Pile caps with inclined shear reinforcement and steel fibers

Abstract

This experimental investigation presents results and a discussion on a series of four reinforced concrete pile caps with and without steel fibers, measuring 400 × 400 × 1000 mm³, which were tested under concentric loading. The study set the steel fiber and the inclined shear reinforcement as variables. The fiber volume fraction was 1.5%, and the concrete compressive strength was 25 MPa. The results showed a tendency to increase ductility and ultimate strength with the use of inclined shear reinforcement; the same behavior was observed with the addition of steel fibers, improving the performance of the tested pile caps. This study opens the possibility of designing slender pile caps, especially when associated with both analyzed parameters.

Full text

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Pile caps with inclined shear
reinforcement and steel bers
Aaron Nzambi1*, Lana Gomes1, Cledinei Amanajás1, Francisco Silva2 & Dênio Oliveira1
This experimental investigation presents results and a discussion on a series of four reinforced
concrete pile caps with and without steel bers, measuring 400 × 400 × 1000 mm3, which were tested
under concentric loading. The study set the steel ber and the inclined shear reinforcement as
variables. The ber volume fraction was 1.5%, and the concrete compressive strength was 25 MPa.
The results showed a tendency to increase ductility and ultimate strength with the use of inclined
shear reinforcement; the same behavior was observed with the addition of steel bers, improving the
performance of the tested pile caps. This study opens the possibility of designing slender pile caps,
especially when associated with both analyzed parameters.
Foundations are among the most important structural elements used for load transfer from a building to piles or
caissons. Pile caps can be classied as rigid or exible based on criteria similar to those used for shallow founda-
tions. erefore, the larger and more rigid the structure is, the more complex its design becomes. According to
NBR 61181, rigid pile caps are not prone to diagonal tension failure; most oen, failure occurs in compression
struts2. However, some doubt remains as to whether this behavior can be modied with strut strengthening. In
the literature, studies3–5 have suggested limiting the height of the block as a function of the angle of inclination
of the strut, ranging from 45° to 55°; this may result in an overdesign of the structure. Fighting the shear cracks
through reinforcement mechanisms that can improve the performance of the blocks is an ideal way to optimize
the design and safety of such structural elements. is can be achieved by using shear reinforcement and/or steel
bers to improve the mechanical properties of concrete in terms of shear, compression, and exure; in addi-
tion, steel ber reinforced concrete (SFRC) enhances performance in energy absorption, cracking control, and
ductility6,7. e use of SFRC is being expanded, and its applications range from oor pavements to special struc-
tural elements or those subjected to an aggressive or corrosive environment without aecting their durability8.
us, this experimental study explores the eectiveness of inclined reinforcement and the contribution of steel
bers in improving the performance of concrete pile caps subjected to shear forces since, economically, a consid-
erable gain in strength increase can make this approach feasible and decrease the volume of concrete in pile caps.
Calculation model
In the present study, the pile caps were designed using the strut-and-tie method (STM), which is the most
widespread calculation model for the design of rigid pile caps. is design is based on the experimental works
previously developed by Blévot and Frémy4. e model consists of designing a spatial truss inside a pile cap using
tension and compression bars that are connected through nodes, as shown in Fig.1.
e eective depth (d) of the pile cap is given by Eq.1. To ensure adequate structural behavior of the pile
cap, Blévot and Frémy4 recommended that θ should be within a 45° ≤ θ ≤ 55° range. For the minimum spacing
between the piles adopted in the work, the distance L was equal to three times the edge distance of the pile (D),
according to the recommendations of Moraes9, (L ≥ 3⋅D).
where
L
is the spacing between piles;
ac
is the larger side of the column.
e determinations of the acting stresses near the column and the pile are calculated through Eqs.(2) and
(3), respectively. e equations also dene the normative verication limits for the design.
(1)
d
=tan θ·
(
0.5 ·
L
−0.25 ·a
c)
(2)
σ
u,tc =
F
d
Ac·
sin2θ≤1.4 ·f
c
OPEN
1Department of Civil Engineering, Federal University of Pará, Belém, PA 66075-110, Brazil. 2Department of Civil
Engineering, University of Amazônia, Belém, PA 66065-205, Brazil. *email: aaronkadima@gmail.com
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where
σu,tc
and
σu,tp
represent the failure stresses of the strut in the regions of the column and the pile, respec-
tively; Ac and Ap are the cross-sectional areas of the column and the pile, respectively; Fd is the design load; and
fc is the concrete compressive strength.
e longitudinal reinforcement area of the tie over the piles was calculated according to Eq.(4). Equation(5),
proposed by Delalibera and Giongo10, was used to calculate the tensile force in the tie.
where Ast is the total area of longitudinal steel reinforcement in the tie, Rst is the tensile force on the tie, and fys
is the yield strength of the longitudinal steel reinforcement.
Experimental setup
Materials and methods. Cement, coarse aggregate, ne aggregate, and water–cement ratio (w/c) were
mixed in a 1:2.90:2.10:0.55 proportion. Superplasticizer additive was used to maintain the constant workability
of concrete. Table1 lists the constituents used for the mixtures, and Table2 lists the mechanical properties of
the crimped steel ber. Flat crimped type C ber (Fig.2), classied according to NBR 1553011, was used in this
research because, according to Soroushian and Bayasi12 and Mahakavi and Chithra13, hooked-end and crimped
bers are more eective at improving the performance of structural elements as a result of their additional
anchoring mechanisms14. e concrete test specimens were molded and cured for 28days in the laboratory with
85% relative air humidity. Table3 presents the results of the characterization tests at 7, 14, and 28days. ere was
no signicant dierence between the plain concrete and the concrete with ber, so average values were adopted
for both mixtures: 25.8MPa, 1.9MPa, and 28.4 GPa, respectively, for compressive strength (fc), tensile strength
(fct), and modulus of elasticity (Ec).
e steel bars used in the tests were classied according to NBR 748015. eir mechanical properties were
determined through axial tensile tests, following the recommendations of NBR ISO 6892-116. ree samples were
used in the tensile test; the test bars measured 5.0mm, 10.0mm and 12.5mm in diameter and were used in the
stirrups, inclined shear reinforcement and exural reinforcement, respectively. Table4 presents the mechanical
properties of the steel used.
(3)
σ
u,tp =
F
d
2·A
p
·sin2θ≤0.85 ·f
c
(4)
A
st =
R
st
fys
(5)
R
st =
F
d·
(2L
−
a
c
)
8·d
Figure1. Strut-and-tie model for a two-pile cap (Note: Fd/2 is the column load for a pile; Rcb is the compressive
force on the strut; Rst is the tensile force on the tie; θ is the angle of inclination of the strut).
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Table 1. Composition of concrete. w/c = 0.55 for all mixtures and slump test workability 140mm;
*Vf = 1.5% = 117.75kg/m3, Cf = Vc × Vf = 0.729 m3 × 117.75kg/m3 = 85.84kg; ρ is the density; Cf is the ber
consumption; Vc is the volumetric fraction of the concrete; and Vf is the volumetric fraction of the ber.
Constituents Typ e ρ (kg/m3)
Weight per unit volume (kg)
Mixture 1 Mixture 2
Cement Portland CPII-Z-32RS 3100 269.52 269.52
Small aggregate Sand (avg. 2.7mm) 2830 781.62 781.62
Large aggregate Coarse aggregates (dmax = 10mm) 2600 566.00 566.00
Fiber Crimped steel ber 7850 – 85.84*
Admixture Superplasticizer – – –
Wat er pH < 9 1000 148.24 148.24
Table 2. Mechanical properties of crimped steel bers. df = equivalent diameter of ber; lf = ber length;
lf/df = aspect ratio; fu,f = ultimate tensile strength of ber; and Ef = elastic modulus of ber.
df (mm) lf (mm) lf/dffu,f (MPa) Ef (GPa)
~ 1.0 38.0 38.00 900.00 200.00
Figure2. Flat crimped steel ber. (Reprinted with permission from Nzambi etal.14.
Table 3. Results for characterization of concrete (avg. values).
Age of concrete (Days) Number of cylindrical specimens fc,m (MPa) fct,m (MPa) Ec (GPa)
07
3
14.30 1.24 21.18
14 16.90 1.38 23.02
28 25.80 1.90 28.44
Table 4. Mechanical properties of the reinforcements used. ∅s = steel bar diameter; εys = strains; fys = yield
stresses; fus = ultimate tensile strength of steel bar; Es = modulus of elasticity.
∅s (mm) εys (‰) fys (MPa) fus (MPa) Es (GPa) Location
5.0 4.63 529.50 550.00 201.70 Stirrups
10.0 2.42 500.00 556.00 206.61 Inclined shear reinforcement
12.5 3.05 610.30 716.00 200.00 longitudinal reinforcement
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Characteristics of the samples. e design of the pile caps followed the strut-and-tie method presented
in “Calculation model” section4. e dimensions were constant for all pile caps, as shown in Table5. e column
located on the upper surface of the piles had a cross-section of 200 × 200 mm2 with a height of 250mm. e
piles had the same dimensions for the cross section, but their height was 200mm (Figs.3, 4). e compressive
strength of the concrete was 25.8MPa for all pile caps mixtures. e longitudinal reinforcement and horizontal
and vertical stirrups were the same. Pile caps PC03SFRC+IR and PC04IR were made with two inclined bars with a
diameter of 10.0mm. e spacing between the bars was 100mm, and each bar had a length of 1000mm. e
following are the other characteristics of each pile cap:
• PC01REF: concrete cast without the addition of steel ber and inclined shear reinforcement, as shown in
Fig.3a;
Table 5. General characteristics of the pile caps. NOTE: REF = reference (plain concrete); SFRC = steel ber
reinforcement concrete; and IR = inclined reinforcement.
Pile cap ac (mm) d (mm) b (mm) h (mm) l (mm) L(mm) Vf (%) Inclined shear reinforcement
PC01REF
200 350 400 400 1000 600
– –
PC02SFRC 1.5 –
PC03SFRC+IR Yes
PC04IR –
Figure3. Details of the two-pile caps.
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• PC02SFRC: concrete cast with the addition of steel ber (Vf = 1.5%) but without inclined shear reinforcement,
as shown in Fig.3b;
• PC03SFRC+IR: concrete characteristic equal to PC02SRC + inclined shear reinforcement, as shown in Fig.3c;
• PC04IR: concrete characteristic equal to PC01REF but with inclined shear reinforcement, as shown in Fig.3d.
Instrumentation. e strains in the steels were measured using electrical resistance strain gauges (EESG,
EXCEL Sensors, PA-06-125AA-120L), positioned as shown in Fig.5. erefore, one strain gauge was installed in
the middle of the central exural reinforcement bar, one in the inclined shear reinforcement bar, and one in the
vertical stirrup at the level of the point of intersection with the inclined reinforcement (Fig.6a), to be in the same
stress line caused by the compression strut. e vertical displacements were measured using a deectometer
placed at the bottom of the pile caps at a distance of l/2 = 500mm, as shown in Fig.6b. Figure7 shows the nal
aspect of the pile caps ready for testing.
Test setup. All pile caps were subjected to centered loading and applied on the face of the column. e test
setup was composed of a hollow hydraulic jack and a hydraulic pump (Enerpac). Both the jack and the pump
had a 1000kN capacity, a digital load cell for 1000kN, a precision of 500N and an Amsler testing machine used
as the gantry system. Figure8 shows the test system. In all test specimens, an initial load was applied to eliminate
looseness.
Figure4. Pile cap dimensions (in mm).
Figure5. Position of strain gauges on the reinforcements: (a) for PC01REF and PC04IR and (b) for PC02SFRC and
PC03SFRC+IR.
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Results and discussion
Table6 presents the results of the experimental bearing capacity. In terms of strength gain, PC02SFRC and PC04IR
presented an increase in the ultimate strength of approximately 40% compared to block PC01REF. Furthermore,
the bers increased the load-bearing capacity of the PC03SFRC+IR pile cap by 7% when used with inclined rein-
forcement compared to PC04IR.
Load–displacement ratio and tenacity. is study focused only on the displacement in the center of
the pile caps (l/2 = 500mm); this way, the analyses were made based on the load–displacement (V − δ) ratio and
the quantities that characterize this ratio. Although PC02SFRC and PC04IR had almost the same ultimate strength,
Table7 and Fig.9 show a slight decrease in displacements with the addition of steel ber; this eect was more
pronounced with PC03SFRC+IR, which showed lower displacements, at a 20%, and 44% reduction, respectively,
compared to PC01REF and PC04IR.
An analysis was made of tenacity (TE), that is, the capacity of the pile caps to absorb strain energy (Table7),
based on the TE,Pilecaps/TE,REF ratio. Clearly, the bers and the inclined reinforcement helped to improve the
tenacity of the pile caps; however, the most relevant values in terms of TE were found for PC04IR, with TE,Pilecaps/
TE,REF = 3.35, w here TE,Pilecaps and TE,REF were the tenacity of the pile caps with some type of additional reinforce-
ment and the reference tenacity, respectively. In terms of displacement, the gains of the pile caps with SFRC and
inclined shear reinforcement were not so substantial, mainly for PC03SFRC+IR (with hybrid reinforcement). It is
assumed that the steel bers inhibited the action of the inclined shear reinforcement, and for this reason, the
Figure6. Instrumentation: (a) installed strain gauges and (b) deectometer placement.
Figure7. Pile cap specimens.
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results of that pile cap were below expectations in terms of ductility. However, this structural element clearly
had major strength gains. Finally, it should be noted that for PC04IR, the δu,Pilecaps/δu,REF ratio = 1.20 was more
signicant.
Mobilization of the exural reinforcement. Table8 shows the maximum strains of the exural rein-
forcement εfu, as expressed in the load–strain ratio. is information enables the analysis of the εfu,Pilecaps/εfu,REF
ratio and the angular constant k. e angular constant, determined by k = V/εf, evaluates the tangent of the
slope angle of the linear portion of the V − εf ratio. e εfu,Pilecaps/εfu,REF ratio shows that the hybrid use of SFRC
with inclined reinforcement (PC03SFRC+IR) had the best performance compared to PC01REF; that is, the increase
in ber consumption strengthened the reinforcement under tensile stress since the pile caps with SFRC had
εfu,Pilecaps/εfu,REF ∈ [0.9–1.3]. Moreover, in general, there was no yield stress in the reinforcements monitored in the
pile caps, with εfu < εsy = 3.05 ‰ (Fig.10). e evaluation of the angular constant shows that the responses in the
elastic phase are within normal limits for the values presented, at k ∈ [4000–10000].
Figure8. Test setup.
Table 6. Ultimate failure loads observed during testing. Vu,Pilecaps = failure loads of
the pile caps with steel bers and/or inclined reinforcement Vu,REF = failure loads
of the pile caps without steel bers and/or inclined reinforcement. *From Eq.(1),
tan θ
=
d/(0.5
·
L
−
0.25
·
a
c
)
=
350/(0.25
·
600
−
0.25
·
200)
=
1.4
→
arctnθ
=
54.46
.
Pile cap Strut angle, θ (°)
Experimental
Ultimate failure Load, Vu (kN) Strength increase, Vu,PileCaps/Vu,REF (%)
PC01REF
54.46*
489.00 –
PC02SFRC 680.00 39
PC03SFRC+IR 720.00 47
PC04IR 685.00 40
Table 7. Parameters dening the V − δ ratio.
Pile cap Vu (kN) δu (mm) TE (kJ) δu,Pilecaps/δu,REF TE,Pilecaps/TE,REF
PC01REF 489.00 3.28 3.62 – –
PC02SFRC 680.00 3.47 7.02 1.06 1.94
PC03SFRC+IR 720.00 2.61 10.02 0.80 2.77
PC04IR 685.00 3.93 12.14 1.20 3.35
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Mobilization of the inclined shear reinforcement. On this occasion, only pile caps PC03SFRC+IR and
PC04IR were analyzed, as they have inclined shear reinforcement. In Fig.11, the results show that strain in the
instrumented reinforcement of PC04IR was higher than yield strain, with εsu, IR > εsy = 2.42‰. However, for the
pile cap with hybrid composition (bers + inclined reinforcement), the inclined reinforcement did not have yield
stress. is nding suggests that the steel bers assumed the function of reinforcement and inhibited the strain
of the inclined reinforcement. In summary, the results indicate that the use of inclined shear reinforcement
together with steel bers can lead to oversizing, i.e., the ber restricts the action of the reinforcement and vice
versa. In addition, the pile caps had similar gains in strength, ductility and tenacity, with the exception of the
reference pile cap; that is, it is hardly practical and economical to use steel bers together with inclined shear
reinforcement.
0
100
200
300
400
500
600
700
800
0.01.0 2.03.0 4.
05.0
V(kN)
δ(mm)
BR1
BR2
BAI1
BAI2
PC02
SFRC
PC01
REF
PC03
SFRC+IR
PC04
IR
Figure9. Load–displacement ratio.
Table 8. Parameters that dene the V − εf ratio.
Pile cap Vu (kN) εfu (‰) k εfu,pilecaps/εfu,REF Failure mode
PC01REF 489.00 0.74 4090.9 –
Shear
PC02SFRC 680.00 0.68 6153.9 0.92
PC03SFRC+IR 720.00 0.95 4500.0 1.28
PC04IR 685.00 0.10 10,000.0 0.14
0
100
200
300
400
500
600
700
800
0.02.0 4.06.0 8.
01
0.
0
V(kN)
ε
s,FLEX
(‰)
BR1
BR2
BAI1
BAI2
ε
ys
=3.1‰(Ø12.5mm)
PC02
SFRC
PC01
REF
PC03
SFRC+IR
PC04
IR
EERG
2
Figure10. Load–strain ratio of the exural reinforcement.
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Mobilization of the stirrups. e analysis of stirrup mobilization was based on the results shown in the
load-strain graph, V − ε (Fig.12). e graph shows that, in general, the results had dierent bilinear behaviors,
since one section represents the elastic phase (without the appearance of diagonal cracks), while the second sec-
tion corresponds to the beginning and progress of shear cracks.
Table9 shows the coordinates that dene the ultimate load (Vu − εsu) as well as the coordinate indicating
the start of the second linear section (V2L − ε2L). e result for strain εsu shows that yield stress occurred in the
transverse reinforcement of all pile caps, εsu > εsy = 4.63 ‰. e εsu,Pilecaps/εsu,REF ratio clearly shows that the level of
strain in the stirrups of the pile caps with additional reinforcement (steel bers and/or inclined reinforcement)
is lower than the level of the reference pile cap, namely, εsu,Pilecaps/εsu,REF ∈ [0.80–0.95].
It can be seen that the reinforcement mechanism provided by the steel bers and the inclined reinforcement
reduces the stress in the reinforcement; therefore, for this study, the transverse reinforcement ratio or even the
eective depth of the pile cap can be reduced. e analyses also show that the V2L,Pilecaps/V2L,REF ∈ ratio [1.00–1.65]
indicates that, at the beginning of transverse reinforcement mobilization, the stirrups of pile caps PC02SRFC,
PC03SRFC+IR and PC04IR underwent more stress than those of the reference pile cap. However, with increased
loading, the bers and the inclined reinforcement tend to assume the function of the main reinforcement. In
0
100
200
300
400
500
600
700
800
0.0 2.04.0 6.08.0
10.0
V(kN)
ε
s,IR
(‰)
BAI1
BAI2
PC03
SFRC+IR
PC04
IR
ε
ys
=2.4‰(Ø10.0 mm)
Figure11. Load–strain ratio of the inclined reinforcements.
0
100
200
300
400
500
600
700
800
0.02.0 4.06.0 8.
01
0.
0
V(kN)
ε
s,ST
(‰)
BR1
BR2
BAI1
BAI2
ε
ys
=4.6‰(Ø5.0 mm)
EERG
3
PC02
SFRC
PC01
REF
PC03
SFRC+IR
PC04
IR
Figure12. Load–strain ratio of the stirrups.
Table 9. Characterization of the V − εs ratio.
Pile cap Vu (kN) εsu (‰) V2L (kN) εs2L (‰) εsu,Pilecaps/εsu,REF V2L,Pilecaps/V2L,REF εs2L,Pilecaps/εs2L,REF
PC01REF 489.00 5.65 320.00 0.51 – – –
PC02SFRC 680.00 4.85 320.00 0.52 0.86 1.00 1.02
PC03SFRC+IR 720.00 5.25 520.00 0.24 0.93 1.63 0.47
PC04IR 685.00 4.75 510.00 1.50 0.84 1.59 2.94
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addition, with the imminence of failure, εsu,Pilecaps/εsu,REF ∈ [0.80–0.95], which conrms the decrease in stress in
the stirrups of the pile caps with additional reinforcements (steel ber and/or inclined reinforcement).
Failure of pile caps. e analysis aims to register the integrity of the pile caps aer the failure of these
structural elements. Figures13 and 14 reveal the fragility of these elements and their failure mode, namely,
shear by diagonal strain. P01REF was the weakest of all, with the least pronounced diagonal crack. e pile caps
Figure13. Final aspect of the pile caps aer their failures without inclined shear reinforcement.
Figure14. Final aspect of the pile caps aer their failures with inclined shear reinforcement.
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PC03SFRC+IR and P04IR demonstrated similar behavior, presenting the formation of multiple cracks. However,
comparing PC03SFRC+IR and PC02SFRC, it can be seen that the combination of inclined reinforcement and steel
bers enhances the bearing capacity, delaying the progression of cracks and inhibiting shear eorts, with the
solicitation of the bers in tension, as the load–strain and load–displacement graphs reveal. erefore, steel b-
ers and shear reinforcement improved the ductility of the pile caps.
Conclusions
e present experimental study has assessed steel ber and inclined shear reinforcement performance in pile
caps, whose variables were the use of steel bers with and without inclined shear reinforcement. Based on the
results, the following conclusions were observed:
• e use of the bers provided the same value of the bearing capacity of the pile cap with the inclined rein-
forcement, with a strength gain of approximately 40%, comparing PC02SFRC and PC04IR with PC01REF.
• e bers contributed to a 7% strength gain when the usage is combined with inclined shear reinforcement;
comparing PC03SFRC+IR with PC04IR.
• e analysis of the load–displacement ratio (V-δ) shows that the load-bearing capacity of the pile cap with
steel bers and inclined reinforcement (PC03SFRC + IR) had the best lower displacements, 20%, and 44% reduc-
tion, respectively, compared to PC01REF and PC04I, and exhibited greater strain capacity, with εfu/εf = 1.28.
• Additionally, the V − δ parameters enabled the assessment of not only strength but also the inuence of
steel bers and inclined shear reinforcement on the ductility and tenacity of the pile caps. ese properties
increased signicantly in pile caps with steel bers and/or inclined shear reinforcement, especially PC04IR,
with δu,Pilecaps/δu,REF = 1.20 and TE,Pilecaps/TE,REF = 3.35.
• e load–strain graph (V − εs, IR) shows that the inclined shear reinforcement of PC03SFRC+IR with hybrid
composition (steel bers + inclined shear reinforcement) did not carry yield stress.
• e mobilization of the stirrups shows that the levels of strain in the transverse reinforcements of pile caps
PC02SFRC, PC03SFRC + IR, and PC04IR were lower than that of the reference pile cap. For this reason, the
additional strengthening mechanisms reduced the shear eorts.
• e steel bers restricted the strain of the inclined shear reinforcement. erefore, it can be hypothesized
that the strengthening mechanisms, under the conditions presented in this study, work satisfactorily by
themselves, as the bers tend to inhibit the action of the inclined shear reinforcement and vice versa.
Data availability
e datasets used and/or analyzed during the current study are available from the corresponding author on
reasonable request.
Received: 5 March 2022; Accepted: 7 June 2022
References
1. ABNT NBR 6118. Procedure: Design of Concrete Structures (ABNT, 2014) (in Portuguese).
2. Mesquita, A. C., Rocha, A. S., Delalibera, R. G. & Silva, W. A. e inuence of connecting pile cap-column in the mechanisms of
break in the two pile caps. Rev. IBRACON Estrut. Mater. 9, 856–882 (2016).
3. Blévot, J. Semelles en béton armé. Annales de l’institut technique du bâtiment et des travaux publics 10, 111–112 (1957).
4. Blévot, J. & Frémy, R. Semelles sur pieux. Annales de l’institut technique du bâtiment et des travaux publics 20, 224–273 (1967).
5. Tomaz, M. A., Delalibera, R. G., Giongo, J. S. & Gonçalves, V. F. Analysis of the nodal stresses in pile caps. Rev. IBRACON Estrut.
Mater. 11, 1208–1257 (2018).
6. Mobasher, B., Yao, Y. & Soranakom, C. Analytical solutions for exural design of hybrid steel ber reinforced concrete beams. Eng.
Struct. 100, 0141–0296 (2015).
7. Gomes, L. D. S. G. et al. Experimental analysis of the eciency of steel bers on shear strength of beams. Latin Am. J. Solids Struct.
15, 1–16 (2018).
8. Bicelli, A. R. A., Oliveira, V. A., Matos, K. S. P. & Oliveira, D. R. C. Eects of accelerated corrosion on rebar bonding in steel ber
concrete. Rev. Matér. 26, 03 (2021).
9. Moraes, M. C. Estruturas de fundações 169 (Editora McGraw – Hill do Brasil Ltda, 1976).
10. Delalibera, R. G. & Giongo, J. S. Numerical analysis of two pile caps with sockets embedded, subject the eccentric compression
load. Rev. IBRACON Estrut. Mater. 16, 436–474 (2013).
11. ABNT NBR 15530. Specication: Steel Fibers for Concrete (ABNT, 2019) (in Portuguese).
12. Soroushian, P. & Bayasi, Z. Fiber-type eects on the performance of steel ber reinforced concrete. ACI Mater. J. 88(2), 129–134
(1991).
13. Mahakavi, P. & Chithra, R. Impact resistance, microstructures and digital image processing on self-compacting concrete with
hooked end and crimped steel ber. Constr. Build. Mater. 220, 651–666 (2019).
14. Nzambi, A. K. L. L., Oliveira, D. R. C., Oliveira, A. M. & Picanço, M. S. Pull-out tests of ribbed steel reinforcing bars embedded in
concrete with steel bres. Proc. Inst. Civ. Eng. Struct. Build. 174(3), 181–189. https:// doi. org/ 10. 1680/ jstbu. 17. 00180 (2021).
15. ABNT NBR 7480. Specication: Steel for the Reinforcement of Concrete Structures (ABNT, 2007) (in Portuguese).
16. ABNT NBR ISO 6892-1. Metallic Materials: Tensile Testing Part 1: Method of Test at Room Temperature (ABNT, 2015) (in
Portuguese).
Acknowledgements
e authors thank the Institute of Ecological Research in the Amazon (IPEAM) for their support in the develop-
ment of this study and other research in the Amazon.
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Author contributions
A.N., L.G., C.A., F.S. and D.O. made important contributions to this manuscript.
Funding
e authors received no specic funding for this work.
Competing interests
e authors declare no competing interests.
Additional information
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