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Page 1 of 9 BEAM-COLUMN JOINTS STRENGTHENED WITH FRP SYSTEMS Ciro FAELLA Full Professor University of Salerno, Department of Civil Engineering Via Ponte don Melillo, 84084 - Fisciano (SA), Italy [email protected] Carmine LIMA Post-doctoral Research Assistant University of Salerno, Department of Civil Engineering Via Ponte don Melillo, 84084 - Fisciano (SA), Italy [email protected] Annalisa NAPOLI Post-doctoral Research Fellow University of Salerno, Department of Civil Engineering Via Ponte don Melillo, 84084 - Fisciano (SA), Italy [email protected] Roberto REALFONZO Associate Professor University of Salerno, Department of Civil Engineering Via Ponte don Melillo, 84084 - Fisciano (SA), Italy [email protected]* Joaquín Guillermo RUIZ PINILLA PhD Student Universitat Politècnica de València , ICITECH Camino de Vera s/n, 46022 Valencia, Spain [email protected] Abstract This paper presents the first results of an experimental campaign performed – at the Laboratory of Materials & Structures of the University of Salerno (Italy) – with the aim to investigate the seismic performance of RC beam-columns joints strengthened with FRP and steel systems. The complete test matrix includes eight specimens realized to be representative of existing exterior beam-column subassemblies with inadequate seismic details. Several technical solutions were selected in order to improve the joint seismic behaviour, and the performance of the first two strengthening systems is investigated in this paper. To this aim, three beam-column joints have been tested so far, i.e. two strengthened specimens and a reference (unstrengthened) one. Test results have begun to provide useful information for the adopted strengthening systems in terms of strength, ductility and energy dissipation capacity. Keywords: Beam-column joints; ductility; experimental tests; FRP; seismic upgrade; strength. 1. Introduction Nowadays, the seismic upgrading of underdesigned reinforced concrete (RC) structures represents a key issue in the civil engineering field. Typically, beam-column assemblages of existing framed buildings were designed to behave in a weak column-strong beam fashion that, under seismic loads, may lead to the formation of local hinges in the column. The

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Page 1 of 9

BEAM-COLUMN JOINTS STRENGTHENED WITH FRP SYSTEMS

Ciro FAELLA

Full Professor

University of Salerno, Department of Civil Engineering

Via Ponte don Melillo, 84084 - Fisciano (SA), Italy

[email protected]

Carmine LIMA

Post-doctoral Research Assistant

University of Salerno, Department of Civil Engineering

Via Ponte don Melillo, 84084 - Fisciano (SA), Italy

[email protected]

Annalisa NAPOLI

Post-doctoral Research Fellow

University of Salerno, Department of Civil Engineering

Via Ponte don Melillo, 84084 - Fisciano (SA), Italy

[email protected]

Roberto REALFONZO

Associate Professor

University of Salerno, Department of Civil Engineering

Via Ponte don Melillo, 84084 - Fisciano (SA), Italy

[email protected]*

Joaquín Guillermo RUIZ PINILLA

PhD Student

Universitat Politècnica de València , ICITECH Camino de Vera s/n, 46022 Valencia, Spain [email protected]

Abstract

This paper presents the first results of an experimental campaign performed – at the Laboratory of Materials & Structures of the University of Salerno (Italy) – with the aim to investigate the seismic performance of RC beam-columns joints strengthened with FRP and steel systems. The complete test matrix includes eight specimens realized to be representative of existing exterior beam-column subassemblies with inadequate seismic details. Several technical solutions were selected in order to improve the joint seismic behaviour, and the performance of the first two strengthening systems is investigated in this paper. To this aim, three beam-column joints have been tested so far, i.e. two strengthened specimens and a reference (unstrengthened) one. Test results have begun to provide useful information for the adopted strengthening systems in terms of strength, ductility and energy dissipation capacity.

Keywords: Beam-column joints; ductility; experimental tests; FRP; seismic upgrade; strength.

1. Introduction

Nowadays, the seismic upgrading of underdesigned reinforced concrete (RC) structures represents a key issue in the civil engineering field. Typically, beam-column assemblages of existing framed buildings were designed to behave in a weak column-strong beam fashion that, under seismic loads, may lead to the formation of local hinges in the column. The

Page 2 of 9

associated failure mode represents, therefore, the lower bound of the hierarchy of strength and is characterized by a brittle structural failure.

A number of technical solutions based on the local strengthening of columns have been proposed in the literature with the aim to improve the seismic performance of deficient RC structures. However, in gravity load-designed structures where beams are often stronger than columns, increasing the strength and, mainly, the ductility of columns is generally not sufficient by itself since the joint panel then becomes the next weakest element due to either lack of transverse reinforcement, discontinuous beam bottom reinforcement, or other nonductile detailing. The brittle failure of joints, significantly reduces the overall ductility of structures and, in some cases, may lead them to the collapse. Therefore, the joint panel should be strengthened by increasing the shear capacity and the effective confinement.

In this paper, the feasibility of novel FRP ("Fiber Reinforced Polymers") strengthening solutions in increasing the seismic performance of exterior RC beam-column joints is investigated. An experimental program was organized at the University of Salerno (Italy) which includes eight specimens representative of existing beam-column subassemblies with inadequate seismic details. Of these, six were strengthened by using different FRP systems while the remaining ones were used as reference benchmark; once damaged, some specimens were also re-tested after being retrofitted with FRP. So far, three beam-column joints have been tested, i.e. two strengthened specimens and a control one, and the preliminary results are presented and discussed herein.

2. Experimental program

The ongoing experimental program includes a total of eight RC beam-column joints to subject to reversed cyclic forces applied at the beam tip by keeping the column under a constant axial load. So far, three tests have been performed and the results are presented and discussed herein. The following sections report a detailed description about the design of test specimens, strengthening layouts, test setup and instrumentation.

2.1 Design of specimens

Two sets of exterior beam-column joints were designed for the experimental campaign, characterized by different amounts of longitudinal steel reinforcement in the beams and columns. Figure 1 depicts the geometry and the rebars configuration of the two sets of joints, labelled "Type 1" (Fig. 1a) and "Type 2" (Fig. 1b), respectively, each including four identical specimens. As shown, the columns are the horizontal members having a square 300x300 mm cross section and a length of 2000 mm, whereas the beams are the vertical ones with rectangular 300x400 mm cross section and a length of 1500 mm. In the specimen Type 1, with the aim of simulating the behaviour of subassemblies with weak column, the longitudinal steel reinforcement in the beam and column members consists of

(3+3)Φ20 and (2+2)Φ14 deformed rebars, respectively. Conversely, in the specimen Type 2, in order to obtain the behavior of subassemblies with strong column, a different amount of steel reinforcement ratio was considered, with beam and column reinforced by using

(4+4)Φ20 and (4+4)Φ14, respectively. The transverse reinforcement in the beam and column members consisted of 8 mm diameter steel stirrups, 100 mm spaced. In order to reproduce subassemblies of RC frames built before the 70’s, no steel stirrups were placed in the joints according to the old Italian practice. Table 1 reports the mechanical properties considered for specimen design, being: fy and Es the average values of the yielding strength and elastic modulus of steel rebars, respectively, fc and Ec the respective values of the compression strength and the modulus of elasticity of concrete,

λ is the steel overstrength factor equal to 1.20.

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15

0

40

30

30

200

8080

stir

rups

Ø8/1

0 c

m

30

30

2 Ø 14 (L = 234 cm)

2 Ø 14 (L = 234 cm)

194

20

20

3 Ø

20

(L

= 2

24

cm

)

17

4

25

25

stirrups Ø8/10 cm

19420

20

3 Ø

20

(L

= 2

24

cm

)

17

4

25

25

End steel plate

Section A-A

Section B-B

B

B

AA

Beam steel

Column steel

15

0

40

30

30

200

8080

stir

rup

s Ø

8/1

0cm

30

30

4 Ø 14 (L = 234 cm)

4 Ø 14 (L = 234 cm)

194

20

20

4 Ø

20

(L

= 2

24 c

m)

17

4

25

25

stirrups Ø8/10cm

19420

20

4 Ø

20

(L

= 2

24 c

m)

17

4

25

25

AA

2424

34

24

10

10Beam stirrup - L=140 cm

stirrups Ø8/10 cm

Column stirrup L=120 cm

Column steelreinforcement

B

B

stirrups Ø8/10cm

reinforcement

reinforcement

End steel plate

Beam steel

reinforcement

Section B-B

Column stirrup L=120 cm

24

24

10

Section A-A

34

24

10Beam stirrup - L=140 cm

Figure 1. Geometry and steel reinforcement configuration for specimens Type 1 (a) and Type 2 (b).

The design of specimens was performed with the aim to achieve the connection failure having the column weaker than the beam but always stronger than the joint panel. To this purpose, five capacity models were selected from the literature and codes provisions in order to estimate the joint shear strength VR,jh, i.e. the models by: Italian Code [1] for evaluating the strength of joints belonging to new structures (model 1a) or assessing those of existing ones (model 1b); Paulay & Priestley [2] (model 2); Vollum & Newman [3] (model 3); Bakir & Boduroglu [4] (model 4); Kim et al. [5] (model 5). A wide overview of all joint strength models proposed in the literature, omitted herein for the sake of brevity, can be found in [6]. Table 2 reports the values of shear strength VR,jh estimated for the two joints types according to the five models, by assuming a constant axial load in the column equal to 300 kN.

Table 1. Mechanical properties of test specimens.

column beam joint Es

[MPa] Ec

[MPa] fy

[MPa] fc

[MPa] fy

[MPa] fc

[MPa] λ

[-] fy

[MPa] fc

[MPa]

540 16 540 16 1.20 540 16 210000 28750

Table 2. Estimated values of the joint shear strength VR,jh [kN]

TYPE Model 1a Model 1b Model 2 Model 3 Model 4 Model 5

1 210.84 174.60 323.15 320.57 204.80 290.60

2 208.48 173.30 360.00 316.63 228.86 313.30

By considering the testing configuration depicted in Figure 2a, the experimental value of the joint shear force Vjh

exp, relying on the force Pexp applied by the actuator the beam tip, can be easily evaluated by equilibrium throughout the joint panel (see Fig. 2b):

exp exp

exp exp exp

, ,2

⋅ ⋅= ⋅ − = −b b

jh s b y b c

y c

P L P LV A f T V

M L (1)

where: Vcexp is the shear force in the column, Texp is the force of the top bars in the beam, As,b

is the area of the beam steel reinforcement in tension; Lb=1580 mm, Lc=1300 mm (Fig 2a).

In Eq. (1) it has been assumed that the joint panel failure occurs before the beam yielding (according to the design criteria), i.e. the experimental bending moment acting on the joint at peak (Mexp = Pexp·Lb) is lower than the value at yielding of the beam (My ).

Type 1 Type 2

beam

column

a) b)

Page 4 of 9

Actuator

Column

Beam

Reaction Wall

Axial

load

Lb

Lc Lc

Figure 2. Test configuration for exterior joints (a); equilibrium throughout the joint panel (b).

By plugging Vjhexp = VR,jh, the ultimate value of Pexp can be finally derived from Eq. (1) and

the results obtained from considering the five strength models are reported in Table 3.

Table 3. Estimated values of the ultimate actuator load Pexp [kN].

TYPE Model 1a Model 1b Model 2 Model 3 Model 4 Model 5

1 44.86 37.15 49.39 68.20 43.57 61.83

2 44.03 36.60 76.03 66.87 48.33 66.16

2.2 Strengthening layouts

Figure 3 depicts the upgrading schemes adopted for the first tested "Type 1" beam-column joints, labelled J-02 (Fig. 3a) and J-03 (Fig. 3b). The strengthening design was based on the following general principles: a) upgrading the join panel; b) once strengthened the joint, avoiding the premature failure of the column during test; c) achieving the most desirable collapse mechanism, i.e. the beam failure. In order to pursue these objectives, both columns and joints panels were strengthened. In both schemes, the column upgrading consisted of longitudinal cold bent steel profiles along the member corners before applying the external continuous wrapping made of two carbon FRP (CFRP) layers. The profiles were four 80x80x6 mm equal leg angles made of structural steel S235; they were always glued to the concrete substrate by means of an epoxy adhesive.

In order to increase the flexural strength of the columns, (2+2)Φ16 threaded rods were glued with epoxy within the concrete cover and anchored in the joint panel. The employed CFRP plies, each 0.22 mm thick, were characterized by an elastic modulus of 390 GPa, a tensile strength of 3000 MPa and an ultimate strain equal to 0.80 %.

150

40

30

Bottom view

80

L-shape steel profiles

30

15 15

2 CFRP layers

b=15

30

15 15

452310

Threaded steel rods

2+2M16 Cl 5.8

7525

2M16 Cl 5.82M16 Cl 5.8

Threaded steel rods2+2M16 Cl 5.8

Front view

150

30

Bottom view

80

2 M16

cl 5.8

30

452310 Steel plates=5

2M16 Cl 5.82M16 Cl 5.8

Steel plates=5

30(int)

33

45(i

nt)

U-shape steel plate

welds

Front view

Threaded steel rods

2+2M16 Cl 5.8

L-shape steel profiles

40

Figure 3. Strengthening layouts for specimens J-02 (a) and J-03 (b).

a) b)

J-02 J-03

a) b)

Lb

Lc Lc

Page 5 of 9

In the case of the specimen J-02, according to a frequently used retrofitting system, the joint panel was strengthened by employing two U-shape CFRP-layers, 150 mm wide, which were anchored on the beam for a length of about 300 mm. In order to simulate the behaviour of an exterior RC joint with three high RC beams (i.e. a "well confined" joint), the joint of the specimen J-03 was strengthened by using a U-shape steel plate, 5 mm thick, properly anchored with threaded rods (with 16 mm diameter) through the joint. This layout may represent the target configuration for strength and stiffness related to out-of plane behaviour.

2.3 Test set-up

Figure 4a shows the set-up adopted for subjecting the beam-column joints to reversed cyclic forces applied at the beam tip by keeping the column under a constant axial load.

The column was mounted horizontally and restrained to both ends by assembling steel elements according to a roller-hinged scheme. It was pre-loaded in compression before applying the horizontal force by using a 1000 kN MTS hydraulic actuator fixed to a reaction steel frame. The axial load N, kept constant during the test, was equal to about 300 kN,

approximately corresponding to a normalized compression load "ν" of 0.20, given by:

cm g

N

f Aν =

⋅ (2)

where Ag is the column cross-section and fcm is the average value of the cylinder compressive strength of concrete. The latter was obtained from the relationship fcm=0.83 Rcm, where Rcm was estimated by testing in compression cubic 150-mm side specimens, taken during the casting of each column and cured under the same environmental conditions.

The horizontal force was cyclically applied in displacement control at the beam tip through a 250 kN MTS hydraulic actuator, mounted at 1430 mm from the beam base and fixed to a reaction steel frame. The time history of the horizontal displacement is shown in Figure 4b. An increment of the imposed horizontal displacement every three cycles was considered in order to evaluate the strength and stiffness degradation at repeated lateral load reversals. The displacement amplitude increment was given as fraction of the estimated beam yield

displacement, ∆y (≈ 14 mm); two different displacement rates were considered during the

tests: 0.2 mm/s before the achievement of ∆y and 1 mm/s after ∆y.

-80

-60

-40

-20

0

20

40

60

80

0 2000 4000 6000 8000

time [s]

Displacement [mm]

v=0.2 mm/s

v=1 mm/s

Figure 4. Test set-up (a); displacement history (b).

The joints were accurately instrumented according to Figure 5 in order to monitor strains, displacements and crack widths. In particular: a) four wire transducers (namely T1, T2, T3 and T4) were arranged along the diagonals of the joint panel for measuring elongation/shortening of the joint during the loading process; b) two LVDTs (L1 and L2) and laser sensors were placed with the aim to monitor the rotation produced on the joint external face; c) four potentiometers (P3, P4, P5 and P6) were arranged on two opposite faces of the

a)

b)

Page 6 of 9

beam (at 100 mm from the beam base) in order to measure vertical displacements and crack widths at the beam-column interface; as shown in Figure 5, the potentiometers P3 and P6 had the pin located at 30 mm from the beam base: in this way, the difference between the readings of P3-P4 and P6-P5 allowed to estimate the crack opening at the base and the slip of the rebars; d) four gauges were used to measure the strain in the stirrups of beams (G3, G5) and columns (G1, G2), while the gage G5 was placed to monitor the strain in a beam rebar. Finally, a further wire transducer, not shown in the Figure, was placed at 1430 mm from the beam base with the aim to monitor the lateral displacement imposed by the actuator.

Laser 1

P5 P4

T1 T2G1

G3G2

G4G5

Laser 2

L1 L2

P6 P3

T3 T4

Figure 5. Joint instrumentation: front view (a); back view (b).

3. Experimental results and discussion

3.1 Cyclic behavior

Table 4 summarizes the main results of the three tests performed so far, namely J-01, J-02 and

J-03. In the table: F+max and F−

min are the peak lateral strengths in the two directions of

loading, whereas ∆+ and ∆− are the corresponding displacements, ∆+85% and ∆−

85% are the maximum displacements exhibited at the conventional collapse (i.e. at the achievement of 15% strength degradation evaluated on the lateral force-displacement envelopes). The last column of the table describes the failure modes experienced by specimens at collapse.

Table 4. Test results and failure modes.

Test fcm

(MPa) ν

F+max

(KN)

F−max

(KN)

∆+

(mm)

∆−

(mm)

∆+85%

(mm)

∆−85%

(mm) Failure mode

J-01 16.4 0.20 62.5 -66.1 16 -10 25.9 -21.1 Joint shear failure

J-02 19.5 0.17 67.6 -80.7 18 -14 27.7 -24.2 FRP delamination followed

by joint shear failure

J-03 15.7 0.21 118.8 -90.3 30 -30 49.2 -45.5 Flexural beam failure

The obtained results have provided useful information about the efficacy of the upgrading schemes considered in the preliminary phase of the experimental campaign. In particular, it is observed that the specimen J-02, having the joint panel upgraded with two "U"-shape CFRP sheets, has shown results slightly better than those of the unstrengthened member J-01. This reduced performance, both in terms of strength and ductility, lies in the premature achievement of the conventional collapse by FRP intermediate debonding. Conversely, significant increases of strength and ductility were obtained in the case of the test J-03 where the upgrading consisted of a steel plate properly anchored with threaded rods through the joint. On the average, the specimen provided an increase of strength and ductility over the member J-01 equal to about 63% and 100%, respectively. In this case, the improved performance of the joint, combined with an effective strengthening of the column, allowed to move the failure in the beam, which represents the upper bound of the hierarchy of strength.

Figure 6 shows the three lateral load (F)-displacement (∆) cyclic curves and the

corresponding F-∆ envelopes. The comparisons better highlight the beneficial effects obtained from the test J-03 and the rather identical behavior observed for the specimens J-01 and J-02.

a) b)

column

beam

Page 7 of 9

-120

-90

-60

-30

0

30

60

90

120

-60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60

Displacement [mm]

Lateral Force [KN]

J-03J-02J-01

-120

-90

-60

-30

0

30

60

90

120

-60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60

Displacement [mm]

Lateral Force [KN]

J-03

J-02

J-01

Figure 6. Load-displacement curves: a) hysteresis loops; b) envelopes.

3.2 Failure mode

Figure 7 shows the scenario of damage exhibited by specimens at the end of tests. The control specimen J-01 highlighted a significant vulnerability of the joint panel region. The first signs of damage occurred at the beam-column interface during an imposed displacement of 5 mm; they consisted of small flexural cracks whose width did not significantly increase during the test. Then, several shear cracks start to develop in the joint region but these did not affect the member strength up to a displacement of 20 mm, i.e. when the cracks along the four diagonal of the panel became dominant (Fig. 7a). In this test, the conventional collapse was characterized by spalling of the concrete outer wedge which left the anchorage of the beam longitudinal reinforcement discovered (Fig. 7b).

Figure 7. Damage pattern of test specimens: J-01 (a,b); J-02 (c,d); J-03 (e).

As mentioned in the previous section, the behavior of the specimen J-02 was strongly influenced by the premature delamination of the FRP layers which were not well anchored on the beam face by proper anchorage systems. This phenomenon was induced by the opening of flexural cracks at the beam-column interface during a displacement value of 10 mm. The damage was then followed by the development of relevant vertical cracks which, starting from the beam-column interface, propagated along the beam parallel to the FRP sheets. At an imposed displacement of 14 mm, the delamination of the FRP was activated at one beam side (Fig. 7c) and progressively developed towards the joint panel; on the opposite beam side,

a) b)

a) b)

c) d) e)

Page 8 of 9

instead, the delamination was experienced at a displacement of 20 mm. In absence of joint confinement, the failure of the specimen was carried out in the same way as J-01 (Fig. 7d). The specimen J-03 exhibited a different response with respect to the other members. The joint strengthening was able to significantly improve the cyclic behavior of the joint panel by moving the rupture of the specimen to the beam. In this case, the strength of the specimen was controlled by the maximum flexural capacity of the beam. As shown in Figure 7e, the damage was characterized by a large flexural crack concentrated at the beam-joint interface.

3.3 Beam rebars strain

The performances of the tested specimens can also be examined through strain data recorded by gauges placed on a longitudinal rebar of each beam close to the beam-joint interface. The rebar strain-displacement envelopes are depicted in Figure 8a. It can be verified that the specimen J-02 showed a slight strain (also related to strength) increase over the specimen J-01. The failure of the specimen J-03 occurred only at the achievement of the maximum beam load capacity where the strain data in tension was well over the strain value at rebar yielding.

3.4 Joint rotation

The envelopes of Figure 8b depict the rotation of the joint exterior face estimated through the measures provided by LVDTs L1 and L2 (see Fig.5). Also in this case, it is shown that the joint rotation is rather similar for the specimens J-01 and J-02, but not for the member J-03, for which lower rotations were experienced.

-3000

-2000

-1000

0

1000

2000

3000

-60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60

Displacement [mm]

Strain[

µε

µε

µε

µε]

J-03

J-02

J-01

-0.012

-0.008

-0.004

0.000

0.004

0.008

0.012

-60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60

Displacement [mm]

Joint Rotation[rad]

J-03J-02J-01

Figure 8. Beam rebar strain (a); joint rotation (b).

3.5 Stiffness degradation and energy dissipation

The mean value of stiffness for the ith cycle has been evaluated by the following ratio [7]:

max, max,

max, max,

+ −

+ −

+=

∆ + ∆

i i

i i

F FK (3)

The stiffness of each cycle was then normalized with respect to the stiffness of the first cycle KI, thus providing a measure of the stiffness degradation. The relationship between the K/KI ratio and the imposed displacement is plotted in Figure 9a. As shown, the stiffness degradation is quite similar for the three specimens approximately up to a displacement value of 10 mm, i.e. when the three joint panels still exhibit a negligible state of damage. After this threshold, a greater stiffness decrease was evaluated for the specimens J-01 and J-02 with respect to the counterpart J-03, as the progressive propagation of damage caused an abrupt reduction of the joint strength. Figure 9b depicts the relationship between the cumulative dissipated energy (E) and the imposed beam displacement. As observed for the stiffness, the energy computed up to the

a) b)

pull

"–"

"+" push

Page 9 of 9

displacement cycle of 10 mm is approximately the same for the three tests. However, the cumulative dissipated energy is considerably higher in the case of the specimen J-03, as the adopted joint strengthening produced a significant increase of the available ductility.

0.0

0.2

0.4

0.6

0.8

1.0

0 10 20 30 40 50 60

Displacement [mm]

K/KI

J-03J-02J-01

0

10

20

30

40

50

0 10 20 30 40 50 60

Displacement [mm]

E [KN m]

J-03J-02J-01

Figure 9. Stiffness degradation (a); Total dissipated energy (b).

4. Conclusions

In this paper, the preliminary results of cyclic tests carried out on exterior RC beam-column joints have been discussed. Three assemblies have been tested so far, i.e: a benchmark (unstrengthened) specimen, used as comparison term, and two upgraded specimens characterized by the strengthening of both column and joint members. The performed tests have highlighted some critical aspects related to a poor design of the joint FRP upgrading. In particular, due to intermediate debonding, the joint strengthened with FRP showed only a slightly better behaviour than that of the unstrengthened one. Conversely, the joint upgrading with steel systems, combined with an effective strengthening of the column, allowed to move the failure in the beam, in full conformity with the hierarchy of strength.

Acknowledgements

The Authors gratefully acknowledge “F.lli Abagnale sas” precasting company (Naples, Italy) for concrete specimens production, and “Interbau srl” firm (Milan, Italy) for the financial support to the experimental program.

References

[1] DECRETO MINISTERIALE 14 gennaio 2008, “Norme Tecniche per le Costruzioni”, G.U. n.29 del 4 febbraio 2008 (in italian).

[2] PAULAY, T., PRIESTLEY, M.J.N., “Seismic design of reinforced concrete and masonry buildings”, John Wiley & Sons eds., 1992, NY, USA.

[3] VOLLUM, R.L., NEWMAN, J.B., “The design of external, reinforced concrete beam column joints”, The Structural Engineer, Vol. 77, No. 23, 1999, pp. 21-27.

[4] BAKIR, P.G., BODUROGLU, H.M., “A New Design Equation for Predicting the Joint Shear Strength of Monotonically Loaded Exterior Beam-to-Column Joints”, Engineering Structures, Vol. 24, 2002, 1105-1117.

[5] KIM, J., LA FAVE, J.M., SONG J., “Joint shear behaviour of reinforced concrete beam-column connections”, Magazine of Concrete Research, Vol. 61, No. 2, 2009, pp. 119-132.

[6] LIMA, C., MARTINELLI, E., FAELLA, C., “Capacity models for shear strength of exterior joints in RC frames: state-of-the-art and synoptic examination”, Bulletin of Earthquake Engineering, January 2012, DOI: 10.1007/s10518-012-9340-4.

[7] MAYES, R.L., CLOUGH R.W., “State of the art in seismic shear strength of masonry – An evaluation and review", EERC Report, 1975, Berkeley, California, USA.

a) b)