Evaluation of Mechanical Anchorage of Eccentric Reinforced Concrete Exterior Beam-column Joints

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4th International Conference on Earthquake Engineering Taipei, Taiwan October 12-13, 2006 Paper No. 092 EVALUATION OF MECHANICAL ANCHORAGE OF ECCENTRIC REINFORCED CONCRETE EXTERIOR BEAM-COLUMN JOINTS SUBJECTED TO CYCLIC LOADING Hung-Jen Lee 1 Si-Ying Yu 2 and Jen-Wen Ko 3 ABSTRACT This paper presents the cyclic responses of eight reinforced concrete exterior beam-column joints, namely, four concentric and four eccentric joints, which are subjected to in-plane lateral displacement reversals. The specimen variables are joint eccentricity, joint aspect ratio, and anchorage of the beam bars terminating within the joint. Four joints used traditional reinforcement for the beam longitudinal bars with standard 90-degree hooks anchored in the joint. The other four connections used headed reinforcement consisting of screw-deformed bars and mechanical anchorage devices to improve the anchorage of the beam bars, the constructability of steel cages, and the seismic performance of connections. Performance of the beam-column joints are evaluated and compared with each other. The behavior of joints with mechanical anchorage devices are as good as, or better than those companion joints with 90-degree hooks. Use of double mechanical devices could avoid push-out failure of the beam bar embedded in the joint, and further improve the ductility and energy dissipation capacity. Joint eccentricity between the beam and column centerlines had detrimental effects on the seismic performance of beam-column joints. Current ACI design produces for estimating the nominal joint shear strength are not capable of preventing the test joints from shear failure at large drift levels. Rather than ACI traditional cross-sectional approach, the proposed strut- and-tie modeling agreed better with the test results. Experimental verification is provided to help further understand the behavior of beam-column joints. Keywords: beam-column; headed reinforcement; eccentric; joint; seismic design; shear; strut INTRODUCTION The current ACI design methods for beam-column connections are given in ACI 318-05 Building Code Sec. 21.5 and its companion report of Joint ACI-ASCE Committee 352 (2002). In these procedures, the nominal joint shear strength is calculated on the effective cross-sectional area within a joint computed from joint depth multiplied to effective joint width. The effects of the column’s aspect ratio and joint eccentricity are considered by limiting or reducing the effective joint width. Joint eccentricities between the beam and column centerlines are common in building frames for architectural reasons. Because relatively few experimental programs of eccentric beam-column connections have been verified to date, more experimental studies in this area are needed. For the beam bars terminated in the exterior or corner joints, the use of standard hooks usually results in congestion with column lateral reinforcement (Fig. 1). The use of headed reinforcement in place of 1 Assistant Professor, National Yunlin University of Science and Technology, Yunlin, Taiwan, [email protected] 2 Former Graduate Research Assistant, National Yunlin University of Science and Technology, Yunlin, Taiwan. 3 PhD Student, National Taiwan University of Science and Technology, Taipei, Taiwan.

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Transcript of Evaluation of Mechanical Anchorage of Eccentric Reinforced Concrete Exterior Beam-column Joints

Page 1: Evaluation of Mechanical Anchorage of Eccentric Reinforced Concrete Exterior Beam-column Joints

4th International Conference on Earthquake Engineering Taipei, Taiwan

October 12-13, 2006

Paper No. 092

EVALUATION OF MECHANICAL ANCHORAGE OF ECCENTRIC REINFORCED CONCRETE EXTERIOR BEAM-COLUMN JOINTS

SUBJECTED TO CYCLIC LOADING

Hung-Jen Lee1 Si-Ying Yu2 and Jen-Wen Ko3

ABSTRACT

This paper presents the cyclic responses of eight reinforced concrete exterior beam-column joints, namely, four concentric and four eccentric joints, which are subjected to in-plane lateral displacement reversals. The specimen variables are joint eccentricity, joint aspect ratio, and anchorage of the beam bars terminating within the joint. Four joints used traditional reinforcement for the beam longitudinal bars with standard 90-degree hooks anchored in the joint. The other four connections used headed reinforcement consisting of screw-deformed bars and mechanical anchorage devices to improve the anchorage of the beam bars, the constructability of steel cages, and the seismic performance of connections. Performance of the beam-column joints are evaluated and compared with each other. The behavior of joints with mechanical anchorage devices are as good as, or better than those companion joints with 90-degree hooks. Use of double mechanical devices could avoid push-out failure of the beam bar embedded in the joint, and further improve the ductility and energy dissipation capacity. Joint eccentricity between the beam and column centerlines had detrimental effects on the seismic performance of beam-column joints. Current ACI design produces for estimating the nominal joint shear strength are not capable of preventing the test joints from shear failure at large drift levels. Rather than ACI traditional cross-sectional approach, the proposed strut-and-tie modeling agreed better with the test results. Experimental verification is provided to help further understand the behavior of beam-column joints. Keywords: beam-column; headed reinforcement; eccentric; joint; seismic design; shear; strut

INTRODUCTION The current ACI design methods for beam-column connections are given in ACI 318-05 Building Code Sec. 21.5 and its companion report of Joint ACI-ASCE Committee 352 (2002). In these procedures, the nominal joint shear strength is calculated on the effective cross-sectional area within a joint computed from joint depth multiplied to effective joint width. The effects of the column’s aspect ratio and joint eccentricity are considered by limiting or reducing the effective joint width. Joint eccentricities between the beam and column centerlines are common in building frames for architectural reasons. Because relatively few experimental programs of eccentric beam-column connections have been verified to date, more experimental studies in this area are needed. For the beam bars terminated in the exterior or corner joints, the use of standard hooks usually results in congestion with column lateral reinforcement (Fig. 1). The use of headed reinforcement in place of 1 Assistant Professor, National Yunlin University of Science and Technology, Yunlin, Taiwan, [email protected] 2 Former Graduate Research Assistant, National Yunlin University of Science and Technology, Yunlin, Taiwan. 3 PhD Student, National Taiwan University of Science and Technology, Taipei, Taiwan.

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standard hooks in joints is a viable option (Wallace 1997). Wallace et al. (1998) have shown that the application of headed reinforcement within exterior or corner beam-column joints is appropriate. Headed reinforcement refers to the process of reinforcing a bar terminated with a head or end anchor plate. Figure 2 shows one type of headed reinforcement consisting of screw-deformed bars and mechanical anchorage devices. The mechanical device is a cast iron forming an anchor plate with a screw nut. The screw-deformed bar is a reinforcing bar with rolled-on deformations forming a screw for mechanical connection and anchorage. Hence, the mechanical device can be screwed onto the bar to provide a head. Because the rolled-on screws are quite loose, a nonshrink, high-strength mortar is grouted into the mechanical device and around the bar using an injector. The outer diameter of an anchor plate is bd5.2 ( bd is the nominal diameter of the bar). As a result, the net bearing area of an anchor plate, or net head area nhA , is 5.25 times the nominal bar area bA . Clearly, the use of headed reinforcement provides a promising way to solve the problem of reinforcement congestion in beam-column joints.

Figure 1. Reinforcement congestion of an Figure 2. Mechanical devices for anchorage

eccentric beam-column corner joint of screw-deformed bars

EXPERIMENTAL PROGRAM Test specimens This paper selected eight joint specimens, four concentric and four eccentric specimens, from two individual test series (Ko 2005 and Yu 2006). Figure 3 illustrates the test matrix, designation, and reinforcing details of the test specimens. The primary specimen variables are the direction of shear, joint eccentricity, and anchorage details of the beam bar within the joint. The test program was designed to model the behavior of a corner beam-column joint isolated from a lateral-force-resisting frame. A T-shaped assembly was chosen to represent a beam framing into a rectangular column. The prototype corner column had a cross section of 400x600 mm, and it used 12 D22 longitudinal bars and D10 hoops with crossties at a spacing of 100 mm throughout the column. Using a concrete compressive strength of 30 MPa and a reinforcement of a specified yield strength of 420 MPa, the column lateral reinforcement was designed to meet the minimum requirement in ACI Code Sec. 21.4.4. The loading beam, which was anticipated to develop a plastic hinge adjacent to the column, had a cross-section of 300x450 mm, and it used four D22 longitudinal bars (steel ratio of 1.29%) at both top and bottom. Closed overlapping hoops were provided through the length of the beam to avoid beam shear failure. Transverse beams and floor slabs were neglected to ease specimen construction and testing. The first group (Group A) was designed to investigate the strength of a corner joint subjected to shear in a strong or weak direction with or without joint eccentricities. The first character (S or W) of the designation represents the direction of the loading beam framing into the joint (South/strong or West/weak). The subsequent numerals denote the eccentricity between the beam and column centerlines in mm. All four joint specimens in Group A used traditional reinforcing details. The beam longitudinal bars used a standard 90-degree hook bent into the joint which was embedded as close as

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possible to the back of the joint. Leaving a 70 mm back cover behind the hook, the development lengths measured from the beam-column interface were equal to bd24 for specimen S0 and S50, but

bd15 for specimen W0 and W150. The development length for specimen W0 and W150 was designed to meet the minimum requirement in ACI. Sec. 21.5.4.1. Following testing and evaluation of the behavior of the first group, the second group (Group B) was constructed to investigate the behavior of joints with mechanical anchorage. The design of specimen in Group B duplicated the design of specimen W0 and W150 in Group A, except for the use of mechanical anchorage for beam longitudinal bars. Specimen designation -M1 or -M2 denotes single or double mechanical device on the beam bar terminating in the joint (Fig. 3). Figure 2 depicts the mechanical anchorage device for screw-deformed bars used in Group B specimens. For comparison with specimen W0 and W150, the embedded length of the headed bar within the joint is bd15 , which left a 70 mm concrete cover behind the end anchor plate.

Group A

TraditionalReinforcement

Group B

HeadedReinforcement

Joint Concentric Eccentric Anchorage

S0

W0

S50

W150

W0-M1

W0-M2

W150-M1

W150-M2

Figure 3. Test matrix and specimen designations

Material properties Table 1 summarizes the material properties at testing date. Eight joint specimens were cast using four batches of concrete with the same mix proportions. For the target design strength of 30 MPa, the variation of the test-day concrete strengths within each batch is small. Thus, the average values for test-day concrete strengths are presented in Table 1. Two sizes of reinforcement meeting ASTM A706 were used for longitudinal and transverse reinforcement in the test program. Group A used traditional deformed bars with standard hooks within the joint, and Group B used screw-deformed bars with mechanical anchorage devices for beam bars terminated in the joint. Lateral reinforcement with the same properties was used in all specimens. Testing method To restrain the column from twisting along the column axis, each T-shaped joint specimen was rotated 90 degrees for test setup, as shown in Fig. 4. The column was tied down with reaction steel beams, cover plates, and rods. Four one-dimensional rollers were seated beside the column to allow in-plane rotation at both ends of the column. Specimens were loaded first by a column axial load of 0.1 cg fA ′ , which was manually held constant during testing. Then a typical lateral displacement history consisting of three cycles at monotonically increasing drift levels (0.25, 0.50, 0.75, 1.0, 1.5, 2, 3, 4, 5, 6, 7, and 8%) was applied using a displacement-controlled actuator in a quasi-static manner. Target displacement amplitudes at the beam tip, Δ , were computed using the following equation:

cbc h.LL 50

ΔδratioDrift +

== (1)

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where =δ inter-story drift of a prototype building frame; =bL length of the beam measured from the critical section to the actuator centerline; =cL length of the column between two roller supports; and

=ch full depth of column in the direction of joint shear to be considered.

Table 1. Material properties

Group Batch Specimen Average cf ′ at testing date

Longitudinal reinforcement

Lateral reinforcement

S0 1 S50 33.2 MPa

W0 A 2 W150 29.5 MPa

5.454=yf MPa

4.682=uf MPa

W0-M1 3 W0-M2 30.7 MPa

W150-M1 B 4 W150-M2 35.8 MPa

3.473=yf MPa 1.667=uf MPa

3.471=yf MPa 3.715=uf MPa

Rea

ctio

n w

all

Figure 4. Test setup

EXPERIMENTAL RESULTS

Cyclic loading response and failure modes Figure 5 display the load-displacement curves and final crack patterns for specimens in Group A. All specimens exhibited beam yielding in the 1.5% drift cycle, and then the development of the anticipated beam plastic hinge in subsequent cycles. After beam yielding, the strength of each test specimen continued to increase due to the strain hardening of the reinforcement, but it was limited by failure in either the beam plastic hinge region or the joint region. The cyclic loading responses of specimens S0 and S50 are very similar with fatter loops, which are typical responses of flexure-dominated systems. Core concrete crushing and subsequent buckling of longitudinal bars in the beam plastic hinge region terminated the tests of specimens S0 and S50 in the 6% and 5% drift cycle, respectively. Only a few hairline diagonal shear cracks and minor concrete cover spalling appeared on the east face of the joint (Fig. 5). Both joints were capable of remaining elastic during the formation of beam plastic hinges. The joint shear capacities of specimens S0 and S50 were greater than the beam flexural capacity. The failure mode of specimen S0 or S50 is classified as beam flexure failure (mode B).

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Figure 5. Cyclic loading responses and final crack patterns for specimens in Group A

On the other hand, the hysteretic curves of specimens W0 and W150 have significant pinching loops (Fig. 5), which are typical responses of the shear or bond-slip mechanism. As the amplitudes of deformations increase, the joint shear capacity may decrease. When the joint shear capacity falls below the beam flexural capacity, the joint will fail in the shear after beam yielding. After beam yielding, specimens W0 and W150 failed in the 5% and 4% drift cycle, respectively. Crushing and spalling of concrete on the east and north faces of the eccentric joint specimen W150 was evident in Fig. 5. For the concentric joint specimen W0, the spalling of concrete cover did not appear on the north face of the column due to a larger distance between the beam and the column edges. Nevertheless, visible expansion and extensive pushout cracks on the east face of the joint of specimen W0 indicated the crushing of core concrete in the joint regions (Fig. 5). The failure mode of specimen W0 or W150 was classified as joint failure after beam yielding (mode BJ). Thus, the strength of specimen W0 or W150 was eventually limited by its joint shear capacity. In Group B of the test matrix, the hysteretic curves of specimens W0-M1 and W150-M1 (Fig. 6) are similar with those of specimens W0 and W150 up to the 4% drift cycle. The use of single mechanical device provided good anchorage capacity for beam bar within the joint. Strength degradation did not appear prior to the 4% drift cycle. The strength of specimen W0-M1 or W150-M1 was limited by its joint shear capacity at a drift level of 4%. The crushing of concrete and widely opened diagonal cracks

E

E

N

NS0

E

E

N

NS50

E

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N

N W0

E

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N W150

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on the north face of the joint showed the evidence of joint shear failure. The rapid strength reduction from the skeleton curve to the backbone curve of specimen W0-M1 or W150-M1 at the 5% drift level was attributed to the pushout of concrete cover on the east face of the column (Fig. 6).

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Figure 6 Cyclic loading responses and final crack patterns for specimens in Group B

Toward the end of testing of specimens W0-M2 and W150-M2, the use of double mechanical devices on each beam bar avoided the push-out of concrete cover on the east face of the column. As shown in Fig. 6, the cyclic loading responses for specimens W0-M2 and W150-M2 had higher ductility and lesser pinching than those for similar specimens in Group A or B. Both specimens W0-M2 and W150-M2 reached maximum loads at the 6% drift level due to the limitation of the joint shear capacities. For eccentric joint specimen W150-M2, rapid strength degradation followed the crushing and spalling of concrete on the north side of the eccentric joint. The concentric specimen W0-M2 had a larger distance between the beam and column edges (Fig. 3), hence the crushing or spalling of concrete did not appear on the north face of the joint (Fig. 6). Nevertheless, the visible concrete expansion on the east face of specimen W0-M2 indicated the crushing of core concrete in the joint region.

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Strength and ductility Table 2 compares the strength and ductility of the test specimens. The nominal yield load ( nP ) was the load corresponding to the nominal moment capacity ( nM ) of the beam critical section, which was calculated using the measured material properties. The nominal yield displacement ( yΔ ) was computed using the measured secant stiffness defined at the measured load of 0.75 nP and the corresponding displacement of 0.75 yΔ in the first cycle of the 1% drift. As shown in column (4) of Table 2, specimens S0 or S50 had an over-strength factor of 1.20 or higher due to a complete formation of a beam plastic hinge. Both joints had enough rigidity to support the flexural compression and tension at the beam column interface. Core concrete crushing and the subsequent buckling of the longitudinal bar in the beam plastic hinge region occurred at a ductility factor greater than 5. For the other six W-series specimens, the buckling of the beam bar did not appeared due to the softening and crushing of core concrete within the joints. As shown in column (4) of Table 2, the over-strength factors for W-series specimens ranged from 1.05 to 1.11 only. Table 2. Strength and ductility

nP yΔ max,jhVSpecimen

kN mm nPPmax

y

P

ΔΔ max

y

P

ΔΔ max8.0

kN cjcn

jh

hbfV

352max,

′γ Failure

mode

(1) (2) (3) (4) (5) (6) (7) (8) (9) S0 158 18.9 1.22 5.41 5.41 832 0.68 B

S50 158 20.1 1.20 5.12 5.12 819 0.67 B W0 147 23.5 1.11 4.58 5.87 778 0.80 BJ

W150 147 24.8 1.05 3.41 4.69 727 0.94 BJ W0-M1 151 24.0 1.05 3.55 > 7.18 756 0.76 BJ

W150-M1 152 24.9 1.05 3.40 > 6.91 763 0.88 BJ W0-M2 151 24.3 1.06 5.27 > 7.09 765 0.77 BJ

W150-M2 152 24.2 1.09 5.25 > 7.10 792 0.92 BJ Specimens S0, S50, W0-M2, and W150-M2 reached each maximum load at a ductility factor greater than 5, but different failure modes were observed during the tests. For specimens W0-M2 and W150-M2, diagonal shear cracking and crushing of concrete strut led to the softening of the joint region, and limited the maximum input shear from the loading beam. Nevertheless, both specimens sustained the imposed cyclic loading up to a lateral drift of 6%, which is much beyond the expected drift level in the seismic design of a building system. Therefore, the performance of specimen W0-M2 or W150-M2 is satisfactory, even though it eventually failed in mode BJ.

EXPERIMENTAL VERIFICATIONS Evaluation of current ACI methods The maximum joint shear force in the horizontal cross section within the joint measured during testing can be estimated by

⎟⎟⎠

⎞⎜⎜⎝

⎛ +−=−=

c

cbbcoljh L

hLjdLPVTV )5.0(

maxmaxmax, (2)

where =maxT maximum force in the tension chord of the beam, kN; =colV shear in the column calculated based on the loading for the beam, kN; =jd internal level arm of the beam section adjacent to the joint, mm. According to a standard moment-curvature analysis of the beam section, the internal lever arm, jd , is about 7/8 of the effective depth of the beam section. For simplicity, the value of jd is assumed to be a constant of 350 mm in this paper.

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The current ACI methods for the calculation of the nominal shear strength ( nV ) of a beam-column joint is given by cjcnn hbfV ′= γ (3) where cn f ′γ is the nominal joint shear stress of cf ′0.1 MPa for corner, interstory connections; The effects of the column’s aspect ratio and joint eccentricity are considered by limiting or reducing the effective joint width.

ACI 352R-02 =352jb the smaller of

( )

⎪⎩

⎪⎨

⎧Σ++

c

cb

cb

bmhb

bb2

2 (4)

where =bb full width of the beam, mm; =cb full width of the column, mm; =ch full depth of the column in the direction of the joint shear to be considered, mm; and m is 0.3 when e is greater than

8cb ; otherwise, m is 0.5. The joint eccentricity, e , was designed to be 8cb for specimen S50 and W75, and to be 4cb for specimen W150. In the column (8) of Table 3, the applied maximum joint shear is about 70% of the nominal shear strength for specimens S0 and S50, about 80% of those for specimens W0 and W0-M1/M2, and 90% of those for specimens W150 and W150-M1/M2. Although all the maximum joint shear forces were below the ACI nominal joint shear strengths, different behavior exhibited between loading in the strong and week direction. Clearly, the joint shear capacity in the strong direction of the rectangular joint (S0 or S50) was greater than that in the weak direction (W0 or W150). This point cannot be reflected on the calculation of a cross-sectional approach within the joint. Following the ACI methods could not avoid joint failure at a large drift level of 4% or 5%, but it is considered acceptable in a real structural system. Conservative results are obtained in the column (8) of Table 3. The test results showed some but not too much difference between each pair of specimens with or without eccentricity. Joint shear-resisting mechanisms Paulay, Park, and Priestly (1978) first discussed that there are two shear-resisting mechanisms exiting in joints, the truss mechanism and the diagonal strut mechanism. The truss mechanism transfers the forces uniformly from the beam and column bars through the bond mechanism. Adequate bond must exist between the reinforcement and concrete to necessitate a truss mechanism, which also requires considerable amounts of horizontal and vertical tie forces in the truss panel to be in equilibrium. Figure 7 illustrates a conceptual model for the degradation of joint shear capacity under increasing drift or ductility ratio. Joints subjected to inelastic displacement reversals often undergo significant bond deterioration along the reinforcing bars from the adjacent beam plastic hinge. At this stage, a part of the joint shear is transferred through the horizontal hoops with fan-shaped struts, while the remainder is carried by the diagonal strut. As the drift or ductility ratio increases, the horizontal hoops would yield progressively, the joint concrete may crack excessively, and the bond of the reinforcing bars within the joint might be lost. Eventually, the joint shear force is directly transferred by the diagonal strut mechanism. Real shear-transferring mechanisms in joints may be a combination of the diagonal strut and the truss mechanism, with the bond deterioration being at a certain degree of longitudinal reinforcement during cyclic loading (Fig. 7). Hence, the joint shear capacity decreases as the cyclic inelastic loading increases, which is referred to as the degradation of the joint shear capacity. When the joint shear capacity falls below the shear demand from beam hinging, the joint will fail in the shear after beam yielding (mode BJ). If the joint shear capacity is greater than the demand, the maximum strength is limited by the beam flexure capacity (mode B).

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Figure 7. Conceptual model for the degradation of joint shear capacity

Proposed model for the degradation of joint shear capacity When good bond exist between reinforcing bars and the joint concrete struts, as shown in Fig. 8, uniformly distributed shear stresses ( jv ) on the effective cross-sectional area within the joint cab be assumed. Therefore the potential joint shear capacity can be estimated by

Truss mechanism cjjtrussjh hbvV ××= 352 (5)

where the maximum joint shear stress could be evaluated by the principal stress criteria

22

, 22 jvhvh

tc vffffp +⎟⎠⎞

⎜⎝⎛ −

±+

= (6)

Solving Eq.(6), the maximum joint shear stress jv is cf ′194.0 when the vertical or axial stress acting on the joint is cf ′10.0 and the maximum principal compressive stress is assumed to be cf ′25.0 , which is referred to the ATC 32 report 1996.

jvvf

jv

cp tp

jv

jv

jv

cptp

tpcp

vf

vf

(a) Stress acting on the joint panel (b) Principal stress criteria for truss mechanism

Figure 8. Potential joint shear capacity for the truss mechanism

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Once bond is lost and the diagonal strut transferred all the shear forces, as shown in Fig. 9(a), the horizontal joint shear capacity can be estimated by θcos××= csce

strutjh AfV (7)

where θ is the angle between the axis of the diagonal strut and the tension chord of the beam; cef is the effective strength of the diagonal strut; csA is the effective cross sectional area of the diagonal strut. The diagonal struts in these joints are bottle-shaped struts with crack-controlled reinforcement satisfying ACI Sec. A3.3. Generally, the struts in joints subjected to cyclic loading have to cross the diagonal cracks developed from the opposite loading direction. Therefore, a smaller value of sβ should be considered for the seismic design of beam-column joints. Therefore, the value of sβ is selected to be 0.40. Accordingly, the effective compressive strength cef is 0.85 cf ′ × 0.40=0.34 cf ′ . A design strength reduction factor of 0.75 or 0.85 is not considered because the analysis is based on the actual material strength. The width of the diagonal strut is assumed to be the effective joint width recommended by ACI 352R-02. As shown in Fig 9(a), the depth of the diagonal strut can be estimated from the depths of the compression zones in the beam and column. ( )θθ sincos352 ×+××= cbjcs aabA (8) Both ba and ca vary with the moment acting on the beam and the column. The depth of the compression zone in the elastic column can be evaluated from a standard moment-curvature analysis of the column section. Due to the formation of the beam plastic hinge, the depth of compression zone in the beam can be estimated by

bc

b bfCorTa×′×

=85.0

(8)

ca352jb

ba

strutjhV

(a) Diagonal strut and nodal zone (b) Strut model for W150 (C) Strut model for W150-M1

Figure 9 Potential joint shear capacity for the truss mechanism If pictures of the cracking pattern in similar structures are available, the locations of the struts and ties can be arranged within the structure such that struts fall between the cracks (Macgregor 2002). According to the observations on the crack patterns of test specimens, a simple diagonal strut model, as shown in Fig. 9(b), is proposed to simulate the stress flow in the bend of the hooked beam bar anchored in the joint. The outer node is arranged at the intersection point of the axis of the tension chord and the tail extension of the 90-degree hook. For test specimens with headed bars, a refined diagonal strut model with the outer node shifting inside, as shown in Fig. 9(c), is proposed to simulate

N

N W150

°= 1.52avgθ°452= .θ

N

N W150-M1

°= 8.57avgθ°357= .θ

Page 11: Evaluation of Mechanical Anchorage of Eccentric Reinforced Concrete Exterior Beam-column Joints

the bearing cone of the head bar. For simplicity, the inner node for each specimen is arranged at the intersection point of the extreme compression bars in the beam and the column. As example illustrated in Fig. 9(b) and 9(c), the angles (θ ) between the axis of the diagonal strut and the tension chord are 52.4 and 57.3 degrees for specimens W150 and W150-M1, respectively. The average angles between the principle diagonal cracks and the beam centerlines are found to be 52.1 and 57.8 degrees for specimens W150 and W150-M1, respectively. The degradation of the potential joint shear capacity initiates when the bond condition deteriorates. As shown in Fig. 10, the degradation will be delayed if good bond condition exists. The rate of degradation is strongly related to the confined condition of the joint concrete. Within the limitations of the test results, a 2%-to-6%-drift linear interpolation between the principal stress criteria and diagonal strut model is proposed to predict the failure of the test beam-column joints, which had well-distributed confining reinforcement.

Load

Joint shear capacity

Drift or Ductility

Bond conditionGoodPoor

Load

Drift or Ductility

Lateral reinforcement

Well-confined

Poorly-

Joint shear capacity

Figure 10. Degradation of potential joint shear capacity

Figure 11 compares the predicted potential joint shear capacities with the measured skeleton and backbone curves for specimens S0 and S50. Significant drops from the skeleton curves to the backbone curves are attributed to the buckling of beam bars. The predicted joint shear capacities for specimens S0 and S50 are greater than the beam flexural capacity. This agrees well with the failure mode for specimens S0 and S50.

-150 -100 -50 0 50 100 150

Displacement (mm)

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

Actu

acto

r loa

d , P

(kN

)

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

P/Pn

-8 -6 -4 -2 0 2 4 6 8Drift (%)

pushpull

S0

-150 -100 -50 0 50 100 150

Displacement (mm)

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

Actu

acto

r loa

d , P

(kN

)

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

P/Pn

-8 -6 -4 -2 0 2 4 6 8Drift (%)

S50

pushpull

Figure 11. Predicted capacities and test results for specimens S0 and S50 The same 2%-to-6%-drift linear degradation model is proposed for specimens W0, W150, W0-M1, and W150-M1. As shown in Fig. 12, the intersection point of the beam flexural capacity and the joint shear capacity indicates the drift capacity of the joint shear failure. The predicted failure points at 5%

Page 12: Evaluation of Mechanical Anchorage of Eccentric Reinforced Concrete Exterior Beam-column Joints

drift agree well with observed drift levels of joint failure for specimens W0 and W0-M1. For eccentric joint specimens W150 and W150-M1, somewhat conservative predictions are obtained using Eq.(4) for the effective joint width.

Displacement (mm)

Act

uact

or lo

ad ,

P (k

N)

0

25

50

75

100

125

150

175

200

225

250

Act

uact

or lo

ad ,

P (k

N)

0 1 2 3 4 5 6 7 8Drift (%)

W0

Predicted flexural capacity

Predicted shear capacity

A

A:Predicted failure point]: Joint failure

]

Displacement (mm)

Act

uact

or lo

ad ,

P (k

N)

0

25

50

75

100

125

150

175

200

225

250

Act

uact

or lo

ad ,

P (k

N)

0 1 2 3 4 5 6 7 8Drift (%)

W150

Predicted flexural capacity

Predicted shear capacity

A

A:Predicted failure point]: Joint failure

]

Displacement (mm)

Act

uact

or lo

ad ,

P (k

N)

0

25

50

75

100

125

150

175

200

225

250

Act

uact

or lo

ad ,

P (k

N)

0 1 2 3 4 5 6 7 8Drift (%)

W0-M1

Predicted flexural capacity

Predicted shear capacity

A

A:Predicted failure point]: Joint failure

]

Displacement (mm)

Act

uact

or lo

ad ,

P (k

N)

0

25

50

75

100

125

150

175

200

225

250

Act

uact

or lo

ad ,

P (k

N)

0 1 2 3 4 5 6 7 8Drift (%)

W150-M1

Predicted flexural capacity

Predicted shear capacity

A

A:Predicted failure point]: Joint failure

]

Figure 12. Predicted capacities and test results for specimens W0/150 and W0/150-M1

For the specimens W0-M2 and W150-M2, the use of double mechanical devices avoided the yield penetration along the beam bar into the joint. Two gauge strain histories on the beam bars embedded in the joints are illustrated in Fig. 13. For specimen W150-M1, the strain history of the beam bar beyond the yield strain in the 3 to 4% drift cycle. For specimen W150-M2, however, the strain history of the beam bar remained elastic up to the 5% drift cycle. Using the same 2%-to-6%-drift degradation model for specimens W0-M2 and W150-M2, the potential joint shear capacities will meet the beam flexural capacities at 4% drift, which is less than the observed failure at 7% to 8% drift cycles during testing. A refined model for specimens with double mechanical devices is recommended. According to the strain histories of specimens W0-M2 and W150-M2, a modified 4%-to-8%-drift linear interpolation between the principal stress criteria and diagonal strut model is proposed. As shown in Fig. 14, the potential joint shear capacities meet the beam flexural capacities at 7% drift for specimen W0-M2 and 6% drift for specimen W150-M2. Actual failure points appeared at 8% drift for specimen W0-M2 and 7% drift for specimen W150-M2. Figure 14 shows conservative prediction on the failure points.

Page 13: Evaluation of Mechanical Anchorage of Eccentric Reinforced Concrete Exterior Beam-column Joints

-1000 0 1000 2000 3000 4000

Micro strain

-200

-150

-100

-50

0

50

100

150

200Ac

tuac

tor l

oad

, P

(kN

)

-1.0

-0.5

0.0

0.5

1.0

P/Pn

W150-M1

4%3%2%Drift

Gaugefailure

Monotonicyield strain

-1000 0 1000 2000 3000 4000

Micro strain

-200

-150

-100

-50

0

50

100

150

200

Actu

acto

r loa

d ,

P (k

N)

-1.0

-0.5

0.0

0.5

1.0

P/Pn

W150-M2

5%Drift

Monotonicyield strain

Available onlyup to 5% drift

2%

Figure 13. Strain histories of Gauge 9 on the beam bar embedded in the joint

Displacement (mm)

Act

uact

or lo

ad ,

P (k

N)

0

25

50

75

100

125

150

175

200

225

250

Act

uact

or lo

ad ,

P (k

N)

0 1 2 3 4 5 6 7 8Drift (%)

W0-M2

Predicted flexural capacity

Predicted shear capacity

A

A:Predicted failure point]: Joint failure

]

Displacement (mm)

Act

uact

or lo

ad ,

P (k

N)

0

25

50

75

100

125

150

175

200

225

250

Act

uact

or lo

ad ,

P (k

N)

0 1 2 3 4 5 6 7 8Drift (%)

W150-M2

Predicted flexural capacity

Predicted shear capacity

A

A:Predicted failure point]: Joint failure

]

Figure 14. Predicted capacities and test results for specimens W0/150-M2

CONCLUSIONS This paper presents the cyclic loading responses of eight specimens of T-shaped beam-column joints that have been carried out to investigate the shear strengths of eccentric beam-column joints and the use of headed reinforcement in place of standard hooks in joints. Two pairs of connections used the standard 90-degree hooks anchored within the joint. Another two pairs of connections used headed reinforcement consisting of screw-deformed bars and mechanical anchorage devices. Each eccentric connection performed worse than each companion concentric connection. Using headed bars with single mechanical device provided anchorage as good as using standard hooks. Specimens with double mechanical devices had no pushout spalling and better seismic performance than companion connections. The strut-and-tie models agree well with the strengths and failure modes of the test specimens, whereas the ACI methods show somewhat unconservative predictions.

ACKNOWLEDGMENTS The authors are grateful to the National Science Council in Taiwan for the financial support under Project No. NSC 93-2211-E-224-010 and No. NSC 94-2211-E224-014. The Fusheng Company provided the screw-deformed bars and mechanical anchorage devices for the test specimens are also acknowledged.

Page 14: Evaluation of Mechanical Anchorage of Eccentric Reinforced Concrete Exterior Beam-column Joints

REFERENCES ACI Committee 318 (2005), “Building Code Requirements for Structural Concrete (ACI 318-05) and

Commentary (ACI 318R-05),” American Concrete Institute, Farmington Hills, Mich.

ACI-ASCE Committee 445 (1998), “Recent Approaches to Shear Design of Structural Concrete,” Journal of Structural Engineering, ASCE, 124(12), 1375-1417.

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

ATC-32, (1996) “Improved Seismic Design Criteria for California Bridges: Provisional Recommendations.” Applied Technology Council., Redwood City, California, 1996, Report No. ATC-32.

Ko, J.W. (2005), “Cyclic Tests of Reinforced Concrete Corner Beam-Column Joints with Eccentricity,” master’s thesis, National Yunlin University of Science and Technology, Yunlin, Taiwan. (in Chinese)

Lee, H.J., and Ko, J.W. (2005), “Performance Evaluation of Exterior RC Beam-Column Joints with Eccentricity,” Proceedings of The 7th Korea-Japan-Taiwan Joint Seminar on Earthquake Engineering for Building Structures (SEEBUS 2005), Seoul, Korea, October 21-22, 2005, 65-74.

Lee, H.J., and Ko, J.W. (2006), “Eccentric RC Corner Beam-Column Connections Subjected to Cyclic Loading in Principal Directions,” submitted to ACI Structural Journal.

MacGregor, J.G. (2002), “Derivation of strut-and-tie models for the 2002 ACI Code,” Reineck, K. H., ed, Examples for the Design of Structural Concrete with Strut-and-Tie Models, SP-208, American Concrete Institute, Farmington Hills, Mich., 7-40.

Paulay, T., Park. R., and Priestly, M.J.N. (1978), “Reinforced Concrete Beam -Column Joints under Seismic Actions,” ACI Journal, 75(11), 585-593.

Paulay, T., and Priestley, M.J.N. (1992), “Seismic Design of Reinforced Concrete and Masonry Buildings,” John Wiley & Sons, NY.

Wallace, J.W. (1997), “Headed Reinforcement: A Viable Option,” Concrete International, 19(12), 47-53.

Wallace, J.W., McConnell, S.W., Gupta, P., and Cote, P.A. (1998), “Use of Headed Reinforcement in Beam-Column Joints Subjected to Earthquake Loads,” ACI Structural Journal, 95(5), 590-606.

Yu, S.Y. (2006), “Behavior of Reinforced Concrete Exterior Beam-Column Connections with Screw-Deformed Bars and Mechanical Devices,” master’s thesis, National Yunlin University of Science and Technology, Yunlin, Taiwan. (in Chinese)