Wall Modeling & Behavior

Transcription

1 Wall Modeling & Behavior John Wallace University of California, Los Angeles with contributions from Mr. Leonardo Massone & Dr. Kutay Orakcal University of California, Los Angeles

2 Presentation Overview Flexure Shear P-M-V Interaction & Modeling Preliminary Test Results 2

3 Modified Beam - Column Model Rectangular walls (h w /l w 2.5) & Flanged walls (h w /l w 3.5): Use of modified beam-column element with added shear spring Nonlinear flexure/shear are uncoupled using this approach Wall Beams Hinges Column at wall centroid Shear spring 3

4 Modified Beam - Column Model Shear force deformation properties 1.0 V V n B IO a Deformation-controlled component b - a LS CP C V y y = h ( Gc 0.4Ec) A = 1 Gc = Ec and ν ν 0.2 A D E c y /h /h 4

5 Fiber Section Model Actual cross section Concrete Fibers Steel Fibers Typically use a more refined mesh where yielding is anticipated; however, Nonlinear strains tend to concentrate in a single element, thus, typically use an element length that is approximately equal to the plastic hinge length (e.g., 0.5l w ). Might need to calibrate them first (this is essential). Calibration of fiber model with test results, or at least a plastic hinge model, is needed to impose a reality check on the element size and integration points used. 5

6 Response Correlation Studies Ten Story Building in San Jose, California Instrumented: Base, 6th Floor, and Roof Moderate Intensity Ground Motions Loma Prieta 4.53 m (14.88 ft) m (36 ft) 8.84 m (29 ft) 8.84 m (29 ft) 1.68 m (5.5 ft) PLAN VIEW: CSMIP BUILDING

7 Response Correlation Studies Ten Story Building in San Jose, California Instrumented: Base, 6th Floor, and Roof Moderate Intensity Ground Motions Loma Prieta Displacement (in.) Analysis - 0.5I g Measured Time (sec) 7

8 Strength Requirements ACI 318 Provisions P n -M n For extreme fiber compression strain of ε c = V n ACI ,02,05 Equation 21-7 ' Vn = A cv αc fc + ρt f y α = 3.0 for h / l 1.5 α c w w = 2.0 for h / l 2.0 c w w Linear interpolation allowed for intermediate values 8

9 Definition of Wall Cross Section Cross-Section Definition Flexural strength b eff 0.25h w A + A A Consider all vertical reinforcement within web and within the effective flange width Consider the influence of openings on the strength and detailing requirements ' ' s, bound s, flange s A + A A ' s, bound s, flange s ACI , 05 Appendix A Strut & Tie Approach 9

10 MVLE (Fiber) Model h k 1 k k H Rigid Beam k n (1-c)h ch Rigid Beam RC WALL WALL MODEL Basic assumptions: Plane sections (rigid rotation of top/bottom beams Uniaxial material relations (vertical spring elements) MVLE Model versus Fiber Model: Similar to a fiber model except with constant curvature over the element height (vs linear for fiber model) m. 2 1 Orakcal, Wallace, Conte; ACI SJ, Sept-Oct

11 Material (Uni-axial) Models σ y E 1 = be 0 ( ε ' c, f' c ) Stress, σ O R E 0 ε y O r (ε 0, 0) Compression Strain, ε Reinforcing Steel: Menegotto and Pinto (1973) Filippou et al. (1984) Simple but effective Degradation of cyclic curvature (ε 0 + ε t, f t ) Strain, ε Tension Not to scale Concrete: Chang and Mander (1994) Generalized (can be updated) Allows refined calibration Gap and tension stiffening 11

12 Model Assessment Approximately 1/4 scale Aspect ratio = 3 Displacement based evaluation for detailing provided at the wall boundaries 12 ft tall, 4 ft long, 4 inches thick #3 vertical steel, 3/16 hoops/ties #2 deformed web steel Constant axial load Cyclic lateral displacements applied at the top of the walls 12

13 Instrumentation Extensive instrumentation provided to measure wall response at various locations Wire Potentiometers (horizontal displacement) Wire Potentiometers (X configuration) RW2 Rigid Reference Frame Steel Strain Gage Levels Wire Potentiometers (vertical displacement) Concrete Strain Gages LVDT's Massone & Wallace; ACI SJ, Jan-Feb Linear Potentiometers (Pedestal Movement) 13

14 Model Details RW mm 51 mm 153 mm 191 mm 153 mm 51 mm 19 mm 19 mm 8 - #3 bars #2 bars (db=6.35 mm) Hoops (db=4.76 mm) (db= mm 19 mm 102 mm 64 mm 19 mm uniaxial element # : h k 1 k 2.. k H..... k n (1-c)h m=16. ch

15 Concrete Model - Unconfined Stress (MPa) Test Results 1 st Story 2 nd Story 3 rd Story 4 th Story Analytical (Unconfined) Strain 15

16 Concrete Model - Confined TW2 Web Stress (MPa) RW2 TW2 Flange Unconfined Model Mander et al. (1988) Saatcioglu and Razvi (1992) Strain 16

17 Concrete Model - Tension (ε t,f t ) r 1.5 Stress (MPa) Chang and Mander (1994) Belarbi and Hsu (1994) Strain 17

18 Reinforcement Material Model 600 Stress (MPa) Tension Compression #3 (RW2 & TW2 Flange) #3 (TW2 Web) #2 (TW2 Web) #2 (RW2 & TW2 Flange) #3 # Test Results #3 rebar #2 rebar 4.76 mm wire Strain 18

19 Model Assessment RW2 Lateral Flexural Drift (%) Lateral Load, P lat (kn) P ax ' 0.07A g f c P lat, top RW2 Test Analysis P ax (kn) Top Flexural Displacement, top (mm) 19

20 Model Assessment RW2 Lateral Flexural Drift (%) Top 4 RW2 Story Number Applied Lateral Drift Levels: 0.75% 1.0 % 1.5% 2.0% 2.5% Test Analysis Lateral Flexural Displacement (mm) 20

21 Model Assessment RW2 Rotation (rad) % 1.5% Data Point Results based on recommended values for material parameters; however, results could vary, maybe significantly, for different element lengths and material parameters (particularly if no strain hardening) Displacement (mm) RW2 (First Story) Test Analysis FEMA 356 CP limit 21

22 Model Assessment - Stability Rebar Buckling at Wall Boundary Rebar Fracture Following Buckling at Wall Boundary Instabilities, such as rebar buckling and lateral web buckling, and rebar fracture are typically not considered in models; therefore, engineering judgment is required. Loss of lateral-load capacity does not necessarily mean loss of axial load capacity22

23 Backbone Curve RW2 Lateral Load (kips) Lateral Drift (%) P = 0.07A g f' c v u,max = 2.32 f' c psi FEMA 356 ( M / h )( h ) 3 n w w δ y = 3EI c cr Analytical prediction, First yield P n (εc=0.003)=29.4 k Top Displacement (in.) Lateral Load (kn) 23

24 Cantilever Wall Tests Paulay, EERI, 2(4), 1986 [Goodsir, PhD 1985 NZ] h = 3.3 m = ft Conforming P=10%, V=3 Conforming P=10%, V=6 (3.94 ) WALL Goodsir, 1985: ' ' As = As & P= fca g & Assume conforming (59 ) 3 3 PL (70 k)(130") Vu 70k δ y = = = 0.4" (10.0 mm) = = E 0.5I 3(~ 3750 ksi)(0.5)(4")(59") /12 ' tl f (4")(59") 3750psi c g w w c δ 0.01(3300 mm) = 33mm δ 0.015(3300 mm) = 50mm a b 24

25 Cantilever Wall Tests Paulay, EERI, 2(4), 1986 [Goodsir, PhD 1985 NZ] h = 3.3 m = ft Conforming P=10%, V=3 Conforming P=10%, V=6 WALL Goodsir, 1985: A = A & P= 0.12 f A & Assume conforming ' ' s s c g (70 )(130") V 70 δ = = = 0.4" (10.0 ) = = 4.6 E I 750 ksi)(0.5)(4")(59") /12 (4")(59") 3750psi 3 3 PL k u k y mm (~3 ' c g tl w w fc δ 0.01(3300mm) = 33mm δb 0.015(3300 mm) = 50mm a 25

26 Summary FEMA 356 Backbone Curves In general, quite conservative This appears to be especially true for cases where moderate detailing is provided around boundary bars Possible reformat Compute neutral axis depth If s <12d b over c/2, then modest ductility If s < 8d b and transverse steel ratio is ~1/2 of ACI , then moderate ductility If s < 8d b and transverse steel ratio is > 3/4 of ACI , then high ductility Do not reduce deformation capacity for shear stress below 5 roots f c 26

27 Presentation Overview Flexure Shear P-M-V Interaction & Modeling Preliminary Test Results 27

28 Shear Design Wall shear studies Aktan & Bertero, ASCE, JSE, Aug Paulay, EERI 1996; Wallace, ASCE, JSE, Eberhard & Sozen, ASCE JSE, Feb Design Recommendations Based on M pr at hinge region Uniform lateral force distribution M pr Vwall = ωv Vu ωv = n/10 M u ( 0.3 )( )( ) V = V + D = W = weight A = EPA wall limit m e Paulay, 1986 Eberhard,

29 Modified Beam - Column Model Use of modified beamcolumn element with added shear spring for both horizontal and vertical wall segments Fiber model or general wall model with nonlinear shear backbone curve (uncoupled flexure/shear) If plastic hinge model EI effective might be less than 0.5EI g lightly-reinforced wall segments Spandrels Pier Joint 29

30 P-M (flexural) Strength Provisions P n -M n for ε c =0.003 Fiber model or general wall model Actual cross section Concrete Fibers Steel Fibers Typically use a more refined mesh where yielding is anticipated However, in this case, where nonlinear shear behavior is anticipated, use enough elements to capture moment gradient. Nonlinear backbone relations (force displacement) relations are commonly used to capture the shear behavior. 30

31 FEMA Modeling Parameters FEMA 356 Tables 6-19: Wall segments Modeling Parameters, Drift % Acceptable Drift % d e c Immediate Occupancy Performance Level Life Safety Collapse Prevention d e - d V n IO LS CP V r c y /h /h 31

32 Shear Strength Provisions V n per ACI ,02,05 Equation 21-7 V = A f + f α α α ' ρ n cv c c t y = 3.0 for h / l 1.5 c w w = 2.0 for h / l 2.0 c w w Linear interpolation allowed for intermediate values If axial load exceeds 0.15A g f c ; then force controlled ρ need not be taken less than 0.15% (Wood, ACI SJ, 1990) 32

33 Shear Strength Database t # of Curtains Researcher Protocol 2 1 Sugano (1973) Monotonic 7 1 Barda Cyclic 6 0 Cardenas Monotonic 0 2 Hidalgo (2002) Cyclic 0 7 Hirosawa (1975) Cyclic 1 0 Aoya Cyclic* 5 0 * One full cycle, then monotonic to failure w f ' c = 3.15 to 6.3 inches 0.25% ρ 0.67% = 3.3 ksi, σ= 1 ksi f = 64 ksi, σ= 14 ksi (7) < 0.12A f, (1)=0.15A f, (1)=0.22A f y ' ' ' g c g c g c 33

34 Shear Strength Expanded Database Vtest / Vn (ACI) One Curtain Two Curtains (ρ fy) min ρ need not be taken less than 0.15% (Wood, 1990) Shear strength is relatively insensitive to the web reinforcement For relatively thin walls, use of one or two curtains of web reinforcement, strength is similar Results similar for monotonic and cyclic tests 34

35 Shear Strength Restricted Database Vtest / Vn (ACI) One Curtain Two Curtains (ρ fy) min Tests with at least minimum reinforcement ρ need not be taken less than 0.15% (Wood, 1990) Shear strength is relatively insensitive to the web reinforcement For relatively thin walls, use of one or two curtains of web reinforcement, strength is similar Results similar for monotonic and cyclic tests 35

36 FEMA Modeling Parameters FEMA 356 Tables 6-19: Wall segments Modeling Parameters, Drift % Acceptable Drift % d e c Immediate Occupancy Performance Level Life Safety Collapse Prevention d e - d V n IO LS CP V r c y /h /h 36

37 Shear Force-Deformation Behavior Shear backbone curve V y y = h ( Gc 0.4Ec) A = V = V (i.e., no hardening) y n 1 Gc = Ec = 0.4Ec 1+ 2ν P/ Ag V = f V ft cr t n f t ( 4 to 6) f = Sozen & Moehle, 1993 EPRI Report ' c Strength of materials τ = Gγ σ=eε 37

38 Revised Backbone Relation Based on prior tests (limited database): 5WCEE, Rome, 1973, pp WCEE, Tokyo, 1988, pp. IV Hidalgo et al, 2002, EERI Spectra Hirosawa, 1975, Japanese Report d e - d V cr V 0.6V V n n r 0.4E c c /h = to

39 Observations Limited test data Stiffness and Deformation capacity specimens tend to be stiff and strong, test control is challenging and reported stiffness and deformation values may be suspect Residual strength most tests not continued beyond modest strength degradation (~20%) One row in FEMA table 6-19 Nominal Strength Test results indicated nominal strength in the range of 100 to 200% of the ACI value 39

40 New Data Since ~1995 Salonikios, Thomas N.; et al. (1999) 11 tests on cantilever walls with axial load of 0.0 and 0.07A g f c Aspect ratios of 1.0 (1.2m tall) and 1.5 (1.8m tall) Cross section: 1.2m x 100mm (4 ft x 4 ) 4 tests with diagonal web bars for sliding Eurocode 8 requires 50% Reasonably-well detailed (Eurocode 8) Hidalgo, Pedro A.; Ledezma, Christian A.; Jordan, Rodrigo M., (2002) 26 tests for reverse bending (zero moment at mid-height), no axial load M/Vl ratios: 1.0(3), 0.69(9), 0.5(7), 0.35(7): 1m x 2m tall; 1.5m x 1.05m tall Cross section: 80 to 120 mm (3.15 to 4.72 ) by 1.0m to 1.7m (40 to 67 ) Light web reinforcement: 0%, 0.125%, 0.25%, 0.375% (only one) Greifenhagen, H.; Lestuzzi, P, (2005) 4 tests on cantilever walls with axial load (0.027, 0.027, 0.043, 0.094A g f c ) M/Vl ratio: 0.69 Cross section: 1 m x 100 mm (40 x 4 ) Light web reinforcement: 0.3%, 0% (one case with no horizontal web bars) Massone, Orakcal, Wallace (2005, 2006) 40

41 Hidalgo et al M/Vl w = 1.0 Specimen #2 Load (kn) 40mm V V ' n = 5.74 fctwlw=57 kips (253 kn) crack = 0.5V = 30 kips (133 kn) n Displacement (mm) Vh n w (56.86 kips)(78.74") δ y = = = 0.02" (0.5 mm) 2 GA 0.4(3040 ksi)(186 in ) δ = h =.004(78.74") = 0.31" (8 mm) y δ = (2000 mm) = 15 mm d δ = 0.02(2000 mm) = 40 mm e w 41

42 Hidalgo et al M/Vl w = 1.0 Specimen #1 Load (kn) V f t l f V ' ' n = 4.4 c w w=43 kips (193 kn) c = 2.81 ksi crack = 0.5V = 22 kips (98 kn) n Displacement (mm) Vh n w (43 kips)(78.74") δ y = = = 0.015" (0.4 mm) 2 GA 0.4(3020 ksi)(186 in ) δ = h =.004(78.74") = 0.31" (8 mm) y δ = (2000 mm) = 15 mm d δ = 0.02(2000 mm) = 40 mm e w

43 Hidalgo et al M/Vl w = 0.69 Specimen #8 Load (kn) V V ' n = 6.6 fctwlw=76 kips (337 kn) crack = 0.5V = 38 kips (169 kn) n Displacement (mm) Vh n w (76 kips)(70.9") δ y = = = " (0.52 mm) 2 GA 0.4(2720 ksi)(242 in ) δ = h =.004(70.9") = 0.284" (7.2 mm) y δ = (1800 mm) = 13.5 mm d δ = 0.02(1800 mm) = 36 mm e w

44 Presentation Overview Flexure Shear P-M-V Interaction & Modeling Preliminary Test Results 44

45 Slender Wall Tests - Results External Instrumentation Lateral displacement at different floor levels Internal Instrumentation Shear deformation at different floor levels Flexural deformation at different floor levels Uncouple deformations Shear/Flexure Assess data reliability Internal External Wall base instrumentation 45

46 Tests Results: Observations Consistent and repeatable results Top displacement Small shear contribution, about 5% 1 st Story Displacement 4-story walls 30% shear contribution Displ. 1st floor (shear + flexural) [in] Shear Xcorrected Y = 1.02 * X Y = 1.20 * X Shear Xoriginal Flexural displ. Y = 0.71 * X Utot Xcorrected Utot Xoriginal U flex (α=0.67) Displ. 1st floor (lateral) [in] 46

47 Test Results - Observations 40 P(@Vn) P(@V = 62 [kips] n ) =62 kips 40 P(@V n ) =62 kips P(@Vn) = 62 [kips] Lateral Load (kips) 20 Uf αh P(@Mn) = 29.4 [kips] P(@M n ) =30 kips θ Uf h 1st Floor 2nd Floor 20 Us P(@Mn) = 29.4 [kips] P(@M n ) =30 kips 1st Floor 2nd Floor Flexural displacement [in/in] flexure / y Shear displacement [in] shear Interaction between nonlinear flexure and shear deformations is evident even for relatively slender walls where V max ~ ½V n 47

48 Modeling P-M-V Interaction 1. Modified MVLE model to incorporate shear flexure interaction 2. Parallel pairs of flexure and shear fibers are used 3. Behavior of each set of springs described by a constitutive RC rotating-angle panel model (e.g., MCFT or RA-STM), that incorporates axial-shear interaction 4. Requires additional model iterations to establish equilibrium condition Strip (i) N, u y M, θ V, u x h ch ε y - trial γ xy - trial ε x - unknown 48

49 Local Iteration Scheme ε y - trial Assigning Iteration Variable γ xy - trial ε x - unknown guess α ε 1 α ε 2 Constitutive Material Models ε 1 α ε 2 σ c1 σ - ε concrete α σ c2 ε y ε x σ - ε steel σ sy σ sx Horizontal (Transverse) Equilibrium σ y = σ cy + ρ y σ sy τ yx σ x = σ cx + ρ x σ sx σ x = 0 iterations α ε x 49

50 Constitutive Panel Element Behavior 8 4 Shear Stress (MPa)12 0 Pang and Hsu (1995) Vecchio and Collins (1982) A2 A3 A4 B1 B2 Test Analysis Shear Strain RC Panel Specimens tested under pure shear Shear Stress (MPa) PV6 PV11 PV16 PV19 Test Analysis Shear Strain 50

51 Model Assessment RW2 Lateral Load, P lat (kn) P ax 0.07A g f c ' P lat, top RW2 Monotonic versus Cyclic comparison Test Analysis Top Displacement, top (mm) Thomsen & Wallace, ASCE JSE, April 2004; Massone et al, 13WCEE & 8NCEE 51

52 Lateral Load (kn) Model Assessment RW Flexural Deformations Test Analysis U f ( ) Shear Deformations Test Analysis P P U s Lateral Flexural Displacement (mm) Lateral Shear Displacement (mm) flexural and shear displacements at first story level of RW2 coupled nonlinear flexural and shear deformations 52

53 Model Assessment Hirosawa (1975) Specimen 74: M/Vl w = Hidalgo (2002) Specimen 10: M/Vl w = Lateral Load (kn) Flexural Analysis Test Analysis Lateral Load (kn) Test Analysis Lateral Displacement (cm) Lateral Displacement (cm) 53

54 Presentation Overview Flexure Shear P-M-V Interaction & Modeling Preliminary Test Results 54

55 Research Motivation & Sponsors Sponsors: St. Joseph Health System KPFF Consulting Engineers St John s, Santa Monica In collaboration with: California Office of Statewide Health Planning & Development (OSHPD) Example pushover 55

56 Test Specimens - Piers Prototype (Actual Building) ¾ Scale Test Specimen l p = 72 l p = 54 h p = 62.5 h p = 48 ρ v = ~0.25% ρ h = ~0.35% t p = 8 ρ v = ~0.25% ρ h = 0.35% t p = 6 56

57 Test Specimens Piers Hooks removed Specimen Geometry (inches) Reinforcement 3 4 P/A g f' c Specimens ID Height Length Thickness Edge 1 Vert. Web 2 Horiz. Web 2 (kips) (#) (1) (2) (3) (4) (5) (6) (7) (8) (9) WP #4 0.26% 0.35% WP #4 0.26% 0.35% WP #4 0.26% 0.35% WH #4 1-#5 0.35% 0.26% WH #5 0.35% 0.26%

58 Test Program - Construction Cast upright, no joints 58

59 Test Program - Setup Reaction block Reaction block Actuator F a δ 1 δ 2 Steel reaction frame Top beam Specimen CL P 1 P 2 δ top Reaction block Strong Floor Foundation Floor anchor rods δ bottom Axial Load = P = P 1 + P (controlled) 2 Lateral Load = F (controlled for the first two levels) Lateral Displacement = (δ top δ bottom ) (controlled after first two levels) Top Rotation θ = (δ 1 δ 2 )/a =0 (controlled) 59

60 Test Program - Setup Reaction Frame Out-of-plane support Specimen Vertical Load Vertical Load Horizontal Load 60

61 Test Program Load History Load [kips] Load Control cycle Disp Displacement Control cycle 61

62 Test Program - Instrumentation ~ 100 Sensors (load, strain, displacement) West Face Instrumentation (flexural deformations) East Face Instrumentation (shear and anchorage deformations) Pedestal sliding and uplift measured Variation of measurements used on repeated tests 62

63 Test Program - Objectives Backbone Relations Failure mode Influence of details Jamb bars No hooks No Hoops/Ties Axial load failure 63

64 FEMA 356 Backbone Curves 2.8.3(1.2): Smooth backbone curve shall be drawn through the intersection of the first cycle curve for the (i)th deformation step with the second cycle curve of the (i-1)the deformation step, for all i steps. Force Backbone curve Deformation FEMA 356 Figure

65 FEMA (1.2) Approach 100 Resulting backbone curve applying 2.8.3(1.2) was suspect

66 Test-Derived Backbone Curves 100 Yield Strength degradation Load Crack 50 Residual Displacement 66

67 Test Photos ~5% Axial Load Yield level 3 x Yield Axial collapse 67

68 Axial Failure 68

69 Deformations Flexure/Shear Same Scale 0 Lateral Load 0 0 flex-exp shear-exp shear-envelope Lateral Displacement Flexural deformations are essentially elastic, nonlinear shear 69

70 Test Derived Backbone Relations (Pier) ~150%V n FEMA FEMA 356 Default Lateral Load Axial load collapse top disp.-exp shear-envelope shear-backbone shear- backbone (+) shear- backbone (-) shear- backbone (avg) 2% Lateral Displacement 1% Not as stiff in the post-cracked range as FEMA relation Post-cracked stiffness ~1/10 to 1/20 of the initial stiffness Peak strength (85 to 175%) of V n Consistent with prior tests Less pronounced strength degradation, less residual strength Deformation capacity > FEMA at initiation of strength degradation 70

71 Additional References Greifenhagen, H.; Lestuzzi, P, Static cyclic tests on lightly reinforced concrete shear walls, Engineering Structures, vol. 27, pp , Sept Palermo, D.; Vecchio, F.J., Compression field modeling of reinforced concrete subjected to reversed loading: verification, ACI Structural Journal. Vol. 101, no. 2, pp Mar.-Apr Hidalgo, Pedro A.; Ledezma, Christian A.; Jordan, Rodrigo M., Seismic behavior of squat reinforced concrete shear walls, Earthquake Spectra. Vol. 18, no. 2, pp May Hwang, Shyh-Jiann; et al., Analytical model for predicting shear strength of squat walls, Journal of Structural Engineering. Vol. 127, no. 1, pp Jan Petrangeli, Marco, Fiber element for cyclic bending and shear of RC structures, II: Verification, Journal of Engineering Mechanics. Vol. 125, no. 9, pp , Sept Salonikios, Thomas N.; et al., Cyclic load behavior of low-slenderness reinforced concrete walls: Design basis and test results, ACI Structural Journal. Vol. 96, no. 4, pp July-Aug Salonikios, Thomas N.; et al., Cyclic load behavior of low-slenderness reinforced concrete walls: Failure Modes, Strength and Deformation Analysis, and design Implications, ACI Structural Journal. Vol. 97, no. 1, pp Jan.-Feb Kappos, A. J.; Salonikios, T. N., Premature sliding shear failure in squat shear walls: fact or myth? Proceedings of the Second Japan-UK Workshop on Implications of Recent, Earthquakes on Seismic Risk; pp Saatcioglu, M.; Wiradinata, S., The effect of aspect ratio on seismic resistance of squat shear walls, Proceedings of the 8th European Conference on Earthquake Engineering; pp. 7.3/ Wiradinata, Sanusi, Behaviour of squat walls subjected to load reversals, Dept. of Civil Engineering, University of Toronto, pp. Paulay, T.; Priestley, M. J. N.; Synge, A. J., Ductility in earthquake resisting squat shearwalls, Journal of the American Concrete Institute. Vol. 79, no. 4, pp July-Aug Lefas, et al., Behavior of RC Structural Walls: Strength, Deformation Characteristics, and Failure Mechanism, ACI Structural Journal, 87(1), pp , Jan Feb Saatcioglu, M., Hysteretic Shear Response of Low-Rise Walls, Concrete Shear in Earthquake, Elsevier Applied Science, New York, New York, pp Bold, underlined: Test results presented 71