Shear-Friction Strength of RC Walls with 550 MPa Bars

Transcription

1 Proeedings of the Tenth Paifi Conferene on Earthquake Engineering Building an Earthquake-Resilient Paifi 6-8 November 215, Sydney, Australia Shear-Frition Strength of RC Walls with 55 MPa Bars Jang-woon Baek & Hong-gun Park Seoul National University, Seoul, South Korea. ABSTRACT: For low-rise walls with aspet ratio less than.5, whih are ommonly used in nulear power plants, sliding failure is the ritial issue in the shear design of the walls under repeated earthquake loading. The present study foused on the appliability of high strength bars to the shear-frition design of reinfored onrete walls. Low-rise walls (aspet ratio =.33 and.5) with Grade 55 MPa bars were tested, to investigate the shearfrition strength under yli loading. The test parameters were shear reinforement ratio, axial ompressive loading, shear frition bars, and surfae onditions of wall-foundation interfae (groove onstrution joint or smooth flat joint). The test results showed that when smooth flat interfae was used without groove joint, the speimens failed due to sliding at the interfae. The test strength was signifiantly less than the shear frition strength of ACI 349. The use of shear frition bars inreased the peak strength, but the peak strength did not reah the shear frition strength. On the other hand, in the ase of walls with groove onstrution joint, shear frition failure was prevented. 1 INTRODUCTION In the onstrution of nulear power plants, a number of large diameter reinforing bars are used in massive reinfored onrete (RC) walls, whih signifiantly affets the onstrutability and eonomy. Thus, to enhane the onstrutability and eonomy, the use of high strength 55 MPa bars needs to be onsidered. Park et al. 1 studied the use of Grade 55 MPa bars for the shear design of low-rise walls (aspet ratio h w /l w =1.). In the study, the behavior of walls with Grade 55 MPa had no signifiant differene with that of Grade 42 MPa bars, in terms of failure mode, shear strength, dutility, and average diagonal shear rak width. Therefore, they reported that Grade 55 MPa bars are appliable to shear reinforement for heavily reinfored low-rise walls. On the other hand, shear-frition strength at wall-foundation interfae is the ritial issue for shear design of walls with aspet ratio h w /l w of walls lower than 1.. In nulear power plant strutures, the majority of the walls have aspet ratios h w /l w less than.5. In this ase, sliding failure an our at the wall-foundation interfae, whih signifiantly dereases the shear apaity. Thus, in the design of short walls, to prevent sliding failure, shear-frition reinforement is plaed at the wall-foundation interfae. Aording to existing results of shear frition test 2, shear-frition apaity in a old joint dereases when high-strength bars are used for the shear-frition reinforement. However, test results of shear frition apaity of walls with high strength bars have not been reported. In the present study, yli lateral loading tests were performed for walls (h w /l w =.33 and.5) with Grade 42 and 55 MPa bars, to investigate the shear-frition strength. The test parameters were the grade and ratio of shear reinforement, axial ompression, shear frition bars, and onditions of wallfoundation interfae (groove onstrution joint or smooth flat surfae). The test results were ompared with the shear-frition strengths predited by urrent design odes. 2 EXPERIMENTAL PROGRAM 2.1 Test speimens The tests were performed for walls with two aspet ratios: 1) h w /l w =.5: 15 mm (length) x 75 mm (height) x 2 mm (thikness), and 2) h w /l w =.33: 15 mm (length) x 5 mm (height) x 2 mm (thikness) (see Fig. 1). Paper Number 18

2 strain gauge 75 A Constrution joint 15 (a) Speimen HF.5 6 D13(667MPa) 12 D13(667MPa) D13@187(667MPa) New onrete D13@2 D13@187 A Old onrete strain gauge 5 16 A Constrution joint 15 () Speimen SF.33D 2 D13(667MPa) 12 D13(667MPa) D1@1(625MPa) New onrete D13@175 D1@1 D1@175 A Old onrete f 42.1MPa SF f 42.1MPa SF D13(667MPa) 2 D13(667MPa) D1@187(625MPa) f 42.1MPa 4 D1(625MPa) SF.5-L D13(667MPa) 4 D13(667MPa) D1@375(625MPa) 2 D13(667MPa) f 42.1MPa SF.5-LL D13(667MPa) 12 D13(667MPa) D1@1(625MPa) 2 2 f 42.1MPa SF.33D 16 D1(625MPa) D13(667MPa) 8 D13(667MPa) D1@167(625MPa) f 42.1MPa SF.33-L D13(667MPa) 12 D13(667MPa) D13@187(667MPa) HF.5 f 38.7MPa SF.5-C f 42.1MPa (b) A-A setion of speimens D13(667MPa) 4 D13(667MPa) D1@167(625MPa) f 42.1MPa SF.33D-L 16 D1(625MPa) Figure 1. Dimensions and reinforement details of speimens Table 1. Design parameters of test speimens Speimens hw /lw Conrete strength f MPa [Compressive load, kn] Vs / Vsmax Horizontal bar fyh MPa ρh Web region ρh fyh Vertial bar fyv MPa ρv Shear-frition bar fysf MPa ρsf Boundary region Vertial bar (%) MPa (%) (%) (%) SF [] / SF.5-L 42.1 [] SF.5-LL 42.1 [] SF.5-C 42.1 [882] HF [735] SF [] SF.33-L 42.1 [] SF.33D 42.1 [] SF.33D-L 42.1 [] In Speimen SF.5 (h w /l w =.5) (Fig. 1(b)), two layers of D13 Grade 55 MPa bars were used for horizontal and vertial reinforement. The horizontal bar ratio ρ h was.68% (Table 1), whih is the permissible maximum bar ratio in aordane with ACI (or ACI ). The flexural strength V f of the speimen was designed to be equal to the shear strength V n, following the design provisions and pratie for RC walls. The flexural strength V f was alulated by setional analysis. The web vertial bar ratio ρ v was.69%. Additional flexural bars were plaed at the wall edges to attain the flexural strength: ρ f = 1.9% (reinforement ratio in wall boundary area). The shear-frition strength V sf was lose to the flexural strength V f ( the shear strength V n ): V sf / V f =.98 (Table 1). The shear-frition strength was alulated in aordane with ACI 349 (or ACI 318), by using the smooth interfae ondition: the fyf MPa ρf Vsf /Vf 2

3 frition oeffiient μ =.6. In Speimens SF.5-L and SF.5-LL (Fig. 1(b)), the horizontal and vertial bar ratios were dereased to almost a half and quarter of those of Speimen SF.5, respetively. The flexural strength V f was the same as the shear strength V n. On the other hand, the shear-frition strength was slightly less than the shear demand (i.e. the flexural strength): V sf / V f =.92 (SF.5-L), and V sf / V f =.9 (SF.5-LL). In Speimen SF.5-C (Fig. 1(b)), axial ompression (.7 A f ) was applied at the top of the wall. The other details were idential to those of SF.5, exept for the flexural bars at the wall edges: the number of flexural bars were dereased onsidering the effet of axial ompression. The shear-frition strength V sf was lose to the shear demand (i.e. the flexural strength V f ): V sf / V f = 1.4. In Speimen HF.5 (Figs. 1(a) and (b)), using a poket metal form around the wall bottom, the onstrution joint was intentionally moved toward the inside of the foundation, to avoid sliding at the wall-foundation interfae. Thus, the oeffiient of shear frition apaity was inreased to μ = 1.4, onsidering the monolithi interfae. Thus, the shear-frition predition V sf was signifiantly inreased to 2,921 kn. However, aording to the permissible maximum one, the shear-frition strength was limited to V sf = 1919 kn: V sf / V f = The other details were idential to those of SF.5-C. In the ase of walls with h w /l w =.5, the shear-frition strength V sf was lose to the flexural strength V f. Thus, shear frition reinforement was not required. In the ase of walls with h w /l w =.33, on the other hand, the shear frition demand inreased due to the redued wall height. Thus, to prevent sliding failure, additional vertial bars for shear frition reinforement were plaed. In Speimen SF.33 (Fig. 1(b)), the shear frition strength was designed to be smaller than the flexural strength to measure aurate shear frition apaity by induing shear frition failure. Thus, the ratio of the shear frition strength to the flexural strength was signifiantly dereased: V sf / V f =.69. Like SF.5, the permissible maximum shear bar ratio was used for shear reinforement: ρ h =.71%, ρ v =.68%, and ρ f = 1.27%. In SF.33-L (Fig. 1(b)), the horizontal and vertial bar ratios were dereased to amost half of those of SF.33: ρ h =.43%, ρ v =.39%, and ρ f = 1.27%. In Speimens SF.33D and SF.33D-L (Figs. 1(b) and ()), additional shear frition bars were plaed so that the shear-frition strength was lose to the flexural strength. For the shear frition bars, eight and five U-type bars were distributed along the wall setion of SF.33D (ρ sf =.38%) and SF.33D-L (ρ sf =.24%) (Table 1), respetively. Consequently, the shear-frition strength was lose to the flexural strength: V sf / V f = 1.1 for SF.33D and.94 for SF.33D-L. In all the speimens, the onrete ompressive strength was 42.1 MPa, exept for 38.7 MPa in HF.5 (Table 1). 2.2 Test proedure and instrumentation An axial ompressive load and a yli lateral load were applied using the test set-up shown in Fig. 2. An axial load of approximately.7 A f (i.e. 882 kn in the ase of 42.1 MPa onrete) was applied at the top of the wall by a displaement-ontrolled atuator. The level of the axial ompressive fore was maintained during yli lateral loading, by automatially ontrolling the vertial displaement. The lateral loading protool followed the Aeptane Criteria for Speial Strutural Walls 5, as shown in Fig. 3. Fig. 2 shows the LVDTs for the measurement of lateral displaements, flexural deformations, shear deformations, and sliding at the base. Figs. 1(a) and (b) show the strain gauges, to measure the strains of the flexural and web vertial shear bars, horizontal bars, and shear-frition bars. 3 TEST RESULT 3.1 Failure mode Fig. 4 shows the damages of the speimens at the end of tests. In the ase of SF.5, SF.5-L, SF.5- LL, and SF.5-C [Fig. 4(a) to (d)]), although shear frition bars were not required in the design, unlike the expetation, sliding failure ourred at the wall-foundation interfae (SF mode). The failure mode was the same as that of SF.33 and SF.33-L [Fig. 4(f) and (g)] whih were intentionally designed for sliding failure. 3

4 Figure 2. Test set-up Lateral Drift (%) Number of Load Cyle Figure 3. Lateral loading protool In Speimens SF.33D and SF.33D-L [Fig. 4(h) and (i)], despite the use of shear-frition bars, sliding failure ourred. The failure surfae was formed along the end of the shear frition bars at a third of the wall height (167 mm above the wall-foundation interfae) (SW mode). In HF.5 with a groove onstrution joint, on the other hand, sliding failure was suessfully prevented, and a mixed failure mode of shear and flexure ourred: rushing in the ompression zone and diagonal tension raking in the tension zone (CC+DT mode). Table 2 summarizes the failure modes. In SF mode speimens (SF.5, SF.5-L, SF.5-LL, SF.5-C, SF.33, and SF.33-L), horizontal splitting tensile raking ourred at the wall-foundation interfae and propagated wider as the load inreased. Conrete spalling ourred near the wall-foundation interfae and the vertial bars were exposed. Ultimately, sliding failure ourred along the old joint. In SF.5-L and SF.5-LL with a half and quarter of the bar ratio of SF.5, respetively, sliding ourred earlier. The number of raks were smaller than that of SF.5. On the other hand, in SF.5-C, sliding was restrained by the ompressive load (.7A f ). In SF.33 and SF.33-L with the lower aspet ratio, splitting raks were onentrated at the interfae, and sliding ourred earlier than that of SF.5 and SF.5-L. In SW mode speimens (SF.33D, and SF.33D-L), diagonal raking ourred at the initial loading and spread over the entire wall panel. As the load inreased, flexural raking initiated at the loation of the shear frition bar end, and the rak width notably inreased. At the maximum load, a new horizontal rak parallel to the wall-foundation interfae was generated at the height of wall enter, and sliding along the horizontal rak ourred. 4

5 Figure 4. Failure modes of speimens at the end of test Table 2. Strengths of test speimens and preditions by urrent design odes Speimen Aspet ratio hw/lw Vtest kn Test results Drift at Vtest % Failure mode Ratio of test strength to preditions ACI 349 flexural provision ACI 349 shear frition provision Vtest / Vsf Vtest / Vf Euroode 2 shear frition provision Vtest / Vni SF / SF.5-L / SF SF.5-LL / SF.5-C / HF /-1. DT+CC SF / SF SF.33-L / SF.33D / SW SF.33D-L / Notes: V f = flexural strength preditions, V test = average value of the measured maximum loads in positive and negative loading diretions, and V sf and V sf = shear-frition preditions provided by the provision of ACI 349 and Euroode 2, respetively. SF is sliding failure at wallfoundation interfae, DT is diagonal tension failure, CC is onrete rushing failure, and SW is sliding failure at wall enter. In CC+DT mode speimen (HF.5), diagonal raking gradually propagated over the entire wall panel. As the load inreased, the width of the diagonal shear raks inreased and onrete spalling ourred at the bottom of the wall edges. Ultimately, onrete rushing ourred in the ompression zone and diagonal tension raking ourred in the tension zone. 3.2 Lateral load-displaement relationships Fig. 5 shows the lateral load-displaement (lateral drift ratio) relationships of the test speimens. The 5

6 lateral displaement indiates the net displaement (L1-L2 in Fig. 2), exluding sliding of the wall base (L2 in Fig. 2). Fig. 5 also shows the shear strength V n, flexural strength V f, and shear frition strength V sf predited by ACI 349 (ACI 318). In all the speimens exept HF.5, the peak strength did not reah the flexural strength V f, whih indiates that the measured maximum lateral load V test was determined by shear failure before flexural yielding (Figs. 6(a) to (d) and (f) to (i)). On the other hand, in HF.5, the peak strength was lose to the flexural strength, showing flexural yielding (Fig. 6(e)). The flexural strength V f was alulated by setional analysis onsidering the effet of axial load. Lateral load (kn) Lateral load (kn) Lateral load (kn) 1,5 1, 5 Lateral drift (%) V f =1351kN V n =1341kN V sf =1216kN V test =744 kn δ m =.43% Lateral drift (%) ,5 V test =45kN 1, δ m =.38% 5 V n =825kN V f =813kN V sf =714kN Lateral drift (%) , δ m =.61% 1, δ m =.61% 1, δ V test = 831kN m =.62% 1, V test = 46kN (a) SF.5 V test = 544kN (b) SF.5 L () SF.5 LL 1,5 1,5 1, ,5 1,5 1,5 V n =1341kN V V test =188kN n =133kN V f =14kN 1, V sf =134kN δ 1, m =1.% 1, V f =1321kN V n =1326kN V f =139kN V V test = 574kN sf =912kN 5 5 δ m =.85% 5 δ m =.35% V test =1368kN δ m = 1.3% δ m =.5% δ m = 1.% V test = 718kN 1, 1, V test = 144kN 1, V test = 186kN (d) SF.5 C (e) HF.5 (f) SF.33 1,5 1,5 1, ,5 1,5 1,5 V n =14kN V 1, V n =944kN 1, test =16kN V test =78kN V sf =1337kN V 5 f =936kN V test =39kN δ V f =1326kN m =1.8% 1, V n =944kN δ m =1.5% V f =936kN V sf =68kN δ m =.47% 5 5 V sf =926kN Figure 5. Lateral load-displaement relationships of speimens 1, 5 V f =596kN V n =542kN V sf =511kN V test =441kN δ m =.28% δ m =.22% 1, V test = 534kN 1, δ m =.66% 1, (g) SF.33 L V test = 131kN (h) SF.33D δ m =.66% (i) SF.33D L V test = 743kN 1,5 1,5 1, Displaement (mm) Displaement (mm) Displaement (mm) In Speimen SF.5 (Fig. 6(a)) with Grade 55 MPa web bars (f yh and f yv =667 MPa, ρ h =.68%, ρ v =.69%, ρ f =1.9%, and ρ h f yh =4.5 MPa), the peak strength ourred at the drift ratio of +.45 and -.6%. The maximum strength V test was +744 and -831 kn in the positive and negative loading diretions, respetively, whih was only 65% of the ACI 349 shear frition strength. In SF.5-L and SF.5-LL (Figs. 6(b) and ()) with smaller bar ratios, the maximum strength V test and lateral drift dereased: in SF.5-L (a half bar ratio), +45 and -544 kn at the drift ratio of +.35 and -.6%, and in SF.5-LL (a quarter bar ratio), +441 and -46 kn at the drift ratio of +.28 and -.6%. However, the safety margin (i.e. the ratio of the test maximum strength to ACI 349 shear frition strength) was inreased to.7 and.83 in SF.5-L and SF.5-LL, respetively, whih implies that the ACI shear frition strength is more unsafe in higher bar ratios. In SF.5-C (Fig. 6(d)) subjeted to axial ompression loading, the maximum strength V test and lateral drift were signifiantly inreased: +188 and -186 kn at the drift ratios of +1. and -1.%. However, the maximum strength did not reah the shear frition predition: V test / V sf =.81. In HF.5 (Fig. 6(e)) with groove onstrution joint and axial ompression loading (Fig. 1(a)), the maximum strength V test exeeded the flexural strength V f : and -144 kn at the drift ratio of

7 and -1.%, showing dutile behavior until the +2. and -2.% drift ratio. In SF.33 (Fig. 6(f)) with aspet ratio h w /l w =.33 (f yh =62 MPa, ρ h =.71%, f yv =667MPa, ρ v =.68%, ρ h f yh =4.45 MPa, and ρ f =1.27%), the maximum strength and drift ratio were smaller than those of SF.5: +574 and -718 kn at the drift ratio of +.35 and -.5%. In SF.33-L (Fig. 6(g))with half bar ratio, the maximum strength V test and lateral drift were dereased: +39 and -534 kn at the drift ratios of +.45 and -.2%. Unlike the speimens with h w /l w =.5, the safety margin of shear frition preditions were similar, regardless of the bar ratio: V test /V sf =.71 and.69 in SF.33 and SF.33-L, respetively. In SF.33D and SF.33D-L (Figs. 6(h) and (i)) using additional shear frition reinforement (f ysf = 62 MPa, ρ sf =.38% in SF.33D, and ρ sf =.24% in SF.33D-L), the maximum strength V test and lateral drift were signifiantly inreased: in SF.33D (maximum shear bar ratio), +16 and -131 kn at the drift ratio of +.75 and -.6%, and in SF.33D-L (a half of the maximum shear bar ratio), +78 and -743 kn at the drift ratio of +1. and -.6%. However, the test strength did not reah the ACI 349 shear frition strength: V test /V sf =.78 and.83 in SF.33D and SF.33D-L, respetively. 3.3 Strains of web bars Fig. 6 shows strain distributions of the horizontal bars along the wall height at.5v max,.75v max, and 1.V max. The loations of the bars and strain gauges are shown in the figure. In all speimens, yielding of the horizontal bars did not our. Wall height (mm) Wall height (mm) Wall height (mm) strain 1.% 187 kn 2.7% 1246kN gauge.2% 735 kn.94% 1427kN.8% 559 kn.4% 1182kN % 718 kn.2% 546 kn % 436 kn.22% 535 kn.12% 431 kn.3% 247 kn 125.6% 825 kn.21% 584 kn.11% 44 kn (a) SF.5 (d) SF.5 C (f) SF.33.37% 519 kn.17% 368 kn.11% 279 kn (b) SF.5 L yield strain (e) HF.5 (g) SF.33 L.63% 544kN.62% 46kN.11% 279kN () SF.5 LL 1.3% 121 kn.3% 754 kn.8% 485 kn (h) SF.33D New onrete Old onrete.48% 743kN.1% 56kN.6% 343kN (i) SF.33D L Mirostrains Mirostrains Mirostrains Mirostrains Figure 6. Measured strains of horizontal bars In HF.5 where sliding failure did not our, the horizontal bar strains were the greatest. In other speimens whih failed due to sliding (SF.5, SF.5-L, SF.5-LL, SF.5-C, SF.33, and SF.33-L), the strains of the horizontal bars were extremely small, whih indiates that the load-arrying apaity was limited by premature sliding failure. In SF.33D and SF.33D-L with shear frition bars, the bar strain inreased as the load-arrying apaity inreased. Fig. 7 shows strain distributions of the vertial web bars at.5v max,.75v max, and 1.V max. The loations 7

8 of the bars and strain gauges are shown in the figure. In the figure, the strains were signifiantly less than the, whih did not agree with the assumption of the ACI 349 shear frition design. This result indiates that the onept of shear frition design needs to be hanged in the ase of walls subjeted to yli lateral loading. Mirostrains Mirostrains 5, 2,5 2,5 2,5-2,5-5, 5, Mirostrains 2,5 2,5.37% 7 kn.17% 529 kn.1% 436 kn.44% 744 kn.19% 58 kn.9% 346 kn (a) SF.5.47% 977 kn.21% 73 kn.11% 419 kn.63% 544kN.17% 368kN.11% 279kN.22% 535 kn.12% 431 kn.3% 247 kn.62% 46 kn.22% 296 kn.4% 26 kn 5, , (d) SF.5 C (e) SF.33 (b) SF.5 L 1.3% 1261kN.63% 1242kN.19% 63 kn (e) HF.5 (f) SF.33 L strain gauge 1.3% 121kN.3% 754 kn.12% 582 kn () SF.5 LL (g) SF.33D Figure 7. Measured strains of vertial bars.48% 743kN.1% 56kN.6% 343kN New onrete Old onrete (h) SF.33D L 5, Wall length (mm) Wall length (mm) Wall length (mm) Wall length (mm) 4 RECOMMENDATION FOR SHEAR FRICTION DESIGN WITH GRADE 55 MPA BARS On the basis of test results, provisional reommendation for shear frition design with Grade 55 MPa bars were made as follows: 1. In walls without onstrution joints (μ = 1.4), design yield strength of 55MPa (atual yield strength = 667MPa) an be used for shear frition bars. However, in the onstrution of massive walls, the use of onstrution joints is inevitable. 2. In walls with onstrution joints (μ =.6), the design yield strength of shear frition bars needs to be limited to 42MPa (When 55MPa bars are used for vertial and horizontal bars, 55MPa an be used for shear design and flexural design, but for shear frition design, the design yield strength should be limited to 42MPa). However, the safety margin of shear frition design is relatively low when ompared to the design shear strength or design flexural strength. Thus, shear frition failure may preede other failure modes. 3. When additional shear frition bars are neessary, the additional shear frition bars should not be terminated at the lower part of walls, but be extended to the upper part. Otherwise, premature shear frition failure an our at the ends of the bars. 5 CONCLUSION To investigate the shear frition apaity of walls with Grade 55 MPa web bars, five speimens with aspet ratio h w /l w =.5 and four speimens with aspet ratio h w /l w =.33 were tested under yli lateral loading. The major findings of the present study are summarized as follows: 8

9 1. In the walls where onstrution joint at the wall-foundation interfae, the test strength did not reah the shear frition strength of ACI 349 (or ACI 318) and Euroode 2. In the ase of walls without shear frition bars, the test strength was 65 ~ 83% of the ACI 349 shear frition strength. 2. In the ase of walls with shear frition bars, the shear frition bars inreased the maximum strength, but the maximum strength did not reah the shear frition strength. The test strength was 78 ~ 83% of the ACI 349 shear frition strength. 3. In the ase of walls subjeted to axial ompression, the test strength inreased, but did not reah the shear-frition predition. The test strength was 81% of the ACI 349 shear frition strength. 4. On the other hand, in the walls with groove onstrution joint, the test strength reahed the wall shear strength, without shear frition failure. 5. Provisional reommendation for shear frition design with Grade 55 MPa bars were made on the basis of the test results. However, further studies are required onsidering other parameters of bar grade (42 MPa bars), roughened surfae (μ =1.), and size effet (larger bar diameter). 6 ACKNOWLEDGMENT This work was supported by the Nulear Power Core Tehnology Development Program of the Korea Institute of Energy Tehnology Evaluation and Planning (KETEP), granted finanial resoure from the Ministry of Trade, Industry & Energy, Republi of Korea (No B). REFERENCES: Park, H.; Baek, J.; Lee, J., and Shin, H., "Cyli Loading Tests for Shear Strength of Low-Rise Reinfored Conrete Walls with Grade 55 MPa Bars," ACI Strutural Journal, 215, 112(3): pp H., Kent A.; Z., Gabriel, and S., Bahram, "Toward an improved understanding of shear-frition behavior," ACI Strutural Journal, 212, 19(6): pp ACI Committee 349, "Code Requirements for Nulear Safety-Related Conrete Strutures (ACI ) and Commentary," 214: Farmington Hills, 2 pp. ACI Committee 318, "Building Code Requirements for Strutural Conrete (ACI ) and Commentary," Farmington Hills, 214, 52 pp. Hawkins, NM, and Ghosh, SK, "Aeptane Criteria for Speial Strutural Walls Based on Validation Testing", 23, Proposed Provisional Standard and Commentary, SK Ghosh Assoiates In., Northbrook, IL. 9