Experimental and analytical investigations of reinforced concrete beam-column joints retrofitted by single haunch

Abstract

Recently, the single haunch with specifications such as less invasive and architectural consistency, and easy to practice have been adopted as one of the considered retrofitting options for deficient reinforced concrete beam-column joints. In this article, by analytical evaluation, the influence parameters such as haunch to beam stiffness ratio, haunch inclination angles, and mounted position were investigated. Analytical equations were also proposed for haunch to beam stiffness ratio in terms of both shear interaction between haunch and beam-column members and reduction of joint shear demand. Moreover, five exterior beam-column joint sub-assemblies were fabricated afterwards four of those retrofitted by various cross-sectional area of single steel haunch. Then, all of these beam-column joints and remaining one (as-built joint) were experimentally subjected to cyclic loading. To validate the analytical results, the experimental responses in four limit states including first diagonal core crack in as-built joint, drift ratio 2%, the first diagonal core crack in all the joints, and ultimate state (peak load) were provided for comparison. Also, by definition of an index as vulnerability index in fraction ratio of available joint shear force to joint shear strength predicted by international codes, the obtained vulnerability index of experimental responses were compared to analytical results.

Keywords

cyclic loading reinforced concrete beam-column joint retrofitting single steel haunch vulnerability index

Introduction

There are yet numerous vulnerable reinforced concrete (RC) buildings with moment resistant frame (MRF) structure in seismic zones that for the various reasons, such as improperly detailed, low quality concrete in practice, and exploitation time additional loads, require to retrofit seismically. RC beam-column joints display key role in transmission of the gravity and seismic loads from beams to columns. The researchers concluded that the concrete compressive strength, $f_{c}^{'}$ , is the most influence parameter on the joint shear strength, ultimate strength, stiffness degradation, and energy dissipation capacity of the joints (Kheyroddin et al., 2016; Tran, 2016; Vandana and Bindhu, 2017).

The deficient MRF structures with low strength concrete and subjected to overloading for joint regions must be retrofitted seismically. Chen (2006) extended initially the haunch retrofit solution (HRS) to shift the hierarchy of damage mechanisms to one in which the RC joint, as a critical component, is protected and damage is forced into the RC beams. The experiments were carried out at the joint sub-assembly level (Genesio, 2012), as well as at structural level (Akbar et al., 2018; Sharma et al., 2014) to evaluate the performance of the HRS. These researchers found that the efficiency of the retrofit solution depends highly on the performance of the anchorage system used to connect the haunch element to RC members and in cases where anchors are bonded, they fulfill their purpose well, forming a clear beam hinge, instead of a joint-shear failure (Genesio, 2012; Sharma et al., 2014). In similar studies, the researchers used the technique of local steel bracing haunch members experimentally and numerically (Khalili et al., 2015; Kheyroddin et al., 2016; Sharbatdar et al., 2012a, 2012b). Because of more satisfaction the retrofit solution architecturally, the researchers with various objects recently investigated the capability and performance of single haunch as a less-invasive retrofit solution for RC frame beam-column joints (Kanchana Devi et al., 2018; Kheyroddin et al., 2016, 2019; Truong et al., 2017). Zhou et al. (2012) experimentally studied the seismic performance of the RC frames with viscous damper haunch braces under sinusoidal waveform steady-state excitations. The results of their investigation showed that the beam-column joint internal forces of the RC frame with viscous damper haunch braces were greatly reduced. Yang et al. (2012) developed a new type of SRC (steel-reinforced concrete) beam transfer structure with supplemental energy dissipation haunch braces to improve the seismic behavior.

For the first time, Kheyroddin et al. (2016) evaluated the single haunch feasibility usage (“one-way steel prop and curbs”) as less-intervention retrofit option with and without steel revival sheets on the beam experimentally. The main idea was usage of a haunch which initially be less-invasive architecturally meanwhile acted as a fuse element to increase the rigidity and strength of deficient system. In another study, they also investigated the effect of different cross-sectional areas of steel haunch on behavior and force transmission mechanism between RC members and single haunch analytically and experimentally (Kheyroddin et al., 2019).

In this study, the affective key parameters on transferred internal forces at an exterior beam-column joint sub-assemblage retrofitted by single haunch are investigated. Moreover, analytical equations are also proposed for haunch to beam stiffness ratio in terms of both shear interaction between haunch and beam-column members and reduction of joint shear demand. Moreover, in experimental part, the influence of various cross-sectional area of the steel haunch is evaluated on reduction of demand joint shear force and experimental responses are compared to obtained results by analytical formulations.

Experimental program

For investigation of efficiency of the single steel haunch practically as a retrofitting option in demand reduction of joint shear force at RC frames, five ½ scaled RC exterior beam–column joints were fabricated and casted. Figure 1 and Table 1 show the geometric properties and reinforcement details of the five half scale two-dimensional (2D) experimental specimens: as-built specimen JS and four retrofitted specimens RJS1, RJS2, RJS3, and RJS4. Average 28-day compressive strength $f_{c}^{'}$ of cylinder samples for JS, RJS1, RJS2, RJS3, and RJS4 specimens were 15.5, 15.3, 16.0, 15.0, and 15.7 MPa, respectively. The yield strengths and elastic modulus for 14, 12, and 8 mm steel bars were, respectively 510, 444, and 398 MPa and 232, 222, and 204 GPa.

Figure 1.

Geometric dimensions and reinforcement details of all specimens (in mm).

Table 1.

Characteristics of the tested experimental specimens.

Name	Specimen	Characteristics
JS	As-built weak joint	Weak joint (the beam height = 150 mm)
RJS1	Retrofitted by single steel haunch	Similar to JS specimen, retrofitted with a steel haunch with sectional area of 120 mm² (a box with dimensions 20 mm × 10 mm × 2 mm)
RJS2	Retrofitted by single steel haunch	Similar to JS specimen, retrofitted with a steel haunch with sectional area of 200 mm² (a box with dimensions 30 mm × 20 mm ×2 mm)
RJS3	Retrofitted by single steel haunch	Similar to JS specimen, retrofitted with a steel haunch with sectional area of 350 mm² (a box with dimensions 60 mm × 30 mm ×2 mm)
RJS4	Retrofitted by single steel haunch and beam revival sheet	Similar to JS specimen, retrofitted with a steel haunch with sectional area of 200 mm² (a box with dimensions 30 mm × 20 mm ×2 mm) plus steel sheets on the upper and lower surface of the beam with dimensions of 900 mm × 300 mm × 5 mm

The overview of the test setup with the specimen supports and other key components are shown in Figure 2(a). The column was supported by a hinge connection at one end and a roller on the other end that was erected on laboratory’s strong floor and the axial load of the column was equal to 0.15P_n = 170 kN. The cyclic loading history of tests shown in Figure 2(b) was based on displacement control imposed.

Figure 2.

Condition loading of the test: (a) test setup and (b) cyclic loading history.

Analytical study

The suggested retrofit solution, “single steel haunch and curbs,” can be utilized for both the interior and exterior beam-column joints as shown in Figure 3(b). The exterior beam-column joints are more vulnerable joints during the earthquake among the other types and categories of beam-column joints, so in this study an exterior T-shape joint is analytically considered.

Figure 3.

Internal forces in the RC joints: (a) governed forces on the retrofitted exterior and interior joints and (b) force diagrams of the as-built and retrofitted joints.

Preliminary analytical study

Generally, the analytical formulations established by Chen (2006) and Pampanin et al. (2006) about the RC joints retrofitted by double haunches are adopted in this study for the single HRS as follows. Therefore, internal force diagrams of shear and bending moment for the as-built and retrofitted joints (by single haunch) subjected to the lateral force of V_b can be plotted as Figure 3(a). Here, also for special study of influence of the single haunch on the RC joint shear force, the governed internal reaction components on that are proposed and presented as Figure 3(b).

Based on Figure 3(a), under the applied load V_b at beam tip, the maximum of beam bending moment, M_b(max) , occurs in a distance of a_h from the column face (connection position of the haunch to beam) as follows

M_{b, max} = V_{b} (\frac{L_{n}}{2} - a_{h})

a_h is the horizontal projected length of the haunch. L_n is the net beam spans length (from face to face of the columns).

From Figure 3(b), if the vertical and horizontal components of the haunch axial force in the connection region to the beam and column are supposed, respectively, β_bV_b and β_cV_c as coefficients of the beam and column shear forces, then F_b and F_c equal equations (2) and (3), respectively

F_{b} = \frac{β_{b} V_{b}}{t a n θ}

And

F_{c} = β_{c} V_{c} t a n θ = β_{b} V_{b}

Thus, the beam and column shear coefficients β_b and β_c are related together as

β_{c} = β_{b} (\frac{2 L_{c}}{L_{b} \cdot t a n θ}) = β_{b} (\frac{V_{b}}{V_{c} \cdot t a n θ})

where θ is the haunch inclination angle into horizontal line as shown in Figure 3, and L_b and L_c are the total beam span length (from center line to center line of columns) and the total inter-story height (from center line to center line of beams), respectively. Also, β_b and β_c are described in the following paragraphs. Moreover, the single haunch axial force, F_h , as shown in Figure 3(b) can be obtained as equation (5)

F_{h} = \frac{β_{b} V_{b}}{s i n θ}

As shown in Figure 3(a), the bending moment at the column face, ${M^{'}}_{b}$ , can be achieved as equation (6)

M_{b}^{'} = M_{b, max} - Δ M_{b} + (1 - β_{b}) V_{b} \cdot a_{h}

where $L_{b}^{'} / 2$ is defined as the distance between the middle span length of the beam and the beam-haunch connection region as the following equation

\frac{L_{b}^{'}}{2} = (\frac{L_{n}}{2}) - a_{h}

Also, $Δ M_{b}$ is defined as

Δ M_{b} = (\frac{d_{b}}{2}) (\frac{β_{b} V_{b}}{t a n θ})

where d_b is the depth of the beam.

As illustrated, the $β$ coefficient can play a key role in the demand reduction of beam-column joint forces. The beam shear coefficient β_b can be determined as proposed by Pampanin et al. (2006), considering the deformation compatibility equations between the axial deformation of the haunch ends and the local vertical and horizontal deformations of the beam and column where the haunch is connected to them. Here, this value is derived with low difference at the last part of formula fraction as equation (9). It is worth noting that in derivation of equation (9) it is assumed that the column and joint deformability are neglected. Thus

β_{b} = (\frac{b_{h}}{a_{h}}) \frac{3 l_{b}^{'} d_{b} + 3 a_{h} d_{b} + 3 b_{h} l_{b}^{'} + 4 a_{h} b_{h}}{3 d_{b}^{2} + 6 b_{h} d_{b} + 4 b_{h}^{2} + \frac{12 I_{b}}{A_{b}} + \frac{12}{λ c o s^{2} θ}}

where b_h is the distance between haunch connection place to column and the joint interface as shown in Figure 3(a). I_b and A_b are, respectively, the cracked moment inertia and cross-sectional area of the RC beam section, and $λ$ factor is defined as haunch to beam stiffness ratio (K_h/K_b ) which can be expressed as below

λ = \frac{K_{h}}{K_{b}} = n \frac{Α_{h}}{Ι_{b}} c o s θ

where n is known as (E_h/E_c ), in other words, the ratio of the haunch material elasticity to concrete elasticity. Also, A_h is cross-sectional area of the haunch element. It should be noted that the column shear coefficient β_c can be obtained using equation (4) by determining the value of β_b .

Evaluation of effective factors on shear coefficients β and joint forces

Using equations (4), (9), and (10), the influence of cross-sectional area of haunch on the beam and column shear coefficient, β_b and β_c , for various values of the haunch angles (θ) and its erection position α (a_h/l_b ) were investigated. For various amounts of α equal to 0.1–0.3, by increasing A_h , both the β_b and β_c coefficients enhance monotonically. Also for any given amount of α and also A_h , with the increase in the haunch angle from 20 to 60 degree, the β_b increases while the column shear coefficient β_c decreases drastically. It indicates that the very flat angle of haunch (i.e. θ < 30°) cannot be effective in reduction of the column face bending moment or joint shear demand and moreover increases the shear demand in column considerably. Also for any given amount of α and A_h , for the haunch angle of less than 60°, β_c is larger than β_b . Although for any given amount of α and A_h , both haunch angle 45 and 60 degree provide approximately same values of β_b , but haunch angle 45° and more than 60° produce shear demand in column which is not desirable. Therefore, the researchers also have accentuated that for less shear demand in beam and column the coefficient β must be less than 2.0 (Chen, 2006; Pampanin et al., 2006).

The variations both of the β_b and β_c with α (at range of 0.05–0.5) were evaluated for various cross-sectional area and inclination angles of the haunch. In Figure 4, the graphs related to various cross-sectional areas of the haunch for angle of 45° are typically presented. Generally, it can be observed that the maximum values of β_b and β_c depend on the haunch sectional area and angle and are obtained for α lesser than 0.2 and for the larger values of that with the increase of the haunch sectional area and angle decreases remarkably and for α equal 0.5 reaches to its minimum values. Also with the increase of the haunch cross-sectional area and for any given haunch angle, the maximum amounts of β_b and β_c are attained in the lesser values of α or in other words the values of α corresponding to maximum of β_b and β_c decrease.

Figure 4.

Variations of the shear coefficients versus amounts of α for various haunch sectionals areal and angle of 45° (d_b = 400 mm): (a) β_b coefficient and (b) β_c coefficient.

It is worth noting that at the haunch inclination angle of lesser than 30°, for any given value of α and A_h , the coefficients of β_c are approximately two to three times larger than β_b correspondingly. Therefore, as already mentioned, it will lead to significant enhancement of the shear demand in the column so that for a weak column building system specially that would not be never desirable. On the other hand, at the haunch inclination angle of 45°–60°, it was observed that the amount of β_c to β_b ratio varies from 1.25 to 0.75 approximately.

As shown in Figure 3(b), the horizontal joint shear force V_jh , at the mid-plane (section i:i) of the exterior retrofitted joint assemblies are respectively proposed as equation (11)

V_{j h} = C - (1 - β_{c}) V_{c} - \frac{β_{b} V_{b}}{2 t a n θ}

11a

V_{j h} = T - V_{c} + \frac{β_{b} V_{b}}{2 t a n θ} = \frac{M_{b}^{'}}{Z_{b}} - (1 - \frac{β_{c}}{2}) V_{c}

11b

Where T and C are the tension/compression forces in the beam longitudinal bars and concrete block, respectively, and V_c is the column shear force as shown in Figure 3. In addition, Z_b is the lever arm of the beam internal forces at the column face.

Unlike what is presented by other researchers for V_jh , herein the authors opine that some of the horizontal components of the single haunch axial force (e.g. $β_{b} V_{b} / 2 t a n θ$ in equation (11)) directly have an effect on joint shear forces. The reason of the claim is uniform distribution of the horizontal component of haunch force on the RC beam section by steel curb. In addition, as will be presented in section “Test results and discussion,” using this procedure better accordance can be obtained between the analytical and experimental results.

As illustrated in equations (6) and (11), both ${M^{'}}_{b}$ and V_jh are functions of the beam and column shear coefficient, β_b and β_c . Hereon, the variation of ${M^{'}}_{b}$ /M_b and V_jh/V_j with values of α (a_h/l_b ) and A_h for various haunch inclination angles were independently investigated. As example, these variations for haunch inclination of 45° are shown in Figure 5. The ${M^{'}}_{b}$ /M_b and V_jh/V_j ratios are the beam moment at column face and the joint shear force ratios of the retrofitted to as-built joints (without single haunch), which M_b and V_j are, respectively, computable based on equations (6) and (11) by substituting value of zero for the β coefficient.

Figure 5.

Influence amount of α for various haunch sectionals areal and inclination angle of 45° in reduction of: (a) beam moment and (b) joint shear demand (d_b = 400 mm).

The most impact values of α in reduction of beam moment and joint shear demand developed about 0.3 to 0.35 for haunches with highest sectional area (i.e. A_h = 800 mm²) to about 0.5 for lowest sectional area (i.e. A_h = 200 mm²) while as before mentioned the maximum values of β_b and β_c are provided at value of α < 0.2.

The variations of $M_{b}^{'}$ /M_b and V_jh/V_j with values of α (a_h/l_b ) and various inclination angles for haunch with A_h of 400 mm² were also compared independently. Those were shown that the influence of variations of α in reduction of the joint forces demand is more than variations of haunch angle θ and moreover the haunch angles of 45°–60° have almost same efficiency.

Proposal analytical equations for shear coefficients β and joint forces in λ ratio

In the event that the optimum state of the haunch application for retrofitted joints be considered as α = 0.15 and θ = 45°, then based on the above analytical data, the variations of β-coefficient and also ${M^{'}}_{b}$ /M_b and V_jh/V_j ratios can be developed in λ-factor (haunch to beam stiffness ratio (K_h/K_b ) in equation (10)) as Figure 6(a) and (b), respectively. As indicated in the figures, these charts present the logarithmic equations for both β_b and β_c and for both ratios of ${M^{'}}_{b}$ /M_b and V_jh/V_j in λ-factor with correlation coefficient (R) of very close to 1 (see equations (12) and (13)). Based on equations (12a) and (12b) for haunch angle 45° and α = 0.15, by the increase of λ ratio, the beam and column shear coefficient (β_b and β_c ) develop logarithmically

Figure 6.

Proposed logarithmic equations in haunch to beam stiffness ratio of λ: (a) for beam and column shear coefficient (β_b and β_c ) and (b) for both ratios of ${M^{'}}_{b} / M_{b}$ and V_jh /V_j .

β_{b} = 0.82 l n λ + 11.6

12a

β_{c} = 1.0 l n λ + 14.4

12b

In addition, based on equations (13a) and (13b) by increase of λ-factor in the range 0.22 × 10⁻⁵ to 1.8 × 10⁻⁵ (1/mm²), corresponding to variations of the β_b coefficient at the range from 1 to 2.70, both ratios of ${M^{'}}_{b}$ /M_b and V_jh/V_j descend logarithmically. Thus, at this range of λ-factor, a reduction of between 25% and 95% in both beam moment at column face and joint shear demands at the retrofitted joints

{M^{'}}_{b} / M_{b} = - 0.28 l n λ + 0.20

13a

V_{j h} / V_{j} = - 0.27 l n λ + 0.24

13b

Design of the single steel haunch

The step-by-step process design of the single HRS after opting for its material can be stated as follows:

Selection of a primal values for the haunch geometry (A_h , L_h , and θ) and determination of α ratio.

Computation of the axial stiffness of the single haunch and λ ratio using equation (10).

Evaluation values of β_b and β_c using equations (9) and (4), respectively.

Estimation of the haunch axial force (F_h ) and internal forces in the beam, column, and joint core for a given beam tip load demand.

Evaluation of available capacity in the RC joint sections and control of undesirable failure modes based on the strength hierarchy stated by Pampanin et al. (2006).

Revise and repeat steps 1–5 for achievement to desired strength hierarchy.

As shown in Table 1, the haunches were designed based on the obtained analytical results (section “Analytical study”) and mentioned design processes so that the beams bearing capacity increase under overloading cyclic condition; moreover, the joints shear demand force reduced. Therefore, by choosing the 500 mm length and 37° inclination angle (L_h = 500 mm and θ = 37°, that is, α = 0.17) the parameters of a_h and b_h for all of the retrofitted specimens were 400 and 300 mm, respectively. The amount of A_h for RJS1, RJS2, RJS3, and RJS4 specimens were 120, 200, 350, and 200 mm² with steel grade 300. Correspondingly, based on the test material, the yielding stresses σ_y and elastic modulus E_h were 330, 312, 320, and 318 MPa and 196, 210, 187, and 195 GPa, respectively. Thus, for the designed haunches with equivalent axial stiffness K_h , 47,000, 84,000, 131,000, and 78,000 kN/m, the beam shear coefficient β_b in accordance with equation (9) for these specimens are 1.6, 2.0, 2.3, and 2.0, respectively.

Test results and discussion

In this part, nominal principle stresses $(σ_{t}, σ_{c})$ were utilized for joint core because that is commonly more reliable than nominal shear stress level (υ_jh ) (Pampanin et al., 2002). According to Mohr’s circle concept, the nominal principle stresses (maximum of diagonal tensile and compression stress; σ_t , σ_c ) governed on the beam-column joint core are computed as equation (14). Based on the equation, σ_t , σ_c are obtained from combination of the nominal horizontal shear stress (υ_jh ) with the effective axial compression stress on the column (σ_N ) in the joint region

σ_{t} = \frac{P_{c}}{2 A_{g}} + \sqrt{{(\frac{P_{c}}{2 A_{g}})}^{2} + {(\frac{V_{j h}}{A_{j}})}^{2}}

14a

σ_{c} = \frac{P_{c}}{2 A_{g}} - \sqrt{{(\frac{P_{c}}{2 A_{g}})}^{2} + {(\frac{V_{j h}}{A_{j}})}^{2}}

14b

where P_c is the effective column axial compressive load in the joint region, A_g is the column gross section area, V_jh is the nominal joint shear force at the mid-plane of as-built and retrofitted joints that can be expressed as equation (11), and A_j is the effective joint area.

As presented in the analytical part, as β-coefficient with the steel haunch stiffness (increasing of haunch section area) increases both of beam bending moment at column face (M′_b ) and the joint shear force V_jh usually decrease remarkably. For validation of the analytical results in estimation of β-coefficient and also the joint shear force, the joint principle stress level at several limit states were estimated using equation (15) and the results compared with concrete cracking behavior of as-built and retrofitted joints core. For evaluation of the joints principle stress level, there were four limit states considered: (1) the first diagonal cracking in as-built joint core at beam tip load of equal to 12.5 kN (V_b = 12.5 kN); (2) drift ratio of 2% in the retrofitted beam-column joints; (3) the first diagonal crack in retrofitted joints core; and (4) peak load capacity (V_b,max ) of all beam-column joints.

The researcher results for exterior beam-column joints present the different values for principal tension/compression strength from $0.20 \sqrt{f_{c}^{'}}$ up to $0.29 \sqrt{f_{c}^{'}}$ and $0.20 \sqrt{f_{c}^{'}}$ up to $0.5 f_{c}^{'}$ , respectively, at first limit states (first diagonal cracking) and the peak load for the various arrangements of beam reinforcement in the joint region (Pampanin et al., 2003; Priestley, 1997).

Table 2 summarizes the analytical and experimental outputs obtained based on both β_pre and β_exp values, respectively, in the terms of β-coefficients, haunch axial force F_h , and beam tip force V_b corresponding to the above mentioned limit states. In addition, Figure 7 shows the compared normalized values of υ_ih , σ_t , and σ_c for all joint specimens analytically and experimentally. In these figures υ_ih and σ_t have been normalized by $\sqrt{f_{c}^{'}}$ value as well as σ_c by $f_{c}^{'}$ value. It should be noted that for calculation of these terms, several procedures and assumptions were taken as listed follows:

Figure 7.

The normalized value of nominal shear stress and principal tension/compression stresses of the joint specimens at four limit states: (a) analytically, (b) experimentally, and (c) the comparison of analytical and experimental at fourth limit state in terms of nominal shear stress.

Table 2.

Comparison of the analytically predicted and experimental results of specimens in the four limit states.

Specimens name		Items
		First limit state (V_b = 12.0 kN and V_c = 10 kN)			Second limit state (drift ratio 2%)			Third limit state (corresponding to first diagonal cracking in joints region)				Fourth limit state (corresponding to peak load capacity of beam-column joints)
		β_b coef	Drift ratio (%)	F_h (kN)	β_b coef	V_b (kN)	F_h (kN)	β_b _- coef	V_b (kN)	Drift ratio (%)	F_h (kN)	β_b coef	V_b (kN)	Drift ratio (%)	F_h (kN)
JS		–	2.5–3	–	–	10.25	–	–	12.0	2.5–3	–	–	15.6	4.5	–
RJS1	β_pre	1.60	1.5–2	31.9	1.60	13.65	36.3	1.60	20.1	4.0	39.7 (Y)	1.60	24.1	6.0	40.0 (Y)
RJS1	β_exp	1.65	1.5–2	32.9	1.53	13.65	34.6	1.19	20.1	4.0	39.7 (Y)	1.00	24.1	6.0	40.0 (Y)
RJS2	β_pre	2.00	1.5	39.9	2.00	17.20	57.2	2.00	23.8	4.0	62.1 (Y)	2.00	27.0	6.0	61.2 (Y)
RJS2	β_exp	2.57	1.5	51.2	2.09	17.20	59.9	1.57	23.8	4.0	62.1 (Y)	1.37	27.0	6.0	61.2 (Y)
RJS3	β_pre	2.30	1.5	45.9	2.3	15.07	57.3	2.30	25.2	4.0	96.3	2.30	27.0	5.0	102.4
RJS3	β_exp	2.07	1.5	41.3	2.26	15.07	56.4	1.88	25.2	4.0	78.8	2.00	27.0	5.0	88.8
RJS4	β_pre	2.00	1–1.5	39.9	2.00	18.05	60.0	2.00	23.1	3.0	68.0 (Y)	2.00	29.8	6.0	81.1 (YH)**
RJS4	β_exp	2.44	1–1.5	48.7	2.13	18.05	63.9 (Y)*	1.78	23.1	3.0	68.0 (Y)	1.64	29.8	6.0	81.1 (YH)**

(Y)* and (YH)** are abbreviation of the yielded and yielding along with strain hardening experimentally for steel haunch.

1. The β_pre and β_exp are defined as the analytically and experimental shear coefficients calculated by equations (9) and (5), respectively. For derivation of β_exp from equation (5), the experimental haunch axial force F_h,exp corresponding to beam tip load, V_b , can be expressed as equation (15)

F_{h, e x p} = E_{h} \cdot ε_{h} \cdot A_{h}

where E_h and A_h are the module elasticity and cross-sectional areal of steel haunch, respectively. ε_h is attained from average of read axial strains of mounted strain gages on the three middle section of steel haunch. Based on the equation, the hysteresis envelop curve of haunch axial force versus beam tip displacement for retrofitted beam-column joints are plotted as Figure 8(b). Thus, in accordance with Table 2, the average of experimental haunch axial force F_h,exp corresponding to any given beam tip displacement or load V_b at positive and negative directions can be provided from Figure 8.

2. It has been supposed that when the steel haunch reaches to its yielding force experimentally and the analytically predicted steel haunch force F_h,pre equals the F_h,exp. .

3. Each RC member is provided by an in-closure steel curb; consequently, the force components of haunch approximately distribute throughout member sections uniformly.

4. The effective column axial load P_c on joint region can be estimated as equation (16) with contribution of the provided column axial compression force (P_N = 170 kN), the haunch vertical force component equal to β_bV_b (or β_cV_c tanθ) and 1/2 of beam tip load (V_b /2) which both of those can act as a compression or tension force on the joint region when the beam tip is subjected to pull and push cyclic loading

P_{c} = P_{N} + \frac{V_{b}}{2} \pm β_{b} V_{b} = P_{N} + V_{b} (\frac{1}{2} \pm β_{b})

5. It has been supposed that lever arm of beam internal forces at column face in calculation of joint horizontal shear force are about 120 mm (equal to 0.9 beam affective depth) for all specimens.

Figure 8.

Force–displacement behavior for all the tested specimens: (a) force–displacement hysteresis loops and envelope curves of the beam tip, and (b) hysteresis envelop curves of the haunches axial force for the retrofitted joints.

Figure 9.

Cracking patterns of the joints core at four limit states: (a) the first and second limit states, (b) the third limit states (first diagonal cracking in core), and (c) the final limit states (corresponding to peak load capacity V_b,max ).

Figure 10.

Comparison of vulnerability index (VI) at ultimate limit state for all specimens: (a) analytically and (b) experimentally.

In Figure 8(a), force–displacement hysteresis loops of the beam tip for all specimens and comparison of their envelope curves are also presented. As illustrated in Table 2, at the first limit state, the steel haunches at each retrofitted joint are not yielded and in accordance with Figure 8 for given value of V_b = 12.0 kN, and the normalized values of υ_ih , σ_t , and σ_c in the specimen JS are at ranges of 1.6–2.6, 2.4–5.0, and 1.05–1.14 times more than that in the retrofitted specimens, respectively. Consequently, as clearly observed in Figure 9(a), there are no evidences of cracking in the joint core of retrofitted specimens on the contrary of the diagonal cracking of as-built joint core.

Generally, as shown in Figure 7(a), based on the analytical outputs by increase in cross-sectional area of steel haunch, the nominal joint shear demand decreases significantly. In the second limit state (when the beam tips displacement is equal to 24 mm) although the retrofitted specimens at drift ratio 25 suffer 14%–50% more load as compared to joint JS (when V_b = 12.0 kN and first diagonal cracking) nonetheless the normalized values υ_ih , σ_t , and σ_c of those were 0.46–0.67, 0.28–0.56, and 0.95–1.0 times of that, respectively, and there is also no evidence of serious diagonal cracking at them joint core (see Figure 9(a)).

It is worth noting that based on the experimental data at this limit state only the steel haunch of specimen RJS4 reaches to its yielding stress. Also it can observed that there are fit conformity between the analytical outcomes and the experimental responses for all the evaluated terms based on the β_pre and β_exp provided by equations (5) and (9).

The experimental and analytical results of all specimens in the third and fourth limit states are summarized in Table 2 and Figure 9(b) and (c), respectively. As indicated in Table 2 unlike to two previous limit states, here exists a significant difference between the analytically predicted and experimental shear coefficients, β_pre and β_exp which can be due to the appearance of nonlinear behavior of materials including cracking propagation in concrete, buckling and yielding of steel haunch, and yielding of beam longitudinal bars in the retrofitted joints (refer to Figures 8 and 9 and Table 2).

Hence, because of decline efficiency of the haunches in force transmission, the whole produced amounts of investigated terms based on β_exp (as Table 2) are more than β_pre except in the terms of β_b and β_c (e.g. see Figure 7(c)). It indicates that in two last limit states for investigated terms based on the experimental observations, the produced values from β_exp seem more actual than β_pre . Also based on both the β_pre and β_exp values, the steel haunches in all retrofitted joints except in RJS3 are yielded. Also as presented in Table 2 and Figure 9(b), the first diagonal cracking in the retrofitted joints developed at upper drift ratio of beam tip with respect to the joint JS; moreover, the values of V_b increase at range of 67%–110% as well as the beam moment demand at column face $M_{b}^{'}$ , decreases up to 42% as compared to joint JS.

As shown in Figure 7(b), the normalized amount of σ_t for the as-built joint JS in first diagonal cracking is 0.23 with existence of single stirrup in the joint core that is lesser than the value reported (i.e. value of 0.29) by Priestley (1997) for the exterior RC joints with beam bars bent into the joint zone (by joint failure). In addition, these normalized amounts based on β_pre and β_exp in the retrofitted joints vary at range of 0.18–0.24 and 0.24–0.3, respectively. Again the normalized value of υ_ih for the joint JS in first diagonal cracking is 0.45 while this value in the retrofitted joints are about 0.35–0.45 and 0.44–0.53 corresponding to the β_pre and β_exp , respectively.

Last column of Table 2 and Figures 8 and 9(c) indicate the output results of all joints at the fourth limit states (corresponding to peak load capacity V_b,max of the beam-column joints) for various evaluated terms. As shown in Figure 8(a), the retrofitted joints reach their V_b,max at upper drift ratio as compared to joint JS and also in this limit state the value of V_b,max growth about 55%–91% and the beam moment demand at column face $M_{b}^{'}$ , lessen up to 52% as opposed to the joint JS. It noting that based on the β_pre and β_exp values, the steel haunches at this limit state in all retrofitted joints are yielded except in RJS3; moreover, the specimen RJS4 after yielding in tension/compression reaches to itself strain hardening behavior as Figure 8(b) (which finally raptures at drift ratio 6%) and the specimen RJS1 after yielding in tension/compression approaches to itself buckling compression load (also, finally at drift ratio 7% buckles totally).

The normalized amount of σ_t in the joint JS (without joint failure) corresponding to V_b,max is 0.34 with existence of single stirrup in joint core that is lesser than value of 0.42 reported by Priestley (1997) (with joint failure). Moreover, in the retrofitted joints these amounts based on the β_pre and β_exp vary at ranges of 0.21–0.32 and 0.27–0.43, respectively. The normalized value of υ_ih for joint JS is 0.58 while these values in the retrofitted joints are about 0.46–0.56 and 0.46–0.68 for both β_pre and β_exp , respectively. It should also be noted that according to experimental responses (see Figure 8(a)) at this limit state, in spite of less bearing capacity of the as-built joint (0.5–0.65 times) with respect to the retrofitted joints, the cracking propagation of its core is approximately more than those (see Figure 9(c)).

As shown in Figure 1, although there were not enough joint reinforcement in the tested joints as that prescribed in updated codes, their normalized values of σ_c at last limit state were lower than 0.5 (see Figure 7). Generally, to prevent premature joint shear failure, the available joint shear strength (V_n ) shall be more than the joint shear demand (V_jh ). There are various international codes such as the American standard ACI 318-14 (ACI Committee 381, 2014), the European code, EC8 (European Committee for Standardization, 2004), the Japanese code Architectural Institute of Japan (AIJ, 1999), and the NZS 3101:2006 (2006) that have a formula for estimating both V_n and V_jh . Based on the current code provisions, the value of V_n is majority defined only as a function of the concrete compressive strength as $k_{i} f_{c}^{' n}$ (where k_i and n are empirical values) and effective joint area (A_j ) (Although EC8 (European Committee for Standardization, 2004) includes the column axial load effect in estimation of V_n ) but it must be noticed that both of the concrete diagonal strut(s) and steel truss mechanisms (as design procedures of the NZS code) are effective in resistance of the joint shear force and international codes prescribe a minimum value of transverse reinforcement. The NZS code proposes that to avoid diagonal compression failure, the value of υ_ih shall be limited to 0.2 f_c′. The Japanese code AIJ in the expressions similar to developed by ACI 318-14 implies that the joint shear strength not to be sensitive to the amount of joint reinforcement.

Generally, definition of the horizontal joint shear demand V_{jh, demand} are quite similar at all of the codes as γA_sf_y -V_col , with this difference that the tension force T of beam longitudinal bars vary with an over strength factor (γ) of 1.2–1.35 for the mentioned codes. The value of V_{jh, demand} for all tested specimens (the RC beam with $3 bar \emptyset 12$ at top and bottom as Figure 1) calculated by considering the overstrength factors based on the ACI 318, EC8, and NZS codes are equal to 173.1, 166.2, and 186.9 kN, respectively. Moreover, the available joint shear force V_jh at ultimate states for all the joints JS, RJS1, RJS2, RJS3, and RJS4 predicted by analytically procedure (based on β_pre ) gives 143.5, 136.4, 123.9, 92.9, and 131.3, respectively. Although these amounts calculated by the experimental data (obtained from β_exp ) are 166, 157, 111.7, and 153.1 for the retrofitted joints RJS1, RJS2, RJS3, and RJS4, respectively.

In Table 3, the values of V_jh obtained by analytically predicted and experimental results for all specimens are compared to V_n estimated by various international codes in the ultimate limit state (peak load capacity). In order to evaluate core damage proportion of the experimented joint, hereon is defined a fraction ratio of V_jh over the joint shear strength estimated by the codes (V_{n, code} ) as a Vulnerability Index (VI) as follows

V u l n e r a b i l i t y I n d e x (V I) = V_{j h} / V_{n, c o d e}

Table 3.

Comparison of the joint shear strength among analytically predicted, experimental results and codes estimations at ultimate limit state.

Specimen name		Terms
Specimen name		β_b coef	β_c coef	V_jh (kN)	V_n,ACI (kN)	V_n,EC8 (kN)	V_n,NZS (kN)	V_n,AIJ (kN)
JS		–	–	143.5	246.2	183.3	193.8	186.4
RJS1	β_pre	1.6	2.55	136.4	244.4	169.4	191.3	184.7
RJS1	β_exp	1.0	1.59	166.0
RJS2	β_pre	2.0	3.18	123.9	250.0	175.5	200.0	190.6
RJS2	β_exp	1.37	2.18	157.0
RJS3	β_pre	2.3	3.66	92.9	242.0	151.1	187.5	182.2
RJS3	β_exp	2.0	3.18	111.7
RJS4	β_pre	2.0	3.18	131.3	247.6	165.3	196.3	188.1
RJS4	β_exp	1.64	2.60	153.1

V_jh calculated by analytically predicted and experimental results (with equation (11)) and V_{n, code} estimated by the codes.

When the fraction ratio approaches 1, it means that the extreme damage have occurred and mutually when this fraction limits to 0, there is a minimum amount of damage in the joint core.

Figure 10 presents compared experimental and analytical VI values calculated for all specimens based on Table 3. As indicated in Table 3 and Figure 10, the ACI codes estimate more values for V_n as well lower values for VI than other practice codes. On the other hand, the European Code by accounting of the affective column axial load provides least values for V_n as well more values VI as compared to other practice codes. Also, for all experimented specimens, the available joint shear force is less than joint shear demand predicted by codes and those are less than nominal joint shear strength estimated by practice codes namely, V_jh < V_{jh, demand} < V_{n, code} . Moreover, the JS and RJS3 specimens have, respectively, most and least VI values based on the analytical prediction by international codes. On the other hand, the calculated experimental VI values for RJS1 and RJS3 are most and least values, respectively.

Conclusion

This article focuses on the efficiency of single haunch system as one of retrofitting strategies with benefits such as less-invasive and intervention, easy implementation, and desirable architecturally for RC frame joints.

In analytical part, equations for exterior and interior RC joint shear demand were represented using analytical development of shear forces interaction mechanism between single haunch and RC members $(β_{b} and β_{c})$ within a beam-column joint sub-assembly. By analytical procedure, the influence parameters such as distance haunch-beam connection situation to column face over beam clear span ratio, $α = a_{h} / L_{b}$ , various cross-sectional area, A_h and inclination angles of steel haunch, θ were investigated on both terms of shear interaction coefficient, $β$ and reduction demand of joint shear force. Furthermore, for an optimum practical state $(α = 0.15, θ = 45 °)$ were proposed equations for those in haunch to beam stiffness ratio, λ. These equations indicated that by enhancement of λ ratio, the values of $β$ increase logarithmically as well as reduction of the joint shear demands. In addition, for steel haunch with cross-sectional area of 200–800 mm², both of beam moment at column face and joint shear demand were declined approximately 25%–80% correspondingly.

In experimental part, four ½ scale exterior joint sub-assemblies were retrofitted by single steel haunch with cross-sectional area of 120, 200, 350 mm² and later 200 mm² by beams steel revival sheets $(with α = 0.17, θ = 37 °)$ which along of as-built joint tested under cyclic loading. Experimental results indicated that bearing capacity of the retrofitted specimens up to 75% increased than as-built joint and that in specimen with the revival sheets was 91%. Tests observations confirmed favorable efficiency of this method in reduction of joint concrete damaging at linear state specially (i.e. two initial limit states).

To validation of the analytical results with experimental responses in the four limit states utilizing Mohr’s circle theory, the principal stress levels of the joints core were evaluated. The experimental and analytical results comparisons showed that there is good conformity at two initial limit states for the above mentioned terms except at two last limit states due to occurrence of nonlinear behaviors in materials.

Normalized analytical and experimental values of σ_t in the retrofitted specimens to as-built were around 0.38–0.77 and 0.41–0.71, respectively, at drift ratio 2%; moreover, bearing capacity ratio of those were about 1.33–1.67. Also, these ratios at ultimate state were around 0.62–0.94 and 0.79–1.27; moreover, the bearing capacity ratio were about 1.55–1.91.

A ratio of available joint shear force to shear strength predicted by international codes was defined as joint vulnerability index (VI) for comparison of the experimental and analytical results at the ultimate state. The ACI and EC 8 codes by producing minimum and maximum amounts of VI estimated, respectively, most and least values for the joint shear strength. It is found that based on the international codes predictions, by increase of the haunch cross-sectional area, A_h (or in other word value of the λ), the amount of joints vulnerability as well as vulnerability index (VI) decreases.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Ebrahim Emami

Ali Kheyroddin

References

ACI Committee 318 (2014) Building Code Requirements for Structural Concrete (ACI 318-14) and Commentary (ACI 318R-14). Farmington Hills, MI: American Concrete Institute.

Akbar

Ahmad

Alam

, et al. (2018) Seismic performance of RC frames retrofitted with haunch technique. Structural Engineering and Mechanics 67(1): 1–8.

Architectural Institute of Japan (AIJ) (1999) Design Guidelines for Earthquake Resistant Reinforced Concrete Buildings Based on Inelastic Displacement Concept. Tokyo, Japan: AIJ (in Japanese).

Chen

(2006) Retrofit strategy of non-seismically designed frame systems based on a metallic haunch system. MSc Thesis, University of Canterbury, Christchurch, New Zealand. Available at: https://ir.canterbury.ac.nz/handle/10092/1222

European Committee for Standardization (2004) EC8 Eurocode 8 (EN 1998-1, EN 1998-5): Seismic Design of Building. Brussels: European Committee for Standardization.

Genesio

(2012) Seismic assessment of RC exterior beam-column joints and retrofit with haunches using post-installed anchors. PhD Dissertation, University of Stuttgart, Stuttgart.

Kanchana Devi

Karusala

Tripathi

, et al. (2018) Novel non-invasive seismic upgradation strategies for gravity load designed exterior beam-column joints. Archives of Civil and Mechanical Engineering 18: 479–489.

Khalili

Kheyroddin

Farahani

, et al. (2015) Behavior and ductility of RC frames strengthened with steel curb and prop. Scientia Iranica International Journal of Science and Technology 22(5): 1712–1722.

Kheyroddin

Emami

Khalili

(2019) RC beam–column connections retrofitted by steel prop: experimental and analytical studies. International Journal of Civil Engineering 18: 501–518. https://doi.org/10.1007/s40999-019-00481-8

10.

Kheyroddin

Khalili

Emami

, et al. (2016) An innovative experimental method to upgrade performance of external weak RC joints using fused steel prop plus sheets. Steel and Composite Structures 21(2): 443–460.

11.

NZS 3101:2006 (2006) Concrete structures standard part 1: the design of concrete structures.

12.

Pampanin

Calvi

Moratti

(2002) Seismic behavior of RC beam–column joints designed for gravity loads. In: 12th European conference on earthquake engineering, London, 9–13 September.

13.

Pampanin

Christopoulos

Chen

(2006) Development and validation of a metallic haunch seismic retrofit solution for existing under-designed RC frame buildings. Earthquake Engineering & Structural Dynamics 35(14): 1739–1766.

14.

Pampanin

Magenes

Carr

(2003) Modelling of shear hinge mechanism in poorly detailed RC beam-column joints. In: Proceedings of the FIB 2003 symposium, Athens, 6–8 May.

15.

Priestley

MJN

(1997) Displacement-based seismic assessment of reinforced concrete buildings. Journal of Earthquake Engineering 1(1): 157–192. https://doi.org/10.1080/13632469708962365

16.

Sharbatdar

Kheyroddin

Emami

(2012a) Cyclic performance of retrofitted reinforced concrete beam-column joints using steel prop. Construction and Building Materials 36: 287–294.

17.

Sharbatdar

Kheyroddin

Emami

(2012b) Experimental seismic investigation of composite RC-diagonal steel prop joints. In: Proceedings of the 15th world conference on earthquake engineering, Lisbon, 24–28 September.

18.

Sharma

Reddy

Eligehausen

, et al. (2014) Seismic response of reinforced concrete frames with haunch retrofit solution. ACI Structural Journal 111(1–6): 1–12.

19.

Tran

(2016) Influence factors for the shear strength of exterior and interior reinforced concrete beam-column joints. Procedia Engineering 142: 63–70.

20.

Truong

Dinh

Kim

, et al. (2017) Seismic performance of exterior RC beam–column joints retrofitted using various retrofit solutions. International Journal of Concrete Structures and Materials 11(3): 415–433.

21.

Vandana

Bindhu

(2017) Influence of geometric and material characteristics on the behavior of reinforced concrete beam-column connections. Canadian Journal of Civil Engineering 44(5): 377–386.

22.

Yang

Zheng

, et al. (2012) Parametric analysis of seismic behaviors of SRC beam transfer structures with supplemental energy dissipation haunch brace. China Civil Engineering Journal 45(9): 74–83.

23.

Zhou

Yin

Lin

(2012) Experimental investigation on seismic performance of RC frame structures with viscous damper energy dissipation haunch braces. Journal of Building Structures 32: 64–73.