Experimental Testing on Reinforced Concrete Beam–Column Connections with Strand Slippage for Seismic Design Bioinspired by the Norway Spruce Tree

Abstract

Seismic assessment of reinforced concrete structures requires characterization of member and connection behavior under large cyclic deformations. Moment-resisting frames are widely adopted in seismic regions, but meeting code requirements is problematic when beams are reinforced with prestressing steel strands because their ultimate elongation differs substantially from that of conventional high-ductility reinforcement (e.g., ε_u,k ≈ 3.5% for Y1770S7 strands versus ε_u,k ≈ 7.5% for B500C rebars). This study reports the findings of an experimental program conducted on reinforced concrete beam–column joints (NGS), representative of moment-resisting frame systems typically employed in seismic regions. To explore innovative structural solutions, a biomimetic design strategy was adopted, drawing inspiration from the micromechanics of Picea abies (Norway spruce). Five half-scale (1:2) specimens were subjected to quasi-static, displacement-controlled cyclic loading following the ACI 374.2R-13 (ACI T.1.1R-01) protocol, and their performance was evaluated against prescribed acceptance criteria. Adding one longitudinal steel strand and partially anchoring it in normal concrete (NGS2) and in biomaterial-adapted grout (NGS4) did not increase the amount of dissipated energy when compared to the reinforced concrete conventional solution (NGS1). Moreover, the effects of replacing the rebars with partially anchored steel strands (NGS3 and NGS5) proved to be negative.

1. Introduction

The goal of this study is to identify and evaluate biomimetic solutions [1,2] for designing the internal structure of reinforced concrete members, which will be used as load-bearing elements in frame structures for buildings located in regions with moderate-to-high seismic activity [3]. The biological model selected is the Norway spruce tree (Picea abies), which typically grows to heights exceeding 30 m. Its morphology and mechanical properties are similar to those of reinforced concrete elements subjected to flexure. In the tree’s internal structure, compression wood in the trunk and branches carries compressive stress, much like concrete, where cellulose fibrils handle tensile stress, akin to the role of reinforcement [1,4,5]. The biomechanical and morphological peculiarity of spruce trees have a high potential to be transferred to concrete structural elements [1], endowing them with viscoelastic damping. The mechanical model is the hydrogel behavior of the adhesion of cellulose fibrils inside the wood cell (Figure 1). Viscoelastic damping is reproduced by incorporating longitudinal reinforcements with controlled slipping that are partially anchored, together with the use of a concrete mixture with the addition of hemicellulose and lignin. The presence of viscoelastic damping could increase the critical damping ratio from ξ = 5%, the standard value given in design codes [6,7], up to 20%.

For moment-resisting frame structures, seismic energy dissipation is designed to occur mainly through incursions into the post-elastic domain (plastic hinging, namely critical regions in EC8 [6] and P100-1 [7]) at both ends of each span of primary seismic beam frames, represented by the cracking of concrete and the yielding of reinforcement. The length of the critical regions at the beams is l_cr = h_w (where h_w denotes the height of the beam) in structures designed for medium ductility class—DCM (5.4.3.1.2 (1)P, EN 1998-1:2004) [6], respectively, l_cr = 1.5·h_w for those designed in high ductility class—DCH (5.5.3.1.3 (1)P, EN 1998-1:2004) [6]. Applying EN 1998-1:2004 to frames with precast prestressed concrete beams requires that the prestressing strands be unbonded over the critical regions; the only continuous reinforcement through the beam–column joint should be the passive reinforcement (top and bottom) anchored in that joint. Prestressing strands exhibit lower ultimate strains than conventional reinforcing steel (e.g., ε_u,k ≈ 3.5% for Y1860S7 versus ε_u,k ≈ 7.5% for B500C). This disparity in ductility affects the end-region behavior of precast prestressed beams under large deformations. Compliance with EN 1998-1:2004—specifically the requirement for unbonded strands in critical regions and continuous passive reinforcement across the beam–column joint—allows the plastic rotational capacity of the beam end to be evaluated using reinforced concrete section models. Application of this approach typically predicts substantial plastic rotation capacity for the beam end.

There is considerable interest in identifying suitable applications of steel strands as longitudinal reinforcement for concrete moment-resisting frames [8,9,10]. Successful implementations have predominantly involved prestressed tendons in precast, self-centering systems, where centrally placed strands provide a restoring force and contribute minimally to bending resistance [11,12,13,14,15,16,17,18]. Use of strands as tensile reinforcement in the upper chord is less common [19]. The experimental studies on specimens with unbonded strands cited before reported large drift capacities (e.g., 3.5%) without abrupt loss of strength or stiffness.

The paper presents experimental results for a bioinspired proposed technical solution involving the low anchoring of bonded strands in the beam–column joint (abbreviated as NGS from the Romanian: “Nod Grindă-Stâlp”). The ends of the strands along the depth of the joint are either embedded in standard concrete C30/37 (labeled as NGS2 and NGS3) or in special bio-material integrated grout (labeled as NGS4 and NGS5), allowing for reduced bond and smoother slippage of the strand. The pull-out strength of the strand was determined experimentally for both standard concrete and concrete with the same compression strength but reduced tensile strength, following a biomimetic approach. The end of the strand is partially anchored in the beam–column joint on a short length so that, during seismic actions, a controlled slide of the strand in the concrete takes place, with a back-and-forth movement. In contrast with a full anchored strand that breaks before it slips, the partially anchored strand will always slip and steel failure will not occur, neither yielding nor rupture. This approach offers two primary advantages: (1) strands can remain bonded within critical regions, eliminating the need to provide an unbonded segment over the critical anchorage length from each beam end; and (2) it enables controlled strand slip within the beam–column joint, producing additional damping through degradation mechanisms. In this way, the plastic rotational capacity of the beam end is not reduced and the amount of seismic energy dissipated may be increased through additional damping. The proposed solution is estimated to enable approximately 15% less steel reinforcement and approximately 10% cost reduction in the overall loadbearing structure.

The present study seeks to develop bioinspired reinforced concrete structural members that:

(a)

Mimic the load-transfer mechanisms of Norway spruce cellulose fibrils;

(b)

Enable the construction frame systems that satisfy the performance acceptance criteria prescribed in ACI T1.1-01 [20];

(c)

Evaluate the seismic performance through hysteretic energy dissipation and equivalent viscous damping ratio.

2. Materials, Specimens, and Methods

2.1. Specimen Design

The minimum acceptance criteria for novel moment-resisting frames located in high seismic regions that do not fully meet the prescriptive requirements of the technical regulations are defined in the standard ACI T1.1-01 “Acceptance Criteria for Moment Frames Based on Structural Testing. Reported by ACI Innovation Task Group 1 and Collaborators” [20]. In the absence of similar European standards, ACI T1.1-01 [20] may be used for designing reinforced concrete frames that follow the strong column–weak beam principle but do not fully meet the requirements of the seismic design codes in force. The acceptance of a new structural solution is based on experimental evidence and mathematical analysis.

The transition from prototype to model must be achieved by scaling down to maximum 1:3 the dimensions of structural elements (e.g., formwork and reinforcement), as well as their load-bearing capacity and applied loads. Here, the model’s dimensions (including reinforcement) and loading conditions were determined using the theory of similitude [21] for a scale of 1:2 (Figure 2).

2.2. Materials and Specimen Preparation

For the tested specimens, a C30/37 [22] cementitious concrete grade was used, characterized by an average compressive strength of 43 MPa (determined on cubes with side length of 100 mm, considering EN 206+A2:2021) [23] and B500 C ribbed steel reinforcement characterized by a 5% fractile tensile strength of 500 MPa (labeled with 1, 2, 3, 6, and 7 in Figure 3). These two are considered ordinary materials to be used in reinforced structural concrete members. Additionally, a passive high-strength steel strand Y1770 S7 with seven wires and 5% fractile tensile strength at rupture of 1770 MPa was used (labeled as 4 and 5 in Figure 3). For mimicking the structural behavior of the Norway spruce tree, a controlled slippage of the high-strength steel strand was designed, implemented through pre-grouting the end of the strand anchored in the column (strand with label 5, Figure 3) and using a special developed mortar mixture CN31 (

Table 1. Composition of the developed cementitious grout with addition of lignin and hemicellulose rich biomaterial (CN31) and of the benchmark (CN10).

	Mixtures	CN31	CN10
Ingredients
Cement (g) CEM II/A-S 52.5 R (Holcim Extradur 52)		200	200
Quartz sand 0–1 mm (g)		400	400
Water (g)		110	148
Lignosulphonate based plasticizer (g) (Sika Plastiment BV-440)		2.3	2.3
Walnut shell—powder (g) (50.3% lignin and 22.4% hemicellulose), fine grinded (0–0.125 mm)		2	-
Water + Plasticizer to Cement ratio (wt% bwoc)		56	75
Plasticizer to Cement percent (wt% bwoc)		1.15	1.15
Walnut shell powder to Cement percent (wt% bwoc)		1	-

). The benchmark for the grout is CN10. For CN31, the water–plasticizer–cement ratio was reduced because its initial high flowability rendered the mixture unsuitable for extruding the specialized grout into the corrugated ducts used for the pre-grouted strand ends in specimens NGS4 and NGS5. Moreover, a lower ratio was advantageous to produce a grout with reduced porosity and to observe its influence on the mechanical behavior.

The reinforcement details of each of the 5 specimens given in Figure 3 can be described as follows:

• Each module is designed to comply with the strong column—weak beam principle, the bending bearing capacity of the column being greater than that of the beam concurrent in the joint;
• A potential plastic region at the beam end over a length of 1.5·h_w (where the beam height is h_w) is detailed to ensure adequate shear and rotational capacity;
• The module geometry is preserved for all 5 NGS1-5 specimens;
• Specimen NGS1 represents the benchmark in this study and fully meets the requirements for reinforced concrete frame structures with rigid joints outlined in the seismic design codes EC8 [6] and P100-1 [7];
• The transverse reinforcement of both the column and beam is identical across all specimens, as well as the column’s longitudinal reinforcement. The variation lies in the beam’s longitudinal reinforcement. For a negative bending moment (top), 2ϕ16 rebars are used for all specimens, while for a positive bending moment (bottom), the following configurations are applied:
  • 2ϕ12 rebars and no longitudinal strands, for NGS1;
  • 2ϕ12 rebars and 1ϕ9.2 strand embedded in normal concrete C30/37, for NGS2;
  • 2ϕ12 rebars and 1ϕ9.2 strand embedded in CN31 grout, for NGS4;
  • No rebars and 2ϕ9.2 strands embedded in normal concrete C30/37, for NGS3;
  • No rebars and 2ϕ9.2 strands embedded in CN31 grout, for NGS5.
• All rebars are fully anchored to their capacity, while strands are anchored to approximately 50% of their capacity.

2.3. Characterization of Special Grout

The particularities introduced by inserting biomaterial in the grout compositions used for strand anchoring were analyzed keeping in mind the grout hydration kinetics and mechanical properties during hardening.

Workability was characterized by using mini-slump tests with a miniaturized slump cone (inner diameters of 22 mm and 37 mm and a 58 mm height) [24]. The spread of the pastes was determined under equilibrium conditions.

The hydration kinetics were monitored using low field NMR relaxometry. A Bruker Minispec MQ20 instrument (Bruker BioSpin GmbH, Rheinstetten, Germany) was operated at a proton resonance frequency of 20 MHz. The transverse relaxation time (T₂) distributions of the molecules confined inside the porous media were determined using the Carr–Purcell–Meiboom–Gill (CPMG) technique [25]. To reduce diffusion effects in the internal gradients, CPMG echo trains comprised 1000 echoes, with short echo time intervals of 80 µs and a recycle delay of 0.5 s. At each evaluated hydration time, 32 echo trains were averaged to enhance the signal-to-noise ratio. The measurements were performed at a working temperature of 22 °C. The echo decay signals were further processed using inverse Laplace transformation algorithms [26]. The extracted transverse relaxation times (T₂) were correlated with the surface-to-volume ratio of water-filled pores, according to the spin relaxation mechanism in the presence of the paramagnetic impurities found on the pore surface sites [27]. Thus, the resulting transverse relaxation time distributions and their changes with the progress of hydration time were analyzed keeping in mind the evolution of the pore classes characteristic to cementitious systems, as consistent with previous works.

Ultrasound pulse velocity (UPV) tests were performed using a MATEST C372M (Matest S.p.A, Treviolo, Italy) ultrasonic velocity tester (400 MHz) in a two-transducer setup having the maximum resonant frequency of 55 kHz. The measurements on fresh mortar samples were performed with a gain setting of 10 dB, voltage amplitude of 100 mV, and a sampling duration of 400 ms. Each sample was measured several times for improved statistics.

Destructive mechanical tests were performed to determine the compression and the tensile strengths of the grout, as well as the bond of the steel strand embedded in grout.

2.4. Testing Protocol for Specimens

An experimental program was undertaken to characterize the hysteretic response of 4 novel beam–column joints (T-shaped modules) labeled with NGS2-NGS5, to quantify their seismic performance and later to compare it to a conventionally reinforced concrete reference, NGS1. The specimens were edge joints at the intermediate level of a frame structure and were tested under reverse cycling in displacement increments, beyond the elastic behavior limit (Figure 4). As the experiment was orientated to observe the mechanical behavior to bending without compression, no axial force was induced in the column.

The beam was loaded with a point load at the free end using two hydraulic pistons under incremental displacement and a quasi-static loading regime. Displacements were applied cyclically in both directions, with a low loading rate that prevented the generation of significant inertia forces [28,29,30,31]. The displacement loading protocol consisted of 11 stages, each with 3 complete cycles, corresponding to relative displacements starting from 0.20% (within the linear elastic response) and ending at 3.50%. The increase in drift must be at least 25% and up to 50% greater than the previous drift. This protocol followed the acceptance criteria for frames with rigid joints based on experimental tests outlined in ACI T1.1-01 “Acceptance Criteria for Moment Frames Based on Structural Testing” [20] and the “Guide for Testing Reinforced Concrete Structural Elements under Slowly Applied Simulated Seismic Loads” [28].

The experimental setup comprises a rigid steel reaction frame bolted to a strong floor with the concrete specimen positioned within the frame. Specimen displacements at the ends of the column and beam were recorded using displacement transducers labeled as F1–F5 and TD1.

3. Results and Discussions

3.1. Characterization of Biomaterial-Adapted Grout

The mini-slump test results indicated that CN10 is highly flowable (105 mm spread), while CN31 (40 mm spread) is soft and extrudable, mainly due to a lower w/c value. Interestingly, it was observed that the addition of walnut shell powder also caused a reduction in the hydration of grout, probably by partially absorbing water, and delayed the hardening of the samples, showing a retarder-like behavior. Considering this, low field NMR investigations were performed to monitor the hydration particularities of the investigated mortars and the effects induced by the presence of the lignin-rich walnut shell powder. Figure 5a shows several echo decay curves with a multiexponential shape, recorded at different hydration ages. The corresponding transverse relaxation time distributions obtained after applying inverse Laplace transforms are represented in Figure 5b. During the first stages of hydration, one can observe a dominant T₂ component around 10 ms, which is attributed to water found in capillary pores [32]. The second contribution initially found at T₂~10⁰ ms was ascribed to water embedded in smaller pores, i.e., within the cement grain agglomerates or the network of the primary hydrate phases [33]. With the progress of cement hydration, during the acceleration stages, this will become the dominant mode due to the consumption of capillary water through hydration reactions and evaporation induced by temperature increase [34]. During the hardening stages, when high CSH concentrations are reached, another mode well known as the “intra-CSH peak” contributes to the Laplace spectra around T₂ = 10⁻¹ ms, well known as the “intra-CSH-mode” [34].

The changes induced by the hydration process over the full Laplace spectrum for samples CN10 and CN31 are shown in Figure 5c,d. The extracted capillary peak centers and the integrated intensities for CN10 and CN31 grouts are shown in Figure 5e,f. The CN31 grout shows smaller relaxation times and intensities due to smaller pores and lower capillary water content originating from lower w/c values and water retention within the walnut microstructure. The time interval when T2 shows a slow decrease is longer for CN31. This is associated with a longer dormancy time and a delayed acceleration stage and confirms that the biomaterial introduced in CN31 also functions as a plasticizer.

The recorded UPV values for CN10 and CN31 grouts were 3400 m/s and 3750, respectively, after hardening for 28 days, indicating a good mechanical quality for the cementitious samples [35].

The results of the mechanical tests on grout are given in

Table 2. Results of mechanical tests on grout.

	Mixtures	CN31	CN10
Mechanical Property
Average compressive strength (MPa)		47.4	34.9
Average flexural tensile strength (MPa)		4.4	5.9

and the variation in the bond strength of the strand bonded over 100 mm in concrete (using CN10) and in grout (using C31) are depicted in Figure 6. It can be noticed that, by adding walnut shell powder, the compressive strength of the grout increases by ca. 35%, while the tensile strength and the maximum bond strength decrease by ca. 25%. The bond–slip curves indicate higher bond strength for the benchmark grout when the slip is below 20 mm, followed by a drop in strength (Figure 6). That is in contrast with the CN31 pull-out samples; here, the curves have a smaller initial inclination, and the maximum bond strength is roughly regained drop after drop (Figure 6). The mechanical behavior of a strand embedded in the special grout matches that of the cellulose fibrils embedded in the hemicellulose–lignin-based matrix (Figure 1).

Additional data and images are available as Supplementary Material: Photo 01 to Photo 19: Grout samples prepared for VICAT, NMR, and UPV testing; Photo 20 to Photo 31: Grout samples prepared for Compression, Flexure, and Pull-out tests; Table 101 and Table 102: Results of mechanical testing.

3.2. Test Results on the NGS Specimens

All specimens exhibited a high deformation capacity which exceeded 3% without complete structural failure. The hysteretic response under incremental loading is shown in Figure 7. Compared to benchmark NGS1, both NGS2 and NGS4 showed an increase of about 20% in the maximum force (from DF2) when the beam was loaded for positive bending moments. In contrast, NGS3 and NGS5 recorded decreases of 45% and 75%, respectively (Figure 7 and Figure 8). It can be observed that, when the reinforcement is mixed (rebars and strand), the maximum positive bending moment increases. However, when the lower beam fiber is reinforced only with partially anchored strands, the bending capacity decreases, as expected. The maximum negative bending moment (reinforced with 2ϕ16) showed variations of up to 7% across the five tested specimens. The ratio of final to initial stiffness was 0.11 (DF2) and 0.13 (DF1) for NGS1. For the other ones, it varied from −60% (DF2) for NGS5 to +34% (DF2) for NGS4, and from −48% (DF1) for NGS4 to +42% (DF1) for NGS3. The observed inconsistency in stiffness between the benchmark and the other specimens can be attributed to two primary mechanisms. First, partial anchorage of the prestressing strands produced strand slip that generated notable residual deformations (Figure 8), which promoted pronounced concrete degradation (cracking and spalling) in the compression zone at the beam end. Second, cyclic bidirectional sliding of the strands induced progressive deterioration of the concrete core within the beam–column joint, further reducing joint stiffness.

The load–displacement hysteresis curves for all NGS specimens exhibit structural asymmetry between the positive and negative loading directions (Figure 7). For the reference specimen (NGS1), this asymmetry stems exclusively from the unequal cross-sectional areas of the top and bottom longitudinal reinforcement. Because the reinforcement steel shares identical material properties and maintains a full bond, the corresponding hysteretic branches display a consistent shape—a behavior also observed in specimens NGS2 and NGS4 thanks to the presence of the 2ϕ12 rebars at the bottom side. However, the integration of a partially anchored strand in NGS2 and NGS4 induces an increased residual drift in the positive direction. This phenomenon is driven by accelerated concrete degradation within the localized zone surrounding the partially anchored steel strand.

In oppositions, the hysteretic loops for NGS3 and NGS5 visually confirm the strong asymmetry between the two directions of loading. For the negative bending moment, the loops are wide and relatively full, with a load-bearing capacity that constantly increases with drift, while for positive bending moment, the behavior is radically different. Because in NGS3 and NGS5 the bottom reinforcement is made up exclusively of partially anchored strands, the loops are strongly pinched—the force remains close to zero for a significant portion of the stroke, a sign of strand slippage, returning abruptly only towards the ends of the cycle. The strangulation of the loops in the positive direction is visibly reduced, and compared to NGS1, the maximum force reached in this direction is almost three times higher than at NGS3 and over five times higher than at NGS5 (Figure 7).

No element failed in shear, but inclined cracks appeared (no. 9) on the lateral face of the beam–column joint in three out of the five specimens (NGS1, NGS2, and NGS4) as shown in Figure 9. Specifically, all specimens with fully anchored reinforcement for both positive and negative bending moments, when subjected to large drifts from DF1, developed inclined cracks in the joint (Figure 9). Shear cracks also appeared at the end of the beam in NGS1. In NGS5, cracks began perpendicular to the beam axis and, as they propagated, developed a slightly inclined path, indicating a combination of bending and shear stress (under the forces from DF2). The constitutive curves of the reinforcement used are later depicted in Figure 10.

The dominant cracking observed in all five tested specimens was bending-related (cracks perpendicular to the beam axis), as depicted in Figure 9. In NGS1, bending cracks were closely spaced, with small intervals between them of approximately 0.3·h_w. In contrast, in all other specimens, the cracks were more widely spaced at approx. 0.5·h_w. Additionally, in NGS5, normal (perpendicular) cracks appeared only on the side of the beam reinforced with two bars (passive reinforcement anchored to capacity). On the side reinforced with partially anchored strands, the beam remained uncracked. The rotation of the beam under positive bending moment (from DF1) occurred only from the opening of a crack at the beam–column interface, combined with the elastic deformation of the stretched concrete, which had a negligible contribution to the total rotation.

A third type of crack occurred at the interface between the reinforcing bars and the concrete. These cracks were visible on the lateral face of the beams along the anchorage of the reinforcing bars in the beam–column joint (in all tested specimens), and were also observed locally, over short lengths (about 70 mm) in front of the ϕ16 bars (Figure 9).

The maximum crack opening was observed for the crack perpendicular to the beam axis, localized at the column interface (Figure 9, crack labeled as no. 1). However, in specimens NGS1, NGS2, and NGS3, this crack extended into the interior of the column, reaching the intersection with the longitudinal reinforcement. The maximum crack opening at positive bending moment and the relationship between it and the imposed drift were similar across all five specimens (Figure 10, brown curves). The maximum crack (no. 1) opening reached 8–10 mm in the final loading cycle (brown curves in Figure 10). At negative bending moment (from DF2), the crack opening was approximately equal to that measured at positive bending moment in NGS1, but in NGS2, NGS3, and NGS4, it ranged between 50% and 65% of the positive bending value, while in NGS5 it was only about one-fifth of that.

Additional data, images and videos are available as Supplementary Material: Photo 170 to Photo 198: Formwork and reinforcement cage of each NGS specimen before concrete casting; Video 01 to Video 03: Cyclic testing of NGS specimens; Photo 201 to Photo 205: Crack maps on NGS specimens after testing; Table 201 to Table 205: Results of large-scale testing on NGS specimens; Presentation 101: Cracking maps for seismic loading of the NGS specimens.

3.3. Evaluation of Structural Performance and Acceptance Criteria

For acceptance, test results on each frame module must meet several criteria [20], as shown in Figure 11:

(a)

The maximum force in the third loading cycle at the 3.5% drift stage must be at least 75% of the maximum force recorded during all stages and cycles for the same loading direction (

Table 3. Evaluation of the performance of the tested specimens (NGS1–NGS5) in relation to the qualification criteria provided by ACI T1.1-01 [20] and ACI 374.2R-13 [28], based on experimental results. The slashed labels are those of the specimens that failed to qualify and the highlighted values are those below the minimum value acceptable.

	Maximum Force		Minimum Force		Fmax/Fmin		Energy Dissipation Capacity		Final Stiffness/ Initial Stiffness
1	2		3		4		5		6
	${\mathrm{F}}_{\mathrm{m}\mathrm{a}\mathrm{x}}^{\mathrm{D}\mathrm{F}2}$	${\mathrm{F}}_{\mathrm{m}\mathrm{a}\mathrm{x}}^{\mathrm{D}\mathrm{F}1}$	${\mathrm{F}}_{\mathrm{m}\mathrm{i}\mathrm{n}}^{\mathrm{D}\mathrm{F}2}$	${\mathrm{F}}_{\mathrm{m}\mathrm{i}\mathrm{n}}^{\mathrm{D}\mathrm{F}1}$	${\mathrm{F}}_{\mathrm{m}\mathrm{a}\mathrm{x}}^{\mathrm{D}\mathrm{F}2}/{\mathrm{F}}_{\mathrm{m}\mathrm{i}\mathrm{n}}^{\mathrm{D}\mathrm{F}2}$	${\mathrm{F}}_{\mathrm{m}\mathrm{a}\mathrm{x}}^{\mathrm{D}\mathrm{F}1}/{\mathrm{F}}_{\mathrm{m}\mathrm{i}\mathrm{n}}^{\mathrm{D}\mathrm{F}1}$	Absolute ${\mathrm{A}}_{\mathrm{h}}$	Relative $\mathsf{\beta }$	${\mathrm{K}}_{\mathrm{f}\mathrm{i}\mathrm{n}\mathrm{a}\mathrm{l}}^{\mathrm{D}\mathrm{F}2}/{\mathrm{K}}_{\mathrm{i}\mathrm{n}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{a}\mathrm{l}}^{\mathrm{D}\mathrm{F}2}$	${\mathrm{K}}_{\mathrm{f}\mathrm{i}\mathrm{n}\mathrm{a}\mathrm{l}}^{\mathrm{D}\mathrm{F}2}/{\mathrm{K}}_{\mathrm{i}\mathrm{n}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{a}\mathrm{l}}^{\mathrm{D}\mathrm{F}1}$
	kN		kN		-		kN·m	-	-
NGS1	33.7	−54.4	31.3	−51.5	0.928	0.947	1.5398	0.2654	0.111	0.130
NGS2	40.6	−54.8	37.7	−52.8	0.929	0.964	1.5349	0.2634	0.078	0.143
NGS4	41.4	−52.2	34.2	−50.7	0.826	0.971	0.6968	0.1255	0.149	0.067
NGS3	18.5	−56.0	11.2	−53.2	0.605	0.950	0.5295	0.1135	0.045	0.185
NGS5	8.3	−58.1	5.9	−57.3	0.711	0.986	0.3765	0.0768	0.044	0.119
Qualification criteria	-		-		≥0.75		-	≥0.125	≥0.05

, column 4);

(b)

The relative energy dissipation, β, calculated from the measured results for the third loading cycle at the 3.5% drift stage, must be at least 0.125 (Table 3, column 5). In previous experimental studies, it was observed that, for frame structures with semi-rigid joints made from partially prefabricated elements, β ≅ 0.30 was obtained at 3.5% drift [36,37,38]. For hybrid reinforced concrete modules with prestressing at 2.5% drift, β ≅ 0.13 was recorded [13]. At a drift of 3.0%, β values of ≅0.30 [39] and ≅0.40 [40] were obtained for reinforced concrete modules, β ≅ 0.17 for hybrid reinforced concrete with prestressing [40], and β ≅ 0.10 for prestressed concrete modules [41,42]. In a frame building, compared to the test module, damping is also provided by incursions into the post-elastic behavior (plastic hinge) of the columns at the base of the frame. Therefore, the β value for frames with rigid joints is likely to be higher than that obtained from module tests;

(c)

The secant stiffness, determined from the measured results for the third loading cycle at the 3.5% drift stage, must be at least 5% of the secant stiffness calculated from the first loading stage at initial drift (Table 3, column 6). K^DF2 is the secant stiffness corresponding to a positive bending moment (from DF2), and K^DF1 is the secant stiffness corresponding to a negative bending moment (from DF1);

(d)

The column must not fail.

The beam–column module NGS1 which meets fully the provisions of EC8-1/2004 [6] and P100-1/2013 [7] has demonstrated favorable mechanical behavior in terms of energy dissipation, rotation capacity, cracking patterns, shear force, and bending moment resistance of the beam, column, and beam–column joint. It successfully meets the acceptance criteria outlined in ACI T1.1-01 [20] and ACI 374.2R-13 [28].

Compared to the reference specimen NGS1, which meets all the requirements of P100-1/2013 [7] and EC8-1/2004 [6], all specimens with partially anchored strands in the joint revealed sufficient rotation capacity (moment–curvature) but exhibited reduced energy dissipation. NGS2 showed a decrease in energy dissipation of less than 1%, while NGS3-NGS5 experienced much more significant reductions, ranging from 55% to 76%.

The critical damping ratio (equivalent viscous damping), ξ, can be calculated as the ratio of the total energy absorbed (A_h) during a complete loading cycle to the product of the maximum force in that cycle (F_max,cycle), the maximum displacement (d_max,cycle), and the factor 2π [42,43]. Finally, it can be expressed as follows:

$$\xi =A_h/\left(2·\pi ·F_{max,cycle}·d_{max,cycle}\right)$$

(1)

For the tested modules, the results are ξ^NGS1 ≅ 0.150, ξ^NGS2 ≅ 0.141, ξ^NGS3 ≅ 0.068, ξ^NGS4 ≅ 0.071, and ξ^NGS5 ≅ 0.045. Compared to the default value of ξ = 0.050 specified for reinforced concrete structures in the seismic design codes EC8 [6] and P100-1 [7], it can be concluded that all solutions, except for NGS5, exhibit a higher critical damping ratio than the default one.

Under cyclic loading, strand slippage induced a secondary effect characterized by the degradation of the concrete adjacent to the anchorage. Consequently, this structural deterioration resulted in a reduction in the bond strength, followed by a decline in both energy dissipation capacity and the damping ratio.

4. Conclusions

4.1. Experimental Findings

Based on the experimental study numerically summarized in Table 3 and on the visual observations during the investigations, it can be concluded that:

(a)

During cyclic loading, strand slippage was observed, with bond strength stabilizing after the initial two cycles. This stabilization is confirmed by the distinct plateau formed by the maximum force on the positive branch of the envelope curves for NGS3 and NGS5 (Figure 8). Consequently, the mechanical behavior of the designed reinforced concrete members seemed to have biomimicked the load-transfer mechanism of Norway spruce cellulose fibrils;

(b)

NGS1, NGS2, and NGS4 meet all the requirements set by the acceptance criteria [20,28]. However, although NGS2 has a higher percentage of reinforcement at positive bending moment (due to the addition of a strand anchored at 50% of its capacity at the tensioned fiber), its energy capacity decreased by 8%, and the cracking behavior was more unfavorable compared to NGS1. This was due to the formation of wide cracks as a closed contour, followed by displacement of the concrete in that area. For NGS4, the situation is even more unfavorable, with energy dissipation reduced with 47% compared to NGS1;

(c)

The use of only partially bonded strands (e.g., NGS 3, NGS 5) failed to meet the qualification criteria [20,28] in terms of energy dissipation;

(d)

The developed bioinspired reinforced concrete structural members failed in proving an increased hysteretic energy dissipation and an elevated equivalent viscous damping ratio. The quantitative analysis indicates that the dissipated energy decreases with the introduction of partially anchored strands in the joint, aspect also confirmed by the cracking patterns of the tested specimens. The benchmark specimen exhibited significant cracking, distributed over a length greater than twice the beam height, with symmetry on both sides. In contrast, the other specimens showed greater spacing between cracks, fewer cracks overall, and symmetrical cracking only in NGS2 and NGS4. In NGS3 and NGS5, the cracking was asymmetrical.

4.2. Design Practice

Due to the fact that, in the current experimental campaign was tested only one specimen for each configuration, namely NGS1-NGS5, any broader design recommendations may be hazardous, especially for NGS4 for which the relative energy dissipation capacity was very close to the acceptance threshold (β = 0.1255 against the required β ≥ 0.125, Table 3). Therefore, considering the previous conclusions, the following recommendations can be considered:

(a)

The use of strands without rebars in the same fiber is not recommended for beam–column joints in frame structures with rigid nodes designed to dissipate seismic energy through formation of plastic hinges at the end of beams;

(b)

Energy dissipation by the sliding of partially anchored strands in the joint has proven ineffective. Therefore, in beams reinforced with strands at the extreme fibers (bottom and/or top), it is recommended to stop the active reinforcement at the column face together with breaking its adhesion along the potential plastic length of the beam;

(c)

The philosophy to start the anchorage length of the longitudinal reinforcement in the beam at the joint, in frame structures with rigid nodes designed for high ductility class (DCH), from the face of the column plus 5 diameters, is confirmed. Experiments have shown that, in most cases, beam cracking due to bending moments did not occur at the column face but deeper within the column, roughly along the longitudinal reinforcement. The normal crack extended into the column through the thickness of the concrete cover and the stirrup bar, until it encountered the longitudinal reinforcement in the column.

Future work addressing the limitations of the current joint structure and strand/anchoring grout interface will further articulate the application and understanding of the proposed bio-inspired model and potentially lead to improved structural designs. Three complementary research directions to the current study are outlined below. First, testing intermediate degrees of strand anchorage (e.g., 30–35%, between the two values investigated in the basic experimental program, 20% and 50%) would allow for a more precise outline of the trade-off between plastic rotation capacity and residual stiffness/strength. Second, extending the mixed configuration tested at NGS4 (2 rebars + 1 strand) to a configuration with a different proportion between the classical and the active reinforcement would clarify whether the benefit observed at NGS4 is predominantly due to the presence of the classical reinforcement as such, or to the specific proportion tested. And third, the calibration of a numerical model (nonlinear finite element or concentrated plastic hinge model, calibrated on the hysteretic curves and the plastic rotation capacity obtained in chapters 4 and 5) would allow the extension of the conclusions beyond the five physically tested specimens, including the evaluation of the behavior of a complete frame, with several nodes of this type, under seismic action—overcoming the inherent limitation of an isolated test module.