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Interaction between the Local and General Zone for the Post-tensioned Girder Anchorage Zone

Authors:

Abstract and Figures

Background The use of post-tensioning in girders causes high bearing and compressive stresses in the anchorage zone. In this study, the behavior of the anchorage zone and the interaction between the local and general zone are investigated. The variables included different reinforcements for both the local and general zones for a block of two anchorage devices. Methods Both experimental and numerical methods have been applied to study the behavior of the anchorage zone. The experimental part of the study involved laboratory testing of sixteen specimens, and the numerical study was conducted using ABAQUS non-linear finite element analysis. Results Tie reinforcement provided additional confinement for the local zone, and this confinement was more for the specimens with originally less confined spiral reinforcement strength. There was a slight or no effect of the local zone reinforcement on the general zone strength and ultimate load of the anchorage zone when the failure was in the general zone. Conclusion Confinement of the local zone prevented the brittle bearing and compression failure of this zone.
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DOI: 10.2174/1874149502115010050, 2021, 15, 50-73
The Open Civil Engineering Journal
Content list available at: https://opencivilengineeringjournal.com
RESEARCH ARTICLE
Interaction between the Local and General Zone for the Post-tensioned Girder
Anchorage Zone
Ghassan M. Werdina1,* and Omar Q. Aziz2
1Department of Water Resources Engineering,, Salahaddin University-Erbil, Erbil, Iraq
2Department of Civil Engineering, Salahaddin University-Erbil, Erbil, Iraq
Abstract:
Background:
The use of post-tensioning in girders causes high bearing and compressive stresses in the anchorage zone. In this study, the behavior of the
anchorage zone and the interaction between the local and general zone are investigated. The variables included different reinforcements for both
the local and general zones for a block of two anchorage devices.
Methods:
Both experimental and numerical methods have been applied to study the behavior of the anchorage zone. The experimental part of the study
involved laboratory testing of sixteen specimens, and the numerical study was conducted using ABAQUS non-linear finite element analysis.
Results:
Tie reinforcement provided additional confinement for the local zone, and this confinement was more for the specimens with originally less
confined spiral reinforcement strength. There was a slight or no effect of the local zone reinforcement on the general zone strength and ultimate
load of the anchorage zone when the failure was in the general zone.
Conclusion:
Confinement of the local zone prevented the brittle bearing and compression failure of this zone.
Keywords: Anchorage zone, Post-tensioning, Local zone, General zone, Spiral reinforcement, ABAQUS.
Article History Received: October 27, 2020 Revised: December 24, 2020 Accepted: January 15, 2021
1. INTRODUCTION
In pre-stressed concrete, internal compressive stresses are
induced by means of pre-stressed reinforcement to reduce
tensile stresses in the concrete due to applied loads. The use of
post-tensioned concrete allows for longer spans and smaller
cross-sections in structures, especially bridges. Post-tensioned
girders are subjected to a high concentration of compressive
stresses at the anchorage zone due to the transfer of
prestressing force at the girder end through bearing plates and
anchors [1 - 3]. One of the most critical aspects of post-
tensioned construction is the anchorage zone which is also
necessary for the success of the system [4]. A local failure may
occur in the immediate vicinity of the anchorage device if
* Address correspondence to this author at Department of Water Resources
Engineering, Salahaddin University-Erbil, Erbil, Iraq; Tel: +964 7504381163; E-
mail: ghassan.werdina@su.edu.krd
the local stresses exceed the compressive strength of the
concrete [5]. To enhance the local compressive strength, spiral
or tie confining reinforcement is used in this region. Moreover,
at the larger distance from the anchorage device, large tensile
stresses develop, which can lead to cracking of the concrete in
tension [6]. It is essential to understand the interaction between
the local zone and general zone, and their influence on the
behavior and strength of the anchorage zone, especially for the
real cases that involve multiple anchorage devices.
A typical anchorage zone has been shown in Fig. (1),
which is defined as the volume of concrete through which the
concentrated pre-stressing force at the anchorage device
spreads transversely to a more linear stress distribution across
the entire cross-section at some distance from the anchorage
device [7 - 9]. Within the anchorage zone, the bending theory
is not valid because the ordinarily assumed linear strain
Interaction between the Local and General Zone The Open Civil Engineering Journal, 2021, Volume 15 51
distribution is disturbed by the introduction of the concentrated
anchorage force.
According to the American Association of State Highway
Transportation Officials (AASHTO) specifications [9], the
longitudinal extent of the anchorage zone in the direction of the
tendon shall be taken between 1.0 h and 1.5 h, where h refers to
the greater transverse dimensions of the anchorage zone.
Moreover, the transverse dimensions of the anchorage zone
may be taken as the depth and width of the section but not
larger than the longitudinal dimension of the component or
segment.
As shown in Fig. (2), there are different types of stresses in
the anchorage zone [7, 10]. The region ahead of the
concentrated force is subjected to high compressive and
bearing stresses. Bursting stresses are lateral tensile stresses
that result from the deviation of the compressive stresses
parallel to the force. This type of stress acts at a region that
extends a certain distance ahead of the anchorage device.
Spalling stresses are local tensile stresses which are found
along the loaded edge of the member.
Fig. ( 3 ) shows the two regions of the anchorage zone that
include the local zone and the general zone [7, 9,11,12].
The region ahead of the anchorage device is the local zone.
In order to resist the high compressive and bearing stresses in
this region, spiral or tie confining reinforcement is provided in
the local zone. AASHTO Specifications [9] recommend the
transverse dimensions of the local zone to be greater than the
bearing plate size with concrete cover and the outer dimension
of confining reinforcement plus concrete cover. The length of
the local zone along the tendon axis is considered greater than
the local zone width and the length of the confining reinfo-
rcement. Pre-stressing force is transferred from the local zone
into the general zone.
The region of concrete outside the vicinity of the local
zone, into which the high concentrated pre-stressing forces
from the anchorage device spread throughout, is called the
general zone.
Fig. (1). Anchorage zone.
Fig. (2). Stress contours of concentrically loaded anchorage zone; (a) Compression, (b) Tension [7].
(a) (b)
1.5h max
1.0h min
Anchorage
Zone
hb
bearing
stresses stresses
spalling
stresses
bursting
52 The Open Civil Engineering Journal, 2021, Volume 15 Werdina and Aziz
Fig. (3). Local zone and General zone.
Fig. (4). Second mode of failure of anchorage zone.
This region is subjected to bursting tensile stresses due to
the spreading of the tendon force into the structure. Transverse
reinforcement is provided in the general zone to resist bursting
stresses.
Three main modes of failure can be recognized in the
anchorage zone [6]. The first mode is due to the high bearing
and compression stresses in the local zone. This failure occurs
if the compressive strength of concrete is insufficient or lacks
confining reinforcement. The surface of rupture is often in the
shape of a pyramid or cone. The second mode of failure occurs
due to insufficient transverse reinforcement for bursting tensile
stresses in the general zone. This mode is characterized by
large cracks running parallel to the duct and extending from the
anchorage device, as shown in Fig. (4). The third mode of
failure is at the interface between the local zone and the general
zone, and is due to compression failure of unconfined concrete
at the end of confining reinforcement.
Three main methods for the analysis of stresses in the
anchorage zone are used. These include Finite Element
analysis, Strut- and-Tie-Model and approximate method. If the
post-tensioned anchorage zone is not properly detailed and
designed to withstand the forces and stresses which develop,
failure of the anchorage zone can occur.
The research project conducted in the early 1990s at the
University of Texas at Austin, under the support of the
National Cooperative Highway Research Program (NCHRP)
[7, 11], is considered one of the main studies in the field of
anchorage zone. Roberts [7, 8,13], as a part of this work,
suggested the following equation to predict the ultimate load
capacity of the local zone:
(1)
Where, Fult is the ultimate load of the local zone, fcʹ is the
concrete compressive strength, A is the effective supporting
area geometrically similar to the shape of the loaded anchorage
plate, Ab is the bearing area, flat is the lateral confining strength,
Acore is the area confined by the local confining reinforcing, s is
the pitch or the spacing of the confining reinforcement, D is the
outside diameter of confining reinforcement.
The experimental investigations of general zones by
Sanders [4, 8, 7] were performed parallel to the analytical
investigations using the linear elastic finite element method
  
  
General Zone
Local Zone
Interaction between the Local and General Zone The Open Civil Engineering Journal, 2021, Volume 15 53
performed by Burdet [6]. Wollmann et al. [14] studied the
design and behavior of end diaphragms when used for the
anchorage of external tendons. The experimental test included
three half-scale specimens. Kim et al. [15] conducted an
experimental and numerical study to predict the ultimate
resisting capacity of the HPC and UHPC anchorage zones,
while many researchers [1,16 - 19] investigated the use of
fiber-reinforced concrete in anchorage zones.
The performance of the anchorage zone is critical for the
safety and stability of the whole concrete structure. It can be
inferred from the literature that the interaction between the
local zone and general zone, and their influence on the
behavior and strength of the anchorage zone with multiple
anchorage devices have not been studied. To overcome this
knowledge gap, the present study investigated the interaction
between the local zone and general zone, and their influence on
the behavior and strength of the anchorage zone with multiple
anchorage devices. The variables included different reinfo-
rcements for both the local and general zones for a block of
two anchorage devices. The anchorage zone with multiple
anchorage devices represents a more realistic case compared to
the single anchorage device in most post-tensioned const-
ructions. The experimental part of the study included casting
and testing sixteen specimens arranged in four groups, and the
numerical part included finite element analysis using the
ABAQUS program.
2. MATERIALS AND METHODS
The following sections present the details of the
experimental work related to preparing and testing the
specimens.
2.1. Size and Shape of the Test Specimens
The test specimen included a concrete block with two
anchorage devices [20]. The standard anchorage device VSL E
5-19 [21, 22], shown in Fig. (5), was selected for modeling the
specimens. The scale factor for the anchorage device was one-
third, which was selected based on the capacity of the loading
frame of the laboratory. As shown in Fig. (6), the final
dimensions of the anchorage plate were 100 mm x 100 mm
with a thickness of 12 mm, and the wedge plate (anchorage
head) was of 60 mm diameter and 25 mm depth.
AASHTO approximate method section 5.8.4.5 was used to
determine the transverse dimensions of the concrete block.
This method recommends a minimum edge distance of 1.5
times the corresponding lateral dimension, “a”, of the ancho-
rage plate for a proper stress distribution of the anchorage
zone. Moreover, the depth of the block was selected to be
within the limits recommended by AASHTO specifications
(refer to Fig. 1). Duct holes were made by using 30 mm
diameter aluminum tubes with a negligible strength. This
diameter represented a scale of one-third of the duct diameter
of 90 mm required for the number of strands for anchorage
devices VSL E 5-19 [21]. The final dimensions of the
specimen were 300 mm x 450 mm x 600 mm.
2.2. Materials and Reinforcement Details
As shown in Fig. (7), the local zone for each anchorage
device was confined by a deformed steel bar spiral of 120 mm
diameter, which was close to the anchorage plate size, and
represented a scale of one-third of the spiral diameter of 365
mm required for the anchorage devices VSL E 5-19 [21, 22].
The spiral consisted of 8 turns with 20 mm pitch and a total
length of 140 mm. Spirals were located 10 mm under the
anchorage plate, and as a result, a total depth of 150 mm of the
anchorage zone was confined. This depth represented the
length of the local zone along the tendon axis, which was
designed according to AASHTO specifications mentioned in
section 1. Ties of deformed steel bars were provided to resist
tensile bursting stresses in the general zone for both directions.
The first tie was fixed at 10 mm from the loading face and
continued for the whole block depth with a spacing of 60 mm.
The spacing of the ties was within the maximum limits of
AASHTO specifications [7,23] of 300 mm and 24 bar diameter
for the bursting reinforcement. As variables, different bar sizes
have been used for the reinforcement of the spirals and ties.
The tested properties of concrete and reinforcing bars are
presented in Table 1.
Fig. (5). Anchorage device VSL E 5-19 [21].
54 The Open Civil Engineering Journal, 2021, Volume 15 Werdina and Aziz
Fig. (6). Dimensions of the test specimens (mm), (a) concrete block, (b) anchorage plate and wedge plate, (c) top view showing the location of the
anchorage plates.
Fig. (7). Specimens reinforcement and molds, (a) details of the reinforcement, (b) molds.
(a)
(b)
60
300
450
600
100
100
25
12
100 100 50 100 100
100
100
100
450
300
(a) (b)
(c)
Interaction between the Local and General Zone The Open Civil Engineering Journal, 2021, Volume 15 55
Table 1. Tested material properties
Test Results
Concrete (results at the age of 56 days) -
Compressive strength (MPa) 49.95
Splitting tensile strength (MPa) 4.7
Elastic modulus (GPa) 33.75
Steel Bars -
Yield stress-ϕ6 mm (MPa) 401
Yield stress-ϕ5 mm (MPa) 495.5
Yield stress-ϕ4 mm (MPa) 428
Table 2. Identification of specimens and variables.
Group Specimen Spiral Tie
No. No. bar size bar size
- - (mm) (mm)
G1
SP1 6 6
SP2 6 5
SP3 6 4
SP4 6 0
G2
SP5 5 6
SP6 5 5
SP7 5 4
SP8 5 0
G3
SP9 4 6
SP10 4 5
SP11 4 4
SP12 4 0
G4
SP13 06
SP14 05
SP15 04
SP16 0 0
2.3. Experimental Variables
As presented in Table 2, the study included sixteen
specimens in four groups to show the interaction between the
local zone and the general zone. Each of the mentioned four
groups included a constant bar size for the spiral reinforcement
(local zone) and different bar sizes for the ties reinforcement
(general zone). Hence for the four groups, there were four
different bar sizes for the spiral reinforcement.
For the control specimen (SP7), the bar size for the spiral
and tie reinforcement was ⱷ5mm and ⱷ4mm, respectively. This
amount of reinforcement, which was based on ABAQUS [24]
finite element analysis prior to the experimental work, was
provided to prevent the general zone failure, and to allow the
failure of the control specimen to occur in the local zone.
Similarly, and based on ABAQUS finite element analysis, one
closed tie of ⱷ4mm surrounding both anchorage plates was
used as spalling reinforcement at the loaded edge for all
specimens.
2.4. Test setup and instrumentation
As shown in Fig. (8), the test machine consisted of a steel
frame with a capacity of 2500 kN. Application of the load was
performed through a hydraulic circular jack to a beam, and
then to the two wedge plates of the anchorage devices. The
specimen was supported over the lower part of the frame
through a plate 50 mm thick. Directly under the specimen,
there was a thin layer of plywood in order to provide uniform
support.
The vertical displacement of the specimen was measured
through the anchorage device axis, shown as point A in Fig.
(9). This displacement was obtained as the difference of the
reading of two dial gauges. The top dial gauge was attached to
the loading plate, and the lower dial gauge was attached to a
plate at the bottom of the specimen, fixed during casting of the
concrete. Two strain gauges with 80 mm length were used to
measure the strain of the concrete at the critical elastic bursting
stresses, at both the short and long sides of the specimen. These
locations, shown in Fig. (9), were determined according to
ABAQUS finite element analysis prior to the experimental
work. Moreover, two strain gauges of 5 mm length were used
to measure the strain of ties. These strain gauges were fixed at
the center of the short and long part of the second tie, which
according to the finite element analysis were found to be the
critical locations.
3. NUMERICAL FINITE ELEMENT MODELING
ABAQUS was used to perform the numerical simulation in
this study. This software can solve a wide range of linear and
non-linear problems.
3.1. Geometric Modeling and Boundary Conditions
To minimize the computational cost, only half of the speci-
men was represented in numerical modeling by ABAQUS, as
the specimen had axes of symmetry located at the mid-plane
between the two anchorage devices. Three-dimensional solid
members were used to model the concrete block, anchorage
and wedge plates. The reinforcements were defined using
deformable “wire” type parts. A wire is represented as a line in
ABAQUS.
The bottom surface of the model was supported in the Y
direction, and the axial load was applied as a specified vertical
displacement over the wedge plates, with the use of amplitude
function (smooth step). The analysis was conducted in step-1
(Dynamic, Explicit), which was after the initial step.
3.2. Material Modeling
In order to represent the behavior of the experimentally
tested specimens with the FE model, the material models in FE
should accurately describe the properties of the materials and
the interactions between them.
56 The Open Civil Engineering Journal, 2021, Volume 15 Werdina and Aziz
Fig. (8). Testing the specimens, (a) Testing machine, (b) distribution beam and top dial gauge, (c) dial gauge at the bottom of the specimen.
Fig. (9). Location of vertical displacement measurement and strain gauges.
3.2.1. Concrete
To describe the behavior of concrete under loading, the
Concrete Damage Plasticity (CDP) model, which is available
in ABAQUS, was used. CDP takes into consideration the
degradation of the concrete, and assumes two main concrete
failure mechanisms which are cracking under uniaxial tension
and crushing under uniaxial compression. The parameters
required to define the plasticity model of concrete are dilation
angle (ψ), the plastic potential eccentricity of concrete, the ratio
of compressive stress in the biaxial state to the compressive
stress in the uniaxial state (fbo / fco), the shape factor of
yielding surface (K) and viscosity parameter. Table 3 presents
the CDP required parameters that were used in this study [24 -
26]. Moreover, a value of 0.18 was selected for Poisson’s ratio
in this study [27 - 29].
The stress-strain relationship of concrete under uniaxial
compression was described using compressive strength test
results (Table 1) and the equation proposed by Saenz [30],
which has the following form:
(2a)
(2b)
Table 3. CDP parameter.
Dilation angle (ψ) 31°
Eccentricity 0.1
biaxial/uniaxial ratio (fbo / fco) 1.16
k 0.667
Viscosity parameter 0
(c)(b)
(a)



  

100mm
90mm
A
Interaction between the Local and General Zone The Open Civil Engineering Journal, 2021, Volume 15 57
(2c)
(2d)
Where, Rσ=4 and Rε=4 may be used, σc is the effective
stress, εc is the effective strain, Ec is the initial modulus of
elasticity and ε is the concrete strain at peak stress which was
assumed to be 0.0025. The curve of the stress-strain relation-
ship for compression in this study is shown in Fig. (10).
The following two equations, which represent the ascen-
ding and descending parts of the curve, have been used for the
stress-strain relationship of concrete in tension [31 - 34].
(3a)
(3b)
Where, εt is the concrete tensile strain, εcr is the concrete
strain at peak stress (at cracking), assumed as 0.0001 in this
study, and ft is the tensile strength of the concrete (peak stress).
The direct tensile strength of concrete is 0.5 to 0.7 of its
splitting tensile strength [35]. In this study, the direct tensile
strength is assumed as 0.6 of the tested splitting tensile strength
mentioned in Table 1, providing a result of 2.82 MPa. The
tensile stress-strain curve for this study is shown in Fig. (11).
Damage parameters dc and dt are used to determine the
degradation of concrete for compression and tension,
respectively. In this study, the compression damage parameter
dc is defined as the ratio of the concrete compression stress
after crushing to the initial yield stress. Similarly, the tension
damage parameter, dt is defined as the ratio of the concrete
tensile stress after cracking to the ultimate tensile stress [26].
Moreover, a value of wc=0.8 has been used for the compressive
stiffness recovery factor, assuming that compressive stiffness is
mostly recovered upon crack closure as the load changes from
tension to compression. The tensile stiffness recovery factor,
wt=0 is used, assuming that tensile stiffness is not recovered as
the load changes from compression to tension once the
crushing of concrete is initiated.
Fig. (10). Stress-strain relationship of concrete under uniaxial compression.
Fig. (11). Tensile stress-strain relationship for concrete.
0
10
20
30
40
50
60
0 0.0025 0.005 0.0075 0.01
0.0125
Stress (MPa)
Strain (mm/mm)
0
0.5
1
1.5
2
2.5
0 0.002 0.004 0.006 0.008
0.01
Stress (MPa)
Strain (mm/mm)
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ߪൌ݂
೎ೝ
଴Ǥସ for ߝ൐ߝ
௖௥
58 The Open Civil Engineering Journal, 2021, Volume 15 Werdina and Aziz
3.2.2. Reinforcement
The reinforcement was modeled as an embedded region
within the concrete, and the definition of its material properties
was based on a linear elastic-perfect plastic behavior model,
with an elastic modulus value of 200 GPa.
3.2.3. Plates
Material properties of wedge and anchorage plates were
defined as linear elastic behavior model, with an elastic
modulus value of 200 GPa. Type of the interaction between the
anchorage plates and concrete, and between anchorage plates
and wedge plate, was “Tie constraints”.
3.3. Element Types and Mesh Generation
All solid members (concrete, anchorage plates and wedge
plates) were meshed using eight nodes bricks type C3D8R,
reduced integration and hourglass control, as shown in Fig.
(12). These are first-order hexahedral elements that provide
good results for minimum cost in three-dimensional analyses.
A two-node, three-dimension truss element type T3D2 was
used for the reinforcement (spirals and ties). The general size
of the elements was 10 mm. The square shape of the anchorage
plate with a circular hole at the center required good meshing
techniques in order to keep the hexahedral element for this
process. This issue led to the use of an element size of 7.5 mm
in certain parts of the plate. Moreover, it was intended to keep
the same meshing shape in the contact parts between the
anchorage plate and the concrete, and between the anchorage
plate and the wedge plate, which uses an element size of 7.5
mm in some parts of these members.
Before using the mesh size of 10 mm, a mesh sensitivity
test was performed to find the effect of mesh size on the
results. Under this test, mesh sizes of 20 mm, 15 mm and 10
mm were applied to the concrete and reinforcement for the
control specimen (SP7). The case of mesh size of 10 mm had
the closest load-displacement relationship and ultimate load
compared to the experimental results. Based on these results,
the mesh size of 10 mm was selected for the FEA in this study.
4. RESULTS AND DISCUSSION
The following sections present the experimental and
numerical results that include the ultimate load, load-displace-
ment behavior, load-strain behavior, bursting stresses, cracking
pattern and failure mode of the specimens.
4.1. Ultimate Load
Table 4 presents values of the ultimate load of the
specimens for both the experimental test and ABAQUS FEA.
The first comparison of the ultimate load was made among the
specimens that were designed to fail in the local zone. In every
group, this included the three specimens that had tie
reinforcement. The ultimate load for group G1 was between
1358.1 kN and 1372 kN for the three specimens that had tie
reinforcement. This implies almost no change in the ultimate
load for group G1 by changing tie bar size from ϕ4 mm to ϕ6
mm. This is justified because the spiral reinforcement of ϕ6
mm for this group provided strong lateral confinement for the
local zone, and hence the additional confinement from ties had
a negligible effect. This was not the case for group G2,
reinforced with ϕ5 mm spirals, as the ultimate load increased
with the increase in tie bar size. The ultimate load for this
group increased from 1266.4 kN (SP7) to 1390 kN (SP5) by
increasing the tie bar size from ϕ4 mm to ϕ6 mm. This
represented an increase of 9.8% in the ultimate load of the
specimens. The influence of tie bar size on ultimate load was
even more in group G3 that included specimens with weak
spiral reinforcement (ϕ4 mm). The ultimate load increased
from 1190 kN (SP11) to 1341 kN (SP9) by increasing the tie
bar size from ϕ4 mm to ϕ6 mm, representing an increase of
12.7%, which was more than the increase in group G2. These
results of groups G1, G2, and G3 showed that the tie
reinforcement influenced the ultimate load of the anchorage
zone. This influence was more when the spiral bar size was less
(almost 0%, 9.8%, and 12.7% for groups G1, G2, and G3,
respectively). This indicated that the tie reinforcement provided
additional confinement for the local zone, and this additional
confinement was more for the specimens with originally less
confined spiral reinforcement strength. Nevertheless, this issue
did not apply to group G4 that includes specimens without
spiral reinforcement. For this group, the maximum ultimate
load was 1187.5 kN for specimen SP13 (tie bar size of ϕ6 mm),
compared to the ultimate load of 1114.5 kN for specimen SP15
(tie bar size of ϕ4 mm), representing an increase of only 6.6%.
This indicated that the tie reinforcement could not significantly
improve the ultimate load of the anchorage zone when the
spiral confinement of the local zone was not available.
The second comparison of the ultimate load was for the
specimens that were designed to fail in the general zone. This
includes the specimens without tie reinforcement (SP4, SP8,
SP12 and SP16 shown in Table 4). The ultimate load and
behavior of these specimens differ from the behavior of other
specimens in these groups. As designed, these specimens did
not include bursting stress reinforcement, and the general zone
failed. This kind of failure was clear in the cracking and failure
pattern of the specimens. All these specimens had a brittle
failure, especially SP16 that had a sudden failure at ultimate
load. The comparison of ultimate load among these four
specimens is explained in more detail as group A4 later in this
section.
The same specimens presented in Table 4 were rearranged
as additional groups in Table 5 by fixing the tie bar size for
each new group and changing the spiral bar size. Hence tie bar
size is ϕ6 mm, ϕ5 mm, and ϕ4 mm for the groups A1, A2, and
A3, respectively. Specimens in group A4 have no tie reinfo-
rcement. For every new group in this table, the effect of spiral
bar size on the ultimate load is investigated. The effect of spiral
reinforcement was more clear for the groups of specimens with
smaller tie bar size (ϕ4 mm compared to ϕ5 mm and ϕ6 mm).
Increasing the spiral bar size increased the ultimate load by just
3.7% for group A1 (tie bar size ϕ6 mm), and 2% for group A2
(tie bar size ϕ5 mm). The same change in spiral bar size
increased the ultimate load for group A3 (tie bar size ϕ4 mm)
by 15.3%.
Interaction between the Local and General Zone The Open Civil Engineering Journal, 2021, Volume 15 59
Fig. (12). Elements and meshing, (a) whole model, (b) reinforcement (c) wedge plate and anchorage plate, (d) concrete.
Table 4. Ultimate load of the specimens.
Gr. Sp. Spiral Tie Exp. ult. FEA ult. PEXP/
No. No. bar size bar size load PEXP load PFEA PFEA
- - (mm) (mm) (kN) (kN) %
G1
SP1 6 6 1371 1356.5 101.1%
SP2 6 5 1358.1 1348.4 100.7%
SP3 6 4 1372 1340 102.4%
SP4 6 01134.4 1287.8 88.1%
G2
SP5 5 6 1390 1307.5 106.3%
SP6 5 5 1354 1293.6 104.7%
SP7 5 4 1266.4 1268 99.9%
SP8 5 01117 1213 92.1%
G3
SP9 4 6 1341 1235 108.6%
SP10 4 5 1331 1219.4 109.2%
SP11 4 4 1190 1210.8 98.3%
SP12 4 01085 1116.6 97.2%
G4
SP13 06 1187.5 990 119.9%
SP14 05 1177.6 985.8 119.5%
SP15 04 1114.5 978 114.0%
SP16 0 0 1098.6 927.2 118.5%
Table 5. Ultimate load of the specimens in rearranged groups.
Gr. Sp. Spiral Tie Exp. ult. FEA ult. PEXP/
No. No. bar size bar size load PEXP load PFEA PFEA
- - (mm) (mm) (kN) (kN) %
A1
SP1 6 6 1371 1356.5 101.1%
SP5 5 6 1390 1307.5 106.3%
SP9 4 6 1341 1235 108.6%
SP13 06 1187.5 990 119.9%
A2
SP2 6 5 1358.1 1348.4 100.7%
SP6 5 5 1354 1293.6 104.7%
SP10 4 5 1331 1219.4 109.2%
SP14 05 1177.6 985.8 119.5%
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(a) (b) (c) (d)
60 The Open Civil Engineering Journal, 2021, Volume 15 Werdina and Aziz
Gr. Sp. Spiral Tie Exp. ult. FEA ult. PEXP/
No. No. bar size bar size load PEXP load PFEA PFEA
- - (mm) (mm) (kN) (kN) %
A3
SP3 6 4 1372 1340 102.4%
SP7 5 4 1266.4 1268 99.9%
SP11 4 4 1190 1210.8 98.3%
SP15 04 1114.5 978 114.0%
A4
SP4 6 01134.4 1287.8 88.1%
SP8 5 01117 1213 92.1%
SP12 4 01085 1116.6 97.2%
SP16 0 0 1098.6 927.2 118.5%
Group A4 in Table 5 included specimens without tie
reinforcement, and as designed, had general zone failure.
Results of this group allowed studying the effect of the spiral
bar size on the ultimate load of the specimens when the failure
was in the general zone. This comparison represented an
investigation of the effect of local zone reinforcement on the
general zone strength. By comparing the specimen SP4 with
SP16, the increase in ultimate load was only 3.3% by using a
spiral bar size of ϕ6 mm compared to the case without spiral
reinforcement. Hence, there was a slight or no effect of the
local zone reinforcement on the general zone strength and
ultimate load of the anchorage zone when the failure was in the
general zone.
The last two columns of Table 4 and Table 5 present
results of the ultimate load of ABAQUS FEA, and the
comparison with the experimental test. FEA results are very
close to the experimental tests, and the percentage of
experimental to FEA ultimate load is within the range of
98.3-109.2% for the specimens that had spiral and tie
reinforcement. Moreover, the FEA showed similar results to
the experimental tests regarding the effect of different variables
on the ultimate load of the anchorage zone.
4.2. Load-displacement Relationship
Figs. ( 13 and 14 ) show the load-vertical displacement
relationship for the specimens in different groups. Initially, the
specimens showed the same linear behavior and then approxi-
mately the same non-linear relationship, especially for the
specimens with a spiral reinforcement. Compared to the other
specimens, the cases without spiral reinforcement (SP13, SP14,
SP15, SP16) showed more brittle failure, especially for the
specimen SP16 (without spiral and tie reinforcement) that had
a sudden failure. Compared to the specimen SP16, the general
zone ties for specimens SP13, SP14 and SP15 provided slight
confinement for the local zone.
The curves also show some agreement between the
experimental and FEA results, with the experimental values of
displacement for most of the specimens slightly more than the
finite element analysis, especially at the beginning stages. This
is justified with respect to the reasons that are detailed in
section 4.3.
It was observed in FEA that at ultimate load, the top turns
of the spiral reinforcement were at yield, and then gradually,
the other turns downward were yielding. This gave a flat
relationship after the ultimate load for the specimens with
spiral reinforcement compared to the specimens without spiral
reinforcement.
4.3. Stiffness
It can be observed in Figs. (13 and 14) that FEA values of
stiffness are greater than the experimental results. This
difference is justified for many reasons that include the
following:
• There are some differences between the FEA modeling
and the experimental specimens. In FEA modeling, perfect
homogenous materials are assumed for concrete, which could
not be the case for the experimental specimens. FEA also
assumes a perfect connection between the concrete and other
parts of the model that include the reinforcement and steel
plates. Moreover, micro-cracks produced by drying shrinkage
would reduce the stiffness of the experimental specimens.
For the experimental data, some secondary vertical
displacement is added as a result of instruments setting, closing
up with the anchorage devices, and secondary movement of the
loading machinery. This additional displacement reduces the
stiffness values for the experimental specimens.
There were some difficulties in measuring the total vertical
displacement of the experimental specimens, which, as shown
in Fig. (8), was determined by the difference of reading of two
dial gauges, fixed at the top and bottom of the specimens. This,
in addition to the secondary displacement mentioned before,
has an effect on the precision which is expected when
comparing the displacement, and hence the stiffness, among
different experimental specimens, taking into consideration
that the required displacement to be measured at the linear
stage was parts of 1 mm.
(Table 5) contd .....
Interaction between the Local and General Zone The Open Civil Engineering Journal, 2021, Volume 15 61
Fig. (13). Load–displacement relationship for the specimens in different groups.
Fig. (14). Load–displacement relationship for the specimens arranged in additional groups.
0
200
400
600
800
1000
1200
1400
0 0.5 1 1.5 2 2.5 3
3.5
Load (kN)
Vertical displacement (mm)
SP1
SP2
SP3
SP4
SP1 FEA
SP2 FEA
SP3 FEA
SP4 FEA
0
200
400
600
800
1000
1200
1400
0 0.5 1 1.5 2 2.5 3
3.5
Load (kN)
Vertical displacement (mm)
SP5
SP6
SP7
SP8
SP5 FEA
SP6 FEA
SP7 FEA
SP8 FEA
0
200
400
600
800
1000
1200
1400
0 0.5 1 1.5 2 2.5 3
3.5
Load (kN)
Vertical displacement (mm)
SP9
SP10
SP11
SP12
SP9 FEA
SP10 FEA
SP11 FEA
SP12 FEA
0
200
400
600
800
1000
1200
1400
0 0.5 1 1.5 2 2.5 3
3.5
Load (kN)
Vertical displacement (mm)
SP13
SP14
SP15
SP16
SP13 FEA
SP14 FEA
SP15 FEA
SP16 FEA
G1
G2
G3
G4
0
200
400
600
800
1000
1200
1400
0 0.5 1 1.5 2 2.5 3
3.5
Load (kN)
Vertical displacement (mm)
SP1
SP5
SP9
SP13
SP1 FEA
SP5 FEA
SP9 FEA
SP13 FEA
0
200
400
600
800
1000
1200
1400
0 0.5 1 1.5 2 2.5 3
3.5
Load (kN)
Vertical displacement (mm)
SP2
SP6
SP10
SP14
SP2 FEA
SP6 FEA
SP10 FEA
SP14 FEA
0
200
400
600
800
1000
1200
1400
0 0.5 1 1.5 2 2.5 3
3.5
Load (kN)
Vertical displacement (mm)
SP3
SP7
SP11
SP15
SP3 FEA
SP7 FEA
SP11 FEA
SP15 FEA
0
200
400
600
800
1000
1200
1400
0 0.5 1 1.5 2 2.5 3
3.5
Load (kN)
Vertical displacement (mm)
SP4
SP8
SP12
SP16
SP4 FEA
SP8 FEA
SP12 FEA
SP16 FEA
62 The Open Civil Engineering Journal, 2021, Volume 15 Werdina and Aziz
The groups G1 and G2 in Fig. (13) show greater stiffness
for the specimens with stronger tie reinforcement in the general
zone. In group G1, the specimens SP1 (with ϕ6 mm tie
reinforcement) and SP2 (with ϕ5 mm tie reinforcement) have
more stiffness than SP3 (with ϕ4 mm tie reinforcement) and
SP4 (without tie reinforcement). In group G2, and for the same
reason, the specimen SP5 has a greater stiffness than the other
specimens in the group. Tie reinforcement resists the tensile
bursting stresses in the general zone, and reduces cracks
propagation, increasing the stiffness of the specimens. The
effect of tie reinforcement on the stiffness of the specimen is
more clear in groups G1 and G2 compared to the other groups.
This is justified with respect to the reason that the local zone in
these two groups is confined with strong spiral reinforcement
(ϕ6 mm and ϕ5 mm). The local zone in these two groups will
not crack at the linear stage, and hence will not affect the
values of the stiffness of the specimens.
Considering the precision that is expected due to the points
mentioned in this section, the other curves in Figs. (13 and 14)
show a close stiffness among most of the experimental
specimens of the same group, except SP8 in Fig. (14).
4.4. Load-strain Relationship
4.4.1. Ties
Load versus axial strain curves for the ties for the short and
long direction are shown in Figs. (15 and 16), respectively. The
strain considered was at the center of the second ties for both
the short and long direction, which represented the critical
location for the tensile stresses. There is a good agreement in
these curves as observed from the FEA and the experimental
results.
The yielding strain for ties was 2005 μm, 2478 μm and
2140 μm for the bar size of ϕ6 mm, ϕ5 mm, and ϕ4 mm,
respectively. For the short direction, the range of the axial
strain in ties at ultimate load was 625-1025 μm, 867-1080 μm
and 1188-2112 μm for the tie bar size of ϕ6 mm, ϕ5 mm, and
ϕ4 mm, respectively. Similarly, for the long direction, the
range of the axial strain in ties at ultimate load was 311-608
μm, 400-450 μm and 251-510 μm for the tie bar size of ϕ6 mm,
ϕ5 mm, and ϕ4 mm, respectively. Hence, for all specimens, the
tie strain at ultimate load was less than the yielding strain,
which indicated the local zone failure rather than bursting
tensile failure in the general zone. Moreover, these experi-
mental values, together with the FEA results, showed that tie
strains at ultimate load for the short direction were greater than
the long direction, which implies that the short direction of the
studied specimens was more critical than the long direction for
the tensile bursting stresses.
The experimental results for the short direction showed
that the minimum tie strain at ultimate load was 625 micro-
strain for the specimen SP1, which had the maximum
reinforcement of ϕ6 mm for both the spirals and ties. For the
same direction, the maximum tie strain at ultimate load was
2112 micro-strain for the specimen SP15, which had the
minimum reinforcement of ϕ4 mm for ties, and had no spiral
reinforcement.
Fig. (15). Load–strain relationship for ties in the short direction.
0
200
400
600
800
1000
1200
1400
0 500 1000 1500
2000
Load (kN)
Strain (microstrain)
SP1
SP2
SP3
SP1 FEA
SP2 FEA
SP3 FEA
0
200
400
600
800
1000
1200
1400
0 500 1000 150 0
2000
Load (kN)
Strain (microstrain)
SP5
SP6
SP7
SP5 FEA
SP6 FEA
SP7 FEA
0
200
400
600
800
1000
1200
1400
0 500 1000 150 0
2000
Load (kN)
Strain (microstrain)
SP9
SP10
SP11
SP9 FEA
SP10 FEA
SP11 FEA
0
200
400
600
800
1000
1200
1400
0 500 1000 1500 2000
2500
Load (kN)
Strain (microstrain)
SP13
SP14
SP15
SP13 FEA
SP14 FEA
G15 FEA
Interaction between the Local and General Zone The Open Civil Engineering Journal, 2021, Volume 15 63
Fig. (16). Load–strain relationship for ties in the long direction.
In order to have a clearer picture of the axial stresses
distribution in ties and spirals at ultimate load, Fig. (17) shows
the FEA results of this type of stress for all specimens that have
tie reinforcement. S11 in Fig. (17) represents the axial stresses
in ties and spirals. For all the specimens, tie axial stresses at
ultimate load were less than the yielding stress of the reinfo-
rcement of 401 MPa, 495.5 MPa and 428 MPa for the bar size
of ϕ6 mm, ϕ5 mm and ϕ4 mm, respectively, a matter which
well agrees with the experimental results. Meanwhile, the axial
stresses in spiral reinforcements reached the yielding stress of
401 MPa, 495.5 MPa and 428 MPa for the bar size of ϕ6 mm,
ϕ5 mm and ϕ4 mm, respectively. As designed, these two facts
indicated the local zone failure rather than the general zone
bursting stresses failure for all the specimens with tie
reinforcement. These results well agree with the failure mode
and cracking pattern of the specimens detailed in section 4.6.
4.4.2. Concrete
Figs. ( 18 and 19 ) show the load-strain relationship for
concrete for the short and long direction, respectively. The
experimental and FEA results are close.
According to the results, the strain at ultimate load in the
short direction was more than the cracking strain of concrete
(141μm), indicating a crack pass at the mid of this direction.
Whereas, the maximum strain in the long direction was 95μm,
which was less than the cracking strain of concrete, indicating
no crack passed the specified location in the mid of this
direction. These results agree well with the experimental
cracking pattern of the specimens. For the short direction, the
accuracy which must be expected regarding the comparison
between the experimental and FEA results is that practically
the cracks may not pass through the line of strain gauges for
some specimens, causing some difference in their experimental
and FEA curves.
4.5. Bursting Stresses
Fig. ( 20 ) shows the FEA bursting stress contours, in the
elastic stage, at the surface of the models for both the long and
short direction for the group G1. S11 and S33 represent the
stresses Sxx and Szz, respectively. Bursting stresses for the
long direction extend in the area between the two anchorage
devices. Moreover, for both the long and short directions, the
concentration of these stresses is in the general zone and within
a depth close to the direction length. Previous studies [7, 8, 19]
provided a similar distribution and location for these stresses.
Bursting stresses distribution was almost the same for all
specimens, which indicated that the studied variables had no
effect on this kind of stresses at the elastic range. Only group
G1 was included in Fig. (19) as the other groups had similar
stress distribution.
0
200
400
600
800
1000
1200
1400
0 100 200 300 400 500 600
700
Load (kN)
Strain (microstrain)
SP1
SP2
SP3
SP1 FEA
SP2 FEA
SP3 FEA
0
200
400
600
800
1000
1200
1400
0 100 200 300 400 500 600
700
Load (kN)
Strain (microstrain)
SP5
SP6
SP7
SP5 FEA
SP6 FEA
SP7 FEA
0
200
400
600
800
1000
1200
1400
0 100 200 300 400 500 600
700
Load (kN)
Strain (microstrain)
sp9
SP10
SP11
SP9 FEA
SP10 FEA
SP11 FEA
0
200
400
600
800
1000
1200
1400
0 100 200 300 400 500
600
Load (kN)
Strain (microstrain)
SP13
SP14
SP15
SP13 FEA
SP14 FEA
SP15 FEA
64 The Open Civil Engineering Journal, 2021, Volume 15 Werdina and Aziz
Fig. (17). Axial stresses in spirals and ties at ultimate load.
SP2
SP3
SP5
SP6
SP7
SP1
Axial stresses in spirals an ate load.Axial stresses in ate load.
SP9
SP10
SP11
SP13
SP14
SP15
Interaction between the Local and General Zone The Open Civil Engineering Journal, 2021, Volume 15 65
Fig. (18). Load–strain relationship for concrete in the short direction.
Fig. (19). Load–strain relationship for concrete in the long direction.
0
200
400
600
800
1000
1200
1400
0 1000 2000 300 0 4000 5000 6000
7000
Load (kN)
Strain (microstrain)
SP1 SP2
SP3 SP4
SP1 FEA
SP2 FEA
SP3 FEA
SP4 FEA
0
200
400
600
800
1000
1200
1400
0 1000 2000 3000 4000 5000 600 0 7000
Load (kN)
Strain (microstrain)
SP5 SP6
SP7 SP8
SP5 FEA
SP6 FEA
SP7 FEA
SP8 FEA
0
200
400
600
800
1000
1200
1400
0 1000 2000 3000 4000 5000 6000
7000
Load (kN)
Strain (microstrain)
SP9 SP10
SP11 SP12
SP9 FEA
SP10 FEA
SP11 FEA
SP12 FEA
0
200
400
600
800
1000
1200
1400
0 1000 2000 300 0 4000 5000 6000
7000
Load (kN)
Strain (microstrain)
SP13 SP14
SP15 SP16
SP13 FEA
SP14 FEA
SP15 FEA
SP16 FEA
0
200
400
600
800
1000
1200
1400
-40-20 0 20406080100
Load (kN)
Strain (microstrain)
SP1
SP2
SP3
SP4
SP1 FEA
SP2 FEA
SP3 FEA
SP4 FEA
0
200
400
600
800
1000
1200
1400
-50 -30 -10 10 30 50 70 90
110
Load (kN)
Strain (microstrain)
SP5
SP6
SP7
SP8
SP5 FEA
SP6 FEA
SP7 FEA
SP8 FEA
0
200
400
600
800
1000
1200
1400
-30 -10 10 30 50 70 90
110
Load (kN)
Strain (microstrain)
SP9
SP10
SP11
SP12
SP9 FEA
SP10 FEA
SP11 FEA
SP12 FEA
0
200
400
600
800
1000
1200
1400
-20 0 20 40 60 80 100
Load (kN)
Strain (microstrain)
SP13
SP14
SP15
SP16
SP13 FEA
SP14 FEA
SP15 FEA
SP16 FEA
66 The Open Civil Engineering Journal, 2021, Volume 15 Werdina and Aziz
Fig. (20). FEA stress contours-MPa.
4.6. Cracking Pattern
Fig. ( 21 ) shows the cracking pattern of the experimental
specimens included in this study. ABAQUS FEA program does
not have a tool to display the cracks extent of the model, but
other parameters like plastic strain, logarithmic strain or tensile
damage can be used as an indication of crack development. In
this study, the tensile damage parameter DAMAGET has been
used as an indication of crack propagation. For every specimen
in Fig. (21), the first image is the tensile damage diagram from
ABAQUS FEA, and the other three are the experimental
cracking patterns in the long direction, short direction and top
surface, respectively. For the FEA, the red color indicates that
the tensile damage ratio is more than 80% in the elements. It
SP3
SP4
SP1
SP2
Interaction between the Local and General Zone The Open Civil Engineering Journal, 2021, Volume 15 67
can be observed that the cracking patterns of the experimental
tests and FEA are very similar, and there is a good agreement
between the two results regarding the cracks propagation and
failure mode. Moreover, the cracking pattern of the first
specimen (SP1) for both the experimental and FE results is
presented in detail with labels. The same presented details
apply to the cracking pattern of the other specimens, except for
the specimens that failed in the general zone (SP4, SP8, SP12,
SP16) and have a long crack in the short direction.
The experimental and FEA cracking patterns of the
specimens can be divided into two main groups, as follows:
• Specimens that failed in the general zone as they had no
tie reinforcement to resist the tensile bursting stresses in this
zone. These specimens included SP4, SP8, SP12, and SP16. As
mentioned in section 1.3, these specimens had large cracks
running parallel to the duct and extending from the anchorage
device, mainly in the short direction. For this group, the main
crack in the short direction extended down to the base and
divided the specimen into two parts, as a result of high tensile
bursting stresses with no tie reinforcement.
• All other specimens that failed in the local zone. These
specimens were designed to resist the tensile bursting stresses
and failure in the general zone. The cracks in both the short and
long directions were mainly concentrated in the upper and
middle parts of these specimens. Compared to the specimens
that failed in the general zone, the crack in the short direction
of this group was shorter and did not extend to the base. The
general zone of the specimens of this group was reinforced
with ties that resisted the tensile bursting stresses and limited
the extent of cracks.
Moreover, the following main points could be observed in
the experimental and FEA cracking patterns of the specimens:
For most of the specimens, the main crack in the short
direction passes through the center of this direction. This
matter well agrees with the strain value of concrete at ultimate
load, measured in the center of the short direction, which was
more than the cracking strain of concrete (section 4.4.2).
A crack did not pass through the center of the long
direction, a matter which well agrees with the experimental
results in section 4.4.2, when the measured strains at this
location were less than the cracking strain of concrete.
The cracks start under the anchorage devices, at the
loaded face of the specimens, which is subjected to very high
stresses and extends down to the sides.
Compared to the long direction, cracks in the short
direction are longer and extend downwards. This issue agrees
well with the experimental and FEA results presented in
section 4.4.1, as the tie strains in the short direction were more
than the tie strains in the long direction.
For the same tie reinforcement, the extent of cracks
increased with the decrease in spiral bar size. Hence, speci-
mens of group G4 (SP13, SP14, SP15 and SP16), which are
without spiral reinforcement, have more extents of cracks as
compared to the other three groups.
SP1
68 The Open Civil Engineering Journal, 2021, Volume 15 Werdina and Aziz
Fig. (21). Cracking patterns of the specimens.
SP2
SP4
SP3
Interaction between the Local and General Zone The Open Civil Engineering Journal, 2021, Volume 15 69
Fig. (21). Cracking patterns of the specimens (contd.).
SP6
SP5
SP8
SP7
70 The Open Civil Engineering Journal, 2021, Volume 15 Werdina and Aziz
Fig. (21). Cracking patterns of the specimens (contd.).
SP9
SP10
SP11
SP12
Interaction between the Local and General Zone The Open Civil Engineering Journal, 2021, Volume 15 71
Fig. (21). Cracking patterns of the specimens (contd.).
CONCLUSION
From the experimental and analytical work performed in
this study, fundamental behavioral understanding of the
anchorage zone with two anchorage devices and the interaction
between the local and general zone was obtained, and the
following main conclusions were drawn:
1. For the specimens that failed in the local zone but had
strong spiral reinforcement (ϕ6 mm), increasing the ties bar
SP13
SP14
SP15
G16
72 The Open Civil Engineering Journal, 2021, Volume 15 Werdina and Aziz
size of the general zone from ϕ4 mm to ϕ6 mm had no
influence on the specimen strength.
2. For the specimens that failed in the local zone and had
weak spiral reinforcement (ϕ4 mm), increasing the tie bar size
of the general zone increased the local zone strength and
ultimate load of the specimens. The ultimate load of the
specimens increased by 12.7% by increasing the tie bar size
from ϕ4 mm to ϕ6 mm. Nevertheless, the same increase in tie
bar size of the specimens without spiral reinforcement
increased the ultimate load by only 6.6%.
3. Tie reinforcement of the general zone provided
additional confinement for the local zone. This additional
confinement was more for the specimens with originally less
confined spiral reinforcement strength (ϕ4 mm). Nevertheless,
tie reinforcement could not significantly improve the ultimate
load of the anchorage zone in case if the spiral confinement of
the local zone was not available (specimens without spiral
reinforcement).
4. For the specimens that failed in the general zone
(specimens without tie reinforcement), there was a slight or no
effect of the local zone reinforcement on the general zone
strength and ultimate load of the specimens. The maximum
increase in ultimate load, in this case, was only 3.3% by using
a spiral bar size of ϕ6 mm compared to the case without spiral
reinforcement.
5. Confinement of the local zone modifies the ductility of
the specimens and prevents the brittle bearing and compression
failure of this zone.
6. For the specimens that failed in the local zone, the
cracks were concentrated at the upper and middle parts, while
the specimens that failed in the general zone had large cracks
running parallel to the duct starting from the anchorage device
and extending down to the base of the specimen.
7. Ultimate loads of the experimental tests were very close
to the ABAQUS FEA results. The percentage of experimental
to FEA ultimate load was within the range of 98.3-109.2% for
the specimens that had spiral and tie reinforcement.
8. Other experimental results, including relationships of
load versus axial strain of the ties, concrete strain at the critical
locations, crack propagation and failure modes, were in good
agreement with the finite element analysis.
CONSENT FOR PUBLICATION
Not applicable.
AVAILABILITY OF DATA AND MATERIALS
The authors confirm that the data supporting the findings
of this study are available within the article.
FUNDING
None.
CONFLICT OF INTEREST
The authors declare no conflict of interest, financial or
otherwise.
ACKNOWLEDGEMENTS
Declared none.
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