Experimental and Theoretical Investigation of Prestressing Steel Strand Subjected To Tensile Load
Experimental and Theoretical Investigation of Prestressing Steel Strand Subjected To Tensile Load
Experimental and Theoretical Investigation of Prestressing Steel Strand Subjected To Tensile Load
www.elsevier.com/locate/ijmecsci
PII: S0020-7403(16)30211-9
DOI: http://dx.doi.org/10.1016/j.ijmecsci.2016.09.006
Reference: MS3411
To appear in: International Journal of Mechanical Sciences
Received date: 1 July 2016
Revised date: 31 August 2016
Accepted date: 3 September 2016
Cite this article as: Yusuf Aytaç Onur, Experimental and theoretical investigation
of prestressing steel strand subjected to tensile load, International Journal of
Mechanical Sciences, http://dx.doi.org/10.1016/j.ijmecsci.2016.09.006
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Experimental and theoretical investigation of prestressing steel strand
Abstract
In this study, the response of prestressing strands to axial tensile load is investigated
theoretically and experimentally. Experimental data acquisitions of prestressing strand
subjected to tensile load are performed by means of strain gages and linear variable
differential transformer (LVDT). Feyrer’s and Costello’s theories are used for theoretical
calculation of strain and stress values occurred on wires of prestressing strand. Linear
regression model is devised to predict tensile load-strain and tensile stress-strain relations by
using experimental results. Results indicate that there is a powerful correlation between
results obtained by experimental data and linear regression model.
Keywords: theory of wire rope, prestressing strand, strain gages, tensile testing of wire rope
1. Introduction
Prestressing strands are used in vast variety of practical applications such as hoisting member
for lifting heavy load, precast concrete industry, post tensioning member in bridges, stadiums
and railway infrastructures. It is mostly subjected to tensile load. The behaviour of strands
subjected to tensile load has been of great deal of interest in many scientists. Investigation on
wire rope dates back to 1950’s. Love [1] presented general theory of bending and twisting of
thin rods. Machida and Durelli [2] gave explicit expressions for the determination of axial
force, bending and twisting moments in the helical wires and for the axial force and twisting
moments in the core of a 7-wire strand subjected to axial and torsional displacements.
Costello and Phillips [3] published a brief note to consider contact stresses between several
initially straight wires which are then twisted and pulled. Costello [4] presented a theory
which will predict stresses in a multi-layered cable subjected to axial, bending and torsional
loads. Velinsky, Anderson and Costello [5] developed a theory to predict static response of
wire rope with complex cross sections. Velinsky [6] developed a theory for the analysis of
fibre core wire rope with multi-layered strands. Velinsky [7] developed a general nonlinear
theory to analyse complex wire rope. Phillips and Costello [8] determined stresses in the
individual wires of complex wire rope. Their theory neglected effects of friction. Kumar and
Cochran [9] developed closed form solutions for elastic deformation characteristics of multi-
layered strands under tensile and torsional loads. Utting and Jones [10] performed
instrumented tests on straight simple steel strands of seven wire construction subjected to
axial loads and with various end restraints. Cappa [11] examined wire strains in a wire rope
strand subjected to static and quasi-static tensile load experimentally by using strain gages.
Costello [12] concerned with various theories of wire ropes in his book. Feyrer’s book [13]
presents wire loads, stresses and deformations on stranded, spiral and rotation resistant ropes
subjected to axial load. Ghoreishi, Messager, Cartraud and Davies [14] assessed the validity
domain of several analytical models such as Hrusca’s, McConnell, Costello etc. for the elastic
static axial behaviour of simple straight metallic strand. Gnanavel, Gopinath and
Parthasarathy [15] attempted to model wire-wire and core-wire contact effects to the
equilibrium equations about twisted wire cable. Argatov [16] employed asymptotic
modeling approach for solving the three-dimensional wear contact problem with
increasing contact zone under a prescribed constant normal load. The developed
asymptotic modeling approach has resulted in simple formulas for the main parameters
of the reciprocating sliding wear governed by Archard's generalized wear equation. The
accuracy of the constructed approximate solution has been verified against the finite
element method simulations taken from the literature. Argatov, Gomez, Tato and
Urchegui [17] applied mathematical models of fretting wear to elaboration of the
analytical results, auhors discussed some implications to fatigue life estimations of wire
ropes. Cho, Kim, Park and Park [18] propose a method enabling to compute the prestressing
strand resistance using strain measured on only one core wire. Numerical analysis is
conducted considering the pitch length of the strand and diameters of the core wire and helical
wires as parameters. Abdullah, Rice, Hamilton and Consolazio [19] conducted an extensive
addition, authors conducted sensitivity study of finite element parameters such as load ramp
profile, load ramp duration, friction model and damping to determine appropriate parameters
for an efficient model and authors used their model to conduct detailed investigation on load
distribution among wires followed by various parametric studies on wire breaks. The aim of
this study is to determine axial strain and tensile stress values occurred on core wire and
helical wires wrapped around core wire of prestressing strand which is 15.24 mm in diameter
Costello [12] and Feyrer [13] are used to calculate theoretical strain and stress values occurred
on core wire and helical wire. Linear regression is done to predict force-strain and stress-
2. Experimental Studies
2.1 Investigated strand
In this study, prestressing steel strand which are frequently used in hoisting member for lifting
heavy load, precast concrete industry, post tensioning member in bridges, stadiums and
and properties of prestressing strand used are selected in accordance with ASTM A416
standard [20] shown in Table 1. It has 5.24 mm diameter one core wire and 5.02 mm diameter
six helical wires wrapped around core wire. It has (1+6) wire construction. Diameter of strand
is 15.24 mm. Pitch length is 210 mm. Strand metallic cross-sectional area is computed by
summing of one core wire area and six outer wire areas as 140.319 mm2. Strand sample
Wisconsin-Madison,WI. Test strand is instrumented by strain gages and LVDT sensors and
chucks are mounted at each ends of prestressing strand to fasten sample to tensile testing rig
as shown in Fig. 1.
Strain gages and LVDT are installed before fastening strand sample to tensile testing
machine. Four strain gages named as SG1 (strain gage 1) , SG2 (strain gage 2), SG3 (strain
gage 3) and SG4 (strain gage 4) in Fig. 1 are carefully instrumented on cleaned wire surfaces
following micro measurements strain gage installation bulletins. Strain gages are then wired
Labview is used as signal conditioner in this study. Two different SCXI modules are used to
connect strain gage wires and LVDT wires to chassis. Quarter bridge wire configuration is
done according to procedure of data acquisition system. Strain gage resistance and gage factor
are important input to be defined in software. SG1 and SG3 grids are parallel to strand axis
and SG2 and SG4 grids are parallel to wire axis. SG3 and SG4 are installed on same outer
wire at a pitch length distant. Chucks used for fastening of test strand comprise of spring, jaw
and barrel. Schaevitz 100 HR type LVDT is used to measure strand axial displacement
thereby strain measurement of core wire or strand. Displacement is same in core wire and
strand. LVDT is thrusted into wood plate hole. A thin rod is connected by wood plate at
upper end and by bracket at bottom end. LVDT ferromagnetic core passing through the
cylinder is hot glued by thin rod which is 885.825 mm in length. This length is LVDT gage
length as shown in Fig. 1. Other side of thin rod is also glued to prevent movement. This
configuration provides parallelism between strand axis and thin rod axis. Due to this reason
strand displacement can be read by LVDT measuring thin rod displacement. Depending on
core’s location two different currents are induced into the secondary coils. These different
current can then be measured. The relationship between the signal voltage, the excitation
voltage, and the displacement to the core is quantified as the sensitivity of the LVDT. The
sensitivity can be thought of as the slope of the line that relates voltages in the device to the
displacement observed by the device. Calibration is done by using LVDT output voltage and
real displacement values and linear relation ratio is applied to results. The displacement is
then calculated depending on the wiring configuration used [21]. A view of experimental
setup is shown in Fig. 2. Static tensile loads are applied to 15.24 mm diameter prestressing
strand sample by means of tensile testing machine depicted in Fig. 2. Test strand is gripped by
using steel plates and chucks at the each to the frame block of test machine which is white
colour in Fig. 2.
Thin rod
LVDT Wood
plate
Test strand
Thin rod bracket Thin rod Steel Chuck
plate
Static tensile test is performed on 15.24 mm diameter prestressing strand sample. Ten
different tensile axial loads are applied to measure micro strains ( ) with strain gages and
displacement ( L ) with LVDT of center wire or strand and outer wires whose surfaces glued
by strain gages. Since experimental studies were conducted in University of Wisconsin
laboratory American unit system has been used for tensile load values which are converted to
Newton unit. The wires were bright and the strand was not lubricated. Displacements read by
experimental strain results on center wire where data collected by LVDT corresponding to
Strain (µε)
LVDT
(experimental)
Tensile load
(N)
8896,443 427,95134
17792,89 711,06596
26689,33 1047,05782
35585,77 1376,18604
44482,22 1716,84023
53378,66 2071,07499
62275,1 2463,65817
71171,55 2822,47622
80067,99 3158,52454
88964,43 3450,21872
Table 3 shows experimental strain results on outer wires where data collected by strain gages
Tensile stresses occurred on wires of prestressing strand can be easily calculated since steel
strand material obey Hook’s law formula ( E. ). Table 4 shows tensile stress occurred on
Stress results
(MPa) LVDT
Tensile load (experimental)
(N)
8896,443 81,182
17792,89 139,724
26689,33 205,75
35585,77 270,4206
44482,22 337,3591
53378,66 406,966
62275,1 484,1088
71171,55 554,6166
80067,99 620,6501
88964,43 677,968
Table 5 shows tensile stress occurred on outer wires corresponding to tensile loads applied.
outer layer as shown in Fig. 1. SG1 and SG3 are parallel to strand axis. The distance between
them is 250 mm. The reason why SG1 and SG3 are installed on outer wires parallel to strand
axis is that whether how outer wires are strained corresponding to strain of strand. It is
expected that if there is not unequal load share in strand wires strains and stresses in same
direction on each wires are same. When strain results are considered on SG1 and SG3 there is
a good harmony in the results obtained. Small deviation in results is caused by strain gage
misalignments with strand axis. It is obvious from results presented in Table 2 and Table 3
that strains on outer wires are smaller than center wire when strand subjected to axial tensile
load. It is found that strain and stress values on center wire obtained by means of LVDT
sensor are 8.44% greater than strain and stress values on outer wires in the direction of strand
axis when average of SG1 and SG3 results is taken. It is found that strain and stress values in
the direction of wire axis of outer wire are 3.34% greater than strain and stress values in the
direction of strand axis of outer wires when average of SG1 and SG3 results and SG2 and
SG4 results are taken. It is an important finding drawn from in Table 2 and Table 3 that outer
wires are subjected to greater strain and stress values in the direction of wire axis than in the
direction of strand axis. It is concluded from findings that center wire suffers a slightly greater
strain and stress than outer wires which obey Costello’s [12] study.
3. Theoretical Studies
There have been several of theoretical models which are based on different assumptions as
explained in the literature survey. In this study, two different analytical models are considered
one of which is Costello’s model and second is Feyrer’s model. Both of theories draw
scientist’s attention for five decades to derive new findings on wire rope technical literature.
3.1 Costello’s theory
Costello’s theory based on Love’s general theory of bending and twisting of thin rods [1].
Axial response of a simple straight strand is expressed by a set of six nonlinear equations of
equilibrium for large deflections assuming that outside wire is not subjected to external
bending moments per unit length. It is assumed that center wire is of sufficient size to prevent
the outer wires from touching each other in theory [12]. It is initially checked before applying
the theory. Fig. 3 shows the configuration and cross section of an unloaded prestressing
straight strand. Costello’s theory first needs strain or center wire strain (ξ1) value and angle of
twist per unit length of the strand (τs) to calculate outer wire strain(ξ2) and change in helix
angle ( 2 ) before and after loading. Equation set (1) is used to calculate ξ2 and 2 .
2
1 2
tan 2
r2 s
2 R R22
2 1 1
tan 2 r2 tan 2
p2
tan 2 (1)
2 r2
where R1 is radius of center wire (mm), R2 is radius of outside wire (mm), r2=R1+R2 is initial
The change in curvature 2 and the change in twist per unit length 2 are then calculated
Bending moment, axial wire tension, twisting moment, shearing fore components on a wire
cross section in the x,y and z directions caused by change in curvature and change in twist per
G2
3
R2 2
ER 2 4
H2
R2 2
ER2
3
4(1 )
F1
2
1
ER1
T2
2
2 (3)
ER 2
where G2 is bending moment on an outside wire in y direction (Nmm), H 2 is twisting moment
on an outside wire (Nmm), F1 is axial force acting on the center wire (N), T2 is the axial
tension in the outside wire (N). Subscript 1 in the force denotes center wire. Subscript 2 in the
Stresses caused by these loads are also given in [12]. In the case of center wire, the axial wire
F1
1 (4)
R1 2
F
The outside wires are subjected to axial, bending and torsional loadings in addition to
shearing load. The stresses caused by the shearing force in general are very small and will be
neglected. The axial stress caused by the load T2 is given in equation (5).
T2
2 (5)
R2 2
T
Maximum normal stress due to the bending moment on an outside wire in y direction is given
in equation (6).
4G2 (6)
G 2
R23
The maximum normal tensile stress acting on an outer wire is given in equation (7).
T 2 + G 2 (7)
Angle of twist per unit length of the strand (τs) is assumed to be zero. Equation (4) gives axial
wire stress on center wire and equation (7) gives tensile stress on an outside wire. LVDT
sensor outputs are taken as center wire strain (ξ1) value in the application of Costello theory.
Outer wire strains (ξ2) calculated by using Costello’s theory are shown in Table 6.
Strain (µε)
Costello
(in the direction of wire axis)
Tensile load
(N)
8896,443 415,1894
17792,89 689,8612
26689,33 1015,834
35585,77 1335,147
44482,22 1665,642
53378,66 2009,313
62275,1 2390,189
71171,55 2738,307
80067,99 3064,334
88964,43 3347,330
It can be seen from Table 6 that there is 2.32% deviation in strain values on an outer wire
obtained by using Costello’s theory than average of SG2 and SG4 strain outputs depicted in
Table 3 which are installed in the direction of wire axis for each tensile loads. Axial wire
stresses on center wire are calculated by using Costello’s theory and presented in Table 7.
Stress results
(MPa)
Tensile load Costello
(N)
8896,443 84,092
17792,89 139,75
26689,33 205,75
35585,77 270,4206
44482,22 337,36
53378,66 406,97
62275,1 484,1088
71171,55 554,617
80067,99 620,65
88964,43 677,97
Tensile stresses on center wire nearly overlap with the LVDT results. Costello’s theory gives
satisfactory results. Tensile wire stresses on an outer wire are calculated by using Costello’s
Stress results
(MPa) Costello
(in the direction of
wire axis)
Tensile load
(N)
8896,443 83,703
17792,89 139,076
26689,33 204,792
35585,77 269,166
44482,22 335,794
53378,66 405,08
62275,1 481,8624
71171,55 552,042
80067,99 617,77
88964,43 674,822
It is easy to see from Table 8 that tensile stress values on an outer wire obtained by using
Costello theory are greater than SG2 and SG4 stress outputs depicted in Table 5. It is found
that stress values on an outer wire obtained by using Costello theory are 4.42% greater than
Feyrer’s book [13] presents a calculation method on wire strain and stress. Forces on a strand
are shown in Fig. 4a neglecting shearing force which is very slight. In fig. 4a, Si is tensile
strand force in strand axis direction (N), Fi is wire tensile force (N) and Ui is circumference
force (N).
It is an important notation change about lay angle (α) that lay angle αi in Feyrer equation is
taken 90- α2=8,72618° in prestressing strand investigated since Feyrer’s equations are derived
by using this lay angle. Simple relation for the tensile force in a wire in the layer i depicted in
Si (8)
Fi
cos( i )
(9)
Ui Fi .sin(i )
The length of the outer wire (li) is found by using equation (10).
ls (10)
li
cos( i )
Elongation of strand or center wire ls is easily calculated by using strand length ls and strand
strain value s correspond to applied tensile load ( s = ls /ls). Strain of a wire in the layer i is
found such a manner that i = li /li. Elongation of a wire in the layer i is found regarding
ls .cos i
li (11)
1 i .sin 2 i
Strand
axis
(a) (b)
Outer wire strain is found by using equation (10) and equation (11). Table 9 show strain
Results indicate that there is a good match between Costello and Feyrer’s theoretical strain
results on one outer wire of prestressing strand at each loading levels. It is easy to see from
Table 9 that strain values on an outer wire obtained by using Feyrer’s theory are greater than
SG2 and SG4 strain outputs depicted in Table 3 for each tensile loads. It is found that there is
2.32% deviation in strain values on an outer wire obtained by using Feyrer’s theory than
ls n zi .cos3 i
S . .Ei . Ai (12)
ls i 0 1 i .sin i
2
where zi is the number of wires in the wire layer i, Ei is modulus of elasticity (MPa) in the
The tensile stress in a wire of specific wire layer k is found by using equation (13).
cos 2 k
.Ek
Fk 1 k .sin 2 k
çk n .S (13)
Ak zi .cos3 i
i 0 1 i .sin i
2
.Ei . Ai
αk in equation (13) is taken as zero in the center wire stress calculation since center wire is
straight. Axial wire stresses on center wire is calculated by using Feyrer’s theory and
Stress results
(MPa)
Feyrer
Tensile load
(N)
8896,443 84,086
17792,89 139,75
26689,33 205,749
35585,77 270,419
44482,22 337,378
53378,66 406,994
62275,1 484,141
71171,55 554,643
80067,99 620,642
88964,43 678,004
Tensile stresses on center wire nearly overlap with Costello and LVDT results. Feyrer’s
theory gives satisfactory results. Tensile wire stresses on an outer wire are calculated by using
8896,443 81,587
17792,89 139,75
26689,33 199,635
35585,77 262,383
44482,22 327,352
53378,66 394,9
62275,1 469,754
71171,55 538,161
80067,99 602,2
88964,43 657,856
It is found from Table 11 that there is 2.64% deviation in tensile stress values on an outer wire
obtained by using Feyrer’s theory than average of SG2 and SG4 strain outputs depicted in
Table 5 for each tensile loads. Feyrer’s tensile stress results for an outer wire give more
Regression analysis is used to investigate the relation between dependant variable and
independent variable(s). First phase of the regression analysis is to find the best mathematical
model definition. In this study, dependent variables are tensile force and tensile stress. There
is independent variable which is strain of center wire or outer helical wire in micro epsilon
unit. Since there is one independent variable author proposes linear regression model adhering
to the experimental results. General form of linear regression model has been shown in
a2 a3 ( ) E (14)
where ai’s are constant and E is residual term. To constitute a novel theoretical prediction
equation authors used the least square method. The least square method is the one of the most
convenient method for curve fitting. The best fit in the least square method means that
minimize the sum of squared residuals. Minimum of the sum of residual squares is found by
resolving the gradient and equalizing them to zero [23]. ai’s are determined by solving
LVDT readings are used as independent variable ( ) to predict tensile load and center wire
stress which are dependent variable. The novel theoretical prediction equations by using the
F 734,9898350059 25,806853053( )
In statistics, in order to check the validity of the theoretical prediction equation the coefficient
[24]. The coefficient of determination (r2) has been found as 0.9990 for F- equation and
There is a powerful correlation between the results obtained by theoretical model presented
and the experiment results since the correlation coefficient converges to 1 [21].
SG2 and SG4 readings are used as independent variable ( ) separately to predict tensile
load and outer wire stress which are dependent variable. Since coefficient of determination is
found greater in SG2 results than SG4 for F- equation only theoretical prediction equation
constituted by using SG2 results is presented in equation set (16). Since coefficient of
determination is found equal in SG2 and SG4 results for - equation author presented one
Negative constant values in equation sets (15) and (16) are only based on mathematical
operations of least square method. Finally, negative constant values are stochastic.
The coefficient of determination (r2) has been found as 0.9998 for F- equation and 0.9999
There is a powerful correlation between the results obtained by theoretical model presented
and the experiment results. Signal conditioners frequently give micro strain ( ) as output
Experimental instrumentation and tensile test studies on prestressing strand have been
Wisconsin-Madison, WI. Axial tensile stress and strain values of center wire and outer wire(s)
are obtained by using several of sensors such as LVDT and strain gages. Experimental data
are collected and presented. Costello and Feyrer’s theory are used to calculate axial tensile
stress and strain values of center wire and outer wire(s) of prestressing strand. Experimental
and theoretical results are compared. Linear regression is performed to obtain novel
Fig. 5 shows -F graph which is obtained by theoretically and experimentally for center
wire.
800
Costello
700 Feyrer
LVDT
600
Tensile Stress (MPa)
500
400
300
200
100
0
8896,443 17792,89 26689,33 35585,77 44482,22 53378,66 62275,1 71171,55 80067,99 88964,43
Tensile stresses obtained experimentally and theoretically on center wire related to tensile
Fig. 6 shows - F graph which is experimentally obtained by LVDT sensor for center wire.
3450,2187 LVDT
3158,5245
2822,4762
2463,6582
micro epsilon
2071,075
1716,8402
1376,186
1047,0578
711,066
427,9513
8896,443 17792,89 26689,33 35585,77 44482,22 53378,66 62275,1 71171,55 80067,99 88964,43
stress and strain calculations of wires of wire rope since LVDT outputs are taken as initial
assumption of center wire strain in the theoretical Costello’s and Feyrer’s calculations.
Fig. 7 shows -% graph which is obtained theoretically and experimentally for an outer
wire.
800
Costello
700
Feyrer
Strain gage 2
600 Strain gage 4
Tensile Stress (MPa)
500
400
300
200
100
0
0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35
%Strain
It is easy to see from Fig. 7 that tensile stress values on an outer wire obtained by using
Costello’s theory are greater than SG2 and SG4 stress outputs depicted in Table 5 for each
load level. When reliability of outer wire of prestressing strand is considered Costello’s safety
factor values become always lower than Feyrer’s and experimental results . It is found that
stress values on an outer wire obtained by using Costello’s theory are 4.42% greater than
average of SG2 and SG4 strain outputs. In addition, there is 2.64% deviation in tensile stress
values on an outer wire obtained by using Feyrer’s theory than average of SG2 and SG4 strain
outputs. Feyrer’s tensile stress results for an outer wire give more accurate than Costello’s
when experimental results are considered. Beside tensile stress results, there is 2.32%
deviation in strain values on an outer wire obtained by using Costello’s theory than average of
SG2 and SG4 strain outputs. There is 2.32% deviation in strain values on an outer wire
obtained by using Feyrer’s theory than averages SG2 and SG4 strain outputs. Results indicate
that there is a good match between Costello and Feyrer’s theoretical strain results on one outer
which reader can also observe - F variation on an outer wire and together with -% graph
as Fig. 7.
800
Costello
700
Feyrer
Strain gage 2
600 Strain gage 4
Tensile Stress (MPa)
500
400
300
200
100
0
8896,443 17792,89 26689,33 35585,77 44482,22 53378,66 62275,1 71171,55 80067,99 88964,43
Author used SG1 and SG3 results to gather strain values on an outer wire of prestressing
strand in the direction of strand axis since wire rope theories only focused on outer wire strain
and stress calculation in the direction of wire axis. When strain results are considered on SG1
and SG3 there is a good harmony in the results obtained. Small deviation in results is caused
by strain gage misalignments with strand axis. It is obvious from results presented in Table 2
and Table 3 that strains on outer wires are smaller than center wire when strand subjected to
axial tensile load. It is found that strain and stress values on center wire are 8.44% greater
than strain and stress values on outer wires in the direction of strand axis when average of
SG1 and SG3 results is taken. It is an important finding drawn from SG1,SG2, SG3 and SG4
results in Table 2 and Table 3 that outer wires suffer greater strain and stress values in the
direction of wire axis than in the direction of strand axis. It is found that strain and stress
values in the direction of wire axis of outer wire are 3.34% greater than strain and stress
values in the direction of strand axis of outer wires when average of SG1 and SG3 results and
SG2 and SG4 results are taken. It is concluded from findings that center wire suffers a slightly
greater strain and stress than outer wires which obey Costello’s[12] study.
Linear regression models are devised to predict force-microstrain and tensile stress-
microstrain relations by using data obtained by experimental studies when prestressing strand
is subjected tensile load for center wire and outer wire. Least square method is used to find
equation constant ai’s. The novel theoretical prediction equations by using the least square
method are given in equation set (15) and (16) for center wire and outer wire separately.
5.Conclusions
In this study, experimental strain measurements of wires of prestressing strand which is 15.24
mm in diameter subjected to tensile load have been performed by using strain gages and
LVDT sensors. Theories proposed by Costello and Feyrer are used to calculate theoretical
strain values occurred on core wire and helical wire. Tensile stresses occurred on center wire
and outer wire of prestressing strand are then calculated and presented experimentally and
theoretically. Linear regression models are devised to predict force-strain and stress-strain
1) There is a good match between Costello and Feyrer’s theoretical strain results on one
factor values become always lower than Feyrer’s and experimental results .
4) Center wire suffers a slightly greater strain and stress than outer wires which obey
Costello’s study.
5) Feyrer’s tensile stress results for an outer wire give more accurate than Costello’s
Acknowledgement
The author is immensely grateful to Prof. Michael G. Oliva who is faculty of University of
Wisconsin-Madison for being advisor during postdoctoral study. Author was supported by
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Highlights
There is a good match between Costello and Feyrer’s theoretical strain results on one
Outer wires suffer greater strain and stress values in the direction of wire axis than in
factor values become always lower than Feyrer’s and experimental results .
Center wire suffers a slightly greater strain and stress than outer wires which obey
Costello’s study.
Feyrer’s tensile stress results for an outer wire give more accurate than Costello’s