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BEHAVIOUR OF RC COLUMNS UNDER VARIABLE LOAD AND BIDIRECTIONAL HORIZONTAL LOADING

Hugo RODRIGUES1, and António ARÊDE2, and José Pedro SILVA3, and Patrício ROCHA4

and André FURTADO5

ABSTRACT

In the last year several earthquakes examples have showed the need for investigation to improve the safety of existing constructions, and have become an important source of information that can help on improving new design methodologies in the evolution of codes and guidelines The behaviour of reinforced concrete (RC) elements subjected to axial loading variation in conjunction with cyclic biaxial bending is recognised as a very important research topic with a a reduced number of experimental results. To study the effects of variable axial load on the hysteretic behaviour of RC building columns under biaxial horizontal loading, six full-scale RC rectangular columns were tested and analysed. The experimental results are presented and discussed in terms of damage evolution, global hysteretic behaviour. The global findings revealed the significant effects of the axial load variation on the hysteretic behaviour of RC columns.

INTRODUCTION

During the last year, several earthquakes have showed the need for investigation to improve the safety of existing constructions (Bertero, 1986; K.S. Pribadi & D.K.Rildova, 2008; Romão et al., 2013; Vicente, Rodrigues, Varum, Costa, & Silva, 2012), and have become an important source of information that can help on improving new design methodologies in the evolution of codes and guidelines. Structural response during recent earthquakes has indicated that the majority of column failures were caused by high shear stresses, lack of concrete confinement and bidirectional load effects (Saatcioglu & Ozcebe, 1989). It is clear that the earthquake-related damage to reinforced concrete elements, is due to multiaxial excitation (Lejano, 2007; Takizawa, Aoyama, & . 1976). As widely known, from the axial load–bending interaction diagrams, it is possible to observe that both yielding and ultimate moments increase with the level of axial load until the balance point is achieved. Variation in the axial load during an earthquake can change the strength, stiffness, and ultimate displacement capacity, as well as all the hysteretic properties of a RC section. Such variations can occur due to the vertical component of the seismic load, or in the external columns of the bottom storeys of RC frames, due to the overturning moments which increase the axial load on one side and decrease it on the opposite side. In fact, the variation in the axial force during the response cycle may

1 Dr, Polytechnic Institute of Leiria, Portugal, hugo.f.rodrigues@ipleiria.pt 2 Dr, Faculty of Engineering of Porto University, Portugal, aarede@fe.up.pt 3 Grant holder, Faculty of Engineering of Porto University, Portugal, josepedrocsilva@gmail.com 4 Professor, Superior School of Technology and Management of Polytechnic Institute of Viana do Castelo, Portugal, procha@estg.ipvc.pt 5 Researcher, Institution, Faculty of Engineering of Porto University, Portugal, afurtado@fe.up.pt

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significantly affect the inelastic response of the columns (Bonet, Barros, & Romero, 2006; CEB, 1996; Sfakianakis & Fardis, 1991). Due to testing difficulties, the number of RC column tested under bidirectional displacement with varying axial load is very reduced and it is always associated with tests with constant axial load, thus, the few available results do not allow for solid conclusions to be drawn about coupling behaviour between biaxial bending and the varying axial force (H. Rodrigues, A. Arêde, H. Varum, & A. Costa, 2012a). In general, most research findings agree that the biaxial transversal load cycles are responsible for increasing the strength and stiffness degradation when compared to the uniaxial response. In addition, the failure mechanism of RC columns is found to be very dependent on the loading path/history, and strongly affects both the ductile and energy dissipation capacity of the columns. On the other hand, there is some experimental evidence that plastic hinge zone lengths tend to be stable at around theoretical values and are not strongly affected by biaxial loading (S.N. Bousias, Verzelleti, Fardis, & Magonette, 1992; CEB, 1996; Rodrigues, Arêde, et al., 2012a; H. Rodrigues, A. Arêde, H. Varum, & A. G. Costa, 2012c). The early results of both Li et al. (CEB, 1996) and Low and Moehle (Low & Moehle, 1987) evidence similar effects of axial load variations on uniaxial and biaxial flexure. In particular, it was found that axial load variation simultaneously with the transverse forces and deformations leads to stiffness and strength increase, while the strength degradation is larger for higher axial load, and also decreases when the axial load decreases. The results obtained by Bousias et al. (Stathis N. Bousias, Verzeletti, Fardis, & Gutierrez, 1995; S.N. Bousias et al., 1992) present a strong coupling between the axial and transverse directions. For the relatively low levels of compressive axial loads considered therein, deflections induce an axial extension which has a magnitude roughly proportional to their resultant vector. For lower compressive loads, the cycling of transverse forces or deflections causes a gradual shortening in the axial direction under the axial load alone, a ratcheting extension that rapidly turns into shortening when failure is imminent. As a result of axial/lateral forces coupling, cycling of the axial force below the balance load causes a ratcheting increase in the deflection under constant transverse force (Rodrigues, Arêde, et al., 2012a). Bechtoula et al. (Bechtoula, Kono, & Watanabe, 2005) found that the axial load intensity had little effect on the envelope curve of the second-cycle of the load-displacement plot for specimens under unidirectional horizontal load with constant or variable axial load. Equivalent viscous damping increased with the increase in axial load, and columns under variable axial load showed equivalent viscous damping values similar to those of columns under constant/moderate and constant/high axial load.

Experimental Setup

Six rectangular RC columns were constructed with the same geometric characteristic and reinforcement detailing, and were cyclically tested for different loading histories. The column specimens are 1.70m high, and are cast in strong square concrete foundation blocks with dimensions 1.30x1.30m2 in plan and 0.50m high. The cross-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 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 and material properties are summarized and shown in Figure 1 and Table 1.

H. Rodrigues, A. Arêde, J.P. Silva, P. Rocha, A. Furtado 3

φ

φ

a)

φφ

φ

φ φ

φ φ

b)

Figure 1 - RC column specimen dimensions and reinforcement detailing: a) Cross-sections details, b) Specimen

dimensions and general scheme of the reinforcement layout

Figure 2 shows the general view of the setup adopted for the experimental testing. The system includes two independent horizontal actuators to apply the lateral loads on the column specimen (one with a capacity of 500kN with +/-150mm stroke and the other with a capacity of 200kN and +/-100mm stroke). A vertical 700kN capacity actuator was used to apply the axial load. Two steel reaction frames and a concrete reaction wall form the reaction system for the three actuators. The column specimens and the 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 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 actuator), which was built to minimise spurious friction effects.

Figure 2 – General View of testing setup.

In order to characterise the response of the column specimens, cyclic lateral displacements were imposed at the top of the column with steadily increasing demand levels. Three cycles were repeated

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for each lateral deformation demand level. This procedure allows for the understanding of the column’s behaviour, a comparison between different tests and provides information for the development and calibration of numerical models. The adopted load paths are summarised in Figure 3, and the following 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.

X

Y

X

Y

Uniaxial – Strong direction Uniaxial – Weak direction Diagonal - 45o

X

Y

X

Y

X

Y

Rhombus Quadrangular Circular Figure 3 - Type displacement paths

Prior to the tests with varying axial loading, the peak capacities, the displacements and the strengths corresponding to the first yield were numerically evaluated based on numerical simulations of the uniaxial tests. With this information the columns axial load was considered variable and proportional to the imposed lateral drift applied until the yielding drift. In the biaxial tests the axial load variation is relative to the displacement observed in the strong direction. Beyond the yielding point the axial load was kept constant. The initial axial load was set on 300kN and variations of ±150kN were considered. The different specimen’s characteristics and loading are presented in Table 1. A schematic representation of the lateral loading pattern and axial loading condition is presented in Figure 4.

Table 1–Specimen specifications and loading characteristics

Specimen

Geometry

[cmxcm]

fcm

[MPa]

fyk

[MPa]

Initial N

[kN

Horizontal Displacement path

type

Var

iab

le A

xial

load

PC01-N19

30x50 27.92 575.6 300

(±150kN)

Uniaxial – Strong

PC02-N20 Uniaxial – Weak

PC12-N21 Rhombus

PC12-N22 45o

PC12-N23 Quadrangular

PC12-N24 Circular

H. Rodrigues, A. Arêde, J.P. Silva, P. Rocha, A. Furtado 5

step

step

Horizontal

displacement in the

strong direction

Axial load

0

dy

dy

Nini+max_var

Nini+max_var

Nini

Figure 4 - Axial loading condition for tests under varying axial load.

Cyclic tests of specimens

For the study of the influence of the biaxial loads and axial load variations in the behaviour of RC columns, the measured drifts and shear force paths (along the X and Y directions) are analysed. Figure 5 show maximum envelopes obtained from shear-drift diagrams shown in Figure 6, Figure 7 and Figure 8 for all the columns under varying axial loads. The detailed experimental results, analysis and discussion about the columns under constant axial load can be found in bibliography (Rodrigues, 2012; H. Rodrigues, A. Arêde, H. Varum, & A. Costa, 2012b; Rodrigues, Arêde, et al., 2012c; Rodrigues, Romão, et al., 2012). A summary of the main findings are presented in Figure 5, although the discussion refers to all results of the complete testing program.

Figure 5 - Envelopes for columns under different load paths and axial load variation.

Concerning the effect of biaxial load paths and the axial load variation, the analysis of the maximum envelopes presented in Figure 5 allow concluding that in the biaxial tests and, particularly, for the sense of axial load increase, the post-yielding plateau tends to be shorter and the softening is more pronounced, i.e. a more abrupt decay of the column strength is observed. The initial column

a) b)

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stiffness in both directions it is not significantly affected by the biaxial load path and, as expected, the maximum strength in one specific direction of the biaxially tested columns is always lower than that of the corresponding uniaxial test.

The biaxial loading under varying axial load induces about 30-40% reduction of the maximum strength for the rectangular columns in their weak direction, Y. The strength reduction in the stronger direction, X, (around 12% for the rectangular columns) is always lower than for the weaker direction. Similarly to what was found for constant axial load tests, this is consistent with the fact that, for rectangular columns, the response in the strong direction is less affected by the damage previously installed in the weak direction than the opposite. This fact agrees with the observed strength reduction in columns under constant axial load (Park & Ang, 1985; Rodrigues, Arêde, et al., 2012c), though intensified by the axial load variation.

Figure 6 - Shear-drift diagrams for columns under uniaxial horizontal load path and axial load variation (PC01-

N19 and PC02-N20).

Figure 7 - Shear-drift diagrams for columns under biaxial horizontal load path and axial load variation (PC12-

N21 and PC12-N22).

H. Rodrigues, A. Arêde, J.P. Silva, P. Rocha, A. Furtado 7

Figure 8 - Shear-drift diagrams for columns under biaxial horizontal load path and axial load variation (PC12-

N23 and PC12-N24).

The influence of the biaxial load path and the effect of the varying axial load was also analysed. From previous studies was already clear that biaxial load influence in the reduction of the columns’ ductility around 35% and could reach a maximum of 75% (Rodrigues, Arêde, et al., 2012c; Tsuno & Park, 2004). Comparing the reduction of the columns’ ductility considering the axial load variation with the tests with constant axial load this influence is steel pronounced. In fact columns under varying axial load, the maximum ductility reductions were found around 20% and 50%, respectively in the weak (Y) and the strong (X) directions). Amongst all the imposed biaxial load paths, the quadrangular and diagonal are those that lead to larger reductions of the ultimate ductility.

Conclusions

Six full-scale rectangular reinforced concrete columns were tested under different horizontal loading panthers (uniaxial and biaxial) and with varying axial load. The experimental results show that the axial load variation combined with the biaxial loading pattern have significant effects on the non-linear behavior and capacity of the column. Experimental results show that the initial stiffness it is not significantly affected by the biaxial load path combined with axial load variation. These loading characteristics reduces the maximum columns strength as well as the post-yielding plateau, leading to faster strength degradation and, naturally, to significant reduction of the columns ultimate ductility. The research described in present paper was focused on the effects of variable axial load on hysteretic behaviour of RC columns under biaxial horizontal loading. The significant changes in the response observed in terms of columns capacity, damage anticipation, stiffness and strength degradation and energy dissipation, suggests that the axial loading effects combined with biaxial behaviour on columns where this two aspects can be expected, like building corner columns, cannot be neglected.

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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.

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