was 9%–22% smaller than that of the RC specimens. This was because (1) smaller number of longitudinal reinforcement was anchored into the topping concrete at the beam–column joint; (2) the shear span length ls was increased by the seating length s due to the critical section at the PC beam–CIP concrete interface in PC specimens, and (3) the concentrated cracking and bar-yielding at the PC beam–CIP concrete interface did not increase the plastic hinge length. Nevertheless, the strength ratios to the predictions by the current design code were greater than 1.0 in the PC specimens.

  4. 4.

    The seismic performance of specimens without the PC column at the joint was comparable to that of specimens with the PC column at the joint, indicating that the RC column had a negligible effect on structural integrity.

  5. 5.

    The deformation capacity, energy dissipation capacity, secant stiffness, and shear strength of the PC specimens were comparable to those of a conventional RC specimen and satisfied the acceptance criteria of moment frame in the ACI 374.1–05 (ACI Committee 374 2005) provision.

This study focused on the interior joints of PC double beam–column connection. However, an exterior joint of PC double beam–column connection, which is common in actual structure and is known to be more vulnerable to seismic excitations, requires careful design procedure and reinforcement arrangement, similar to those carried out for other new construction methods (Chalioris and Bantilas 2017; Ghayeb et al. 2017). Thus, further study is necessary to investigate the exterior joint of PC double beam–column connection.

Availability of data and materials

Some data analyzed in this study are available in the master’s course thesis of J.Y. Kim at Chungbuk National University in 2018.

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Acknowledgements

This research was carried out with the support of the Researcher Support Program (NRF-2018R1A2B6007559) hosted by  the National Research Foundation of Korea (NRF), and this work (Grants No. C0353376) was supported by Business for Cooperative R&D between Industry, Academy, and Research Institute funded Korea Small and Medium Business Administration in 2015.

Authors' information

J. W. Baek is an Assistant Professor in the Department of Civil Engineering and Environmental Sciences at Korea Military Academy, Seoul, South Korea. He received his BE, MS, and PhD in the Department of Architecture & Architectural Engineering at Seoul National University. His research interests include design and behavior of shear wall under seismic or blast loads.

S. M. Kang is an Associate Professor in the School of Architecture at Soongsil University, Seoul, South Korea. He received his BE, MS, and PhD in the Department of Architecture & Architectural Engineering at Seoul National University. His research interests include earthquake design of building structures (Corresponding Author).

T. H. Kim is a general manager in Architecture Engineering & Research Team at Daelim Industrial Company. He received his PhD in the Department of Architectural Engineering at SungKyunKwan University. His research interests include the design of precast concrete structures.

J. Y. Kim is an Assistant Manager in SENVEX Co. Ltd, Seoul, Korea. He received his BE, MS in the Department of Architectural Engineering at Chungbuk National University. His research interests include development of beam–column joint to secure seismic performance.

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The first author, J. W. Baek, analyzed the data and wrote this manuscript. The corresponding author, S. M. Kang, planned and supervised the project, and reviewed this manuscript. T. H. Kim designed the PC double-beam system, and J.Y. Kim performed the experiments and provided the experimental data. All authors read and approved the final manuscript.

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Correspondence to Su-Min Kang.

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Baek, JW., Kang, SM., Kim, TH. et al. Structural Performance of PC Double Beam–Column Connection Under Gravity and Seismic Loading. Int J Concr Struct Mater 14, 60 (2020). https://doi.org/10.1186/s40069-020-00439-4

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Keywords

  • precast concrete double beam
  • precast beam–column connection
  • cyclic loading test
  • gravity loading test
  • precast concrete slab construction method
  • construction duration