EXPERIMENTAL STUDY OF FLEXURAL BEHAVIOR
OF REINFORCED CONCRETE WALLS
Sergio Sunley∗
MEE10513

Supervisor:

Koichi KUSUNOKI∗∗

ABSTRACT
Design codes prescribe equations for ultimate state design of RC walls with flange walls as boundary
elements considering part of the length of the flange wall as an effective width to resist lateral loads.
However, the damage state and the accuracy of the effective width used in calculation have not been
discussed. Therefore, loading test was carried out in Yokohama National University on two 1/3 scalespecimens in order to evaluate the strength, damage state, energy dissipation and behavior of RC
structural walls in flexure. One specimen without flange walls and one with flange walls were tested.
The strength and response of each specimen were described, and the prediction accuracy of the design
flexural strength given by design codes ACI, Eurocode and AIJ was examined.
Experimental strain data was used to describe the behavior of the flange wall, in order to know themechanism it develops when the in plane wall is loaded, and to confirm the accuracy of the effective
width prescribed by design codes in tension and compression.
The result of the experimental study revealed that design prescriptions given by ACI, Eurocode andAIJ guidelines can estimate conservatively the flexural strength for RC walls without flanges, but they
underestimate the flexural strength for flanged walls. This underestimation is due to the lack ofknowledge of the mechanism developed at the flange.
It was not possible to determine a specific value of flexural effective width. However, it was
confirmed that the flange width is underestimated by design codes and it increases with imposed drift
level. The stress distribution at the flange in the out of plane direction was found not uniform, a factthat is different as the design assumptions.
Keywords: Flange Wall, Effective width, Flexural Strength.
1. INTRODUCTION
The use of Reinforced Concrete walls as structural element to resist the lateral loads imposed byearthquakes is a widely used system in countries prone to strong ground motion seismicity. Generally,
reinforced concrete walls are called shear walls, because in the common case they resist the lateralload as a shear behavior element prior to flexural. When flange walls, are attached to structural inplane walls (web), they contribute to the lateral resistance. After 2010 Chile earthquake the importanceto enhance the knowledge and design for flexural behavior of RC walls was evidenced. Several
damages were caused in different buildings where the main resistant system consisted of RC walls
without frames. The main objective of this study is to acquire knowledge of the behavior of RC walls
in flexure, especially of the mechanism the flange walls develop. This is accomplished by analyzing
the experimental results of a cyclic loading test conducted in Yokohama National University.

∗

Universidad Centroamericana José Simeón Cañas.
Associate Professor, Yokohama National University, Japan∗∗M

In the case boundary elements
are RC walls, the practice consists ofQconsidering the plane wall section as abeam with flanges, Figure 1. In this casethe length of the flange wall that resist partσof the moment caused by lateral load iscalled effective width.
It is possible to define theM
Figure2. Effective
effective width according to the stresswidth of flange walls
distribution in the flange wall. The stress
distribute as shown in Figure 2, the stress
Flange wall
σt, is the highest at the in-plane wall and it decreases going far fromthe center of the flange wall. The total force in the flange walls F can
Web wallbe calculated as the integral of the tensile stress for tension orcompression.
The effective length “B” is given by Eq. (1), where t is the thickness of the web wall.
Figure1.Scheme of flanged walls
σt × B×t = F(1)
AIJ guideline uses the Eq. (2) for the calculation of flexural strength. ACI and Eurocode use
a linear strain distribution using the concept of stress compression block at the concrete.
·

·

0.5

·

·

0.5 ·

(2)

2. EXPERIMENTAL TEST
2.1 Overview of the specimens
The specimen N1 is a wall without flange walls at the ends andspecimen N2 is a wall with flange walls in both ends in plane
designed taking into account the effective width of the wall
which is 6 times the thickness of the central wall, according to
the AIJ Guidelines prescription. The reinforcement description
and material properties for the concrete and steel are shown in
Table 1 and Table 2 respectively. Plain view of each specimen
is shown in Figure 3 and Figure 4. Specimens wereintentionally designed to fail in flexural prior shear failure
according to the provisions of AIJ Guidelines.
Table 1. Dimensions and reinforcement arrangement

Figure 3.Plan view, specimen N1

Steel reinforcement
Description
N1
N2

In-plane
In-planeFlange

80 mm

At
ends
2-D4@150 2-D5@150 2-D5

Pwe
(%)
0.37

80 mm

2-D4@150 2-D5@150 2-D5

0.24

ThicknessverticalHorizontal

Table 2. Material properties
Young Tensile Ultimate
Young Yielding Ultimate
Steel
Concrete
Modulus Stress Stress Properties Modulus StressStressProperties(MPa) (Mpa) (SD295) ( MPa) (MPa) (Mpa)(MPa)
N1
2.54X104 2.48
31
D4
1.85X105 356
505.8
4
N2
2.53X10 2.26
31
D5
1.92X105 364
524.4

Figure 4.Plan view, specimen N2

2.2 Load system
Cyclic reversal lateral loading was applied statically to each specimen through one 1MN hydraulicjack. The load was transmitted by a rigid beam at the top of the wall and controlled by displacement at
the same level. Figure 5 shows the applied loading system. Two 200 kN hydraulic jacks keep thevertical load in zero, so that the wall does not carry axial load.
The loading protocol consisted of the following drift target angles: ±1/6400, ±1/3200,±1/1600, ±1/800, ±1/6400, ±1/400, ±1/200, ±1/100, ±1/66, ±1/50 and ±1/25. Positive direction ispushing toward to south. After ±1/800 each cycle is repeated once.

Figure 5. Load system
3. EXPERIMENTAL RESULTS AND ANALYSIS
3.1 Specimen N1
The first crack was observed at the drift angle of +1/3200 (R=+1/3200) at the north lower corner of thewall. This horizontal crack is a clear pattern of flexural behavior expected at the wall. And the same
crack was observed at the south side when the load was directed to the opposite direction. At R=+1/1600 diagonal cracks appeared at the low north corner. The same pattern of diagonal cracks at thebottom of the wall developed in the following cycles in both directions appearing new ones going up
to the height of the wall. Important cracks were measured from drift angle R=-1/800, at which the
maximum crack width was 0.3 mm. The first reinforced bar yielded at the north side at R= +1/800 and
at R= ±1/400 all the bars at the corners of the bottom of the wall yielded at load 58.6 kN f and 52 kN
for positive and negative direction respectively. The maximum load was observed at R=±1/200. And it
was 67 kN for the positive direction and 71kN for the negative direction. After this drift angle, thesame crack pattern continued with the consequent growing of cracks. At R=± 1/100 sliding of the baseof the wall occurred and at R=±1/50 compression failure was observed for the concrete at the lower
corners with steel buckling, with cracks opened 5mm and 4.5 mm respectively. The wall resistancedecreased slightly exhibiting ductile behavior. The specimen lost carrying capacity at
R=2.5%.Thereafter, the test continued until R=+4.48%, when it was stopped because of the equipment
limitation.
3.2 Specimen N2
In this test, small cracks were observed at R=+1/6400 at the south side in the intersection of the web
and flange walls. At R= +1/1600, a horizontal crack appeared at the base of the north flange andsimilar crack developed at the base of the south flange at R=-1/1600. The maximum load of 150 kN
occurred just before reaching the drift angle of R=+1/800, followed by the sudden formation of adiagonal crack extended from the north upper corner to the south lower corner of the wall and thesudden decrease of the restoring force. The diagonal crack at this drift was also extended to the northflange, and it measured the width of 0.85mm at the repetition of the loading cycle. Several diagonal
cracks were developed after drift of R=1/400 in both directions and those cracks were also extended to
the flange walls. At R=+ 1/100 the vertical reinforcing bars started to yield at the base of the corner of
each side at a load of 124 kN. At the same stage, openings were measured at diagonal cracks with the
maximum width of 5mm and 6mm at positive and negative peaks respectively. At R=1.20 %,( at cycle
R=+1/66) most of the bars at the specimen yielded. After this step, the wall decreased its carrying
capacity. The bigger crack opening was observed at the repetition of the load at the drift R=±1/50 andit was 18mm at the diagonal crack. The test stopped at R=2.10% because of the tensile failure of thevertical reinforcement bars occurred at the top of the north corner of the wall. This is attributed to theloading system, which consisted of a rigid beam, which causes concentration of stresses around thezone fixed to the wall. No compression failure of the concrete was observed during the test.

Figure 6. Load drift angle, specimen N1

Figure7. Load drift angle, specimen N2

The skeleton curve and Energy Dissipation capacity is shown in Figure8 and Figure 9. The
calculation methods used to estimate the flexural strength are: JBDPA-AIJ, ACI 318-08 andEurocode2 (2004). Three cases are presented:a)Flexural strength for specimen N1b)
Flexural strength for specimen N2, using each design code proposed effective widthc)Flexural strength for specimen N2, considering the complete flange is the effective width.
Table 3 and Table 4 show the result of the calculation compared with the values obtained
from test for specimen N1 and N2 respectively in terms of the lateral force.
For the calculated values, the percentage respect to the force where all the reinforcing bars
yieded is shown in parenthesis.

Figure 8. Skeleton curve

Figure 9. cumulative dissipated energy (kN mm)

Table 3. Ultimate flexural strength capacity, N1 (kN) TableU 4. aUltimate
flexuralstrength capacity, N2 (kN)
e a
u oad
e u e acco d g o des g codes ( N)Calculated

N1

From test
80 % Yielding of Ultimate
AIJ
ACI Eurocode
bars
Max
Load
52.4
54.5
54.4
65.9
45.4
53.9
(79.5%) (82.7%) (82.6%)(R=0.25%) (R=2.52%)

Calculated
AIJ

ACI

N2

70.9
(57.2%)

76.2(61.4%)

N2( totalflange)137.1(110.6%)147.5(119%)

From test
80 % Yielding of
Ultimate
Eurocode
Max
bars
Load
76.1
(61.4%)
124
124
119.9
(R=1.20%) (R=1.20%)
147.5(119%)

4. ESTIMATION OF EFFECTIVE WIDTH
The calculation of the effective width is performed for specimen N2 based on the basic concept
presented in Figure 2 for both tension and compression. Using the strain history from strain gauges
pasted at 90 of height from the bottom of the wall, the stress distribution can be obtained and with thatstress, the value of the effective width “B” can be also obtained.

Effective width at the flange is calculated dividing the integral of the total area under the stress
distribution by the value of the central stress. For the flange walls,
lectures from the strain gauges pasted at the lowest section are takenfrom lines AA’, BB’, CC’ and DD’ at each peak of the
Load-displacement. Figure 10 shows a plain view of the strain gauges
distribution. When compression effective width is calculated, lectures
taken by lines AA’ and BB’ come from the positive displacementpeaks, and the lectures taken for lines CC’ and DD’ come from thenegative displacement peaks. For tension the opposite convention isused. For compression effective width, the stress of concrete wascalculated considering linear behavior of material, so that, the stress isgiven by the multiplication of the strain and young modulus of the
Figure 10. Plain view ofconcrete. Only strain data from layers AA’ and DD were used in thespecimen N2
calculation of compression effective width because it was determinedthat BB’ and CC’ carry tensile stress. For steel the stress was calculated with the strain history by theusing of the bilinear model and young modulus and yielding forces as parameters for the model for all
the layers.

Figure 11. Effective tension width

Figure 12. Effective compression width

Figure 11 and Figure 12 shows the variation of the calculated compression and tension effective width
for this tested specimen respectively, where the length of the wall is 1250 mm. According to the curve
corresponding to line AA’ and BB’ the values of effective width resulted from the calculation arelarger than the real length of the flange wall. This is fact leads incongruence, because it implies theeffective width is larger than the real length of the flange wall. It was determined that this result givesthat trend because stress, according to stress distribution is not always the maximum at the center.
Taking the lectures of the strain gauges pasted on the concrete the depth of the compression zone inplane was determined assuming a linear distribution of strain; the result is shown in Figure 13.
According to this result it was impossible to calculate the effective width using the proposed method,and it implies the stress distribution in plane is not uniform at flange walls.
It is important to know not only theeffective width of the flange wall,
but the amount of reinforcing steel
that was effective to resist tensile
force. The total force carried byeach flange was using the calculated
stress values, and then the required
area of steel at each drift angle is found.

Figure 13. Compression zone at flanges in plain view

The ratio between of the sum of the stresses ofthe flange wall and the yielding stress gives theequivalent number of yielded bars that resist thetensional force due to flexure moment.
The total area of steel is found by multiplying
the equivalent number of bars, by the area of
each steel bar. The result is expressed in termsof the yielding strength of bars D4. The
calculated area of steel is expressed as thereinforcement ratio on the gross area of the walland it means the amount of yielded
reinforcement necessary to resist the tensile
force in the flange at each peak of the loading test
Figure 14. Effective reinforcement ratio
and it is shown in Figure 14. From the figure, it isnoted that the amount of steel needed to resist the tensile force at the test is smaller than thereinforcement ratio provided by the whole flange. The maximum required reinforcement ratio is0.32 % at the south flange that is also more than the correspondent value for the width “6 t”.
5. CONCLUSIONS
•
•
•
•
•

Conventional methods to determine the ultimate flexural strength for RC walls predictedconservatively the flexural strengths observed for specimen without flanges but
underestimated the flexural ultimate strength for flanged specimen.
Specimen with flange walls showed larger energy dissipation capacity than specimen without
flanges. However, specimen without flange walls presented larger and more stable value ofequivalent viscous damping than flanged specimen.
The calculation revealed that effective width is underestimated by design codes
The test result suggests that stress distribution at the flange wall in the out of plane direction is
not uniform.
This experimental study confirms that the flange width increases with imposed drift level
6. RECOMMENDATION

Future test must be carried out to know the behavior of RC walls with flange walls as boundary
elements, in order to confirm the results of this test. The combination of the axial and flexural
behavior should be included and the dimensions of the wall should simulate continuous walls of morethan one story, with larger slenderness ratio than the presented in this test, in order to reproduce thereal scenario of RC walls in buildings
AKNOWLEDGEMENT
I want to express my gratitude to my adviser Dr. Taiki Saito, for involved me at experimental test at
the laboratory and to my lab fellow Shingo Yamaguchi to let me join at the experiment he planned.
REFERENCES
American Concrete Institute, 2008, ACI 318-08.
Akenori, Shibata, 2010, Dynamic Analysis of Earthquake R.Structures, Tohoku Univ
Architectural Institute of Japan, 2005, Architectural Institute of Japan
Architectural Institute of Japan, 2010, Architectural Institute of Japan (in Japanese)

European Committee for Standardization, 2003, “Eurocode 2”, EN 1992-1-1:2004 (E)European Committee for Standardization, 2003, “Eurocode 8”, EN 1998-1:2004 (E)