2025 Enhancing flexural performance of reinforced concrete beams using UHPC ove osites

Prévia do material em texto

Enhancing flexural performance of reinforced concrete beams using UHPC 
overlay and external bonding of CFRP composites
Taraka M.R. Balla *,1 , Rahul Reddy Morthala 1 , S. Suriya Prakash
Department of Civil Engineering, Indian Institute of Technology Hyderabad, India
A R T I C L E I N F O
Keywords:
Strengthening
Overlay
RC beams
UHPC
CFRP
Flexure Loading
DIC
A B S T R A C T
Engineers constantly look for reliable and long-lasting strengthening solutions for deteriorated bridges and 
building systems. Ultrahigh-performance concrete (UHPC) overlays can be an effective solution for repairing and 
strengthening bridge decks, beams and slabs in buildings to increase durability and structural performance. This 
study explores the effectiveness of an innovative hybrid strengthening technique for flexural members using 
UHPC overlay and external bonding of carbon fibre-reinforced polymer (CFRP) composites. UHPC has a dense 
material composition that results in high strength, stiffness, and durability. The flexural behaviour of reinforced 
concrete (RC) beams strengthened with various hybrid configurations of UHPC overlay, and CFRP strengthening 
is experimentally assessed in this study. Five full-scale specimens with different strengthening configurations are 
tested under four-point loading. Test results show a maximum increase in flexural capacity of 63 % with only 
UHPC overlay and 129 % with the hybrid configuration compared to the control RC beam. In addition, the digital 
image correlation (DIC) results revealed an improved serviceability performance in terms of lesser deflections 
and reduced crack widths due to UHPC overlay and FRP strengthening. The moment-curvature and load- 
displacement response from the test results are compared with predictions of the analytical approach gener-
ated from the cross-section and member-level analysis. The cracking moment and ultimate strength of all the 
tested beams are predicted using the proposed analytical approach. Predictions had a coefficient of variation 
(COV) of 0.05 and 0.04, respectively, with test results.
1. Introduction
Strengthening reinforced concrete (RC) buildings and bridges are 
often required for various reasons. They are often required to address 
corrosion and deterioration due to extreme environmental conditions 
and additional loading requirements due to changes in the use [1]. Also, 
deterioration of top layers of bridge decks due to vehicular impact and 
ageing, damage due to accidental loading, such as impact and blast 
[2–4], defects in design and construction and upgradation of existing 
structures need structural strengthening [5–7]. The combined effects of 
vehicular loading, cracking, water and chloride ingress, concrete 
delamination, and reinforcement corrosion lead to significant deterio-
ration of bridge elements. Strengthening using the overlay technique is 
employed to restore the longevity and functionality of damaged bridge 
decks [8,9].
Various materials, such as conventional concrete, high-performance 
concrete, polymer-based composites and ultrahigh-performance 
concrete (UHPC), are used in overlay applications [10–12]. The 
different types of overlays are chosen based on factors such as the extent 
of deterioration, budget constraints, and the desired lifespan of the 
repaired structure. Overlay using UHPC is a prominent solution as it has 
superior properties such as high strength, durability, and resistance to 
environmental deterioration [13,14]. UHPC has raw materials like 
cement, silica fume, river sand and steel fibres [15]. UHPC has an 
exceptionally dense composition, developed using the modified 
Andreasen and Andersen model [16]. Mix design using the particle 
packing model can result in a highly impervious UHPC mix. The com-
parison of particle packing of conventional concrete and UHPC in 
equivalent scale is shown in Fig. 1.
UHPC offers exceptional durability, high energy absorption, chemi-
cal resistance, and low permeability. It significantly blocks the entry of 
harmful substances like water and chlorides compared to normal- 
strength concrete (NSC). UHPC has a high compressive strength of 
more than 120 MPa, a tensile strength of more than 6 MPa, and 
considerable tensile strain hardening and softening behaviour. UHPC 
* Corresponding author.
E-mail addresses: tarakaballa.iitr.iith@gmail.com (T.M.R. Balla), ce22resch01007@iith.ac.in (R.R. Morthala), suriyap@ce.iith.ac.in (S.S. Prakash). 
1 Equivalent First Author
Contents lists available at ScienceDirect
Engineering Structures
journal homepage: www.elsevier.com/locate/engstruct
https://doi.org/10.1016/j.engstruct.2025.119951
Received 14 July 2024; Received in revised form 27 December 2024; Accepted 18 February 2025 
Engineering Structures 330 (2025) 119951 
Available online 24 February 2025 
0141-0296/© 2025 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies. 
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has good rheological qualities like workability and self-compacting 
properties, making casting easy using concreting equipment. It is an 
outstanding choice for restoring and retrofitting deteriorated concrete 
structures [17,18]. Using UHPC overlay is an effective solution for 
repairing and strengthening deteriorated and damaged RC structural 
elements to improve their strength and extend the service life of the 
structure [19,20].
Some studies in the past have focused on understanding the effect of 
flexural strengthening using UHPC [6,17,21,22]. Lampropoulos et al. 
[17] investigated the flexural behaviour of RC beams strengthened using 
UHPC. They validated the finite element (FE) models using the existing 
test database to conduct the parametric study and understand the 
different UHPC overlay combinations. They noted that all UHPC overlay 
configurations were effective in improving flexural strength. Adding 
reinforcement in the UHPC layer on the tension side was more effective 
than only UHPC. Kadhim et al. [22] investigated the flexural behaviour 
of CFRP-reinforced UHPC overlays in the tension side of RC beams both 
experimentally and numerically. A significant improvement in the 
flexural strength is observed with an increase in the CFRP reinforcement 
in the overlays.
Paschalis et al. [6] conducted an experimental and numerical study 
to understand the flexural behaviour of RC beams strengthened using 
the UHPC overlay (on the tension side) with and without steel rein-
forcement. The UHPC overlay on the tension face is effective in delaying 
the cracks. However, only the marginal flexural strength is observed. 
They found that the UHPC overlay with steel reinforcement is highly 
effective in improving the flexural strength. The existing studies [23–25]
revealed that using the CFRP fabric and laminates was highly effective in 
improving the flexural performance of RC beams.
Providing UHPC overlay thickness (Fig. 2) increases the lever arm to 
the existing reinforcement, improving the flexural capacity. External 
bonding of fibre-reinforced polymer (FRP) composites on the tension 
face, in addition to the UHPC overlay on the compression side can be an 
effective hybrid strengthening solution for flexural members (Fig. 2). A 
hybrid combination of UHPC overlay and externally bonded FRP can 
significantly improve flexural performance in strength and ductility. 
FRP has several advantages, such as a high strength and stiffness-to- 
weight ratio, ease of installation, minimal labour,lightweight 
Notation
Pp Peak load
Pcr Cracking load
Py Load at yield point
Pp Load at peak load
Pu Load at ultimate point
δcr Displacement at 1st crack
δy Displacement at yield point
δp Displacement at peak load
δu Displacement at the ultimate point
L Shear span length
εt strain at the compression side of the concrete
εb strain at the tension side of the concrete
z Distance between the top fibre and bottom fibre where the 
strains are measured
Φ Curvature from experimental results
P Load from the activator
Δ Mid displacement of the beam
εm Strain of the steel/precured laminate/fabric
yic Distance between the centroid of the ith layer to the top of 
the cross-section
εic Strain in concrete at ith layer
n Number of layers assumed
B Width of the beam
Aic Area o the ith layer of concrete
Fic Force in the ith layer of the concrete
tl Thickness of the layer
Fm Force in material (steel, precured laminate and fabric)
Am Area of material
fm Stress in material
fic Stress in concrete at ith layer
fiNSC Stress in NSC at ith layer
fiUHPC Stress in UHPC at ith layer
yNA Neutral axis depth from the top of the cross-section.
ϵtf Top fibre strain
ϕ Curvature from the analytical calculation
Mpred Predicted moment from the analytical model
H Depth of the beam
ym Material level from the top of the cross-section.
COV Coefficient of variance
SD Standard deviation
[EI] Stiffness matrix calculated from moment curvature
[L] Load matrix
[M] Moment matrix
[ϕ] Curvature matrix
[S] Global stiffness matrix
[D] Displacement Matrix
Mcr,Exp Experimental cracking moment
Mcr,pred Predicted cracking moment
Mp,Exp Experimental moment capacity
Mp,pred Predicted moment capacity
Fig. 1. Comparison of particle packing of (a) NSC and (b) UHPC.
Fig. 2. Strengthening of the bridge deck using UHPC and FRP.
T.M.R. Balla et al. Engineering Structures 330 (2025) 119951 
2 
material, and corrosive resistance [26–28]. In the hybrid combination, 
the UHPC overlay also functions as a high-quality protective layer, of-
fering greater compressive strength in the compression zone and 
increasing the lever arm to the FRP materials. Thus, hybrid strength-
ening using UHPC overlay and FRP on the tension side leads to synergy 
and contributes to load resistance.
The existing studies have only focused on understanding the effect of 
UHPC overlay on the tension side. This study focuses on an innovative 
hybrid combination of UHPC overlay on the compression side and FRP 
strengthening using laminates/fabric on the tension side. The service-
ability performance of the FRP-strengthened beams in terms of crack 
width and propagation can be effectively monitored using digital image 
correlation (DIC) [3,29,30].
2. Research significance and objectives
Most of the existing studies have focused on understanding the 
enhancement of the flexural performance of RC beams using external 
bonding (EB) with FRP fabric [31] and laminates [32,33], and UHPC 
overlay [6,17,21,22]. However, combining UHPC overlay and CFRP 
strengthening is a prominent solution for addressing serviceability 
problems (deck deterioration, cracking and penetration of water and 
chlorides, etc) and strength enhancement. However, no existing studies 
have focused on understanding the behaviour of RC beams strengthened 
using UHPC overlay and FRP strengthening under flexure. It is necessary 
to investigate the performance of RC beams strengthened with UHPC 
overlay and FRP before broader implementation in the field. Hence, by 
testing five RC beams, this study examines the flexural behaviour of RC 
beams strengthened using a UHPC overlay and FRP. In addition, digital 
image correlation (DIC) is used to understand the serviceability per-
formance in minimising crack widths and propagation. Also, an 
analytical model is developed to predict the load-displacement response 
of the control and beams strengthened using different configurations of 
UHPC overlay and FRP strengthening. The results of this work will be 
beneficial in creating a test database and understanding the flexural 
behaviour of beams of strengthened with UHPC and FRP.
3. Experimental program
3.1. Test specimen details
Five RC beams sized 300 x 300 x 3500 mm are cast and strengthened 
using various configurations. Fig. 3 shows the specimen details of all the 
control and strengthened beams. Eight rebars of longitudinal rein-
forcement with a diameter of 12 mm are used. The beam includes 
transverse reinforcement with a diameter of 8 mm, spaced at 150 mm 
from centre to centre. The longitudinal and volumetric transverse 
reinforcement ratios are 1.0 % and 0.4 %, respectively. Among the five 
beams, one RC beam is labelled as control RC, as shown in Fig. 3(a). The 
UHO(C) refers to the RC beam strengthened with a 50 mm thick UHPC 
overlay on its compression surface, as shown in Fig. 3(b). The UHO(T) 
refers to an RC beam strengthened by applying a 50 mm thick UHPC 
overlay on its tension surface, which is the bottom surface, as shown in 
Fig. 3(c). The UHO(C)+PL(T) is an RC beam strengthened with a 50 mm 
thick UHPC overlay on the top surface (compression side) and three 50 x 
1.75 mm CFRP laminate on the tension surface (bottom surface), as 
shown in Fig. 3(d). The UHO(C)+FAB(T) configuration refers to an RC 
beam strengthened with a 50 mm thick UHPC overlay on the top surface 
(compression surface) and two layers of 400 g per square metre (GSM) 
CFRP fabric on the tension surface (bottom surface) as shown in Fig. 3
(e). Table 1 provides a comprehensive description of the specimen de-
tails and complete descriptions of the strengthening configuration.
Fig. 4 illustrates the sequential technique for strengthening and 
assessment processes. Firstly, steel cages are fabricated for each beam, 
and normal-strength concrete is poured and left to cure for 28 days. 
Following a 28-day water curing period, the FRP laminate/fabric is 
bonded to the bottom of the beams. The surface of the beam is rough-
ened with grooves, and shear connections of diameter 6 mm are 
installed at 150 mm c/c for proper bonding between the NSC and UHPC, 
as shown in Fig. 4(b). The details of the shear connecter are provided in 
Fig. 4(e). The 40 mm length of the shear connecter is inserted in the 
concrete, as shown in Fig. 4(e). The surface roughness index is deter-
mined using the sand-filling method [34,35]. The surface roughness 
Fig. 3. Details of the tested specimens: (a) Control RC, (b) UHO(C), (c) UHO 
(T), (d) UHO(C)+PL(T) and (e) UHO(C)+FAB(T).
Table 1 
Details of the test matrix.
S. 
No
Specimen 
ID
UHPC Overlay 
(50 mm 
thickness)
400 GSM of 
CFRP fabric 
(tension 
surface)
FRP pre-cured 
laminate (tension 
surface)
1 Control RC - - -
2 UHO(C) compression 
side
- -
3 UHO(T) tension side - -
4 UHO(C)+
PL(T)
compression 
surface
- 3 No of 
50 mm× 1.75 mm
5 UHO(C)+
FAB(T)
compression 
surface
Two layers -
T.M.R. Balla et al. Engineering Structures 330 (2025) 119951 
3 
index (SRI) of the interface formed on the surface of the beam is 
observed to be 0.34 mm. Following the completion of surface prepara-
tion, a UHPC overlay is applied to the beam, as shown in Fig. 4(c). 
UHPC-strengthened beams are water cured for 28 days. After the water 
curing period of 28 days, the beams are tested under flexure using 
four-point bending, as shown in Fig. 5(a).
3.2. Material properties
The NSC was designed with a target cube compressive strength of 
25 MPa as per IS: 10262–09 [36]. The compressive strength of NSC 
cylinders was measured by testing after 28 days of water curing. The 
concrete cubeof size 150 × 150 × 150 mm was tested per the IS: 
516–04 [37], while the cylinders of diameter 150 mm and height 
300 mm were tested according to the ASTM C39/C39M-21 [38]. The 
mean compressive strength of the three cylinders and cubes is 28.5 and 
34 MPa, respectively. UHPC used in this study is developed using locally 
available raw ingredients such as cement, fly ash, un-densified micro--
silica, and river sand. The composition and components used in this 
investigation are outlined in Table 2. The water-to-binder ratio of 0.173 
(w/b) is used for manufacturing UHPC. A poly-carboxylate-based 
admixture, a high-range water reduction agent, is added at a concen-
tration of 1.7 % of the binder content to improve flowability. Micro steel 
fibres measuring 13 mm in length and 0.2 mm in diameter enhance the 
post-peak response under compression and tension. This study uses a 
volume fraction of 1 % of steel fibres. The UHPC cube of size 
100 × 100 × 100 was tested per ASTM C1856/C1856M-17 [39]. The 
average UHPC cube compressive strength is 131 MPa after 28 days of 
water curing.
Steel reinforcement of Fe 550D grade was used. The steel rein-
forcement samples are tested using the guidelines specified in IS 1608 
(Part − 1)-22 [40]. CFRP fabric and laminate coupons are fabricated and 
tested under uniaxial tension loading as per ASTM D3039/D3039M-17 
[41]. Table 3 shows the mechanical characteristics of steel rebar, CFRP 
fabric, and CFRP laminate.
4. Test setup and instrumentation
All the control and strengthened RC beams are tested under flexural 
loading using a four-point bending setup with an MTS actuator of 
1000 kN capacity. The beams are tested under displacement control 
mode at 2 mm per minute. Fig. 5(a) depicts the test set-up and instru-
mentation details. The beams are tested with a shear span of 1350 mm, 
as shown in the schematic diagram in Fig. 5(b). Fig. 5 illustrates the 
positioning of one linear variable differential transducer (LVDT) at the 
mid-span of the beam and two LVDTs at the loading points to measure 
the displacement of beams. Additionally, two LVDTs are positioned 
horizontally on the beam to measure the deformations experienced by 
the top and bottom layers of the beam. The curvature can be determined 
from horizontal LVDTs. LVDTs are connected to a data acquisition sys-
tem (DAQ) to measure data continuously. The DAQ system is connected 
to a laptop to capture and store the data, as shown in Fig. 5.
A two-dimensional (2D) DIC technique is used to quantify strains and 
deformations occurring on the surface of the concrete. DIC is an optical 
method used to accurately quantify the changing coordinates of points 
on the surface of a specimen throughout a test. The DIC setup uses 
cameras with a high resolution of 1024 × 768 and a 50 mm lens to 
enhance the focus of photos, as shown in Fig. 5. The VIC 2D software is 
used to post the process of the collected pictures [42].
5. Experimental results
Flexural performance of the control RC strengthened with UHPC 
overlay, hybrid configurations of UHPC overlay and CFRP strengthening 
are evaluated. The load displacement, moment versus curvature, 
average crack width, and strain responses are compared to evaluate the 
performances of various strengthening configurations.
5.1. Load - displacement behaviour
Fig. 6 illustrates the load-displacement behaviour of all the tested 
beams. The displacement shown in the graph represents the vertical 
displacement at the midpoint of the span. All the strengthened RC beams 
demonstrated superior flexural capacity and increased stiffness 
compared to the control RC beam. The flexural capacity of specimens 
with overlay on the compression UHO(C) and overlay on the tension 
UHO(T) increased by 63 % and 17 %, respectively. Combining the 
overlay on the compression and laminates on the tension side, i.e., UHO 
(C)+PL(T), increased the flexural capacity by 101 %. Also, combined 
UHPC overlay on the compression and externally bonded FRP fabric on 
the tension side, i.e., UHO(C)+FAB(T), increased the capacity by 129 % 
against the control RC beam. Providing a 50 mm UHPC overlay in all the 
beams resulted in an increased lever arm, increasing flexure capacity. In 
addition, the UHO(C)+PL(T) and UHO(C)+FAB(T) exhibited a 23 % and 
41 % increase in flexure capacity, respectively, when compared to UHO 
(C). The CFRP fabric or CFRP laminate acts as the additional tensile 
reinforcement and results in an increase in the flexural capacity. Fig. 6
shows the stiffness of all the reinforced specimens is greater than the 
stiffness of the control RC beam.
The experimental findings at various test stages, including the first 
crack, yield point, peak load, and ultimate point, are summarised in 
Table 4. Fig. 7 compares loads at the first crack, yield point, and peak 
load of the tested beams. The UHO(C), UHO(T), UHO(C)+PL(T), and 
UHO(C)+FAB(T) enhanced the flexural capacity at the first crack by 
5 %, 128 %, 52 %, and 53 % respectively, when compared to Control RC 
specimen. At the yield point, the addition of UHPC in UHO(C), UHO(T), 
UHO(C)+PL(T), and UHO(C)+FAB(T) increased the flexure capacity by 
56 %, 35 %, 95 %, and 138 % correspondingly, compared to control RC 
beam. Due to the increased lever arm for the tension reinforcement with 
Fig. 4. Illustration of the casting and strengthening process: (a) reinforcement 
cage, (b) shear link and NSC surface preparation, (c) casting of UHPC, (d) beam 
after UHPC overlay, and (e) details of the shear connectors.
T.M.R. Balla et al. Engineering Structures 330 (2025) 119951 
4 
Fig. 5. Pure bending test setup and instrumentation details: (a) test setup and instrumentation details and (b) test setup schematic diagram.
Table 2 
UHPC Mix Design.
Material Cement 
(PPC)
Fly 
Ash
Micro 
Silica
River 
Sand
Steel 
Fibres
HRWRA
*
Water
Weight 
(kg/ 
m3)
670 180 180 1050 78.5 17.5 178
* HRWRA – High range water reducing agent
Table 3 
Material properties of the CFRP materials and steel rebar.
Materials Tensile strength 
(MPa)
Elastic Modulus 
(GPa)
Steel rebar 550* 200
Two-layer CFRP fabric (hand 
layup)
850 75
CFRP pre-cured laminate 2700 182
Note: *Yield Strength of the steel rebar
T.M.R. Balla et al. Engineering Structures 330 (2025) 119951 
5 
UHPC overlay, the flexural capacity of the highly under-reinforced 
cross-section significantly enhanced at crucial loads, particularly at 
the first crack, yield point, and peak load.
5.2. Energy absorption and ductility
The post-yield behaviour of the employed strengthening technique is 
assessed by measuring the energy dissipation and ductility. The integral 
of the load-displacement curve represents the amount of energy dissi-
pation. Ductility is measured by the ratio of final displacement to yield 
displacement. Fig. 8 shows the comparison of the energy dissipation of 
all the specimens. The energy dissipation of UHO(C) and UHO(C)+PL(T) 
is reported to be 21 % and 42 % higher, respectively, compared to the 
Control RC specimen. Furthermore, the UHO(C)+FAB(T) saw a decrease 
in energy dissipation due to its failure in the flexure-shear mode, as 
shown in Figs. 9 and 10(e). Table 4 presents a summary of the experi-
mental findings, including the energy absorption and ductility of all the 
specimens compared to the Control RC.
5.3. Failure modes
The comparison of the failure modes of all the tested beams is shown 
in Fig. 9. The failure modes of the tested beams and their failure sche-
matic are shown in Fig. 10. As shown in Fig. 10(a), Control RChas 
multiple flexure cracks; slight concrete crushing is observed, and the 
final load drops in Fig. 6 are due to the rupture of the steel reinforce-
ment. As shown in Fig. 10(b), UHO(C) also has multiple flexure cracks.
The final load drop in load-displacement response is due to the 
crushing of the UHPC on the top surface of the beam, as shown in Fig. 10
(b). As shown in Fig. 10(c), UHO(T) has few flexure cracks, and the NSC 
crushing observed. Progressive debonding of CFRP laminates one by one 
was observed in the UHO(C)+PL(T) specimen. It resulted in load drops, 
Fig. 6. Load displacement response of the tested beams.
Table 4 
Summary of the experimental results.
Beam Specimen ID Control RC UHO(C) UHO(T) UHO(C)+ PL(T) UHO(C) +FAB(T)
At 1st Crack Load Pcr (kN) 20.1 21.2 45.9 30.6 30.8
Displacement δcr (mm) 1.48 1.56 2.16 1.03 1.30
At yield point Load Py (kN) 76.7 119.3 103.6 149.3 182.7
Displacement δy (mm) 15.92 16.30 14.16 11.07 14.51
At Peak Load Load Pp (kN) 101.9 165.8 119.7 204.8 233.6
% increase in Pp – 63 % 17 % 101 % 129 %
Displacement δp (mm) 60.12 64.71 26.85 18.70 21.77
At Ultimate Load Pu (kN) 65.8 111.8 80.4 94.4 161.8
Displacement δu (mm) 146.22 97.20 81.33 120.11 61.41
Ductility δu/ δy 9.18 5.96 5.74 10.85 4.23
% Ductility increase – − 35 % − 37 % 18 % − 54 %
Strain Energy (kNmm) 13641 16496 8797 19410 11534
% Increase in Strain Energy – 21 % − 36 % 42 % − 15 %
Fig. 7. Comparison of the loads at the first crack, yield, and peak point.
Fig. 8. Comparison of energy absorption of all the tested beams.
T.M.R. Balla et al. Engineering Structures 330 (2025) 119951 
6 
and increasing capacity trends are observed in the UHO(C)+PL(T) 
specimen, as shown in Fig. 6. The first three load drops show the 
debonding of the three laminates. In contrast, the fourth load drop 
shows that the beam failed due to compression failure as shown in 
Fig. 10(d). The debonding failure of CFRP fabric is also observed in the 
UHO(C)+FAB(T) specimen. The specimen strengthened with the com-
bination of UHO(C) and FAB(T) failed in flexure-shear mode, as shown 
in Fig. 10(e).
5.4. DIC analysis results
5.4.1. Validation of DIC results with LVDT data
The inspection gauge is used at mid-span, as shown in Fig. 11(a). In 
Vic 2D software, the displacement values are exported to plot a load- 
displacement response. The DIC analysis results of the load- 
displacement response of all the specimens are compared with LVDT 
data, as shown in Fig. 11. From Fig. 11, it is observed that the DIC 
analysis results agree with the LVDT data.
5.4.2. Moment curvature
The moment-curvature response of all the tested beams is shown in 
Fig. 9. Failure modes of the tested beams.
Fig. 10. Schematic of beams showing the types of failure modes (a) Control RC, (b)UHO(C), (c) UHO(T), (d) UHO(C)+PL(T) and (e) UHO(C)+FAB(T).
T.M.R. Balla et al. Engineering Structures 330 (2025) 119951 
7 
Fig. 12. The moment can be calculated from the load and shear span 
length. The length of the shear span considered in this study is 1.35 m. 
Eq. (1) is used to calculate the moment. The curvature of the tested 
beams is determined using Eq. (2). 
M = PL/2 (1) 
Here, P is load in (kN) and L in is shear span length in m 
Φ =
εt − εb
z
(2) 
Where Φ is the curvature in ( 1
mm),
εt is the strain at the compression side of the concrete,
εb is strain at the tension side of the concrete.
z is the distance between the top fibre and bottom fibre where the 
Fig. 11. Validation of the DIC analysis data with mid-span LVDT data (a) inspection gauge for data extraction, (b) Control RC, (c) UHO(C), (d) UHO(T), (e) UHO(C)+
PL(T) and (f) UHO(C)+FAB(T).
T.M.R. Balla et al. Engineering Structures 330 (2025) 119951 
8 
strains are measured.
The curvature data is derived from the measurements obtained from 
the LVDTs or by DIC analysis. Fig. 13 displays the measurements of εt , εb, 
and z obtained by DIC analysis of the beam. Similarly, the curvature is 
computed for each beam, and the moment-curvature behaviour of all the 
beams is computed (Fig. 12). Fig. 12 shows that the stiffness of all the 
strengthened beams is superior to that of the control RC specimen. The 
correlation is lost in the DIC analysis for Control RC, UHO(C), and UHO 
(C)+PL(T) specimens near the ultimate load due to significant cracking. 
The flexural cracks are initially observed in the UHO(C)+FAB(T) spec-
imens. However, the failure mode is shifted to flexure-shear after the 
peak load as shown in Fig. 10(e). The flexure-shear cracks are formed 
under the loading point. It results in a reduction in the flexural cracks 
after the peak load. Therefore, all the UHO(C)+FAB(T) responses 
(moment-curvature and load vs crack width) are terminated after 
reaching the peak load.
5.4.3. Strain at bottom longitudinal rebar level
The load versus strain relationship for all the beams is shown in 
Fig. 14(a). Fig. 14(b) shows the load-strain response up to the strain 
value of 0.02. The strain is determined using DIC analysis by placing the 
strain gauge at the longitudinal steel level, which is 34 mm from the 
bottom surface of the beam, as shown in Fig. 15. The correlation was lost 
in the DIC analysis for Control RC, UHO(C), and UHO(C)+PL(T) speci-
mens near the ultimate point.
The load vs strain response is the same in Control RC and UHO(C) till 
the NSC is cracked as the same amount of steel reinforcement is used. 
After the NSC cracked, and the strain in the Control RC specimen 
increased compared to UHO(C). The load-strain response of the UHO(T) 
is stiffer than that of a Control RC beam as UHPC overlay is used on the 
tension side of a beam and it has higher tensile strength compared to the 
NSC. After the initial cracking in the UHPC bottom layer of UHO(T), the 
strain increase and stiffness reduction are observed due to the strain 
localization phenomenon, as shown in Fig. 14(b). The stiffer load-strain 
responses are observed in the hybrid configurations (UHO(C)+PL(T) 
and UHO(C)+FAB(T)) compared to another specimen, as shown in 
Fig. 14. The CFRP pre-cured laminate and fabric act as additional 
reinforcement. It results in higher flexural rigidity and higher flexural 
capacity.
5.4.4. Crack width and number of cracks
The crack width of beams is crucial in maintaining structural integ-
rity, longevity, aesthetics, serviceability, and safety. The crack widths of 
all the beams are assessed by DIC analysis since it is not feasible to 
evaluate them using LVDTs. Two inspection gauges were installed to 
record lateral deformation at every crack, as shown in Fig. 16(a). The 
relative displacement of the average lateral displacements of the left 
gauge and right gauge is the average crack width, as shown in Fig. 16(b). 
UHO(C)+PL(T) combination is used as an example to determine the 
average crack width of the beam analysed in this study, as shown in 
Fig. 16(b). The load vs average crack width response of all the beams is 
shown in Fig. 17.
The load resistance, with an average design crack width of 0.3 mm 
increased proportionally based on the type of strengthening scheme. The 
design crack width of 0.3 mm is considered as per EN 1992–1–1 [43]
and IS 456 [44]. Beams such as Control RC, UHO(C), UHO(T), UHO(C)+
PL(T), and UHO(C)+FAB(T) had 54 kN, 96 kN, 72 kN, 154 kN, and 
Fig. 12. Moment curvature response of thetested beams.
Fig. 13. Installation of the strain gauge for curvature calculation.
Fig. 14. Load-strain response of the tested beams (a) failure and (b) strain up to 
0.020 (Zoomed portion).
Fig. 15. Strain gauge installation at rebar level for extracting strains from 
DIC analysis.
T.M.R. Balla et al. Engineering Structures 330 (2025) 119951 
9 
178 kN, respectively at crack width of 0.3 mm. In addition, UHO(C)+PL 
(T) and UHO(C)+FAB(T) exhibited greater load-carrying capability than 
Control RC, UHO(T) and UHO(C) for all average crack widths. Thus, it 
can be concluded that the combination of UHO(C) and PL(T), as well as 
UHO(C) and FAB(T), significantly enhanced the serviceability perfor-
mance in terms of lesser crack widths at a particular load or had higher 
load resistance at a particular crack width.
Fig. 18 displays the number of cracks observed in the pure bending 
region of the control and strengthened beams at three critical stages: 
yield, peak, and ultimate load points. In the Control RC beam, cracks 
increase steadily from the yield point to the ultimate load. This behav-
iour indicates limited crack control, with the cracks progressively 
forming as the load increases. The number of cracks remains relatively 
stable across the loading stages in UHO(C) and UHO(T). In UHO(C)+PL 
(T) and UHO(C)+FAB(T), the cracks increase moderately from the yield 
to the peak point and then stabilize at the ultimate load. The efficiency 
of the strengthened systems can be observed from more distributed 
cracks formed in the strengthened beams than in the Control RC beam, 
as shown in Fig. 19.
5.4.5. Crack propagation and strain contours
The crack propagation and the strain contours of the beams at critical 
points such as the first crack, yield point, peak load are shown in Fig. 19. 
In Fig. 19, negative values of the strains represent compressive strains, 
and positive values represent tensile strains. The strain contours of the 
beams are obtained from the DIC analysis. Fig. 19 shows that the strains 
in the strengthened beams are much lower than those in the Control RC 
beam. Crack propagation of the control RC and UHO(C) is similar. The 
crack propagation in the hybrid configuration (UHO(C)+PL(T) and UHO 
(C)+FAB(T)) strengthened specimens is much lower than the Control RC 
and UHO specimens as CFRP materials resist crack propagation on the 
tension face. The concrete compression (crushing) failure was observed 
in both UHO(C) and UHO(C)+PL(T). Since the failure of UHO(C)+FAB 
(T) is in the flexure-shear mode, the propagation of flexural cracks in the 
bending area is limited.
5.4.6. Depth of neutral axis
The effectiveness of the strengthening techniques can be investigated 
by analysing the neutral axis and crack depth using the DIC analysis. 
Fig. 20(a) illustrates the distribution of the compressive and tensile 
zones across the depth of the beam through DIC analysis. The neutral 
axis is the location at which there is no strain. Hence, the compression 
and tension zone depth is determined based on the most significant 
critical crack in the beams. Fig. 20 illustrates the comparison of the 
compression zone and tension zone depth across the beam at yield, peak, 
and ultimate load.
The beam was considerably under-reinforced, and the tension zone 
increased significantly at all crucial points. UHPC being is a high- 
strength and stiff material, so the compression zone of UHO(C) is 
much less than the compression zone of the Control RC beam. Fig. 20(b) 
shows that at the yield point, the compression zone of the UHO(C) is less 
than the UHO(C)+PL(T) and UHO(C)+FAB(T). This is because the FRP 
strengthening is applied on the tension surface, which prevents crack 
propagation and restricts the tensile stress over the depth. By examining 
Fig. 20(c) and (d), it is noted that the tension zone in UHO(C) increases 
from the yield point to the peak point. The tension zone in the UHO(C) 
specimen does not experience a significant rise from the peak to the 
ultimate point, as it fails due to compression failure, as shown in Figs. 10
(b) and 19. The increase in the tension zone from the peak to ultimate in 
UHO(C)+PL(T) is minimal due to the concrete compression failure, as 
shown in Figs. 10(d) and 19. There is no significant increase in the 
tension zone from the peak to the ultimate point in the UHO(C)+FAB(T) 
specimen as it fails in flexure-shear mode.
5.4.7. Interface slip between UHPC-NSC
Interface slip is a critical parameter for UHPC overlay beams as it 
Fig. 16. Evaluation of critical crack width using DIC analysis: a) location of 
inspection gauges (b) typical average crack width calculation of UHO(C) +PL 
(T) specimen.
Fig. 17. Load – average crack width response of the tested beams.
Fig. 18. Comparison of the number of cracks of the beams at critical loads.
T.M.R. Balla et al. Engineering Structures 330 (2025) 119951 
10 
Fig. 19. Strain contours and crack propagation of beams at different critical points.
Fig. 20. Comparison of change in compression and tension zone over the depth of the beam (a) measurement of compression and tension zone, (b) at yield point, (c) 
at peak point, (d) at the ultimate point.
T.M.R. Balla et al. Engineering Structures 330 (2025) 119951 
11 
directly affects the stress transfer between the NSC and UHPC layers. 
The interface slips between UHPC and NSC of all the strengthened 
beams are assessed using DIC analysis. Two inspection gauges were 
installed to record lateral deformation at three positions, as shown in 
Fig. 21(a). The relative lateral deformation of the top gauge (TG) in 
UHPC and bottom gauge (BG) in NSC is the interface slip between UHPC 
and NSC. The interface slip considered in Fig. 21(b) is the average 
interface slip of three positions.
The interface slips between UHPC-NSC for UHO(C), UHO(T), UHO 
(C)+PL(T) and UHO(C)+FAB(T) at peak load is 1.33, 0.1, 0.07 and 
0.09 mm respectively. It shows that the NSC-UHPC interface with 
grooves and shear links is very effective in stress transfer even in the 
hybrid configurations (UHO(C)+PL(T) and UHO(C)+FAB(T)). The 
hybrid specimens exhibit the highest load-carrying capacity and 
moment resistance with minimal slip, emphasizing the effectiveness of 
this configuration in stress transfer and structural performance.
6. Analytical study
An analytical approach is developed using the Python program [45]
to predict the moment-curvature and load deflection behaviour of the 
control RC and strengthened beams. The model fairly estimates the 
moment-curvature relationship based on material stress-strain parame-
ters. The moment-curvature response is developed using a layer-by-layer 
technique.
6.1. Constitutive relations of materials
The multi-linear model is used for the stress-strain response of the 
UHPC in compression. [46,47]and tension, as shown in Fig. 22(b) [15]. 
The parabolic model [48] is used for the compressive stress-strain 
response of the NSC, as shown in Fig. 22(a). Tensile stress-strain is 
taken as linear up to 10 % of the peak strength. After the peak tensile 
strength of NSC response is assumed to be zero, it is assumed that the 
elastic modulus of NSC in tension is equal to the elastic modulus in 
compression. A bi-linear approach was adopted in both compression and 
tension for the steel reinforcements, asshown in Fig. 22(c). The tensile 
stress-strain of CFRP laminate is shown in Fig. 22(d).
6.2. Cross-section analysis
6.2.1. Strain compatibility
UHPC and NSC are assumed to have perfect bonds, and test results 
showed an agreement with the assumption. Consequently, it will follow 
the strain compatibility at the interface of UHPC and NSC. Hence, it is 
postulated that the strain distribution is linear across the beam’s cross- 
sectional area. A layer-by-layer approach is followed, and the beam is 
divided into ‘n’ number of layers. In this investigation, the number of 
layers is set to 10,000. Therefore, the thickness of each layer is 0.03 for 
Control RC beams and 0.035 for other strengthened beams. As shown in 
Fig. 23, strain in the ith layer of the concrete is given by εic. Eq. (3) is used 
to calculate εic it is derived from similar triangles. 
εic = εtf
(
1 −
yic
yNA
)
(3) 
Where εic is strain in concrete at ith layer, εtf is the top fibre strain in 
concrete, yic is the distance between the centroid of the ith layer to the 
top of the cross-section as shown in Fig. 23. yNA is the neutral axis depth 
from the top of the cross-section. The neutral axis is the point where the 
strain at the point is zero as shown in Fig. 23. 
εm = εtf
(
1 −
ym
yNA
)
(4) 
Eq. (4) is used to calculate the strain in the steel rebar, CFRP fabric, 
and CFRP laminate where εm is the strain of the steel/FAB/PL at ym 
distance from the top of the cross-section to the steel/PL/FAB level. 
From the strains calculated above, concrete, steel, fabric, and laminate 
stresses are calculated from their respective stress-strain relationship.
6.2.2. Calculation of forces in concrete
Force and the area of the ith layer of concrete can be calculated by 
Eqs. (5) and (6). 
Fic = fic × Aic (5) 
Aic = tl × b (6) 
Here, Fic is a force in the ith layer of the concrete, b is the width of the 
cross-section 300 mm for all the beams and tl is the thickness of the 
layer, tl = d
n. In the equations, d is the depth of beam which is 300 mm 
for control RC and 350 mm for all other strengthened specimens. The 
stress in UHPC/NSC is taken as fic
fic = fiNSC for Control RC specimen
For UHO(C), UHO(C)+PL(T), and UHO(C)+FAB(T)
fic = fiUHPC if tl × i ≤ 50 mm, fic = fiNSC if tl × i > 50 mm
For UHO(T)
fic = fiNSC if tl × i ≤ 300 mm, fic = fiUHPC if tl × i > 350 mm
Where i is the layer number.
6.2.3. Calculation of force in reinforcement (steel rebar, CFRP fabric and 
laminate)
Force in the reinforcement can be calculated by Eq. (7)
Fm = fm ∗ Am (7) 
Where Fm is the force in the material. Am is an area of the material. where 
m is equal to st1, st2, st3, fab, and pl for three levels of steel reinforce-
ment, fabric and pre-cured laminate respectively as shown in Fig. 23. For 
equilibrium, the summation of forces in concrete and steel/Fabric/pre- 
cured laminate should be zero, should satisfy the Eq. (8). 
Fig. 21. Load – interface slip between UHPC-NSC (a) location of inspection 
gauges for evaluating interface slip (b) load – interface slip response of the 
tested beams.
T.M.R. Balla et al. Engineering Structures 330 (2025) 119951 
12 
∑
Fic +
∑
Fm = 0 (8) 
Since the layer-by-layer approach is followed in the calculation of 
forces, the value on the left-hand side of the equation may not precisely 
match the right-hand side of the equation. Hence, some tolerance values 
must be chosen to achieve convergence. In calculating all the results, a 
tolerance of 10− 5 N is assumed. The moment and curvature can be 
calculated by the Eqs. (9) and (10), respectively. 
Mpred =
∑
Fic ∗
(
H
2
− yic
)
+
∑
Fm ∗
(
H
2
− ym
)
(9) 
ϕ =
ϵtf
yNA
(10) 
Where H = depth of the beam
ym is the material level from the top of the cross-section.
Fig. 24 shows the moment-curvature behaviour of both the experi-
mental data and the analytical prediction. It is assumed that the CFRP 
pre-cured laminate and CFRP fabric are delaminated after they achieve 
the tensile strains of 0.00538 and 0.0087, respectively, based on the 
experimental observations. For peak load, the difference between the 
experimental and analytical results for Control RC, UHO(C), UHO(C)+
PL(T), and UHO(C)+FAB(T) is 8 %, 4 %, 2 %, and 1 %, respectively. The 
peak moment resistance exhibited a maximum variance of less than 8 % 
in all specimens. In general, the analytical predictions of moment- 
curvature responses are in good agreement with the experimental re-
sponses. The moment-curvature relationship obtained from the section 
analysis is limited to a certain range of curvature as the concrete ulti-
mate stain value is limited in the analytical models. However, the 
redistribution of stresses is expected in the member after the concrete 
reaches the maximum strain value.
Table 5 compares the experimental and analytical predictions for the 
first crack and peak load. Table 5 also presents the mean, standard de-
viation (SD) and coefficient of variance (COV) of Mexp/Mpred values at 
cracking and peak point. The mean, SD and COV of Mcr,Exp/Mcr,pred are 
1.030, 0.054 and 0.052 respectively. The mean, SD and COV of Mp,Exp/ 
Mp,pred are 1.020, 0.040 and 0.039 respectively. Therefore, the proposed 
analytical model could predict the cracking moment and moment 
Fig. 22. Constitutive relations of materials (a) NSC, (b) UHPC, (c) steel, (d) CFRP laminate.
Fig. 23. Cross-sectional analysis of one of the beams: (a) beam cross-section; (b) strain profile; (c) NSC stress diagram; (d) UHPC stress diagram; (e) Rebar/FRP stress.
T.M.R. Balla et al. Engineering Structures 330 (2025) 119951 
13 
capacity of all the strengthened beams with COV of 5.24 and 3.94 %, 
respectively.
6.3. Member-level analysis
The moment-curvature data obtained from the cross-sectional anal-
ysis are used as input for member-level analysis. Fig. 25 shows the 
flowchart for computing load-displacement response using member- 
level analysis. The steps for member-level analysis followed in this 
paper are explained below. The stiffness matrix method is used in this 
study to compute load displacement using the moment-curvature 
response of the control and strengthened beams. Initially, EI is calcu-
lated from the moment-curvature response obtained from the cross- 
sectional analysis. The boundary conditions of the hinge and roller are 
considered at the supports. The beam is divided into n number of ele-
ments. In the first step (starting with k = 1), the load matrix [L] is 
defined by applying the load value of M[k]/1.35 at x = 1.35 m and at 
x = 1.95 m. Here, M[k] represents the kth moment value in the moment 
matrix. For computing the element stiffness matrix, EI is interpolated 
from the EI matrix for ϕi. The curvature at the ith element, ϕi is extracted 
from the assumed curvature profile, as shown below. 
Forx ≤ 1.35 m ϕi = ϕ[k] ×
(x
a
)D 
1.35 1.95 m ϕi = ϕ[k] ×
(
L − x
a
)D 
Where L = 3.3 m, a = shear span(1.35 m), D =
max(EI)
EI[k]
The element stiffness matrix for all the elements is assembled to form 
the global stiffness matrix [S]. The displacement D matrix is computed 
by using Eq. (11). 
[D] = [S− 1][L] (11)
Mid-span displacement is calculated using Eq. (11), and load value is 
calculated using P =
M[k]×2
a . The above process is followed for all the 
curvature values in the ϕ matrix by incrementing k with 1 up to 
k = length of ϕ matrix. Fig. 26 shows the comparison of load- 
displacement behaviour of experimental and analyticalresults of all 
the tested beams. The maximum variation of 8 % is observed between 
the analytical predictions and experimental results of all the specimens. 
Thus, the analytical predictions are in good agreement with the exper-
imental results.
7. Summary and conclusions
The effect of different configurations of UHPC overlay and FRP 
composite strengthening on the flexural behaviour of RC beams was 
studied. In addition, both sectional and member-level analyses of all the 
tested configurations were carried out. Predictions from moment- 
curvature analysis and load-displacement behaviour were compared 
with the experimental results. The effectiveness of the different 
strengthened configurations in improving the serviceability perfor-
mance in terms of crack widths and propagation was evaluated using the 
DIC analysis. The following conclusions can be drawn based on the re-
sults presented in this study: 
Fig. 24. Comparison of experimental and analytical Moment-Curvature results (a) Control RC, (b) UHO(C), (c) UHO(T), (d) UHO(C)+PL(T) and (e) UHO(C)+FAB(T).
Table 5 
Comparison of the experimental and analytical at cracking and peak load.
Specimen ID Mcr, 
Exp 
(kNm)
Mcr, 
Pred 
(kNm)
Mcr, 
Exp/ 
Mcr pred
Mp Exp 
(kNm)
Mp, Pred 
(kNm)
Mp,Exp/Mp, 
Pred
Control RC 13.6 14.1 0.97 68.8 63.5 1.08
UHO(C) 14.3 13.1 1.09 111.9 107.1 1.04
UHO(T) 30.9 31.4 0.98 80.81 83.3 0.97
UHO(C)+PL 
(T)
20.6 19.7 1.05 138.3 136.1 1.02
UHO(C)+FAB 
(T)
20.8 19.4 1.07 157.7 155.6 1.01
Mean - - 1.03 - - 1.02
SD - - 0.054 - - 0.040
COV (%) - - 5.24 - - 3.94
Note: SD: Standard Deviation and COV: Coefficient of Variance.
T.M.R. Balla et al. Engineering Structures 330 (2025) 119951 
14 
• Specimen strengthened with UHPC overlay on the compression side 
was highly effective in improving the flexural capacity by 63 % 
compared to the control RC specimen.
• A marginal flexural strength improvement of 17 % is observed for 
the beams strengthened with only UHPC overlay on the tension side. 
UHPC overlay on the tension side. Also, they effectively improve 
serviceability performance with lesser crack widths and deflection 
compared to the control RC beam.
• Both experimental and analytical results showed that a hybrid 
combination of UHPC overlay and FRP composites is highly effective 
in enhancing the strength and ductility in flexure.
• The flexural capacity increased by 101 % and 129 % for specimens 
strengthened with a hybrid combination of UHPC overlay with CFRP 
laminates (UHO(C) +PL(T)) and CFRP fabric (UHO(C)+FAB(T)), 
respectively compared with control RC beam.
• DIC analysis results show that the beams strengthened with the 
hybrid configuration of UHPC overlay and CFRP on the tension side 
are highly effective in enhancing the serviceability performance. It 
leads to lesser crack widths and crack propagation than specimens 
strengthened only with UHPC overlay.
• The hybrid specimens UHO(C) +PL(T) and UHO(C)+FAB(T) 
improved the flexural capacity by 154 % and 219 %, respectively, at 
the design crack width of 0.3 mm compared with the control RC 
beam.
• The interface preparation with grooves and shear connectors of 
6 mm diameter is very effective in stress transmission between NSC 
and UHPC. Minimal interface slip observed in all specimens high-
lights the critical role of proper surface preparation for UHPC overlay 
applications.
• The proposed analytical model accurately predicted the cracking 
moment and moment capacity of all the strengthened beams with a 
mean of 1.03 and 1.02 and coefficient of variation(COV) of 0.05 and 
0.04, respectively.
CRediT authorship contribution statement
Shanmugam Suriya Prakash: Writing – review & editing, Valida-
tion, Methodology, Investigation, Funding acquisition, Conceptualiza-
tion. Morthala Rahul Reddy: Writing – original draft, Visualization, 
Validation, Investigation, Formal analysis, Data curation. Balla Taraka 
Malleswara Rao: Writing – original draft, Visualization, Validation, 
Methodology, Investigation, Formal analysis, Data curation, 
Conceptualization.
Fig. 25. Flow chart for member-level analysis for computing load-displacement response.
T.M.R. Balla et al. Engineering Structures 330 (2025) 119951 
15 
Declaration of Competing Interest
We have no conflict of interest to declare
Acknowledgments
The authors thankfully acknowledge the NCC (Nagarjuna Construc-
tion Company) CSR Grant and the National Highways Authority of India 
(NHAI) for providing scholarships to the first two authors. The authors 
also wish to acknowledge The Bhor Chemicals and Plastics Pvt. Ltd for 
providing FRP materials. The authors would like to acknowledge the 
NCC CSR Grant and NHAI Transportation Research and Innovation Hub 
(TRI HUB) G480-G for funding the experimental part of this work. The 
authors want to acknowledge the help provided by Dr. Nikesh Tham-
mishetti in the critical review of the work. The authors also acknowledge 
the help provided by Mr. M Muthuraja during casting.
Data availability
Data will be made available on request.
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FAB(T).
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	Enhancing flexural performance of reinforced concrete beams using UHPC overlay and external bonding of CFRP composites
	1 Introduction
	2 Research significance and objectives
	3 Experimental program
	3.1 Test specimen details
	3.2 Material properties
	4 Test setup and instrumentation
	5 Experimental results
	5.1 Load - displacement behaviour
	5.2 Energy absorption and ductility
	5.3 Failure modes
	5.4 DIC analysis results
	5.4.1 Validation of DIC results with LVDT data
	5.4.2 Moment curvature
	5.4.3 Strain at bottom longitudinal rebar level
	5.4.4 Crack width and number of cracks
	5.4.5 Crack propagation and strain contours
	5.4.6 Depth of neutral axis
	5.4.7 Interface slip between UHPC-NSC
	6 Analytical study
	6.1 Constitutive relations of materials
	6.2 Cross-section analysis
	6.2.1 Strain compatibility
	6.2.2 Calculation of forces in concrete
	6.2.3 Calculation of force in reinforcement (steel rebar, CFRP fabric and laminate)
	6.3 Member-level analysis
	7 Summary and conclusions
	CRediT authorship contribution statement
	Declaration of Competing Interest
	Acknowledgments
	Data availability
	References