rc structural walls under cyclic loading

RC STRUCTURAL WALLS UNDER CYCLIC LOADING EXPERIMENTAL VERIFICATION OF CODE OVERESTIMATION OF TRANSVERSEREINFORCEMENTREDUCTION POTENTIALS S. Papatzani1, I. Giannakis2, K. Paine1,M. D. Kotsovos2 1. University of Bath, UK 2. National Technical University of Athens, Greece

ABSTRACT. In the present study a shear wall of 1.7 m length, 1.7 m height and 0.15 m width was designed, in compliance with the Greek Code for Reinforced Concrete (GCRC) and the Compressive Force Path method (CFP). The 1.7 m long wall, designed according to the current GCRC was constructed and tested under cyclic loading, applied in two phases. Under the first one, the specimen reached a displacement of 38.5 mm and a load of 710 kN and under the second one, the maximum displacement was 72 mm and the load 675 kN. It was concluded that the load carryingcapacity of the wall was 25% greater than the design value estimated by the GCRC. The experimental value of uncracked stiffness was ¼ of the value delivered according to the GCRC. The ductility of the specimen was 3.3 in the first phase of the testing procedure (uncracked state) while in the second (first crack had occurred) was 6.2. The widest and longest crack was formed at the base of the wall, where predicted. Moreover, the steel structure used for the experiment remained flexible, notwithstanding alterations made. This fact biasedthe results, since the displacementat the base of the actuator was also partially included. For absolute results, the steel frame should be stiffened in future experiments. The comparison of the wallreinforcement designed according to the GCRC and the CFP showed that the latter method demands less amount of transverse reinforcement to achieve the same objectives as the former. Keywords: Ductility, Compressive Force Path, cyclic loading, transverse reinforcement, Reinforced Concrete

Dr Styliani Papatzani is a researcher in Cement Technology & Concrete Design at the University of Bath, UK and a chartered civil/structural engineer in Athens, Greece. Her research interests include nanomodified cements and concrete durability and performance and reinforced concrete design. Mr Ioannis Giannakisis an MSc Civil Engineer running a design office in Athens, Greece. His research interest is focused on innovative structural design of reinforced concrete members.

Dr Kevin Paine, is a Reader in Civil Engineering at the BRE Centre for Innovative Construction Materials, University of Bath. Dr Paine’s research focuses on low carbon and sustainable forms of concrete construction. Professor Michael D Kotsovos, is the former Director of the Laboratory of Reinforced Concrete Structures at the National University of Athens, has published over 150 papers and books and has developed the compressive force path method for the design of reinforced concrete structural members.

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INTRODUCTION Currently, for the design of structural walls, three types of reinforcement are required by the Greek Code for Reinforced Concrete (GCRC) provisions[1], differing slightly [2]fromEurocode 2 provisions[3]; (i) vertical reinforcement, providing flexural resistance, (ii) horizontal web reinforcement, providing shear resistance before flexural capacity is reached and (iii) stirrup reinforcement confining concrete in the concealed columns (CC) regions at the two edges of the wall, providing ductility. The horizontal web reinforcement extends in the CC regions where the stirrups are placed. The main problem encountered by designers and contractors then, is the congestion of transverse reinforcement (horizontal and stirrups) in the CC regions, rendering concreting and compaction difficult, compromising the safety of the structureand increasing the construction cost. The current paper is focused on the experimental study of the response of a reinforced concrete (RC) structural wall designed according to GCRC. Resultsshowed that the stiffness delivered by the current code is overestimated in practice.So was the load carrying capacity of the wall. Therefore, analternativetransverse reinforcement configuration could have been more beneficial. In fact, design according to the compressive force path (CFP) was additionally carried out, as a suggestion for further experimental work. The main advantage of CFP, unlike GCRC or Eurocode 2 provisions is that the third type of reinforcement, that in the CC regions, is not specified[4]. Hence, further experimentation is expected to yield interesting results with respect to designing beyond the current codes.

RC DESIGN ACCORDING TO CODES - GCRC[1]& BEYOND CODES CFP [4] Current code provisions are based on the limit-state philosophy.The core element of RC design, adopted by both Eurocodes and the Greek code for RC design (Figure 1)is the truss analogy model, which in the simplest form is the beam-like element. The truss analogy model incorporated concepts such as aggregate interlock, strain softening, dowel action and others at the ultimate limit state and has been furtherrefined by strut-and-tie model and compressionfield theory. A number of incompatibilities of the truss analogy model have been identified by the work of Kotsovos MD [4], [5], that is to say incompatibility with: i. the auxiliary mechanisms of shear resistance (aggregate interlock & dowel action) ii. the inclined struts of the truss model iii. the assumptions made with respect to the flexural capacity of RC elements iv. the critical regions v. the points of contraflexure Particularly, with reference to the critical regions and points of contraflexure, codes require a significant amount of stirrup reinforcement, which can guarantee concrete confinement within the compressive zone, following Poisson’s principle. Consequently, the ductility of the structural elementwill be increased. On the other hand, although there has been published experimental evidence indicating the locations of points of contraflexure as potential

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locations of brittle failure, current codes do not recognize these locations as critical regions[4]. M

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Figure 1: Truss analogy model of the GCRC[1] An alternative design concept is provided by the compressive force path method, according to which,“the loading capacity and failure mechanism of a beam are related to the region ofthe member containing the path of the compressive stress resultant which developswithin the beam due to bending, just before failure occurs” [4, p. 23]. All concepts comprising the CFP method are described in literature [4], [5]. Here a brief introduction is given as a background to the analysis carried out. According to the CFP method, in a simply supported RC beam, without stirrups under external load, the internal compressive forces developed within the member, transfer the stresses to the supports following a path denoted as “concrete frame” in Figure 2. This path, functioning as a compressive force field, is the only uncracked region within the member. The transverse rebar is functioning as a tension tie and the “concrete teeth” are functioning as cantilevers of unreinforced concrete, transferring the shear forces from steel to concrete through bond. There are four different modes of failure. Types II and III account for brittle, non-flexural modes of failure and types I and IV for ductile response with only a nominal amount of transverse reinforcement [6]. It should be noted, however, that the inclined crack related to type III failure, is formed independently from pre-existing flexural or inclined cracks [4].

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Figure 2: Physical model employed by the CFP model[4] The CFP model of the simply supported beam can also be applied to the design of structural walls, as they can be viewed as cantilevers, subjected to a transverse point load exerted at the free end of the member. The wall to be investigated was characterized by type III behaviour and the CFP model is shown in Figure 3. Therefore, an inclinedcompressive force area is expected to be formed starting from the point of the exertion of the force at the free end of the wall until the diagonally opposite fixed end.Plastic hinge formation can be expected at the lower end of the compressive force.Type III behaviour does not lead to immediate failureand if the structural element is adequately reinforced with horizontal reinforcement the mode of failure can be flexural[4].

Figure 3: The physical model of the wall according to the CFP method

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EXPERIMENTAL PROGRAMME Materials Concrete C30/37 complying withGCRC [1]was used.Six cylinders of 300 mm height and 150 mm diameter and 3 cubes 150 mm x 150 mm x 150 mm were casted and kept in the laboratory environment, just like the wall. The meancylinder compressive strength at day 28 was found to be42.7 MPa and the mean cube compressive strength at day 28 was found to be57.2MPa. Three steel bars of 10 mm diameter and three of 14 mm diameter were tested in tension. The mean values of the yield (fy) and ultimate (fu) stress of the steel bars are shown in Table 1. For the theoretical calculation of the stress, the stress strain curves of Figure 4 were considered[7].

Table 1: Tensile yield and ultimate strength of D10 & D14 steel bars D 10 D 14

fy (MPa) 560 594

fu (MPa) 652 676

Figure 4: Steel stress-strain diagram

Test set-up The configuration of the experimental set-up is depicted in Figure 5. Two frames made of standard steel columns, HEB 300 and steel beams IPE 600 were connected to transverse steel beams HEB 450 and HEB 300. Diagonal HEA 160 beams completed the rigid frame on

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which the actuator was attached. The short HEB 300 was added to provide additional stiffness to the steel structure.

Figure 5: Experimental set-up

Reinforced Concrete Wall design The wall was designed for a height of 1.7 m. It was monolithically connected to a top prism of 60 mm x40 mm cross sectionand length equal to the length of the wall, through which the load would be applied and a bottom prism of 60 mm height and breadth and 2.9 m length (longer than the wall to provide a stiff foundation). Both prisms were over-sized and overreinforced to simulate rigid body behaviour. The wall was fixed to the laboratory floor through the bottom prism in order to simulate fully fixed-end conditions. The test specimen was only designed according to the GCRC. The size was predefined, scaling down to approximately 55% of the dimensions of full-scale structural wall (i.e. 2.6 m length, 2.6 m height and 0.4 m width). The vertical reinforcement was designed first so that the wall would withstand the maximum displacing force by the actuator. The horizontal web reinforcement was next designed and lastly the stirrup reinforcement in the confined regions of the CC. The wall was also designed according to the CFP, in order to demonstrate the difference in the reinforcement configurations. It should be clarified that in this research only the specimen

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designed according to the GCRC was constructed and tested. The greatest difference between the Greek RC design code and the compressive force path method lies with the amount transverse (horizontal and stirrup) reinforcement as can be seen in Table 2 and Figure 6 to Figure 8. The congestion in the two concealed columns’ areas can be clearly seen in Figure 9. Table 2: Difference in transverse reinforcement between the CFP and GCRC Transverse reinforcement according to the GCRC 18 horizontal web + 35 stirrups for CC

Transverse reinforcement according to the CFP 6 horizontal web + 0 stirrups for CC

Figure 6: Reinforcement configuration according to (A) GCRC & (B) CFP

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Figure 7: Section 1-1 according to GCRC

Figure 8: Section 1-1 according to CFP

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Figure 9: Realized reinforcement of wall according to GCRC The wall was casted in-situ monolithically as shown in Figure 10.

Figure 10: In-situ concreting The finished specimen can be seen in Figure 11.

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Figure 11: Finished specimen

Loading regimes The experiment took place in two phases: In the first series of loading, the aim was to start at a lower applied force so that the specimen could undergo several cyclic excitations. The maximum force applied and the deflection measured comprised of the following pattern: F1 = 50 kN, 3 cycles were allowed and the maximum measured displacement was 0.5 mm. F2 = 175 kN*, 3 cycles were allowed and the maximum measured displacement was 1.5 mm. (* i.e. 1/3 of the theoretical ultimate load) F3 = 280 kN, 3 cycles were allowed and the maximum measured displacement was 5.0 mm. F4 = 530 kN, 3 cycles were allowed and the maximum measured displacement was 15.0 mm. F5 = 670 kN, 3 cycles were allowed and the maximum measured displacement was 25.0 mm. F6 = 712kN, 1 cycle was allowed and the maximum measured displacement was 38.5 mm.

The second series of loading took place several days later and allowed for greater displacements to be recorded, at fewer cycles. Displacement was imposed and the force was measured: D1 = + 46 mm and the recorded strength was equal to 562 kN& D2 = - 46 mm and the recorded strength was equal to 660 kN D3 = + 51mm and the recorded strength was equal to 550 kN& D4 = + 76.5 mm and the recorded strength was equal to 675 kN of

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RESULTS AND DISCUSSION As shown in Figure 12 the maximum load the wall sustained was equal to 712 kN. The slight shift to the right can be attributed to the liftingof the bottom prism, possibly due to its inadequate fixing to the laboratory floor.

Figure 12: Response of the wall under 1st series of loading

The displacements in the second series of loading were measured (a) directly from LVDTs placed on the wall (blue curve in Figure 13) or (b) after a correction was applied by taking into consideration the displacement at the base of the actuator (red curve in Figure 13). In both cases there was a significant disparity between the two methods for the displacement estimation and for this reason the median was also calculated(green line in Figure 13).

In the second series of cyclic loading, during the first cycle, the wall did not yield in the area of positive displacements, but entered the plastic region in the area of negative displacements. Moreover, during the second cycle the response of the wall was different in the two directions; the positive displacements were significantly lower than the negative ones. This fact could only be attributed to theout of plane bending of the specimen.In fact, before the assumed twist the wall was upright as shown inFigure 15. However,the bending of the steel backpropping on the one side of the wall (Figure 16) and the dropping of the steel backpropping of the other, was pointing to this conclusion, i.e. that the wall twisted. The reduction in the slope of the curve for the second cycle of loading signalled the stiffness reduction of the specimen.

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Figure 13: Response of the wall under 2nd series of loading

The difference of about 10 mm between the red and the blue curve was attributed to the lack of geometric symmetry during the construction of the specimen. In addition to this, it is possible that the base prism was lifted at its longer side (2),expected to form a plastic hinge in the areaenclosed by the dotted line (1), as shown in Figure 14. The maximum corrected displacement for the second series of loading was hereafter taken as 72 mm.

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Figure 14:Failure of the compressive zone leading to loss of load-carrying capacity (1) and base prismlifting(2) area----lifting at the other side------

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Figure 15: The wall and backpropping before the out of plane bending

Figure 16: The wall and backpropping after the out of plane bending

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Crack propagation patterns are shown in Figure 17 to Figure 22. The diagonal cracks observed in Figure 17 and particularly in Figure 18 show the compressive force path.

Figure 17: Beginning of crack propagation @ 1st series of loading

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Figure 18: Diagonal crack development @ 1st series of loading

The widest crack was formed at the base of the wall and was horizontal, as shown in Figure 19 and Figure 20. After this crack propagation no further cracking was observed. Upon the completion of the first series of testing, the specimen exhibitedresidualdeformation.

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Figure 19: Main horizontal crack at the base @ 1st series of loading

Figure 20: Main horizontal crack at the base @ 1st series of loading 18

During the second series of loading the plastic hinge was formed at right side of the base as discussed with respect to Figure 14. This main horizontal crack at the base of the wall propagated to the whole length of the wall, to the extent of concrete crushing andspalling and uncovering of the reinforcement - debonding(Figure 21 and Figure 22). The plastic hinge formation at the one side of the wall base was eventually responsible for the much larger negative displacements recorded. The wall underwentflexuralmode of failure, as indicated by the horizontal crack at the base.

Figure 21: Crack propagation @ 2nd series of loading at base

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Figure 22: Subsequent loading failure at the base - hinge formation

FURTHER CONSIDERATIONS In the first series of cyclic loading it was calculated that the wall yieldedat a loading force of about 497 kN, at a displacement of 11.6 mm. The maximum displacement reached was 38.5 mm. Therefore,ductility can be estimated as 38.5/11.6 = 3.3. Higher values of ductility could have been achieved, had the steel structure been stiffer. If higher loading had been imposed the existing steel structure on which the actuator was mounted, would have deformed. In the second series of cyclic loading, the achieved ductility was even higher than that in the first series, even at a lower loading. The maximum recorded displacement was equal to 72 mm (as corrected by the green curve in Figure 13), hence the ductility was equal to 6.2. For the theoretical load carrying capacity of the wall, all safety factors were taken equal to one. The load that would cause flexuralmode of failure, then, was found to be equal to 570 kN.The maximum load recorded, however, was equal to 712kN. Hence, the actual load carrying capacity of the wall was 25% higher than the estimated one.

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If strain hardening of steel and the measured compressive strength of concrete had been taken into consideration, the theoretical load carrying capacity of the wall, upon revaluation was found to be equal to 685 kN. Therefore having an error of the order of 4%, approximately compared to the actual load carrying capacity of the wall. Theuncracked stiffness according to the GCRC can be estimated by the following formula:

2 3EI K = 491 kN/m , 3 h3 whereh = 2 m (the lever arm from the base of the prism to the point of force exertion, E = elastic modulus and I = second moment of area. K=

The actual (cracked) stiffness, however, was estimated by the experimental loadcarrying capacity (P) and the corresponding displacement for the 5 loading phases, during the first loading series, as shown in the following table: Table 3: Calculated values of cracked stiffness with respect to the experimental load carrying capacity P (kN) δ (mm) K (kN/m)

1 184,40 1,498 123.097

2 273,67 4,670 58.600

3 550,46 14,100 39.040

4 660,46 24,436 27.030

5 707,45 38,530 18.360

It can be clearly seen that, indeed, the theoretical stiffness values suggested by the GCRC is significantly higher than the experimental values.

CONCLUDING REMARKS Although several factors affecting the abovementioned results have been identified, the paper suggests that the current Greek RC design code clearly underestimates the load-currying capacity and overestimates the stiffness of RC structural walls. Matters that can induce experimental errors: i) Inadequate size and reinforcement detailing of the top and bottom prisms avoided ii) Inadequate fixing of the bottom prism to the laboratory floor - sustained iii) Constructional geometrical asymmetries - sustained As shown theoretically in this paper and experimentally in more recent studies[6], [4], [8] the compressive force method can be applied in order to reduce the reinforcement congestion in concealed columns areas without compromising the load carrying capacity and the ductility of the structural elements. It would be interesting to extend the method by applying it to structural elements made of recycled aggregate concrete[9], in an effort to design greener concretes, which are adequate for structural design. Experimental verification and comparison with both current codes and alternative methods is necessary.

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ACKNOWLEDGEMENTS

REFERENCES [1]

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[3]

Eurocode 2 (EC2) Design of concrete structures. Part 1-1: general rules and rules of building. British Standards Institution, London. 2004.

[4]

M. D. Kotsovos, Compressive Force-Path Method. Unified Ultimate Limit-State Design of Concrete Structures. Springer International Publishing Switzerland, 2014.

[5]

M. D. Kotsovos and M. N. Pavlović, Ultimate limit-state design of concrete structures : a new approach. London: London : Thomas Telford, 1999.

[6]

N. St. Zygouris, G. M. Kotsovos, D. M. Cotsovos, and M. D. Kotsovos, “Design for earthquake-resistent reinforced concrete structural walls,” Meccanica, vol. 50, no. 2, pp. 295–309, 2015.

[7]

Σ. Παπατζανή, Ι. Γιαννάκης, and Δ. Αθανασίου, “Συμπεριφορά τοιχίων και πλαισίων από ωπλισμένο σκυρόδεμα υπό ανακυκλιζόμενη φόρτιση,” Μεταπτυχιακή Εργασία Εθνικό Μετσόβιο Πολυτεχνείο, 2006.

[8]

N. S. Zygouris, M. D. Kotsovos, and G. M. Kotsovos, “Effect of transverse reinforcement on short structural wall behaviour,” Mag. Concr. Res., vol. 65, no. 17, 2013.

[9]

S. Papatzani and K. Paine, “Overview of construction and demolition waste legislation in EU and Greece & state of the art on recycling CDEW in concrete,” in Fifth International Conference on Environmental Management, Engineering, Planning and Economics (CEMEPE 2015) & SECOTOX Conference-accepted, 2015.

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