Hysteresis Behavior of RC Beam–Column Joints of Existing Substandard RC Structures Subjected to Seismic Loading–Experimental and Analytical Investigation

Abstract

Four exterior reinforced concrete beam–column joint subassemblages with poor reinforcement details and low-quality materials were constructed and subjected to cyclic lateral deformations under constant axial loading of the columns. The longitudinal rebars at the top of the beams were well-anchored in the joint region with a 90° hook and transversely welded to prevent premature slippage. The same was true for the longitudinal rebars at the bottom of the beam of the first specimen. Contrarily, the anchorage of the rebars at the bottom of the beam of the other three subassemblages was straight and of insufficient length. One of these specimens (the second) also had deficient lap splices of the column reinforcement, while the other three specimens had continuous column rebars. The third and the fourth subassemblage were designed with different joint aspect ratio and beam shear span/depth ratio values. The overall seismic performance of the specimens was evaluated and compared. The failure mode of the subassemblages was accurately predicted by the proposed analytical model. It was clearly demonstrated that the anchorage of the rebars, the length of the lap splices, the joint aspect ratio and the shear span/depth of the beam ratio value crucially affect the cyclic response of beam–column joints and, hence, may cause a severe detrimental impact to the overall structural integrity.

1. Introduction

During strong seismic events, the common regions where reinforced concrete beams and columns are connected are subjected to significantly higher stresses with respect to the stresses developed at the linked members [1]. Therefore, if the beam–column joints are not appropriately designed to withstand these stresses, brittle failure of the joint regions can occur, resulting in a partial or even general collapse of the structure. This is particularly common in existing reinforced concrete (RC) structures, which were not designed according to the capacity design philosophy, and it is also a possibility even for the modern RC structures designed to satisfy the recommendations of Eurocode 2 and 8 [2,3] for ductility class medium (DCM) [4].

When the anchorage of the beam longitudinal reinforcement in an exterior beam–column connection is artfully detailed and provides sufficient bonding between the bars and the surrounding concrete, significant horizontal shear stresses are placed on the joint region during cycling. For favorable steel–concrete bond conditions, the same is also true for the column longitudinal rebars passing through the joint, which introduce significant vertical shear stresses to the joint. Consequently, brittle shear failure of the connection will be triggered immediately after the shear stresses introduced to the joint exceed its shear capacity [5,6]. It is worth emphasizing that damage evolution and the extensive degradation of the overall bearing capacity are extremely rapid when the joint is totally unconfined or poorly confined [7,8]. Nevertheless, the joint shear failure cannot be effectively prevented solely by adding ties and by ensuring that the capacity design ratio value is higher than 1.30 (according to Eurocode 8), unless the developed shear stresses are limited to one half of the joint shear capacity (or lower) [4,9,10]. Otherwise, the evolution of shear damage in the beam–column joint may be delayed but, eventually, the desirable elastic–plastic failure mechanism with plastic hinges formed solely in the beams will not be achieved.

The anchorage deficiency and degradation of bonding conditions significantly affect the seismic performance of the beam–column connection, since the shear strain to which a joint is subjected is directly related to the bond stresses developed between the beam and column rebars passing through the joint (or anchored inside it) and the surrounding concrete. For this reason, civil engineers must always take into consideration the influence of bond conditions on the overall cyclic behavior of beam–column joints to avoid a possible false interpretation of the pathology of earthquake-damaged RC structures. For instance, it is quite frequent after strong earthquakes to observe poorly detailed existing RC structures with almost (or even totally) undamaged beam–column joints, while the damage is limited solely to a particularly wide-open crack in the beams in the juncture with the joints. This type of damage may be mistakenly perceived by the inexperienced civil engineer as a result of ductile flexural failure and, hence, be insufficiently repaired during the retrofit process (i.e., be repaired solely by injecting epoxy resin). However, this failure does not by any means indicate the satisfactory hysteresis behavior of the joints. Contrarily, it conceals a particularly dangerous brittle failure mode: the pullout of the beam rebars from the joint region. This was clearly observed in a previous work of the authors [11], where the seismic performance of exterior RC beam–column joint subassemblages with deficient straight anchorages of the longitudinal rebars at both the top and the bottom of the beam was investigated experimentally and analytically.

Another parameter which critically affects the performance of RC beam–column joints under cyclic lateral loading is the joint aspect ratio value, α = h_b/h_c. In combination with the axial load of the column, the values of the joint aspect ratio, α, may cause the development of increased or decreased shear stresses in the beam–column joint region during an earthquake. In the experimental works of Meinheit and Jirsa [12] and Parate and Kumar [13], it was observed that the increase of the joint aspect ratio values resulted in an improved seismic performance, while Paulay and Park [14] concluded that the beam–column joints of multi-story buildings with aspect ratio values greater than 1.0 are able to withstand significant shear stresses during cycling. Besides, the ratio α is related to the sectional dimensions of the connected structural members (beams and columns). Thus, an increase in the beam height, h_b, results in an increase in the ultimate shear capacity of the joint, as it is calculated according to the Tsonos model [6,15]. Of course, it should be noted that this increase in the beam height should be reasonable enough with respect to the column’s section height, h_c, and in accordance with the capacity design conception, which requires that the flexural strength ratio ΣM_Rc/ΣM_Rb should be greater than 1.30 [3] or 1.20 [16,17]. Otherwise, the strong beam(s) may shift the seismic damage to the joint region or/and the columns. Meanwhile, the beam height, h_b, also affects the beam shear span/depth ratio value, a/d. For instance, a decrease in the beam height implies an increase in the beam shear span/depth ratio value, a/d, which, in turn, reduces the shear stresses developed in the beam. Thereby, a different seismic performance of the beam itself may be expected. The influence of the joint aspect ratio value, α, and of the value of the beam shear span/depth ratio, a/d, is even greater for poorly (non-seismically) detailed existing RC structures with respect to the modern ones. This is owed to the poor confinement provided to the joint region and the critical regions of beams and columns in combination with the low inherent strength and low quality of both concrete and steel.

The research found in the literature regarding the influence of the aforementioned parameters, especially when combined, in the hysteresis response of poorly detailed exterior RC beam–column joints is particularly limited. Kalogeropoulos and Tsonos experimentally investigated the seismic performance of original column subassemblages typical of substandard RC buildings built prior to the 1960–1970s with deficient lap splices, as well as the behavior of similar specimens retrofitted using thin steel jackets, RC jackets and CFRP jackets. They also proposed an analytical formulation for calculating the necessary confinement to achieve yielding of the deficiently lap-spliced rebars [18,19,20]. Anagnostou et al. [21] used a database with experimental results of 67 RC columns with lap-spliced steel bars, strengthened externally with FRP jackets subjected to pseudo-seismic loading to investigate the predictive performance of EC8.3 [22] and KANEPE [23] in calculating V_R and θ_u. In the experimental and analytical work of Sasmal et al. [24], the seismic behavior of the exterior beam–column subassemblages of RC structure, designed and detailed according to the provisions of Eurocode and Indian Standards at different stages of their evolution (gravity load design, non-ductile, and ductile), was evaluated. Hakuto et al. [25] performed seismic tests on interior and exterior RC beam–column joint subassemblages with a lack of or poor transverse reinforcement in the joint region, poor anchorage of the longitudinal bars passing through the interior joint, and beam rebar hooks bent out of the exterior joint core. Calvi et al. [26] tested beam–column joint subassemblages typical of buildings designed in the 1950s and 1960s with plain steel rebars anchored with terminal hooks, without transverse reinforcement. They concluded that damage in the joints started at early stages, leading to hybrid failure mechanisms. In the experimental research of Zhao et al. [27], the vulnerability of non-seismically detailed exterior connections with setback in columns was highlighted. The seismic behavior of non-seismically designed RC joints, regarding the effects of the beam–column depth ratio, column longitudinal reinforcement, and stirrups in joints on the seismic performance and shear strength of the joints, was investigated experimentally by Wong and Kuang [28]. An empirical model on unreinforced beam–column RC joints with hook-ended plain bars was proposed by Teresa De Risi et al. [29] to account for the peculiarities in terms of failure mode and concrete-to-steel interaction mechanisms. Beam tests and pull-out tests were performed by Fabrocino et al. [30] to study in detail the force–slip relation of the bond mechanism for straight rebars and that of anchoring end details, i.e., circular hooks with a 180◦ opening angle. Verderame et al. [31] experimentally investigated the seismic response of exterior unreinforced RC beam–column joints, representative of the existing non-conforming RC frame buildings, with different longitudinal reinforcements (plain or deformed), designed to be representative of two typical design practices (for gravity loads only or according to an obsolete seismic code). They observed different failure modes, namely joint failure with or without beam yielding. Recently, Karayannis et al. [32] Naoum et al. [33] and Karabini et al. [34] tested full-scale beam–column joint subassemblages without stirrups in the joint region, while also using piezoelectric lead zirconate titanate (PZT) transducers for the examination of the efficiency of an innovative strengthening technique of RC columns and beam–column joints, which included external strengthening with carbon fiber-reinforced polymer (C-FRP) ropes. Fanaradelli et al. [35] used pseudo-dynamic three-dimensional finite-element modeling to study the axial mechanical behavior of square and rectangular substandard RC columns, confined with fiber reinforced polymer (FRP) jackets and continuous composite ropes in seismic applications. The use of other innovative materials, such as glass fiber-reinforced polymer (GFRP) to strengthen existing structures, is also becoming more and more common [36]. In the experimental work of Garcia et al. [37], three full-scale substandard exterior RC beam–column joint specimens with inadequate detailing in the joint core zone were tested under cyclic loading and, subsequently, the damaged concrete of the joint was replaced by high strength concrete and the specimens were strengthened with CFRP sheets, showing a significant improvement in their hysteresis performance. Helal et al. [38] investigated, experimentally and numerically, the seismic response of full-scale exterior RC beam–column joints with poor reinforcement details strengthened using post-tensioned metal straps for active confinement. A high ductile metal strap confinement, for the strengthening of low strength concrete columns, was used by Ijmai et al. [39].

At this point, it is worth noting that the existing RC framed structures, built in the 1950–1970s period or earlier, possess numerous structural deficiencies; hence, their seismic response is dominated by the poor inelastic performance of the weaker structural members, namely the beam–column connections or/and the columns. The latter was clearly demonstrated many times in the aftermath of the strong earthquakes of the last 60 years, with the most recent examples being the seismic events in Turkey and Mexico in 2023. Furthermore, it cannot be ignored that the majority of RC structures worldwide were built prior to the imposition of modern code requirements for the design of earthquake-resistant RC structures. However, extending the service life of these structures and securing their ductile performance during future earthquakes through retrofitting processes are both rather challenging aims, but they also remain a more cost-effective and environmentally beneficial solution than demolishing and rebuilding. Thereupon, the satisfactory design of retrofit schemes, to allow for the strengthened structures to meet increased earthquake demands, requires a good understanding of the influences of various crucial design parameters in the seismic behavior of the beam–column joints, as well as of the developing failure mechanisms. Furthermore, the strengthening techniques and retrofit schemes should focus on combining measures exclusively undertaken for effectively improving bond conditions, for restoring the deficient anchorages, and for ensuring the load transfer and yielding of the lap-spliced column rebars, with the use of innovative materials and methods of application, which are less labor-demanding, easy to apply, cost-effective and environmentally friendly.

Along these lines, the present study aims to evaluate, both experimentally and analytically, the influence in the hysteresis behavior of critical parameters which are commonly combined in existing RC structures, namely the deficient anchorages of the beam longitudinal rebars in exterior beam–column joints, the inadequacy of the lap splices found in the columns, as well as the joint aspect ratio and beam shear span/depth ratio values. Intriguingly, the great number of design flaws and combined parameters examined herein allows for a better simulation of the actual behavior of substandard RC structures, while similar work found in the literature is extremely rare. Hence, the current experimental and analytical investigation provide a significant impetus to further the understanding of the overall hysteresis performance of existing structures, which can not be easily perceived when critical design parameters are examined separately.

2. Materials and Methods

Brittle failures are associated with catastrophic collapses of RC structures. Admittedly, there are multiple structural deficiencies, especially in the existing substandard structures built before the 1960–1970s, which trigger the development of brittle failure mechanisms in the most vulnerable members of the load bearing system, namely the columns and, particularly, the beam–column joints. Such shortcomings include the use of plain steel bars, the use of low compressive strength concrete, the inadequacy of anchorage and of the lap splice length of reinforcing bars, low confinement, etc. For this reason, an experimental program was conducted herein to evaluate the influence and profound implications of combined design defects on the seismic performance of substandard RC structures. After all, it is imperative to deeply understand how the hysteresis behavior is affected by these factors in order to effectively design the retrofit schemes for the earthquake-resistant rehabilitation of the existing RC structures.

Four exterior beam–column joint subassemblages with poor reinforcement details, representative of structural members found in existing substandard RC structures, were constructed and subjected to earthquake-type loading. The reinforcement details, cross-sectional dimensions and material properties of the specimens are summarized in Table 1 and Figure 1. Plain steel rebars with $f_y=374\left(\mathrm{M}\mathrm{P}\mathrm{a}\right)$ were used as longitudinal reinforcement, while the transverse reinforcement consisted of plain steel ties with $f_{yw}=263.5\left(\mathrm{M}\mathrm{P}\mathrm{a}\right)$. The concrete compression strength of the specimens was measured by using 150 × 300 mm cylinder compression tests (see Table 1). The subassemblages were designated using a number, representing the number of the column longitudinal rebars, followed by the letters L (when lap splices of the column reinforcement exist), T (when the anchorage of the beam top rebars in the joint region is achieved with a 90° degree hook), B (when the anchorage of the beam bottom rebars in the joint region is achieved with a 90° degree hook) and one final letter (A or B) which corresponds to the shear span/depth of the beam ratio value (see Table 1). In Table 2, the nominal flexural moment capacity of the columns ($M_{Rc}$) and of the beam ($M_{Rb}$), the nominal shear capacity of the beam ($V_{Rb}$), and the capacity design ratio (${\Sigma M}_{Rc}/{\Sigma M}_{Rb}$) for all specimens are summarized.

Figure 1. Reinforcement details and cross-sections of beam–column joint subassemblages (a) 4TB-A, (b) 4LT-A, (c) 8T-A and (d) 8T-B.

Figure 1. Reinforcement details and cross-sections of beam–column joint subassemblages (a) 4TB-A, (b) 4LT-A, (c) 8T-A and (d) 8T-B.

The seismic tests of the beam–column joint subassemblages 4TB-A, 4LT-A, 8T-A and 8T-B were conducted in the test setup shown in Figure 2a,b, which is located at the Laboratory of Reinforced Concrete and Masonry Structures of the Aristotle University of Thessaloniki. The exterior RC beam–column joint subassemblages simulate the part of a real-world RC building between the points of contra-flexure, almost at the middle of the column height and the beam length, where the flexural moment from the seismic loading is near zero. This is depicted in Figure 2b. The subassemblages did not include the RC slab. It should be noted that it is possible for beams at the perimeter of an RC building to experience torsional damage if significant stress is introduced into them by the slab. The inflection points of the columns were simulated using specific arrangements connected to the reaction frame and to the free ends of the columns by hinges. As a result, the vertical and the horizontal displacements of the columns’ ends were restrained, while still being able to rotate. The earthquake-type loading of the specimens was performed by subjecting the free end of the beam of each subassemblage to a large number of cycles of incremental inelastic lateral displacement amplitudes, according to the displacement-controlled schedule depicted in Figure 3b, under a constant axial loading of the columns equal to 150 kN. A two-way actuator was used to apply the lateral displacements to the free end of the beam, while the resisted shear force was measured by a load cell (see Figure 2a,b). The axial loading of the columns was achieved using a hydraulic jack. A calibrated linear variable differential transducer (LVDT) was used to measure the load point displacement. The steps of loading were determined using a test specimen similar to the examined ones, which was first loaded to its yield displacement. This was measured from the plot of resisted shear force-versus-displacement of the test specimen for the point when a significant decrease in stiffness occurred. This was further verified by the yielding of the longitudinal beam reinforcement at the column face. Thereupon, the loading was continued in the same direction (upper push half cycle) to 1.5 times the yield displacement, and the subassemblage was subsequently loaded in the opposite direction (upper and lower pull half cycle) to the same lateral displacement (see Figure 3a). After the first cycle of loading, the maximum displacement of each subsequent cycle was incremented by 0.5 times the yield displacement [25,40,41]. During the seismic tests, the subassemblages were subjected to a strain rate which corresponded to static conditions. As a result, the strengths exhibited by the specimens were somewhat lower than the strengths they would exhibit if subjected to load histories similar to actual seismic events, during which the strain rates are higher than the ones corresponding to static conditions [42,43,44].

Table 1. Reinforcement details and design parameters of the beam–column joint subassemblages.

Specimen	Section Dimensions (mm) Column/ Beam	Longitudinal Reinforcement (mm) Column/ Beam	Transverse Reinforcement (mm) Column/ Beam	Anchorage of Beam Rebars	Lap Splices of Column Rebars (mm)	Shear Span/ Depth Ratio	fc (MPa)
4TB-A	200 × 200/ 200 × 300	4Ø10/ 3Ø10 top 3Ø10 bottom	Ø6/200/ Ø6/200	90° hook (top) 90° hook (bottom)	-	3.89	7.0
4LT-A	200 × 200/ 200 × 300	4Ø10/ 3Ø10 top 3Ø10 bottom	Ø6/200/ Ø6/200	90° hook (top) Straight (bottom)	200	3.89	7.0
8T-A	200 × 200/ 200 × 300	8Ø10/ 3Ø10 top 3Ø10 bottom	Ø6/200/ Ø6/200	90° hook (top) Straight (bottom)	-	3.89	8.0
8T-B	200 × 200/ 200 × 200	8Ø10/ 3Ø10 top 3Ø10 bottom	Ø6/200/ Ø6/200	90° hook (top) Straight (bottom)	-	6.18	8.0

Table 1. Reinforcement details and design parameters of the beam–column joint subassemblages.

Specimen	Section Dimensions (mm) Column/ Beam	Longitudinal Reinforcement (mm) Column/ Beam	Transverse Reinforcement (mm) Column/ Beam	Anchorage of Beam Rebars	Lap Splices of Column Rebars (mm)	Shear Span/ Depth Ratio	fc (MPa)
4TB-A	200 × 200/ 200 × 300	4Ø10/ 3Ø10 top 3Ø10 bottom	Ø6/200/ Ø6/200	90° hook (top) 90° hook (bottom)	-	3.89	7.0
4LT-A	200 × 200/ 200 × 300	4Ø10/ 3Ø10 top 3Ø10 bottom	Ø6/200/ Ø6/200	90° hook (top) Straight (bottom)	200	3.89	7.0
8T-A	200 × 200/ 200 × 300	8Ø10/ 3Ø10 top 3Ø10 bottom	Ø6/200/ Ø6/200	90° hook (top) Straight (bottom)	-	3.89	8.0
8T-B	200 × 200/ 200 × 200	8Ø10/ 3Ø10 top 3Ø10 bottom	Ø6/200/ Ø6/200	90° hook (top) Straight (bottom)	-	6.18	8.0

Figure 2. (a) Aerial view of the test setup and the instrumentation used; (b) reaction frame of the Laboratory of Reinforced Concrete and Masonry Structures of the Aristotle University of Thessaloniki where the seismic tests were performed, and the part of a RC structure which is simulated by the exterior beam–column joint subassemblages.

Figure 2. (a) Aerial view of the test setup and the instrumentation used; (b) reaction frame of the Laboratory of Reinforced Concrete and Masonry Structures of the Aristotle University of Thessaloniki where the seismic tests were performed, and the part of a RC structure which is simulated by the exterior beam–column joint subassemblages.

Table 2. Values of the nominal flexural and shear capacity, column shear force and capacity design ratio of the subassemblages.

	4TB-A	4LT-A	8T-A	8T-B
Nominal flexural capacity of the columns MRc (kNm)	(Over) 12.32 (Under) 11.20	(Over) 12.32 (Under) 11.20	(Over) 17.28 (Under) 16.64	(Over) 17.92 (Under) 17.28
Nominal flexural capacity of the beam MRb (kNm)	20.16	20.16	21.60	12.80
Nominal shear capacity of the beam VRb (kN)	21.22	21.22	22.74	13.47
Capacity design ratio ΣMRc/ΣMRb	1.17	1.17	1.57	2.75

Table 2. Values of the nominal flexural and shear capacity, column shear force and capacity design ratio of the subassemblages.

	4TB-A	4LT-A	8T-A	8T-B
Nominal flexural capacity of the columns MRc (kNm)	(Over) 12.32 (Under) 11.20	(Over) 12.32 (Under) 11.20	(Over) 17.28 (Under) 16.64	(Over) 17.92 (Under) 17.28
Nominal flexural capacity of the beam MRb (kNm)	20.16	20.16	21.60	12.80
Nominal shear capacity of the beam VRb (kN)	21.22	21.22	22.74	13.47
Capacity design ratio ΣMRc/ΣMRb	1.17	1.17	1.57	2.75

Figure 3. (a) Qualitative deformed shape of the specimens; (b) displacement-controlled schedule.

Figure 3. (a) Qualitative deformed shape of the specimens; (b) displacement-controlled schedule.

3. Results

3.1. Hysteresis Performance of the Subassemblages

A thorough interpretation of the acquired experimental data is subsequently performed, to evaluate the seismic response of the beam–column joint subassemblages. In particular, the overall hysteresis performance of the specimens is evaluated in terms of lateral bearing capacity, stiffness degradation, energy dissipation capacity and viscous damping (see Figure 4, Figure 5 and Figure 11b). Moreover, for each specimen, the cracking propagation, as well as the developed failure mechanisms, are explained and documented (see Figure 6, Figure 7, Figure 8 and Figure 9).

Specimens 4TB-A and 4LT-A were designed with capacity design ratio value of 1.17, which is lower than the required value (${\Sigma M}_{Rc}/{\Sigma M}_{Rb}=1.30$) according to the current Eurocode (EC8) provisions (see Table 2). This is particularly common in most cases of existing RC structures built prior to the 1960–1970s, which were not designed based on the controllable and hierarchically developed damage control philosophy. In the case of specimens 8T-A and 8T-B the capacity design ratio equaled 1.57 and 2.75, respectively. This is slightly higher with respect to the required value 1.30 for subassemblage 8T-A but substantially increased in the case of 8T-B, due to the short height and the low flexural and shear bearing capacity of the beam (see Table 2).

All specimens exhibited poor hysteresis behavior dominated by catastrophic damages of brittle nature, namely shear failure or/and excessive slipping of reinforcement. At this point it is worth noting that, despite it being expected for existing RC structures with numerous structural inadequacies to be severely damaged during a strong seismic event, it is particularly crucial to acknowledge and understand the relation between the structural inadequacies and the developed failure mechanisms, in order to effectively design the retrofit schemes for the pre-earthquake or post-earthquake strengthening of the existing RC structures. For this reason, the influence of the reinforcement anchorage conditions, lap splice length, joint aspect ratio and beam shear span/depth ratio values in the seismic performance of the subassemblages is subsequently evaluated.

3.1.1. Subassemblage 4TB-A

The beam longitudinal reinforcement of subassemblage 4TB-A was well-anchored into the joint region with 90° hooks, while 2Ø10 bar segments were welded transversely to the longitudinal beam rebars at the point of curvature to further improve bond conditions and preclude premature bar slipping (see Figure 1a). As a result, the anchorage of the beam top and bottom reinforcing bars in the joint region was ideal for the non-seismically designed existing RC structures. Moreover, one tie was provided in the joint region, which contributed to holding the beam rebars in place after the loss of the concrete cover in the rear face of the joint (see Figure 1a). The damage was initiated during the first cycle of the earthquake-type loading with the formation of hairline flexural and flexural-shear cracks in the beam (see Figure 6a). Further dilation of these cracks during testing was minor, while for the amplitudes of lateral displacement reversals, corresponding to drift angle R = 1.90% (second cycle), hairline shear cracks were formed in both diagonal directions of the beam–column joint region (see Figure 6b). Responsible for the premature shear cracking of the joint of specimen 4TB-A were the increased shear stresses inserted to the joint from the well-anchored beam rebars with respect to its low ultimate shear capacity. This is clearly documented in Section 3.4 using the proposed analytical model, according to which the shear damage of the joint region can be safely precluded only if the ratio of the developed shear stress, when the yielding of the beam reinforcement occurs to the ultimate shear capacity of the joint, is lower than 0.50 (${\tau }_{cal}/{\tau }_{ult}<0.50$). However, as observed in Table 3, the calculated ratio value ${\tau }_{cal}/{\tau }_{ult}$, for specimen 4TB-A equaled 1.685; hence, the premature shear failure of the joint region was expected. Indeed, the experimental shear stress to the ultimate joint shear capacity ratio was calculated as ${\tau }_{exp}/{\tau }_{ult}=0.76$, which is higher than the value 0.50. Due to the poor confinement of the joint region, the shear damage evolved rapidly during the subsequent cycles of lateral displacement, causing severe dilation of the diagonal cracks, the opening of new ones and, eventually, the disintegration of the concrete core (see Figure 6c,d). Furthermore, hairline splitting cracks were formed along the longitudinal column rebars in the back side of the specimen for drift angle R = 2.38%, which propagated and dilated significantly, resulting in loss of the concrete cover for lateral displacement equal to 35 mm (drift angle R = 3.33%) (see Figure 6d). As a result, the cross-section of the already disintegrated concrete core was reduced, causing the severe deterioration of the axial load bearing capacity. Thus, for drift angle values higher than R > 3.81%, significant buckling of the longitudinal column reinforcement occurred, indicating catastrophic collapse (see Figure 6e,f and Figure 9a).

The damage evolution of the beam–column joint subassemblage 4TB-A is clearly reflected in the hysteresis loops illustrated in Figure 4a. The descending slope of the envelope curves of the diagram during the first five upper and the first five lower half-cycles are milder than those corresponding to the fifth and sixth upper and lower half-cycles. This results from the evolution of shear damage and, eventually, from the severe deterioration of the axial load bearing capacity followed by the buckling of reinforcement for increased lateral displacements. In particular, the latter occurred for the drift angle equal to R = 3.33% and affected the lateral bearing capacity as well. For the drift angle equal to R = 1.90% (second cycle of loading), specimen 4TB-A maintained 94.6% (upper half-cycle) and 100% (lower half-cycle) of its lateral bearing capacity. The corresponding values at the end of the fourth cycle (R = 2.86%) were 89.19% and 88.57%, respectively. However, thereafter the lateral strength of 4TB-A rapidly reduced, while at the end of testing it was limited to 48.65% and 40% of its initial values during the first upper and lower half-cycle, respectively (see Figure 4a).

Due to the premature joint shear failure of specimen 4TB-A, the peak-to-peak stiffness degraded significantly during the consecutive cycles of the earthquake-type loading (see Figure 5a). A 27.08% reduction in stiffness value was observed for the drift angle R = 1.90% with respect to the initial stiffness during the first cycle. The degradation rate remained almost the same during testing, at the end of which (drift angle equal to R = 4.29%) the peak-to-peak stiffness of specimen 4TB-A was limited to 14.81% of its initial value.

Being dominant, the shear damage of subassemblage 4TB-A resulted in a poor energy dissipating hysteresis performance. This is clearly demonstrated in Figure 5b and Figure 11b. During the second cycle of the lateral displacement sequence (load-point displacement of 20 mm), the dissipated seismic energy was reduced by 25.17% with respect to the value of energy dissipated during the first cycle. Subsequently, the energy dissipation capacity of 4TB-A showed a marginal increase, while remaining lower than the initial value during the first cycle until the drift angle, R, equaled R = 3.81%. During the last cycle (R = 4.29%), the dissipated seismic energy value was only 21.86% higher than the initial value during the first cycle. The low energy dissipation capacity of specimen 4TB-A is also reflected in the area of the hysteresis loops, which is limited (see Figure 4a).

3.1.2. Subassemblage 4LT-A

The beam–column joint subassemblages 4TB-A and 4LT-A had the same cross-section dimensions and the same column and beam reinforcement. However, contrary to specimen 4TB-A, the anchorages of the beam bottom rebars in the joint region of 4LT-A were straight and of deficient length. Furthermore, at the lower part of the upper column of specimen 4LT-A, just above the joint region, the longitudinal reinforcing bars were inadequately lap-spliced. As a result, specimen 4LT-A demonstrated an entirely different hysteresis behavior with respect to the seismic response of 4TB-A (see Figure 4b). In particular, during the first upper half-cycle, the main flexural crack and a secondary one were formed at the upper half part of the beam (see Figure 7a). Subsequently, for the reversed lateral displacement amplitudes of the first lower half-cycle, a significantly wider crack was formed at the lower half part of the beam, as a consequence of the excessive slipping (pullout) of the deficiently anchored beam bottom rebars. Meanwhile, a unidirectional hairline diagonal shear crack was formed in the joint region due to the increased shear stresses initially placed on the joint from the well-anchored beam top rebars (see Figure 7a). The latter is documented in Section 3.4 using the proposed analytical model. In particular, the ratio value ${\tau }_{cal}/{\tau }_{ult}$ for specimen 4LT-A equaled 1.685 (see Table 3), which is significantly higher than the limit value, 0.50, according to the proposed model for preventing joint shear damage. As a result, the premature shear failure of the joint was expected to occur. Furthermore, the ${\tau }_{exp}/{\tau }_{ult}$ ratio value was calculated as 0.74, which is also higher than the value 0.50, thus confirming that the increased developed shear stresses caused the shear cracking of the joint region of 4LT-A. It should be noted that, contrary to specimen 4TB-A, the joint shear damage in case of subassemblage 4LT-A occurs in one direction only, due to the early bond-slip failure and pullout of the insufficiently anchored beam bottom rebars.

Noteworthy, no further dilation of the joint shear crack was observed throughout testing. The latter is owed to the rapid dilation of the pullout crack, which propagated and connected with the flexural crack at the upper half part of the beam, causing the beam’s top reinforcing bars mainly to possess dowel action (and deform correspondingly) rather than being subjected to tension–compression alternations during cycling. Henceforth, during the consecutive cycles of lateral displacement reversals, the increase in the shear stresses placed on the joint from the beam bars was marginal, preventing the further evolution of the shear damage in the joint region. Moreover, for drift angle, R, equal to R = 1.90%, significant slipping of the inadequately lap-spliced column reinforcing bars also occurred, resulting in the formation of a pullout crack at the lower part of the column (see Figure 7b). Hereafter, damage evolution was limited in the beam with gradual dilation of the pullout crack due to the unbridled free movement of the beam bottom rebars. Eventually, the seismic test of specimen 4LT-A was terminated after nine cycles of incremental amplitudes of lateral displacement reversals (R = 5.24%).

The failure mode of specimen 4LT-A (see Figure 7d and Figure 9b) resulted from a complicated combination of failure mechanisms, triggered by the structural inadequacies of the subassemblage. The peculiar form of the hysteresis loops of 4LT-A (see Figure 4b), is extremely rarely found in the international literature, which perspicuously reflects the devastating influence of the anchorage and lap splice length deficiency in the seismic performance of the existing RC structures. The uncommon and severe asymmetry observed in the hysteresis loops between the upper and lower half-cycles demonstrates the annihilation of the lateral bearing capacity and, hence, of the stiffness and energy dissipation capacity in the lower half-cycles due to premature bond-slip failure and the pullout of the beam’s bottom reinforcing bars from the joint region. In particular, the initial lateral bearing capacity of 4LT-A for the peak load-point displacement of the first lower half-cycle was only 3.21% of its corresponding value of the first upper half-cycle. Moreover, this negligible lateral strength of the lower half-cycles remained almost unchanged until the end of testing.

For drift angle R = 1.90%, a 29.6% reduction in the stiffness value of specimen 4LT-A was observed with respect to the initial value during the first cycle, while after nine cycles of reversed amplitudes of lateral displacement (R = 5.24%) the subassemblage retained 21.5% of its initial stiffness (see Figure 5a). However, the initial peak-to-peak stiffness of subassemblage 4LT-A was only a mere portion (46%) of that of specimen 4TB-A. This is owed to the particularly limited lateral strength of 4LT-A during the first lower half-cycle. The same was also true for the subsequent cycles until the end of testing. Thus, despite the obviously lower reduction rate achieved by 4LT-A with respect to that exhibited by specimen 4TB-A, the stiffness of 4LT-A was always significantly lower than that of specimen 4TB-A (see Figure 5a and Figure 11a), due to the inadequacy of anchorage and lap splice length.

The beam–column joint subassemblage 4LT-A exhibited a mixed-type brittle failure mode which combined minor unidirectional joint shear damage, premature lap splice failure of the column rebars, and early pullout failure of the beam bottom reinforcement. Hence, the hysteresis performance of 4LT-A was particularly poor. In Figure 11b the energy dissipation capacity-versus-load point displacement is illustrated. As observed, the amount of seismic energy dissipated during the second cycle of the earthquake-type loading was only 81.4% of that dissipated during the first cycle. Moreover, the ratio of seismic energy dissipated during each cycle to that dissipated during the first cycle (see Figure 5b) ranged from 0.81 to 1.01 until the seventh cycle, while the value for drift angle R = 5.24% (end of testing) equaled 1.32. The deterioration of dissipated energy values during consecutive cycles of the earthquake-type loading clearly reflects the severe impact of the premature brittle failure in the hysteresis performance of specimen 4LT-A [40,45].

3.1.3. Subassemblage 8T-A

Specimen 8T-A was a counterpart of subassemblages 4TB-A and 4LT-A, with the same cross-section dimensions and the same beam reinforcement. Similarly to specimen 4LT-A, the beam–column joint 8T-A had a deficient straight anchorage of the beam’s bottom reinforcement in the joint region. However, the column longitudinal rebars of 8T-A (8Ø10 mm bars S220) were continuous and not lap-spliced as in the case of subassemblage 4LT-A (4Ø10 mm bars S220). Furthermore, no ties were provided in the joint area of 8T-A. Due to these differences and notwithstanding the great asymmetry observed in the hysteresis loops, the beam–column joint subassemblage 8T-A demonstrated a more stable hysteresis performance in both the upper half cycles and the lower ones with respect to specimens 4TB-A and 4LT-A (see Figure 4c). Damage initiation included the formation of the main flexural crack at the upper half part of the beam in the juncture with the joint during the first upper push half cycle (see Figure 9c). Subsequently, excessive slipping of the beam’s bottom reinforcing bars occurred for reversed amplitudes of lateral displacement, resulting in the formation of a wide pullout crack at the lower half part of the beam. Due to anchorage inadequacy and the pullout of the beam bottom rebars, the behavior of subassemblage 8T-A during the lower half cycles was almost similar to that of specimen 4LT-A, requiring only a portion of the lateral shear force to achieve each load point displacement with respect to that required for the upper half cycles (see Figure 4b,c). Shear cracking of the joint region occurred along the one diagonal direction only. Nevertheless, this hairline shear crack was not formed before the seventh cycle of the lateral loading (drift angle R = 4.29%), while further evolution of shear damage in the joint of 8T-A was not observed until the end of testing (R = 4.76%). The joint shear failure of 8T-A is documented in Section 3.4 using the proposed analytical model. As observed in Table 3, the ratio value ${\tau }_{cal}/{\tau }_{ult}$ for specimen 8T-A equaled 1.481, which is significantly higher than the limit value, 0.50, according to the proposed model for preventing joint shear damage. As a result, premature shear failure of the joint was expected to occur. Moreover, the ${\tau }_{exp}/{\tau }_{ult}$ ratio value was calculated as 0.77, which is also higher than the value 0.50, thus confirming that the increased developed shear stresses caused the shear cracking of the joint region.

The continuity of the column longitudinal reinforcement in subassemblage 8T-A prevented the excessive slipping of the rebars and the consequential deterioration of lateral strength. Hence, the preservation of lateral strength was achieved in the case of specimen 8T-A, contrary to subassemblage 4LT-A, which exhibited gradual lateral strength degradation due to the premature failure of the lap splices.

The seismic behavior of 8T-A is characterized by particularly asymmetric hysteresis loops, similar to those of specimen 4LT-A. Admittedly, the overall damage of 8T-A was more limited with respect to the damage observed in subassemblages 4TB-A and 4LT-A. Nevertheless, similarly to subassemblages 4TB-A and 4TL-A, specimen 8T-A demonstrated poor hysteresis performance, dominated mainly by the premature pullout failure of the beam bottom rebars.

The lateral strength of 8T-A for the peak load-point displacement of the first lower half cycle was 31.6% of that of the first upper half cycle. Due to the preservation of lateral bearing capacity, at the end of testing (drift angle R = 4.29%) the corresponding value equaled 29.7% (see Figure 4c). Meanwhile, at the end of the seismic test, the lateral strength of the upper half cycles and the lower ones showed a minor reduction of 2.6% and 9.1%, respectively.

The peak-to-peak stiffness of the beam–column joint subassemblage 8T-A was reduced by 26.5% for drift angle R = 1.90% (see Figure 5a). The deterioration rate was reduced during the subsequent cycles, while at the end of the earthquake-type loading (displacement of 50 mm) 8T-A retained 28.8% of its initial stiffness during the first cycle.

The limited area of the asymmetric hysteresis loops of 8T-A (see Figure 4c), which showed no substantial variation during the subsequent cycles of the lateral displacement sequence (see Figure 11b), is indicative of poor hysteresis performance and low energy dissipation capacity due to the brittle nature of the damage. The energy dissipation value during the second cycle equaled only 68.9% of the value corresponding to the first cycle. Furthermore, during the six subsequent cycles the value of energy dissipated during each cycle to that dissipated during the first cycle ratio equaled 0.767, 0.888, 0.877, 0.801, 0.892 and 0.852, respectively (see Figure 5b).

3.1.4. Subassemblage 8T-B

The columns of subassemblage 8T-B had the same cross-sectional details as the columns of specimen 8T-A. However, the beam height of 8T-B equaled 2/3 of that of 8T-A. As a result, both the joint aspect ratio value and the shear span/depth ratio of the beam were affected. In particular, due to the significantly reduced beam height, the joint aspect ratio value equaled 1.0, while the shear span/depth ratio equaled 6.18 which is significantly higher than 3.89, the corresponding value for subassemblages 4TB-A, 4LT-A and 8T-A (see Table 1). Thus, the behavior of the beam itself of specimen 8T-B was expected to be dominated by flexure rather than shear, based on the Kani and MacGregor theory [46,47]. Indeed, no shear cracks were formed in the beam of specimen 8T-B, contrary to specimen 8T-A. Moreover, a substantial increase in the capacity design ratio value of 8T-B (2.75) was caused with respect to that of 8T-A (1.57).

As it was also observed in the case of subassemblage 8T-A, the damage of 8T-B was initiated with the formation of the main flexural crack at the upper half part of the beam during the first upper push half cycle. Subsequently, the wide pullout crack was formed at the lower half part of the beam for the reversed lateral displacements of the first lower pull half cycle. However, due to the particularly reduced height of the beam of 8T-B, the pullout crack joined rapidly with the flexural one, forming a single particularly wide through crack in the beam in the juncture with the joint (see Figure 8 and Figure 9d). As a consequence, the beam shear force was, henceforth, resisted solely by the beam top reinforcing bars, causing them to act as dowels. Hence, the local deformation of the beam top rebars prevented significant shear forces from entering the joint region. Therefore, the shear cracking of the joint was not observed, while the hysteresis response of 8T-B was dominated by the premature pullout failure of the beam bottom rebars.

The overall lateral strength of subassemblage 8T-B was lower than the lateral bearing capacity of specimens 4TB-A, 4LT-A and 8T-A. Nevertheless, similarly to 8T-A, the absence of lap splices allowed for the preservation of lateral strength of 8T-B throughout testing. As observed by the asymmetric hysteresis loops illustrated in Figure 4d, the value of lateral strength for the peak load-point displacement of the first lower half cycle equaled 22.7% of the corresponding value for the first upper half cycle. For drift angle R = 5.24%, the corresponding value equaled 19%. Furthermore, at the end of the earthquake-type loading specimen, 8T-B retained 95.5% and 80% of its initial lateral strength of the upper and lower half cycles, respectively.

Specimen 8T-B showed the lowest reduction rate of its peak-to-peak stiffness with respect to subassemblages 4TB-A, 4LT-A and 8T-A; however, it also demonstrated the lower stiffness among all. At the end of testing (drift angle R = 5.24%) 8T-B retained 27.8% of its initial stiffness during the first cycle (see Figure 5a).

The poor energy dissipating hysteresis behavior of 8T-B is clearly reflected on the hysteresis loops (see Figure 4d and Figure 11b) the area of which is particularly limited and shows no significant increase throughout testing. In particular, the ratio of energy dissipated during each cycle to that dissipated during the first cycle ranges from 0.775 to 1.054 (see Figure 5b).

Figure 4. Plots of resisted shear force-versus-displacement of the beam–column joint subassemblages (a) 4TB-A, (b) 4LT-A, (c) 8T-A and (d) 8T-B.

Figure 4. Plots of resisted shear force-versus-displacement of the beam–column joint subassemblages (a) 4TB-A, (b) 4LT-A, (c) 8T-A and (d) 8T-B.

Figure 5. (a) Peak-to-peak stiffness of subassemblages 4TB-A, 4LT-A, 8T-A and 8T-B; (b) Plots of the energy dissipated during each cycle to that dissipated during the first cycle, and ratio-versus-load point displacement of subassemblages 4TB-A, 4LT-A, 8T-A and 8T-B.

Figure 5. (a) Peak-to-peak stiffness of subassemblages 4TB-A, 4LT-A, 8T-A and 8T-B; (b) Plots of the energy dissipated during each cycle to that dissipated during the first cycle, and ratio-versus-load point displacement of subassemblages 4TB-A, 4LT-A, 8T-A and 8T-B.

Figure 6. Evolution of the seismic damage and failure mode of beam–column joint subassemblage 4TB-A. (a) phase 1, (b) phase 2, (c) phase 3, (d) phase 4, (e) phase 5, (f) failure mode.

Figure 6. Evolution of the seismic damage and failure mode of beam–column joint subassemblage 4TB-A. (a) phase 1, (b) phase 2, (c) phase 3, (d) phase 4, (e) phase 5, (f) failure mode.

Figure 7. Evolution of the seismic damage and failure mode of beam–column joint subassemblage 4LT-A. (a) phase 1, (b) phase 2, (c) phase 3, (d) failure mode.

Figure 7. Evolution of the seismic damage and failure mode of beam–column joint subassemblage 4LT-A. (a) phase 1, (b) phase 2, (c) phase 3, (d) failure mode.

Figure 8. Interpretation of the failure mode of subassemblage 8T-B. The joint remains intact due to the low shear stress values (region 1-1) and due to the pullout of the longitudinal beam bars (region 2-2).

Figure 8. Interpretation of the failure mode of subassemblage 8T-B. The joint remains intact due to the low shear stress values (region 1-1) and due to the pullout of the longitudinal beam bars (region 2-2).

Figure 9. Failure mode of beam–column joint subassemblages (a) 4TB-A, (b) 4LT-A, (c) 8T-A and (d) 8T-B.

Figure 9. Failure mode of beam–column joint subassemblages (a) 4TB-A, (b) 4LT-A, (c) 8T-A and (d) 8T-B.

3.2. Comparison of the Seismic Behavior of the Subassemblages

The comparative analysis and interpretation of the experimental results for all the beam–column joint subassemblages is essential, to allow for the in-depth understanding and evaluation of the critical parameters influencing the inelastic cyclic response of the specimens. This is exceptionally valuable for practice engineers when deciding and designing the retrofit schemes for the earthquake-resistant rehabilitation of substandard RC structures, in order to be satisfactory and efficient without compromising the safety of residents and structural integrity.

In Figure 10a,b the lateral load ratios-versus-load point displacement, 4LT-A/4TB-A, 8T-B/8T-A, 8T-A/4TB-A and 4LT-A/8T-A, are depicted for the upper and lower half cycles of the earthquake-type loading, respectively. The ratio value 8T-A/4TB-A for the upper half cycles ranges from 1.03 to 2.0 (see Figure 10a), due to the significant progressive joint shear damage of specimen 4TB-A and the deterioration of its lateral strength. Therefore, it is apparent that despite the adequacy of anchorage of the beam longitudinal reinforcement in the beam–column connection of 4TB-A, the lack of sufficient confinement in the joint region may result in excessive shear damage and the loss of lateral (and axial) bearing capacity. The range of lateral strength ratio 4LT-A/4TB-A for the upper half cycles is similar to that of ratio 4LT-A/8T-A. The shear damage of 4LT-A was limited with respect to specimen 4TB-A. However, gradual lateral strength degradation of 4LT-A was also borne by the excessive slipping of the beam bottom rebars and the lap-spliced column reinforcement. Nevertheless, for drift angle R ≥ 3.33% the ratio value 4LT-A/4TB-A for the upper half cycles increased significantly, since the lateral (and axial) load carrying capacity of 4TB-A further exacerbated rapidly. The lateral strength ratio value 8T-B/8T-A for the upper half cycles was almost stable because both specimens exhibited a similar failure mode, mainly dominated by the premature pullout failure of the beam bottom rebars.

The changes in lateral load ratios-versus-load point displacement 4LT-A/4TB-A, 8T-B/8T-A, 8T-A/4TB-A and 4LT-A/8T-A for the lower half cycles closely resemble the ones for the upper half cycles (see Figure 10b). It is evident that the behavior of specimens 4LT-A, 8T-A and 8T-B during the lower half cycles was dominated by the premature pullout failure of the beam bottom rebars.

It should also be mentioned that, contrary to subassemblage 4TB-A, the loss of the cover concrete at the back face of the joint of specimens 4LT-A, 8T-A and 8T-B did not occur, allowing for the preservation (in specimens 8T-A and 8T-B) or mild reduction in lateral strength (specimen 4LT-A) during the cyclic loading tests.

Figure 10. Lateral load ratio values 4LT-A/4TB-A, 8T-B/8T-A, 8T-A/4TB-A and 4LT-A/8T-A for (a) the upper half cycles and (b) the lower half cycles.

Figure 10. Lateral load ratio values 4LT-A/4TB-A, 8T-B/8T-A, 8T-A/4TB-A and 4LT-A/8T-A for (a) the upper half cycles and (b) the lower half cycles.

The peak-to-peak stiffness ratios-versus-load point displacement 4LT-A/4TB-A, 8T-B/8T-A, 8T-A/4TB-A and 4LT-A/8T-A are illustrated in Figure 11a. The stiffness ratio value 8T-B/8T-A was stable throughout testing (ranging from 0.52 to 0.55), because both subassemblages exhibited similar seismic behavior, mainly dominated by premature excessive slipping of the beam bottom rebars, while the beam height of specimen 8T-B was 33% shorter than that of 8T-A, making it less stiff. A limited variation of the stiffness ratio 4LT-A/4TB-A was also observed for drift angle R ≤ 3.81%, due to the minor shear cracking of the joints of both specimens until then. However, for drift angle values higher than 3.81%, the rapid evolution of the brittle shear damage of the joint region of 4TB-A occurred, resulting in significant lateral strength and stiffness degradation. The latter is also apparent in the hysteresis loops shown in Figure 4a. Consequently, the ratio value 4LT-A/4TB-A increased by 64.2% (from 0.53 to 0.87) during the last cycle of the earthquake-type loading. Premature pullout failure of the beam bottom rebars dominated the hysteresis behavior of specimens 4LT-A and 8T-A. Thus, the stiffness ratio value 4LT-A/8T-A was almost stable during the seismic tests ranging from 0.55 to 0.66. The progressive bidirectional diagonal joint shear damage observed in the joint region of specimen 4TB-A caused the gradual disintegration of the core concrete. Contrarily, the shear damage of the joint area of subassemblage 8T-A was unidirectional and minimal. Thus, a mild increase in the stiffness ratio value 8T-A/4TB-A (from 0.69 to 0.78) was observed until drift angle R = 3.33%. Subsequently, the expeditious evolution of shear damage of 4TB-A caused the collapse of the specimen and the ratio value increased by 88.5%.

Figure 11. (a) Peak-to-peak stiffness ratio values 4LT-A/4TB-A, 8T-B/8T-A, 8T-A/4TB-A and 4LT-A/8T-A; (b) Plots of energy dissipation capacity-versus-load point displacement-versus-equivalent viscous damping coefficient of subassemblages 4TB-A, 4LT-A, 8T-A and 8T-B.

Figure 11. (a) Peak-to-peak stiffness ratio values 4LT-A/4TB-A, 8T-B/8T-A, 8T-A/4TB-A and 4LT-A/8T-A; (b) Plots of energy dissipation capacity-versus-load point displacement-versus-equivalent viscous damping coefficient of subassemblages 4TB-A, 4LT-A, 8T-A and 8T-B.

Energy dissipation capacity is directly related to the extent and level of damage. Significantly increasing values of energy dissipation during consecutive cycles of inelastic deformations indicate ductile failure modes, which allow for the development of overstrength at the plastic hinges. The latter is possible only if brittle failure modes, such as shear or the extensive slipping of reinforcement, are effectively precluded. Accordingly, this is clearly perceived in the hysteresis loops, which are of a spindle-shaped form. Conversely, a stable or degrading dissipation capacity during testing clearly foreshows that the structural member exhibits poor hysteresis behavior dominated by brittle failure mechanisms. As a result, the hysteresis loops are narrow and show pinching around the axes or/and horizontal branches.

Subassemblages 4LT-A, 8T-A and 8T-B showed almost stable or degrading dissipating hysteresis performance (see Figure 11b) due to the brittle nature of the seismic damage, which was characterized by excessive bar slipping (specimens 4LT-A, 8T-A and 8T-B) and minor shear cracking (specimens 4LT-A and 8T-A). In particular, during the last cycle of loading specimen 4LT-A dissipated only 32% more energy with respect to the amount of energy dissipated during the first cycle. The ratio of energy dissipated during each cycle to that dissipated during the first cycle for 4LT-A ranged from 0.81 to 1.32 (see Figure 5b). The corresponding energy ratios for specimens 8T-A and 8T-B ranged from 0.69 to 1.0 and from 0.78 to 1.05, respectively. Moreover, a reduction in the amount of energy dissipated during the last cycle with respect to the initial value during the first cycle was observed (14.8% in the case of specimen 8T-A and 6.8% in the case of 8T-B). The energy dissipation value of subassemblage 4TB-A was initially reduced by 25.2% during the second cycle of loading, however, in the following consecutive cycles it showed a minimal increase, which was equal to 21.9% for drift angle R = 4.29% (end of testing). Intriguingly, it was observed that none of the examined subassemblages performed in a ductile manner, which reveals the indisputably devastating influence of the parameters associated with the inadequacy of the anchorage of reinforcement and of the length of lap splices of the column rebars, as well as the deficiency of confinement of the beam–column joint region, the joint aspect ratio and the shear span/beam depth ratio, in the seismic response of RC beam–column joints.

The dissipation of energy induced to RC structures by earthquakes through damping depends on the displacement ductility. Therefore, the performance under seismic actions is closely related to the deformability and the inelastic characteristics of the structural member, as well. Thus, as an evaluation measure for the seismic behavior, the equivalent viscous damping coefficient, ζ_eq, was used (see Figure 11b), which consists of both the hysteretic and the elastic damping. The values of the viscous damping ratio are higher for structural members which possess a ductile dissipating hysteresis behavior, while a poor energy dissipation capacity may result in the collapse of the structural member due to the cumulative seismic energy under small deformations [6]. The coefficient ζ_eq is expressed as the ratio of the energy dissipated within a given cycle of loading to the elastic strain energy corresponding to this cycle (see Figure 11b). Furthermore, in Figure 12a,b the cumulative dissipated energy and the cumulative viscous damping coefficient values are illustrated. From the low and degrading values of ζ_eq observed in Figure 11b, it is evident that subassemblages 4LT-A, 8T-A and 8T-B underperformed during the seismic tests due to the brittle premature pullout failure of the beam bottom rebars (and also due to the excessive slipping of the lap-spliced column reinforcement in specimen 4LT-A). The shear damage of 4LT-A and 8T-A was limited, hence, it only slightly affected the seismic response of the subassemblages. The significant increase in the value of ζ_eq for specimen 4TB-A during the last cycle of loading is owed to the substantial reduction in its shear resistance for drift angle R = 4.29%, which resulted in notably lower elastic strain energy during the last cycle. Also, the sudden increase in the value of ζ_eq of subassemblage 4LT-A for load-point displacement of 35mm is owed to the decreased value of the resisted shear force for the peak displacement of the 5th upper half-cycle (5.41kN) with respect to the corresponding values of the 4th and the 6th upper half-cycles (9.04kN and 8.09kN, respectively) (see Figure 4b), which results in a lower elastic strain energy area for the 5th cycle. Furthermore, the hysteretic energy dissipated during the 5th cycle of the earthquake-type loading of 4LT-A is also increased with respect to that dissipated during the 4th and 6th cycles (see Figure 11b).

Figure 12. (a) Plots of cumulative energy dissipation-versus-load point displacement; (b) plots of cumulative viscous damping coefficient-versus-load point displacement of subassemblages 4TB-A, 4LT-A, 8T-A and 8T-B.

Figure 12. (a) Plots of cumulative energy dissipation-versus-load point displacement; (b) plots of cumulative viscous damping coefficient-versus-load point displacement of subassemblages 4TB-A, 4LT-A, 8T-A and 8T-B.

3.3. Steel Bar Micro-Strain Monitoring

Monitoring of the steel bar micro-strain during the earthquake-type loading allows for the further documentation of the inelastic response of the subassemblages. In particular, electrical resistant strain gages were attached to the reinforcing bars at specific locations (illustrated in Figure 13a,b). Based on the data acquired during testing, the steel strain-versus-load point displacement plots, shown in Figure 14a–f, were drawn. Similar works can be found in the literature [48,49], where the transverse reinforcement and fiber hoop strains were monitored experimentally. The recorded strain values from strain gages No. 2 and No. 3, which were attached to the column lap-spliced reinforcement and the bottom beam rebar of subassemblage 4LT-A, were significantly lower than the yield strain value, ε_y = 1.87‰. For instance, the maximum value of steel strain from strain gage No. 2 equaled 0.3‰ and the maximum value from strain gage No. 3 equaled 0.26‰. This confirms the premature bond-slip failure of the lap-spliced column reinforcement and the premature pullout failure of the inadequately anchored beam bottom rebar in the joint region, respectively. An instant increase in the steel strain recorded by strain gage No. 4 to substantially high values is owed to the propagation of the unidirectional diagonal shear crack at the location where the gage was attached. It should be noted that the particularly increased strain values, recorded by strain gage No. 1, which was attached on the well-anchored beam top rebar of specimen 4LT-A, were caused by the excessive local deformation of the bar, which performed as a dowel at the location where the gage was attached, by no means results from the formation of a plastic hinge in the beam. Additionally, this is also evident from the failure mode of the subassemblage depicted in Figure 9b, where it is observed that the deformation of the rebar is limited solely at the location of the main flexural crack in the beam in the juncture with the joint. Ultimately, the local nature of the steel bar inelastic deformation is indicative of the brittle damage, which did not allow for the formation of a plastic hinge in the beam, where a significant amount of seismic energy would have been dissipated due to increased ductility.

The steel strain values, measured from both the strain gage attached to the longitudinal beam bottom rebar and from the strain gage attached to the tie of the joint of subassemblage 4TB-A, exceeded the yield strain value ε_y = 1.87‰. In the case of the tie at the joint region this resulted from the evolution of the joint shear damage and the disintegration of the concrete core, which stressed the tie. However, in the case of the longitudinal beam rebar the increased deformation was of local nature (at the position where the strain gage was attached), since the main hairline flexural crack showed no further dilation during testing due to the immediate shifting of the damage in the joint region. This is also confirmed by the failure mode of the subassemblage shown in Figure 9a and for the hysteresis loops (see Figure 4a), where it is observed that the maximum developed shear resistance of 4TB-A is lower than the beam shear resistance, V_Rb (see Table 2).

Figure 13. Location of the strain gages on subassemblages (a) 4LT-A; (b) 4TB-A.

Figure 13. Location of the strain gages on subassemblages (a) 4LT-A; (b) 4TB-A.

Figure 14. Plots of the load point displacement-versus-strain of reinforcement: (a) Specimen 4LT-A, Strain gage No. 1; (b) Specimen 4LT-A, Strain gage No. 2; (c) Specimen 4LT-A, Strain gage No. 3; (d) Specimen 4LT-A Strain gage No. 4; (e) Specimen 4TB-A, Strain gage No. 1 (f) Specimen 4TB-A, Strain gage No. 3.

Figure 14. Plots of the load point displacement-versus-strain of reinforcement: (a) Specimen 4LT-A, Strain gage No. 1; (b) Specimen 4LT-A, Strain gage No. 2; (c) Specimen 4LT-A, Strain gage No. 3; (d) Specimen 4LT-A Strain gage No. 4; (e) Specimen 4TB-A, Strain gage No. 1 (f) Specimen 4TB-A, Strain gage No. 3.

3.4. Theoretical Considerations

Tsonos [9,10,15] proposed an analytical model for preventing the collapse of RC buildings subjected to a large number of reversed inelastic lateral displacements, by predicting the seismic performance RC beam–column joints during strong seismic excitations. In particular, the model allows for the prediction of the joint ultimate shear capacity and, hence, for the satisfactory design of the beam–column connection and/or the design of the retrofit schemes to effectively preclude seismic damage in the joint region while shifting the damage and the formation of the plastic hinges in the adjacent beam(s).

At this point it should be mentioned that the application of the analytical model is particularly valuable when the structural member is short or very short, as defined by the shear span/depth ratio value, α/d, because, in these RC members, significantly increased shear stresses are developed under both monotonic and cyclic loading. Thus, it can also be effectively applied to short and very short RC columns, beams and walls [5,50].

Moreover, Kalogeropoulos and Tsonos [18,19,20] recently proposed a modified version of the analytical model which allows for the prediction of the seismic behavior of RC columns by controlling the adequacy of the length of lap-spliced reinforcement. The modified formulation is also used to precisely determine the necessary confinement to be provided by the strengthening material to prevent premature lap splice failure and allow for the yielding of reinforcement and the development of the column’s nominal flexural moment capacity.

According to the Tsonos model (a thorough presentation of which can be found in ref. [15]) the ultimate shear capacity of the beam–column connection is initially computed and subsequently compared to the shear stress, which is developed when the yielding of the beam longitudinal reinforcement occurs. Two mechanisms are considered to resist the shear forces acting in the core of a beam–column connection of a moment-resisting RC frame: the diagonal compression strut acting between diagonally opposite corners of the joint core, and the truss mechanism formed by the vertical and horizontal reinforcing bars and diagonal concrete compression struts. Thus, the ultimate strength of the beam–column joint depends on the concrete strength of the joint core under tension/compression, while the strength limitation take place after concrete failure, due to gradual crushing along the cross-diagonal cracks, particularly along the potential failure planes (see Figure 15a).

$${\left(x+\psi \right)}^5+10\psi -10x=1$$

(1)

$$x-\psi =-0.1$$

(2)

$$x=\frac{\alpha ·\gamma }{2\sqrt{f_c}}$$

(3)

$$\psi =\frac{\alpha ·\gamma }{2\sqrt{f_c}}\sqrt{1+\frac{4}{{\alpha }^2}}$$

(4)

$$f_c=k·f_c^{\prime }$$

(5)

$$k=1+\frac{{\rho }_s·f_{yh}}{f_c^{\prime }}$$

(6)

Figure 15. (a) Interior beam–column joint and the potential failure plane; (b) concrete biaxial strength curve represented by a parabola of 5th degree and the substitute linear branch BC [4,6,15].

Figure 15. (a) Interior beam–column joint and the potential failure plane; (b) concrete biaxial strength curve represented by a parabola of 5th degree and the substitute linear branch BC [4,6,15].

The calculation of the ultimate shear strength of the joint region can be achieved by solving a fifth-degree parabola (Equation (1)) or a simplified linear form (Equation (2)) with negligible effect on the results [6,15] (see Figure 15b). It is worth noting that the joint aspect ratios in real practice are lower than 2.0. Thus, the line Equation x − ψ = −0.1 (Equation (2)) is adopted for the realistic representation of the concrete biaxial strength curve in order to calculate the beam–column joint’s ultimate strength (see Figure 15b). In the present research, two values of the joint aspect ratio were used equal to 1.5 and 1.0, which are both lower than 2.0. The increased concrete compression strength (Equations (5) and (6)) due to the confinement of the joint [43], as well as the joint aspect ratio, α, define the joint ultimate shear strength, ${\tau }_{ult}={\gamma }_{ult}·\sqrt{f_c}$. A standard mathematical analysis gives the value of coefficient ${\gamma }_{ult}$, which is the solution of the system of Equations (2)–(4). The developed joint shear stress, ${\tau }_{cal}={\gamma }_{cal}·\sqrt{f_c}$ (in MPa), is calculated from the horizontal joint shear force, assuming that the beam reinforcement under tension yields. In Equations (5) and (6) $f_c^{\prime }$ is the concrete compression strength; $f_c$ is the increased joint concrete compressive strength due to confinement [43]; $f_{yh}$ is the yield strength of the horizontal hoops; and ${\rho }_S$ is the volume ratio of transverse reinforcement.

The experimental and predicted values of concrete shear stress in the potential failure plane of the beam–column joint subassemblages 4TB-A, 4LT-A, 8T-A and 8T-B are summarized in Table 3. When the calculated joint shear stress value, ${\tau }_{cal}$, is higher or equal to the ultimate strength value, ${\tau }_{ult}$, then the predicted actual value of joint’s shear stress, ${\tau }_{pred}$, is expected to be near ${\tau }_{ult}$ because the connection fails earlier than the adjacnt beam(s). Otherwise, when the calculated joint shear stress, ${\tau }_{cal}$, is lower than the joint’s ultimate strength, ${\tau }_{ult}$, then the predicted actual value of connection’s shear stress, ${\tau }_{pred}$, should be near ${\tau }_{cal}$, while the connection allows for the yielding of reinforcement of the adjacent beam. When the calculated joint shear stress is less than half the joint shear capacity (${\tau }_{cal}\le 0.50{\tau }_{ult}$), then shear damage of the joint region is precluded [4,9,10].

The analytical model is slightly modified when applied in the lap splice region. Details of the lap-spliced column rebars are shown in Figure 16a,b. The shear forces act on a 45° angle [51], while they are resisted by the concrete compression struts acting between the diagonally opposite corners of each rectangular section “abcd”. The concrete compressive strength controls the diagonal compression strut mechanism, hence the failure of the concrete results in the strength limitation of the lap splice due to the crushing along the cross-diagonal cracks, particularly along the potential failure plane “KLMN” illustrated in Figure 16a. The latter triggers the slipping of the lap-spliced bars.

The system of Equations (2)–(4) gives the ultimate strength of the lap splice. In Equations (3) and (4) the aspect ratio value, α = h/b, always equals 1.0 [51]. Equations (5) and (6) are also used to calculate the increased compression strength of the concrete due to confinement (if provided). The shear capacity, as well as the predicted actual value of the of the shear stress in the lap splices in the case of subassemblage 4LT-A, are summarized in Table 4. The value of the actual shear stress in the potential failure plane (as described in Figure 16a) when the yielding of the lap-spliced rebars is achieved is ${\tau }_{cal}={\gamma }_{cal}·\sqrt{f_c}$. The value of coefficient ${\gamma }_{cal}$ is calculated from the bond force developed between the rebar and the surrounding concrete along the lap splice, $V_n={\gamma }_{cal}·\sqrt{f_c}·A$ (where $A=3·d_b·l_s$ is the area of the potential failure plane), when equal to the tension force acting in the bar, $V_u=A_s·f_y$. The solution of Equations (2)–(4) gives the value of the coefficient ${\gamma }_{ult}$ used to calculate the ultimate shear stress, ${\tau }_{ult}={\gamma }_{ult}·\sqrt{f_c}$. Furthermore, the coefficient ${\gamma }_{exp}$ is determined from the expression $A_s·{\sigma }_s={\gamma }_{exp}·\sqrt{f_c}·A$, where ${\sigma }_s$ is the stress value according to the Hook’s law (${\sigma }_s=E·{\epsilon }_{s,max}$) using the maximum strain value, ${\epsilon }_{s,max}$. The latter is measured experimentally using strain gages. For a maximum strain value ${\epsilon }_{exp}$ higher than the yielding strain, ${\epsilon }_y$, the yielding strain is used for calculating the developed shear stress (${\epsilon }_{s,max}={\epsilon }_y$) because the Hook’s law is only applied in the elastic range. The modified analytical formulation applied to the lap splice region works similarly with the original model applied in the beam–column joint region. Although, there are some differences. In particular, when the actual shear stress, ${\tau }_{cal}$, is lower than the ultimate shear strength, ${\tau }_{ult}$, then the predicted value of the lap splice shear stress will be near ${\tau }_{cal}$, because the lap splice permits the yielding of reinforcement (${\tau }_{pred} {=\tau }_{cal}$). Contrarily, when ${\tau }_{cal}$ > ${\tau }_{ult}$ then the lap splice fails prematurely because the developed shear stress exceeds the shear capacity, while yielding is not achieved (${\tau }_{pred} {=\tau }_{ult}$). An additional control is, however, necessary in the case of totally unconfined lap splices when the lap splice length is extremely short with respect to the required one, for the yielding of reinforcement to be achieved. In this case, the developed shear stress is significantly lower than the ultimate shear strength of the concrete in the lap splice region; nevertheless, the early failure of the lap splice occurs due to excessive bar slipping prior to the exhaustion of the ultimate concrete shear strength. Thus, the predicted shear stress will be near ${\tau }_{avail}={\gamma }_{avail}·\sqrt{f_c}$ < ${\tau }_{ult}$, (${\tau }_{pred} {=\tau }_{avail}$).

Figure 16. (a) Critical regions of the lap splices and potential failure plane; (b) forces acting in the lap splice through section I-I from concrete compression strut mechanism [18].

Figure 16. (a) Critical regions of the lap splices and potential failure plane; (b) forces acting in the lap splice through section I-I from concrete compression strut mechanism [18].

It is worth mentioning that the application of the proposed analytical formulation for predicting the performance of the beam–column joint under seismic actions is possible when the anchorage of the beam longitudinal reinforcement is adequate. Therefore, the predictions summarized in Table 3 for subassemblages 4LT-A, 8T-A and 8T-B refer solely to the well-anchored beam top rebars (joint shear failure in one diagonal direction), while for specimen 4TB-A they refer to both the top and bottom rebars of the beam (joint shear failure in both diagonal directions). The failure mode of the subassemblages was predicted with a high accuracy of approximately 80 percent. This small deviation from 100 percent (which is the usual accuracy of the Tsonos model in most of the cases found in literature) derives from the immediate formation of the through pullout crack from the first half cycle of the earthquake-type loading, resulting from the anchorage inadequacy of the beam bottom rebars. In particular, due to the increased dilation of the pullout crack from the first cycle, the beam undergoes significant initial strain and, hence, fails to develop the expected lateral strength even when the displacement amplitudes are reversed during cycling. This is evident from the hysteresis loops and failure mode of specimens 4LT-A, 8T-A and especially in the case of 8T-B (see Figure 4 and Figure 9). The latter exhibited a seismic response completely dominated by the pullout failure of the beam bottom rebars, while, due to the short height of the beam, the rapid propagation of the pullout crack to the top of the beam occurred immediately, resulting in the formation of a single particularly wide through crack in the beam in the juncture with the joint. Therefore, the development of significant shear stress in the joint was eventually prevented and no shear failure of the joint of 8T-B was observed.

In the case of subassemblage 4LT-A, the premature lap splice failure of the column reinforcement was effectively predicted with exceptional accuracy (100 percent) (see Table 4).

Table 3. Experimental and predicted values of concrete shear stress in the potential failure plane of the joint region.

Specimen	${\mathit{f}}_{\mathit{c}}^{\prime }$ (MPa)	${\mathit{\gamma }}_{\mathit{c}\mathit{a}\mathit{l}}$	${\mathit{\gamma }}_{\mathit{u}\mathit{l}\mathit{t}}$	${\mathit{\gamma }}_{\mathit{e}\mathit{x}\mathit{p}}$	${\mathit{\tau }}_{\mathit{c}\mathit{a}\mathit{l}}$ (MPa)	${\mathit{\tau }}_{\mathit{u}\mathit{l}\mathit{t}}$ (MPa)	${\mathit{\tau }}_{\mathit{p}\mathit{r}\mathit{e}\mathit{d}}$ (MPa)	${\mathit{\tau }}_{\mathit{c}\mathit{a}\mathit{l}}/{\mathit{\tau }}_{\mathit{u}\mathit{l}\mathit{t}}$	${\mathit{\tau }}_{\mathit{e}\mathit{x}\mathit{p}}/{\mathit{\tau }}_{\mathit{p}\mathit{r}\mathit{e}\mathit{d}}$
4TB-A	7.0	0.876	0.520	0.395	2.318	1.376	1.376	1.685	0.76
4LT-A	7.0	0.876	0.520	0.385	2.318	1.376	1.376	1.685	0.74
8T-A	8.0	0.815	0.550	0.424	2.305	1.556	1.556	1.481	0.77
8T-B	8.0	0.885	0.457	0.388	2.503	1.293	1.293	1.936	0.85

Joint aspect ratio α = 1.5 for specimens 4TB-A, 4LT-A and 8T-A and α = 1.0 for specimen 8T-B.

Table 3. Experimental and predicted values of concrete shear stress in the potential failure plane of the joint region.

Specimen	${\mathit{f}}_{\mathit{c}}^{\prime }$ (MPa)	${\mathit{\gamma }}_{\mathit{c}\mathit{a}\mathit{l}}$	${\mathit{\gamma }}_{\mathit{u}\mathit{l}\mathit{t}}$	${\mathit{\gamma }}_{\mathit{e}\mathit{x}\mathit{p}}$	${\mathit{\tau }}_{\mathit{c}\mathit{a}\mathit{l}}$ (MPa)	${\mathit{\tau }}_{\mathit{u}\mathit{l}\mathit{t}}$ (MPa)	${\mathit{\tau }}_{\mathit{p}\mathit{r}\mathit{e}\mathit{d}}$ (MPa)	${\mathit{\tau }}_{\mathit{c}\mathit{a}\mathit{l}}/{\mathit{\tau }}_{\mathit{u}\mathit{l}\mathit{t}}$	${\mathit{\tau }}_{\mathit{e}\mathit{x}\mathit{p}}/{\mathit{\tau }}_{\mathit{p}\mathit{r}\mathit{e}\mathit{d}}$
4TB-A	7.0	0.876	0.520	0.395	2.318	1.376	1.376	1.685	0.76
4LT-A	7.0	0.876	0.520	0.385	2.318	1.376	1.376	1.685	0.74
8T-A	8.0	0.815	0.550	0.424	2.305	1.556	1.556	1.481	0.77
8T-B	8.0	0.885	0.457	0.388	2.503	1.293	1.293	1.936	0.85

Joint aspect ratio α = 1.5 for specimens 4TB-A, 4LT-A and 8T-A and α = 1.0 for specimen 8T-B.

Table 4. Experimental and predicted values of concrete shear stress in the potential failure plane of the lap splice region.

Specimen	${\mathit{f}}_{\mathit{c}}$ (MPa)	${\mathit{f}}_{\mathit{c}}^{\prime }$ (MPa)	${\mathit{\gamma }}_{\mathit{c}\mathit{a}\mathit{l}}$	${\mathit{\gamma }}_{\mathit{u}\mathit{l}\mathit{t}}$	${\mathit{\gamma }}_{\mathit{a}\mathit{v}\mathit{a}\mathit{i}\mathit{l}}$	${\mathit{\gamma }}_{\mathit{e}\mathit{x}\mathit{p}}$	${\mathit{\gamma }}_{\mathit{p}\mathit{r}\mathit{e}\mathit{d}}$	${\mathit{\tau }}_{\mathit{e}\mathit{x}\mathit{p}}/{\mathit{\tau }}_{\mathit{P}\mathit{r}\mathit{e}\mathit{d}}$
4LT-A	7.0	7.0	1.857	0.430	0.320	0.326	0.320	1.02

Table 4. Experimental and predicted values of concrete shear stress in the potential failure plane of the lap splice region.

Specimen	${\mathit{f}}_{\mathit{c}}$ (MPa)	${\mathit{f}}_{\mathit{c}}^{\prime }$ (MPa)	${\mathit{\gamma }}_{\mathit{c}\mathit{a}\mathit{l}}$	${\mathit{\gamma }}_{\mathit{u}\mathit{l}\mathit{t}}$	${\mathit{\gamma }}_{\mathit{a}\mathit{v}\mathit{a}\mathit{i}\mathit{l}}$	${\mathit{\gamma }}_{\mathit{e}\mathit{x}\mathit{p}}$	${\mathit{\gamma }}_{\mathit{p}\mathit{r}\mathit{e}\mathit{d}}$	${\mathit{\tau }}_{\mathit{e}\mathit{x}\mathit{p}}/{\mathit{\tau }}_{\mathit{P}\mathit{r}\mathit{e}\mathit{d}}$
4LT-A	7.0	7.0	1.857	0.430	0.320	0.326	0.320	1.02

4. Conclusions

An experimental and analytical investigation was conducted to evaluate the influence of critical design flaws, which are extremely common in existing substandard RC structures, on their seismic performance. Four subassemblages were designed with poor details to simulate the equivalent of structural members found in existing substandard RC structures. In particular, contrary to the provisions of modern codes for the design of earthquake-resistant RC structures (such as the Eurocode or ACI 318-19(22)), no consideration of the factors affecting the rebar anchorage was made (i.e., the location of the bar, the bar form, the provided concrete cover, the confinement provided by transverse reinforcement when welded to the rebar or not or by transverse pressure, or the bending diameter of bent reinforcing bars in the exterior RC beam–column joints). Furthermore, the ties used in the subassemblages were not closed with 135° hook-ends, as current building codes recommend. Instead, the ties of the subassemblages had 90° hook-ends, as used to be the practice during the 1950–1970s period. The lap splices of the longitudinal column reinforcing bars were of insufficient length in the case of subassemblage 4LT-A, as used to be the case in non-seismically designed RC structures. According to the provisions of the modern design codes, however, the design of col-umn lap splices of reinforcement must ensure load transfer between the spliced rebars under tension-compression reversals during seismic events, resulting in significantly increased lengths of lap splices.

Therefore, critical parameters, such as the use of plain steel bars and concrete with low compressive strength, the inadequacy (or adequacy) of anchorage of the beam bottom rebars in the joint region, the inadequacy of lap splice length of the column longitudinal reinforcement, and the joint aspect ratio and the shear span/depth of the beam ratio values, were examined. Based on the data acquired during testing, the interpretation of the results and the application of the proposed analytical formulation, the following conclusions are drawn.

The combination of design flaws and parameters examined herein critically affect the failure mode and the overall seismic response of the subassemblages, while allowing for the better simulation of the actual behavior of substandard RC structures. The latter can not be easily perceived when critical design parameters are examined separately. In particular:

The shear failure of the beam–column joint region, especially when unconfined, has a devastating impact on the seismic response of RC structures, being responsible for the disintegration of the joint concrete core and the consequential catastrophic collapse due to the loss of the axial load bearing capacity.

The inadequacy of the beam bottom rebar anchorage in the joint region results in premature bond-slip failure, excessive slipping and pullout of the bars. Hence, the shear forces inserted to the joint region from the beam bottom reinforcing bars is minimal, preventing shear failure from occurring in both diagonal directions of the joint. However, the hysteresis performance is particularly poor due to the excessive slipping of reinforcement (which is a brittle failure mode), and is dominated by the inability of the structure to dissipate seismic energy.

What is worth noting is, despite the concrete core of the joint in this case not being significantly disintegrated, the collapse of the structure can still occur due to the cumulative seismic energy under small deformations.

This also clearly demonstrates that the restoration of the beam rebar anchorage is imperative during the retrofit process to prevent the pullout of the beam rebars during a future earthquake and avoid the brittle response of the strengthened structure.

The inadequate lap splice length of the column rebars (especially when unconfined) further exacerbates the hysteresis performance, while preventing the development of the nominal flexural moment capacity of the column. Given that the lap splices are located in the potential plastic hinge region where a significant amount of seismic energy must be dissipated, the premature lap splice failure results in low plastic rotation capacity and possible collapse.

The column longitudinal reinforcement of subassemblages 8T-A and 8T-B was double the longitudinal reinforcement found in the columns of 4TB-A and 4LT-A. As a result, the nominal flexural moment capacity of the columns of 8T-A and 8T-B was increased with respect to that of subassemblages 4TB-A and 4LT-A. The same was true for the capacity design ratio values of subassemblages 8T-A and 8T-B, which were significantly higher than the corresponding values of 4TB-A and 4LT-A and with respect to the recommended value 1.30 (according to the Eurocode 8). However, this was not enough to ensure the ductile seismic response of the subassemblages, which exhibited poor hysteresis behavior dominated by the excessive slipping (pullout) of the beam bottom reinforcement. This further underlines the severe impact of the anchorage inadequacy in the seismic performance of existing poorly detailed RC structures.

Early bond-slip failure and premature slipping (or pullout) of the beam’s or/and column’s rebars prevent the development of the nominal flexural moment capacity of the beams or/and columns, while also significantly affecting the capacity design ratio value, the shear stresses inserted to the joint and, ultimately, the overall hysteresis behavior and failure mode of the beam–column joint. Eventually, the influence in the seismic behavior of both the lap splice length and the anchorage inadequacy can not be ignored when designing the retrofit schemes. Otherwise, the cyclic response of the strengthened structures may be overestimated and, hence, their structural integrity may be seriously jeopardized during future seismic events. Evidently, it is imperative to undertake specific measures exclusively for effectively improving bond conditions, for restoring the deficient anchorages, and for ensuring the load transfer and yielding of the lap-spliced column rebars. Moreover, based on the proposed analytical model, the design of the retrofit schemes should ensure that the beam–column joints of the strengthened structures will remain elastic during strong seismic excitations, while damage will be shifted and concentrated solely in the adjacent beams. This is possible when the calculated joint shear stress is less than half the joint shear capacity (${\mathsf{\tau }}_{\mathrm{c}\mathrm{a}\mathrm{l}}\le 0.50{\mathsf{\tau }}_{\mathrm{u}\mathrm{l}\mathrm{t}}$).

For a RC beam–column connection with a rather low joint aspect ratio, α, despite demonstrating lower ultimate shear capacity with respect to a similar specimen with the same concrete compressive strength, $f_c$, and a higher aspect ratio value, α, shear damage may not be developed due to the premature pullout of beam rebars, which dominates the failure mode, resulting in the formation of a significantly wide through crack in the beam. Thus, substantial local deformation of the well-anchored beam top rebars is owed to the dowel action, while minor shear forces are introduced to the joint region which remains intact.