BEHAVIOR OF STANDARD HOOK ANCHORAGE MADE WITH CORROSION RESISTANT REINFORCEMENT By GIANNI T. CIANCONE A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ENGINEERING UNIVERSITY OF FLORIDA 2007 1
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BEHAVIOR OF STANDARD HOOK ANCHORAGE MADE WITH CORROSION RESISTANT REINFORCEMENT
By
GIANNI T. CIANCONE
A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ENGINEERING
2 LITERATURE REVIEW .......................................................................................................15
Hook Behavior and Geometry ................................................................................................15 Current Hook Design Practice ................................................................................................16 High-Strength Steel Reinforcement........................................................................................21 Strut and Tie Evaluation of Anchorage ..................................................................................21
Formwork ........................................................................................................................33 Casting.............................................................................................................................34 Test Setup ........................................................................................................................34 Data Acquisition Setup....................................................................................................35
4 RESULTS AND DISCUSSION.............................................................................................47
4-4 Crack pattern for concrete splitting failure. .......................................................................64
4-5 Concrete crushed inside of bend radius .............................................................................64
4-6 Load-displacement for mild steel.......................................................................................65
4-7 Mild steel results in terms of hook capacity. .....................................................................65
4-8 Load-slip for specimens.....................................................................................................65
4-9 Locations where relative slip was measured......................................................................66
4-10 Load-slip for specimen. .....................................................................................................66
4-11 Typical load-slip behavior for #5 mild steel specimens with 180-degree hook (60_5_180_35_2 shown). ..................................................................................................66
4-12 Relative slip at locations D1 and D2 for unconfined specimens with debonded length..................................................................................................................................67
4-13 Typical load-slip behavior for #7 mild steel specimens with 180-degree hook (60_7_180_35_4 shown). ..................................................................................................67
4-14 Load - displacement for stainless steel. .............................................................................68
4-15 Stainless steel results in terms of hook capacity. ...............................................................68
4-16 Load-slip for specimens . ...................................................................................................68
4-17 Typical load-slip behavior for 16mm stainless steel specimens with both 90 and 180-degree hooks (SS_16_180_35_4 show).............................................................................69
4-18 Typical load-slip behavior for 20mm stainless steel specimens with both 90 and 180-degree hooks (SS_20_90_35_2 shown).............................................................................69
4-19 Load-displacement for MMFX steel..................................................................................70
4-20 MMFX results in terms of hook capacity. .........................................................................70
10
11
4-21 Typical load-slip behavior for #5 MMFX specimens with both 90 and 180-degree hooks (MM_5_90_25_2 shown)........................................................................................70
4-22 Typical load-slip behavior for #7 MMFX specimens with both 90 and 180-degree hooks (MM_7_180_35_4 shown)......................................................................................71
5-2 Comparison of normalized bond stress at capacity............................................................84
5-3 Comparison of ductility ratios ...........................................................................................85
B-1 Crack patterns, load-slip, and stress-strain curves for mild steel hooked bars. .................90
B-2 Crack patterns, load-slip, and stress-strain curves for stainless steel hooked bars. ...........97
B-3 Crack patterns, load-slip, and stress-strain curves for MMFX hooked bars....................106
Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Engineering
BEHAVIOR OF STANDARD HOOK ANCHORAGE MADE WITH CORROSION RESISTANT REINFORCEMENT
By
Gianni T. Ciancone
December 2007
Chair: H. R. Hamilton Major: Civil Engineering
The objective of this study was to evaluate the behavior of standard hooks that are made
using high strength reinforcing bars and tested in tension. The bars evaluated were ASTM A615,
316LN Stainless Steel and MMFX microcomposite steel. The impetus is that the current
ACI/AASHTO equations for the development length of standard hooks do not address the use of
high-strength and corrosion resistant steel bars. The development length of standard hooks was
evaluated in terms of concrete strength, bar size, hook geometry, concrete covers, debonded
length, and lateral reinforcement.
Forty-eight specimens with different development length of standard hooks were
constructed in accordance with ACI 318 and AASHTO Bridge Design Specifications. Four
specimen design configurations were used as unconfined, confined with stirrups, unconfined
with debonded length for 90 degree hooked bar and unconfined with debonded length for 180
degree hooked bar.
Compressive cylinders tests were conducted in order to determine the target of average
concrete strength of 5500 psi. Also, rebar samples were tested in tension to obtain the yield, and
tensile strength.
12
13
A test frame was constructed in the University of Florida-Structures Lab to test
specimens in tension by means of a center hole hydraulic jack. During the test, cracks pattern
were observed, and load-displacement were recorded.
Test results were compared in function of anchorage capacity, bond stress, ductility, and
K-factor. Also, test results indicated that mild steel was consistent and agreeable with ACI and
AASHTO requirements for development lengths. For #7 MMFX hooked bars, however, further
investigation need to be conducted to evaluate the proper development length.
Based on the results obtained from this research the test setup and the procedures using the strut
and tie approach appear to provide an adequate basis to evaluate the unconfined anchorage
capacities of grade 60 hooked bars.
CHAPTER 1 INTRODUCTION
Mild steel reinforcing bars have been used for decades in buildings, bridges, highways,
and other construction projects. One weakness of reinforcement is its lack of corrosion resistance
if the concrete cover is breached or penetrated by corrosive elements such as chlorides. This
issue can drastically reduce the service life of the structure requiring costly repairs or even
replacement early in the life of the structure. One potential solution that has been explored is the
use of corrosion resistant steels such as stainless steel, and MMFX. These materials typically
have higher strengths than that of mild steel. However, the use of high-strength and corrosion
resistant bars has been presented as a substitute for coated and uncoated Grade 60 bars. On the
other hand, high-strength reinforcing steel bar reduces not only the use of steel in structural
elements but also the labor costs.
The main objective of this research was to evaluate the behavior of standard hook
anchorages made with high-strength bars as Stainless Steel and MMFX microcomposite steel
relative to Grade 60 steel. Since the current ACI/AASHTO Code specifications do not address
the use of these kinds of materials, equations for the development length of standard hooks made
with high-strength and corrosion resistant steel bars need to be evaluated. The development
length of standard hook was evaluated in terms of concrete strength, bar size, hook geometry,
concrete covers, slip, anchorage capacity, ductility, bond stress, and K-factor. Also, cracks
pattern were evaluated with respect to the failure modes.
14
CHAPTER 2 LITERATURE REVIEW
The structural performance and flexural behavior of high-strength steel reinforcement has
been evaluated as a substitute for Grade 60 bars. Limited research, however, has been conducted
dealing with the behavior of standard hook anchorages made with high-strength reinforcement.
Hook Behavior and Geometry
The structural concrete codes are designed so that, wherever possible, the reinforcement
will yield before the concrete crushes when the nominal strength of a reinforced concrete
element is reached. Development of the yield strength of a reinforcing bar requires that a
sufficient length of bond is available on either side of the critical section where capacity is
expected to occur. In locations where space is limited, insufficient space may be available to
allow a reinforcing bar to develop. In these cases, it is common to bend the bar to form either a
90-degree or 180-degree hook. Figure 2-1 gives an example of one possible situation where a
concentrated load is located near the end of a cantilever beam. The critical section for flexural
strength is located at the face of the support. If the required straight development length is
longer than the cantilever, then the bar would protrude from the concrete. The typical method to
deal with this situation is to turn the bar down into the section, creating a 90-degree hook.
The required length to develop the hook is shorter due to the mechanical advantage
provided by the concrete located at the inside radius of the bend. Figure 2-2 shows the normal
bar stresses in a #7 90-degree hook as reported by Marques and Jirsa (1975). The stresses in the
bar increase dramatically around the bend of the hook (from 13 ksi to 57 ksi), indicating that the
bearing of the inside of the hook against the concrete provides a significant portion of the
anchorage. These bearing stresses cause significant lateral tensile stresses, which can result in a
splitting failure when confinement reinforcement is not present.
15
Because the strength of hooked anchorages is determined empirically, it was necessary to
create a standard geometry for hooks. Figure 2-3 shows the dimensions for “standard hooks”
that are the same in both ACI and AASHTO design specifications. The development length
approach was first proposed by Pinc, Watkins, and Jirsa (1977). Table 2-1 shows the minimum
hook dimensions proposed in this research.
Current Hook Design Practice
Standard hook anchorages are currently designed using either the provisions of AASHTO
Bridge Design Specifications (2004) for bridges or ACI Building Code and Commentary (2005)
for buildings. The ACI Equation is
f 'c
yf
bλd02.0
dhl
eψ= (2-1)
and AASHTO LRFD Specifications equation is:
60y
f
f c
bd38
l 'dh= (2-2)
where ldh is the hook development length in in., ψe is the coating factor, λ is the lightweight
aggregate concrete factor, db is the bar diameter in in., f’c is the specified concrete strength in psi,
and fy is the specified yield strength of the bar in psi.
These provisions were developed in the early 1970s and were finally implemented into
the code in their present form in 1979.
16
Minor and Jirsa (1975) studied the factors that affect the anchorage capacity of bent
deformed bars. Specimen geometry was varied to determine the effect of bond length, bar
diameter, inside radius of bend, and angle included in the bend. Slip between the bar and the
concrete was measured at several points along the bar as load was applied. Load-slip curves were
used to compare different bar geometries. The results indicated that most of the slip occurred in
the straight and curve portion of the hook.
Marques and Jirsa (1975) investigated the anchorage capacity of hooked bars in beam-
column joints and the effect of the confinement at the joint. The variables considered were size
of anchored bars, hook geometry, embedment length, confinement, and column axial load. Full
scale beam-columns specimens were designed in order to allow the use of large diameter hooked
bars in accordance with ACI 318-71 code hook geometry standards. The test used #7 and #11
mild steel bars anchored in the columns. ACI 318-71 specifications were used for 90 or 180
degree standard hooks. Also, for 90 and 180 degree standard hooks, slip of the bar relative to the
surrounding concrete was measured at five points along the anchored bar (Figure 2-4).
As results, the slip measured on the tail extension of the hook was very small in
comparison with slip measured at the point (1H) and the point (2H). The slip measured at the
lead was greatest in most of the cases. Also, the slip at point (2H) was similar to the slip at point
(1H) when the lead straight embedment was short. In addition, the strength of the bars was
evaluated using the ACI 318-71 design provisions for hooked bar. The strength was determined
by calculating the stress developed by the hook (fh) plus an additional straight lead embedment
(ll). It was found that the straight lead embedment calculated using the basic equation for
development length was not enough to develop the yield stress in the hooked bar. On the other
17
hand, the use of shorter straight embedment did not improve the stress transferring from the bar
to the concrete.
Marques and Jirsa (1975) found that the equations from ACI 318-71 underestimated the
anchorage capacity of the hooks. They found that for their test specimens the tensile stress in the
bar when the bond capacity was reached was:
'f)d3.01(700f cbh ψ−= (2-3)
where fh can not be greater than fy in psi, db is the diameter of the bar in in., f’c is the average
concrete strength in psi, and ψ is a coefficient factor which depends on the size of the bar, the
lead straight embedment, side concrete cover and cover extension of the tail.
They also determined the straight lead embedment length (ll) between the critical section
and the hook could be expressed as follows:
''
chybl l]f/)ff(A04.0[l +−= (2-4)
where l’ is 4db or 4 in., whichever is greater, Ab is the bar area in sq. in., fy the yield strength of
the bar in psi, fh the tensile stress of the bar in psi, and f’c is the average concrete strength in psi.
Pinc, Watkins, and Jirsa (1977) also studied beam-column joints to determine the effect
of lead embedment and lightweight aggregate concrete on the anchorage capacity of the hook.
The first approach consisted in examining the hook and lead embedment separately. Variables as
fl/f’c0.5 and ll/db were correlated to obtain the straight embedment strength (fl). The total strength
of the anchored bar (fu) resulted by adding the straight embedment strength (fl) and the hook
strength (fh) equation:
18
'cblbu f)d/l8.0d4.01(550f ψ+−= (2-5)
Also, the variables fu/f’c
0.5 and ldh/db were plotted to obtain the following equation:
bdh d/fl50f 'cu ψ= (2-6)
As results, it was found that Equation 2-5 and Equation 2-6 were practically the same
except for the number of terms in each equation. Equation 2-6 can be rearranged into a form that
gives the development length, a parameter that is more useful in design:
'
c
ybdh f
fd02.0l
ψ= (2-7)
where ldh represents the development length for a hooked bar in in., db is the diameter of the bar
in in., fy is the yield strength of the bar, f’c is the average concrete strength in psi, and ψ is a
coefficient factor which depends on the size of the bar.
The ACI 408.1R-79 presented recommendations for standard hook provisions for
deformed bars in tension based on the study reported by Pinc, Watkins, and Jirsa (1977), and
those recommendations were discussed and explained by Jirsa, Lutz, and Gergely (1979). The
development length (ldh) for standard hook proposed for the ACI 408 committee was the result of
the product of the basic development length (lhb) and the applicable factors. The basic
development length was computed as:
'
c
bhb f
d960l
φ= (2-8)
19
where lhb represents the basic development length for a hooked bar in in., db is the diameter of
the bar in in., f’c is the average concrete strength in psi, and ϕ represents the factor for anchorage
which was incorporated in the design equation.
The applicable factors included in ACI 408 committee were fy/60,000 for reinforcement
having yield strength over 60,000 psi, 0.7 for side cover, 0.8 for use of stirrups, 1.25 for use of
lightweight aggregate, and Asr/Asp for reinforcement in flexural members in excess. Figure 2-5
shows the recommended ϕ factor not only for splices but also for hooked bar, and it compares
the test/calculated values for ACI 318-77 with proposed ϕ factor of 0.8.
Figure 2-6 shows a comparison between the development length proposed and ACI 318-
77. The proposed development length was computed as a lineal function of the diameter of the
bar (Figure 2-6), the greater the diameter of the bar the greater the development length. For ACI
318-77, the development length was underestimated from #3 until #8 bars and overestimated for
bars greater than #8 in comparison with the proposed.
Basically, the ACI 318 for basic development length for hooked bar has not changed
since 1979. Also, most of the applicable factors have not changed except for the inclusion of the
epoxy-coated factor of 1.2 which was proposed by Hamad, Jirsa, and D’Abreu de Paulo (1993)
and included in the ACI 318-95.
For ACI 318-02, the basic development length equation changed in the way as the terms
were arranged. Applicable factors as epoxy-coated (β), lightweight concrete (λ) and the yield
strength of the bar (fy) were included in the equation rather than being multiplier factors.
Additionally, in this code was included a factor of 0.8 for 180 degree hook enclosed within ties
or stirrups.
20
Finally, the development length and the factors included in the current ACI 318 code are
the same as ACI 318-02.
High-Strength Steel Reinforcement
High strength steel reinforcement has been introduced as a material which is more
durable than steel reinforcing bars. The use of high strength reinforcing bars is increasingly
rapidly due to the advantages that can offer over conventional reinforcing steel such as fatigue
resistance, corrosion resistant, toughness, and ductility. Also, high strength reinforcing bars can
be used in bridges and other structures where the high seismic activity is prevalent. Stainless
Steel and MMFX are one of the materials categorized as high strength steel due to they do not
have well-defined yield points and do not exhibit a yield plateau. Stainless Steel reinforcing bars
can be used in reinforced concrete structures where very high durability is required and the life
cost analysis is justified. Also, stainless rebar has been used thoroughly in North America and
Europe. Stainless rebar might be considered to be used in marine structures where chloride ion is
present. As Stainless Steel, MMFX reinforcement is a corrosion-resistant material and stronger
than conventional steel. MMFX reinforcing bars have been also used in structures across North
America including bridges, highways, parking garage, and residential and commercial projects.
Several researches using stainless steel and MMFX reinforcing bars have been conducted and
published by universities throughout the United States and sponsored for the Federal Highway
Administration (FHWA), and State Departments of Transportation (DOTs). These third parties
have conducted studies investigating bond stress behavior, corrosion evaluation, tensile tests, and
bending behavior in concrete structures.
Strut and Tie Evaluation of Anchorage
The strut-and-tie method was proposed by Schlaich, Schäfer, and Jennewein (1987). This
method was incorporated in AASHTO LRFD Specifications in 1994 and in ACI 318 - Appendix
21
A in 2002. The design basis of the strut-and-tie method is based on a truss model. The truss
model has been used in beams loaded in bending, shear and torsion. However, this model just
takes into account certain parts of the structure. The strut-and-tie method consists of struts and
ties connected by means of nodes as a real truss. The struts represent the compressive member
(concrete) and they serve either as the compression chord in the truss or as the diagonal struts.
Diagonal struts use to be oriented parallel to the expected axis of cracking. The ties represent the
tension member (stirrups and longitudinal reinforcement) where the anchorage of the ties is
crucial to avoid anchorage failure.
In order to apply correctly the strut-and-tie model, the structure is classified in B and D
regions. The B-regions (B for Bernoulli or beam) are based on the Bernoulli hypothesis which
facilitates the flexural design of reinforced concrete structures by allowing a linear strain
distribution for any loading stages (bending, shear, axial forces and torsional moments). On the
other hand, D-regions (D for discontinuity, or disturbance) are portions of a structure where the
strain distribution is nonlinear. D-regions are characterized for changes in geometry of a
structural portion (geometrical discontinuities) or concentrated forces (statical discontinuities).
For most types of D-regions as retaining walls, pier cap, and deep beam, the use of standard
hooks are common as anchorage (Figure 2-7).
Additionally, the strut-and-tie model is based on the lower bound theorem of plasticity
which allows yielding the bar (ties or stirrups) before crushing of concrete (struts and nodes).
The nodes can be classified according with the sign of the forces. At least three forces
should act on the node for equilibrium. A C-C-C node represents three compressive forces, a C-
C-T node represents two compressive forces and one tensile force, a C-T-T node represents two
tensile forces and one compressive force, and a T-T-T node represents three tensile forces. A C-
22
23
C-T node (Figure 2-8) show the nodal zone and extended nodal zone which serve to transfer
strut-and-tie forces. The extended nodal zone is defined as the portion limited by the intersection
of the strut width (ws) and the tie width (wt). The anchorage length (lanchorage) as shown in Figure
2-8 represents the development length of the hooked bar which is anchored in the nodal and
extended nodal zone.
Figure 2-9a shows the beam-column specimen used for Marques and Jirsa (1975) and
Figure 2-9b shows the strut-and-tie behavior of the hooked bar.
B Figure 4-19. Load-displacement for MMFX steel A) #5, and B) #7.
P u/A
b (k
si)
0
40
80
120
160
90 180 90 180
143 144
103 106
Bend Angle:Bar Size: #5 #7
Figure 4-20. MMFX results in terms of hook capacity.
Slip (in.)
Loa
d (k
ip)
Stre
ss (k
si)
0 0.05 0.1 0.15 0.20
10
20
30
40
50
60
0
30
60
90
120
150
180Pu
Py
D1D2
Figure 4-21. Typical load-slip behavior for #5 MMFX specimens with both 90 and 180-degree
hooks (MM_5_90_25_2 shown).
70
71
Slip (in.)
Loa
d (k
ip)
Stre
ss (k
si)
0 0.1 0.2 0.3 0.40
20
40
60
80
0
30
60
90
120Pu
Py
D1D2
Figure 4-22. Typical load-slip behavior for #7 MMFX specimens with both 90 and 180-degree
hooks (MM_7_180_35_4 shown).
CHAPTER 5 ANALYSIS OF RESULTS
The results presented in the previous chapter can be qualitatively summarized as follows:
1. The mild steel specimens generally behaved as would be expected, indicating that the test specimen design and test set-up provide an effective method of testing hook bar anchorages.
2. ACI/AASHTO equations appear to ensure that both the 16 and 20-mm bars develop their
yield strength.
3. ACI/AASHTO equations appear to ensure that the #5 MMFX hooked anchorage can
develop well beyond its yield strength, but that the #7 MMFX hooked anchorage was unable to develop significant additional force or deformation beyond yield.
This chapter presents the results of several analyses that are intended to quantitatively
analyze results of the hooked anchorage tests and determine the suitability of the current design
equations.
Anchorage Capacity
One method that can be used to compare the results of tests on high strength bars is the
excess force capacity available beyond the yield point. Mechanical couplers are required to reach
least 1.25 times the yield strength (fy) of the bar when splicing reinforcement (ACI 318-05
Section 12.14.3.2). The rationale for this approach is not clear but it has also been used by
Marques and Jirsa (1975) and by Ueda, Lin, and Hawkins (1986) in evaluating the capacity and
ductility of hooked bar anchorages that used mild steel. The disadvantage of this approach,
however, is that the current research is comparing steels that have different yield strengths and
post-yield mechanical properties than that of mild steel. Consequently, the bars already vary in
how much post-yield strength is available, both in the absolute and relative sense.
Figure 5-1 shows the calculated anchorage capacity ratios compared to the limit of 1.25.
The anchorage capacity ratio was calculated by dividing the peak measured load (anchorage
72
capacity) by bar yield strength (Pu/Py), which was taken from the results of the bar tests using the
0.2% offset method.
For mild steel specimens the anchorage capacity ratio exceeded the coupler requirement
of 1.25 by about 12% and 40% for #5 with bend angle of 90 and 180 degrees. For #7 bars the
anchorage capacity ratio was exceeded by 14% and 16%, respectively (see Figure 5-1 and Table
5-1).
For 16mm stainless steel specimens with bend angle of 90-degree, the anchorage capacity
ratio was sufficient to yield the bar but less than the limit of 1.25. However, the anchorage
capacity ratio was exceeded by about 22% and 34% for 16 mm specimens with 180-degree as the
development length increased. For 20 mm stainless steel specimens with bend angles of 90 and
180 degrees, the anchorage capacity ratios increased about 14% (Figure 5-1 and Table 5-2).
The anchorage capacity ratio was exceeded by 43% for #5 MMFX specimens with bend
angle of 90-degree, and with strut angles of 25 degree. For #5 MMFX specimens with bend
angle of 180-degree, the anchorage capacity ratio increased about 25%. For three #7 MMFX
specimens, however, the anchorage capacity ratio was less than the limit of 1.25 but it was
sufficient to yield the bar (Figure 5-1 and Table 5-3). The remainders of the specimens were at
anchorage capacity ratio of less than 1.0, a clear indication that the anchorage capacity was
insufficient.
Criteria for judging the anchorage capacity of high strength bars in concrete is not clearly
defined. It is rational to judge the results of this tests not only based on anchorage capacity ratio
but also on the bond capacity, ductility and K-factor.
Bond Stress
Another method that can be used to compare the relative performance of the different
steel types is to examine the bond stress. Figure 5-2 shows the bond stress normalized by the
73
square root of the measured concrete strength. The bond stress was calculated by dividing the
peak measured load by the nominal surface area of the straight, bonded portion of the hook.
The straight portion of the in unconfined specimens is lesser than in confined specimens
with stirrups, and unconfined specimens with debonded length. Also, it was found that the bond
stress for #5 mild steel specimens was greater than #7 specimens (Figure 5-2A). The bond stress
for #5 mild steel unconfined specimens with debonded length improved as the concrete strength
and the strut angle increased from 43.19 ksi to 53.30 ksi respectively. Bond stresses were similar
for #7 mild steel specimens with stirrups and without stirrups with debonded length, and with 90
and 180-degree bend angle (Figure 5-2A and Table 5-4).
The bond stress for 20 mm stainless steel specimens was greater than for 16 mm
specimens (Figure 5-2B and Table 5-5). For 16 mm stainless steel specimens with 90-degree
hooked bar, the bond stress was similar about 22 ksi. Also, the bond stresses were similar for 20
mm specimens with bend angle of 90 and 180-degree, and with same development length
(Figure 5-2B).
The bond stress for #5 MMFX specimens was greater than for #7 specimens (Figure 5-2C
and Table 5-6). For #5 specimens with 90-degree hooked bar, the bond stress was similar about
24 ksi. The bond stresses were similar for #7 specimens with bend angle of 90 degree (Figure
5-2C and Table 5-6).
Bond stress for mild steel, stainless steel, and MMFX are shown in Table 5-4, Table 5-5,
and Table 5-6. Pu represents the maximum peak load, ls represents the straight length of the
hooked bar and db represents the diameter of the bar. umax represents the maximum bond stress,
and umax/f'c1/2 represents the bond stress normalized by the square root of the measured concrete
strength.
74
Ductility
Yet another option is to compare hook behavior based on the displacement capacity of
the specimen beyond the yield point. A ductility ratio was then calculated as the ratio of the
strain at peak measured stress (Su) to the strain at yield corresponding with the 0.2% offset
method (Sy).
Ductility ratios for bend angle, 90 to 180 degrees, varied from 12.25 at 5490 psi to 14.80
at 6100 psi for #5 mild steel specimens. Also, for #7 mild steel specimens, ductility ratios for
bend angle, 90 to 180 degrees, varied from 7.72 at 5490 psi to 8.80 at 6330 psi. However, the
ductility ratio varied from 5.65 at 6330 psi to 8.83 at 6330 psi for #7 specimens with 180-degree
as the development length increased (Figure 5-3A and Table 5-7).
Ductility ratios for bend angle, 90 to 180 degrees, varied from 32.34 at 6350 psi to 37.80
at 6100 psi for 16 mm stainless steel specimens. Also, for 20 mm specimens, ductility ratios for
bend angle, 90 to 180 degrees, varied from 8.10 at 6100 psi to 11.13 at 6100 psi (Figure 5-3B
and Table 5-8).
Ductility ratios for bend angle, 90 to 180 degrees, varied from 6.20 at 6450 psi to 3.92 at
6450 psi for #5 MMFX specimens. Also, ductility ratios for #7 MMFX specimens was less than
1 because of most of them did not reach yield point. Only three #7 MMFX specimens reached
yield point (Figure 5-3C and Table 5-9).
K-Factor
Another way to compare the hook behavior was by means of the K-factor. The
development length for standard hooks proposed by the ACI 318-07 can be expressed as:
f 'c
yf
bKd
dhl = (5-1)
75
76
where the K-factor represent the constant value of 0.02, the coating and lightweight concrete
factors equal to 1.0, and an applicable modification factor of 0.7.
The side cover and cover on bar extension beyond hook were not less than 2-1/2 in. and 2
in. for all hooked specimens. The K-factor used to calculate the development length for all the
specimens was 0.014.
After testing, an experimental K-factor was computed as shown in Equation 5-2, and it was
compared with the K-factor used in the Equation 5-1.
'cfsf
bdlK testeddh−= (5-2)
where ldh-tested represents the development length tested, db represents the diameter of the bar, fs
represents the peak stress at failure, and f’c represents the average concrete strength.
Table 5-10, Table 5-11, and Table 5-12 show the experimental K-factor obtained for each
specimen.
For Grade 60, stainless steel, and #5 MMFX bars, the average experimental K-factor were
0.009, 0.012, and 0.0104, respectively. Also, these average K-factors were less than the K-factor
of 0.014 used in the Equation 5-1. Therefore, for all the specimens as Grade 60, Stainless Steel,
and #5 MMFX, the development length calculated was enough either to yield the hooked bar or
in most cases to exceed the anchorage capacity of 1.25 times the yield strength.
In contrast, for #7 MMFX bars, the average experimental K-factor was similar or in some
cases greater than the K-factor of 0.014 (Table 5-12) resulting in insufficient development length
to yield the bar.
Table 5-1. Anchorage capacity ratio for mild steel.
APPENDIX B CRACKS PATTERNS, LOAD-SLIP, AND LOAD-DISPLACEMENT
Top Front Rear Bottom
Right Left
60_5_90_1
Bar yield followed by concrete splitting
Top Front Rear Bottom
Right Left
60_5_90_S
Bar Rupture
Slip (in.)
Loa
d (k
ip)
Stre
ss (k
si)
Load-Slip for Linear Pots60_5_90_1
0 0.05 0.1 0.15 0.20
5
10
15
20
25
30
0
15
30
45
60
75
90
Linear pot 1Linear pot 2
Slip (in.)
Loa
d (k
ip)
Stre
ss (k
si)
Load-Slip for Linear Pots60_5_90_S
0 0.05 0.1 0.15 0.20
5
10
15
20
25
30
0
15
30
45
60
75
90
Linear pot 1Linear pot 2
Displacement (in.)
Loa
d (k
ip)
Loa
d (K
N)
Load-Displacement60_5_90_1 vs. 60_5_90_S
0 0.08 0.16 0.24 0.320
4
8
12
16
20
24
28
0
20
40
60
80
100
120
60_5_90_160_5_90_S
Figure B-1. Crack patterns, load-slip, and stress-strain curves for mild steel hooked bars.
90
Top Front Rear Bottom
Right Left
60_5_90_25_1
Bar yield followed by concrete splitting
Top Front Rear Bottom
60_5_90_25_2
Bar yield followed by concrete splitting
Right Left
Slip (in.)
Loa
d (k
ip)
Stre
ss (k
si)
Load-Slip for Linear Pots60_5_90_25_2
0 0.05 0.1 0.15 0.20
5
10
15
20
25
30
0
15
30
45
60
75
90
Linear pot 1Linear pot 2
Displacement (in.)
Loa
d (k
ip)
Loa
d (K
N)
Load-Displacement60_5_90_25_1 vs. 60_5_90_25_2
-0.01 0.04 0.09 0.14 0.190
5
10
15
20
25
30
0
20
40
60
80
100
120
-0.01 0.04 0.09 0.14 0.190
5
10
15
20
25
30
0
20
40
60
80
100
120
60_5_90_25_160_5_90_25_2
Strain (in/in)
Stre
ss (k
si)
Stre
ss (M
Pa)
Stress-Strain60_5_90_25_1 vs. 60_5_90_25_2
-0.01 0.01 0.03 0.050
20
40
60
80
100
0
150
300
450
600
60_5_90_25_160_5_90_25_2
Figure B-1. Continued.
91
60_5_180_35_1
Bar Rupture
Top Front Rear Bottom
Right Left
60_5_180_35_2
Bar Rupture
Top Front Rear Bottom
Right Left
Slip (in.)
Loa
d (k
ip)
Stre
ss (k
si)
Load-Slip for Linear Pots60_5_180_35_1
0 0.05 0.1 0.15 0.20
6
12
18
24
30
36
0
20
40
60
80
100
Linear pot 1Linear pot 2
Slip (in.)
Loa
d (k
ip)
Stre
ss (k
si)
Load-Slip for Linear Pots60_5_180_35_2
0 0.05 0.1 0.15 0.20
6
12
18
24
30
36
0
20
40
60
80
100
0 0.05 0.1 0.15 0.20
6
12
18
24
30
36
0
20
40
60
80
100
Linear pot 1Linear pot 2
Displacement (in.)
Loa
d (k
ip)
Loa
d (K
N)
Load-Displacement60_5_180_35_1 vs. 60_5_180_35_2
0 0.06 0.12 0.18 0.24 0.30
6
12
18
24
30
36
0
25
50
75
100
125
150
60_5_180_35_160_5_180_35_2
Strain (in/in)
Stre
ss (k
si)
Stre
ss (M
Pa)
Stress-Strain60_5_180_35_1 vs. 60_5_180_35_2
0 0.02 0.04 0.06 0.080
20
40
60
80
100
120
0
150
300
450
600
750
60_5_180_35_160_5_180_35_2
Figure B-1. Continued.
92
Top Front Rear Bottom
Right Left
60_7_90_1
Bar yield followed by concrete splitting
Top Front Rear Bottom
Right Left
60_7_90_S
Bar yield followed by concrete splitting
Slip (in.)
Loa
d (k
ip)
Stre
ss (k
si)
Load-Slip for Linear Pots60_7_90_1
0 0.04 0.08 0.12 0.160
10
20
30
40
50
60
0
15
30
45
60
75
90
Linear pot 1Linear pot 2
Slip (in.)
Loa
d (k
ip)
Stre
ss (k
si)
Load-Slip for Linear Pots60_7_90_S
0 0.04 0.08 0.12 0.160
10
20
30
40
50
60
0
15
30
45
60
75
90
Linear pot 1Linear pot 2
Displacement (in.)
Loa
d (k
ip)
Loa
d (K
N)
Load-Displacement60_7_90_1 vs. 60_7_90_S
0 0.025 0.05 0.075 0.10
10
20
30
40
50
60
0
40
80
120
160
200
240
60_7_90_160_7_90_S
Figure B-1. Continued.
93
Top Front Rear Bottom
Right Left
60_7_90_47_1
Bar yield followed by concrete splitting
Top Front Rear Bottom
Right Left
60_7_90_47_2
Bar yield followed by concrete splitting
Slip (in.)
Loa
d (k
ip)
Stre
ss (k
si)
Load_Slip for Linear Pots60_7_90_47_2
0 0.08 0.16 0.24 0.320 0
10 17
20 33
30 50
40 67
50 83
60 100
Linear pot 1Linear pot 2
Displacement (in.)
Loa
d (k
ip)
Loa
d (K
N)
Load-Displacement60_7_90_47_1 vs. 60_7_90_47_2
0 0.15 0.3 0.45 0.60
10
20
30
40
50
60
0
40
80
120
160
200
240
60_7_90_47_160_7_90_47_2
Strain (in/in)
Stre
ss (k
si)
Stre
ss (M
Pa)
Stress-Strain60_7_90_47_1 vs. 60_7_90_47_2
-0.01 0.01 0.03 0.050
20
40
60
80
100
0
150
300
450
600
60_7_90_47_160_7_90_47_2
Figure B-1. Continued.
94
Top Front Rear Bottom
Right Left
60_7_180_35_1
Bar yield followed by concrete splitting
Top Front Rear Bottom
60_7_180_35_2
Bar yield followed by concrete splitting
Right Left
Slip (in.)
Loa
d (k
ip)
Stre
ss (k
si)
Load-Slip for Linear Pots60_7_180_35_1
0 0.08 0.16 0.24 0.320
10
20
30
40
50
60
0
15
30
45
60
75
90
Linear pot 1Linear pot 2
Slip (in.)
Loa
d (k
ip)
Stre
ss (k
si)
Load-Slip for Linear Pots60_7_180_35_2
0 0.08 0.16 0.24 0.320
10
20
30
40
50
60
0
15
30
45
60
75
90
Linear pot 1Linear pot 2
Displacement (in.)
Loa
d (k
ip)
Loa
d (K
N)
Load-Displacement60_7_180_35_1 vs. 60_7_180_35_2
0 0.05 0.1 0.15 0.20
10
20
30
40
50
60
0
40
80
120
160
200
240
0 0.05 0.1 0.15 0.20
10
20
30
40
50
60
0
40
80
120
160
200
240
60_7_180_35_160_7_180_35_2
Strain (in/in)
Stre
ss (k
si)
Stre
ss (M
Pa)
Stress-Strain60_7_180_35_1 vs. 60_7_180_35_2
0 0.008 0.016 0.024 0.0320
20
40
60
80
100
0
150
300
450
600
0 0.008 0.016 0.024 0.0320
20
40
60
80
100
0
150
300
450
600
60_7_180_35_160_7_180_35_2
Figure B-1. Continued.
95
Top Front Rear Bottom
60_7_180_35_3
Bar yield followed by concrete splitting
Right Left
Top Front Rear Bottom
60_7_180_35_4
Bar yield followed by concrete splitting
Right Left
Slip (in.)
Loa
d (k
ip)
Stre
ss (k
si)
Load-Slip for Linear Pots60_7_180_35_3
0 0.1 0.2 0.3 0.4 0.50
10
20
30
40
50
60
70
0
15
30
45
60
75
90
105
Linear Pot 1Linear Pot 2
Slip (in.)
Loa
d (k
ip)
Stre
ss (k
si)
Load-Slip for Linear Pots60_7_180_35_4
0 0.1 0.2 0.3 0.4 0.50
10
20
30
40
50
60
70
0
15
30
45
60
75
90
105
Linear Pot 1Linear Pot 2
Displacement (in.)
Loa
d (k
ip)
Loa
d (K
N)
Load-Displacement60_7_180_35_3 vs. 60_7_180_35_4
0 0.08 0.16 0.24 0.320
10
20
30
40
50
60
70
0
40
80
120
160
200
240
280
60_7_180_35_360_7_180_35_4
Strain (in./in)
Stre
ss (k
si)
Stre
ss (M
Pa)
Stress-Strain60_7_180_35_3 vs. 60_7_180_35_4
0 0.01 0.02 0.03 0.04 0.050
15
30
45
60
75
90
105
0
100
200
300
400
500
600
700
60_7_180_35_360_7_180_35_4
Figure B-1. Continued.
96
Top Front Rear Bottom
Right Left
SS_16_90_25_1
Bar yield no rupture stroke limit reached
Top Front Rear Bottom
Right Left
SS_16_90_25_2
Bar yield no rupture stroke limit reached
Slip (in.)
Loa
d (k
ip)
Stre
ss (k
si)
Load-Slip for Linear PotsSS_16_90_25_1
0 0.08 0.16 0.24 0.320
8
16
24
32
40
0
25
50
75
100
125
Linear pot 1Linear pot 2
Slip (in.)
Loa
d (k
ip)
Stre
ss (k
si)
Load-Slip for Linear PotsSS_16_90_25_2
0 0.08 0.16 0.24 0.320
8
16
24
32
40
0
25
50
75
100
125
Linear pot 1Linear pot 2
Displacment (in.)
Loa
d (k
ip)
Loa
d (K
N)
Load-DisplacmentSS_16_90_25_1 vs. SS_16_90_25_2
0 0.15 0.3 0.45 0.60
8
16
24
32
40
0
30
60
90
120
150
180
SS_16_90_25_1SS_16_90_25_2
Strain (in/in)
Stre
ss (k
si)
Stre
ss (M
Pa)
Stress-StrainSS_16_90_25_1 vs. SS_16_90_25_2
0 0.06 0.12 0.18 0.240
20
40
60
80
100
120
0
150
300
450
600
750
SS_16_90_25_1SS_16_90_25_2
Figure B-2. Crack patterns, load-slip, and stress-strain curves for stainless steel hooked bars.
97
Top Front Rear Bottom
Right Left
SS_16_90_35_1
Bar yield no rupture stroke limit reached
Top Front Rear Bottom
Right Left
SS_16_90_35_2
Bar yield no rupture stroke limit reached
Slip (in.)
Loa
d (k
ip)
Stre
ss (k
si)
Load-Slip for Linear PotsSS_16_90_35_1
0 0.1 0.2 0.3 0.4 0.50
8
16
24
32
40
0
25
50
75
100
125
Linear pot 1Linear pot 2
Slip (in.)
Loa
d (k
ip)
Stre
ss (k
si)
Load-Slip for Linear PotsSS_16_90_35_2
0 0.1 0.2 0.3 0.4 0.50
8
16
24
32
40
0
25
50
75
100
125
Linear pot 1Linear pot 2
Displacement (in.)
Loa
d (k
ip)
Loa
d (K
N)
Load-DisplacementSS_16_90_35_1 vs. SS_16_90_35_2
0 0.25 0.5 0.75 10
8
16
24
32
40
0
30
60
90
120
150
180
SS_16_90_35_1SS_16_90_35_2
Strain (in/in)
Stre
ss (k
si)
Stre
ss (M
Pa)
Stress_StrainSS_16_90_35_1 vs. SS_16_90_35_2
0 0.06 0.12 0.18 0.240
20
40
60
80
100
120
0
150
300
450
600
750
SS_16_90_35_1SS_16_90_35_2
Figure B-2. Continued.
98
Top Front Rear Bottom
Right Left
SS_16_180_35_1
Bar yield no rupture stroke limit reached
Top Front Rear Bottom
Right Left
SS_16_180_35_2
Bar yield followed by concrete splitting
Slip (in.)
Loa
d (k
ip)
Stre
ss (k
si)
Load-Slip for Linear PotsSS_16_180_35_1
0 0.1 0.2 0.3 0.4 0.50
10
20
30
40
0
30
60
90
120
Linear pot 1Linear pot 2
Slip (in.)
Loa
d (k
ip)
Stre
ss (k
si)
Load-Slip for Linear PotsSS_16_180_35_2
0 0.1 0.2 0.3 0.4 0.50
10
20
30
40
0
30
60
90
120
Linear pot 1Linear pot 2
Displacement (in.)
Loa
d (k
ip)
Loa
d (K
N)
Load-DisplacementSS_16_180_35_1 vs. SS_16_180_35_2
0 0.25 0.5 0.75 10
8
16
24
32
40
0
30
60
90
120
150
180
SS_16_180_35_1SS_16_180_35_2
Strain (in/in.)
Stre
ss (k
si)
Stre
ss (M
Pa)
Stress-StrainSS_16_180_35_1 vs. SS_16_180_35_2
0 0.06 0.12 0.18 0.240
20
40
60
80
100
120
140
0
150
300
450
600
750
900
SS_16_180_35_1SS_16_180_35_2
Figure B-2. Continued.
99
Top Front Rear Bottom
Right Left
SS_16_180_35_3
Bar Rupture
Top Front Rear Bottom
Right Left
SS_16_180_35_4
Bar yield no rupture stroke limit reached
Slip (in.)
Loa
d (k
ip)
Stre
ss (k
si)
Load-Slip for Linear PotsSS_16_180_35_3
0 0.1 0.2 0.3 0.40
10
20
30
40
0
30
60
90
120
Linear pot 1Linear pot 2
Slip (in.)
Loa
d (k
ip)
Stre
ss (k
si)
Load-Slip for Linear PotsSS_16_180_35_4
0 0.1 0.2 0.3 0.40
10
20
30
40
0
30
60
90
120
Linear pot 1Linear pot 2
Displacement (in.)
Loa
d (k
ip)
Loa
d (K
N)
Load-DisplacementSS_16_180_35_3 vs. SS_16_180_35_4
0 0.2 0.4 0.6 0.80
10
20
30
40
0
40
80
120
160
SS_16_180_35_3SS_16_180_35_4
Strain (in/in)
Stre
ss (k
si)
Stre
ss (M
Pa)
Stress-StrainSS_16_180_35_3 vs. SS_16_180_35_4
0 0.06 0.12 0.18 0.240
20
40
60
80
100
120
140
0
150
300
450
600
750
900
SS_16_180_35_3SS_16_180_35_4
Figure B-2. Continued.
100
Top Front Rear Bottom
Right Left
SS_20_90_35_1
Bar yield followed by concrete splitting
SS_20_90_35_2
Bar yield followed by concrete splitting
Top Front Rear Bottom
Right Left
Slip (in.)
Loa
d (k
ip)
Stre
ss (k
si)
Load-Slip for Linear PotsSS_20_90_35_1
0 0.06 0.12 0.18 0.24 0.30
10
20
30
40
50
60
70
0
20
40
60
80
100
120
140
Linear pot 1Linear pot 2
Slip (in.)
Loa
d (k
ip)
Stre
ss (k
si)
Load-Slip for Linear PotsSS_20_90_35_2
0 0.06 0.12 0.18 0.24 0.30
10
20
30
40
50
60
70
0
20
40
60
80
100
120
140
Linear pot 1Linear pot 2
Displacement (in.)
Loa
d (k
ip)
Loa
d (K
N)
Load-DisplacementSS_20_90_35_1 vs. SS_20_90_35_2
0 0.06 0.12 0.18 0.24 0.30
15
30
45
60
75
0
60
120
180
240
300
SS_20_90_35_1 SS_20_90_35_2
Strain (in/in)
Stre
ss (k
si)
Stre
ss (M
Pa)
Stress-StrainSS_20_90_35_1 vs. SS_20_90_35_2
0 0.01 0.02 0.03 0.04 0.050
20
40
60
80
100
120
140
0
150
300
450
600
750
900
SS_20_90_35_1SS_20_90_35_2
Figure B-2. Continued.
101
Top Front Rear Bottom
Right Left
SS_20_90_35_3
Bar yield followed by concrete splitting
Top Front Rear Bottom
Right Left
SS_20_90_35_4
Bar yield followed by concrete splitting
Slip (in.)
Loa
d (k
ip)
Stre
ss (k
si)
Load-Slip for Linear PotsSS_20_90_35_3
0 0.06 0.12 0.18 0.24 0.30
10
20
30
40
50
60
70
0
20
40
60
80
100
120
140
Linear pot 1Linear pot 2
Slip (in.)
Loa
d (k
ip)
Stre
ss (k
si)
Load-Slip for Linear PotsSS_20_90_35_4
0 0.06 0.12 0.18 0.24 0.30
10
20
30
40
50
60
70
0
20
40
60
80
100
120
140
Linear pot 1Linear pot 2
Displacement (in.)
Loa
d (k
ip)
Loa
d (K
N)
Load-DisplacementSS_20_90_35_3 vs. SS_20_90_35_4
-0.02 0.02 0.06 0.1 0.140
20
40
60
80
0
80
160
240
320
SS_20_90_35_3SS_20_90_35_4
Strain (in/in)
Stre
ss (k
si)
Stre
ss (M
Pa)
Stress-StrainSS_20_90_35_3 vs. SS_20_90_35_4
-0.005 0.005 0.015 0.0250
20
40
60
80
100
120
140
0
150
300
450
600
750
900
SS_20_90_35_3SS_20_90_35_4
Figure B-2. Continued.
102
SS_20_180_35_1
Bar yield followed by concrete splitting
Top Front Rear Bottom
Right Left
SS_20_180_35_2
Bar yield followed by concrete splitting
Top Front Rear Bottom
Right Left
Slip (in.)
Loa
d (k
ip)
Stre
ss (k
si)
Load-Slip for Linear PotsSS_20_180_35_1
0 0.05 0.1 0.15 0.2 0.250
20
40
60
80
0
40
80
120
160
Linear pot 1Linear pot 2
Slip (in.)
Loa
d (k
ip)
Stre
ss (k
si)
Load-Slip for Linear PotsSS_20_180_35_2
0 0.05 0.1 0.15 0.2 0.250
20
40
60
80
0
40
80
120
160
Linear pot 1Linear pot 2
Displacement (in.)
Loa
d (k
ip)
Loa
d (K
N)
Load-DisplacementSS_20_180_35_1 vs. SS_20_180_35_2
0 0.1 0.2 0.3 0.40
20
40
60
80
0
80
160
240
320
SS_20_180_35_1SS_20_180_35_2
Strain (in/in)
Stre
ss (k
si)
Stre
ss (K
N)
Stress-StrainSS_20_180_35_1 vs. SS_20_180_35_2
0 0.02 0.04 0.06 0.080
20
40
60
80
100
120
140
0
150
300
450
600
750
900
SS_20_180_35_1SS_20_180_35_2
Figure B-2. Continued.
103
Top Front Rear Bottom
Right Left
SS_20_180_35_3
Bar yield followed by concrete splitting
Top Front Rear Bottom
Right Left
SS_20_180_35_4
Bar yield followed by concrete splitting
Slip (in.)
Loa
d (k
ip)
Stre
ss (k
si)
Load-Slip for Linear PotsSS_20_180_35_3
0 0.04 0.08 0.12 0.16 0.20
10
20
30
40
50
60
0
20
40
60
80
100
120
Linear pot 1Linear pot 2
Slip (in.)
Loa
d (k
ip)
Stre
ss (k
si)
Load-Slip for Linear PotsSS_20_180_35_4
0 0.04 0.08 0.12 0.16 0.20
10
20
30
40
50
60
0
20
40
60
80
100
120
Linear pot 1Linear pot 2
Displacement (in.)
Loa
d (k
ip)
Loa
d (K
N)
Load-DisplacementSS_20_180_35_3 vs. SS_20_180_35_4
0 0.02 0.04 0.06 0.080
10
20
30
40
50
60
0
50
100
150
200
250
SS_20_180_35_3SS_20_180_35_4
Strain (in/in)
Stre
ss (k
si)
Stre
ss (M
Pa)
Stress-StrainSS_20_180_35_3 vs. SS_20_180_35_4
0 0.003 0.006 0.009 0.0120
25
50
75
100
125
0
150
300
450
600
750
SS_20_180_35_3SS_20_180_35_4
Figure B-2. Continued.
104
Top Front Rear Bottom
Right Left
MM_5_90_25_1
Bar rupture
Top Front Rear Bottom
Right Left
MM_5_90_25_2
Bar rupture
Slip (in.)
Loa
d (k
ip)
Stre
ss (k
si)
Load-Slip for Linear PotsMM_5_90_25_1
0 0.03 0.06 0.09 0.120
10
20
30
40
50
60
0
30
60
90
120
150
180
Linear pot 1Linear pot 2
Slip (in.)
Loa
d (k
ip)
Stre
ss (k
si)
Load-Slip for Linear PotsMM_5_90_25_2
0 0.03 0.06 0.09 0.120
10
20
30
40
50
60
0
30
60
90
120
150
180
Linear pot 1Linear pot 2
Displacement (in.)
Loa
d (k
ip)
Loa
d (K
N)
Load-DisplacementMM_5_90_25_1 vs. MM_5_90_25_2
0 0.04 0.08 0.12 0.160
10
20
30
40
50
60
0
40
80
120
160
200
240
MM_5_90_25_1MM_5_90_25_2
Strain (in/in)
Stre
ss (k
si)
Stre
ss (M
Pa)
Stress-StrainMM_5_90_25_1 vs. MM_5_90_25_2
0 0.02 0.04 0.06 0.080
30
60
90
120
150
180
0
200
400
600
800
1000
1200
MM_5_90_25_1MM_5_90_25_2
Figure B-2. Continued.
105
Top Front Rear Bottom
Right Left
MM_5_90_35_1
Bar yield followed by concrete splitting
Top Front Rear Bottom
Right Left
MM_5_90_35_2
Bar yield followed by concrete splitting
Slip (in.)
Loa
d (k
ip)
Stre
ss (k
si)
Load-Slip for Linear PotsMM_5_90_35_1
0 0.08 0.16 0.24 0.320
10
20
30
40
50
60
0
30
60
90
120
150
180
Linear pot 1Linear pot 2
Slip (in.)
Loa
d (k
ip)
Stre
ss (k
si)
Load-Slip for Linear PotsMM_5_90_35_2
0 0.08 0.16 0.24 0.320
10
20
30
40
50
60
0
30
60
90
120
150
180
Linear pot 1Linear pot 2
Displacement (in.)
Loa
d (k
ip)
Loa
d (K
N)
Load-DisplacementMM_5_90_35_1 vs. MM_5_90_35_2
0 0.04 0.08 0.12 0.16 0.20
10
20
30
40
50
60
0
40
80
120
160
200
240
MM_5_90_35_1MM_5_90_35_2
Strain (in/in)
Stre
ss (k
si)
Stre
ss (M
Pa)
Stress-StrainMM_5_90_35_1 vs. MM_5_90_35_2
0 0.01 0.02 0.03 0.04 0.050
30
60
90
120
150
180
0
200
400
600
800
1000
1200
MM_5_90_35_1MM_5_90_35_2
Figure B-3. Crack patterns, load-slip, and stress-strain curves for MMFX hooked bars.
106
Top Front Rear Bottom
Right Left
MM_5_180_35_1
Bar yield followed by concrete splitting
Top Front Rear Bottom
Right Left
MM_5_180_35_2
Bar yield followed by concrete splitting
Slip (in.)
Loa
d (k
ip)
Stre
ss (k
si)
Load-Slip for Linear PotsMM_5_180_35_1
0 0.02 0.04 0.06 0.08 0.10
10
20
30
40
50
60
0
30
60
90
120
150
180
Linear pot 1Linear pot 2
Slip (in.)
Loa
d (k
ip)
Stre
ss (k
si)
Load-Slip for Linear PotsMM_5_180_35_2
0 0.02 0.04 0.06 0.08 0.10
10
20
30
40
50
60
0
30
60
90
120
150
180
Linear pot 1Linear pot 2
Displacement (in.)
Loa
d (k
ip)
Loa
d (K
N)
Load-DisplacementMM_5_180_35_1 vs. MM_5_180_35_2
0 0.025 0.05 0.075 0.10
10
20
30
40
50
60
0
40
80
120
160
200
240
MM_5_180_35_1MM_5_180_35_2
Strain (in/in)
Stre
ss (k
si)
Stre
ss (M
Pa)
Stress-StrainMM_5_180_35_1 vs. MM_5_180_35_2
0 0.007 0.014 0.021 0.0280
30
60
90
120
150
180
0
200
400
600
800
1000
1200
MM_5_180_35_1MM_5_180_35_2
Figure B-3. Continued.
107
Top Front Rear Bottom
Right Left
MM_5_180_35_3
Bar yield followed by concrete splitting
Top Front Rear Bottom
Right Left
MM_5_180_35_4
Bar rupture
Slip (in.)
Loa
d (k
ip)
Stre
ss (k
si)
Load-Slip for Linear PotsMM_5_180_35_3
0 0.06 0.12 0.18 0.240
10
20
30
40
50
60
0
30
60
90
120
150
180
Linear pot 1Linear pot 2
Slip (in.)
Loa
d (k
ip)
Stre
ss (k
si)
Load-Slip for Linear PotsMM_5_180_35_4
0 0.06 0.12 0.18 0.240
10
20
30
40
50
60
0
30
60
90
120
150
180
Linear pot 1Linear pot 2
Displacement (in.)
Loa
d (k
ip)
Loa
d (K
N)
Load-DisplacementMM_5_180_35_3 vs. MM_5_180_35_4
0 0.04 0.08 0.12 0.160
10
20
30
40
50
60
0
40
80
120
160
200
240
MM_5_180_35_3MM_5_180_35_4
Strain (in/in)
Stre
ss (k
si)
Stre
ss (M
Pa)
Stress-StrainMM_5_180_35_3 vs. MM_5_180_35_4
0 0.01 0.02 0.03 0.040
30
60
90
120
150
180
0
200
400
600
800
1000
1200
MM_5_180_35_3MM_5_180_35_4
Figure B-3. Continued.
108
Top Front Rear Bottom
Right Left
MM_7_90_25_1
Concrete splitting
Slip (in.)
Loa
d (k
ip)
Stre
ss (k
si)
Load-Slip for Linear PotsMM_7_90_25_1
0 0.1 0.2 0.3 0.40
20
40
60
80
0
60
120
180
240
Linear pot 1Linear pot 2
Slip (in.)
Loa
d (k
ip)
Stre
ss (k
si)
Load-Slip for Linear PotsMM_7_90_25_2
0 0.1 0.2 0.3 0.40
20
40
60
80
0
60
120
180
240
Linear pot 1Linear pot 2
Displacement (in.)
Loa
d (k
ip)
Loa
d (K
N)
Load-DisplacementMM_7_90_25_1 vs. MM_7_90_25_2
0 0.008 0.016 0.024 0.0320
20
40
60
80
0
80
160
240
320
MM_7_90_25_1MM_7_90_25_2
Strain (in/in)
Stre
ss (k
si)
Stre
ss (M
Pa)
Stress_StrainMM_7_90_25_1 vs. MM_7_90_25_2
0 0.0015 0.003 0.0045 0.0060
25
50
75
100
125
0
150
300
450
600
750
MM_7_90_25_1MM_7_90_25_2
Figure B-3. Continued.
109
Top Front Rear Bottom
Right Left
MM_7_90_35_1
Bar cast out of position
Top Front Rear Bottom
Right Left
MM_7_90_35_2
Bar cast out of position
Slip (in.)
Loa
d (k
ip)
Stre
ss (k
si)
Load-Slip for Linear PotsMM_7_90_35_1
0 0.08 0.16 0.24 0.320
20
40
60
80
0
30
60
90
120
Linear pot 1Linear pot 2
Slip (in.)
Loa
d (k
ip)
Stre
ss (k
si)
Load-Slip ComparisonMM_7_90_35_2
0 0.08 0.16 0.24 0.320
20
40
60
80
0
30
60
90
120
Linear pot 1Linear pot 2
Displacement (in.)
Loa
d (k
ip)
Loa
d (K
N)
Load-DisplacementMM_7_90_35_1 vs. MM_7_90_35_2
0 0.008 0.016 0.024 0.0320
20
40
60
80
0
80
160
240
320
MM_7_90_35_1MM_7_90_35_2
Strain (in/in)
Stre
ss (k
si)
Stre
ss (M
Pa)
Stress-StrainMM_7_90_35_1 vs. MM_7_90_35_2
0 0.001 0.002 0.003 0.0040
20
40
60
80
100
120
0
150
300
450
600
750
MM_7_90_35_1MM_7_90_35_2
Figure B-3. Continued.
110
Top Front Rear Bottom
Right Left
MM_7_90_35_3
Concrete splitting
Top Front Rear Bottom
Right Left
MM_7_90_35_4
Bar yield followed by concrete splitting
Displacement (in)
Loa
d (k
ip)
Loa
d (K
N)
Load_DisplecementMM_7_90_35_3 vs. MM_7_90_35_4
0 0.02 0.04 0.06 0.080
20
40
60
80
0
80
160
240
320
MM_7_90_35_3MM_7_90_35_4
Strain (in/in)
Stre
ss (k
si)
Stre
ss (M
Pa)
Stress-StrainMM_7_90_35_3 vs. MM_7_90_35_4
0 0.002 0.004 0.006 0.008 0.010
40
80
120
160
0
300
600
900
MM_7_90_35_3MM_7_90_35_4
Figure B-3. Continued.
111
Top Front Rear Bottom
Right Left
MM_7_180_35_1
Concrete Splitting
Top Front Rear Bottom
Right Left
MM_7_180_35_2
Bar yield followed by concrete splitting
Slip (in.)
Loa
d (k
ip)
Stre
ss (k
si)
Load-Slip for Linear PotsMM_7_180_35_1
0 0.05 0.1 0.15 0.20
20
40
60
80
0
30
60
90
120
Linear pot 1Linear pot 2
Slip (in.)
Loa
d (k
ip)
Stre
ss (k
si)
Load-Slip for Linear PotsMM_7_180_35_2
0 0.05 0.1 0.15 0.20
20
40
60
80
0
30
60
90
120
Linear pot 1Linear pot 2
Displacement (in.)
Loa
d (k
ip)
Loa
d (K
N)
Load-DisplacementMM_7_180_35_1 vs. MM_7_180_35_2
0 0.015 0.03 0.045 0.060
20
40
60
80
0
80
160
240
320
MM_7_180_35_1MM_7_180_35_2
Strain (in/in)
Stre
ss (k
si)
Stre
ss (M
Pa)
Stress-StrainMM_7_180_35_1 vs. MM_7_180_35_2
0 0.002 0.004 0.006 0.0080 0
32 224
64 448
96 672
128 896
MM_7_180_35_1MM_7_180_35_2
Figure B-3. Continued.
112
113
Top Front Rear Bottom
Right Left
MM_7_180_35_3
Concrete Splitting
Top Front Rear Bottom
Right Left
MM_7_180_35_4
Bar yield followed by concrete splitting
Slip (in.)
Loa
d (k
ip)
Stre
ss (k
si)
Load-Slip for Linear PotsMM_7_180_35_3
0 0.1 0.2 0.3 0.40
20
40
60
80
0
30
60
90
120
Linear pot 1Linear pot 2
Slip (in.)
Loa
d (k
ip)
Stre
ss (k
si)
Load-Slip for Linear PotsMM_7_180_35_4
0 0.1 0.2 0.3 0.40
20
40
60
80
0
30
60
90
120
Linear pot 1Linear pot 2
Displacement (in.)
Loa
d (k
ip)
Loa
d (K
N)
Load-DisplacementMM_7_180_35_3 vs. MM_7_180_35_4
0 0.02 0.04 0.06 0.080
20
40
60
80
0
80
160
240
320
MM_7_180_35_3MM_7_180_35_4
Strain (in/in)
Stre
ss (k
si)
Stre
ss (M
Pa)
Stress-StrainMM_7_180_35_3 vs. MM_7_180_35_4
0 0.003 0.006 0.009 0.0120
25
50
75
100
125
0
150
300
450
600
750
MM_7_180_35_3MM_7_180_35_4
Figure B-3. Continued.
LIST OF REFERENCES
AASHTO (2001). “ Standard Specifications for Highway Bridges.” American Association of States Highway and Transportation Officials.
ACI 408.1R-79 (1979). “Suggested Development, Splice, and Standard Hook Provisions for Deformed Bars in Tension.” American Concrete Institute.
ACI Committee 318 (1977). “Building Code Requirements for Reinforced Concrete (ACI 318-77).” American Concrete Institute.
ACI Committee 318 (1995). “Building Code Requirements for Reinforced Concrete (ACI 318-95).” American Concrete Institute.
ACI Committee 318 (2002). “Building Code Requirements for Reinforced Concrete (ACI 318-02).” American Concrete Institute.
ASTM A 370 (2007). “Standard Test Methods and Definitions for Mechanical Testing of Steel Products.” American Society for Testing and Materials.
ASTM A1035/A1035M (2007). “Standard Specification for Deformed and Plain, Low-carbon, Chromium, Steel Bars for Concrete Reinforcement.” American Society for Testing and Materials.
ASTM C 39 (1999). “Standard Test Method for Compressive Strength of Cylindrical Concrete Specimens.” American Society for Testing and Materials.
ASTM C 143 (2000). “Standard Test Method for Slump of Hydraulic Cement Concrete.” American Society for Testing and Materials.
Ahlborn, Tess and DenHarting Tim (2002). “A Comparative Bond Study of MMFX Reinforcing Steel in Concrete”. Michigan Technological University. Center for Structural Durability. Final Report CSD-2002-03.
Hamad, B.S., Jirsa, J.O. and D’Abreu de Paulo, N.I (1993). “Anchorage Strength of Epoxy-Coated Hooked Bars.” ACI Structural Journal, 90(2), 210-217.
Jirsa, J.O., Lutz, L.A. and Gergely, P (1979). “Rationale for Suggested Development, Splice, and Standard Hook Provisions for Deformed Bars in Tension.” Concrete International, 79(7), 47-61.
Marques, J.L.G., and Jirsa, J.O (1975). “A Study of Hooked Bar Anchorages in Beam-Column Joints.” ACI Journal, 72(5), 198-209.
Minor, J., and Jirsa, J.O (1975). “Behavior of Bent Bar Anchorages.” ACI Journal, 72(4), 141-149.
114
115
Pinc, R.L., Watkins, M.D. and Jirsa, J.O (1977). “Strength of Hooked Bar Anchorages in Beam-Column Joints.” CESRL Report No. 77-3, Department of Civil Engineering, The University of Texas, Austin, Texas.
BIOGRAPHICAL SKETCH
Gianni T. Ciancone was born in Caracas, Venezuela, to Maria Teresa and Raffaele
Ciancone. He received his Bachelor of Science in Civil Engineering in Summer of 1993 from the
University of Santa Maria, Venezuela. Gianni worked in a Power Company for 14 years in
several positions not only in the Design and Construction field but also in the Business field.
Gianni continued his education by entering graduate school to pursue a Master of
Engineering in the Structural Group of the Civil and Coastal Engineering Department at the
University of Florida in Fall 2005. During his stay at the University of Florida, Gianni worked as
graduated research assistant for Dr. H.R. Hamilton III. Gianni plans to pursue a career in the