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Modeling the cyclic response of fiber reinforced concrete joints
Engineering Structures 29 (2007) 2960–2967 www.elsevier.com/locate/engstruct
Modeling the cyclic response of fiber reinforced concrete joints M. Jamal Shannag a,∗ , Ghazi Abu-Farsakh b , Nabeela Abu-Dyya b a Civil Engineering Department, King Saud University, Riyadh 11421, Saudi Arabia b Department of Civil Engineering, Jordan University of Science and Technology, Jordan
Received 28 April 2006; received in revised form 2 October 2006; accepted 8 February 2007 Available online 23 March 2007
Abstract A nonlinear static (pushover) procedure (NSP) was used to model the behavior of interior beam–column (B–C) joints under lateral cyclic loading. The results of the analytical and numerical solutions were compared with the results obtained from experimental tests. Ten 1/3scale interior beam–column joints, part of a prototype building designed according to the existing practice in Jordan, were tested under cyclic reverse loading. Most of these joints lacked transverse reinforcement, column lap splices and continuous bottom beam reinforcement. They were strengthened using high performance steel fiber reinforced concrete (HPFRC) in place of ordinary concrete in two types of joint region, extending 200 and 300 mm from the face of the column. The experimental results were found to be in good agreement with the results of the applied modeling technique and assumptions made. The static pushover analysis appears to be a viable tool for predicting the load–deflection and moment–curvature responses of beam–column joints. c 2007 Elsevier Ltd. All rights reserved.
Keywords: Pushover analysis; Beam–column joints; Fiber reinforced concrete
1. Introduction Extensive experimental studies have previously been performed to investigate the seismic behavior of beam–column (B–C) joint details in reinforced concrete buildings, and to investigate the joint behavior under simulated seismic loading [1–9]. The behavior of beam–column (B–C) joints is complex and still not fully understood. Recent developments in fiber reinforced cement-based composites, and their increasing use in earthquake-resistant design for achieving higher ductility at a lesser cost, made it very difficult to cover all the variables that affect the B–C joint by experimental testing alone, and a reliable analytical model could provide a significant contribution to a detailed experimental study. Therefore the main objective of this study was to develop a numerical model that could be utilized as an investigative tool in conjunction with an experimental program. The recent advent of performance-based design has brought the nonlinear static pushover analysis procedure (NSP) to the ∗ Corresponding author. Tel.: +966 1 4676928, +966 4683076; Mob: +966 559661230; fax: +966 1 4677008. E-mail addresses: [email protected], [email protected] (M.J. Shannag).
c 2007 Elsevier Ltd. All rights reserved. 0141-0296/$ - see front matter doi:10.1016/j.engstruct.2007.02.003
Fig. 1. Force–deformation for a pushover hinge.
forefront [10]. Pushover analysis is a static, nonlinear procedure, by which the magnitude of the structural loading is incrementally increased in accordance with a certain predefined pattern. With the increase in the magnitude of the loading, weak links and failure modes of the structure are found. The loading is monotonic with the effects of the cyclic and load reversals being estimated by using modified monotonic force–deformation criteria. The force–deformation criterion for hinges used in pushover analysis is defined as shown in Fig. 1. Static pushover
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Fig. 2. Specimen geometry and steel detailing of reference specimens no. 2 through 10, with critical detailing in the joint region. Specimen no. 1 is the same without critical detailing in the joint region.
analysis is an attempt by the structural engineering profession to evaluate the real strength of the structure and it promises to be a useful and effective tool for performance-based design. There are a large number of variables interacting to control the capacity of the joint and even an extensive experimental program cannot fully validate all combinations. The SAP 2000 static pushover analysis capabilities, which are fully integrated into the program, allow quick and easy implementation of the pushover procedures for predicting the theoretical values of load–displacement and moment–curvature curves for the tested frames.
Table 1 Proportions and properties of HPFRC-mix materials Material
Proportion
Properties
Fiber (BCSF or HSF)
2% or 4% by volume
(Dramix 6/0.15) tensile yield strength = 2950 MPa. (Dramix 30/0.5) tensile yield strength = 1172 MPa.
Cement
1
Portland Pozzolana cement; complying with Jordanian specifications
Coarse aggregate
2.30
Crushed limestone with Dmax = 9.5 mm, BSG = 2.6
2. Experimental program
Limestone
0.26
BSG = 2.65 Fineness modulus = 3.1
Two concrete mixes were used for preparing the B–C joint specimens in this investigation: normal concrete mix and high performance steel fiber reinforced concrete mix. The normal concrete mix consists of cement, coarse aggregate, fine aggregate, and water with a corresponding proportion of 1:3.1:2.6:0.55 by weight of cement. The mix was designed in accordance with ACI method [11] to achieve a cylindrical compressive strength of about 27 MPa and a good workability to facilitate the handling of the mix. The mix had a slump of 7 cm. The high performance concrete mix was especially designed to have a high compressive strength of about 75 MPa, splitting tensile strength of about 8 MPa, high workability, and good durability [12–14]. The properties of the materials used for preparing this mix and its mix proportions are shown in Table 1.
Silica sand
1.7
Dmax = 0.2 mm, BSG = 2.6 Fineness modulus = 2.66
Silica fume
0.15
Sico silica fume
Water/cement ratio
0.45
By weight
Super plasticizer
0.03
Cico fluid type ME1
2.1. Specimen geometry and reinforcement details One-third-scale reinforced concrete interior beam–column joint specimens were prepared in this study. A schematic sketch of the specimen used is shown in Fig. 2 and the reinforcement details are listed in Table 2 and demonstrated in Fig. 2. A photograph of the actual laboratory test specimen with its boundary conditions (supports) and the applied loads is shown
Fig. 3. Details of the experimental test set-up.
in Fig. 3. The reinforcing steel used consisted of deformed bars with a measured yield strength of about 310 MPa. Table 2 outlines the number of specimens cast and the parameters
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Table 2 Experimental program Specimen no.
Beam Bottom steel
Top steel
Stirrups
S1
Continuous (2Φ10)
Continuous (2Φ14)
Φ8@150 mm
S2
Discontinuous (2Φ10)
Continuous (2Φ14)
S3
Discontinuous (2Φ10)
S4
Column Main steel
Ties
Joint Type of fiber and joint region
Ties
% of fiber
Continuous (4Φ14)
Yes
......
Yes
......
Φ8@150 mm
Lap splices (4Φ14)
Yes
......
No
......
Continuous (2Φ14)
Φ8@150 mm
Lap splices (4Φ14)
Yes
BCSF (Type 1)
No
2%
Discontinuous (2Φ10)
Continuous (2Φ14)
Φ8@150 mm
Lap splices (4Φ14)
Yes
BCSF (Type 2)
No
2%
S5
Discontinuous (2Φ10)
Continuous (2Φ14)
Φ8@150 mm
Lap splices (4Φ14)
Yes
BCSF (Type 1)
No
4%
S6
Discontinuous (2Φ10)
Continuous (2Φ14)
Φ8@150 mm
Lap splices (4Φ14)
Yes
BCSF (Type 2)
No
4%
S7
Discontinuous (2Φ10)
Continuous (2Φ14)
Φ8@150 mm
Lap splices (4Φ14)
Yes
HSF (Type 1)
No
2%
S8
Discontinuous (2Φ10)
Continuous (2Φ14)
Φ8@150 mm
Lap splices (4Φ14)
Yes
HSF (Type 2)
No
2%
S9
Discontinuous (2Φ10)
Continuous (2Φ14)
Φ8@150 mm
Lap splices (4Φ14)
Yes
HSF (Type 1)
No
4%
S10
Discontinuous (2Φ10)
Continuous (2Φ14)
Φ8@150 mm
Lap splices (4Φ14)
Yes
HSF (Type 2)
No
4%
investigated in this study. Parameters of interest included steel detailing of the joint region [14], type and volume fraction of the fibers. 2.2. Strengthening method This study involved strengthening both the joint and column regions of the interior beam–column connections that are the weakest link in the building, using HPFRC. Ten 1/3-scale specimens representing interior beam–column connections were prepared; one of them simulates reference/asbuilt specimens without critical reinforcement details and another one was prepared with critical reinforcement details that include the column main reinforcement lap spliced just above joint region, discontinuous bottom beam reinforcement, and little or no joint transverse reinforcement as shown in Fig. 2. The remaining eight specimens were strengthened using high strength concrete containing 2% or 4% by volume of brass-coated (BCSF) or hooked steel fibers (HSF) in the joint region. HPFRC mix was designed and poured in two types of joint regions; in both types HPFRC was poured into the entire joint column region and extended on both sides from the joint face along the beam 200 mm (depth of beam, h) for the type 1 joint and 300 mm (3/2 h) for the type 2 joint region as shown in Fig. 4. The specimens were left to dry for 48 h at laboratory temperature, and cured for one week, wrapping with wet burlap until the time of testing.
Fig. 4a. Geometry of joint region 1: For specimens nos. 3, 5, 7, and 9.
2.3. Test set-up The test set-up consists of a hydraulic actuator of a 150 kN capacity in tension and 250 kN in compression, that provides
Fig. 4b. Geometry of joint region 2: For specimens nos. 4, 6, 8, and 10.
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Fig. 5. General model layout showing boundary conditions.
Fig. 7. Location of LVDTs. Fig. 6. Cyclic loading history used in this study.
the cyclic loading on the top column of the beam–column joint, with zero axial column load; roller supports at both beam-ends and hinged support at the bottom of the lower column as shown in Figs. 3 and 5; the point of load at the upper column end is free to rotate in the loading plane. The supports were made from hardened steel plates, cut and formed in the engineering workshop of our university with a suitable thickness to sustain the applied load without any deformation that may affect the test results. A convenient cyclic loading history (simulating earthquake loading) was applied in testing the specimens, as shown in Fig. 6. All specimens were tested under stroke control at a rate of 0.02 mm/s using a hydraulic actuator jack with a cyclic loading applied at the top of the column. Six linear variable differential transducers (LVDTs) were used to measure the curvatures and the joint shear strain as shown in Fig. 7. The LVDTs, and the corresponding load and top column displacement, were connected to a data acquisition system that recorded the data every 10 s [13]. 3. Test results 3.1. Load–displacement hysteretic results The load–displacement hysteresis loop for reference specimen S2, Fig. 8, is rather poor and verifies the weak
performance of this connection. The column joint region, especially the joint, exhibited pinching and reduction in strength, while the beams remained elastic. This weak behavior was due to the combination of the three most critical reinforcement details of the beam–column joint. The transverse shear reinforcement that was provided within the joint region, reference specimen S1, serves to confine the concrete, thereby increasing its compressive resistance (in the compressive diagonal) and preserving integrity of the connection. The effect of this transverse reinforcement is clearly shown in Fig. 8. Both positive and negative strengths were more than the strengths of S2, but they were still less than those for the HPFRC specimens. The peak horizontal load and the net drift of reference specimens S1 and S2 were (18.56, 11.494 kN, 15.15, 9.09 mm) respectively. Horizontal load–displacement hysteresis loops of the strengthened specimens verify the strong behavior of the connections and show a significant increase in the strength and net drift as shown in Figs. 9 and 10. Specimens S3, S4 (with 2% and 4% BCSF) exhibited a peak horizontal load and net drift of (24.05, 27.25 kN, 22.45, 29.81 mm), respectively. Horizontal load–net drift loops of HSFRC specimens showed the most significant improvement in the performance due to the geometry of the fibers that resulted in larger bond strength. Specimens S7 and S8 exhibited a peak horizontal load and net
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Fig. 8. Horizontal load–net drift hysteresis loops of reference specimens S1 and S2.
Fig. 9. Horizontal load–net drift hysteresis loops of specimens strengthened with 2% brass-coated steel fibers (BCSF), S3: joint type 1, S4: joint type 2.
Fig. 10. Horizontal load–net drift hysteresis loops of specimens strengthened with 2% hooked steel fibers (HSF), S7: joint type 1 and S8: joint type 2.
drift of (32.56, 33.75 kN, 34.99, 63.3 mm) respectively. The test results and failure modes of all the specimens tested are given in detail in Reference [14]. 3.2. Moment–curvature hysteretic results The measured curvatures versus applied moments at the critical sections of the beams and columns shown in Fig. 7 were used to verify the ductile behavior of the interior beam–column connections. The resulting moment–curvature hysteresis loops obtained at the specified sections on the beams of the specimens were plotted as shown in Figs. 11 through 13. Poor ductile performance of the reference specimens (S1, S2) is clearly shown in the figures, since they attained small moment and curvature values. S1 attained a larger increase in the moment and curvature values, more than S2, but this increase is still not enough to cause a ductile behavior. The specimens strengthened
using hooked steel fibers showed the largest increase in moment and curvature values and attained the highest ductility. By comparing the moment–curvature loops of both reference and strengthened specimens it can be seen that the moment carrying capacities have been increased to approximately twice. 3.3. Effect of fiber content on the hysteretic behavior As a measure of the dissipated energy of the specimens, the area under the full load–displacement envelopes was computed and defined as the energy that could be dissipated by the specimens before the system loses its stability. The best energy dissipation was exhibited by the specimens strengthened using hooked steel fibers. The dissipated energy increased significantly with increase in fiber content as shown in Table 3. For the full response, the energy dissipation of the strengthened specimens increased substantially compared to that of reference
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Fig. 11. Beam moment–curvature for reference specimens S1 and S2.
Fig. 12. Beam moment–curvature for specimens S3 and S4.
Fig. 13. Beam moment–curvature for specimens S7 and S8.
specimens, as seen from Table 3, and the areas enclosed by the hysteretic loops, being small for reference specimens and large for strengthened ones, as shown in Figs. 8–10. 4. Model layout The general model layout of the X Z -plane frame was generated with geometry, reinforcement detailing and boundary conditions as shown in Fig. 5. The frame was divided into fourteen frame elements using material property data for the tested frames; reference and strengthened specimens. The analysis was conducted using SAP-2000 static pushover analysis with P–Delta and large displacement geometric nonlinearity effects to predict the performance of the frame structure. SAP-2000 default properties were used for the nonlinear pushover analysis. Moment–curvature plots were
Table 3 Cumulative energy dissipation of tested specimens Specimen #
Full energy dissipation (kN m)
1 2 3 4 5 6 7 8 9 10
3.74 1.13 6.68 16.25 11.17 18.82 21.85 31.69 25.79 33.71
determined for frame elements 5 and 12, in accordance with the location of LVDTs in the tested specimens. All frame elements
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Fig. 14. Load–displacement envelopes for reference specimens.
Fig. 16. Load–displacement envelopes for joint type (2) specimens.
Fig. 17. Moment–curvature envelopes for reference specimens. Fig. 15. Load–displacement envelopes for joint type (1) specimens.
in the reference specimens were made with Normal Strength Concrete (NSC) properties. The strengthened specimens for joint region 1 as shown in Fig. 4a were made with High Strength Concrete (HSC) properties at elements 1–6 and 9–12, whilst elements 7, 8, 13 and 14 are made of NSC. With respect to the strengthened specimens for joint region 2 as shown in Fig. 4b, all elements are strengthened using HSC except elements 7 and 14 which are made of NSC. 4.1. Assumptions Fig. 18. Moment–curvature envelopes for joint type (1) specimens.
The assumptions used in this model are: 1—For normal strength concrete [15] Concrete compressive strength ( f c0 ) = 27 MPa. Concrete elastic√modulus (E c ) = 4700 f c0 = 24 421.92 MPa. 2—For high strength concrete [11,16] f c0 = 75 MPa √ E c = 3321.445 f c0 + 6895 = 35 659.55 MPa. The pushover results for load–displacement values and moment–curvature are used to draw the theoretical curves. These diagrams will be used to indicate whether the tested specimens have experimental values similar to them or not. 4.2. Modeling of test specimens Theoretical and experimental values of load–displacement envelopes and moment–curvature envelopes are shown in Figs. 14 through 19. It appears from the figures that the experimental values are very close or similar to the theoretical
Fig. 19. Moment–curvature envelopes for joint type (2) specimens.
values especially for reference specimens and BCSFRC strengthened specimens. The predicted load carrying capacities were reasonably close to the experimental capacities. The ratios of the theoretical to the experimental capacities were 0.85 and 1.36 for reference specimens S1 and S2, respectively. The ratios of the theoretical to the experimental capacities were 1.06, 0.97, 0.76, and 0.73 for joint type (1) specimens
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S3, S5, S7, and S9, respectively, while they were 0.9, 0.78, 0.71, 0.68 for joint type (2) specimens S4, S6, S8, and S10, respectively. The positive influence of the geometry and high aspect ratio of HSF is clear in the figures; thus HSFRC specimens attained values more than the theoretical ones. 5. Conclusions The proposed model showed a good correlation between the theoretical curves of load–displacement and moment–curvature of the tested frames and the experimental results especially for ordinary concrete and BCSFRC strengthened connections. The static pushover analysis (NSP) appears to present design guidelines that, for similar cases, would allow the choice of the upgrade level for the joint and the column depending on the desired strength and ductility with ductile failure mode. Using high performance steel fiber reinforced concrete (HPFRC) in place of ordinary concrete in the joint region significantly improved the seismic behavior of non-seismically designed beam–column joints such that higher load levels, moments, curvatures, and larger displacements were attained. Acknowledgment The authors acknowledge the technical and financial support provided by Jordan University of Science and Technology. References [1] Beres A, Pessiki S, White R, Gergely P. Implications of experiments on the seismic behavior of gravity load designed RC beam-to-column connections. Earthquake Spectra 1996;12:185–98.
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[2] Baglin S, Scott R. Finite element modeling of reinforced concrete beam–column connections. ACI Structural Journal 2000;92:711–23. [3] Bracci J, Reinhorn A, Mander J. Seismic retrofit of reinforced buildings designed for gravity loads. ACI Structural Journal 1995;97:886–94. [4] Filiatrault A, Ladicani K, Massicotte B. Seismic performance of codedesigned fiber reinforced concrete joints. ACI Structural Journal 1993;91: 564–71. [5] Tsonos AG. Lateral load response of strengthened reinforced concrete beam-to-column joints. ACI Structural Journal 1999;96:46–56. [6] Hakuto S, Park R, Tanaka H. Seismic load tests on interior and exterior beam–column joints with substandard reinforcing details. ACI Structural Journal 2000;97:11–25. [7] Filiatrault A, Pineau S, Houde J. Seismic behavior of steel–fiber reinforced concrete interior beam–column joints. ACI Structural Journal 1995;92:543–52. [8] Parra-Montesinos G, Wight J. Seismic repair of hybrid RCS beam–column connections. ACI Structural Journal 2001;98:762–70. [9] Shannag MJ, Alhassan M. Seismic upgrade of interior beam–column subassemblages with high performance fiber-reinforced concrete jackets. ACI structural Journal 2005;102(1):131–8. [10] Habibullah A, Pyle S. Practical three dimensional nonlinear static pushover analysis. Structure Magazine, Winter 1998. [11] Mehta P. Concrete, structure, properties and materials. NJ: Prentice Hall Inc.; 1986. [12] Shannag M. High-performance cementitious grouts for structural repair. Cement and Concrete Research 2002;32:803–8. [13] Abu-Dayya N. Structural seismic behavior of beam–column joints using high performance concrete. Master thesis. Civil Engineering Department, Jordan University of Science and Technology; 2002. [14] Shannag MJ, Abu-Dyya N, Abu-Farsakh M. Lateral load response of high performance fiber reinforced concrete beam–column joints. Construction and Building Materials Journal 2005;19:500–8. [15] ACI Committee 318. Building code requirements for reinforced concrete. Detroit: American Concrete Institute; 1995. [16] ACI Committee 363. State of the art report on high strength concrete. ACI Journal 1984;84(4):364–411.
Modeling the cyclic response of fiber reinforced concrete joints M. Jamal Shannag a,∗ , Ghazi Abu-Farsakh b , Nabeela Abu-Dyya b a Civil Engineering Department, King Saud University, Riyadh 11421, Saudi Arabia b Department of Civil Engineering, Jordan University of Science and Technology, Jordan
Received 28 April 2006; received in revised form 2 October 2006; accepted 8 February 2007 Available online 23 March 2007
Abstract A nonlinear static (pushover) procedure (NSP) was used to model the behavior of interior beam–column (B–C) joints under lateral cyclic loading. The results of the analytical and numerical solutions were compared with the results obtained from experimental tests. Ten 1/3scale interior beam–column joints, part of a prototype building designed according to the existing practice in Jordan, were tested under cyclic reverse loading. Most of these joints lacked transverse reinforcement, column lap splices and continuous bottom beam reinforcement. They were strengthened using high performance steel fiber reinforced concrete (HPFRC) in place of ordinary concrete in two types of joint region, extending 200 and 300 mm from the face of the column. The experimental results were found to be in good agreement with the results of the applied modeling technique and assumptions made. The static pushover analysis appears to be a viable tool for predicting the load–deflection and moment–curvature responses of beam–column joints. c 2007 Elsevier Ltd. All rights reserved.
Keywords: Pushover analysis; Beam–column joints; Fiber reinforced concrete
1. Introduction Extensive experimental studies have previously been performed to investigate the seismic behavior of beam–column (B–C) joint details in reinforced concrete buildings, and to investigate the joint behavior under simulated seismic loading [1–9]. The behavior of beam–column (B–C) joints is complex and still not fully understood. Recent developments in fiber reinforced cement-based composites, and their increasing use in earthquake-resistant design for achieving higher ductility at a lesser cost, made it very difficult to cover all the variables that affect the B–C joint by experimental testing alone, and a reliable analytical model could provide a significant contribution to a detailed experimental study. Therefore the main objective of this study was to develop a numerical model that could be utilized as an investigative tool in conjunction with an experimental program. The recent advent of performance-based design has brought the nonlinear static pushover analysis procedure (NSP) to the ∗ Corresponding author. Tel.: +966 1 4676928, +966 4683076; Mob: +966 559661230; fax: +966 1 4677008. E-mail addresses: [email protected], [email protected] (M.J. Shannag).
c 2007 Elsevier Ltd. All rights reserved. 0141-0296/$ - see front matter doi:10.1016/j.engstruct.2007.02.003
Fig. 1. Force–deformation for a pushover hinge.
forefront [10]. Pushover analysis is a static, nonlinear procedure, by which the magnitude of the structural loading is incrementally increased in accordance with a certain predefined pattern. With the increase in the magnitude of the loading, weak links and failure modes of the structure are found. The loading is monotonic with the effects of the cyclic and load reversals being estimated by using modified monotonic force–deformation criteria. The force–deformation criterion for hinges used in pushover analysis is defined as shown in Fig. 1. Static pushover
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Fig. 2. Specimen geometry and steel detailing of reference specimens no. 2 through 10, with critical detailing in the joint region. Specimen no. 1 is the same without critical detailing in the joint region.
analysis is an attempt by the structural engineering profession to evaluate the real strength of the structure and it promises to be a useful and effective tool for performance-based design. There are a large number of variables interacting to control the capacity of the joint and even an extensive experimental program cannot fully validate all combinations. The SAP 2000 static pushover analysis capabilities, which are fully integrated into the program, allow quick and easy implementation of the pushover procedures for predicting the theoretical values of load–displacement and moment–curvature curves for the tested frames.
Table 1 Proportions and properties of HPFRC-mix materials Material
Proportion
Properties
Fiber (BCSF or HSF)
2% or 4% by volume
(Dramix 6/0.15) tensile yield strength = 2950 MPa. (Dramix 30/0.5) tensile yield strength = 1172 MPa.
Cement
1
Portland Pozzolana cement; complying with Jordanian specifications
Coarse aggregate
2.30
Crushed limestone with Dmax = 9.5 mm, BSG = 2.6
2. Experimental program
Limestone
0.26
BSG = 2.65 Fineness modulus = 3.1
Two concrete mixes were used for preparing the B–C joint specimens in this investigation: normal concrete mix and high performance steel fiber reinforced concrete mix. The normal concrete mix consists of cement, coarse aggregate, fine aggregate, and water with a corresponding proportion of 1:3.1:2.6:0.55 by weight of cement. The mix was designed in accordance with ACI method [11] to achieve a cylindrical compressive strength of about 27 MPa and a good workability to facilitate the handling of the mix. The mix had a slump of 7 cm. The high performance concrete mix was especially designed to have a high compressive strength of about 75 MPa, splitting tensile strength of about 8 MPa, high workability, and good durability [12–14]. The properties of the materials used for preparing this mix and its mix proportions are shown in Table 1.
Silica sand
1.7
Dmax = 0.2 mm, BSG = 2.6 Fineness modulus = 2.66
Silica fume
0.15
Sico silica fume
Water/cement ratio
0.45
By weight
Super plasticizer
0.03
Cico fluid type ME1
2.1. Specimen geometry and reinforcement details One-third-scale reinforced concrete interior beam–column joint specimens were prepared in this study. A schematic sketch of the specimen used is shown in Fig. 2 and the reinforcement details are listed in Table 2 and demonstrated in Fig. 2. A photograph of the actual laboratory test specimen with its boundary conditions (supports) and the applied loads is shown
Fig. 3. Details of the experimental test set-up.
in Fig. 3. The reinforcing steel used consisted of deformed bars with a measured yield strength of about 310 MPa. Table 2 outlines the number of specimens cast and the parameters
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Table 2 Experimental program Specimen no.
Beam Bottom steel
Top steel
Stirrups
S1
Continuous (2Φ10)
Continuous (2Φ14)
Φ8@150 mm
S2
Discontinuous (2Φ10)
Continuous (2Φ14)
S3
Discontinuous (2Φ10)
S4
Column Main steel
Ties
Joint Type of fiber and joint region
Ties
% of fiber
Continuous (4Φ14)
Yes
......
Yes
......
Φ8@150 mm
Lap splices (4Φ14)
Yes
......
No
......
Continuous (2Φ14)
Φ8@150 mm
Lap splices (4Φ14)
Yes
BCSF (Type 1)
No
2%
Discontinuous (2Φ10)
Continuous (2Φ14)
Φ8@150 mm
Lap splices (4Φ14)
Yes
BCSF (Type 2)
No
2%
S5
Discontinuous (2Φ10)
Continuous (2Φ14)
Φ8@150 mm
Lap splices (4Φ14)
Yes
BCSF (Type 1)
No
4%
S6
Discontinuous (2Φ10)
Continuous (2Φ14)
Φ8@150 mm
Lap splices (4Φ14)
Yes
BCSF (Type 2)
No
4%
S7
Discontinuous (2Φ10)
Continuous (2Φ14)
Φ8@150 mm
Lap splices (4Φ14)
Yes
HSF (Type 1)
No
2%
S8
Discontinuous (2Φ10)
Continuous (2Φ14)
Φ8@150 mm
Lap splices (4Φ14)
Yes
HSF (Type 2)
No
2%
S9
Discontinuous (2Φ10)
Continuous (2Φ14)
Φ8@150 mm
Lap splices (4Φ14)
Yes
HSF (Type 1)
No
4%
S10
Discontinuous (2Φ10)
Continuous (2Φ14)
Φ8@150 mm
Lap splices (4Φ14)
Yes
HSF (Type 2)
No
4%
investigated in this study. Parameters of interest included steel detailing of the joint region [14], type and volume fraction of the fibers. 2.2. Strengthening method This study involved strengthening both the joint and column regions of the interior beam–column connections that are the weakest link in the building, using HPFRC. Ten 1/3-scale specimens representing interior beam–column connections were prepared; one of them simulates reference/asbuilt specimens without critical reinforcement details and another one was prepared with critical reinforcement details that include the column main reinforcement lap spliced just above joint region, discontinuous bottom beam reinforcement, and little or no joint transverse reinforcement as shown in Fig. 2. The remaining eight specimens were strengthened using high strength concrete containing 2% or 4% by volume of brass-coated (BCSF) or hooked steel fibers (HSF) in the joint region. HPFRC mix was designed and poured in two types of joint regions; in both types HPFRC was poured into the entire joint column region and extended on both sides from the joint face along the beam 200 mm (depth of beam, h) for the type 1 joint and 300 mm (3/2 h) for the type 2 joint region as shown in Fig. 4. The specimens were left to dry for 48 h at laboratory temperature, and cured for one week, wrapping with wet burlap until the time of testing.
Fig. 4a. Geometry of joint region 1: For specimens nos. 3, 5, 7, and 9.
2.3. Test set-up The test set-up consists of a hydraulic actuator of a 150 kN capacity in tension and 250 kN in compression, that provides
Fig. 4b. Geometry of joint region 2: For specimens nos. 4, 6, 8, and 10.
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Fig. 5. General model layout showing boundary conditions.
Fig. 7. Location of LVDTs. Fig. 6. Cyclic loading history used in this study.
the cyclic loading on the top column of the beam–column joint, with zero axial column load; roller supports at both beam-ends and hinged support at the bottom of the lower column as shown in Figs. 3 and 5; the point of load at the upper column end is free to rotate in the loading plane. The supports were made from hardened steel plates, cut and formed in the engineering workshop of our university with a suitable thickness to sustain the applied load without any deformation that may affect the test results. A convenient cyclic loading history (simulating earthquake loading) was applied in testing the specimens, as shown in Fig. 6. All specimens were tested under stroke control at a rate of 0.02 mm/s using a hydraulic actuator jack with a cyclic loading applied at the top of the column. Six linear variable differential transducers (LVDTs) were used to measure the curvatures and the joint shear strain as shown in Fig. 7. The LVDTs, and the corresponding load and top column displacement, were connected to a data acquisition system that recorded the data every 10 s [13]. 3. Test results 3.1. Load–displacement hysteretic results The load–displacement hysteresis loop for reference specimen S2, Fig. 8, is rather poor and verifies the weak
performance of this connection. The column joint region, especially the joint, exhibited pinching and reduction in strength, while the beams remained elastic. This weak behavior was due to the combination of the three most critical reinforcement details of the beam–column joint. The transverse shear reinforcement that was provided within the joint region, reference specimen S1, serves to confine the concrete, thereby increasing its compressive resistance (in the compressive diagonal) and preserving integrity of the connection. The effect of this transverse reinforcement is clearly shown in Fig. 8. Both positive and negative strengths were more than the strengths of S2, but they were still less than those for the HPFRC specimens. The peak horizontal load and the net drift of reference specimens S1 and S2 were (18.56, 11.494 kN, 15.15, 9.09 mm) respectively. Horizontal load–displacement hysteresis loops of the strengthened specimens verify the strong behavior of the connections and show a significant increase in the strength and net drift as shown in Figs. 9 and 10. Specimens S3, S4 (with 2% and 4% BCSF) exhibited a peak horizontal load and net drift of (24.05, 27.25 kN, 22.45, 29.81 mm), respectively. Horizontal load–net drift loops of HSFRC specimens showed the most significant improvement in the performance due to the geometry of the fibers that resulted in larger bond strength. Specimens S7 and S8 exhibited a peak horizontal load and net
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Fig. 8. Horizontal load–net drift hysteresis loops of reference specimens S1 and S2.
Fig. 9. Horizontal load–net drift hysteresis loops of specimens strengthened with 2% brass-coated steel fibers (BCSF), S3: joint type 1, S4: joint type 2.
Fig. 10. Horizontal load–net drift hysteresis loops of specimens strengthened with 2% hooked steel fibers (HSF), S7: joint type 1 and S8: joint type 2.
drift of (32.56, 33.75 kN, 34.99, 63.3 mm) respectively. The test results and failure modes of all the specimens tested are given in detail in Reference [14]. 3.2. Moment–curvature hysteretic results The measured curvatures versus applied moments at the critical sections of the beams and columns shown in Fig. 7 were used to verify the ductile behavior of the interior beam–column connections. The resulting moment–curvature hysteresis loops obtained at the specified sections on the beams of the specimens were plotted as shown in Figs. 11 through 13. Poor ductile performance of the reference specimens (S1, S2) is clearly shown in the figures, since they attained small moment and curvature values. S1 attained a larger increase in the moment and curvature values, more than S2, but this increase is still not enough to cause a ductile behavior. The specimens strengthened
using hooked steel fibers showed the largest increase in moment and curvature values and attained the highest ductility. By comparing the moment–curvature loops of both reference and strengthened specimens it can be seen that the moment carrying capacities have been increased to approximately twice. 3.3. Effect of fiber content on the hysteretic behavior As a measure of the dissipated energy of the specimens, the area under the full load–displacement envelopes was computed and defined as the energy that could be dissipated by the specimens before the system loses its stability. The best energy dissipation was exhibited by the specimens strengthened using hooked steel fibers. The dissipated energy increased significantly with increase in fiber content as shown in Table 3. For the full response, the energy dissipation of the strengthened specimens increased substantially compared to that of reference
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Fig. 11. Beam moment–curvature for reference specimens S1 and S2.
Fig. 12. Beam moment–curvature for specimens S3 and S4.
Fig. 13. Beam moment–curvature for specimens S7 and S8.
specimens, as seen from Table 3, and the areas enclosed by the hysteretic loops, being small for reference specimens and large for strengthened ones, as shown in Figs. 8–10. 4. Model layout The general model layout of the X Z -plane frame was generated with geometry, reinforcement detailing and boundary conditions as shown in Fig. 5. The frame was divided into fourteen frame elements using material property data for the tested frames; reference and strengthened specimens. The analysis was conducted using SAP-2000 static pushover analysis with P–Delta and large displacement geometric nonlinearity effects to predict the performance of the frame structure. SAP-2000 default properties were used for the nonlinear pushover analysis. Moment–curvature plots were
Table 3 Cumulative energy dissipation of tested specimens Specimen #
Full energy dissipation (kN m)
1 2 3 4 5 6 7 8 9 10
3.74 1.13 6.68 16.25 11.17 18.82 21.85 31.69 25.79 33.71
determined for frame elements 5 and 12, in accordance with the location of LVDTs in the tested specimens. All frame elements
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Fig. 14. Load–displacement envelopes for reference specimens.
Fig. 16. Load–displacement envelopes for joint type (2) specimens.
Fig. 17. Moment–curvature envelopes for reference specimens. Fig. 15. Load–displacement envelopes for joint type (1) specimens.
in the reference specimens were made with Normal Strength Concrete (NSC) properties. The strengthened specimens for joint region 1 as shown in Fig. 4a were made with High Strength Concrete (HSC) properties at elements 1–6 and 9–12, whilst elements 7, 8, 13 and 14 are made of NSC. With respect to the strengthened specimens for joint region 2 as shown in Fig. 4b, all elements are strengthened using HSC except elements 7 and 14 which are made of NSC. 4.1. Assumptions Fig. 18. Moment–curvature envelopes for joint type (1) specimens.
The assumptions used in this model are: 1—For normal strength concrete [15] Concrete compressive strength ( f c0 ) = 27 MPa. Concrete elastic√modulus (E c ) = 4700 f c0 = 24 421.92 MPa. 2—For high strength concrete [11,16] f c0 = 75 MPa √ E c = 3321.445 f c0 + 6895 = 35 659.55 MPa. The pushover results for load–displacement values and moment–curvature are used to draw the theoretical curves. These diagrams will be used to indicate whether the tested specimens have experimental values similar to them or not. 4.2. Modeling of test specimens Theoretical and experimental values of load–displacement envelopes and moment–curvature envelopes are shown in Figs. 14 through 19. It appears from the figures that the experimental values are very close or similar to the theoretical
Fig. 19. Moment–curvature envelopes for joint type (2) specimens.
values especially for reference specimens and BCSFRC strengthened specimens. The predicted load carrying capacities were reasonably close to the experimental capacities. The ratios of the theoretical to the experimental capacities were 0.85 and 1.36 for reference specimens S1 and S2, respectively. The ratios of the theoretical to the experimental capacities were 1.06, 0.97, 0.76, and 0.73 for joint type (1) specimens
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S3, S5, S7, and S9, respectively, while they were 0.9, 0.78, 0.71, 0.68 for joint type (2) specimens S4, S6, S8, and S10, respectively. The positive influence of the geometry and high aspect ratio of HSF is clear in the figures; thus HSFRC specimens attained values more than the theoretical ones. 5. Conclusions The proposed model showed a good correlation between the theoretical curves of load–displacement and moment–curvature of the tested frames and the experimental results especially for ordinary concrete and BCSFRC strengthened connections. The static pushover analysis (NSP) appears to present design guidelines that, for similar cases, would allow the choice of the upgrade level for the joint and the column depending on the desired strength and ductility with ductile failure mode. Using high performance steel fiber reinforced concrete (HPFRC) in place of ordinary concrete in the joint region significantly improved the seismic behavior of non-seismically designed beam–column joints such that higher load levels, moments, curvatures, and larger displacements were attained. Acknowledgment The authors acknowledge the technical and financial support provided by Jordan University of Science and Technology. References [1] Beres A, Pessiki S, White R, Gergely P. Implications of experiments on the seismic behavior of gravity load designed RC beam-to-column connections. Earthquake Spectra 1996;12:185–98.
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[2] Baglin S, Scott R. Finite element modeling of reinforced concrete beam–column connections. ACI Structural Journal 2000;92:711–23. [3] Bracci J, Reinhorn A, Mander J. Seismic retrofit of reinforced buildings designed for gravity loads. ACI Structural Journal 1995;97:886–94. [4] Filiatrault A, Ladicani K, Massicotte B. Seismic performance of codedesigned fiber reinforced concrete joints. ACI Structural Journal 1993;91: 564–71. [5] Tsonos AG. Lateral load response of strengthened reinforced concrete beam-to-column joints. ACI Structural Journal 1999;96:46–56. [6] Hakuto S, Park R, Tanaka H. Seismic load tests on interior and exterior beam–column joints with substandard reinforcing details. ACI Structural Journal 2000;97:11–25. [7] Filiatrault A, Pineau S, Houde J. Seismic behavior of steel–fiber reinforced concrete interior beam–column joints. ACI Structural Journal 1995;92:543–52. [8] Parra-Montesinos G, Wight J. Seismic repair of hybrid RCS beam–column connections. ACI Structural Journal 2001;98:762–70. [9] Shannag MJ, Alhassan M. Seismic upgrade of interior beam–column subassemblages with high performance fiber-reinforced concrete jackets. ACI structural Journal 2005;102(1):131–8. [10] Habibullah A, Pyle S. Practical three dimensional nonlinear static pushover analysis. Structure Magazine, Winter 1998. [11] Mehta P. Concrete, structure, properties and materials. NJ: Prentice Hall Inc.; 1986. [12] Shannag M. High-performance cementitious grouts for structural repair. Cement and Concrete Research 2002;32:803–8. [13] Abu-Dayya N. Structural seismic behavior of beam–column joints using high performance concrete. Master thesis. Civil Engineering Department, Jordan University of Science and Technology; 2002. [14] Shannag MJ, Abu-Dyya N, Abu-Farsakh M. Lateral load response of high performance fiber reinforced concrete beam–column joints. Construction and Building Materials Journal 2005;19:500–8. [15] ACI Committee 318. Building code requirements for reinforced concrete. Detroit: American Concrete Institute; 1995. [16] ACI Committee 363. State of the art report on high strength concrete. ACI Journal 1984;84(4):364–411.