LOAD-PATH INFLUENCE IN RC COLUMNS UNDER HORIZONTAL BIAXIAL …

Proceedings of the 6th International Conference on Mechanics and Materials in Design,

Editors: J.F. Silva Gomes & S.A. Meguid, P.Delgada/Azores, 26-30 July 2015

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PAPER REF: 5729

LOAD-PATH INFLUENCE IN RC COLUMNS UNDER HORIZONTAL

BIAXIAL BENDING

Hugo Rodrigues1 (*)

, André Furtado2, António Arêde

2, Humberto Varum

2

1School of Technology and Management, Polytechnic Institute of Leiria, Leiria, Portugal 2Faculty of Engineering, University of Porto, Porto, Portugal (*)Email: [email protected]

ABSTRACT

The cyclic behaviour of reinforced concrete (RC) columns has been object of many

experimental studies in the last years, mostly focused on the unidirectional transversal loading

of columns with constant axial load conditions. This research work is focus on the evaluation

of the horizontal load-path effects in the response of RC columns under biaxial bending. For

this, four series of full-scale quadrangular columns were tested under different horizontal

load-path conditions. Twelve RC columns were tested under constant axial and four were

subjected to variable axial loading conditions. In this paper, the experimental results are

presented, and the global behaviour of the tested columns is discussed, particularly focusing

on the evaluate the relationship between the biaxial and the uniaxial test about the maximum

strength, ductility, initial stiffness and energy dissipation.

Keywords: RC columns, biaxial cyclic tests, Horizontal load-path, shear-drift response.

INTRODUCTION

Since columns are key structural elements for the seismic performance of buildings, special

attention should be given to their structural response under cyclic loading demands.

Moreover, earthquake effects generally require the inclusion of horizontal demands in two

directions that are recognized to inflict more complex demands than single direction actions.

Rodrigues et al. (Rodrigues et al., 2010, Rodrigues, 2012, Rodrigues et al., 2012, Rodrigues et

al., 2012, Rodrigues et al., 2013) tested several RC specimens with four types of full-scale

rectangular building columns tested for different loading histories. The horizontal loading

patterns considered were: cruciform; diamond; expanding quadrangular; and circular. In this

study the comparison of the biaxial results is performed with similar columns under uniaxial

load. Based on the obtained results, it was verified that: i) The initial column stiffness in both

directions it is not significantly affected by the biaxial load path; ii) when comparing the

maximum strength in one specific direction of the columns, for each biaxial test against the

corresponding uniaxial test, lower values were obtained for all biaxial tests than uniaxial ones

(the biaxial loading induces a 20-30% reduction of the columns maximum strength in their

weak direction, while reductions from 8-15% for the stronger direction); iii) the ultimate

ductility is significantly reduced in columns subjected to biaxial load paths; iv) the strength

degradation is practically zero, in the first loading cycles, increasing after displacement

ductility demands of about 3. (from the strength degradation analysis, more pronounced

strength degradation was observed for biaxial tests when compared with corresponding

uniaxial tests; v) the biaxial loading can introduce higher energy dissipation (circular,

rhombus and cruciform load paths) than uniaxial loading, as previously recognized by other

Symposium_10

Seismic Behaviour Characterization and Strengthening of Constructions

authors; vi) the viscous damping

repetition of cycles, for the same maximum displacement level, has practically no influence

on the equivalent damping).

The experimental work presented is part of a large testing campaign undertaken at t

Laboratory of Earthquake and Structural Engineering (LESE), of the Faculty of Engineering

of Porto University (FEUP), for the study of RC columns (of buildings and bridges) under

horizontal cyclic loadings. The main objective of this experimental campai

cyclic behaviour of RC columns, under uniaxial and biaxial horizontal cyclic loadings in

order: i) to contribute for the experimental results database of the RC columns under biaxial

bending; ii) to contribute for understanding the effe

the uniaxial bending and iii) to test the influence of different biaxial load paths in the

column’s response (Rodrigues et al., 2013, 2013).

SUMMARY OF THE EXPERIMENTAL CAMPAIGN

Specimens’ description and experiment

Four series of rectangular reinforced concrete

geometric characteristic and reinforcement detailing, and were cyclically tested for different

loading paths. A total of eighteen

square concrete foundation blocks with dimensions 1.30x1.30m

cross-section dimensions and the reinforcement detailing are presented in Figure 1. Four holes

are drilled in the foundation block to

cantilever model it is assumed that the inflection point of a 3.0m height column is located at

its mid-height (1.5m), representing the behaviour of a column at the base of a typical building

when subjected to lateral demands induced by earthquakes. An extra 0.20m height is added

for attaching the actuator devices. Details of the reinforcement

material properties (concrete compressive ultimate strength (fc), the reinforc

modulus, yielding strength, ultimate strength and ultimate strain

(a)

Fig. 1 - RC column specimen a) cross


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authors; vi) the viscous damping highly depends on the biaxial load path (however the


The experimental work presented is part of a large testing campaign undertaken at t



horizontal cyclic loadings. The main objective of this experimental campai



bending; ii) to contribute for understanding the effects of biaxial bending when compared to


column’s response (Rodrigues et al., 2013, 2013).

SUMMARY OF THE EXPERIMENTAL CAMPAIGN

Specimens’ description and experimental setup

reinforced concrete columns were constructed with


A total of eighteen column specimens with 1.70m high, and are cast in strong

square concrete foundation blocks with dimensions 1.30x1.30m2 in plan and 0.50m high. The

section dimensions and the reinforcement detailing are presented in Figure 1. Four holes

are drilled in the foundation block to fix the specimen to the laboratory strong floor. With the


height (1.5m), representing the behaviour of a column at the base of a typical building

ubjected to lateral demands induced by earthquakes. An extra 0.20m height is added

for attaching the actuator devices. Details of the reinforcement are shown in Figure 1 and the

(concrete compressive ultimate strength (fc), the reinforc

modulus, yielding strength, ultimate strength and ultimate strain are summarized

(b)

RC column specimen a) cross-section and reinforcement detailing b) general dimensions and c) general

view of the experimental test setup.

highly depends on the biaxial load path (however the


The experimental work presented is part of a large testing campaign undertaken at the



horizontal cyclic loadings. The main objective of this experimental campaign was to study the



cts of biaxial bending when compared to


columns were constructed with three different


70m high, and are cast in strong

in plan and 0.50m high. The

section dimensions and the reinforcement detailing are presented in Figure 1. Four holes

fix the specimen to the laboratory strong floor. With the


height (1.5m), representing the behaviour of a column at the base of a typical building

ubjected to lateral demands induced by earthquakes. An extra 0.20m height is added

are shown in Figure 1 and the

(concrete compressive ultimate strength (fc), the reinforcement elastic

are summarized in Table 1.

(c)

etailing b) general dimensions and c) general


Editors: J.F. Silva Gomes & S.A. Meguid, P.Delgada/Azores, 26

The experimental setup includes

axial load and 2 horizontal

columns (one with a capacity of 500kN with +/

of 200kN and +/-100mm stroke)

by 2 steel reaction frames and a

reaction frames were fixed to the strong floor of the laboratory with prestressed steel bars to

avoid sliding or overturning of the specimen during testing, or sliding of the reaction frame.

Since the axial load actuator remains

specimen laterally deflects, a sliding device is used (placed between the top

actuator), which was built to minimise spurious friction effects.

two sliding steel plates that exist between the top

with the main purpose of to measure these small friction forces

horizontal directions were connected to the upper plate (that is expected not to displace

laterally) and the corresponding measured forces

load cells of the horizontal actuators

Horizontal loading condition

In order to characterize the response of the column specimens, several loading conditions

were considered. Cyclic lateral displacements were imposed at the top of the column with

steadily increasing displacement

and for each lateral deformation demand level

nominal peak displacement levels (in mm) were considered: 3, 5, 10, 4, 12, 15, 7, 20, 25, 30,

35, 40, 45, 50, 55, 60, 65, 70, 75, 80.

horizontal load paths types in order to evaluate the e

columns response. Five different horizontal displacement paths types were applied and are

illustrated in Figure 2. The group series 1, 2 and 3 were subjected to a constant axial load and

the group series number 4 was sub

each specimen and corresponding loading condition

(a) (b)

Fig. 2 - Horizontal displacement paths types a) Uniaxial (strong) b) Uniaxial (weak) c) Cruciform d) Diamond

Prior to the tests with varying

and the strengths corresponding to the first

columns axial load was considered variable and proportional to the

applied until the yielding drift. In the biaxial tests the axial load variation is relative to the

displacement observed in the strong direction.

kept constant. The initial axial load

considered. A schematic representation of the lateral loading pattern and axial loading

condition is presented in Fig. .



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includes a vertical 700kN capacity actuator that was used to apply the

independent actuators to apply the lateral load

(one with a capacity of 500kN with +/-150mm stroke and the other with a capacity

100mm stroke), and the reaction system for the three actuators

steel reaction frames and a concrete reaction wall form. The column specimens and the



Since the axial load actuator remains in the same position during the test while the column

specimen laterally deflects, a sliding device is used (placed between the top

actuator), which was built to minimise spurious friction effects. This device is composed by

exist between the top column section and the actuator.

to measure these small friction forces, load cells in the two

connected to the upper plate (that is expected not to displace

aterally) and the corresponding measured forces were subtracted from the forces read by the

load cells of the horizontal actuators.

Horizontal loading condition


Cyclic lateral displacements were imposed at the top of the column with

displacement levels. The adopted load paths are summarized in

for each lateral deformation demand level, three cycles were repeated


35, 40, 45, 50, 55, 60, 65, 70, 75, 80. For the four series of specimens it was applied different

horizontal load paths types in order to evaluate the effect of the load pattern in the RC


The group series 1, 2 and 3 were subjected to a constant axial load and

the group series number 4 was subjected to variable axial load. All the information relative to

each specimen and corresponding loading condition are indicated in Table 1.

(c) (d)

tal displacement paths types a) Uniaxial (strong) b) Uniaxial (weak) c) Cruciform d) Diamond

and e) Quadrangular.

with varying axial loading (Series 4), the peak capacities,

corresponding to the first yield were evaluated. With this information

columns axial load was considered variable and proportional to the imposed


d in the strong direction. Beyond the yielding point the axial load

initial axial load was set on 300kN and variations

A schematic representation of the lateral loading pattern and axial loading

.

was used to apply the

actuators to apply the lateral load paths on the

150mm stroke and the other with a capacity

reaction system for the three actuators is composed

column specimens and the



in the same position during the test while the column

specimen laterally deflects, a sliding device is used (placed between the top-column and the

This device is composed by

column section and the actuator. However,

load cells in the two

connected to the upper plate (that is expected not to displace

subtracted from the forces read by the


Cyclic lateral displacements were imposed at the top of the column with

summarized in Figure 2,

hree cycles were repeated. The following


it was applied different

ffect of the load pattern in the RC


The group series 1, 2 and 3 were subjected to a constant axial load and

All the information relative to

Table 1.

(e)

tal displacement paths types a) Uniaxial (strong) b) Uniaxial (weak) c) Cruciform d) Diamond

the peak capacities, the displacements

were evaluated. With this information the

imposed lateral drift


the yielding point the axial load was

s of ±150kN were

A schematic representation of the lateral loading pattern and axial loading

Symposium_10


Fig. 3-Axial loading condition for tests under varying axial load

Table 1 - Specimens’ specifications, mechanical properties and loading conditions

Series Specimen Geometry

[cm x cm]

1

PB01-N01

20 x 40 PB02-N02

PB12-N03

PB12-N04

2

PB01-N05

30x40 PB02-N06

PB12-N07

PB12-N08

3

PB01-N09

30x50 PB02-N10

PB12-N11

PB12-N12

4

PC01-NV19

30x50

PC02-NV20

PC12-NV21

PC12-NV23


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Axial loading condition for tests under varying axial load – Series 4.

Specimens’ specifications, mechanical properties and loading conditions

fcm [MPa]

fyk

[MPa]

Axial Load

[kN] ν

N/(Ac.fcm)

Horizontal Displacement path

48.35 432.63 170 0.04

Uniaxial

Uniaxial

21.40 429.69 300 0.12

Uniaxial

Uniaxial

Quadrangular

24.39 429.69 300 0.08

Uniaxial

Uniaxial

Quadran

27.92 575.6 300

(±150kN)

0.07

(±0.03)

Uniaxial

Uniaxial

Quadrangular

Series 4.

Specimens’ specifications, mechanical properties and loading conditions

Horizontal Displacement path

type

Uniaxial – Strong

Uniaxial - Weak

Cruciform

Diamond

Uniaxial – Strong

Uniaxial - Weak

Diamond

Quadrangular

Uniaxial – Strong

Uniaxial - Weak

Diamond

Quadrangular

Uniaxial – Strong

Uniaxial - Weak

Diamond

Quadrangular



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EXPERIMENTAL RESULTS

Aiming at evaluating the effect of the biaxial load paths on the stiffness and strength

degradation of the RC columns, the maximum envelopes of the shear-drift hysteresis

envelopes and the lateral peak-to-peak stiffness degradation were analysed. Because of the

loading paths adopted in the experiments, the first cycle of each displacement level in the

biaxial tests always occurs in the same direction (i.e., the positive X direction). This induces a

different response in the first cycle of each displacement amplitude level, but the effect is

reduced in the subsequent cycles for the same displacement amplitude.

The analysis of the force-displacement hysteretic behaviour focused on the following main

issues: i) the comparison and identification of the main differences in the shapes of the

envelopes of the uniaxial and biaxial response test results; ii) the evaluation of the lower

ductility in biaxial tests when compared with the corresponding uniaxial tests; iii) the

interpretation of the strong coupling between the responses in the two directions as observed

in the 2D tests; and iv) the characterisation of the correlation found between the maximum

strength and the yield force.

The results’ analysis can be summarised as described in the following:

The initial column stiffness is not significantly affected by the biaxial loading path in either

direction.

For each cycle of the biaxial test on the square columns, the maximum horizontal force in the

Y direction was between 10 and 20% smaller than that in the X direction, an effect that has

been also reported by other authors (Mutsuyoshi et al., 1994, Tsuno et al., 2004). As

mentioned before, this effect is induced by the first push along the loading path, which always

occurs in the X direction.

As expected, when the maximum columns’ strength of the in each direction for each biaxial

test was compared with the results from the corresponding uniaxial test, lower values were

found in the biaxial cases.

The relationship between the biaxial and the uniaxial experimental tests results are plotted in

Fig. 5a for the maximum strength Fmax and in Fig. 5b for ductility µ. The biaxial loading

produced a reduction of approximately 20% in the maximum strength of the rectangular

columns in their weak direction (Y), while reductions ranging from 25 to 30% were observed

in the square columns. The strength reduction in the weaker direction is always larger than

that observed in the corresponding test along the stronger direction (X), which is

approximately 8%. This is because, for rectangular columns, the response in the strong

direction is less affected by the damage previously produced in the weak direction than does

the response in the weak direction due to damage in the strong direction.

Symposium_10


(a)

Fig. 2 - Shear – Drift envelopes for

-5 -4 -3 -2 -1 0 1-80

-60

-40

-20

0

20

40

60

80

Shear (kN)

Drift X (%)

PB01-N01

PB12-N03

PB12-N04

-5 -4 -3 -2 -1 0 1-140

-120

-100

-80

-60

-40

-20

0

20

40

60

80

100

120

140

Shear (kN)

Drift X (%)

PB01-N05

PB12-N07

PB12-N08

PB12-N17

-5 -4 -3 -2 -1 0 1-200

-180

-160

-140

-120

-100

-80

-60

-40

-20

0

20

40

60

80

100

120

140

160

180

200

Shear (kN)

Drift X (%)

PB01-N09

PB12-N11

PB12-N12

PB12-N18


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(b)

Drift envelopes for different load paths a) Strong direction b) Weak direction.

2 3 4 5 -5 -4 -3 -2 -1 0-80

-60

-40

-20

0

20

40

60

80

Shear (kN)

Drift Y (%)

PB02-N02

PB12-N03

PB12-N04

2 3 4 5 -5 -4 -3 -2 -1 0-140

-120

-100

-80

-60

-40

-20

0

20

40

60

80

100

120

140

Shear (kN)

Drift Y (%)

PB02-N06

PB12-N07

PB12-N08

PB12-N17

2 3 4 5 -5 -4 -3 -2 -1 0 1-200

-180

-160

-140

-120

-100

-80

-60

-40

-20

0

20

40

60

80

100

120

140

160

180

200

Shear (kN)

Drift Y (%)

PB02-N10

PB12-N11

PB12-N12

PB12-N18

different load paths a) Strong direction b) Weak direction.

1 2 3 4 5

Drift Y (%)

1 2 3 4 5

Drift Y (%)

1 2 3 4 5

Drift Y (%)



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(a) (b)

Fig. 5 - Ratio between biaxial experimental tests and uniaxial experimental tests (a)

Maximum strength (b) Ductility µ.

CONCLUSION

An experimental campaign was carried out on 16 RC columns with: three different

geometries and reinforcement; subjected to similar 3 biaxial horizontal displacement paths;

and with constant and variable axial load. The study was focus on the influence of the

horizontal displacement path on the behavior of columns under certain load conditions.

Additionally it was studied the horizontal displacement path effect associated with variable

axial load.

For each cycle of the biaxial test on the square columns, the maximum horizontal force in the

Y direction was between 10 and 20% smaller than that in the X direction. The biaxial loading

produced a reduction of approximately 20% in the maximum strength of the rectangular

columns in their weak direction (Y), while reductions ranging from 25 to 30% were observed

in the square columns. The strength reduction in the weaker direction is always larger than

that observed in the corresponding test along the stronger direction (X), which is

approximately 8% in the rectangular columns.

Further tests should be performed in order to analyze other relationships between different

axial load variations and horizontal biaxial displacement paths. It is of full importance to

increase the experimental tests database in order to achieve relationships between the

maximum strength, initial stiffness, ductility and energy dissipation reduction.

ACKNOWLEDGMENTS

This paper reports research developed under financial support provided by “FCT - Fundação

para a Ciência e Tecnologia”, Portugal, namely through the research project

PTDC/ECM/102221/2008

REFERENCES

[1]-Mutsuyoshi, H., A. Machida, W. Tanzo and N. Mashiko (1994). "Inelastic seismic

response of RC bridge pier using pseudodynamic test method." Transactions of the Japan

Concrete Institute 16: 265-272

Symposium_10


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[2]-Rodrigues, H. (2012). Biaxial seismic behaviour of reinforced concrete columns. PhD

Thesis, University of Aveiro.

[3]-Rodrigues, H., A. Arêde, H. Varum and A. Costa (2012). "Behaviour of RC building

columns under cyclic loading: experimental study." Journal of Earthquake and Tsunami, JET,

World Scientific Publishing 6(4) DOI: 10.1142/S1793431112500261.

[4]-Rodrigues, H., A. Arêde, H. Varum and A. Costa (2013). "Damage evolution in reinforced

concrete columns subjected to biaxial loading " Earthquake Engineering and Structural

Vibration 42: 239-259

[5]-Rodrigues, H., A. Arêde, H. Varum and A. Costa (2013). "Experimental evaluation of

rectangular reinforced concrete column behaviour under biaxial cyclic loading." Earthquake

Engineering and Structural Dynamics 43: 239-259

[7]-Rodrigues, H., A. Arêde, H. Varum and A. G. Costa (2010). Experimental study on the

biaxial bending cyclic behaviour of RC columns. 14th European Conference on Earthquake

Engineering Ohrid, Republic of Macedonia.

[8]-Rodrigues, H., A. Arêde, H. Varum and A. G. Costa (2012). "Experimental evaluation of

rectangular reinforced concrete column behaviour under biaxial cyclic loading." Earthquake

Engineering Structural Dynamics

[9]-Tsuno, K. and R. Park (2004). "Experimental study of reinforced concrete bridge piers

subjected to bi-directional quasi-static loading." Struct. Engrg Structures, JSCE 21, No 1 11s-

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