Design Recommendations for Columns Made of Ultra-High-Performance Concrete and NiTi SMA Bars

Abstract

The use of new materials in construction endows structures with better mechanical characteristics. The combination of ultra-high-performance concrete (UHPC) and nickel and titanium (NiTi) shape memory alloy (SMA) improves the behavior of building structures by increasing both their ductility and dissipation energy due to the low-damage and self-centering properties of NiTi SMA. Since UHPC and NiTi SMA are expensive materials and still scarce in distribution channels, this article tries to offer design recommendations to reduce the length of the column-beam connection in which these new materials should be introduced, leaving the rest of the column with conventional materials. To achieve this, a nonlinear static pushover analysis of columns using finite element software, SeismoStruct, was performed. This model was calibrated using experimental results. Next, a parametric analysis was carried out to propose the design recommendations. Results indicated that an adequate design for the column–beam connection, considering both economy and performance, should include a main zone with UHPC and SMA reinforcements, a transition zone with UHPC and steel reinforcements, and another zone with conventional reinforced concrete. The transition zone improved the hybrid column’s performance without excessively raising the cost. The main zone length, the transition zone length, and the strength of the concrete in the rest of the column must be determined to ensure that the critical section of the column was in the main zone to develop the maximum strength and ductility. The length of the main zone depended on the compressive strength of the conventional concrete, the relative axial load of the column, and the required ductility.

Full text

Citation: Pereiro-Barceló, J.; Bonet,
J.L.; Martínez-Jaén, B.;
Cabañero-Escudero, B. Design
Recommendations for Columns
Made of Ultra-High-Performance
Concrete and NiTi SMA Bars.
Buildings 2023,13, 991. https://
doi.org/10.3390/buildings13040991
Academic Editors: Andrea Pranno
and Umberto De Maio
Received: 11 March 2023
Revised: 2 April 2023
Accepted: 4 April 2023
Published: 8 April 2023
Copyright: © 2023 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
buildings
Article
Design Recommendations for Columns Made of
Ultra-High-Performance Concrete and NiTi SMA Bars
Javier Pereiro-Barceló1, * , JoséL. Bonet 2, Begoña Martínez-Jaén2and Beatriz Cabañero-Escudero 2
1Departamento de Ingeniería Civil (DIC), Universidad de Alicante, San Vicente del Raspeig, Carretera San
Vicente del Raspeig Unnumbered, 46022 Alicante, Spain
2
Instituto Universitario de Ciencia y Tecnología del Hormigón (ICITECH), Universitat Politècnica de València,
46022 Valencia, Spain
*Correspondence: javier.pereiro@ua.es
Abstract:
The use of new materials in construction endows structures with better mechanical char-
acteristics. The combination of ultra-high-performance concrete (UHPC) and nickel and titanium
(NiTi) shape memory alloy (SMA) improves the behavior of building structures by increasing both
their ductility and dissipation energy due to the low-damage and self-centering properties of NiTi
SMA. Since UHPC and NiTi SMA are expensive materials and still scarce in distribution channels,
this article tries to offer design recommendations to reduce the length of the column-beam connection
in which these new materials should be introduced, leaving the rest of the column with conventional
materials. To achieve this, a nonlinear static pushover analysis of columns using finite element
software, SeismoStruct, was performed. This model was calibrated using experimental results. Next,
a parametric analysis was carried out to propose the design recommendations. Results indicated that
an adequate design for the column–beam connection, considering both economy and performance,
should include a main zone with UHPC and SMA reinforcements, a transition zone with UHPC and
steel reinforcements, and another zone with conventional reinforced concrete. The transition zone
improved the hybrid column’s performance without excessively raising the cost. The main zone
length, the transition zone length, and the strength of the concrete in the rest of the column must
be determined to ensure that the critical section of the column was in the main zone to develop the
maximum strength and ductility. The length of the main zone depended on the compressive strength
of the conventional concrete, the relative axial load of the column, and the required ductility.
Keywords: UPHC; SMA; NiTi; column; ductility
1. Introduction
Earthquakes are catastrophic natural events that have a special impact on reinforced
concrete structures due to the horizontal forces they create. Current seismic structural
designs are based on the capacity to guarantee that the plastic hinges occur in beams
before columns [
1
,
2
]. However, according to ACI 441R-96 (1996) [
3
], plastic hinges end up
appearing at column ends during earthquakes. It is also desirable that this deformation
capacity be associated with high-energy dissipation to mitigate the effects of tremors. The
level of structural damage during an earthquake should be kept as low as possible, as
well as the subsequent drift and residual deformation since, even if the building does not
actually collapse during the event, repair costs can be high. Structures should thus fulfill
the following protection requirements: high deformation capacity, dissipated energy in
each load cycle, low damage, and residual deformation.
According to design codes such as CE [
4
], EC-8 [
1
], and NCSE-02 [
5
], high deformation
capacity can be achieved by a high transverse reinforcement ratio in areas where plastic
hinges form; nevertheless, concrete casting can be difficult. For this reason, various au-
thors [
6
–
11
] replaced part of the transverse reinforcement with fiber-reinforced concrete
Buildings 2023,13, 991. https://doi.org/10.3390/buildings13040991 https://www.mdpi.com/journal/buildings

Buildings 2023,13, 991 2 of 24
and found that the fibers improved deformation capacity and energy dissipation and
reduced damage.
The usual method of achieving energy dissipation involves causing damage to the
materials, such as concrete cover spalling, concrete crushing, and reinforcement yielding.
Unfortunately, this approach results in high residual deformations, making it challenging
to design precast structures with both high deformation and strength capacity while
maintaining high energy dissipation and minimizing damage and residual deformations.
To address this issue, the present study utilizes advanced materials, including ultra-high-
performance concrete (UHPC) and nickel and titanium (NiTi) shape memory alloy (SMA)
bars with superelasticity, to connect the column and the foundation. By employing these
innovative materials, the study aims to achieve the desired deformation and strength
capacity while minimizing residual deformations and damage to the structure.
UHPC is a type of concrete characterized by a high cement and silica fume content and
a low water-to-cement ratio (0.15–0.25 [
12
]), leading to an ultra-high compressive strength
and a low permeability [
13
–
17
]. The materials employed to make UHPC include water,
cement, quartz sand, silica fume, high-range superplasticizer, fibers (
≥
2% by volume [
12
]),
and optionally supplemental fine materials (e.g., quartz powder, micro-silica, and nano-
silica [
18
–
20
]). The supplemental fine materials maximize the packing density (particle
packing density ranges between 0.825 and 0.855 [
12
]) and, in addition, in the case of
micro-silica and nano-silica, the pozzolanic effect increases the bond between aggregates
and cement paste [
18
,
19
]. Regarding the mechanical characteristics, UHPC compressive
strength is beyond 120 MPa [
21
–
23
]. Amini et al. [
20
] stated that the addition of nano-silica
to UHPC increased its compressive strength. Amini et al. [
20
,
24
] also experimentally and
numerically studied the local bond stress between UHPC and steel rebars and concluded
that the addition of micro-silica increased the local bond stress. The UHPC flexural tensile
strength can reach 45 MPa according to Walraven [
25
], and its post-cracking tension strength
varies from 5.6 to 9.0 MPa for fiber volumes between 0.8% and 1.6%, respectively [
25
]. The
high steel fiber content of UHPC confers great ductility on structural elements without
increasing the transverse reinforcement ratio [
25
–
34
]. UHPC also undergoes less damage
than other types of concrete under equal loading conditions [
30
,
35
,
36
] and has a greater
capacity to dissipate energy [31,37].
On the other hand, SMA is a highly ductile alloy capable of reaching high strains
before failure (45%) and can return to their original shape after being unloaded or heated.
Although Fe-based SMAs and Cu-based SMAs also exist, NiTi is the most commonly used
alloy in structural applications, with a composition of approximately 50% nickel and 50%
titanium. In the field of structural engineering, SMA bars are recognized for their three key
properties: shape memory effect (SME), superelasticity, and damping capacity. The SME
enables the material to recover its predefined shape after being heated, while superelasticity
allows the original shape to recover after an unloading process. Finally, damping capacity
is linked to the other two properties and allows the structure’s movements and vibrations
to be reduced by converting mechanical energy into thermal energy. These remarkable
properties of SMA result from the reversible transformation phase they undergo, called the
martensitic transformation. By replacing traditional steel bars with SMA bars in critical
areas of structural members where plastic hinges will form, it is possible to increase
the member’s ductility [
38
–
47
], improve energy dissipation [
48
,
49
], and reduce residual
deformations due to the material’s superelasticity [48–52].
Considering the capabilities of the previous two materials, the combination of NiTi
SMA and UHPC reinforcements leads to small residual deformations in the structure and
enables the concrete to withstand the large strains experienced by NiTi in both compression
and tension [
48
,
49
,
53
]. This means that critical sections can develop a large curvature that
is supported by both concrete and NiTi SMA without resulting in excessive damage. In a
previous investigation conducted by Pereiro-Barcelóet al. [
49
], the beam–column connec-
tion made in situ was tested using specimens fabricated entirely with high-performance
concrete (HPC) with a compressive strength of 80 MPa and a 1% fiber content by volume,

Buildings 2023,13, 991 3 of 24
and others entirely fabricated with UHPC where all longitudinal reinforcements in the
beam–column connection were SMA bars. The results showed that HPC was unable to
withstand the large strains required for SMA to develop considerable stresses due to its
low elasticity modulus of around 60 GPa.
However, given that both materials are expensive and scarce, the aim of this paper
is to provide design recommendations that limit the regions of the column where these
new materials should be introduced, while using conventional materials in the remaining
parts of the column (hybrid column). Pereiro-Barcelóet al. [
49
] conducted experimental
studies on the combination of new and old materials in the same column, but no design
recommendations were derived due to the limited number of specimens tested (only four).
To address this, a numerical model of hybrid columns has been created and calibrated
using experimental results, which will be used to conduct a parametric study to obtain
sufficient results for design recommendations.
2. Numerical Model Calibration
A nonlinear static pushover analysis using a distributed-plasticity model was em-
ployed to predict the load and ductility performance of hybrid reinforced concrete columns
made with UHPC and NiTi SMA bars. Energy dissipation was not considered as a parame-
ter because current design codes do not take it into account in designing actual structures,
which is based on strength and ductility for seismic analysis (modal response spectrum
analysis) [
54
,
55
]. Conducting cyclic numerical analysis would be required to assess energy
dissipation, which would increase the model’s uncertainty by adding new parameters to
calibrate.
SeismoStruct [
56
], a finite element software that can conduct nonlinear analysis and
predict the structural behavior of different load conditions, was used in this study. The
numerical model was calibrated based on the results of cyclic tests conducted by Pereiro-
Barcelóet al. [
48
,
49
] and Castro [
28
]. No monotonic tests were found in the scientific
literature that had the appropriate characteristics for the purpose of this article. The
skeleton curves of the experimental cyclic test results were used to calibrate the parameters
of the pushover analysis. These skeleton curves represent safety-side results in terms of
maximum load and ductility if used in the pushover calibration, as they take into account
material degradation, which reduces maximum load and ductility. This procedure is
useful for providing design recommendations based on the results of parametric pushover
analysis, which was the goal of the study.
2.1. Summary of Experimental Results
The notation employed in this section is as follows:
fcm: average compressive concrete strength (MPa).
Ec: elasticity modulus of concrete (MPa).
fLOP: limit of proportionality in the flexural tensile strength test (MPa).
fR,j
: (for j= 1–3) residual tensile strengths that corresponded to the crack mouth opening
displacement (CMOD) of 0.5, 1.5 and 2.5 mm, respectively (MPa).
fy: yield stress of steel reinforcements (MPa).
εy: strain that corresponded to the yield stress of steel reinforcements.
fsh: stress at which the hardening branch begins of steel reinforcements (MPa).
εsh: strain associated with fsh of steel reinforcements.
fu: maximum stress of steel reinforcements (MPa).
εu: strain associated with the maximum stress of steel reinforcements.
Es: elasticity modulus of steel reinforcements (MPa).
As: transformation temperature for the beginning of the austenitic transformation (◦C).
Af: transformation temperature for the end of the austenitic transformation (◦C).
Ms: transformation temperature for the beginning of the martensitic transformation (◦C).
Mf: transformation temperature for the end of the martensitic transformation (◦C).
fA: austenite to martensite starting stress (MPa).

Buildings 2023,13, 991 4 of 24
εA: strain that corresponded to fA.
fM: austenite to martensite finishing stress (MPa).
εM: strain associated with fM.
EA: austenitic modulus (MPa).
EM: martensitic modulus (MPa).
Pereiro-Barcelóet al. [
48
,
49
] and Castro [
28
] conducted experimental campaigns on
columns under cyclic loading. The specimens were designed to represent two semi-columns
in two successive stories connected by a central element (stub). The total length of all
specimens was 3300 mm (Figure 1), and the length of each semi-column (
Ls
) was 1500 mm.
The shear slenderness ratio (
λV=Ls/h
, where
h
is the total cross-section depth) equaled
5.77 in all the specimens. Specimens were subjected to a constant axial force
N
and a cyclic
lateral force
V
. To ensure that the failure took place in one specific semi-column, the other
semi-column was reinforced with two additional reinforcing bars of 16 mm diameter and
1000 mm long (Figure 1c, Section A–A’).
Buildings 2023, 13, x FOR PEER REVIEW 5 of 24
Figure 1. Specimen 1–4 details: (a) dimensions (unit: mm), (b) longitudinal reinforcement, and (c)
cross-section details.
Regarding concrete types, in Castro [28] and Pereiro-Barceló et al. [48], the whole
specimen was made of UHPC. In Pereiro-Barceló et al. [49], two types of concrete were
used: UHPC and high-strength concrete (HSC) with no fibers. The semi-column under
study was composed of the first, second, and third zones made of UHPC and SMA rein-
forcements, UHPC and steel reinforcements (transition zone), and HSC and steel rein-
forcements, respectively (Figure 1). The mixture constituents and proportions are de-
picted in Table 2. The steel fibers used were DRAMIX 80/30 BP with 30-mm-long hooked
ends, 0.5-mm diameter, an aspect ratio (L/d) of 80, a yield stress of 3070 MPa, and an elas-
ticity modulus of 200 GPa. The other fiber type was 13-mm-long DRAMIX 13/0.16 with a
straight geometry, a 0.16-mm diameter, an aspect ratio (L/d) of 81.25, a yield stress of 2750
MPa, and an elasticity modulus of 200 GPa. The concrete characterization results are
shown in Table 3. Steel was B500SD [58] and C class [5]. Table 4 shows the results of the
characterization tests of both the longitudinal and transverse steel reinforcements.
The NiTi SMA bars were supplied with a polished surface. A differential DSC scan-
ning calorimetry test was carried out to determine the four transformation temperatures
(𝑀 = −49.15 °C, 𝑀 = −31.23 °C, 𝐴 = −20.75 °C, and 𝐴 = −7.70 °C). A mechanical char-
acterization of NiTi (Table 5) was also made using tensile and compression tests. The test
room temperature was 27–30 °C.
Figure 1.
Specimen 1–4 details: (
a
) dimensions (unit: mm), (
b
) longitudinal reinforcement, and (
c
)
cross-section details.
The main characteristics of the specimens are shown in Table 1, where
ν
is the relative
axial force (
ν=N/(Ac·fcm)
being
N
de axial load,
Ac
the gross section area, and
fcm
the concrete average compressive strength. The longitudinal reinforcement ratio (
ρ
l) was
1.16%. This reinforcement was made entirely of steel in the Castro [
28
] specimens. In

Buildings 2023,13, 991 5 of 24
Pereiro-Barcelóet al. [
48
,
49
], the steel rebars connecting the stub and the rest of the column
were replaced by smooth NiTi bars. In all these specimens, the NiTi bars crossed the joint
between the stub and the hybrid connection. At least 150 mm of the NiTi bars remained in
the stub. The NiTi bars were 580 mm long. Clamping screw couplers joined the steel and
NiTi reinforcements. Three screws tightened each bar. The screw heads fractured at a given
torque.
Table 1. Details of specimens.
Id Specimen N (kN) νJoint Column
Concrete
Longitudinal Reinforcements
at Critical Section
1 HCV01C [49] 450.96 0.10 Continuous UHPC + HSC SMA
2 HCV02C [49] 943.00 0.20 Continuous UHPC + HSC SMA
3 HCV01D [49] 509.00 0.10
Discontinuous
UHPC + HSC SMA
4 HCV02D [49] 993.95 0.20
Discontinuous
UHPC + HSC SMA
5 VHPC-V01S100 [48] 497.68 0.10 Continuous UHPC SMA
6 VHPC-V02S100 [48] 945.76 0.20 Continuous UHPC SMA
7 AS11–3 [28] 946.85 0.20 Continuous UHPC B500S
The transverse reinforcement distribution was uniform throughout the element in all
cases and consisted of 8 mm-diameter steel stirrups separated by 100 mm (c
φ
8/100), which
equaled 8.33D, where D is the diameter of the longitudinal reinforcement (12 mm). The
transverse reinforcement separation was greater than the maximum spacing recommended
to avoid local longitudinal steel reinforcement buckling, as proposed in ACI-318 [
57
] and
EC-8 [55].
Regarding concrete types, in Castro [
28
] and Pereiro-Barcelóet al. [
48
], the whole spec-
imen was made of UHPC. In Pereiro-Barcelóet al. [
49
], two types of concrete were used:
UHPC and high-strength concrete (HSC) with no fibers. The semi-column under study was
composed of the first, second, and third zones made of UHPC and SMA reinforcements,
UHPC and steel reinforcements (transition zone), and HSC and steel reinforcements, re-
spectively (Figure 1). The mixture constituents and proportions are depicted in Table 2.
The steel fibers used were DRAMIX 80/30 BP with 30-mm-long hooked ends, 0.5-mm
diameter, an aspect ratio (L/d) of 80, a yield stress of 3070 MPa, and an elasticity modulus of
200 GPa. The other fiber type was 13-mm-long DRAMIX 13/0.16 with a straight geometry,
a 0.16-mm diameter, an aspect ratio (L/d) of 81.25, a yield stress of 2750 MPa, and an
elasticity modulus of 200 GPa. The concrete characterization results are shown in Table 3.
Steel was B500SD [
58
] and C class [
5
]. Table 4shows the results of the characterization tests
of both the longitudinal and transverse steel reinforcements.
The NiTi SMA bars were supplied with a polished surface. A differential DSC scan-
ning calorimetry test was carried out to determine the four transformation temperatures
(
Mf
=
−
49.15
◦
C,
Ms
=
−
31.23
◦
C,
As
=
−
20.75
◦
C, and
Af
=
−
7.70
◦
C). A mechanical
characterization of NiTi (Table 5) was also made using tensile and compression tests. The
test room temperature was 27–30 ◦C.
A constant horizontal load equal to the relative axial force was applied in all specimens.
The quasistatic cyclic lateral load was applied at a constant rate of 0.2
±
0.05 mm/min.
The test sequence of the displacement-controlled cycles was expressed in terms of drift
ratio. Three complete cycles were applied for each drift ratio (0.5, 0.75, 1, 2, 3
. . .
) and were
limited by drift ratio values. Three complete cycles were applied for each drift ratio.

Buildings 2023,13, 991 6 of 24
Table 2. Mixture proportions (kg/m3).
Description UHPC HSC
Cement 1000 525
Water 177 196
Gravel (Dmax 6 mm) - 450
Sand (Dmax 4 mm) - 1045
Sand (Dmax 0.8 mm) AF_T_0/8_S 575 -
Sand (Dmax 0.4 mm) AF_T_0/4_S 310 -
Lime-stone filler - 200
Silica fume 150 -
Steel fibers DRAMIX 80/30 BP 60 -
Steel fibers DRAMIX 13/0.5 90 -
Super-plasticizer 29 8.13
Average compressive strength (MPa) 123.6 83.9
Average elasticity modulus (MPa) 44,535 34,325
Table 3. Concrete mechanical properties.
Specimen
UHPC HSC
fcm
(MPa)
Ec
(MPa)
fLOP
(MPa)
fR,1
(MPa)
fR,2
(MPa)
fR,3
(MPa)
fcm
(MPa)
Ec
(MPa)
HCV01C [49]
115.63 43,074
11.77 23.4 23.53 21.78 84.3
33,126
HCV02C [49]
120.94 43,259
10.58 18.53 20.97 18.83 85.82
34,014
HCV01D [49]
130.49 46,481
14.58 25.97 25.54 21.85 82.7
35,445
HCV02D [49]
127.43 45,329
17.65 29.41 26.97 24.42 82.62
34,714
VHPC-V01S100 [48]
123.46 44,415
11.30
19.006
17.54 12.85 - -
VHPC-V02S100 [48]
118.78 47,905
11.84 19.83 18.06 14.01 - -
AS11–3 [28]
119.35 45,636
10.21 18.33 15.06 5.5 - -
Table 4. Steel reinforcement mechanical properties.
Mechanical
Parameter
Longitudinal Transverse
Ø12 Ø16 Ø8
fy(MPa) 547 543 574
εy0.0026 0.0024 0.0028
fsh (MPa) 550 558 574
εsh 0.037 0.0314 0.0215
fu(MPa) 634 637 646
εu0.2611 0.2555 0.0456
Es(MPa) 212,136 228,712 203,773
Table 5. NiTi reinforcement mechanical properties.
Mechanical Parameter Tension Compression
fA(MPa) 450.2 450.2
εA0.00696 0.00696
fM(MPa) 609.8 710.1
εM0.0656 0.0450
EA(MPa) 64,647 64,647
EM(MPa) 2104 28,125
2.2. Finite Element Model
The hybrid semi-column of the specimens in Section 2.1 was modeled as an equivalent
cantilever column (Figure 2a), and a monotonic static pushover was performed. A constant

Buildings 2023,13, 991 7 of 24
vertical force was first applied to the end of the column by force control, followed by
a lateral load, by controlling the horizontal displacement of the node at the top of the
cantilever column (Node 4 in Figure 2b). The steel bar transmitted a force to the NiTi SMA
bar with negligible bar slippage inside the coupler.
Buildings 2023, 13, x FOR PEER REVIEW 7 of 24
mm/min. The test sequence of the displacement-controlled cycles was expressed in terms
of drift ratio. Three complete cycles were applied for each drift ratio (0.5, 0.75, 1, 2, 3 …)
and were limited by drift ratio values. Three complete cycles were applied for each drift
ratio.
2.2. Finite Element Model
The hybrid semi-column of the specimens in Section 2.1 was modeled as an equiva-
lent cantilever column (Figure 2a), and a monotonic static pushover was performed. A
constant vertical force was first applied to the end of the column by force control, followed
by a lateral load, by controlling the horizontal displacement of the node at the top of the
cantilever column (Node 4 in Figure 2b). The steel bar transmied a force to the NiTi SMA
bar with negligible bar slippage inside the coupler.
Figure 2. Numerical model: (a) equivalent cantilever column with the applied loads; (b) finite ele-
ment discretization to model specimens 1–4.
A sensitivity analysis determined the number of elements into which the support was
divided and integration sections in the elements in order to correctly represent the plastic
hinge in the UHPC zone. The elements with fewer integration sections plus adequate fi-
nite element size fit best due to UHPC’s softening behavior. Figure 3 shows an example
of the sensitivity analysis of the HCV02C support.
Figure 3. Influence of finite element size and number of integration sections.
As can be seen, the adjustment in each case is precise in the ascent branch until reach-
ing the peak load, with negligible differences between the different specimens. However,
each case in the descending branch is different, being as close as possible to the experi-
mental one in the case of three integration sections per element with three elements along
the support, representing the three zones with different materials. The minimum number
0
10
20
30
40
50
60
70
80
90
0123
Lateral load, V (kN)
Drift ratio [Δ/L
s
] (%)
EXPERIMENTAL
3 elem 3 secc
3 elem 5 secc
8 elem 3 secc
16 elem 3 secc
16 elem 5 secc
Figure 2.
Numerical model: (
a
) equivalent cantilever column with the applied loads; (
b
) finite
element discretization to model specimens 1–4.
A sensitivity analysis determined the number of elements into which the support was
divided and integration sections in the elements in order to correctly represent the plastic
hinge in the UHPC zone. The elements with fewer integration sections plus adequate finite
element size fit best due to UHPC’s softening behavior. Figure 3shows an example of the
sensitivity analysis of the HCV02C support.
Buildings 2023, 13, x FOR PEER REVIEW 7 of 24
mm/min. The test sequence of the displacement-controlled cycles was expressed in terms
of drift ratio. Three complete cycles were applied for each drift ratio (0.5, 0.75, 1, 2, 3 …)
and were limited by drift ratio values. Three complete cycles were applied for each drift
ratio.
2.2. Finite Element Model
The hybrid semi-column of the specimens in Section 2.1 was modeled as an equiva-
lent cantilever column (Figure 2a), and a monotonic static pushover was performed. A
constant vertical force was first applied to the end of the column by force control, followed
by a lateral load, by controlling the horizontal displacement of the node at the top of the
cantilever column (Node 4 in Figure 2b). The steel bar transmied a force to the NiTi SMA
bar with negligible bar slippage inside the coupler.
Figure 2. Numerical model: (a) equivalent cantilever column with the applied loads; (b) finite ele-
ment discretization to model specimens 1–4.
A sensitivity analysis determined the number of elements into which the support was
divided and integration sections in the elements in order to correctly represent the plastic
hinge in the UHPC zone. The elements with fewer integration sections plus adequate fi-
nite element size fit best due to UHPC’s softening behavior. Figure 3 shows an example
of the sensitivity analysis of the HCV02C support.
Figure 3. Influence of finite element size and number of integration sections.
As can be seen, the adjustment in each case is precise in the ascent branch until reach-
ing the peak load, with negligible differences between the different specimens. However,
each case in the descending branch is different, being as close as possible to the experi-
mental one in the case of three integration sections per element with three elements along
the support, representing the three zones with different materials. The minimum number
0
10
20
30
40
50
60
70
80
90
0123
Lateral load, V (kN)
Drift ratio [Δ/L
s
] (%)
EXPERIMENTAL
3 elem 3 secc
3 elem 5 secc
8 elem 3 secc
16 elem 3 secc
16 elem 5 secc
Figure 3. Influence of finite element size and number of integration sections.
As can be seen, the adjustment in each case is precise in the ascent branch until reaching
the peak load, with negligible differences between the different specimens. However, each
case in the descending branch is different, being as close as possible to the experimental
one in the case of three integration sections per element with three elements along the
support, representing the three zones with different materials. The minimum number of
elements (three) were thus chosen, one for each section with different materials, as well as
the minimum number of integration sections (three):
- Hybrid connection element:
-
430-mm long made with UHPC and NiTi SMA rebars for the specimens 1–4
(Figure 2b).
-
600-mm long made with UHPC and NiTi SMA rebars for specimens 5–6 because
longer SMA bars were employed in the experimental tests.
- 430-mm long made with UHPC and steel rebars for specimen 7.

Buildings 2023,13, 991 8 of 24
- Transition zone element:
- 170-mm long made with UHPC and steel bars for all specimens (Figure 2b).
- Rest of the column element:
-
900-mm long element made with HPC and steel bars for specimens 1–4
(Figure 2b)
.
- 730-mm long element made with UHPC and steel bars for specimens 5–6.
- 900-mm long element made with UHPC and steel bars for specimen 7.
Every finite element has two nodes each with three degrees of freedom: two trans-
lations and one rotation. To simulate a discontinuous joint, UHPC tensile behavior was
not considered in the finite element immediately above the base but was in the rest of
the column.
The sections were discretized into 148 cells to carry out the equilibrium in every section
(Figure 4). The area of concrete on the cover was distinguished from that in the core, in
which the effect of concrete confinement was considered.
Buildings 2023, 13, x FOR PEER REVIEW 8 of 24
of elements (three) were thus chosen, one for each section with different materials, as well
as the minimum number of integration sections (three):
- Hybrid connection element:
- 430-mm long made with UHPC and NiTi SMA rebars for the specimens 1–4 (Fig-
ure 2b).
- 600-mm long made with UHPC and NiTi SMA rebars for specimens 5–6 because
longer SMA bars were employed in the experimental tests.
- 430-mm long made with UHPC and steel rebars for specimen 7.
- Transition zone element:
- 170-mm long made with UHPC and steel bars for all specimens (Figure 2b).
- Rest of the column element:
- 900-mm long element made with HPC and steel bars for specimens 1–4 (Figure
2b).
- 730-mm long element made with UHPC and steel bars for specimens 5–6.
- 900-mm long element made with UHPC and steel bars for specimen 7.
Every finite element has two nodes each with three degrees of freedom: two transla-
tions and one rotation. To simulate a discontinuous joint, UHPC tensile behavior was not
considered in the finite element immediately above the base but was in the rest of the
column.
The sections were discretized into 148 cells to carry out the equilibrium in every sec-
tion (Figure 4). The area of concrete on the cover was distinguished from that in the core,
in which the effect of concrete confinement was considered.
Figure 4. Section discretization.
2.3. Material Constitutive Models
The characteristics of the materials were taken from the experimental characteriza-
tion. The bilinear steel model was used to simulate steel bars. The input parameters were
Youn g ’ s modu l u s 𝐸, hardening modulus 𝐸, and yield stress 𝑓, which are depicted in
Table 4 for each specimen.
A uniaxial model was used for a superelastic SMA (NiTi SMA), programmed by Fu-
gazza [59], which followed the constitutive relationship proposed by Auricchio and Saco
[60]. This model did not consider nonzero residual strains for zero stress and assumed
constant stiffness in both the fully austenitic and martensitic domains. The main input
parameters were the austenite to martensite starting stress and strain (𝐸 and 𝜀) and the
austenite to martensite finishing stress and strain (𝐸 and 𝜀). The same SMA bars were
used for all specimens, and the characterization values were: 𝐸 = 450.2 MPa, 𝜀 =
0.00696, 𝐸 = 609.8 MPa, and 𝜀 = 0.0656, respectively (Table 5).
The trilinear concrete model was used for HSC (RC-80) [61] because it is a simple
model that facilitates convergence. The inputs are shown in Figure 5, where 𝑓 is the
average compressive strength and 𝐸 is the elasticity modulus. The values for each spec-
imen are shown in Table 3.
Figure 4. Section discretization.
2.3. Material Constitutive Models
The characteristics of the materials were taken from the experimental characterization.
The bilinear steel model was used to simulate steel bars. The input parameters were
Young’s modulus
Es
, hardening modulus
Eh
, and yield stress
fy
, which are depicted in
Table 4for each specimen.
A uniaxial model was used for a superelastic SMA (NiTi SMA), programmed by
Fugazza [
59
], which followed the constitutive relationship proposed by Auricchio and
Saco [
60
]. This model did not consider nonzero residual strains for zero stress and assumed
constant stiffness in both the fully austenitic and martensitic domains. The main input
parameters were the austenite to martensite starting stress and strain (
EA
and
εA
) and the
austenite to martensite finishing stress and strain (
EM
and
εM
). The same SMA bars were
used for all specimens, and the characterization values were:
EA
= 450.2 MPa,
εA
= 0.00696,
EM= 609.8 MPa, and εM= 0.0656, respectively (Table 5).
The trilinear concrete model was used for HSC (RC-80) [
61
] because it is a simple model
that facilitates convergence. The inputs are shown in Figure 5, where
fcm
is the average
compressive strength and
Ec
is the elasticity modulus. The values for each specimen are
shown in Table 3.
Buildings 2023, 13, x FOR PEER REVIEW 9 of 24
Figure 5. HSC constitutive model.
Regarding UHPC, the compressive constitutive equation employed is the one pro-
posed by the NF P18-710 [62]. It is defined by the following expressions, which take ac-
count the fibers’ confinement effect through the post-cracking strength 𝑓:
𝜎=
𝑓
 

,
󰇧

,
󰇨

(1)
Expression in which
𝜀, =󰇩14
𝑓

𝐾 ·
𝑓
󰇪10.16 𝑘
𝑓

800
𝑓



𝐾 (2)
𝑓 being mean value of compressive strength (MPa) and where
𝑘=𝐸
𝑓


 (3)
𝜂= 𝑘
𝑘−1 (4)
where 𝑘=𝐸𝜀,
𝑓
 (5)
𝐾 =1.25 according to the Annex T of NF P 18-710 [63]
𝜑=⎩
⎪
⎨
⎪
⎧
1 𝑖𝑓 𝜀≤ 𝜀,
𝑙𝑛1−𝜂 𝜂
0.7𝜀,
𝜀,
𝜂·𝑙𝑛𝜀,
𝜀, 𝑖𝑓 𝜀 𝜀, (6)
𝜀, =󰇩115
𝑓

𝐾 ·
𝑓
󰇪120
𝑓
10.16 𝑘
𝑓

800
𝑓



𝑘 (7)
where
𝑓: mean value of the post-cracking strength. If there is no local peak, 𝑓 is the
stress associated to a crack width of 0.3 mm.
Tensile stress-strain relationships were deduced by an inverse analysis based on the
results of the flexural tensile strength tests on UHPC concrete according to UNE EN 14651:
2007 [64]. The flexural tensile strength results are shown in Table 3.
The software used in this study did not consider the NF P18-710 [62] equation. There-
fore, Chang-Mander’s curve [65] was used to assimilate both the NF P18-710 equation [62]
Figure 5. HSC constitutive model.

Buildings 2023,13, 991 9 of 24
Regarding UHPC, the compressive constitutive equation employed is the one proposed
by the NF P18-710 [
62
]. It is defined by the following expressions, which take account the
fibers’ confinement effect through the post-cracking strength fct f m :
σ=fcm
ηε
εc1, f
η−1+ε
εc1, fϕη (1)
Expression in which
εc1, f="1+4fct f m
Kglobal ·fcm #1+0.16 k0
f2
cm +800 f
2
3
cm
K0
(2)
fcm being mean value of compressive strength (MPa) and where
k0=Ecm
f
1
3
cm
(3)
η=k
k−1(4)
where
k=Ecm
εc1, f
fcm (5)
Kglobal =1.25 according to the Annex T of NF P 18-710 [63]
ϕ=






1i f ε≤εc1, f
ln1−η+η
0.7
εcu1, f
εc1, f
η·lnεc u1,f
εc1, fi f ε>εc1, f
(6)
εcu1, f="1+15 fct f m
Kglobal ·fcm #1+20
fcm 1+0.16 k0
f2
cm +800 f
2
3
cm
k0
(7)
where
fct f m
: mean value of the post-cracking strength. If there is no local peak,
fct f m
is the
stress associated to a crack width of 0.3 mm.
Tensile stress-strain relationships were deduced by an inverse analysis based on the
results of the flexural tensile strength tests on UHPC concrete according to UNE EN 14651:
2007 [64]. The flexural tensile strength results are shown in Table 3.
The software used in this study did not consider the NF P18-710 [
62
] equation. There-
fore, Chang-Mander’s curve [
65
] was used to assimilate both the NF P18-710 equation [
62
]
for modeling UHPC under compression and the results of the inverse analysis for modeling
UHPC under tension. Chang and Mander [
65
] proposed a shape factor,
r=fc/5.2 −1.9
(in MPa), which modifies the descending branch of the stress–strain curve based on the
experimental results of unconfined concrete specimens up to 85 MPa. Hence, in the
Chang–Mander nonlinear model in SeismoStruct [
56
], the same
r
factor, which depends
on compressive concrete strength, is used for both the compression and tension envelope
curve. This meant that this model did not correctly reflect the UHPC tensile behavior since
the tensile post-peak behavior differs from the compression post-peak behavior (response
in tension is more ductile than in compression). To fix this issue, the SeismoStruct code [
56
]
was modified in this study so that Chang and Mander’s equation [
65
] allowed for a form
factor for the compression curve
rc
and another for the tension curve
rt
(both independent
of the compressive concrete strength). This modification enabled proper UHPC modeling.
The main parameters of the modified Chang and Mander’s equation were compressive

Buildings 2023,13, 991 10 of 24
strength
fc
, tensile strength
ft
, modulus of elasticity
Ec
, strain for the peak compressive
stress
εcc
, strain for the peak tensile stress
εt
, critical dimensionless strain in compression
xcr
, critical dimensionless strain in tension
xtr
, form factor for compression curve
rc
, and
a form factor for tension curve
rt
. Figure 6provides an example of matching the Chang–
Mander’s [
65
] curve to both the NF P18-710 [
62
] curve in compression (Figure 6a) and the
inverse analysis curve in tension for specimen HCV02C (Figure 6b). The parameters of the
modified Chang–Mander’s equation [65] are also given in Figure 6.
Buildings 2023, 13, x FOR PEER REVIEW 10 of 24
for modeling UHPC under compression and the results of the inverse analysis for model-
ing UHPC under tension. Chang and Mander [65] proposed a shape factor, 𝑟=
𝑓5.2−1.9
⁄ (in MPa), which modifies the descending branch of the stress–strain curve
based on the experimental results of unconfined concrete specimens up to 85 MPa. Hence,
in the Chang–Mander nonlinear model in SeismoStruct [56], the same 𝑟 factor, which de-
pends on compressive concrete strength, is used for both the compression and tension
envelope curve. This meant that this model did not correctly reflect the UHPC tensile be-
havior since the tensile post-peak behavior differs from the compression post-peak behav-
ior (response in tension is more ductile than in compression). To fix this issue, the Seismo-
Struct code [56] was modified in this study so that Chang and Mander’s equation [65]
allowed for a form factor for the compression curve 𝑟 and another for the tension curve
𝑟 (both independent of the compressive concrete strength). This modification enabled
proper UHPC modeling. The main parameters of the modified Chang and Mander’s equa-
tion were compressive strength 𝑓, tensile strength 𝑓, modulus of elasticity 𝐸, strain for
the peak compressive stress 𝜀, strain for the peak tensile stress 𝜀, critical dimensionless
strain in compression 𝑥, critical dimensionless strain in tension 𝑥, form factor for com-
pression curve 𝑟, and a form factor for tension curve 𝑟. Figure 6 provides an example of
matching the Chang–Mander’s [65] curve to both the NF P18-710 [62] curve in compres-
sion (Figure 6a) and the inverse analysis curve in tension for specimen HCV02C (Figure
6b). The parameters of the modified Chang–Mander’s equation [65] are also given in Fig-
ure 6.
Figure 6. Example of the constitutive curve of concrete for UHPC (modification of Chang and Man-
der’s model [59]) for HCV02C: (a) compression envelope; (b) tension envelope.
2.4. Comparison with the Experimental Results
The experimental results were used to validate the finite element model results. Fig-
ure 7 shows how the numerical model can predict the lateral load–drift ratio skeleton
curves. Drift values follow the following expression: ∆𝐿

⁄, where ∆ is de horizontal dis-
placement of the upper node and 𝐿 is the length of the cantilever column. As previously
stated, the skeleton curves of the cyclic test results are safety-side results in terms of max-
imum load and ductility if used in the pushover calibration because they consider material
degradation, which reduces the maximum load and ductility. This procedure is thus use-
ful for providing design recommendations based on the results of the parametric pusho-
ver analysis. The numerical model satisfactorily matches the experimental results in terms
of maximum lateral load and pre-peak and post-peak behavior.
0
20
40
60
80
100
120
140
0.00 0.01 0.02 0.03 0.04
Stress (MPa)
Strain
NF P18-710 (2016)
Modification of Chang & Mander
f
c
= 120.94 MPa
E
c
= 43259 MPa
r
c
= 2.00
= 1.30
0
2
4
6
8
10
12
0.00 0.01 0.02 0.03 0.04 0.05 0.06
Stress (MPa)
Strain
Inverse analysis method
Modification of Chang & Mander
f
t
= 9.8 MPa
E
c
= 43259 MPa
r
t
= 4.00
= 1.80
(a) (b)
Figure 6.
Example of the constitutive curve of concrete for UHPC (modification of Chang and
Mander’s model [59]) for HCV02C: (a) compression envelope; (b) tension envelope.
2.4. Comparison with the Experimental Results
The experimental results were used to validate the finite element model results.
Figure 7shows how the numerical model can predict the lateral load–drift ratio skele-
ton curves. Drift values follow the following expression:
∆/Ls
, where
∆
is de horizontal
displacement of the upper node and
Ls
is the length of the cantilever column. As previ-
ously stated, the skeleton curves of the cyclic test results are safety-side results in terms
of maximum load and ductility if used in the pushover calibration because they consider
material degradation, which reduces the maximum load and ductility. This procedure is
thus useful for providing design recommendations based on the results of the parametric
pushover analysis. The numerical model satisfactorily matches the experimental results in
terms of maximum lateral load and pre-peak and post-peak behavior.

Buildings 2023,13, 991 11 of 24
Buildings 2023, 13, x FOR PEER REVIEW 11 of 24
Figure 7. Calibration results: (a) Specimen 1: HCV01C; (b) Specimen 2: HCV02C; (c) Specimen 3:
HCV01D; (d) Specimen 4: HCV02D; (e) Specimen 5: VHPC-V01S100; (f) Specimen 6: VHPC-
V02S100; (g) Specimen 7: AS11-3.
3. Parametric Study
In this section, a parametric study was carried out based on the numerical model
described above.
3.1. Parametric Study Description
In this section, a parametric study was carried out based on the numerical model
described above. In all cases, a nonlinear static pushover analysis of a cantilever column
subjected to constant axial force and a lateral load was run by controlling the horizontal
0
10
20
30
40
50
60
70
80
00.511.522.53
Lateral Load, V (kN)
Drift ratio (Δ/L
s
) [%]
Experimental c urve
Numerical curve
2 - HCV02C
0
10
20
30
40
50
60
70
80
00.511.522.53
Lateral Load, V (kN)
Drift ratio (Δ/L
s
) [%]
Experimental curve
Numerical curve
1 - HCV01C
0
10
20
30
40
50
60
70
80
0 0.5 1 1.5 2 2.5 3
Lateral Load, V (kN)
Drift ratio (Δ/L
s
) [%]
Experimental curve
Numerical curve
4 - HCV02D
0
10
20
30
40
50
60
70
80
00.511.522.53
Lateral Load, V (kN)
Drift ratio (Δ/L
s
) [%]
Experimental c urve
Numerical curve
3 - HCV01D
0
10
20
30
40
50
60
70
80
00.511.522.53
Lateral Load, V (kN)
Drift ratio (Δ/L
s
) [%]
Experimental curve
Numerical curve
5 - VHPC-V01S100
0
10
20
30
40
50
60
70
80
00.511.522.53
Lateral Load, V (kN)
Drift ratio (Δ/L
s
) [%]
Experimental curve
Numerical curve
6 - VHPC-V02S100
0
10
20
30
40
50
60
70
80
00.511.522.53
Lateral Load, V (kN)
Drift ratio (Δ/L
s
) [%]
Experimental curv e
Numerical curve
7 - AS11-3
(a) (b)
(c) (d)
(e) (f)
(g)
Figure 7.
Calibration results: (
a
) Specimen 1: HCV01C; (
b
) Specimen 2: HCV02C; (
c
) Specimen 3:
HCV01D; (
d
) Specimen 4: HCV02D; (
e
) Specimen 5: VHPC-V01S100; (
f
) Specimen 6: VHPC-V02S100;
(g) Specimen 7: AS11-3.
3. Parametric Study
In this section, a parametric study was carried out based on the numerical model
described above.
3.1. Parametric Study Description
In this section, a parametric study was carried out based on the numerical model
described above. In all cases, a nonlinear static pushover analysis of a cantilever column

Buildings 2023,13, 991 12 of 24
subjected to constant axial force and a lateral load was run by controlling the horizontal
displacement of the node at the top of the column. The main and transition zones were
distinguished in the hybrid connection of the column (Figure 8). Both zones always had the
same concrete type, but the reinforcements could differ (steel or NiTi) depending on the pa-
rameters being studied. The range of values studied in the experimental
program [28,48,49]
was extrapolated to analyze the influence of the following variables: relative axial force,
concrete type in the hybrid connection and in the rest of the column, main zone length,
transition zone length, and joint type at the base of the column (Figure 8).
Buildings 2023, 13, x FOR PEER REVIEW 12 of 24
displacement of the node at the top of the column. The main and transition zones were
distinguished in the hybrid connection of the column (Figure 8). Both zones always had
the same concrete type, but the reinforcements could differ (steel or NiTi) depending on
the parameters being studied. The range of values studied in the experimental program
[28,48,49] was extrapolated to analyze the influence of the following variables: relative
axial force, concrete type in the hybrid connection and in the rest of the column, main zone
length, transition zone length, and joint type at the base of the column (Figure 8).
Figure 8. The parameters analyzed in the numerical simulation.
The values of the analyzed parameters were the following:
- Relative axial load (ν): 0.1, 0.2, 0.3, 0.4, 0.5, 0.55, 0.6, 0.65
- Concrete type in the hybrid connection: RC-30, RC-60, RC-90, UHPC
- Concrete type in the rest of the column: RC-30, RC-60, RC-90, UHPC
- Main zone length (L) (in m): 0.30, 0.60, 0.90, 1.20
- Transition length (L
tr
) (in m): 0, 0.05, 0.10, 0.15, 0.20
- Joint at the base of the column: continuous, discontinuous
The aim was to analyze how incorporating the new materials modified the behavior
of the column so as to propose design criteria for hybrid columns (combinations of mate-
rials and geometric design). The range of relative axial forces went from 𝜈 = 0.1 to the
maximum in which a column could be designed (𝜈 = 0.65󰇜 for a medium ductility class
(DCM) according to EC-8 [1]. The minimum main zone length approximately equaled
twice the plastic hinge length 𝑙 and was more than twice the critical length 𝑙 recorded
in the experimental tests [28,49].
The following variables were fixed: cross-section (150 × 260 mm), relative concrete
cover (𝑟ℎ
⁄=0.15, where 𝑟 is the distance from the center of the bar to the outer surface
of the concrete and ℎ is the height of the cross section), column length (𝐿=1500 𝑚𝑚),
shear slenderness (𝜆=𝐿ℎ
⁄=5.77), the longitudinal reinforcement ratio (𝜌=1.16%),
and the transverse reinforcement ratio (cϕ8/100).
The mechanical characteristics of the materials were the average of those obtained in
the experimental program. Specifically in the case of UHPC, the following parameters of
the modified Chang and Mander’s equation [65] were employed: compressive strength 𝑓
= 122.3 MPa; tensile strength 𝑓 = 12.5 MPa; modulus of elasticity 𝐸= 45,157 MPa; strain
for the peak compressive stress 𝜀 = 0.0055; strain for the peak tensile stress 𝜀= 0.002;
critical dimensionless strain in compression 𝑥 = 1.3; critical dimensionless strain in
Figure 8. The parameters analyzed in the numerical simulation.
The values of the analyzed parameters were the following:
- Relative axial load (ν): 0.1, 0.2, 0.3, 0.4, 0.5, 0.55, 0.6, 0.65
- Concrete type in the hybrid connection: RC-30, RC-60, RC-90, UHPC
- Concrete type in the rest of the column: RC-30, RC-60, RC-90, UHPC
- Main zone length (L) (in m): 0.30, 0.60, 0.90, 1.20
- Transition length (Ltr) (in m): 0, 0.05, 0.10, 0.15, 0.20
- Joint at the base of the column: continuous, discontinuous
The aim was to analyze how incorporating the new materials modified the behavior of
the column so as to propose design criteria for hybrid columns (combinations of materials
and geometric design). The range of relative axial forces went from
ν=
0.1 to the maximum
in which a column could be designed (
ν=0.65)
for a medium ductility class (DCM)
according to EC-8 [
1
]. The minimum main zone length approximately equaled twice the
plastic hinge length
lp
and was more than twice the critical length
lcr
recorded in the
experimental tests [28,49].
The following variables were fixed: cross-section (150
×
260 mm), relative concrete
cover (
r/h=
0.15, where
r
is the distance from the center of the bar to the outer surface of
the concrete and
h
is the height of the cross section), column length (
Ls=
1500
mm
), shear
slenderness (
λV=Ls/h=
5.77), the longitudinal reinforcement ratio (
ρl=
1.16%), and the
transverse reinforcement ratio (cφ8/100).
The mechanical characteristics of the materials were the average of those obtained in
the experimental program. Specifically in the case of UHPC, the following parameters of
the modified Chang and Mander’s equation [
65
] were employed: compressive strength
fc= 122.3 MPa;
tensile strength
ft
= 12.5 MPa; modulus of elasticity
Ec
= 45,157 MPa; strain
for the peak compressive stress
εcc
= 0.0055; strain for the peak tensile stress
εt
= 0.002;

Buildings 2023,13, 991 13 of 24
critical dimensionless strain in compression
xcr
= 1.3; critical dimensionless strain in tension
xtr = 1.8; form factor for compression curve rc= 2; form factor for tension curve rt= 4.
The parametric study was divided into five phases (Table 6) to study the effect of the
new materials on the strength and ductility of the columns:
-
Phase 1: the behavior of a homogeneous column manufactured with different concrete
types and steel bars was analyzed. The joint at the base of the column was continuous.
-
Phase 2: the behavior of a hybrid column, whose reinforcements were made of steel
along the entire length, was analyzed. The hybrid connection was manufactured with
UHPC. The behavior of the column with different concrete types in the rest of the
column and different hybrid connection lengths was analyzed. The joint at the base of
the column was continuous.
-
Phase 3: the effect of replacing steel bars with NiTi bars at the hybrid connection was
analyzed for previous cases. The studied variables were concrete type in the rest of
the column and hybrid connection length. The joint at the base of the column was
continuous.
-
Phase 4: the effect of including a transition zone (UHPC + steel bars) in the hybrid
connection was analyzed. The studied variables were concrete type in the rest of the
column and transition zone length. The joint at the base of the column was continuous.
-
Phase 5: For the cases analyzed in Phase 3, the effect of a discontinuous joint type on
the base of the column was analyzed. The studied variables were concrete type in the
rest of the column and hybrid connection length.
Table 6. Parametric study.
Joint Concrete at
Hybrid
Connection
Secondary
Concrete in
the Rest of
the Column
Main
Zone
Rebar
Material
Transition
Zone
Rebar
Material
Secondary
Concrete
Zone Rebar
Material
Hybrid Connection Secondary
Concrete
Length
Design
Validity
Main
Zone
Length
Transition
Zone
Length
Phase 1
Continuous
RC-30 -
B500SD -B500SD
- - - -
RC-60 - - - - -
RC-90 - - - - -
UHPC - - - - -
Phase 2
Continuous
UHPC RC-30 B500SD -B500SD
0.30 -1.20 Not valid
0.60 -0.90 Not valid
0.90 -0.60 Valid for
ν≤0.1
1.20 -0.30 Valid for
ν≤0.3
UHPC RC-60 B500SD -B500SD
0.30 -1.20 Not valid
0.60 -0.90 Valid for
ν≤0.2
0.90 -0.60 Valid for
ν≤0.4
1.20 -0.30 Valid
UHPC RC-90 B500SD -B500SD
0.30 -1.20 Valid
0.60 -0.90 Valid
0.90 -0.60 Valid
1.20 -0.30 Valid

Buildings 2023,13, 991 14 of 24
Table 6. Cont.
Joint Concrete at
Hybrid
Connection
Secondary
Concrete in
the Rest of
the Column
Main
Zone
Rebar
Material
Transition
Zone
Rebar
Material
Secondary
Concrete
Zone Rebar
Material
Hybrid Connection Secondary
Concrete
Length
Design
Validity
Main
Zone
Length
Transition
Zone
Length
Phase 3
Continuous
UHPC RC-30 NiTi -B500SD
0.30 -1.20 Not valid
0.60 -0.90 Valid for
ν≤0.1
0.90 -0.60 Valid for
ν≤0.2
1.20 -0.30 Valid for
ν≤0.3
UHPC RC-60 NiTi -B500SD
0.30 -1.20 Not valid
0.60 -0.90 Valid for
ν≤0.3
0.90 -0.60 Valid for
ν≤0.4
1.20 -0.30 Valid for
ν≤0.5
UHPC RC-90 NiTi -B500SD
0.30 -1.20 Valid
0.60 -0.90 Valid
0.90 -0.60 Valid
1.20 -0.30 Valid
Phase 4
Continuous
UHPC RC-30 NiTi B500SD B500SD
0.60
0.05 0.85 Valid for
ν≤0.1
0.10 0.80 Valid for
ν≤0.1
0.15 0.75 Valid for
ν≤0.1
0.20 0.70 Valid for
ν≤0.1
UHPC RC-60 NiTi B500SD B500SD
0.05 0.85 Valid for
ν≤0.3
0.10 0.80 Valid for
ν≤0.3
0.15 0.75 Valid for
ν≤0.4
0.20 0.70 Valid for
ν≤0.4
UHPC RC-90 NiTi B500SD B500SD
0.05 0.85 Valid
0.10 0.80 Valid
0.15 0.75 Valid
0.20 0.70 Valid
Phase 5
Discontinuous
UHPC RC-30 NiTi -B500SD
0.30 -1.20 Not valid
0.60 -0.90 Valid for
ν≤0.1
0.90 -0.60 Valid for
ν≤0.2
1.20 -0.30 Valid for
ν≤0.3
UHPC RC-60 NiTi -B500SD
0.30 -1.20 Not valid
0.60 -0.90 Valid for
ν≤0.3
0.90 -0.60 Valid for
ν≤0.4
1.20 -0.30 Valid for
ν≤0.5
UHPC RC-90 NiTi -B500SD
0.30 -1.20 Valid
0.60 -0.90 Valid
0.90 -0.60 Valid
1.20 -0.30 Valid

Buildings 2023,13, 991 15 of 24
3.2. Parametric Study Results and Discussion
The parametric study results show the maximum load reached in each test and the
displacement ductility
µ∆u=∆u/∆yI
, where
∆u
is the ultimate displacement of the column
and
∆yI
is the effective elastic displacement. To obtain the ductility, the lateral load–drift
ratio curves were idealized according to Esmaeeli et al. [
66
] to bi-linear diagrams, which
consist of an elastic branch and a perfect plastic branch (Figure 9).
∆u
is defined as the
displacement of a 20% loss of peak load.
∆yI
is obtained from a bi-linear curve, which is
created by fulfilling two conditions: (i) the sum of areas
∆i
from Figure 9must be zero
(
∑Ai=
0), and (ii) the deviation between the curve and the idealized bi-linear diagram
must be the minimum (
∑|Ai|=
0 according to Figure 9). To obtain the relative axial load,
the UHPC strength in the hybrid connection is taken as a reference
υ=N
bh fcm 
, where
N
is the applied axial load,
b
is the with of the columns,
h
is the depth of the column, and
fcm
is the UHPC strength in the hybrid connection.
Buildings 2023, 13, x FOR PEER REVIEW 13 of 24
tension 𝑥 = 1.8; form factor for compression curve 𝑟 = 2; form factor for tension curve
𝑟 = 4.
The parametric study was divided into five phases (Table 6) to study the effect of the
new materials on the strength and ductility of the columns:
- Phase 1: the behavior of a homogeneous column manufactured with different concrete
types and steel bars was analyzed. The joint at the base of the column was continuous.
- Phase 2: the behavior of a hybrid column, whose reinforcements were made of steel
along the entire length, was analyzed. The hybrid connection was manufactured with
UHPC. The behavior of the column with different concrete types in the rest of the
column and different hybrid connection lengths was analyzed. The joint at the base of
the column was continuous.
- Phase 3: the effect of replacing steel bars with NiTi bars at the hybrid connection was
analyzed for previous cases. The studied variables were concrete type in the rest of
the column and hybrid connection length. The joint at the base of the column was
continuous.
- Phase 4: the effect of including a transition zone (UHPC + steel bars) in the hybrid
connection was analyzed. The studied variables were concrete type in the rest of the
column and transition zone length. The joint at the base of the column was continuous.
- Phase 5: For the cases analyzed in Phase 3, the effect of a discontinuous joint type on
the base of the column was analyzed. The studied variables were concrete type in the
rest of the column and hybrid connection length.
3.2. Parametric Study Results and Discussion
The parametric study results show the maximum load reached in each test and the
displacement ductility 𝜇 =/, where  is the ultimate displacement of the col-
umn and  is the effective elastic displacement. To obtain the ductility, the lateral load–
drift ratio curves were idealized according to Esmaeeli et al. [66] to bi-linear diagrams,
which consist of an elastic branch and a perfect plastic branch (Figure 9).  is defined as
the displacement of a 20% loss of peak load.  is obtained from a bi-linear curve, which
is created by fulfilling two conditions: (i) the sum of areas  from Figure 9 must be zero
(∑𝐴=0), and (ii) the deviation between the curve and the idealized bi-linear diagram
must be the minimum (∑|𝐴|=0 according to Figure 9). To obtain the relative axial load,
the UHPC strength in the hybrid connection is taken as a reference 󰇡𝜐=𝑁𝑏ℎ𝑓
󰇢, where
𝑁 is the applied axial load, 𝑏 is the with of the columns, ℎ is the depth of the column,
and 𝑓 is the UHPC strength in the hybrid connection.
Figure 9. Idealized lateral load–drift ratio curve.
Figure 9. Idealized lateral load–drift ratio curve.
3.2.1. Phase 1
Figure 10 shows the results of Phase 1. As expected, strength capacity was similar for
all concrete types for the null axial force except for UHPC, given its flexural tensile strength
capacity. The maximum lateral load differed for higher axial forces and was always greater
in the columns with greater concrete strength because failure was caused by concrete and
not by tensioned reinforcements, since the axial force was higher. Ductility decreased with
relative axial force since the higher the relative axial force, the more the compression strains
underwent the compressed fibers in the section, so that the concrete reached a descending
branch of its constitutive curve. Ductility also decreased with concrete strength in the
columns manufactured with concrete without steel fibers (RC-30, RC-60 and RC-90) due
to the fragility of high-strength concretes. In general, the conventional concrete (RC-30)
columns showed higher displacement ductility than those manufactured with UHPC due to
the fragility of high-strength concretes. Even high fiber-content UHPC could not counteract
the fragility of the high-strength concrete for higher relative axial force levels.

Buildings 2023,13, 991 16 of 24
Buildings 2023, 13, x FOR PEER REVIEW 15 of 24
0.90 - 0.60 Valid for ν ≤ 0.2
1.20 - 0.30 Valid for ν ≤ 0.3
UHPC RC-60 NiTi - B500SD
0.30 - 1.20 Not valid
0.60 - 0.90 Valid for ν ≤ 0.3
0.90 - 0.60 Valid for
ν
≤ 0.4
1.20 - 0.30 Valid for ν ≤ 0.5
UHPC RC-90 NiTi - B500SD
0.30 - 1.20 Valid
0.60 - 0.90 Valid
0.90 - 0.60 Valid
1.20 - 0.30 Valid
3.2.1. Phase 1
Figure 10 shows the results of Phase 1. As expected, strength capacity was similar for
all concrete types for the null axial force except for UHPC, given its flexural tensile
strength capacity. The maximum lateral load differed for higher axial forces and was al-
ways greater in the columns with greater concrete strength because failure was caused by
concrete and not by tensioned reinforcements, since the axial force was higher. Ductility
decreased with relative axial force since the higher the relative axial force, the more the
compression strains underwent the compressed fibers in the section, so that the concrete
reached a descending branch of its constitutive curve. Ductility also decreased with con-
crete strength in the columns manufactured with concrete without steel fibers (RC-30, RC-
60 and RC-90) due to the fragility of high-strength concretes. In general, the conventional
concrete (RC-30) columns showed higher displacement ductility than those manufactured
with UHPC due to the fragility of high-strength concretes. Even high fiber-content UHPC
could not counteract the fragility of the high-strength concrete for higher relative axial
force levels.
Figure 10. Maximum load and displacement ductility in the specimens made entirely of one con-
crete type and B500SD reinforcements. Continuous joint (Phase 1): (a) lateral load–axial load; (b)
displacement ductility–relative axial load.
3.2.2. Phase 2
Figure 11 shows Phase 2 results. The behavior of the homogeneous column manufac-
tured with UHPC concrete and steel bars is also given as a reference. In all cases, axial
forces were calculated by taking the concrete strength of the hybrid connection as a refer-
ence 󰇛𝑓 = 120 MPa󰇜. In some cases, the critical section was at the beginning of the sec-
ondary concrete zone when the main zone length (𝐿) was insufficient, since the secondary
concrete could not bear the compression stresses, which reduced the strength and the col-
umn’s displacement ductility 𝜇. For example, this took place for RC-30 or RC-60 with
𝐿=0.30 m (Figure 11a,b).
0
20
40
60
80
100
120
0 500 1000 1500 2000 2500 3000 3500
Lateral Load, V
max
(kN)
Axial Load (kN)
RC-30 RC-60
RC-90 UHPC
0
1
2
3
4
5
6
7
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Displacement Ductility, μ
Δu
Relative axial load (ν)
RC-30
RC-60
RC-90
UHPC
(a) (b)
Figure 10.
Maximum load and displacement ductility in the specimens made entirely of one concrete
type and B500SD reinforcements. Continuous joint (Phase 1): (
a
) lateral load–axial load; (
b
) displace-
ment ductility–relative axial load.
3.2.2. Phase 2
Figure 11 shows Phase 2 results. The behavior of the homogeneous column man-
ufactured with UHPC concrete and steel bars is also given as a reference. In all cases,
axial forces were calculated by taking the concrete strength of the hybrid connection as
a reference
(fcm =120 MPa)
. In some cases, the critical section was at the beginning of
the secondary concrete zone when the main zone length (
L
) was insufficient, since the
secondary concrete could not bear the compression stresses, which reduced the strength
and the column’s displacement ductility
µ∆u
. For example, this took place for RC-30 or
RC-60 with L=0.30 m (Figure 11a,b).
Greater secondary concrete strength enabled the critical section of the column to be
located in the hybrid connection and of similar strength and displacement ductility to those
of the reference column. Likewise, a longer hybrid connection length allowed the column
to be combined with lower quality secondary concrete, and the elements achieved similar
strength and ductility to those shown in the reference column. It should be noted that
although the strength of the hybrid column equaled that of the reference column, from the
ductility point of view, the main zone (
L
) must be long enough to develop plastic behavior
in the hybrid connection without being limited by the behavior of the rest of the column
(e.g., see Figure 11c,d, for column RC-60 with relative axial force up to
ν=
0.20). In other
words, if a hybrid column is designed with the same features as the reference column, the
main zone length (
L
) and the strength of the concrete of the rest of the column must be able
to at least ensure the same strength capacity and ductility.
Figure 11 shows that a UHPC hybrid connection and a concrete of 30 MPa for the rest
of the column cannot be combined to design the column according to the characteristics of
the studied columns. In this case, it was not possible to use a reasonable hybrid connection
length for any applied axial level. If the concrete in the rest of the column is RC-90, the
combination is possible for any axial force with a minimum length of 0.30 m.
Figure 12 shows how load capacity and ductility were affected by varying the compres-
sive strength of the secondary concrete in the HCV02C support tested in the experimental
program. For all cases in which strength was greater than 40 MPa, the results were prac-
tically the same, so that these strengths would be enough to accompany the UHPC. The
idea that UHPC is not compatible with conventional low-strength concrete was reaffirmed.
Regarding ductility, few variations were observed from a strength of 40 MPa, since the
length of the hybrid connection was sufficient to develop the plastic hinge.

Buildings 2023,13, 991 17 of 24
Buildings 2023, 13, x FOR PEER REVIEW 16 of 24
Greater secondary concrete strength enabled the critical section of the column to be
located in the hybrid connection and of similar strength and displacement ductility to
those of the reference column. Likewise, a longer hybrid connection length allowed the
column to be combined with lower quality secondary concrete, and the elements achieved
similar strength and ductility to those shown in the reference column. It should be noted
that although the strength of the hybrid column equaled that of the reference column,
from the ductility point of view, the main zone (𝐿) must be long enough to develop plastic
behavior in the hybrid connection without being limited by the behavior of the rest of the
column (e.g., see Figure 11c,d, for column RC-60 with relative axial force up to 𝜈=0.20).
In other words, if a hybrid column is designed with the same features as the reference
column, the main zone length (𝐿) and the strength of the concrete of the rest of the column
must be able to at least ensure the same strength capacity and ductility.
Figure 11. Maximum load and displacement ductility in the specimens made of two concrete types
and steel reinforcements. Continuous joint (Phase 2): (a) lateral load–relative axial load for L = 0.3
m; (b) displacement ductility–relative axial load for L = 0.3 m; (c) lateral load–relative axial load for
L = 0.6 m; (d) displacement ductility–relative axial load for L = 0.6 m; (e) lateral load–relative axial
load for L = 0.9 m; (f) displacement ductility–relative axial load for L = 0.9 m.
Figure 11 shows that a UHPC hybrid connection and a concrete of 30 MPa for the rest
of the column cannot be combined to design the column according to the characteristics
0
20
40
60
80
100
120
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Lateral Load, V
max
(kN)
Relative axi al load (ν)
RC-30 RC-60
RC-90 UHPC
L=0.30 m
0
1
2
3
4
5
6
7
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Displacement Ductility, μ
Δu
Relative axi al load (ν)
RC-30 RC-60
RC-90 UHPC
L=0.30 m
0
20
40
60
80
100
120
0 0.1 0.2 0.3 0. 4 0.5 0.6 0.7
Lateral Load, V
max
(kN)
Relative axi al load (ν)
RC-30 RC-60
RC-90 UHPC
L=0.60
m
0
1
2
3
4
5
6
7
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Displacement Ductility, μ
Δu
Relative axi al load (ν)
RC-30 RC-60
RC-90 UHPC
L=0.60 m
0
20
40
60
80
100
120
0 0.1 0.2 0.3 0.4 0.5 0. 6 0.7
Lateral Load, V
max
(kN)
Relative axial load (ν)
RC-30 RC-60
RC-90 UHPC
L=0.90
m
0
1
2
3
4
5
6
7
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Displacement Ductility, μ
Δu
Relative axial load (ν)
RC-30 RC-60
RC-90 UHPC
L=0.90 m
(b)(a)
(d)(c)
(f)(e)
Figure 11.
Maximum load and displacement ductility in the specimens made of two concrete types
and steel reinforcements. Continuous joint (Phase 2): (
a
) lateral load–relative axial load for
L = 0.3 m
;
(
b
) displacement ductility–relative axial load for L = 0.3 m; (
c
) lateral load–relative axial load for
L = 0.6 m
; (
d
) displacement ductility–relative axial load for
L = 0.6 m
; (
e
) lateral load–relative axial
load for L = 0.9 m; (f) displacement ductility–relative axial load for L = 0.9 m.
Buildings 2023, 13, x FOR PEER REVIEW 17 of 24
of the studied columns. In this case, it was not possible to use a reasonable hybrid connec-
tion length for any applied axial level. If the concrete in the rest of the column is RC-90,
the combination is possible for any axial force with a minimum length of 0.30 m.
Figure 12 shows how load capacity and ductility were affected by varying the com-
pressive strength of the secondary concrete in the HCV02C support tested in the experi-
mental program. For all cases in which strength was greater than 40 MPa, the results were
practically the same, so that these strengths would be enough to accompany the UHPC.
The idea that UHPC is not compatible with conventional low-strength concrete was reaf-
firmed . Rega rding ducti lity, few variatio ns were o bserved from a st rengt h of 40 MPa, since
the length of the hybrid connection was sufficient to develop the plastic hinge.
Figure 12. Influence of secondary concrete in maximum lateral load and displacement ductility.
3.2.3. Phase 3
Figure 13 gives the results of this phase and shows that replacing the longitudinal
steel bars with NiTi SMA bars reduced the hybrid columns’ strength below that of the
reference column because the steel yield stress was 547 MPa and the NiTi starting marten-
sitic transformation stress was 450.2 MPa. However, replacing the NiTi SMA bars im-
proved displacement ductility 󰇛𝜇∆󰇜 over the hybrid column when only steel bars were
used (see Figure 13 vs. Figure 11). The reason for the increased ductility was that the slope
of martensitic transformation branch of the NiTi constitutive curve was not null, unlike
the steel yield plateau. For this reason, NiTi could partially counter the load capacity loss
caused by concrete degradation. As in the previous study, for the columns under study it
was not possible to combine UHPC and a concrete of 30 MPa (RC-30). For example, for
RC-90 and the hybrid connection length of 𝐿 = 0.30 m, similar ductility was achieved to
that of the reference column for any relative axial force.
0
1
2
3
4
5
6
0
10
20
30
40
50
60
70
80
20 30 40 50 60 80 100
Displacement Ductility (μ
Δu
)
Maximum Lateral Load, V
max
(kN)
Average concrete compressive strength (f
cm
) [MPa]
Vmax (kN)
Ductiliy
HCV02C
Figure 12. Influence of secondary concrete in maximum lateral load and displacement ductility.

Buildings 2023,13, 991 18 of 24
3.2.3. Phase 3
Figure 13 gives the results of this phase and shows that replacing the longitudinal steel
bars with NiTi SMA bars reduced the hybrid columns’ strength below that of the reference
column because the steel yield stress was 547 MPa and the NiTi starting martensitic
transformation stress was 450.2 MPa. However, replacing the NiTi SMA bars improved
displacement ductility (µ∆u)over the hybrid column when only steel bars were used (see
Figure 13 vs. Figure 11). The reason for the increased ductility was that the slope of
martensitic transformation branch of the NiTi constitutive curve was not null, unlike the
steel yield plateau. For this reason, NiTi could partially counter the load capacity loss
caused by concrete degradation. As in the previous study, for the columns under study it
was not possible to combine UHPC and a concrete of 30 MPa (RC-30). For example, for
RC-90 and the hybrid connection length of
L
= 0.30 m, similar ductility was achieved to
that of the reference column for any relative axial force.
Buildings 2023, 13, x FOR PEER REVIEW 18 of 24
Figure 13. Maximum load and displacement ductility in the specimens made with UHPC–NiTi bars
at the hybrid connection with no transition zone. Continuous joint (Phase 3): (a) lateral load–relative
axial load for L = 0.3 m; (b) displacement ductility–relative axial load for L = 0.3 m; (c) lateral load–
relative axial load for L = 0.6 m; (d) displacement ductility–relative axial load for L = 0.6 m.
3.2.4. Phase 4
Figure 14 shows the results of Phase 4 of the parametric study. If these results are
compared with those obtained in Phase 3 for main zone length 𝐿= 0.60 m (Figure 13c,d),
it can be seen that including a transition zone of length 󰇛𝐿󰇜 made with UHPC and steel
bars improved the columns’ strength and displacement ductility when the concrete types
in the rest of the column were RC-30 and RC-60. This was because the secondary concrete
(RC-30, RC-60) was further from the fully fixed end due to the transition zone, so that the
sectional forces in the part of the column made of secondary concrete decreased according
to the column’s bending moment and shear diagram. Including a transition zone im-
proved column performance without excessively raising the cost of the hybrid connection,
since no NiTi alloy bars were used in the transition zone. Including this zone when the
concrete in the rest of the column was RC-90 did not improve either strength or ductility
since the critical section was in the main zone length.
0
20
40
60
80
100
120
0 0.10.20.30.40.50.60.7
Lateral Load, V
max
(kN)
Relative axial load (ν)
RC-30 RC-60
RC-90 UHPC
L=0.30
m
0
1
2
3
4
5
6
7
0 0.10.20.30.40.50.60.7
Lateral Load, V
max
(kN)
Relative axial load (ν)
RC-30 RC-60
RC-90 UHPC
L=0.30 m
0
20
40
60
80
100
120
0 0.10.20.30.40.50.60.7
Lateral Load, V
max
(kN)
Relative axial load (ν)
RC-30 RC-60
RC-90 UHPC
L=0.60
m
L=0.30
m
0
1
2
3
4
5
6
7
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Lateral Load, V
max
(kN)
Relative axial load (ν)
RC-30 RC-60
RC-90 UHPC
L=0.60 mL=0.30 m
(b)(a)
(d)(c)
Figure 13.
Maximum load and displacement ductility in the specimens made with UHPC–NiTi
bars at the hybrid connection with no transition zone. Continuous joint (Phase 3): (
a
) lateral load–
relative axial load for L= 0.3 m; (
b
) displacement ductility–relative axial load for L= 0.3 m; (
c
) lateral
load–relative axial load for L= 0.6 m; (d) displacement ductility–relative axial load for L= 0.6 m.
3.2.4. Phase 4
Figure 14 shows the results of Phase 4 of the parametric study. If these results are
compared with those obtained in Phase 3 for main zone length
L=
0.60
m
(Figure 13c,d),
it can be seen that including a transition zone of length
(Ltr)
made with UHPC and steel
bars improved the columns’ strength and displacement ductility when the concrete types
in the rest of the column were RC-30 and RC-60. This was because the secondary concrete
(RC-30, RC-60) was further from the fully fixed end due to the transition zone, so that the
sectional forces in the part of the column made of secondary concrete decreased according
to the column’s bending moment and shear diagram. Including a transition zone improved
column performance without excessively raising the cost of the hybrid connection, since
no NiTi alloy bars were used in the transition zone. Including this zone when the concrete

Buildings 2023,13, 991 19 of 24
in the rest of the column was RC-90 did not improve either strength or ductility since the
critical section was in the main zone length.
Buildings 2023, 13, x FOR PEER REVIEW 19 of 24
Figure 14. Maximum load and displacement ductility in the specimens with a main zone length L
of 0.60 m and several transition zone lengths Ltr (Phase 4): (a) lateral load–relative axial load for Ltr
= 0.05 m; (b) displacement ductility–relative axial load for Ltr = 0.05 m; (c) lateral load–relative axial
load for Ltr = 0.20 m; (d) displacement ductility–relative axial load for Ltr = 0.20 m.
3.2.5. Phase 5
Figure 15 offers the results of Phase 5 of the parametric study. Compared to those
obtained in Phase 3 (Figure 13) for a continuous joint, both strength capacity and displace-
ment ductility were slightly less in those with discontinuous joints, as these did not de-
velop flexural tensile strength. The conclusions reached in Phase 3 on the influence of
main zone length, concrete type for the column, and the axial level for the continuous joint
can also be applied to the discontinuous joint specimens.
3.2.6. Global Analysis
The last column in Table 6 shows the range of validity of the combinations studied
regarding the maximum relative axial load ν for which the combination of parameters is
suitable. They are suitable if there is no sudden drop in strength or ductility. For example,
Figure 11.e and Figure 11.f show that a main zone length of 90 cm and RC-30 for the rest
of the specimen is valid up to ν = 0.2 for strength but up to ν = 0.1 for ductility, so that this
combination is valid up to ν = 0.1. Following this criterion, Table 6 shows that if the sec-
ondary concrete is RC-90, all the analyzed main zone lengths are valid for the range of the
studied relative axial loads (0.1–0.65), with or without a transition zone. Therefore, for
these specimens, the most economical design for RC-90 as secondary concrete is a main
zone of 30 cm without a transition zone. However, RC-30 cannot be used in any case as a
secondary concrete if the length of the main zone is 30 cm. If this length is 60 cm, RC-30 is
valid up to ν = 0.1 (except for steel main zone reinforcement (Phase 2)), which is a rather
low relative axial load for columns. RC-30 therefore makes sense as a secondary concrete
for main zone lengths of 90 cm and over (ν ≤ 0.2 for SMA reinforcements and ν ≤ 0.1 for
steel reinforcements). RC-60 can be used with main zone lengths of 60 cm and over since
there was no drop in strength or deformation capacity when ν ≤ 0.3 for main zone SMA
reinforcements and ν ≤ 0.2 for main zone steel reinforcements. Adding a transition zone
0
1
2
3
4
5
6
7
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Displacement Ductility, μ
Δu
Relative axial load (ν)
RC-30 RC-60
RC-90 UHPC
L=0.60 m L
tr
=0.05 m
0
20
40
60
80
100
120
0 0.10.20.30.40.50.60.7
Lateral Load, V
max
(kN)
Relative axial load (ν)
RC-30 RC-60
RC-90 UHPC
L
tr
=0.05 mL=0.60m
0
1
2
3
4
5
6
7
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Displacement Ductility, μ
Δu
Relative axial load (ν)
RC-30 RC-60
RC-90 UHPC
L=0.60 m L
tr
=0.20 m
0
20
40
60
80
100
120
0 0.1 0.2 0.3 0. 4 0.5 0.6 0.7
Lateral Load, V
max
(kN)
Relative axial load (ν)
RC-30 RC-60
RC-90 UHPC
L
tr
=0.20 mL=0.60m
(b)(a)
(d)(c)
Figure 14.
Maximum load and displacement ductility in the specimens with a main zone length L
of 0.60 m and several transition zone lengths L
tr
(Phase 4): (
a
) lateral load–relative axial load for
Ltr = 0.05 m
; (
b
) displacement ductility–relative axial load for L
tr
= 0.05 m; (
c
) lateral load–relative
axial load for Ltr = 0.20 m; (d) displacement ductility–relative axial load for Ltr = 0.20 m.
3.2.5. Phase 5
Figure 15 offers the results of Phase 5 of the parametric study. Compared to those
obtained in Phase 3 (Figure 13) for a continuous joint, both strength capacity and displace-
ment ductility were slightly less in those with discontinuous joints, as these did not develop
flexural tensile strength. The conclusions reached in Phase 3 on the influence of main zone
length, concrete type for the column, and the axial level for the continuous joint can also be
applied to the discontinuous joint specimens.

Buildings 2023,13, 991 20 of 24
Buildings 2023, 13, x FOR PEER REVIEW 20 of 24
can increase the range of relative axial loads for this case in 0.1 (see Table 6, Phase 4). The
joint between the stub and the main zone can be discontinuous or continuous according
to requirements. Continuous joints increased strength by 5% on average but reduced duc-
tility by up to 28%.
Figure 15. Maximum load and displacement ductility in the specimens made with UHPC–NiTi bars
at the hybrid connection and secondary concrete and steel reinforcement in the rest of the column.
Discontinuous joint (Phase 5): (a) lateral load–relative axial load for L = 0.3 m; (b) displacement
ductility–relative axial load for L = 0.3 m; (c) lateral load–relative axial load for L = 0.6 m; (d) dis-
placement ductility–relative axial load for L = 0.6 m.
4. Conclusions
A nonlinear static pushover analysis was run to predict the performance of hybrid
columns. The model was first calibrated from experimental results, after which a paramet-
ric study was carried out to obtain design recommendations for hybrid columns with the
aim of reducing the regions of the column in which these new materials should be intro-
duced, leaving the rest of the column with conventional materials since both UHPC and
NiTi SMA are expensive and not in plentiful supply.
The conclusions and design recommendations can be summarized as follows:
An adequate design for the hybrid connection between column and stub, considering
both economy and performance, should include a main zone and a transition zone of
UHPC concrete. The NiTi SMA bars were placed in the main zone, while the steel bars
were placed in the transition zone. The transition zone improved the hybrid column’s
performance without excessively raising the cost.
For each case, it was necessary to determine the main zone length, the transition zone
length, and the strength of the concrete in the rest of the column (secondary concrete) to
ensure that the critical section of the column was in the main zone, to develop the maxi-
mum strength and ductility of the hybrid connection. On the other hand, the axial load
and bending moment applied could cause the failure of a section with secondary concrete
or in the transition zone.
(b)(a)
(d)(c)
0
1
2
3
4
5
6
7
8
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Displacement Ductility, μ
Δu
Relative axial load (ν)
RC-30 RC-60
RC-90 UHPC
L=0.60 m
0
20
40
60
80
100
120
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Lateral Load, V
max
(kN)
Relative axial load (ν)
RC-30 RC-60
RC-90 UHPC
L=0.60
m
0
20
40
60
80
100
120
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Lateral Load, V
max
(kN)
Relative axial load (ν)
RC-30 RC-60
RC-90 UHPC
L=0.30
m
0
1
2
3
4
5
6
7
8
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Displacement Ductility, μ
Δu
Relative axial load (ν)
RC-30 RC-60
RC-90 UHPC
L=0.30 m
Figure 15.
Maximum load and displacement ductility in the specimens made with UHPC–NiTi
bars at the hybrid connection and secondary concrete and steel reinforcement in the rest of the
column. Discontinuous joint (Phase 5): (
a
) lateral load–relative axial load for L= 0.3 m; (
b
) displace-
ment ductility–relative axial load for L= 0.3 m; (
c
) lateral load–relative axial load for L= 0.6 m;
(d) displacement ductility–relative axial load for L= 0.6 m.
3.2.6. Global Analysis
The last column in Table 6shows the range of validity of the combinations studied
regarding the maximum relative axial load
ν
for which the combination of parameters is
suitable. They are suitable if there is no sudden drop in strength or ductility. For example,
Figure 11.e and Figure 11.f show that a main zone length of 90 cm and RC-30 for the rest
of the specimen is valid up to
ν
= 0.2 for strength but up to
ν
= 0.1 for ductility, so that
this combination is valid up to
ν
= 0.1. Following this criterion, Table 6shows that if the
secondary concrete is RC-90, all the analyzed main zone lengths are valid for the range of
the studied relative axial loads (0.1–0.65), with or without a transition zone. Therefore, for
these specimens, the most economical design for RC-90 as secondary concrete is a main
zone of 30 cm without a transition zone. However, RC-30 cannot be used in any case as a
secondary concrete if the length of the main zone is 30 cm. If this length is 60 cm, RC-30 is
valid up to
ν
= 0.1 (except for steel main zone reinforcement (Phase 2)), which is a rather
low relative axial load for columns. RC-30 therefore makes sense as a secondary concrete
for main zone lengths of 90 cm and over (
ν≤
0.2 for SMA reinforcements and
ν≤
0.1 for
steel reinforcements). RC-60 can be used with main zone lengths of 60 cm and over since
there was no drop in strength or deformation capacity when
ν≤
0.3 for main zone SMA
reinforcements and
ν≤
0.2 for main zone steel reinforcements. Adding a transition zone
can increase the range of relative axial loads for this case in 0.1 (see Table 6, Phase 4). The
joint between the stub and the main zone can be discontinuous or continuous according to
requirements. Continuous joints increased strength by 5% on average but reduced ductility
by up to 28%.

Buildings 2023,13, 991 21 of 24
4. Conclusions
A nonlinear static pushover analysis was run to predict the performance of hybrid
columns. The model was first calibrated from experimental results, after which a parametric
study was carried out to obtain design recommendations for hybrid columns with the aim
of reducing the regions of the column in which these new materials should be introduced,
leaving the rest of the column with conventional materials since both UHPC and NiTi SMA
are expensive and not in plentiful supply.
The conclusions and design recommendations can be summarized as follows:
An adequate design for the hybrid connection between column and stub, considering
both economy and performance, should include a main zone and a transition zone of
UHPC concrete. The NiTi SMA bars were placed in the main zone, while the steel bars
were placed in the transition zone. The transition zone improved the hybrid column’s
performance without excessively raising the cost.
For each case, it was necessary to determine the main zone length, the transition zone
length, and the strength of the concrete in the rest of the column (secondary concrete) to
ensure that the critical section of the column was in the main zone, to develop the maximum
strength and ductility of the hybrid connection. On the other hand, the axial load and
bending moment applied could cause the failure of a section with secondary concrete or in
the transition zone.
Not all combinations of secondary concrete strength and hybrid connection length
achieve the required performance. The most suitable strength and length combination
depend on both the reduced axial load and the required ductility.
The greater the strength of the secondary concrete of the column, the shorter the
hybrid connection needed to achieve similar strength and ductility to that of the reference
column manufactured entirely with UHPC and steel bars.
Although the strength of the hybrid column entirely reinforced with steel rebars
equaled that of the reference column, the ductility of both columns could be different. The
main zone length must enable plastic behavior to develop in the hybrid connection without
being limited by the behavior of the rest of the column.
Replacing steel bars by SMA bars with
fA≤fy
and
EA≤Es
in the hybrid connection
reduced strength and improved ductility.
The use of continuous joints slightly increases strength and displacement ductility
because this type of joint can develop flexural tensile strength, unlike discontinuous joints.
The overall behavior with respect to the main zone length and secondary concrete type is
the same whatever the joint type.
5. Possible Directions for Future Studies
The main limitation of this research lies in the fact that only an isolated column has
been analyzed. For this reason, in future research, the authors will propose an optimization
of the design based on the analysis of complete structures, in order to provide optimized
numerical values for the main zone length, transition zone length, and other remaining
design parameters, taking into account the behavior of the entire building structure and
the requirements of design regulations.
Author Contributions:
Conceptualization, J.L.B.; methodology, J.L.B. and J.P.-B.; software, B.M.-J.
and B.C.-E.; validation, B.M.-J. and B.C.-E.; formal analysis, J.P.-B.; investigation, J.P.-B.; resources,
J.P.-B.; data curation, J.P.-B.; writing—original draft preparation, J.P.-B.; writing—review and editing,
J.P.-B.; visualization, J.P.-B.; supervision, J.P.-B.; project administration, J.P.-B. and J.L.B.; funding
acquisition, J.L.B. All authors have read and agreed to the published version of the manuscript.
Funding:
This work was supported by the Spanish Ministry of Economy and Competitiveness
through Project BIA2012-32645 and by the European Union through European Regional Development
Funds (ERDF). The project was executed at the Concrete Science and Technology Institute (ICITECH)
of the Universitat Politècnica de València (UPV). The article processing charge was paid by the

Buildings 2023,13, 991 22 of 24
University of Alicante (UA). The authors wish to thank the Spanish Ministry of Education, Culture
and Sport for Grant FPU12/01451.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement:
Any data not shown in this manuscript will be provided to interested
parties on request.
Acknowledgments:
The authors thank Universidad de Alicante (UA) for their support of
this research.
Conflicts of Interest:
The authors certify that they have no affiliations with or involvement in any
organization or entity with any financial interest (such as honoraria; educational grants; participation
in speakers’ bureaus; membership, employment, consultancies, stock ownership, or other equity
interest; and expert testimony or patent-licensing arrangements) or non-financial interest (such as
personal or professional relationships, affiliations, knowledge or beliefs) in the subject, matter, or
materials discussed in this manuscript.
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