ACI STRUCTURAL JOURNAL TECHNICAL PAPER

Title no. 109-S03

Cracking and Tension Stiffening of High-Strength

Concrete Panels
by N. Dawood and H. Marzouk

An experimental program was conducted recently at the Memorial an experimental investigation on uniaxial tension members
University of Newfoundland (MUN) to study the tension-stiffening of both NSC (40 MPa [5800 psi]) and HSC (80 MPa
and cracking behavior of orthogonally reinforced concrete panels [11,600 psi]). A model for the average tensile stress-strain
subjected to axial tension. The experimental program involved relationship of cracked concrete was developed. Cho
testing eight reinforced concrete panels with different concrete et al.10,11 conducted tension tests of six half-thickness
strengths under uniaxial or biaxial tension loading. During the
concrete wall elements as part of the Korea Atomic Energy
duration of the tests, applied loads, strains, and crack widths
were recorded. The average stress-strain relationship and crack Research Institute (KAERI) program. Constitutive models
width for concrete panels under direct tension were examined at for the ascending and descending response of the concrete
different steel stress levels. The main objectives of this paper are to panels were developed. Shima et al.12 studied the bond and
investigate the cracking behavior and tension-stiffening response tension stiffening of the cracked concrete; based on that
of axially loaded high-strength reinforced concrete (HSC) panels investigation, a model to introduce the average tensile stress
and compare this behavior with the normal-strength concrete strain for concrete was developed.
(NSC) panels. Based on the test results, a model is recommended Most of the current research and existing analytical model
for predicting the tensile stress-strain relationship of HSC panels equations for predicting cracking behavior only take into
under axial loading. consideration the effect of applying the load in the uniaxial
direction and the influence of the longitudinal reinforcement
Keywords: axial loading; biaxial; concrete panels; cracking behavior;
nuclear containments; offshore structures; stress-strain; uniaxial. in the loading direction and ignore the influence of applying
the load in the biaxial direction and the effect of transverse
INTRODUCTION reinforcement. The main objective of this research is to
A reinforced concrete structure can easily crack due to study the cracking behavior of reinforced concrete panels
low tensile strength. There are certain types of structures, with different concrete strengths subjected to in-plane
however, such as offshore platforms, containment structures loading in terms of tension-stiffening behavior, cracking
for nuclear power plants, and water tanks, where tensile load, crack pattern, crack spacing, and crack width of the
cracks can cause very serious problems. A review of the panels. Meanwhile, a model representing the stress-strain
relationship of reinforced concrete under tension is provided
literature reveals several experimental studies on the response
to predict the tensile response of concrete specimens before
of reinforced concrete specimens under uniaxial tension.
and after cracking. The model is based on the best fit to the
Two extensive and independent testing programs were
test results.
conducted by Rizkalla et al.1 and Rizkalla and Hwang2 to
study the cracking behavior of reinforced concrete members
RESEARCH SIGNIFICANCE
subjected to pure uniaxial tension. The influence of the
This study examines the cracking behavior and tension-
transverse reinforcement on the cracking response was stiffening response of reinforced concrete panels subjected
discussed and a model for the crack spacing was proposed. to axial loading, taking into consideration the effect of the
Williams3 prepared a technical report to investigate the concrete strength, reinforcement ratio, and biaxial loading.
cracking behavior of normal-strength concrete (NSC) panels. This study introduces an expression for predicting the pre-
The main objective of the report was to compare the results and postcracking of the average tensile stress-strain response
obtained from the experimental program to the existing of HSC panels subjected to in-plane axial tensile loading.
design code and other formulae for the tension stiffening
of reinforced concrete. MacGregor et al.4 and Simmonds et EXPERIMENTAL INVESTIGATION
al.5 tested specimens of typical dimensions 800 mm (31.5 in.) In this experimental investigation, two NSC panels and six
square and 260 mm (10.2 in.) thick with a nominal concrete HSC panels are fabricated and the effects of the concrete
compressive strength of 31.7 MPa (4500 psi) to study the compressive strength, reinforcement ratio, and application of
cracking response of reinforced and prestressed concrete the load in the uniaxial or biaxial direction are investigated.
wall segments. Marzouk and Chen6,7 studied the cracking The selected sizes of the tested panels are 600 x 600 x 190 mm
behavior of concrete prisms under direct uniaxial tension (23.6 x 23.6 x 7.5 in.), as shown in Fig. 1. The experimental
loading and recommended a suitable tension-softening and
tension-stiffening model for high-strength concrete (HSC)
that considered the postcracking behavior and fracture ACI Structural Journal, V. 109, No. 1, January-February 2012.
energy principles. Other experimental projects that aimed MS No. S-2009-128.R5 received January 21, 2011, and reviewed under Institute
publication policies. Copyright © 2012, American Concrete Institute. All rights
to provide a clear understanding of the cracking response reserved, including the making of copies unless permission is obtained from the
of NSC and HSC panels tested under uniaxial tension were copyright proprietors. Pertinent discussion including author’s closure, if any, will be
published in the November-December 2012 ACI Structural Journal if the discussion
conducted by Wollrab et al.8 Fields and Bischoff9 performed is received by July 1, 2012.

ACI Structural Journal/January-February 2012 21

ACI member N. Dawood is a PhD Candidate and Research Assistant at the Memorial work is carried out using a special test frame. This test setup
University of Newfoundland, St. John’s, NL, Canada, and a Lecturer at Menoufiya consists of three main parts—namely, the fixed reaction
University, Shebin El-Kom, Egypt. He received his BS and MS from Menoufiya frame, four moving walls, and eight hydraulic jacks. The
University in 2000 and 2004, respectively. His research interests include the cracking
behavior of offshore structures.
hydraulic jacks are placed in between the fixed reaction
frame and moving walls to apply forces on the moving walls
ACI member H. Marzouk is Chair of the Civil Engineering Department at Ryerson (refer to Fig. 2). The main function of this setup is to apply
University, Toronto, ON, Canada. He received his MSc and PhD from the University of direct axial tension loads in one and/or two perpendicular
Saskatchewan, Saskatchewan, SK, Canada. He is a member of ACI Committees 209,
Creep and Shrinkage in Concrete; and 213, Lightweight Aggregate and Concrete. His
directions to simulate in-plane uniaxial and biaxial stress
research interests include structural and material properties of high-strength concrete, states. All of the specimens in the experimental program are
lightweight high strength, creep, and finite element analysis. reinforced in two perpendicular directions with deformed
bars placed in two layers. Two levels of compressive
strength are used to cast the specimens. The average
concrete compressive strength f c′ is found to equal 35 MPa
(5075 psi) for the NSC specimens and 75 MPa (10,900 psi)
for the HSC specimens.
Grade 400 reinforcing Canadian steel bars conforming to
CAN/CSA-G40.20-M92 are used. The reinforcement used
in the specimens consists of deformed bars of 15 and 20 mm
(5/8 and 6/8 in.) in diameter with a yield stress and ultimate
tensile strength of 410 and 650 MPa (58,000 and 94,300 psi),
respectively. Complete details for the reinforced concrete
panels and the reinforcement are provided in Table 1.
The strains of the steel bars are typically measured by strain
gauges affixed to the bars, as shown in Fig. 3(a). Figure 3(b)
shows five linear potential differential transducers (LPDTs)
that are attached to the top of the concrete surface for
measuring the deformations and cracking properties. The
total displacement of the LPDTs is 50 mm (1.97 in.) and
mainly works on the base of the linear relationship between
the resistance of the internal spring and displacement due
to the deformations’ occurrence. The experimental data are
continuously recorded from the load cells, LPDTs, and strain
gauges. Afterward, the data are collected and automatically
Fig. 1—Configuration and dimensions of panels. (Note: 1 mm processed using a data acquisition system.
= 0.0394 in.)
TEST PROCEDURE
The load is applied by using 1000 kN (224.8 kips) capacity
hydraulic jacks. Load is transmitted from the loading jacks
to the specimen by using a specially designed test setup
and end gripping blocks, as shown in Fig. 2. All of the
longitudinal reinforcing bars protrude outside the concrete
panel and embed inside the concrete gripping blocks with
equal and sufficient lengths to adjust the transferred loads
to each reinforcing bar to provide uniformly distributed
forces on the concrete specimen. Before applying the load
to the specimen, initial measurements are recorded on the
sensors and strain gauges. Load is applied in increments;
a continuous record of the deformations is made using the
LPDTs. The readings of the strain gauges are also recorded
for every loading stage. In addition, the crack opening is
measured at regular intervals using digital crack gauges with
an accuracy of 0.001 mm (4 × 10–5 in.). After the start of
loading, the load is never intentionally decreased until the
test is completed.

CRACKING OF CONCRETE PANELS UNDER

AXIAL LOADING
When a symmetrical uncracked reinforced concrete panel
is loaded in tension, the tensile force is distributed between
the reinforcing steel and concrete in proportion to their
respective stiffness13,14

Fig. 2—Test setup. (Note: 1 mm = 0.0394 in.) P = Pc + Ps = ( Ec Ac + nEc As ) e t (1)

22 ACI Structural Journal/January-February 2012

Table 1—Reinforced concrete panel segments of experimental program
Specimen Specimen dimensions, mm Concrete strength f c′, MPa Bar diameter, mm Bar spacing, mm Reinforcement ratio, % Ec, MPa
NS-U-15-2.5-6 40 15 150 1.2 19,740
HS-U-15-2.5-6 90 15 150 1.2 29,154
NS-B-15-2.5-6 35 15 150 1.2 19,080
HS-B-15-2.5-6 75 15 150 1.2 27,900
600 x 600 x 190
HS-U-20-2.5-6 75 20 150 2.0 26,283
HS-B-20-2.5-6 75 20 150 2.0 29,750
HS-U-20-2.5-4 80 20 300 1.2 26,250
HS-B-20-2.5-4 75 20 300 1.2 28,270
Notes: NS is normal-strength concrete; HS is high-strength concrete; U is uniaxial tension loading; B is biaxial tension loading; 2.5 is ratio of concrete cover to bar diameter (Cc/db
= 2.5); 6 is six bars in each direction; 4 is four bars in each direction; 1 mm = 0.0394 in.; 1 MPa = 145 psi.

Fig. 3—(a) Location of strain gauges; and (b) location of LPDTs.

Assuming that the values of Ag and Ac are very close

Pcr = ( Ec Ac + nEc As )e t′ (4)
P = Ec Ag (1 − r + nr)e t = ( EA)uc e t (2)

where Ec is the modulus of elasticity of concrete; Ac is Pcr (5)

ft ′ = − rEs e t′
the cross-sectional area of the concrete; As is the area Ac
of the reinforcement; Ag is the gross sectional area of the
reinforced concrete panel (Ac + As); (EA)uc is the stiffness of and the steel stress at cracking load can be calculated as
the uncracked cross section; and et is the tensile strain of the follows13
concrete. Hence, each load transferred into the concrete and
reinforcement can be derived as follows
Pcr 1  (6)
fscr = = f t ′  − 1 + n
As r 
 1  (3a)
Pc =  P
 1 + nr 
Table 2 summarizes the loads and measured concrete
strains at the cracking stage for different concrete specimens
obtained from the experiments. The tensile strength f t′ for
 nr  (3b) different concrete specimens obtained from the experiments
Ps =  P conducted on the concrete panels is also presented in Table 2.
 1 + nr 
In the meantime, Table 2 shows a comparison between the
steel stress at the cracking stage observed experimentally
where Pc and Ps are the loads sustained by the concrete and and the calculated steel stress from Eq. (6).
reinforcement, respectively; and n is the modular ratio of
the concrete and reinforcement. At the time when the first TEST RESULTS
crack occurs, P = Pcr, et = et′, and Ecet′ = f t′. This can be This section summarizes the main test results of the tensile
written as follows cracking behavior of the tested panels subjected to uniaxial

ACI Structural Journal/January-February 2012 23

Table 2—Stress of concrete and steel at cracking stage
Cracking stage Steel stress
Pc, kN Ps, kN fscr, MPa Relative decrease in f t′
Specimen f c′, MPa f t′, MPa et(ex)′ Pcr(ex), kN Eq. (3a) Eq. (3b) fscr(ex), MPa Eq. (6) (f t′(U) – f t′(B))/f t′(U), %
NS-U-15-2.5-6 40 2.10 89.4 240 214 25 200 195
8
NS-B-15-2.5-6 35 1.92 91 220 194 26 166 175
HS-U-15-2.5-6 90 3.20 133.1 400 354 46 333 295
15
HS-B-15-2.5-6 75 2.72 96.5 310 277 33 260 251
HS-U-20-2.5-6 75 3.10 113 360 300 60 200 185
5
HS-B-20-2.5-6 75 2.96 97.6 335 280 55 186 175
HS-U-20-2.5-4 80 3.00 115.5 330 295 35 270 277
10
HS-B-20-2.5-4 75 2.70 85.4 315 280 35 260 250
Notes: 1 MPa = 145 psi; 1 kN = 0.2248 kips.

or biaxial loading conditions. The influences of different test loading conditions can be discussed using an analysis of
parameters on the cracking and tension-stiffening behavior the cracking response of Panels NS-U-15-2.5-6 and HS-
of the tested panels are also examined. U-15-2.5-6. Panel NS-U-15-2.5-6 is made with NSC and
subjected to uniaxial loading in the east-west direction.
Cracking loads and concrete cracking stresses As the tension force is applied, the average strain in the
Cracking loads can be captured at the point that shows the longitudinal upper and lower reinforcing bars gradually
first change in the slope of the stress-strain curve at which increases. When the tension force reaches approximately
the first crack appears. Panels NS-U-15-2.5-6 and NS-B-15- 240 kN (53.9 kips), the first crack appears on the surface
2.5-6 are cast with NSC and subjected to uniaxial and biaxial along the transverse reinforcing bar placed along the
tension loads, respectively. Panel NS-U-15-2.5-6 cracks at a center line of the specimen in the north-south direction, as
load of approximately 240 kN (53.9 kips) with an average indicated in Fig. 4(a), at which an average tensile stress of
tensile stress of 2.1 MPa (310 psi) that is sustained by the 200 MPa (29,000 psi) is induced by the reinforcing bars in
concrete, equivalent to 6% of fc′, where fc′ is the compressive the east-west direction. The measured initial crack width is
strength of the concrete resulting from the cylinder tests. found to equal 0.122 mm (0.0048 in.). Another crack occurs
However, Panel NS-B-15-2.5-6 cracks when the tension at a load of 510 kN (114.65 kips) on the surface along the
force reaches approximately 220 kN (49.5 kips) and the first transverse reinforcing bar placed nearest to the east
average tensile stress of the concrete is 1.92 MPa (280 psi), edge of the specimen and extended to approximately half of
which represents 5.5% of f c′. the width of the concrete panel, as shown in Fig. 4(a). At a
Meanwhile, Panels HS-U-15-2.5-6 and HS-B-15-2.5-6 are steel stress of 270 MPa (39,100 psi), which represents two-
cast with HSC and tested under uniaxial and biaxial tension thirds of the yield stress of the reinforcement (steel stress at
loads, respectively. At a tensile force of 400 kN (89.9 kips), the service load),15 the measured crack width increases to
Panel HS-U-15-2.5-6 starts cracking; with an average 0.212 mm (0.0084 in.).
concrete tensile stress of 3.2 MPa (450 psi), this is equivalent Panel HS-U-15-2.5-6 is cast using HSC and subjected to
to 3.47% of f c′. Panel HS-B-15-2.5-6 cracks when the tension uniaxial loading in the east-west direction. When the tension
force reaches approximately 310 kN (69.7 kips) and the force reaches approximately 400 kN (89.9 kips), two cracks
average tensile stress of 2.72 MPa (394 psi) is sustained by occur on the surface: one along the first transverse reinforcing
the concrete. This is equivalent to 3.6% of f c′. bar placed nearest to the west edge of the specimen and
The test results revealed that the use of HSC has a the other along the middle transverse bar. The measured
significant effect on the cracking behavior of axially average tensile steel stress is 333 MPa (48,300 psi). The
loaded panels. Once the concrete strength is increased measured initial crack opening is 0.21 mm (0.0083 in.).
from 40 to 90 MPa (5080 to 13,050 psi) (125%), the concrete As the test progresses, another crack appears at the first
tensile stress at the first cracking load increases by 52% transverse reinforcing bar placed nearest to the east edge of
for panels subjected to uniaxial loading. For panels tested the specimen, crossing the full width and thickness of the
under biaxial loading, however, as the concrete strength is specimen at a load of 450 kN (101.1 kips); the measured
increased from 35 to 75 MPa (5075 to 10,900 psi) (100%), average crack width is approximately 0.32 mm (0.012 in.).
the concrete stress at the first cracking load increases by Some cracks also occur in the east-west direction at the
42%, as shown in Table 2. Moreover, the experimental results end of the specimen. This phenomenon appears to be due
show that applying the biaxial loading has some influence to the bond failure between the reinforcement and concrete,
on the cracking behavior of the reinforced concrete panels. as the reinforcing bars exceed the yield stress, as shown in
In comparison with panels tested under uniaxial loading Fig. 4(b).
conditions, applying the biaxial loading causes the tensile Panels subjected to biaxial loading—As a result of
concrete strength to decrease by 5% and 15% for NSC and applying the axial load in a biaxial direction, the cracking
HSC panels, respectively. behavior can be investigated by analyzing the response of
Panels NS-B-15-2.5-6 and HS-B-15-2.5-6. Panel NS-B-15-
Cracking properties (crack width and spacing) 2.5-6 is cast with NSC and subjected to biaxial loading in the
Panels subjected to uniaxial loading—The cracking north-south and east-west directions with a loading ratio of
behavior of reinforced concrete panels subjected to uniaxial 1:1. The average tensile strain in the longitudinal upper and

24 ACI Structural Journal/January-February 2012

Fig. 4—Final crack patterns for tested panels. (Note: 1 kN = 0.2248 kips.)

lower reinforcing bars gradually increases in both directions. direction of the applied loads in each direction. For Panel HS-B-
When the tension force reaches approximately 220 kN (49.5 20-2.5-4 with bar spacing equal to 300 mm (11.8 in.), some
kips), the first crack appears along the surface perpendicular rotational cracks extended between the reinforcing bars due
to the east-west direction, directly above the first transverse to the higher distance between reinforcement compared with
reinforcing bar near the west edge of the panel. The average Panel HS-B-20-2.5-6 with lower bar spacing (S = 150 mm
tensile steel stress is 166 MPa (24,076 psi). The measured initial [5.9 in.]). The final crack patterns for all tested panels at the
crack width is found to equal 0.095 mm (0.0037 in.). At a stabilized crack stage are marked manually at each stage of
tension force of 280 kN (62.9 kips), the second crack occurs loading throughout the experiment, as shown in Fig. 4.
at 150 mm (5.9 in.) away from the first crack in the north- Crack spacing of axially loaded panels—The authors16,17
south direction along the line at which the reinforcement is have developed a rational crack spacing model that consid-
placed and eventually propagates to cross through the full ers the equilibrium, compatibility equations, and contri-
width of the specimen. The measured average crack width bution of transverse reinforcement of the concrete panel
is 0.14 mm (0.0055 in.). At the same time, two cracks occur subjected to in-plane axial stresses. As a result of the
in the east-west direction along the surface, directly above presence of the reinforcement in two-way perpendicular
the longitudinal reinforcing bars in the east-west direction, directions and considering a firm connection between the
as shown in Fig. 4(c). At the serviceability limit and steel longitudinal and transverse reinforcements, when the load
stress of 270 MPa (37,700 psi), the measured crack width is applied in the longitudinal direction and the stretching
increases to 0.179 mm (0.007 in.). of longitudinal bars and concrete matrix surrounding them
Identical to Panel NS-B-15-2.5-6 in configuration and are considered, the transverse bars in the perpendicular
loading method, Panel HS-B-15-2.5-6 is made using HSC. direction can be assumed to bear against the surrounding
While applying tensile load in the east-west direction, equal concrete.18 The influence of the main parameters that affect
tensile load is simultaneously applied in the north-south direc- the cracking behavior of reinforced concrete structures
tion. When the tension force reaches approximately 310 kN are taken into consideration, such as the tensile strength
(69.7 kips), the first crack occurs along the surface perpen- of concrete, reinforcement ratio, longitudinal bar diameter
dicular to the east-west direction, directly above the middle j1, and spacing S1. Moreover, the effect of the transverse
transverse reinforcing bar in the north-south direction, with reinforcement is incorporated into this model in terms of
an average tensile steel stress of 260 MPa (37,700 psi). The the transverse bar diameter j2 and transverse spacing S2.
measured initial crack width is found to equal 0.13 mm Hence, the proposed analytical model for maximum crack
(0.0051 in.). As the test progresses, the second crack occurs spacing can be expressed as the following
approximately 150 mm (5.9 in.) away from the first crack
in the north-south direction at a tension force of 330 kN
(74.2 kips) along the line at which the steel bar is placed.
 2 t b reff f j S  (7)
The measured average crack width is 0.19 mm (0.007 in.). Smax = ft ′ /  + bb 2 1 
At the same time, two cracks occur in the east-west direction  j1 Act S2 
along the surface, directly above the longitudinal reinforcing
bars in the east-west direction, as shown in Fig. 4(d).
The cracks in the panels tested under biaxial loading where Smax is the maximum crack spacing; fbb is the concrete
propagate in both directions perpendicular to the resultant bearing stress (half of the tensile strength of concrete

ACI Structural Journal/January-February 2012 25

Table 3—Measured and calculated average crack db/2) and t/2.15 Table 3 shows a comparison of the average
spacing of reinforced concrete panels under crack spacing between the results of the experimental work
axial loading conducted in this study and the developed model in Eq. (7).
Measured average crack The ratio of the maximum to average crack spacing Smax/Sm
spacing, mm Proposed model Sm(Exp)/Sm(Tho),* was previously defined to have a range of approximately
Specimen Sm(Exp) Sm, Sm(Tho), mm % 1.34 to 1.5.1,2,19
NS-U-15-2.5-6 151 155.9 3.3
NS-B-15-2.5-6 144 148.5 3.2 Effect of concrete strength on tension-stiffening
response
HS-U-15-2.5-6 152 166.9 10 The experimental results show that changing the compres-
HS-B-15-2.5-6 151 157 4 sive strength of concrete will lead to significant changes in
HS-U-20-2.5-6 150 156.6 4.5
the tension-stiffening and cracking behavior of the reinforced
concrete panels. Figures 5 and 6 illustrate the influence of
HS-B-20-2.5-6 148 147.2 0.6 using HSC on the tension-stiffening behavior of reinforced
HS-U-20-2.5-4 300 246.7 16.7 concrete panels under uniaxial and biaxial loading, respec-
tively. The changes can be summarized in the following
HS-B-20-2.5-4 275 265 3.7
*
observations: a rise in the cracking load due to the higher
Sm(Exp) is measured average crack spacing; Sm(Tho) is calculated average crack spacing
(Eq. (7)). tensile strength of HSC, an increase of the cracking strain in
Note: 1 mm = 0.0394 in. the case of the HSC panel due to a higher cracking load, and
lower strains and greater tension-stiffening effects at a given
load level due to improvement of the bond of the reinforcing
steel bars to the HSC matrix.
Generally, four distinct regions characterize the typical
tension-stiffening behavior of the panels tested under
axial loading: 1) the uncracked phase, where the concrete
composite shows a linear and elastic behavior; 2) the crack
formation phase, in which the axial stiffness of the concrete
panel gradually decreases due to the occurrence of cracks;
3) the stabilized cracking phase, where the concrete panels
and the bare reinforcing bars show an almost identical slope
for the stress-strain response; and 4) the failure phase, which
accompanies the yielding of the reinforcement, as illustrated
in Fig. 5.
HSC sustains tension forces well up to the point of the first
crack occurrence, corresponding to higher steel stress levels
compared to the NSC panels, as implied in Fig. 5 and 6. The
panels placed with HSC show a larger discrepancy in the
members’ strain at the cracking load due to the HSC’s brittle
Fig. 5—Average stress-strain curves for Panels NS-U-15-
nature, however, where this leads to a tension-stiffening
2.5-6 and HS-U-15-2.5-6. (Note: 1 MPa = 145 psi.)
response that can be quite different from that of NSC. On the
other hand, after the first crack appearance, the slope of the
stress-strain curve for the HSC panels radically decreases
up to the yield point of the reinforcement with continuous
variation of the slope through several steps. This indicates
the occurrence of additional cracks in the panel.
Comparisons for the average tensile stress-strain relation-
ship between reinforced NSC and HSC panels tested under
uniaxial and biaxial loading conditions are presented in
Fig. 7 and 8, respectively. The tensile strains of the concrete
are obtained and averaged from four LPDTs that are installed
at several locations to the surface of the specimens, as the
average strain from the LPDTs reflects the global behavior
of the cracked reinforced concrete panels under the applied
tensile load. Thus, the average strain et can be determined as

1 4
Fig. 6—Average stress-strain curves for Panels NS-B-15- ∑ Di
2.5-6 and HS-B-15-2.5-6. (Note: 1 MPa = 145 psi.) e t = 4 i =1 (8)
lg
based)18; tb is the bond stress at the steel-concrete interface;
reff is the effective reinforcement ratio; and Act is the effective
area around the reinforcing bars, where the thickness of the where ∆i is the individual reading from the LPDTs; and lg is
effective area may be taken as the lesser of 2.0(Cover + the gauge length of the LPDTs.

26 ACI Structural Journal/January-February 2012

Fig. 7—Average stress-strain curves of concrete for Panels NS- Fig. 8—Average stress-strain curves of concrete for Panels NS-
U-15-2.5-6 and HS-U-15-2.5-6. (Note: 1 MPa = 145 psi.) B-15-2.5-6 and HS-B-15-2.5-6. (Note: 1 MPa = 145 psi.)
It appears that the tensile strength of the concrete increases
as the compressive strength increases. However, the tensile
strength slightly increases at a much lower rate compared to
the compressive strength. Also, it can be seen that the initial
axial stiffness of HSC panels appears to be higher than that
of NSC panels, reflecting the stiffer nature of HSC. The
stress-strain curve of HSC panels descends more sharply
after the peak stress in comparison to NSC panels, however,
which show a gradual decrease, confirming the higher
brittle nature of HSC. The maximum observed ultimate
strain value emax, as measured from the experimental tests,
is approximately 16 to 20 times the value of the strain at
cracking e t′.

Effect of reinforcement ratio

The influence of changing the reinforcement ratio on the
tension-stiffening and cracking response can be examined
by comparing the experimental results of Panels HS-U-15-
2.5-6 (r = 1.2%) and HS-U-20-2.5-6 (r = 2%). In this series Fig. 9—Average stress-strain curves for Panels HS-U-15-
of tests, the layout of the bars is identical, but the diameter 2.5-6 and HS-U-20-2.5-6. (Note: 1 MPa = 145 psi.)
varies from 15 to 20 mm (5/8 to 6/8 in.), where a constant
reinforcing bar spacing of 150 mm (5.9 in.) is chosen, as 2.5-4 shows that the cracks’ locations are not significantly
shown in Table 2. There is a trend whereby the concrete affected by the location of the transverse bars, as the spacing
surrounding the smaller bar diameter carries a higher stress between these bars exceeds the required length to develop the
at the same steel stress level than that surrounding the larger tensile strength of concrete compared to the other specimen
bar diameter for the same bar spacing, especially during the (Panel HS-U-20-2.5-6) with closer transverse bar spacing.
crack formation stage, as shown in Fig. 9. Thus, the tension- Thus, smaller bar spacing means an anticipated higher
stiffening contribution decreases for the panels with higher number of cracks, and these cracks are smaller in width. At
reinforcing bar diameters. These results clearly match the a steel stress of 350 MPa (50,700 psi), the measured average
ACI 224R-0120 recommendations with regard to using well- crack width is 0.29 and 0.17 mm (0.011 and 0.007 in.) for
distributed reinforcing bars with a smaller bar diameter to Panels HS-B-20-2.5-4 and HS-B-20-2.5-6, respectively.
improve the cracking response of the reinforced concrete Furthermore, Fig. 10 shows that the panel with higher bar
members. Also, it should be noted that increasing the spacing develops a lower tension-stiffening contribution of
reinforcement ratio by increasing the bar diameter has an concrete for various loading stages.
insignificant influence on the cracking strength of concrete,
whereas changing the reinforcement ratio from 1.2 to 2% Effect of biaxial tension loads
causes the tensile strength to drop by 3% (refer to Table 2). The experimental test results presented in this study can
Meanwhile, the effect of the reinforcement ratio on be used to provide a clear understanding of the behavior of
the tension-stiffening behavior can be investigated by reinforced concrete structures subjected to biaxial tension. A
changing the bar spacing and using the same bar diameter. comparison of the stress-strain response of reinforced NSC
Figure 4(e) and (g) represents the crack patterns for panels tested under uniaxial and biaxial loading conditions
Panels HS-U-20-2.5-6 (r = 2%) and HS-U-20-2.5-4 (r = is presented in Fig. 11. Figure 12 shows the stress-strain
1.2%), respectively. The analysis of the failure mechanism behavior of reinforced HSC panels subjected to uniaxial
and the final crack pattern recorded for Panel HS-U-20- and biaxial loading. NSC and HSC panels subjected to

ACI Structural Journal/January-February 2012 27

 Fig. 13—Average stress-strain curves of concrete for
Fig. 10—Average stress-strain curves for Panels HS-U-20- Panels HS-U-20-2.5-6 and HS-B-20-2.5-6. (Note: 1 MPa =
2.5-6 and HS-U-20-2.5-4. (Note: 1 MPa = 145 psi.) 145 psi.)

biaxial loading show a lower tension-stiffening contribution

of concrete for different steel stress levels in comparison
to the identical panels tested under uniaxial loading. This
reduction in the tension stiffening is more obvious during the
crack formation phase but decreases at the stabilized crack
and failure phases, as illustrated in Fig. 11 and 12. The main
reason for this reduction in the tension stiffening is the gradual
degradation of the axial stiffness of the reinforced concrete
panel due to the additional cracks in the transverse direction.
Figure 13 presents a comparison of the average stress-strain
curves of the concrete between Panels HS-U-20-2.5-6, tested
under uniaxial loading, and HS-B-20-2.5-6, tested under biaxial
loading. Prior to the cracking stage, a slight difference in the
tensile stress-strain response is observed. After the cracking
stage, however, the effect of applying the load in the biaxial
direction becomes more obvious. Generally, the concrete
Fig. 11—Average stress-strain curves for Panels NS-U-15- stresses resulting from the biaxial tension tests are lower
2.5-6 and NS-B-15-2.5-6. (Note: 1 MPa = 145 psi.) than those from the uniaxial tension tests, and the average
contribution of the concrete after cracking decreases at a higher
rate with increasing the strains, as shown in Fig. 13.
Furthermore, applying the axial load in the biaxial direction
causes an increase in the average crack width compared to
the identical panel tested under a uniaxial loading condition.
The value of the average crack width for Panels HS-U-20-
2.5-4 and HS-B-20-2.5-4 reaches approximately 0.165 and
0.215 mm (0.0065 and 0.0085 in.), respectively, at the
service stress level in reinforcement (2/3fy).15

TENSILE STRESS-STRAIN RELATIONSHIP

Figure 14 shows the best mathematical form to fit the
ascending and descending branches of the experimental
stress-strain curve of HSC panels subjected to axial
loading conditions.
For predicting the member response before cracking, it is
assumed that prior to cracking, the steel reinforcement and
concrete behave elastically and that the concrete and the
reinforcement are all rigidly anchored together. Thus, the
Fig. 12—Average stress-strain curves for Panels HS-U-20- stresses and strains can approximately relate by a straight
2.5-6 and HS-B-20-2.5-6. (Note: 1 MPa = 145 psi.) line expressed as

28 ACI Structural Journal/January-February 2012

 ft e t
= (9)
ft ′ e t′

where ft /f t′ represents the normalized tensile stress; et is the

tensile strain of the concrete; and e t′ is the average value
of the strain at the cracking stage for the different tested
specimens. The average of all cracking strains for the NSC
specimens is found to be approximately 90 me.17 The value
for the average concrete strain at cracking for the HSC
specimens, however, is found to be approximately 102 me.
After the occurrence of cracking, the steel carries all the
tensile force at the crack locations. The following model
can represent the best fit of the descending branch for the
HSC panels tested in this study, taking into consideration the
influence of transverse bars

Fig. 14—Ascending and descending branches model of

−0.0008 tensile stress-strain curves of HSC panels.
ft a trans
( e t − e t′ )
(10)
=e
ft ′

The influence of the transverse bars on the stress distribu-

tion of the panels tested under uniaxial and biaxial loading
conditions can be considered by a factor atrans, where the value
of atrans is found to equal approximately 0.90.17 On the basis
of the R2 value (R2 = 0.92), the previous model in Eq. (10)
represents the best-fit curve for the data set extracted from the
conducted experimental program in this study.
Figure 15 shows a comparison of the previously proposed
models2,6,7,9,12 inclusive of the proposed model in Eq. (9)
and (10) in the ascending and descending portions in this
study, respectively. All of these models were obtained
from the experimental study for the behavior of reinforced
concrete members under uniaxial loading. It should be
noted that the proposed model represents an average value Fig. 15—Average stress strain of concrete.
between the previously proposed models for the tensile
stress-strain response of reinforced concrete, as shown in
Fig. 15. Furthermore, the experimental results of the average
tensile stress-strain response for Panel HS-U-20-2.5-4 are
compared with the proposed model for predicting the tensile
response parallel with the previously proposed models (refer
to Fig. 16). A favorable agreement between the experimental
and predicted tensile stress-strain behavior is noted.

SUMMARY AND CONCLUSIONS

An experimental investigation is carried out to study the
cracking behavior of reinforced concrete panels with different
concrete strengths subjected to pure tension (uniaxial or
biaxial loading). The influences of the main parameters that
affect the cracking behavior and tension-stiffening response
of the reinforced concrete panels are investigated, such
as the compressive strength, reinforcement ratio, and the
application of the load in the uniaxial or biaxial direction.
The best fit to the test results is developed for the pre- and Fig. 16—Average stress-strain relationship of reinforced
postcracking stress-strain behavior of HSC panels. Based on concrete Panel HS-U-20-2.5-4.
this study, the following conclusions are drawn:
1. Once the concrete strength is increased from 40 to 90 MPa from 35 to 75 MPa (5075 to 10,900 psi) (100%), the concrete
(5080 to 13,050 psi) (125%), the concrete tensile stress stress at the cracking stage is increased by 42%.
at the cracking stage is also increased by 52% for panels 2. The panels tested under biaxial loading conditions show
subjected to uniaxial loading. For panels tested under biaxial a lower concrete tensile strength compared with the panels
loading, however, as the concrete strength is increased subjected to uniaxial loading conditions. This reduction

ACI Structural Journal/January-February 2012 29

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This research is granted by the Natural Science and Engineering Council of
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30 ACI Structural Journal/January-February 2012

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