Response Of Reinforced Concrete Shear Walls With Various Detailing Of .

(or perfectly bonded); inherently, the model eliminates prediction of bar buckling. The model wasdeveloped using a newly introduced continuum shell element (SC8R) in ABAQUS (2017) whichrepresents the thickness of walls and flanges (if any) using the nodal coordinates unlike theconventional shell elements where thickness is input separately. The shell normal is defined using aright-hand screw rule from bottom surface to the top surface; Fig 1 shows the surface 1-2-3-4 as bottomand 5-6-7-8 as top. With only three translational degrees of freedom, SC8R resembles a solid ‘brick’element; however, its kinematic and constitutive behaviour is similar to conventional shell elements.Further, this continuum shell element allows defining layers within the solid (continuum) which is usefulto specify the constitutive properties of the cover and core concretes.Figure 1: Continuum shell element.Concrete damage plasticity material model available in ABAQUS was used to represent the constitutivebehaviour of concrete. The damage model assumes mainly two failure mechanisms that are tensilecracking and compressive crushing of concrete. The elastic-plastic behaviour was defined as theconstitutive material model for the reinforcement. The constitutive properties of a typical 40MPaconcrete and a normal ductile steel reinforcing bar is shown in Fig. 2.(c) Steel Tensile Stress(b) Concrete Tension –(a) Concrete CompressionStrain ResponseDamage Evolution– Damage EvolutionFigure 2: Constitutive Properties of Concrete and Steel.Fig. 2 shows the constitutive properties of core concrete of 40MPa grade; the corresponding coverconcrete was assumed to possess 70% of the core concrete strength both in compression and tension.The steel property was taken from Li et al (2015) and Blandon et al (2018) – as their experimentalresults were used to validate the formulated FE model. The experimental study from Li et al (2015) wastaken to model and verify the behaviour of double layer RCSW and the testing result of Blandon et al(2018) was used to numerically verify the behaviour of single layer RCSW. The provided reinforcementamount, geometrical and material properties of experimental RCSWs are given in Table 1.Table 1. Experimental data used for numerical model verification.PropertiesWall referenceL (m) H (m) t (mm)Aspect Ratio H/LSingle/ Double Layer SteelCompressive Strength of Concrete, (MPa)Yield/ Ultimate strengths of reinforcement bar (MPa)Vertical web reinforcement ratio/ (%)Horizontal web reinforcement ratio/ (%)Axial load to Compressive Strength RatioAxial Load (kN)Li et al (2015)LW12.0 2.5 1201.25Double40.2427 (497)0.50.500Blandon et al (2018)W42.5 2.4 1000.96Single39.1563 (691)0.270.270.05470Core and cover concrete properties were assigned to the distinct layers of the wall. The details ofmodelling of the double layer RCSW taken from Li et al (2015) is shown in Fig. 3.

Figure 3: FE modelling of double flanged double layer reinforced shear wall.Fig. 3 shows the idealisation of the double flanged double layer reinforced shear wall tested by Li et al(2015). Blandon et al (2018) tested single flanged single layer reinforced concrete shear walls (detailsin Table 1); their wall was also modelled similarly in ABAQUS. The predicted failure modes of the twowalls are presented in Fig. 4. Shear stress contours presented in Fig. 4 exhibit diagonal cracking in bothwalls at a drift level of 0.4%. The load-drift responses of the two walls and their correspondingexperimental data are presented in Fig. 5. Good predictions are obtained for both walls.Figure 4: Failure patterns of RCSWs (a) Li et al (2015) and (b) Blandon et al (2018).Figure 5. Experimental and numerical Load vs. drift responses.

Although the two tests were performed at two different countries (double flanged wall in Singapore andthe single flanged wall at Mexico) some five years apart, it is remarkable to note that the peak load andfailure mode of the two walls were not significantly different owing to their aspect ratios being similar;both exhibited shear dominant failure. Although the single flange wall was considered susceptible toout-of-plane buckling, authors reported none detected based on their video imaging technique.Concerns for post-peak out-of-plane buckling triggering potential collapse of wall thus seems tooconservative and disregard the redundancy in walls unlike the columns as part of framed structurescould suffer a major collapse.The deformability of the double layer reinforced, double flanged wall is better than that of the singleflanged single layer wall. To examine the effect of the single layer steel versus double layer wall, thedouble flanged wall (Li et al, 2015) was reanalysed with the steel positioned at the mid thickness of wallin a single layer; the area of steel reinforcing bars (vertical and horizontal) were kept unchanged. Allother parameters were also kept unchanged. The result of the re-analysis is plotted with the originalanalysis and the experimental result in Fig.6.Figure 6. Effect of single vs double layer reinforcement in a double flanged RCSW.The double flanged wall, irrespective of the type of reinforcement has shown similar level of ductility;the minor reduction in the lateral load capacity perhaps is associated with the loss of core confinement.This result has prompted to examine the effect of single versus double layer reinforcement detailing forvarious levels of steel ratios, imposed vertical load and compressive strength of concrete. The ensuingsection provides the results of these parametric studies.3Parametric study and DiscussionsThe validated FE model was used to examine the effect of changes to some selected design parametersto the lateral load capacity and ductility of RCSWs. The following parameters were considered:(i) Compressive strength of concrete(ii) Percentage of steel( f ) : 25MPa, 32 MPa, 40MPa and 50MPa'c( ) : 0.25%, 0.50% and 1.0%(vertical to horizontal steel ratio 1.0)(iii) Vertical compression load to compressive strength ratio p N : 0, 0.05 and 0.2Ltw f c' (iv) Detailing of steel reinforcement: single layer and double layerThese combinations resulted in( 72 4 3 3 2 ) analyses.As establishing mesh was very timeconsuming, it was decided to use the double flanged wall tested by Li et al (2015); all 72 analyses were,therefore, carried out using the same wall. All models were run for 1.3% drift (although the lightly loadedwalls were showing no rapid loss of lateral load resistance), where the analyses were terminated tominimise computational time and post processing time. In some instances, walls failed prior to attaining1.3% drift – especially walls containing 50MPa concrete.The lateral load – lateral displacement curves of two extreme cases (one with the lowest compressivestrength, lowest % of steel with zero Precompression; and the other for the highest compressive

strength, largest % of steel and the largest Precompression) for both the single and double layerRCSWs are shown in Fig. 7.(a) 25MPa; 0.25%; 0 – single layer(b) 25MPa; 0.25%; 0 – double layer(c) 50MPa; 1%; 0.2 – single layer(d) 50MPa; 1%; 0.2 – double layerFigure 7. Predicted Load vs. drift responses of RCSWs.It can be seen that when the RCSW is made from low strength concrete, irrespective of single- ordouble-layer detailing, the wall exhibits high level of deformability sustaining the peak load for well over1% drift that is considered useable in multi-storied buildings. When the compressive strength isincreased (doubled in this instant to 50MPa) and subject to high vertical precompression, the capacityof the wall increased by 150% (from approximately 300kN to 750kN). In real world, walls subject tohigh gravity loading (precompression) are likely to be designed with high strength concrete as steel isconsidered ineffective to improve compression capacity of walls. Even when these 50MPa concretewalls are detailed with 1% vertical and horizontal steel reinforcing bars, the walls lost their peak loadsustaining capability (or, deformability) with their drift well below 1%. Detailing reinforcing bars in doublelayer has improved the deformability to approximately 0.9%, but still below the 1% level. These resultsare concerning as the walls contain double flange; a combination of high compressive strength concreteand high precompression is detrimental to ductility of the walls. Delayed cracking due to higher tensilestrength of the 50MPa concretes is also a reason for this brittle response.The load-displacement curves were transformed into bilinear form using the well-known equivalent areamethod to identify the yield displacement; the ultimate displacement was taken corresponding to 20%drop in peak load. Ductility was determined as the ratio of the ultimate displacement to the yielddisplacement.The peak load of each of the 72 analyses and the ductility determined from the load-displacementcurves of the 72 analyses are plotted against the compressive strength of concrete used in the walls inFig. 8. Six sub figures each containing results of 12 analyses are include in Fig. 8. Each sub figurecontains family of percentage of reinforcing bars and precompression levels and contain the peak loadand ductility values.It can be seen that in all cases, the peak load increased with the increase in compressive strength ofconcrete. The precompression has also significantly increased the peak load of walls irrespective of thecompressive strength of concrete. The steel ratio has only marginal effect on the peak load of the walls.Ductility decreased with the increase in compressive strength of concrete in walls. Ductility was alsoadversely affected by the presence of larger precompression. A combination of higher compressivestrength and higher precompression is lethal to ductility. For example, wall with 25MPa concrete,

double layer steel and no precompression exhibited very high level of ductility of approximately 12,whilst walls with 50MPa concrete under a precompression load equal to 20% of their compressioncapacity only attained ductility of approximately 2.0 even when double layer steel was used.Single steel layerDouble steel layersFigure 8. Responses of RCSWs to key parameters.4ConclusionThis paper has presented finite element modelling of single- and double-layer steel reinforced concreteshear walls. Such a study was prompted by the recent changes to the shear wall design in the Australianconcrete structures standard. The standard AS3600 (2018) has discouraged design of shear walls withsingle layer reinforcement detailing by forcing such walls as nonductile with a ductility of 1.0. Thestringency in these provisions is based on evidences of collapse of single layer reinforced shear wallsin the 2011 Christchurch earthquake that was believed to be an intraplate aftershock of the 2010Canterbury earthquake. As Australia is susceptible to intraplate earthquakes, the standards committee

justified such stringencies. On completely unrelated matter, as the standard does not allow designersto use steel reinforcement to resist gravity loading, most likely walls in tall building basements bedesigned using high strength concrete. The analyses presented in this paper has shown that thecombination of high strength concrete and high levels of precompression are lethal to the deformabilityof the RCSWs. It is shown that for very high level of precompression (equal to 20% of compressioncapacity of walls) a 25MPa wall exhibits ductility of 4.0 whilst a 50MPa wall exhibits ductility of 2.0 eventhough the steel bars are arranged in double layer form.It was shown that higher the compressive strength of concrete used in wall and higher theprecompression, higher was the in-plane shear load capacity of RCSWs. Trends in ductility was showninversely proportional to the trends in peak load capacity.Although detailing walls with double layer is a good practice that provides additional confinement to thecore concrete, the benefit of the detailing to the ductility of the wall considered in this paper is not clear.Analyses presented in this paper utilised a double flanged squat shear wall dominated by shear modeof failure. Further work is ongoing whether such conclusions will hold for walls with no flanges throughexperimental and finite element studies.5References1. Standards Australia, “AS 3600-2018: Concrete Structures Standard”, 2018, Sydney.2. Henry, R.S., “Assessment of the minimum vertical reinforcement limits for RC walls”, Proc.NZSEE Conference, 2013, paper 135, pp1-12.3. Menagon, S.J., Wilson, J.L. et al., “RC Walls in Australia: Seismic Design and Detailing toAS1170.4 and AS3600”, Australian Journal of Structural Engineering, 2017,Doi.org/10.1080/13287982.2017.1410309.4. Standards Australia, “AS3700-2018: Masonry Structures Standard”, 2018, Sydney.5. Hoult, R., “Minimum Longitudinal Reinforcement Requirements for Boundary Elements ofLimited Ductile Walls for AS 3600”, Electronic J of Structural Engineering, 2017, pp 43-52.6. Greifenhagen, C. and Lestuzzi P., “Static cyclic tests on lightly reinforced concrete shear walls”,Engineering Structures, 27(11), 2005, pp 1703-1712.7. Dazio, A., Beyer, K. et al., “Quasi-static cyclic tests and plastic hinge analysis of RC structuralwalls”, Engineering Structures, 31(7), 2009, pp 1556–71.8. Li, B., Pan, Z. et al., “Experimental evaluation of seismic performance of squat RC structuralwalls with limited ductility reinforcing details” J. Earthquake Eng., 19(2), 2015, pp 313–331.9. Lu ,Y., Henry, R S. et al., “Cyclic Testing of Reinforced Concrete Walls with DistributedMinimum Vertical Reinforcement”, ASCE Journal of Structural Engineering, 143(5), 2017.10. Carrillo, J., Lizarazo, J.M. et al., “Effect of lightweight and low-strength concrete on seismicperformance of thin lightly-reinforced shear walls”, Engg Structures, 93, 2015, pp 61-69.11. Hube, MA., Marihuen, AN. et al., “Seismic behaviour of slender reinforced concrete walls”,Engineering Structures, 80, 2014, pp 377–88.12. Haider, W., and Dhanasekar, M., “Experimental study of monotonically loaded wide spacedreinforced masonry walls”, Australasian J of Structural Engineering, 5(2), 2004, pp 101-118.13. Zhao, Y., Wang, F.L., “Experimental studies on behavior of fully grouted reinforced-concretemasonry shear walls”, Earthquake Engg and Vibration, 14, 2015, pp 743–757.14. Banting, BR., and El-Dakhakhni, WW., “Force and Displacement-Based Seismic PerformanceParameters for RMSWs with Boundary Elements”, ASCE Journal of Structural Engineering,138(12), 2012, pp 1477-1491.15. Xu, W., Yang, X. et al., “Experimental Investigation on the Seismic Behavior of NewlyDeveloped Precast RCBM Shear Walls”, Journal of Applied Science, 8, 1071, 2018.16. Robazza, BR., Brzev, S. et al., “Out-of-Plane Behavior of Slender RMSWs under In-PlaneLoading: Experimental Investigation”, ASCE Journal of Structural Engineering, 144(3), 2018.17. Canadian Standards Association, “CSA S304-14: Masonry design of buildings”, 2014.18. Dashti, F., Dhakal, RP. et al., “Numerical Modeling of Rectangular Reinforced ConcreteStructural Walls”, ASCE Journal of Structural Engineering, 143(6), 2017.19. ABAQUS, Finite element software documentation, Dassault Systèmes, Simulia 2017, RI, USA.20. Blandon, CA., Arteta, CA. et al., “Response of thin lightly-reinforced concrete walls under cyclicloading”, Engineering Structures,176, 2018, pp 175–187.

Keywords: RC Shear walls; Single layer reinforced; Double layer reinforced; In-plane shear strength; Ductility 1 Introduction Reinforced concrete shear walls (RCSW) are key lateral load resisting elements in concrete buildings; adequate capacity and ductility of these walls are central to the safety of the shear wall dominated buildings.