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ACI Structural Journal/May-June 2013 403 Title no. 110-S31 ACI STRUCTURAL JOURNAL TECHNICAL PAPER ACI Structural Journal, V. 110, No. 3, May-June 2013. MS No. S-2011-138.R3 received July 4, 2012, and reviewed under Institute publication policies. Copyright © 2013, American Concrete Institute. All rights reserved, including the making of copies unless permission is obtained from the copyright proprietors. Pertinent discussion including author’s closure, if any, will be published in the March-April 2014 ACI Structural Journal if the discussion is received by November 1, 2013. Cyclic Loading Test for Beam-Column Connection with Prefabricated Reinforcing Bar Details by Tae-Sung Eom, Jin-Aha Song, Hong-Gun Park, Hyoung-Seop Kim, and Chang-Nam Lee A Prefabricated Reinforcing Bar Construction (PRC) Method was developed for fast construction and cost savings. In this study, a prefabricated reinforcing bar connection method for the earthquake design of beam-column connections was developed. Three interior and one exterior full-scale beam-column connections, including a conventional reinforced concrete (RC) specimen, were tested under cyclic loading. The test specimens were designed to satisfy the requirement of the special moment frame specified in ACI 318-08. In the proposed connection method, reinforcing bar welding, coupler splice, and headed bar anchorage were used, considering the PRC Method. The test results showed that the story drift ratio of the PRC beam-column connections exceeded 3.5%, which is the requirement of ACI 374.1-05. The load-carrying capacity, yield stiffness, and energy dissipation capacity of the PRC specimens were comparable to those of the conventional RC specimen. The major failure modes of the PRC specimens were flexural concrete crushing and reinforcing bar fracture at the beam plastic hinge region. The welding of the reinforcing bars and the coupler splice did not significantly affect the performance of the specimens. Keywords: beam-column connection; prefabricated reinforcement details; reinforced concrete; seismic design. INTRODUCTION For fast construction and cost savings of cast-in-place reinforced concrete (RC) construction, various Prefabricated Reinforcing Bar Construction (PRC) methods have been developed. Figure 1 shows two representative methods that are currently used in practice. In the Welded Reinforcement Grid (WRG) 1-3 Method (Fig. 1(a)) and the SEN Steel- Concrete (TSC) Construction Method 4 (Fig. 1(b)), welded reinforcing bar cages are used for vertical members, columns, and walls. On the other hand, in the proposed PRC Method, prefabri- cated reinforcing bar cages are more actively used for beams and columns (refer to Fig. 2). The reinforcing bar cages for columns and beams are prefabricated in reinforcing bar shops. After shipping to the construction site, the column reinforcing bar cage is erected and the beam reinforcing bar cage is connected to it. As shown in Fig. 2, for the fabri- cation of the reinforcing bars, transverse bars are welded to longitudinal bars. For the beam-column connection, coupler splices, steel band plates, and headed bar anchorage are used. The reinforcing bar details differ from those of conventional RC, and in current earthquake design provi- sions, including KCI 2007 5 and ACI 318-08, 6 reinforcing bar welding is not permitted in the potential plastic hinge zone of RC members. Thus, the earthquake resistance of the PRC beam-column connection needs to be verified. Prefabricated reinforcing bars with welded joints have been studied to investigate the effect and failure mode of the welded bars. According to Burton and Hognestad, 7 the fatigue life of the reinforcing bars with tag weld connec- tions was decreased under the working stress level. Razvi and Saatcioglu 8 and Furlong et al. 9 studied the axial load capacities of the columns with welded wire reinforcement. Although the columns were subjected to inelastic strains greater than the yield strain, any detrimental effect or failure in the weld connection was not reported in both studies. Saatcioglu and Grira 1 used WRGs for the lateral confine- ment of columns. Although the WRG failed at large inelastic lateral deformations, the longitudinal bars, which were weld-connected to the WRGs, did not fail. From the test results, Saatcioglu and Grira 1 recommended that, to secure ductile behavior of columns under lateral loading, the grid bar having a welded joint should have at least 4% elongation capacity in tension. In this study, prefabricated reinforcing bar details for inte- rior and exterior beam-column connections were developed. The PRC connections were tested under cyclic loading to investigate earthquake resistance. The PRC connections were designed to full scale to satisfy the requirements of the special moment frame specified in ACI 318-08. 6 The perfor- Fig. 1—Existing prefabricated reinforcing bar construc- tion methods.

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Page 1: ACI STRUCTURAL JOURNAL TECHNICAL PAPER - …senkuzo.com/sen/wp-content/uploads/2014/12/1000033.pdf · ACI Structural Journal/May-June 2013 403 Title no. 110-S31 ACI STRUCTURAL JOURNAL

ACI Structural Journal/May-June 2013 403

Title no. 110-S31

ACI STRUCTURAL JOURNAL TECHNICAL PAPER

ACI Structural Journal, V. 110, No. 3, May-June 2013.MS No. S-2011-138.R3 received July 4, 2012, and reviewed under Institute

publication policies. Copyright © 2013, American Concrete Institute. All rights reserved, including the making of copies unless permission is obtained from the copyright proprietors. Pertinent discussion including author’s closure, if any, will be published in the March-April 2014 ACI Structural Journal if the discussion is received by November 1, 2013.

Cyclic Loading Test for Beam-Column Connection with Prefabricated Reinforcing Bar Detailsby Tae-Sung Eom, Jin-Aha Song, Hong-Gun Park, Hyoung-Seop Kim, and Chang-Nam Lee

A Prefabricated Reinforcing Bar Construction (PRC) Method was developed for fast construction and cost savings. In this study, a prefabricated reinforcing bar connection method for the earthquake design of beam-column connections was developed. Three interior and one exterior full-scale beam-column connections, including a conventional reinforced concrete (RC) specimen, were tested under cyclic loading. The test specimens were designed to satisfy the requirement of the special moment frame specified in ACI 318-08. In the proposed connection method, reinforcing bar welding, coupler splice, and headed bar anchorage were used, considering the PRC Method. The test results showed that the story drift ratio of the PRC beam-column connections exceeded 3.5%, which is the requirement of ACI 374.1-05. The load-carrying capacity, yield stiffness, and energy dissipation capacity of the PRC specimens were comparable to those of the conventional RC specimen. The major failure modes of the PRC specimens were flexural concrete crushing and reinforcing bar fracture at the beam plastic hinge region. The welding of the reinforcing bars and the coupler splice did not significantly affect the performance of the specimens.

Keywords: beam-column connection; prefabricated reinforcement details; reinforced concrete; seismic design.

INTRODUCTIONFor fast construction and cost savings of cast-in-place

reinforced concrete (RC) construction, various Prefabricated Reinforcing Bar Construction (PRC) methods have been developed. Figure 1 shows two representative methods that are currently used in practice. In the Welded Reinforcement Grid (WRG)1-3 Method (Fig. 1(a)) and the SEN Steel-Concrete (TSC) Construction Method4 (Fig. 1(b)), welded reinforcing bar cages are used for vertical members, columns, and walls.

On the other hand, in the proposed PRC Method, prefabri-cated reinforcing bar cages are more actively used for beams and columns (refer to Fig. 2). The reinforcing bar cages for columns and beams are prefabricated in reinforcing bar shops. After shipping to the construction site, the column reinforcing bar cage is erected and the beam reinforcing bar cage is connected to it. As shown in Fig. 2, for the fabri-cation of the reinforcing bars, transverse bars are welded to longitudinal bars. For the beam-column connection, coupler splices, steel band plates, and headed bar anchorage are used. The reinforcing bar details differ from those of conventional RC, and in current earthquake design provi-sions, including KCI 20075 and ACI 318-08,6 reinforcing bar welding is not permitted in the potential plastic hinge zone of RC members. Thus, the earthquake resistance of the PRC beam-column connection needs to be verified.

Prefabricated reinforcing bars with welded joints have been studied to investigate the effect and failure mode of the welded bars. According to Burton and Hognestad,7 the fatigue life of the reinforcing bars with tag weld connec-tions was decreased under the working stress level. Razvi

and Saatcioglu8 and Furlong et al.9 studied the axial load capacities of the columns with welded wire reinforcement. Although the columns were subjected to inelastic strains greater than the yield strain, any detrimental effect or failure in the weld connection was not reported in both studies. Saatcioglu and Grira1 used WRGs for the lateral confine-ment of columns. Although the WRG failed at large inelastic lateral deformations, the longitudinal bars, which were weld-connected to the WRGs, did not fail. From the test results, Saatcioglu and Grira1 recommended that, to secure ductile behavior of columns under lateral loading, the grid bar having a welded joint should have at least 4% elongation capacity in tension.

In this study, prefabricated reinforcing bar details for inte-rior and exterior beam-column connections were developed. The PRC connections were tested under cyclic loading to investigate earthquake resistance. The PRC connections were designed to full scale to satisfy the requirements of the special moment frame specified in ACI 318-08.6 The perfor-

Fig. 1—Existing prefabricated reinforcing bar construc-tion methods.

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404 ACI Structural Journal/May-June 2013

Tae-Sung Eom is an Assistant Professor at Catholic University of Daegu, Daegu, South Korea. He received his BS, MS, and PhD in architectural engineering from Seoul National University, Seoul, South Korea. His research interests include numer-ical analysis and earthquake design of reinforced concrete structures.

Jin-Aha Song is a Graduate Student at Seoul National University. She received her BS in architectural engineering from Ewha Womans University, Seoul, South Korea. Her research interests include earthquake resistance of beam-column connections.

Hong-Gun Park is a Professor of architectural engineering at Seoul National University. He received his BS and MS in architectural engineering from Seoul National University and his PhD in civil engineering from the University of Texas, Austin, Austin, TX. His research interests include numerical analysis and earthquake design of reinforced concrete structures.

Hyoung-Seop Kim is a Project Manager at SEN Structural Engineers Co., Ltd., Seoul, South Korea. He received his BE and MS in architectural engineering from Incheon National University, Yeonsu-gu, South Korea, and Dankook University, Yongin, South Korea, respectively. His research interests include seismic control and design of buildings.

Chang-Nam Lee is a CEO and President of SEN Structural Engineers Co., Ltd. He received his BS and MS in architectural engineering from Seoul National University. His research interests include seismic retrofit design, structural safety monitoring, and structural safety inspection.

mance of the PRC connections—including load-carrying capacity, stiffness, deformation capacity, energy dissipation capacity, and failure mode—was evaluated on the basis of the requirements of ACI 374.1-05.10 In this test, axial load was not applied to columns. If axial load were applied to columns, the overall behavior of beam-column connections would be more realistic. However, this study focused on the effects of the proposed reinforcing bar details such as coupler splice, endplate anchorage, weld connection, and others on the overall earthquake resistance of beam-column connec-tions. The performance of such reinforcing bar details is not directly affected by the axial load of the columns.

PRFABRICATED REINFORCING BAR DETAILSFigure 2 shows the proposed PRC Method. The column

reinforcing bar cage is prefabricated by shop welding between the longitudinal reinforcing bars and transverse hoops. At the location of the beam-column joint, steel band plates with holes and U-grooves for the connection of beam reinforcing bars are welded to the column reinforcing bars. The holes are used to connect the reinforcing bars in the beam reinforcing bar cage, and the U-grooves are used to place additional beam reinforcing bars after assembling the column cage and the beam cage. The beam reinforcing bar cage is also prefabricated by shop welding and consists of top and bottom reinforcing bars (four longitudinal reinforcing bars), transverse hoops, and diagonal bars (Fig. 2(a)). The prefabricated beam reinforcing bar cage has a form of truss so that the beam reinforcing bar cage can resist full or partial construction load, including its self-weight.

As shown in Fig. 2(b), couplers are used to connect the beam cage reinforcing bars to the reinforcing bars in the joint. To prevent reinforcing bar slip in the beam-column joint, the couplers are tightened toward the steel band plate. Only four reinforcing bars in the beam cage are connected to the joint reinforcing bars via couplers. Figure 2(c) shows the assembly of the PRC moment frame. When the four reinforcing bars are not sufficient to resist the negative and positive moments of the beam, additional top and bottom reinforcing bars are placed in the beam reinforcing bar cage. Figure 2(d) shows the prefabricated reinforcing bar detail of an exterior beam-column connection. In the exterior beam-column joint, headed bars are used for the anchorage of the beam reinforcing bars.

Fig. 2—Proposed PRC Method.

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ACI Structural Journal/May-June 2013 405

RESEARCH SIGNIFICANCEAs shown in Fig. 2, the proposed PRC Method uses

reinforcing bar welding, coupler splice, and headed bar anchorage, which differ from the reinforcing bar details for conventional RC structures. Therefore, the effects of the following aspects on the earthquake resistance of the proposed PRC beam-column connection should be verified:

1. The coupler splices for the top and bottom reinforcing bars of the beam are located at the column face that is the flexural critical section of the beam. Thus, large plastic strains are concentrated at the coupler splices, and this may cause premature tensile fracture of the couplers or the reinforcing bars.

2. In current design codes, reinforcing bar welding is not permitted in potential plastic hinge zones. Reinforcing bar welding used in the proposed PRC Method may cause tensile fracture in the reinforcing bars by developing residual stresses and microcracks due to welding heat and/or by making a change to the reinforcing bar section.

3. The coupler splices and the headed bars should prevent excessive reinforcing bar slip in the beam-column joint.

TEST PROGRAMFour full-scale beam-column connections, including

a conventional RC specimen, were tested under cyclic loading. Figure 3 shows the dimensions and details of the specimens. Table 1 presents the properties of the specimens. Specimens PRC1, PRC2, and RC (a conventional RC spec-imen) were cruciform specimens. Specimen PRC3 was a T-shaped specimen. All specimens were designed according to the strong-column/weak-beam concept. The spacing and number of lateral reinforcing bars in the column and beam, shear strength of the beam-column joint, and

ratio of the column depth to the reinforcing bar diameter (hc/db) satisfied the requirements for the special moment frame in ACI 318-08.6 The design details of the specimens are presented in the Appendix.*

Figure 3(a) shows the cruciform Specimen PRC1. The net height of the column and the net length of the beam were 2100 and 4760 mm (82.7 and 187 in.), respectively. The dimensions of the cross sections were 600 x 700 mm (23.6 x 27.6 in.) for the column and 400 x 500 mm (15.7 x 19.7 in.) for the beam. Six D29 (db = 29 mm [1.14 in.]) and four D22 (db = 22 mm [0.866 in.]) bars were used as the longitudinal reinforcing bars in the column. For transverse hoops, D16 (db = 16 mm [0.63 in.]) bars with 100 mm (3.94 in.) spacing were used. The hoops were welded to the longitudinal reinforcing bars by tack welding. As shown in Fig. 3(a), at the beam-column joint, the upper and lower band plates with holes and U-grooves were welded to the longitudinal column reinforcing bars. The size, location, and number of the holes and U-grooves are determined by those of the beam reinforcing bars passing through. Four D29 (r = 0.0149) and two D22 + one D25 (db = 25 mm [0.984 in.]) (r = 0.0073) were used as the top and bottom reinforcing bars of the beam, respectively. For the reinforcing bar connection at the beam-column joint, coupler splices were used for the two D29 and two D22 bars located at the four corners of the beam cross section (refer to Fig. 4). To minimize the number of coupler splices, the remaining two D29 bars and one D25 bar were placed through the U-grooves of the steel band plates without coupler splices after assembling the column and beam cages

*The Appendix is available at www.concrete.org in PDF format as an addendum to the published paper. It is also available in hard copy from ACI headquarters for a fee equal to the cost of reproduction plus handling at the time of the request.

Fig. 3—Dimensions and reinforcing bar details of test specimens. (Note: Dimensions in mm; 1 mm = 0.03937 in.)

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406 ACI Structural Journal/May-June 2013

Figure 3(b) shows the reinforcing bar detail of the cruci-form Specimen PRC2. The configuration, dimensions, and reinforcement of the column were the same as those of PRC1. In PRC2, to avoid the shear damage and reinforcing bar slip that could occur at the beam-column joint, the beam-column joint was strengthened with four additional hooked reinforcing bars. By using the strengthening strategy, it was intended that plastic hinges of beams would develop away from the column face (refer to the Appendix). The top hooked reinforcing bars (two D29; 180-degree hook) and the bottom hooked reinforcing bars (two D22; 90-degree hook) were extended to 250 and 400 mm (9.84 and 15.7 in.) from the column face, respectively (refer to Fig. 3(b)), so that concrete damage was not concentrated at a location. The 180-degree hook was used for the top D29 bars because the beam depth did not accommodate the vertical bar length of the standard 90-degree hook (ACI 318-08,6 Section 12.5)—that is, 12 times the bar diameter extension. As shown in Fig. 3(b) and Table 1, two D29 + two D25 (r = 0.0133) and three D22 (r = 0.0066) bars were used for the top and bottom reinforcing bars in the beam, respectively. The reinforcing bar areas of PRC2 were less than those of PRC1. However, because the critical sections for the beam flexural moment were moved by 250 and 400 mm (9.84 and 15.7 in.) away from the column face, the load-carrying capacity of PRC2 was expected to be slightly greater than that of PRC1.

Figure 3(c) shows the T-shaped Specimen PRC3, which is an exterior beam-column connection. The net height of the column and the net length of the beam were 2100 and 2380 mm (82.7 and 93.7 in.), respectively. The dimensions of the cross section were 500 x 500 mm (19.7 x 19.7 in.) for the column and 400 x 500 mm (15.7 x 19.7 in.) for the beam. As shown in Table 1 and Fig. 3(c), the reinforcing bar details of the beam were the same as those of PRC1. Because the top and bottom reinforcing bars of the beam were terminated at the

Fig. 4—Coupler splice and headed bar anchorage. (Note: 1 mm = 0.03937 in.)

Table 1—Properties of test specimens

Specimens RC (cruciform) PRC1 (cruciform) PRC2 (cruciform) PRC3 (T-shaped)

Beam

Dimensions, mm x mm 400 x 500 400 x 500 400 x 500 400 x 500

Top reinforcing bars (r, %) 4 D29 (1.49) 4 D29 (1.49) 2 D29+ 2 D25 (1.33) 4 D29 (1.49)

Bottom reinforcing bars (r, %) 2 D22 + 1 D25 (0.73) 2 D22 + 1 D25 (0.73) 3 D22 (0.66) 2 D22 + 1 D25 (0.73)

Joint strengthening bars* (dj, mm) — —2 D29 and 2 D22

(250 and 400)—

Stirrups at plastic hinge (rv, %) D13 at 100 (0.66) D13 at 100 (0.66) D13 at 100 (0.66) D13 at 100 (0.66)

Positive and negative Mn (Mn′)†, kN∙m 300 and 524 301 and 530264 and 521

(422 and 747)302 and 537

Column

Dimensions, mm x mm 700 x 600 700 x 600 700 x 600 500 x 500

Main reinforcing bar ratio (r, %) 6 D29 + 4 D22 (1.31) 6 D29 + 4 D22 (1.31) 6 D29 + 4 D22 (1.31) 6 D29 + 4 D22 (1.89)

Hoops (rh, %) D16 at 100 (1.31) D16 at 100 (1.31) D16 at 100 (1.31) D16 at 100 (1.89)

Mn (=Mnc), kN∙m 779 782 785 449

Jointhc/db

‡ 24.4 24.4 41.8 14.5

Joint shear Vjn and Vju, kN§ 2390 and 2163 2538 and 2160 2723 and 2375 1750 and 1419

Column-to-beam moment ratio SMnc/SMnb|| 1558/824 = 1.89 1563/831 = 1.98 1569/1169 = 1.34 898/537 = 1.67

*Ninety-degree hooked bars—two D22 and two D29—were used at top and bottom of beam section, respectively (refer to Fig. 3(b)). †Mn is positive and negative moment capacity at critical section. In case of PRC2, Mn′ is moment capacity at column face, including contribution of strengthening 90-degree hooked bars (refer to the Appendix). ‡hc is column dimension parallel to beam reinforcing bars and db is maximum diameter of beam top and bottom reinforcing bars. For PRC2 and PRC3, (hc + Sdj)/db and ldh/db were used, respectively. Refer to the Appendix. §Calculations are presented in detail in the Appendix and Fig. A1. ||In RC, PRC1, and PRC3, Mnb = Mn. In PRC2, Mnb = Mnln/(ln – dj), where dj = 250 or 400 mm (9.84 or 15.7 in.) and ln = 2030 mm (79.9 in.). Refer to the Appendix and Fig. A1. Notes: 1 mm = 0.03937 in.; 1 kN∙m = 8851 lbf; 1 kN = 0.2248 kip.

(refer to Fig. 3(a)). In the beam cage, transverse hoops (D13) were connected to the top and bottom reinforcing bars by tack welding (flare-bevel-groove welding; refer to Fig. 5(a)). The lap splice of the transverse hoops was welded by flare-V-groove welding, and the effective weld length of the lap splice was lh = 65 mm (2.65 in.) (=5.0dh ≥ 4.4dh; refer to Fig. 5(b)). According to ACI 318-08,6 Chapter 21, the first hoop was located within 50 mm (2 in.) from the column face, and the spacing of the hoops was 100 mm (4 in.) (rv = 0.0066). Diagonal reinforcing bars (D13; db = 13 mm [0.512 in.]) on each side of the beam were also welded to the top and bottom reinforcing bars by flare-bevel-groove welding (refer to Fig. 5(a)).

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ACI Structural Journal/May-June 2013 407

beam-column joint, a mechanical anchorage consisting of a nut and washer was used for the reinforcing bar development (refer to Fig. 3(c) and 4). The nut and washer were tightened with band plates to prevent anchorage slip. The development length of the headed bars (=420 mm [16.5 in.]) satisfied the minimum requirement 0.75afydb/(6.2 cf ′ )(=281 mm [11.1 in.]) specified in ACI 352R-0211 (a = material over-strength factor = 1.25; fy = yield stress of reinforcing bar = 519 MPa [75.3 ksi]; fc′ = 61.0 MPa [8.85 ksi]; and db = 29 mm [1.14 in.]).11-13

Cruciform Specimen RC was a conventional beam-column connection constructed by in-place reinforcing bar work. Figure 3(d) shows the reinforcing bar details of Specimen RC. The dimensions and reinforcing bar arrange-ment of the column and beam were the same as those of PRC1 (refer to Table 1). However, reinforcing bar welding, coupler splice, band plate, diagonal reinforcing bar, and headed reinforcing bar anchorage were not used.

Table 2 shows the material properties of the concrete and reinforcing bars. High-strength concrete of fc′ equaling approximately 47.0 to 61.0 MPa (6.96 to 8.85 ksi) was used. The concrete strengths were the means of three compression tests. For the D22, D25, and D29 reinforcing bars, SD500W steel grade (Korean Industrial Standard Grade 500, weldable reinforcing bars) was used. Table 2 shows the areas, yield strengths, tensile strengths, strains at hardening, and strains at fracture of the reinforcing bars. The tension tests of rein-forcing bar specimens were conducted in accordance with

the Korean Industrial Standard (KS B 0802) for direct tension test of steel bars, which is an equivalent to ASTM A370. The material properties were the mean values of three tension tests. Particularly, D25 bars used for the beam bottom bars showed a relatively small fracture strain—5.36%—which was less than 12%, the minimum requirement specified in the Korean Industrial Standard. The couplers for reinforcing bar splice were verified by direct tension tests, satisfying the requirement of Type 2 mechanical splice specified in ACI 318-08.6 For shop welding between reinforcing bars, flux-cored arc welding (FCAW) and YFW-C50DR (E71T-1; fy = 545 MPa [79 ksi]; fu = 572 MPa [83 ksi]) were used for the welding method and the weld metal, respectively.

Figure 5 shows the shop welding details of the hoop and diagonal bars, according to KS B ISO 17660-1:2007 (Korean Industrial Standard for reinforcing bar welding certified by the International Organization for Standardization [ISO]). The hoops and diagonal bars were welded to the outside face and the inside face of the top and bottom longitudinal bars, respectively (refer to Fig. 5(a)). Basically, the welding between the reinforcing bars is used for the temporary erec-tion and fabrication of the column and beam bar cages during construction. For this purpose, the standard welding details specified in KS B ISO 17660-1:2007 provide suffi-cient strength and rigidity for the reinforcing bar joints. An exception, however, is the welded lap splice of the trans-verse hoops in the beam cage (refer to Fig. 5(b)). Because the transverse hoops are designed to develop the yield stress,

Fig. 5—Details of reinforcing bar welding.

Table 2—Material tests

Concrete Reinforcing bars

Specimen RC PRC1 PRC2 PRC3 Bar size D22 D25 D29

Compressive strength fc′, MPa 47 53 61 61

Area, mm2 387 507 642

Yield stress fy, MPa 538 564 519

Tensile strength fu, MPa 684 594 661

Strain at hardening 0.0179 0.0105 0.0092

Strain at fracture 0.121 0.0536 0.120

Notes: 1 MPa = 145 psi; 1 mm2 = 0.00155 in.2

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408 ACI Structural Journal/May-June 2013

the welded lap splice should be able to develop the yield strength of the transverse reinforcing bar. Thus, the length of the welded lap splice should satisfy the following condition

2

0.64

hh yw yh

dal f f

p≥ (1)

where a is the thickness of the weld joint; lh is the length of the welded lap splice (refer to Fig. 5(b)); fyw and fyh are yield strengths of the weld metal and the transverse hoops, respectively; and dh is the diameter of the transverse hoop. By assuming a ≥ 0.3dh (refer to Fig. 5) and fyw ≥ fyh, approxi-mately, the length of the welded lap splice should satisfy lh ≥ 4.4dh.

Figure 6 shows the loading and support condition of the specimens. The column was supported at the bottom hinge. The beam ends were vertically supported, allowing the horizontal movement. Cyclic lateral loading was applied at the top of the column with a 1000 kN (225 kip) actuator, controlled by the lateral displacement. The target lateral

drift ratio d (=D/h, where D is the lateral displacement at the loading point and h is the net height of the column) was increased by 0.25% until the total lateral drift ratio reached 1.0% and then increased by 0.5%. Load cycles were repeated three times at each lateral drift ratio. Linear vari-able displacement transducers (LVDTs) were installed at all hinge and roller supports to measure the rigid-body motions of the specimens.

TEST RESULTSLateral load-drift ratio relationship and failure mode

Figure 7 shows the lateral load-drift ratio relationships of the test specimens. Figure 8 shows the crack patterns and failure modes at the end of the tests. The maximum strength Pu, maximum displacement Du (maximum drift ratio du), yield displacement Dy (yield drift ratio dy), ductility (m = Du/Dy), yield stiffness ky, and failure mode were summarized in Table 3. The yield displacement Dy was defined using the equal energy principle.14 The maximum displacement Du was defined as the post-peak displacement corresponding to 75% of the maximum strength Pu.10

Figure 7(a) shows the lateral load-drift ratio relation-ship of the conventional RC specimen. Yielding of the beam flexural reinforcing bars occurred at a 1.10% drift ratio. Significant strength degradation did not occur during repeated cyclic loading until the maximum drift ratio du = 4.26%. Figure 8(a) shows the failure mode of Specimen RC. Significant inelastic flexural deformation occurred at the beam plastic hinge zone. For this reason, concrete crushing occurred at the bottom of the beam end and, at the same time, bar buckling occurred. Ultimately, tensile fracture of the bottom D25 bar occurred due to the low-cycle fatigue.15 In Table 2, D25 bars exceptionally showed a low fracture strain. Such poor ductility of D25 bars can accelerate reinforcing bar fracture. In other specimens (PRC1, PRC2, and PRC3), however, bar fracture occurred in D22 bars. This result indi-

Fig. 6—Test setup for interior and exterior connection speci-mens. (Note: 1 mm = 0.03937 in.)

Fig. 7—Lateral load-drift ratio relationships of specimens. (Note: 1 kN = 0.2248 kip.)

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ACI Structural Journal/May-June 2013 409

cates that the low ductility of the D25 bars was not the direct cause for the bar fracture.

As presented in Table 1, hc/db (=24.4) of RC was greater than the minimum requirement (=20fy/420 = 23.8; fy in MPa) specified in ACI 352R-0211 (hc is the column dimension parallel to beam reinforcing bars, and db is the maximum diameter of beam reinforcing bars). Furthermore, in Table 1, the nominal shear capacity Vjn at the beam-column joint was greater than the shear demand Vju (refer to the Appendix). As a result, bond slip and diagonal cracking were minimized at the beam-column joint (refer to Fig. 8(a)). Thus, pinching was not severe in the lateral load-drift ratio relationship in Fig. 7(a).

Figures 7(b) and 8(b) show the lateral load-drift ratio relationship and the failure mode of PRC1. The test result of PRC1 was similar to that of Specimen RC. Yielding of the beam plastic hinge occurred at a 1.23% drift ratio. At the maximum drift ratio du = 4.94%, flexural concrete crushing occurred at the beam end. Ultimately, tensile fracture occurred in the bottom D22 bars due to the low-cycle fatigue15 (refer to Fig. 8(b) and Table 3). Similarly to Specimen RC, diagonal cracking at the beam-column joint

was minimized. As shown in Fig. 7(b), however, a sudden strength decrease occurred during the second load cycle at a –1.85% drift ratio. The investigation after the end of the test showed that in one out of eight couplers, reinforcing bar slip occurred due to the loosened thread of the coupler (refer to Fig. 8(b)). The reinforcing bar, however, was not pulled out from the coupler completely. Thus, the reinforcing bar slip did not significantly decrease the overall load-carrying capacity of PRC1.

Figures 7(c) and 8(c) show the test results of Specimen PRC2, which was strengthened with hooked reinforcing bars. The maximum strength Pu of PRC2 was 9.8% greater than that of RC and PRC1. However, the maximum drift ratio du = 3.63% of PRC2 was less than that of RC and PRC1. As shown in Fig. 8(c), due to the hooked reinforcing bars strengthening the beam-column joint, the beam plastic hinge occurred far from the column face. At the plastic hinge zone, flexural concrete crushing occurred. Ultimately, PRC2 failed due to crushing of the bottom and web concrete and tensile fracture of the bottom D22 bars (refer to Fig. 8(c)). Neither the reinforcing bar slip nor the fracture occurred at the coupler splice. As mentioned,

Fig. 8—Crack patterns and failure modes of specimens.

Table 3—Summary of test results

Specimen

Load-carrying capacity, kN Deformation capacity (mm, %)Yield stiffness,

kN/mmky (=Py/Dy)

Failure mode*

Observed Pu Predicted Pn Pu/Pn Yield Dy (dy)Maximum

Du (du)Ductility m

(=Du/Dy)Beam plastic

hingeCoupler splice

RC(+) 509 460 1.11 23.1 (1.10) 80.5 (4.26) 3.87 20.8EC/BF NA

RC (–) 508 460 1.10 23.1 (1.10) 86.9 (4.14) 3.76 20.9

PRC1 (+) 531 464 1.14 25.8 (1.23) 104 (4.94) 4.02 19.4EC/BF Bar slip

PRC1 (–) 470 464 1.01 23.3 (1.11) 87.4 (4.16) 3.75 17.9

PRC2 (+) 578 515 1.12 28.4 (1.35) 76.2 (3.63) 2.79 19.6 EC/WB/BFNo failure

PRC2 (–) 564 515 1.10 28.8 (1.37) 80.6 (3.84) 2.80 18.5 EC/WB/BF

PRC3 (+) 356 286 1.25 34.2 (1.63) 80.0 (3.81) 2.34 10.0 ECNo failure

PRC3 (–) 164 161 1.02 30.9 (1.47) 104 (4.95) 3.37 4.9 BF*EC is flexural concrete crushing at bottom end; BF is reinforcing bar fracture; WC is web concrete crushing; NA is not available; 1 kN = 0.2248 kip; 1 mm = 0.03937 in.; 1 kN/mm = 5.710 kip/in.

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410 ACI Structural Journal/May-June 2013

the beam plastic hinge of PRC2 was moved by dj = 250 and 400 mm (9.84 and 15.7 in.) from the column face due to the hooked reinforcing bars, and this allowed the ability to increase the development length of the beam reinforcing bars in the beam-column joint. Thus, the hc/db ratio of PRC2 was increased to 41.8 by the increased effective joint depth hc + Sdj (that is, the distance between the right and left beam critical sections) (refer to Table 1 and the Appendix). As a result, diagonal cracking and bond slip were restrained at the beam-column joint, and pinching was significantly reduced in the lateral load-drift ratio relationship.

Figure 7(d) shows the test result of the exterior beam-column connection Specimen PRC3. Because the amount of bottom reinforcing bars in the beam was half of that of the top reinforcing bars, the lateral load-drift ratio relationship showed an asymmetric cyclic curve. The maximum strength Pu (= +356 kN [+80.0 kip]) of the positive loading was two times greater than Pu = –164 kN (–36.9 kip) of the negative loading. However, the maximum drift ratio du = 3.81% of the positive loading was less than du = 4.95% of the negative loading. As shown in Fig. 7(d) and 8(d), a sudden strength degradation occurred at a 3.30% drift ratio due to the flexural concrete crushing at the beam bottom. Ultimately, tensile fracture of the bottom D22 bars occurred under the nega-tive loading (refer to Fig. 8(d)). The development length of

the headed bars satisfied the minimum requirement specified in ACI 352R-0211 (refer to the Appendix). Thus, significant bond slip and anchorage failure did not occur at the beam-column joint. There was no failure at the coupler splices of the top and bottom reinforcing bars in the beam.

Load-carrying capacityBecause the specimens were designed according to

the strong-column/weak-beam concept, the load-carrying capacity of the specimens can be calculated by using the moment capacities at the beam plastic hinge zone. In Fig. 9, the load-carrying capacity Pn of the interior and exterior connections can be calculated as follows.

( )1 2 for interior connection2nlP R Rh

= + (2a)

for exterior connectionnlP Rh

= (2b)

where R1, R2, and R are the vertical reactions at the beam supports; h is the net height of the column; and l is the net length of the beam. The vertical reactions at the beam supports (R1, R2, and R) can be calculated by dividing the moment capacity at the beam critical section by the beam shear span between the roller support and the critical section (refer to Fig. 9). As shown in Fig. 9, the beam critical sections of RC, PRC1, and PRC3 are located at the column face. In PRC2, the beam critical sections are located at the end of the hooked reinforcing bars (refer to Fig. 3(b)).

The nominal load-carrying capacities Pn of the test speci-mens predicted by Eq. (2a) and (2b) are presented in Table 3. The predicted load-carrying capacities Pn of the specimens were less than the measured maximum strengths Pu. Such underestimation of the load-carrying capacity is attributed to the cyclic strain hardening of the flexural reinforcing bars, which was not considered in the calculation. In Table 3, the Pu/Pn ratio for PRC1(–) with a loosened coupler is 1.01, which is 10% less than the other Pu/Pn ratios. The other Pu/Pn ratios are greater than 1.10, except for that of PRC3(–). Thus, considering the effect of reinforcing bar strain hard-ening increasing the strength by 10%, the strength Pu of PRC1(–) was decreased by 10% by the loosened thread of the coupler.

In the case of the PRC specimens, the diagonal D13 bars may contribute somewhat to the strength, stiffness, and diagonal cracking of the specimens. However, such favor-able effects of the diagonal D13 reinforcing bars are not reliable in the ultimate state because the tag weld connec-tion between the diagonal and longitudinal reinforcing bars cannot guarantee full development of the reinforcing bar strength. Therefore, in this study, the favorable effect of the diagonal D13 bars was not considered in the calculation of the lateral load-carrying capacity of the specimens.

Deformation capacity and ductilityFigure 10(a) shows the envelope curve of the test speci-

mens. The maximum drift ratio du, yield drift ratio dy, and ductility m obtained from the test are presented in Table 3. Figure 10(b) shows the definition of du and dy. According to the equal energy principle, the yield drift ratio dy was defined by using the idealized bilinear curve (solid line in Fig. 10(b)),

Fig. 9—Calculation of load-carrying capacity. (Note: Dimensions in mm; 1 mm = 0.03937 in.)

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ACI Structural Journal/May-June 2013 411

dissipating the same energy as the envelope curve (dashed line in Fig. 10(b)).14 The ductility m was then calculated as du/ dy. As shown in Table 3, the maximum drift ratio du of the conventional Specimen RC was 4.26%. The PRC Specimens PRC1, PRC2, and PRC3 showed du = 3.63 to 4.95%, which were greater than the minimum requirement of 3.5% for the earthquake-resistant moment frame specified in ACI 374.1-05.10 The displacement ductility m of the test specimens ranged from 2.34 to 4.02.

As presented in Table 3, the maximum drift ratio and ductility of PRC1 were du = 4.94% and m = 4.02, respec-tively, which are comparable to those of the conventional Specimen RC (du = 4.26% and m = 3.87). On the other hand, PRC2, which was strengthened by hooked reinforcing bars, showed less deformation capacity (du = 3.63% and m = 2.69) than that of RC. The reason for this can be explained as follows. First, because of the strengthening hooked reinforcing bars, the yielding of beam reinforcing bars and subsequent flexural concrete crushing were concentrated at the location of the hook anchorage, which was the beam critical section. Furthermore, because of the relocation of the beam plastic hinge zone, the net beam length between the critical section and the vertical support was decreased, which increased the plastic rotation demand at the critical section (refer to Fig. 11).

In the exterior beam-column connection in Specimen PRC3, the maximum deformation capacity was du = 3.81% and m = 2.34 for the positive loading and du = 4.95% and m = 3.37 for the negative loading. The deformation capacity of PRC3 was less in the positive loading, which caused a negative moment in the beam.

Yield stiffness and hysteretic energy dissipationThe yield stiffnesses ky (=Py/Dy; Py is yield strength

[refer to Fig. 10(b)]) of the test specimens are presented in Table 3. As shown in Table 3, the yield stiffnesses of PRC1 and PRC2 were comparable to that of the conven-tional connection in Specimen RC.

Figure 12(a) and (b) compare the hysteretic energy dissipa-tion ED per load cycle and the hysteretic energy ratio ED/Eep, respectively. The variable ED denotes the area enclosed by a load cycle, and Eep denotes the area of the parallelogram by the idealized elastic-perfectly plastic behavior (refer to Fig. 12(b)). The maximum strength Pu of PRC2 was greater than that of RC and PRC1. Furthermore, reinforcing bar slip was minimized at the beam-column joint (refer to the following section). For this reason, as shown in Fig. 12(a), the hysteretic energy dissipation ED per load cycle of PRC2 was slightly greater than that of RC and PRC1. In the exterior beam-column connection Specimen PRC3, only one plastic hinge developed at the beam. Thus, ED of PRC3 was approx-imately half of RC or PRC1. ACI 374.1-0510 requires that at the lateral drift ratio du = 3.5%, the hysteretic energy ratio ED/Eep should be greater than 0.125. As shown in Fig. 12(b), all specimens with the proposed connection details satisfied the energy requirement of ACI 374.1-05.10

Reinforcing bar strain at beam-column jointFigure 13 compares the strains of the bottom reinforcing

bars in the beams. In the figure, BB1 and BB2 are reinforcing bar strain gauges located at the center of the beam-column joint and at 30 mm (1.18 in.) inside the joint, respectively. BB3 and BB4 indicate strain gauges outside the joint at 30 and 400 mm (1.18 and 15.7 in.) from the column face,

Fig. 10—Envelope curves of test specimens. (Note: 1 kN = 0.2248 kip.)

Fig. 11—Beam plastic rotation demand varying with plastic hinge location.

respectively. In the case of RC, PRC1, and PRC3, BB3 and BB4 were subjected to tensile plastic strains during cyclic loading, while BB1—at the center of the joint—remained elastic (refer to Fig. 13(a), (b), and (d)). Although BB2 was located inside the joint, plastic strains were developed by the propagation of reinforcing bar yielding from the beam

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412 ACI Structural Journal/May-June 2013

Fig. 13—Strains of bottom reinforcing bars in beams. (Note: 1 mm = 0.03937 in.; 1 kN = 0.2248 kip.)

Fig. 12—Hysteretic energy dissipation of beam-column connections. (Note: 1 kN-m = 0.737 kip-ft.)

BB4, located 400 mm (15.7 in.) from the column face, was subjected to tensile plastic strain.

The beam reinforcing bars of RC, PRC1, and PRC3 were subjected to tensile plastic strains at BB2, which was inside the joint. Such plastic strains inside the joint can create reinforcing bar slip to some extent at the column face of RC, PRC1, and PRC3, as shown in Fig. 14. On the other hand, the beam reinforcing bars of PRC2 remained elastic at BB2 and BB3 because the beam-column joint was strengthened with

plastic hinge. In particular, BB2 of Specimen RC was subjected to greater plastic strains than those of PRC1 and PRC3. This is because the couplers and steel band plates for the beam reinforcing bar splice restrained the propa-gation of reinforcing bar yielding. Figure 13(c) shows the reinforcing bar strains of PRC2 strengthened with addi-tional hooked reinforcing bars. Because the hook anchorage was located 250 mm (9.84 in.) from the column face, BB1, BB2, and BB3 remained elastic during cyclic loading, while

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ACI Structural Journal/May-June 2013 413

hooked reinforcing bars (refer to Fig. 3(b)). Therefore, the reinforcing bar slip at the joint can be minimized.

SUMMARY AND CONCLUSIONSIn this study, the earthquake resistance of the beam-column

connections with prefabricated reinforcing bar details was investigated. In the proposed PRC Method, reinforcing bar welding, coupler splice, steel band plates, and headed bar anchorage were used for the fabrication of the reinforcing bar cages of the beams, columns, and beam-column connec-tions. Cyclic loading tests were performed for full-scale interior and exterior beam-column connections, including a conventional RC specimen. The structural capacity of the specimens, such as the yield stiffness, load-carrying capacity, deformation capacity, energy dissipation capacity, and failure mode, were compared with those of the conven-tional RC specimen. The test results and design consider-ations for the PRC connections are summarized as follows:

1. The structural performance of the PRC specimens, including the load-carrying capacity, deformation capacity, energy dissipation capacity, and yield stiffness, was compa-rable to that of the conventional RC specimen. The structural performance satisfies the requirements for the earthquake-resistant moment frame specified by ACI 374.1-05.10

2. The PRC specimens failed due to the flexural concrete crushing at the beam plastic hinge zone. The failure mode was the same as that of the conventional RC specimen. Bond slip and diagonal cracking at the beam-column joint were minimized.

3. The coupler splices at the beam-column joint success-fully transferred the reinforcing bar forces without brittle failure, even though they were located at the beam critical sections. In one out of 15 couplers, however, reinforcing bar slip occurred due to the loosened threads of the coupler, which decreased the load-carrying capacity of Specimen PRC1 by 10%. Attention should be paid to the coupler splice in the PRC connections.

4. In Specimen PRC2, the beam-column joint was strength-ened by hooked bars to avoid probable brittle failure at the beam-column joint. The use of hooked bars successfully relocated the plastic hinge zone far away from the column face and minimized concrete cracking and bond slip at the beam-column joint. However, the deformation capacity of the beam-column connection decreased due to the stress concentration at the hook anchorage and increased rotation demand at the beam plastic hinge zone.

5. The reinforcing bar welding at the beam plastic hinge zones did not have a detrimental effect on the structural performance of the specimens. The fracture of the beam reinforcing bars in the PRC specimens occurred at the same story drift ratio as that for the RC specimen. The reinforcing bar fracture in the beam plastic hinge was caused by the low-cycle fatigue after concrete crushing, rather than by the reinforcing bar welding. However, because ACI 318-086 does not permit the use of reinforcing bar welding at the poten-tial plastic hinge zones, further studies on the effect of reinforcing bar welding are required.

In the proposed PRC Method, the potential problems of the coupler splice and weld connection of reinforcing bars under large inelastic deformations are significantly affected by the prefabricated reinforcement details, construction quality, and stress and strain conditions. Thus, to ensure the structural capacity of the PRC Method, further studies on the coupler splice and weld connection subjected to significant load and strain reversals are required.

ACKNOWLEDGMENTSThis research was financially supported by SEN Engineering Corporation

and the Small and Medium Business Administration in Korea (No. 00045821).

REFERENCES1. Saatcioglu, M., and Grira, M., “Confinement of Reinforced Concrete

Columns with Welded Reinforcement Grids,” ACI Structural Journal, V. 96, No. 1, Jan.-Feb. 1999, pp. 29-39.

2. Choi, C. S., and Saatcioglu, M., “An Experimental Study on the Structural Behavior of Concrete Columns Confined with Welded Reinforcement Grids,” Journal of the Korea Concrete Institute, V. 11, No. 2, 1999, pp. 187-196.

3. Saatcioglu, M., and Grira, M., “Concrete Columns Confined with Welded Reinforcement Grids,” Report OCEERC 96-05, Ottawa Carleton Earthquake Engineering Research Center, Ottawa, ON, Canada, 1996, 89 pp.

4. Hwang, H.; Park, H.; Lee, C.; Park, C.; Lee, C.; Kim, H.; and Kim, S., “Seismic Resistance of Concrete-Filled U-Shaped Steel Beam-to-RC Column Connections,” Journal of the Korean Society of Steel Construction, V. 23, No. 1, 2011, pp. 83-97.

5. Korea Concrete Institute, “Code Requirements for Structural Concrete (KCI 2007),” Korea Concrete Institute, Seoul, Korea, 2007, 334 pp.

6. ACI Committee 318, “Building Code Requirements for Structural Concrete (ACI 318-08) and Commentary,” American Concrete Institute, Farmington Hills, MI, 2008, 473 pp.

7. Burton, K. T., and Hognestad, E., “Fatigue Tests of Reinforcing Bars—Tack Welding of Stirrups,” ACI Journal, V. 64, No. 5, May 1967, pp. 244-252.

8. Razvi, S. R., and Saatcioglu, M., “Confinement of Reinforced Concrete Columns with Welded Wire Fabric,” ACI Structural Journal, V. 86, No. 5, Sept.-Oct. 1989, pp. 615-623.

9. Furlong, R. W.; Fenvs, G. L.; and Kasl, E. P., “Welded Structural Wire Reinforcement for Columns,” ACI Structural Journal, V. 88, No. 5, Sept.-Oct. 1991, pp. 585-591.

10. ACI Committee 374, “Acceptance Criteria for Moment Frames Based on Structural Testing and Commentary (ACI 374.1-05),” American Concrete Institute, Farmington Hills, MI, 2005, 9 pp.

11. ACI Committee 352, “Recommendations for Design of Beam-Column Connections in Monolithic Reinforced Concrete Structures (ACI 352R-02),” American Concrete Institute, Farmington Hills, MI, 2002, 38 pp.

12. ACI Committee 439, “Types of Mechanical Splices for Reinforcing Bars (ACI 439.3R-07),” American Concrete Institute, Farmington Hills, MI, 2007, 20 pp.

13. Chun, S.; Oh, B.; Lee, S.; and Naito, C. J., “Anchorage Strength and Behavior of Headed Bars in Exterior Beam-Column Joints,” ACI Structural Journal, V. 106, No. 5, Sept.-Oct. 2009, pp. 579-590.

14. Park, R., “Ductility Evaluation from Laboratory and Analytical Testing,” Proceedings of Ninth World Conference on Earthquake Engineering, Tokyo, Japan, V. 8, 1988, pp. 605-616.

15. Higai, T.; Nakamumra, H.; and Saito, S., “Fatigue Failure Criterion for Deformed Bars Subjected to Large Deformation Reversals,” Finite Element Analysis of Reinforced Concrete Structures, SP-237, L. Lowes and F. Filippou, eds., American Concrete Institute, Farmington Hills, MI, 2006, pp. 37-54.

Fig. 14—Mechanism of reinforcing bar slip at beam-column joint.

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414 ACI Structural Journal/May-June 2013

NOTES:

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APPENDIX –EARTHQUAKE DESIGN OF SPECIMENS

The beam-column connection specimens were designed to satisfy the requirements for the

Special Moment Frame in ACI 318-08,6 as follows (see Table 1).

1) Table 1 shows the moment capacity ratios between the column and beam at the faces of

the joint, nc nbM / MΣ Σ . The moment capacities ncM and nbM of the column and beam

were calculated from sectional analysis, using the material strengths cf ′ and yf presented

in Table 2. In case of PRC2 with strengthening bars, the beam moment capacity nbM at

the column face was calculated as

( )nb n n n jM M l / l d= − where nM is the moment

capacity at the critical section located at jd = 250 or 400 mm [9.84 or 15.7 in] from the

column face (see Fig. 9(b)). nl is the net length of the beam from the vertical support to

the column face (= 2030 mm [79.9 in]). As presented in Table 1, all specimens satisfied

the requirement of strong column- weak beam behavior specified in ACI 318-087 sec. 21,

nc nbM / MΣ Σ ≥ 1.2.

2) ACI 318-087 requires the column depth-to bar diameter ratio, c bh d ≥ 20. ACI 352R-0211

requires c bh d ≥ 20 yf / 420 ( yf in MPa). In RC and PRC1, c bh d = 24.4, which

satisfied the requirements. In PRC2, because of the strengthening 90°-hooked bars, the

actual embedment length of the beam re-bars was increased to the effective joint depth

c jh dΣ+ = 700 + 250 + 400 = 1350 mm [53.2 in] between the left and right critical

sections of the beam (see Table 1 and Fig. 9(b)). Thus, the effective joint depth-to-bar

diameter ratio was increased to c j b( h d ) dΣ+ = 41.8. In the exterior connection PRC3,

the embedment length of the headed bars was dhl = 420 mm [16.5 in]): dh bl d =14.5. The

development length of the headed bars was greater than the minimum requirement

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0.75 /(6.2 )y b cf d fα ′ (= 281mm [11.1 in], yf = 519 MPa [75.3 ksi] and cf ′ = 61.0 MPa

[8.85 ksi] ], and bd = 29 mm [1.14 in]) specified in ACI 352R-02.11

3) In PRC2 with the strengthening bars, to assure flexural yielding at the beam critical

section, the beam moment capacity at the column face should be greater than the moment

demand that is developed by the moment capacity at the critical section. Fig. A1 shows

the beam moment capacities and demands, and the location of the beam critical section.

The positive moment capacity nM at the beam critical section and nM′ at the column face,

respectively, were calculated as 264 kN-m [194 kip-ft] and 422 kN-m [310 kip-ft] from

sectional analysis (see Table 1 and Fig. A1). In the calculation of nM′ , the contribution of

the strengthening 90° hooked bars to the flexural strength was included. The negative

moment capacity nM at the beam critical section and nM′ at the column face were

calculated as 521 kN-m [383 kip-ft] and 747 kN-m [549 kip-ft], respectively (see Table 1

and Fig. A1). At the column face, the moment capacities nM ′± = 422 kN-m [310 kip-ft]

and 747 kN-m [549 kip-ft] were greater than the moment demands

( )nb n n n jM M l / l d± = ± − = 328 kN-m [241 kip-ft] and 594 kN-m [437 kip-ft], respectively

(see Fig. A1). Thus, first yielding of the beam re-bars was expected to occur at the beam

critical sections.

4) The nominal shear capacities and shear demands of the beam-column joints are presented

in Table 1. The nominal shear capacity was calculated as jnV 0.083 c j cf b hγ ′= , where

γ = constant depending on connection type and classification, jb = effective joint width,

and ch = joint depth. The shear demand was calculated as juV ( )y st sb colf A A Vα= + − for

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RC and PRC1 and y st colf A Vα − for PRC3, where stA and sbA = areas of top and bottom

re-bars of the beam, respectively, colV = column shear force from the test (= uP , see Table

3), and α = 1.25.11 In case of PRC2, since the beam plastic hinge was shifted by the

hooked re-bars, the ultimate joint shear force was modified

as juV 1 2( / ) ( / )y st n s y sb n s colf A l l f A l l Vα α= + − , where nl = net length of the beam between

the roller support to the column face (= 2030 mm [79.9 in]), and 1sl and 2sl = shear span

lengths of the beam between roller supports to the critical section ( 1sl =1780 mm [70.1 in]

and 2sl = 1630 mm [64.2 in], see Fig. A1). γ = 12 for all specimens. jb and ch were 500

mm [19.7 in] and 700 mm [27.6 in] for RC, PRC1, and PRC2, and 450 mm [17.7 in] and

500 mm [19.7 in] for PRC3. stA and sbA were 2580 and 1284 mm2 [4.00 and 1.99 in2]

for RC, PRC1, and PRC3 and 2310 and 1161 mm2 [3.58 and 1.80 in2] for PRC2. The

hooked re-bars were not included in stA and sbA of PRC2. In the calculation of jnV and

juV , the actual material strengths cf ′ and yf shown in Table 2 were used. As shown in

Table 1, the nominal shear capacities jnV at the beam-column joint were greater than the

shear demands juV .

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Fig. A1 Moment capacities and demands of beams in PRC2 [1 in = 25.4 mm, 1 kips-ft =

1.36 kN-m]