Shear Strength of Squat Reinforced Concrete Walls with Flanges and Barbells

Transcription

1 Transations, SMiRT 19, Toronto, August 2007 Shear Strength of Squat Reinfored Conrete Walls with Flanges and Barbells Cevdet K. Gule 1), Andrew S. Whittaker 1), Bozidar Stojadinovi 2) 1) Dept. of Civil, Strutural and Environmental Engineering, State University of New York, Buffalo, NY 2) Dept. of Civil and Environmental Engineering, University at California at Berkeley, Berkeley, CA ABSTRACT Squat reinfored onrete walls are important omponents in nulear strutures. Shear strength is one of the key parameters for the fore-based design of suh walls. Preditive equations are available in the open literature for the shear strength of squat walls under seismi loading but these equations vary signifiantly in format and yield onsiderably different estimations for a given wall. Results of prior tests of 187 small-to-large sale squat walls with boundary elements (138 barbell and 49 flanged walls) are evaluated with the objetive of analyzing the utility of four preditive equations: Chapter 21 of ACI [1], Chapter 11 of ACI [1], Barda et al. [2] and ASCE 43 [3]. ASCE 43 equation provides the best estimates of ultimate shear strength of squat reinfored onrete walls with barbells and flanges with a median ratio of the predited to measured strengths lose to 1.0 with a small oeffiient of variation. All four equations overestimate the ultimate shear strength in a median sense. KEYWORDS: reinfored onrete; squat walls; ultimate shear strength; INTRODUCTION Squat reinfored onrete walls are widely used in safety-related nulear strutures. Building odes, manuals of pratie, guidelines and the open literature provide a number of preditive equations for the peak shear strength of suh walls. These proedures use parameters suh as aspet ratio, horizontal rebar ratio, vertial rebar ratio and axial fore to estimate shear strength. Prior studies have indiated that the satter in the shear strength predited by these equations is substantial, whih is problemati beause shear strength is the key variable for fore-based design and performane assessment. Herein, the results of tests of 187 squat walls with boundary elements (138 barbell and 49 flanged ross setions) with aspet ratios (h w / l w ) up to 1.60 are ompiled and redued to evaluate peak strength. First, the experimentally measured peak (ultimate) strengths of the 187 walls are ompared with nominal (ultimate) strengths predited by four equations 1 : 1) Chapter 21 of ACI [1]; 2) Chapter 11 of ACI [1]; 3) Barda et al. [2]; and 4) ASCE 43 [3]. Nominal rather than design strengths are used for the omparison beause the strength redution fator is not intended to aount for bias in the strength equation. In the omparison that follows, reported material strengths and member dimensions are used to ompute nominal strengths. The mean and median values as well as the satter in the ratio of the omputed to measured strengths provide valuable insight into the utility of eah strength equation and the simplified models upon whih the equations are based. In a ompanion study [4], the authors investigated the utility of these equations to predit the ultimate shear strength of squat retangular walls without boundary elements. The study revealed that the proedures of ACI [1] provides better estimates of the ultimate shear strength than the proedures of Barda [2] and ASCE 43 [3], with mean and median values of the ratio of predited to experimental strength lose to 1.0. The proedures of Barda [2] and ASCE 43 [3] onsistently over-predited the ultimate shear strength of squat retangular walls without boundary elements. EXPERIMENTAL DATA A signifiant number of tests of squat reinfored onrete walls with various ross setions (retangular, barbell and flanged) were onduted from ira 1950 to date in ountries inluding the United States, Canada, Chile, England, Frane, Germany, Japan, New Zealand, Switzerland, Portugal, Mexio, and Taiwan. Experiments with barbell ross-setions intended to simulate walls framed by olumns at both ends and flanged ross setions simulated walls framed by other walls oriented in the perpendiular diretion. The authors ompiled the response data for retangular walls elsewhere [4]: this study summarizes the response of barbell and flanged walls only. The data for the 187 squat walls onsidered in this study were ompiled in [5], originating from the experiments of Antebi et al., Barda et al., Benjamin and Williams, Bouhon et al., Hirosawa, Kabeyasawa and Somaki, Kitada et al., Maier and Thürlimann, Mo and Chan, Naze and Sidaner, Ogata and Kabeyasawa, Palermo and Vehio, Rothe, Shiga et al., Synge, and XiangDong. 1 The equations presented by the Chapters 11 and 21 of ACI [6] to alulate the ultimate shear strength of reinfored onrete squat walls are idential to the orresponding equations presented by Chapters 11 and 21 of ACI

2 Transations, SMiRT 19, Toronto, August 2007 The 187 walls were seleted based on the following riteria: 1) minimum web thikness of 50 mm (1.97 in.); 2) symmetri rebar layout; 3) no diagonal reinforement or additional wall-to-foundation rebar to ontrol sliding shear; and 4) aspet ratios (h w / l w ) less than or equal to 1.60, orresponding to a maximum moment-to-shear ratio 1 (M / Vl w ) of Although the walls in the database inluded walls with aspet ratios (h w / l w ) up to 1.60, 57% of the walls had aspet ratios between 0.5 and 0.75 and 89% of the walls had aspet ratios less than 1.0. The web thikness of the walls ranged from 50 to 200 mm (1.97 to 7.87 in.). Approximately 80% of the walls had web thiknesses between 50 and 80 mm (1.97 to 3.15 in.) Wall length varied between 507 and 3960 mm (19.96 and in.); the wall height varied between 400 and 2020 mm (15.75 and in.). The ratios of the boundary element area (total flange or barbell area, A be ) to the total area of the wall (A t ) varied between and Approximately 75% perent of the walls had A be /A t values between 0.3 and 0.5. Fiftyfour walls were tested with axial load 2 that ranged between A t f ' and A t f '. Reported onrete ompressive strength 3 varied from 10 to 66 MPa (1451 to 9573 psi), 78% of the walls had ompressive strengths between 15 and 35 MPa (2176 and 5076 psi). Horizontal rebar ratios ranged between 0.00 and ; 63% of the walls had horizontal rebar ratios less than and 91% of the walls had horizontal rebar ratios less than Vertial rebar ratios ranged between 0.00 and ; 62% of the walls had vertial rebar ratios less than and 91% of the walls had rebar ratios less than Boundary element reinforement (rebar in the flanges or barbells) was provided in all 187 walls within a range of 0.35 and 8.27% of eah boundary element area. Eight of the 187 walls in the dataset did not have horizontal web reinforement; eight walls did not have vertial web reinforement; seven had neither horizontal nor vertial web reinforement and inluded only boundary element reinforement at wall ends. The reported yield stress of the wall vertial and horizontal web reinforement ranged between 271 and MPa (39.3 and 90.5 ksi). The reported yield stress for the boundary element reinforement ranged between and 605 MPa (37.8 and 87.7 ksi). The seleted walls were tested using one of five types of loading: monotoni (stati); repeated (stati), yli (quasistati), blast and dynami. Monotonially loaded speimens (58 of 187) were subjeted to inrementally inreasing load in one diretion until failure. Repeatedly loaded speimens (7 of 187) were loaded in one diretion and were unloaded prior to being subjeted to a higher lateral fore. Cylially loaded speimens (88 of 187) were subjeted to fully reversed fore or displaement histories following onventional testing protools. Blast tests (30 of 187) onsisted of speimens loaded with large amplitude dynami pulses. Dynami tests (4 of 187) were onduted using earthquake simulators. ULTIMATE SHEAR STRENGTH OF SQUAT REINFORCED CONCRETE WALLS Four sets of equations based on the proedures provided in Chapter 21 of ACI [1], Chapter 11 of ACI [1], Barda et al. [2] and ASCE 43 [3], are used herein to predit the peak (ultimate) shear resistane of the 187 squat walls. ACI provides two semi-empirial equations, both based on the modified truss analogy approah, for evaluating the strength of squat reinfored onrete walls. The equation in Setion 21.7 of ACI (Speial reinfored onrete strutural walls and oupling beams) is intended for seismi design. The seond equation, in Setion (Speial provisions for walls), is to be used for general design. Equation Set I below is from Setion 21.7 of ACI ( ) = α +ρ (1) V1 f hfyh Aw 0.83 fa w Chapter 21 of ACI imposes an upper limit of 0.83 f MPa (10 f psi) on the ultimate shear stress a limit intended to prevent diagonal ompression failure. A lower limit of 0.25% is imposed on the horizontal and vertial wall reinforement ratios. For walls with aspet ratios less than or equal to 2.0, ACI Chapter 21 requires that the vertial reinforement ratio be no less than the horizontal reinforement ratio. The proedure for evaluating the shear strength per Setion of ACI , Equation Set II, is given by the following four equations. V = V + V 0.83 f t d (2) 1 2 s w V N d u 1 = ftwd1 + (3) 4lw 1 Moment-to-shear ratios are normalized by the atual wall length in this paper. 2 Self weight of the speimen was not inluded in the axial load alulation. 3 Some authors used ube strength rather than ylinder strength to report the ompressive strength of onrete; ube strengths were onverted to ylinder strengths per Mindess et al. [7]. 2

3 Transations, SMiRT 19, Toronto, August N M l w 1 u u w V = 0.05 f + lw f + / t d lwtw Vu 2 (4) Af v yhd1 Vs = (5) s The following onditions apply per Setion of ACI : the shear strength provided by onrete is taken as the lesser of the values provided by equations (3) and (4); and equation (4) does not apply when M u /Vu l w /2 0. ACI Chapter 11 imposes an upper limit of 0.83 f MPa (10 f psi) on the ultimate shear stress. The ratio of the minimum horizontal reinforement is restrited to 0.25%; the ratio of minimum vertial reinforement ratio is determined by h w ρ v = ( ρh ) (6) lw Equation Set III was proposed by Barda et al. [2] to predit the ultimate shear strength of squat walls. hw N u V3 = f f + +ρvfyv t d lw 4lwt (7) w w 2 Equation Set IV is presribed by Equations and of ASCE 43 [3] (equations (8) through (10) below) to ompute the ultimate shear strength of squat walls with barbells or flanges. The equation is appliable for walls with aspet ratios h w / l w of 2 or less and vertial and horizontal reinforement ratios less than or equal to 1%. If the reinforement ratios exeed 1%, the ombined reinforement ratio ρ se, (alulated using equation 10) is limited to 1%. ASCE 43 imposes an upper limit of 1.66 f MPa (20 f psi) on the ultimate shear stress. V = υ d t w (8) 4 n 3 h w Nu υ n = f f ρsefy 1.66 f lw 4lwt (9) w ρ = Aρ + Bρ (10) se v h EFFECT OF BARBELLS AND FLANGES ON THE ULTIMATE SHEAR STRENGTH The effet of barbells and flanges on the ultimate shear strength of squat reinfored onrete walls has not been studied and the effet is ignored in design pratie. Lee and Stojadinovi [8] and Kim et al. [9] studied a geometrially similar and relevant problem, namely, the transfer of shear fore from a steel W-shape beam (wall with flanges or barbells) to a olumn (foundation). Those studies, albeit of a different material, showed that beam theory does not apply at disontinuities of stiffness (the beam-olumn interfae), that in the elasti range up to 50% of the shear fore is transferred from the beam (wall) to the olumn (foundation) through the beam (wall) flanges, and that the shear stress is minimized near the mid-depth of the beam (wall). The perentage of shear fore transferred through the beam web inreased slightly with plasti straining of the beam flanges. The same trends are expeted for reinfored onrete walls with flanges and barbells on a stiff foundation beause the boundary onditions are similar. Aside from materials, the major differene between the steel onnetions and the squat walls onsidered here is the moment-to-shear ratio, whih is high for the steel onnetions and low for the squat walls. (Plasti straining of the flanges in a reinfored squat wall due to overturning moments will be negligible.) None of the four sets of preditive equations presented above aount for the effet of the barbells and flanges on the ultimate shear strength of reinfored onrete squat walls, and assume, per Bernoulli beam theory, that only the web of the wall is effetive in resisting shear fore. Sine the four sets of preditive equations were alibrated using data from tests of walls with barbells and flanges, they overestimate the shear resistane of retangular walls [4], whih is unonservative for fore-based design and inappropriate for performane-based seismi design. Figure 1 presents the variation of shear stress [normalized by the produt of web area A w and f ] obtained using experimentally determined ultimate strength (V ult ) with M / Vl w for squat walls with and without barbells and flanges. All 3

4 Transations, SMiRT 19, Toronto, August 2007 walls represented in the figure were shear-ritial (see the assumptions in the following setion); detailed information on the walls with retangular ross-setions an be found elsewhere [4]. Figure 2 presents a similar plot to figure 1 exept the experimentally determined ultimate shear strength is normalized by the total wall area (A t ) and not by the web area (A w ). In figure 1, the normalized shear stresses obtained for walls with barbells and flanges are signifiantly higher than those obtained for walls with retangular ross setions. Figure 1 reveals that the effetive shear area for walls with barbells and flanges is substantially larger than the web area and that barbells and flanges an signifiantly inrease the ultimate shear strength of squat walls. Figure 2 reinfores this observation by showing that the data is not lustered with respet to the rosssetion type (as in figure 1) when the ultimate shear strength is normalized by the total wall area (A t ). Analysis of the failure mehanisms in the walls with normalized shear stress greater than 10 f (psi units) is on-going. Fig. 1 Variation of shear stress [normalized by the produt of web area (A w ) and f ] obtained using experimentally determined ultimate strength (V ult ) with M / Vl w Fig. 2 Variation of shear stress [normalized by the produt of total wall area (A t ) and f ] obtained using experimentally determined ultimate strength (V ult ) with M / Vl w COMPARISON OF PREDICTIONS AND EXPERIMENTAL RESULTS During data evaluation, it was observed that the walls tested under large amplitude dynami pulses (blast loading) had 25% higher ultimate shear strength on average than idential walls tested under pseudo-stati monotoni loading (Antebi et al.). This result is expeted sine the ompressive and tensile strengths of onrete inrease substantially at high-strain rates. Given that the fous of the study is the seismi behavior of squat walls, for whih the strain-rate effets are insignifiant, the data from the blast tests (30 of the 187 seleted walls) were not inluded in the dataset that is analyzed below. To ompare the shear strength preditions with the experimental results, the failure mode of the tested walls must be dominated by shear. The theoretial moment apaity of eah wall was estimated using ross-setion strain ompatibility analysis. A ommerially available ross-setion analysis ode (XTRACT) [10] was used to model eah wall using the wall geometry, material properties (onrete ompressive strength, rebar yield strength and rebar rupture strength), reinforement layouts and axial fores identified in the soure douments. The shear fore assoiated with the development of wall flexural strength (shear-flexural strength, V flex ) was alulated and ompared with the measured ultimate strength (V ult ) for eah wall in the database. Twenty-three walls (10 barbell and 13 flanged) of the 157 walls that developed their theoretial flexural strength prior to peak measured moment in the wall were exluded from further analysis. The auray of the four preditive equations identified above is evaluated using the experimentally measured peak strengths of the 134 shear-ritial squat walls remaining in the database: 98 barbell and 36 flanged walls. The effetive depth of the tension reinforement (used in equations 2, 3, 4, 5, 7 and 8) for eah wall in the database was omputed using XTRACT [10]. ACI Chapter 21 Equation Figure 3 presents the variation of the V 1 / V ult and V 1* / V ult ratios with wall horizontal reinforement ratio, in whih V 1* is alulated using Equation Set I without imposing the upper shear stress limit of 0.83 f MPa (10 f psi). The 4

5 Transations, SMiRT 19, Toronto, August 2007 vertial dashed line in this figure (and in figure 4) represents the limiting value of ρ h f yh in Chapter 21.7 of ACI for Grade 60 reinforement. Values of V 1 / V ult and V 1* / V ult greater than 1.0 represent an overpredition (unonservative estimate) of the measured ultimate strength. Equation Set I overpredits the ultimate shear strength of 13% of the walls in the database yielding mean and median V 1 / V ult ratio values of 0.73 and 0.66, respetively. The standard deviation and oeffiient of variation assoiated with the V 1 / V ult ratio values are 0.27 and 0.37, respetively. A omparison of the preditions of V 1 and V 1* in figure 3 indiates that the upper shear stress limit, linked to the hange of failure mode from diagonal tension to diagonal ompression, governs the ultimate shear strength of walls with ρ h f yh larger than approximately 3 MPa (435 psi). ACI Chapter 11 Equations Figure 4 presents the variation of V 2 / V ult with wall horizontal reinforement ratio. Comparison of figures 3 and 4 shows that Equation Set II yields more onservative preditions of ultimate shear strength than Equation Set I, whih is expeted sine the effetive shear area for Equation Set II (d 1 t w ) is smaller than that of Equation Set I (A w ). Both equations follow similar trends with respet to ρ h f yh. Equation Set II overpredits the ultimate shear strength of 9% of the walls in the database. The mean and median ratios of V 2 / V ult are 0.64 and 0.60, respetively. The standard deviation and oeffiient of variation assoiated with the V 2 / V ult ratios are 0.22 and 0.34, respetively. Fig. 3 Variation of V 1 / V ult and V 1* / V ult with ρ h f yh Fig. 4 Variation of V 2 / V ult with ρ h f yh Barda et al. (1977) Equation Equation Set III is based on the work of Barda et al. [2] who tested 8 reinfored onrete squat walls with flanges. Figure 5 presents the variation of V 3 / V ult with wall vertial reinforement ratio 1. The dashed line in figure 5 (and in figure 6) represents the limiting value of ρ v f yv in Chapter 21.7 of ACI for Grade 60 reinforement. As seen in figure 5, Equation Set III underpredits the ultimate shear strength of the majority of the walls that do not omply with the minimum vertial reinforement requirements of ACI Equation Set III overpredits the ultimate shear strength of 26% of the walls in the database with mean and median of V 3 / V ult ratio values of 0.85 (0.86 for flanged walls, 0.85 for barbell walls) and 0.83, respetively. The standard deviation and oeffiient of variation of the ratio V 3 / V ult are 0.25 (0.27 for flanged walls, 0.24 for barbell walls) and 0.29, respetively. Figure 6 presents the variation of shear stress [fore normalized by the produt of effetive shear area (d 2 t w ) and f ] omputed using Equation Set III (V 3 ) and the measured ultimate strength (V ult ), with ρ v f yv. The shear strength preditions of Equation Set III are not subjet to an upper bound, whih is not the ase for the other three equation sets. As seen in figure 6, Equation Set III produes onservative estimates of the experimentally observed ultimate shear strength for 1 Equation Set III uses the vertial and not horizontal reinforement ratio to alulate ultimate shear strength. 5

6 Transations, SMiRT 19, Toronto, August 2007 lightly reinfored walls, with the degree of onservatism dereasing as the wall reinforement ratio inreases. ASCE 43 Equations Figure 7 presents the variation of the V 4 / V ult and V 4* / V ult ratios with the ombined wall reinforement ratio (ρ se f y ), where V 4* is alulated using Equation Set IV without the upper shear stress limit of 1.66 f MPa (20 f psi). The ASCE 43 equation provides reasonable estimates of ultimate shear strength with mean and median predited vs. measured ratio values of 0.97 and 0.96, respetively. The standard deviation and oeffiient of variation for the V 4 / V ult ratios are 0.26 and 0.27, respetively. Equation Set IV overpredits the ultimate strength of 47% of the walls in the squat wall database whih orresponds to the highest perentage of unonservative estimations of ultimate shear strength of the four equation sets studied. The upper shear stress limit of 1.66 f MPa (20 f psi) ontrols the shear strength of 8 of the 134 walls in the database (figure 7). The effet of the upper shear stress limit of 1.66 f MPa (20 f psi) on the shear strength preditions of Equations Set IV is modest. The mean and median ratios of V 4* / V ult are both Figure 8 presents the variation of shear stress [fore normalized by the produt of effetive shear area (d 3 t w ) and f ] omputed using Equation Set IV (V 4 ) and the measured ultimate strength (V ult ), with ρ se f y. The measured normalized shear stresses for 18 walls exeeded the upper shear stress limit of 1.66 f MPa (20 f psi). Fig. 5 Variation of V 3 / V ult with ρ v f yv Fig. 6 Variation of normalized shear stress obtained using Equation Set III (V 3 ) and experimentally determined ultimate strength (V ult ) with ρ v f yv SUMMARY AND CONCLUSIONS The experimentally measured peak (ultimate) strengths of the 134 reinfored onrete squat walls (98 barbell and 36 flanged walls) were ompared with nominal (ultimate) strengths predited by four different equations of Chapter 21 of ACI [1], Chapter 11 of ACI [1], Barda et al. [2] and ASCE 43 [3]. The median ratios of predited ultimate shear strength to the experimental ultimate shear strength for these proedures are 0.66, 0.60, 0.83 and 0.96, respetively. The satter in the values of ultimate shear strength predited by all equations is substantial. The best preditions of ultimate shear strength squat walls with barbells and flanges were obtained using ASCE 43 equation (equation set IV), whih gave median and mean values of strength ratios (predited / experimental) lose to 1.0 and produed the smallest oeffiient of variation for the walls in the database. The effet of barbells and flanges on the ultimate shear strength of squat walls is signifiant. Relevant studies on steel W-shape beams have learly indiated the importane of elements beyond the web for the omputation of shear resistane. However, none of the proedures evaluated herein either aount for the effet of barbells and flanges or aommodate failure mehanisms that aknowledge the presene of these elements. Importantly, although the preditive equations generally produe low estimates of maximum strength, they annot be used with onfidene to predit the shear 6

7 Transations, SMiRT 19, Toronto, August 2007 resistane of squat walls with geometries or rebar distributions that are different from those of the walls in the database beause the modes of failure of suh walls are not understood and thus not inorporated in the equations. Fig. 7 Variation of V 4 / V ult and V 4* / V ult with ρ se f y Fig. 8 Variation of normalized shear stress obtained using Equation Set IV (V 4 ) and experimentally determined ultimate strength (V ult ) with ρ se f y ACKNOWLEDGEMENTS The authors thank Professors Sharon Wood, Jak Moehle, Mete Sozen, Detlef Rothe and Yi-Lung Mo for providing their assistane in populating the squat wall database. NOMENCLATURE A be = total boundary element area (mm 2 ) A t = total wall area (mm 2 ) A v = area of horizontal reinforement within a distane of s (mm 2 ) A w = area of the wall bounded by the web thikness (t w ) and wall length (l w ) (mm 2 ) d 1 = distane from extreme ompression fiber to area entroid of the wall vertial reinforement in tension and assumed equal to 0.8l w unless a larger value is determined by a strain ompatibility analysis (mm) d 2 d 3 f ' f y f yh f yv h w l w M u N u s t w V V flex = distane from extreme ompression fiber to area entroid of the wall vertial reinforement in tension (mm) = distane from the extreme ompression fiber to the loation of the resultant of fores in vertial reinforement in tension, whih may be determined from a strain ompatibility analysis and is assumed equal to 0.6l w if no analysis is performed (mm) = ompressive strength of onrete (MPa) = rebar yield stress (MPa) = yield stress of the horizontal rebar (MPa) = yield stress of the vertial rebar (MPa) = heigth of the wall (mm) = length of the wall (mm) = moment at the setion (N-mm) = axial load that is negative in tension (N) = spaing of the horizontal reinforement in the wall (mm) = thikness of the wall (mm) = nominal shear strength provided by the onrete (N) = shear fore assoiated with the development of flexural strength (N) 7

8 Transations, SMiRT 19, Toronto, August 2007 V s V u V ult = nominal shear strength provided by horizontal reinforement (N) = shear fore at the setion (N) = experimentally-determined shear strength (N) V 1 = shear strength (N) predited using proedures of Chapter 21.7 of ACI [1] V 2 = shear strength (N) predited using proedures of Chapter of ACI [1] V 3 = shear strength (N) predited using Barda equation [2] V 4 = shear strength (N) predited using proedures of ASCE 43 [3] α ρ h ρ se ρ v ν n = aspet-ratio oeffiient, whih per ACI , is equal to 0.25 for h w / l w 1.5, for h w / l w 2 and varies linearly for 1.5 h w / l w 2 = horizontal rebar ratio within the wall-web = ombined reinforement ratio that is equal to Aρ v +Bρ h (A and B are defined in table 1 as a funtion of aspet ratio) = vertial rebar ratio within the wall-web = nominal maximum shear stress (MPa) Table 1. Variables used in ASCE 43 strength equations (Equation Set IV) h w / l w 0.5 A = 1 B = h w / l w 1.5 A = h w / l w +1.5 B = h w / l w 0.5 h w / l w 1.5 A = 0 B = 1 REFERENCES 1. ACI, Building ode requirements for strutural onrete (ACI ), Amerian Conrete Institute, Farmington Hills, MI, Barda, F., Hanson, J. M. and Corley, W. G., Shear strength of low-rise walls with boundary elements, Reinfored Conrete Strutures in Seismi Zones, SP-53-8, Amerian Conrete Institute, Farmington Hills, MI, 1977, pp ASCE, Seismi Design Criteria for Strutures, Systems, and Components in Nulear Failities (ASCE 43-05), Amerian Soiety of Civil Engineers, Reston, VA, Gule, C. K., Whittaker, A. S. and Stojadinovi, B., Shear strength of squat retangular reinfored onrete walls, Paper submitted for publiation in the ACI Strutural Journal, January Gule, C. K., Whittaker, A. S. and Stojadinovi, B., Shear strength of squat reinfored onrete walls with barbells and flanges, Paper in preparation, ACI Strutural Journal. 6. ACI, Code requirements for nulear safety related onrete strutures (ACI ), Amerian Conrete Institute, Farmington Hills, MI, Mindess, S., Young, J. F. and Darwin D, Conrete, Prentie Hall, NJ, Lee, K. H., Goel, S. C. and Stojadinovi, B., Boundary effets in welded steel moment onnetions, Report No. UMCEE 97-20, Department of Civil and Environmental Engineering, Ann Arbor, MI, Kim, T., Whittaker, A. S., Gilani, J., Bertero, V. V. and Takhirov, S. M., Cover-plate and flange-plate steel momentresisting onnetions, Journal of Strutural Engineering, Vol. 128, No.4, April 2002, pp XTRACT v.3.0.5, Imbsen and Assoiates, In. 8