the effects of cross sectional dimensions on the behavior ... · the effects of cross sectional...

Journal of Civil Engineering and Architecture 10 (2016) 1355-1363 doi: 10.17265/1934-7359/2016.12.006

The Effects of Cross Sectional Dimensions on the

Behavior of L-Shaped RC Structural Members

Mehmet Hasnalbant1 and Cemal Eyyubov2

1. Institute of Natural and Applied Science, Erciyes University, Kayseri 38010, Turkey

2. Department of Civil Engineering, Faculty of Engineering, Erciyes University, Kayseri 38010, Turkey

Abstract: The behavior of L-Shaped RC (reinforced concrete) shear walls was investigated in the Erciyes University Earthquake Investigation Laboratory under the influence of constant axial load together with reversed cyclic lateral load. The objective of this study was to evaluate the effects of cross sectional dimensions on the behavior of L-shaped structural members and to assess their earthquake performance. In order to investigate L-shaped RC structural members, the special experiment setup and four type of 1/2 scaled specimens which have different aspect ratio were constructed. The specimens were loaded in line with the major principal axes direction laterally. Axial load ratio was 0.1 and cross section height to thickness ratios were 3:1, 5:1, 8:1, 10:1. Cross section thickness was 120 mm which corresponds to (360:120), (600:120), (960:120), (1,200:120) wall legs cross sectional dimensions in mm. The specimens height was 1,500 mm, together with upper and lower slabs overall height was 2,000 mm. Concrete compression strength was 30 N/mm2, steel yield stress 420 N/mm2 and vertical reinforcement ratio was 1% for all specimens. According to the test results, the specimen of which the aspect ratio is 3 (360:120) has shown column behavior, the specimen of which the aspect ratio is 5 (600:120) has shown slender wall behavior and last two specimens of which the aspect ratios are 8 (960:120) and 10 (1,200:120) have shown squat wall behavior. When considering the cracking patterns and hysteretic behavior, since the aspect ratio 8, the specimens show flexure-shear interaction behavior and prone to brittle failure. Key words: Shear wall, reinforced concrete, L-shaped, ductility, stiffness.

1. Introduction

Shear walls are frequently used to resist lateral

forces. Because of their high strength and stiffness,

they can effectively reduce lateral displacements and

limit damages of structural and non structural elements.

Although planar walls commonly are used and can

prevent buildings from collapse, sometimes it is

necessary to use more efficient lateral load resisting

systems to provide required performance level. As the

tools for conducting nonlinear response history have

improved with the advent of performance based

seismic design, reinforced concrete walls and core

walls are often employed as the only lateral force

resisting system [1].

Because of the architectural, lateral stiffness

Corresponding author: Cemal Eyyubov, professor,

research fields: steel structures, earthquake engineering and structural dynamic.

necessities, to maximize the window space, designers

may prefer non planar shear walls. L-shaped shear

walls are formed by combining two orthogonal planar

shear walls and have two directional strength and

stiffness. Considering the response of these wall

components along each of the principle plan direction

separately is not reasonable. Combining the planar

walls leads to unsymmetric bending and complicated

interaction between wall parts. Responses of non

planar walls with at least one cross sectional principal

axes that is not a symmetry axis are typically governed

by unsymmetric bending and would be influenced by

inelastic biaxial interactions more significantly than

those of planar walls [2].

Stiffness, strength and ductility of shear walls with

asymmetric cross section can be completely different

and can exhibit different failure mode in opposite

directions [3].

D DAVID PUBLISHING

The Effects of Cross Sectional Dimensions on the Behavior of L-Shaped RC Structural Members

1356

1.1 Numerical Studies in Literature

The strength and deformational behavior of

L-shaped tied columns have been studied by Hsu [4]

under combined biaxial bending and axial compression

experimentally and analytically. Dündar [5] has been

proposed an approach to the ultimate strength

calculation and the dimensioning of arbitrarily shaped

RC (reinforced concrete) sections subject to combined

biaxial bending and axial compression. Rodriguez [6]

offered a general formulation by which the biaxial

interaction diagrams of an arbitrary reinforced concrete

cross sections. The proposed method uses nonlinear

stress-strain relationship for the concrete and

multi-linear elastoplastic one for the reinforcement. So

it can be utilized to study the effects of creep and

confinement of the concrete and strain hardening of the

steel by modifying the input parameters. Khairallah [7]

presented numerical model for the prediction of three

dimensional characteristics of reinforced concrete

L-shaped shear wall structures. Orakçal [8]

investigated modeling approaches for reliable

prediction of reinforced concrete wall response. They

proposed multiple vertical line element macro

model.

1.2 Experimental Studies in Literature

Nakachi [9] investigated deformation capacity of

multistory reinforced concrete core walls after flexural

yielding. Four core walls were constructed and tested.

Test parameters were the concrete confinement at the

corner, the amount of confining steel at the corner and

the area of concrete confinement. They have found that

confining reinforcement at the corner had significant

effect on deformation capacity.

Hosaka [10] investigated structural performance of

L-shaped shear walls experimentally and analytically

by using fiber model. They produced 1/6 scaled four

specimens. Lateral load was applied under varied axial

loads. Parameters were concrete strength and rebar

arrangement. Due to the test results, flexural

deformations at the section about 1L (L is the height

which is equal to the wall length) from the bottom

were dominant.

Inada [11] constructed three L-shaped core wall with

1/4.5 scale. They studied the effect of loading direction

and the section configuration on the seismic behavior

of the core wall. The wall that was loaded in the arm

direction failed due to crushing of boundary zone in

compression. Other unequal leg wall’s damage was

more effective in the short leg. Strain distribution was

not linear in the section. The hypothesis of plane

sections remaining plane was not valid. They

recommended increasing the confinement area at the

corner of the section.

Karamlou [12] tested 1/2 scaled, four L-shaped

shear walls which were built with industrialized

reinforced insulating concrete form panels. They

investigated the behavior of L-shaped shear wall

constructed with this system. The specimens had the

same geometrical dimensions but differed in their

confining boundary rebars. Dimensions of the

specimens were 1,500 mm high, 750 mm wide and 100

mm thick. They have found that web crushing reduces

the stiffness, strength and ductility, on the other hand,

increases the rotation of shear walls, higher flexural

strength of the walls in one direction against the other,

increases the possibility of web crushing.

Li [13] tested L-shaped cross section shear walls of

which the height-thickness ratio is between 5-8. They

constructed six specimens and loaded in the web plane.

Axial load ratio was in the range of 0.1~0.4 . They have

found that the specimen, of which the axial load ratio is

0.1 and height-thickness ratio is 6.5, has the most

excellent ductility and energy dissipation capacity.

2. Experimental Study

Four different cross section dimensioned, 1/2 scaled

reinforced concrete specimens were constructed and

tested.

The compressive strength of concrete was

30 N/mm2, steel yield stress was 420 N/mm2, the cross

section thickness of all specimens were 120 mm, and


1357

the height of all specimens was 1,500 mm.

Additionally, 200 mm thick upper slab was constructed

for vertical load, 300 mm thick lower slab was

constructed for foundation. Initially, 0.1Acfc axial load

was applied at centroid and kept constant during test.

After the vertical load reaching the required level, the

cyclic lateral load was applied at the major principal

axes direction for all specimens:

Ac = cross sectional concrete area;

fc = concrete compression strength on the test day.

Specimens design parameters are given in Table 1

and cross section size and reinforcement are shown in

Fig. 1.

2.1 Specimens Construction

Specimens were constructed by on-site casting with

wood formwork in the Erciyes University Earthquake

Investigation Laboratory. 10 mm diameter vertical

reinforcement with 0.01 volumetric ratio and 8 mm

diameter horizontal reinforcement with 0.0072

volumetric ratio were used in the specimens.

Reinforcement yield stress was 420 MPa.

Table 1 Specimens characteristics.

Notation Cross section dimension (mm)

Cross section ratio

Shear span ratio

Axial load ratio

Vertical reinforcement ratio

Horizontal reinforcement ratio

Concrete strength

L120x360 120 × 360 × 360 3 4.17 0.06 0.013 0.0072 37 N/mm2

L120x600 120 × 600 × 600 5 2.5 0.10 0.012 0.0072 21 N/mm2

L120x960 120 × 960 × 960 8 1.56 0.09 0.012 0.0072 21 N/mm2

L120x1200 120 × 1,200 × 1,200 10 1.25 0.05 0.011 0.0072 37 N/mm2

Fig. 1 Specimens cross sections and reinforcements (units in mm).

360

L120x360

360

120

12? 0

960

L120x960

960

120

32? 0

1200

L120x1200

1200

120

40? 0

600

L120x600

600

120

20? 0


1358

2.2 Test Setup

The reaction frame was constructed by using steel

profiles. The frame is hinged at the lower end and can

move together with the specimens upper slab. The

finished steel plate was placed at the vertical load

applied joint on the upper slab. The special end element

was produced for the vertical hydraulic jacks junction

point with the steel plate. While the lateral loading,

tension force was transmitted to the other side of the

specimens through two steel rods.

The vertical load was applied at the cross section

centroid by a 1,000 kN hydraulic jack that was

mounted on top girder of the reaction frame. To create

biaxial bending effect, lateral load was applied in line

with major principle axes direction of the specimens.

To apply the lateral load, another 1,000 kN hydraulic

jack was connected between top slab of the specimens

and the reaction wall horizontally. By placing a hinge

between hydraulic jack and the top slab bending

moment, the displacements were released.

2.3 Measuring Instruments

In the experiment, load cells, strain gauges, LVDTs

(linear variable displacement transducers),

potentiometer, dial gauges were used as a measuring

devices. Applied vertical and horizontal loads were

measured by load cells during the test. Horizontal and

vertical displacements were measured by LVDTs,

potentiometer, dial gauges. Additionally, some strain

gauges were mounted on boundary reinforcement to

monitor the yielding and strain process.

2.4 Loading Protocol

In the experiments, the axial load upper limit was

adopted as 500 kN for safety reasons. Therefore, the

largest specimens axial load was taken as 500 kN. At

first, the entire vertical load was divided in 8 to10 times

and applied gradually. Deal gauges values were read

and recorded at each step. After reaching the full axial

load, horizontal load began to apply. When calculating

the cyclic load increment for each specimen, it was

considered to reach their lateral load capacity in 10 steps.

Fig. 2 Reinforcement.

Fig. 3 Test setup.


1359

Fig. 4 Lateral loading protocol.

Fig. 5 L120x360 cracking pattern.

Concrete crushing or reinforcement buckling was

considered to ultimate load capacity.

Corresponding lateral load increment for each

specimens are as follows:

L120x360 5kN;

L120x600 10kN;

L120x960 20kN;

L120x1200 30kN.

3. Experimental Results

In this section, experimental results including

cracking pattern, hysteretic behavior, ductility factor of

each specimen are presented.

3.1 Cracking Patterns

For the specimen L120x360, under the cyclic

loading, only horizontal bending crack was formed and



-390

-290

-190

-90

10

110

210

310

1 3 5 7 9 111315171921232527For

ce(k

N)

Load Step

Lateral Loading

L120x1200

L120x960

L120x600

L120x360

The

1360

Fig. 8 L120x

Fig. 9 Analy

e Effects of Cr

x1200 cracking

ytical model.

ross Section

g pattern.

al Dimensionns on the Beh

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the

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the

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havior of L-Sh

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bending mom

For the spec

nding cracks w

specimen. T

ger at the lo

ntinuously i

ar-flexure c

cks were long

d negative dir

length due to

ure was obse

For the sp

izontal bend

plying higher

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ective than be

s observed.

gth and distan

mation of com

To the specim

ead througho

erefore it has

stic hinge re

mber is und

eraction and p

Three dimen

nerated by usi

Ductility Beh

Displacement

ich is summ

q. (1)) by usin

u) displaceme

ere: +∆y = po

+∆u = positiv

∆y = negative

∆u = negativ

+μ = positive

μ = negative

haped RC Str

was observe

ment effect an

imen L120x

were observe

These horizo

ower region

increasing

racks appea

ger than inclin

ection horizo

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pecimen L12

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r levels of la

peared and s

ending stress.

When consi

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out whole su

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marized in T

ng the top sla

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μ = ∆u/

ositive directi

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direction duc

direction duc

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of the specim

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ontal cracks w

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ateral load, l

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. Shear-flexur

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ctility factor;

ctility factor.

bers

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al direction.

shear cracks

he specimen.

mation of the

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hear-moment

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s (Fig. 9).

he specimens

re calculated

and ultimate

(1)

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acement;

ment;

acement;

r

l

f

s

o

d

e

e

t

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t

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d

e

n

s

e

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.

e

l

t

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)

The

Table 1 Duc

Notation

L120x360

L120x600

L120x960

L120x1200

3.3 Hysteret

-150

For

ce(k

N)

-50

For

ce(k

N)

e Effects of Cr

ctility factors.

+∆y

11mm

10.4mm

3.8mm

5.3mm

tic Behavior

-100 -

D

L120x

-

-

-30

D

L120

ross Section

+∆u

44mm

40.7mm

15.8mm

24.7mm

(a)

(c)

(e)

-100

-50

0

50

100

-50 0

Displacement

x360 Test hys

-150

-100

-50

0

50

100

150

-10 10

Displacement(

0x600 Test Hy

al Dimension

-∆y

7.7mm

7.7mm

3.5mm

4mm

50

t(mm)

steresis loop

30

(mm)

ysteresis Loo

ns on the Beh

-∆u

25.6mm

23mm

10mm

14.7mm

100

50

op

havior of L-Sh

+μ

m 4

3.91

4.15

m 4.66

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2.9

2.8

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m

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98 3

86 3

68 4

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mean μ

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.50

4.17


1362

(g) (h)

Fig. 10 Load deformation behavior: (a) L120x360 test hysteresis loop; (b) L120x360 Ansys hysteresis loop; (c) L120x600 test hysteresis loop; (d) L120x600 Ansys hysteresis loop; (e) L120x960 test hysteresis loop; (f) L120x960 Ansys hysteresis loop; (g) L120x1200 test hysteresis loop; (h) L120x1200 Ansys hysteresis loop.

4. Conclusions

Four 1/2 scale reinforced concrete L-shaped

structural members test results have shown that:

Energy dissipation capacity increasing with arm

lengths for all specimens;

Ductility ratio is nearly equal for all specimens

(≈ 4). It is not possible to achieve high ductility ratio

with existing reinforcement distribution. In addition,

the increase in the axial load ratio will adversely affect

the ductility;

When considering the hysteretic behavior, the

L360x120 and L600x120 specimens have shown better

seismic performance than the others. Since the cross

section ratio is 8, pinching effect was observed in the

hysteresis loops. There are two reasons for this

formation. First, unsymmetrical distribution of

reinforcement according to acting force direction.

Second is the low shear span ratio. The L960x120

specimens shear span ratio is 1.56 and the L1200x120

specimens shear span ratio is 1.25, both of them are

lower than 2. In this case, these structural members

become shear critic elements. Increasing arm length

will improve negative effects of these factors on the

members behavior;

When examining the cracking characteristics, the

L360x120 and L600x120 specimens have shown

bending deformation and the L360x120 behaved like

column, the L600x120 behaved like slender wall. The

L960x120 and L1200x120 have influenced with

shear-flexure interaction and shearing stress more

effective. They behaved like squat walls. There were

no observed plastic hinge formation, so these

specimens are prone to brittle failure.

References

[1] Wallace, J. 2007. “Modelling Issues for Tall Reinforced Concrete Core Wall Buildings.” The Structural Design of Tall and Special Buildings 16: 615-32.

[2] Huria, V., Raghavendrachar, M., and Aktan, M. 1991. “3D Characteristics of RC Wall Response.” Journal of Structural Engineering 117: 3149-67.

[3] Thomsen, J., and Wallace, J. 1995. Displacement Based Design of RC Structural Walls: Experimental Studies of Walls with Rectangular and T-Shaped cross Section. Report No. CU/CEE-95/06, Department of Civil and Environmental Engineering, Clarkson University, Potsdam, NY.

[4] Hsu, C. T. 1985. “Biaxially Loaded L-Shaped Reinforced Concrete Columns.” Journal of Structural Engineering 111 (12): 2576-95.

[5] Dündar, C. 1993. “Arbitrarily Shaped Reinforced Concrete Members Subject to Biaxial Bending and Axial Load.” Computers and Structures 49 (4): 643-49.

[6] Rodriguez, J., and Aristizabal, O. 1999. Biaxial Interaction Diagrams for Short Reinforced Concrete Columns of Any Cross Section.” Journal of Structural Engineering 125 (6): 672-83.

[7] Khairallah, F., and Arai, Y. 1997. “Numerical Model to Predict the 3-Dimensional Characteristics of Reinforced Concrete L-Shaped Shear Walls.” Journal of Structural

-600

-400

-200

0

200

400

600

-10 -5 0 5 10

For

ce(k

N)

Displacement(mm)

L120x1200 Ansys Hysteresis LoopL120x1200 Test Hysteresis Loop

For

ce(k

N)

Displacement(mm)


1363

Construction Engineering 493: 73-81. [8] Orakçal, K., Massone, L., and Wallace, J. 2006. Analytical

Modeling of Reinforced Concrete Walls for Predicting Flexural and Coupled Shear-Flexural Responses. PEER Report 2006/07. University of California, Los Angeles, USA.

[9] Nakachi, T., Toda, T., and Tabata, K. 1996. “Experimental Study on Deformation Capacity of Reinforced Concrete Core Walls after Flexural Yielding.” In Proceedings of the 11th World Conference on Earthquake Engineering .

[10] Hosaka, G., Funaki, H., Hosoya, H., and Imai, H. 2008. “Experimental Study on Structural Performance of RC Shear Wall with L-Shaped Section.” In Proceedings

of the 14th World Conference on Earthquake Engineering.

[11] Inada, K., Chosa, K., Sato, H., Kono, S., and Watanabe, F. 2008. “Seismic Performance of RC L-Shaped Core Structural Walls.” In Proceedings of the 14th World Conference on Earthquake Engineering.

[12] Karamlou, A., and Kabir, M. Z. 2012. “Experimental Study of L-Shaped Slender R-ICF Shear Walls under Cyclic Lateral Loading.” Engineering Structures 36: 134-46.

[13] Li, W., and Li, Q.-N. 2012. “Seismic Performance of L-Shaped RC Shear Wall Subjected to Cyclic Loading.” The Structural Design of Tall and Special Buildings 21 (12): 855-66.

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