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Proceedings of the 8th U.S. National Conference on Earthquake Engineering April 18-22, 2006, San Francisco, California, USA Paper No. 382 DRIFT CAPACITY MODELS AND SHEAR STRENGTH DEGRADING MODELS FOR SLAB-COLUMN CONNECTIONS Thomas H.-K. Kang1 and John W. Wallace2 ABSTRACT Data collected from shake table tests of two, approximately one-third scale, two story flat plate frames utilizing shear reinforcement, as well as data from prior tests, were evaluated to assess the inter-story drift ratios when punching failures occur for reinforced concrete and post-tensioned slab-column connections with and without shear reinforcement. The drift ratios at punching for the shake table specimens were approximately equal to values reported for quasi-static tests of specimens without shear reinforcement. The existing drift capacity model of the slab-column connections was re-examined based on the existing test data and available shear strength degrading models. Typically, these models include two parameters, the displacement ductility at which the shear strength begins to degrade and the rate at which the shear strength degrades. Using tests data, these parameters were determined for the slab-column connections. The revised models allow better prediction of the nominal shear strength of the slab-column connections when flexural yielding occurs, as well as provide a means to assess the need for shear reinforcement based on the slab span-to-thickness ratios. Introduction Slab-column frames are commonly used to resist gravity and lateral loads in regions of low-to-moderate seismicity and well-established design requirements exist to avoid punching failures at the slab-column connections (ACI 318-05). To avoid punching shear failures at slab- column connections, the shear stress on the slab critical section due to direct shear (Vu/bod) and eccentric shear (γvMu,unbc/Jc) cannot exceed the nominal shear stress capacity of the critical section (vn = vc + vs), where γv is the portion of the unbalanced moment (Mu,unb) transferred by eccentric shear (e.g., ~40% for square, interior columns), vc and vs are the nominal shear stress capacities provided by the concrete and the shear reinforcement, respectively. If the calculated shear stress exceeds the nominal shear stress capacity, a punching failure is anticipated, and the design must be modified until the stress is acceptable (e.g., thicker slab, larger column). For slab-column frames subjected to lateral displacements due to earthquakes, punching failures are possible even if the shear stress on the slab critical section does not exceed the nominal shear stress (i.e., no stress-induced failure). In this case, it is hypothesized that the shear stress capacity of the slab critical section degrades (e.g., Hawkins and Mitchell, Pan and Moehle, 1 Faculty Fellow, Dept. of Civil Engineering, University of California (UCLA), Los Angeles, CA 90095 2 Professor, Dept. of Civil Engineering, University of California (UCLA), Los Angeles, CA 90095 Moehle), and punching failure occurs when the shear capacity degrades to the point where it equals the demand (Figure 1). In this paper, this is referred to as a drift-induced failure, to differentiate it from a stress-induced failure discussed in the preceding paragraph. Stress-induced Shear Capacity 0.09 RC connections without shear reinforcement Isolated RC "Interior" Punching Shear Demand . Connections Shear Capacity (Vn) Shear Demand (Vu) 0.08 Subassemblies . Nine-panel Frame . Drift Ratio at Punching Drift-induced 0.07 Relationship Isolated RC "Edge" Connections . Punching for RC with stud-rails (Robertson et al. 2002) σRes : Stadard Deviation of the Residuals 0.06 around the Regression Line 0.05 0.04 Best-Fit Line for Interior Connections without 0 1 2 3 4 5 0.03 Shear Reinforcement Ductility (µ) (Best-Fit Line) plus one σRes 0.02 (Best-Fit Line) Figure 1. Shear demand-capacity relation. 0.01 minus one σRes ACI 318-05 Limit 0 ACI 318-05 (S21.11.5) assesses the 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Gravity Shear Ratio (Vg /φVc), where Vc = (1/3) f'c1/2bod need for shear reinforcement at slab-column 0.09 RC connections Relationship Isolated RC int. with stud-rails . connections based on the inter-story lateral with shear reinforcement 0.08 for RC with stud-rails Isolated RC int. with stirrups . (Robertson et al. drift ratio and the gravity shear stress on the 2002) Subassembly with stirrups . RC edge with stud-rails . Drift Ratio at Punching 0.07 critical section. Alternatively, calculations Best-Fit Line for Interior PT interior without shear reinf. . (Best-Fit Line) Connections can be made to show that the connection is 0.06 with Shear Reinforcement plus one σRes capable of sustaining the drift associated with 0.05 the design displacement without punching. 0.04 The relationship between gravity shear ratio, 0.03 (Best-Fit Line) minus one σRes lateral drift ratio, and punching failure in ACI 0.02 318-05, as well as a best-fit line for test data Best-Fit Line for Interior Connections without Qaisrani 0.01 Shear Reinforcement derived from tests of isolated RC slab-column ACI 318-05 Limit connections without shear reinforcement, are 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 depicted in Figure 2(a). Test results indicate Gravity Shear Ratio (Vg /φVc), where Vc = (1/3) f'c1/2bod PT connections without 0.09 that the lateral drift ratio at punching . shear reinforcement (Kang) Trongtham et al. ('77) - Int. . Qaisrani ('93) - Int. . 0.08 σRes : Stadard Deviation of the Residuals decreases as the gravity shear ratio increases, around the Regression Line Pimanmas ('04) - Int. . . Trongtham ('77) - Ext. Drift Ratio at Punching . Shatila ('87) - Ext. and that the relationship in ACI 318-05 is 0.07 Foutch et al. ('90) - Ext. . Martinez ('93) - Ext. . close to a lower bound estimate of the drift 0.06 Best-Fit Line for Martinez ('93) - Corner . PT without Shear capacity at punching failure for all gravity 0.05 Reinforcement (Best-Fit Line) plus one σRes shear stress ratios for the connection type 0.04 (Best-Fit Line) minus one σRes tested (only 4/76 tests fall below the ACI 0.03 relation). It is noted that relatively little data 0.02 exist for gravity shear ratios greater than 0.6; Best-Fit Line for PT Subjected to however, for such large ratios, the new ACI 0.01 Reversed Cyclic Loading ACI 318-05 Limit provision requires shear reinforcement unless 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 the drift is less than 0.005. Gravity Shear Ratio (Vg /φVc), where Vc = (0.29f'c1/2+0.3fpc)bod Use of shear reinforcement at slab-column connections has become a relatively common way to increase the punching shear capacity without increasing the effective depth of the slab (e.g., providing drop panels). Stirrup placement can be cumbersome; therefore, alternatives such as stud-rails (Megally and Ghali) and shear-bands (Pilakoutas and Ioannou), have been developed and shown to be effective. Results plotted in Figure 2(b) for connections with shear reinforcement indicate substantial scatter, with drift ratios at punching ranging from roughly 0.035 to 0.075 for a gravity stress ratio of approximately 0.3, and that relatively sparse data exist for gravity stress ratios greater than approximately 0.4. Robertson et al. (2002) assessed the relationship between the lateral drift ratio at punching and gravity shear ratio for isolated connections with shear (stud-rail) reinforcement and recommended the relationship shown in Figures 2(a) and 2(b). The relationship recommended by Robertson et al. (2002) suggests that slab-column connections with shear stud-rails have roughly twice the drift capacity at punching for a given gravity shear stress ratio as connections without shear reinforcement (for Vg/φVc between 0.2 and 0.6). The existing database for post-tensioned connections is limited to three isolated slab- column interior connections tested by Qaisrani (Figure 2(b)). Results from these tests suggest that post-tensioned (PT) slab-column frames can sustain higher lateral drift ratios prior to punching than conventionally-reinforced slabs without shear reinforcement. The higher drift ratios may be in-part due to the larger span-to-thickness ratios (l1/h) used in PT slab-column construction relative to reinforced concrete (RC) construction (i.e., ~25 for RC versus ~40 for PT, Kang and Wallace 2005), as well as the increase of the shear strength of the slab-column critical section due to the in-plane compression forces (fpc) generated by the PT (generally 1.03 to 1.38 MPa; 150 to 200 psi). The impact of the in-plane compression on the drift capacity at punching can be assessed using Figure 2(a) with a modified nominal shear strength (i.e., Equation (11-36) of ACI 318-05), whereas the influence of the span-to-thickness ratio is addressed later in this paper. Review of Prior Experimental Research The influence of the direct gravity shear stress on the lateral-load ductility of slab- column connections has long been recognized (Hawkins et al.). A review of the relationship between punching failure and lateral drift capacity as influenced by the gravity shear stress ratio for reinforced concrete slab-column connections and frames, with and without post-tensioning reinforcement, is presented in the following subsections. Reinforced Concrete Slab-Column Connections Pan and Moehle, and Moehle reviewed test results for 23 isolated, reinforced concrete slab-column interior connections without shear reinforcement to study the influence of the direct gravity shear stress on lateral-load ductility. This database was extended by: (1) Dilger and Brown, Luo and Durrani, Hueste and Wight, and Robertson et al. (2002, 2003) to add results from 18 isolated, reinforced concrete slab-column interior connections tested without shear reinforcement, (2) Robertson and Durrani to add results for three interior connections based on tests on slab-column subassemblies consisting of one interior and two exterior connections, and (3) Hwang and Moehle to add results for a nine-panel frame subjected to biaxial cyclic lateral drift. For the test by Hwang and Moehle, a single point is plotted for a representative gravity shear ratio of 0.28 (for an interior connection) relative to the drift at a peak lateral load (4%), given that punching was first observed to occur at the interior connections. Based on the review of the data plotted in Figure 2(a), a clear trend of decreasing drift at punching for increasing gravity shear ratios (Vg/φVc) is noted, with φ is 1.0 and using as- measured material properties. Trends in the data from the additional studies reported in this paper for isolated, RC connections are consistent with the prior observations. The database for reversed-cyclic tests of reinforced concrete exterior connections without shear reinforcement is effectively limited to the four, isolated connections subjected to reversed, cyclic loading tested by Megally. Although test results are available for some subassembly tests, these results are not included because torsional stirrups were provided (Robertson and Durrani) or insufficient information was collected to assess behavior for individual connections (Hwang and Moehle). Although limited data are available for reversed-cyclic tests of reinforced concrete exterior connections without shear reinforcement, results plotted in Figure 2(a) for four specimens indicate that the trend for interior connections also applies to exterior connections. Test results for isolated, reinforced concrete slab-column connections with shear reinforcement (Figure 2(b)) were assembled by Megally and Ghali, and Robertson et al. (2002) to study the influence of gravity shear ratio (Vg/φVc) on punching failures. The database includes 21 interior connections with stirrups or stud-rails and one multiple-connection specimen with stirrups (Robertson and Durrani). Trends noted in Figure 2(b) indicate that isolated connections with shear reinforcement tested under quasi-static reversed cyclic loads achieved significantly larger drift ratios than the isolated connections tested without shear reinforcement. As well, it is noted that the drift capacity for specimens with stud-rails is approximately 35% higher then those without stirrups (for Vg/φVc between 0.15 and 0.50). Post-Tensioned Slab-Column Connections For post-tensioned slab-column connections, the database of available tests (Figure 2(c)) includes eight interior, nine exterior, and two corner connections without shear reinforcement. These studies include specimens without shear reinforcement subjected to monotonic (4), repeated (7) and reversed cyclic (8) lateral loading. The gravity shear force on some of the connections was increased at specific times during the test for 15 of the 19 test specimens, versus being held constant for the duration of the test; therefore, only the gravity shear stress ratio at punching is reported by Kang. For post-tensioned connections, Vc is calculated using the provisions of ACI 318-05 Section 126.96.36.199. An overview of each test program and a detailed assessment of drift capacities at punching for each test are provided by Kang. Shake Table Studies of RC and PT Slab-Column Systems Relatively few studies of the dynamic responses of flat plate systems have been conducted (Moehle and Diebold, Hayes et al., and Kang and Wallace 2005). Of these studies, the specimens tested by Moehle and Diebold and Hayes et al. included perimeter beams, and punching failures at individual interior connections were not assessed. Kang and Wallace (2005) subjected the two, approximately one-third scale, two by two bay, two-story specimens to earthquake table motions. The slab span-to-thickness ratios (l1/h) are 23.1 (RC) and 37.3 (PT) and the gravity shear ratios (Vg/φVc) for a design strength of f’c = 28 MPa (4 ksi) for the interior connections were 0.33 and 0.44 for the RC and PT slabs, respectively; where φ = 0.75. Shear reinforcement, in the form of stud-rails, was used to increase the nominal shear strength of the slab-column connections. The specimens were subjected to several runs of uniaxial shaking using the CHY087W record from the 21 September 1999 Chi Chi Taiwan earthquake, with the intensity of shaking increased for each subsequent run. Results are presented in detail elsewhere (Kang and Wallace 2005) for both the RC and PT specimens. More detailed information on the tests is provided by Kang. Punching Failure – Shake Table Tests Relationships for drift capacity at punching versus gravity shear ratio for individual connections of the specimens were assessed using a variety of approaches (Kang and Wallace 2006, Kang). For the individual connections, it was possible to assess punching by examining the relationship between slab curvature and column curvature, where slab and column curvatures were calculated as the difference between either two rebar strain gauge readings or two average strain readings from displacement gauges obtained on opposite sides of a column or a slab, divided by the distance between the gauges. Since yield of column longitudinal reinforcement did not occur other than at the base of the first story, a drop in the column curvature (or moment) for increasing slab curvatures indicates a drop in the unbalanced moment being transferred to the column (i.e., punching). However, in some cases, insufficient quality data existed to reliably determine these relationships. In such cases, punching was assessed by examining the story shear versus inter-story drift relations. For the RC specimen, both approaches were used (for most connections), whereas for the PT specimen, only the latter approach was used. Mean Drift Ratio [%] Mean Drift Ratio [%] -4 -3 -2 -1 0 1 2 3 4 -4 -3 -2 -1 0 1 2 3 4 500 Peak t= 12.68sec t= 12.72sec t= 11.13sec t= 11.08sec Base Shear; B.Speak 400 B.Speak 300 0.60(B.Speak - B.Sres) 0.65(B.Speak - B.Sres) 200 B.Sres B.Sres Base Shear [kN] 100 0 -100 -200 B.Sres B.Sres True Hinges at True Hinges at All Connections All Connections -300 (B.Sres)/2 (B.Sres)/2 -400 (B.Sres)/2 (B.Sres)/2 -500 (a) RC Specimen (b) PT Specimen -80 -60 -40 -20 0 20 40 60 80 -80 -60 -40 -20 0 20 40 60 80 Top Displacement Relative to Footing [mm] Top Displacement Relative to Footing [mm] * B.Sres; Residual base shear of the frame, given that all the connections are perfectly hinged. Figure 3. Base shear versus mean drift ratio. The drift levels at punching for the connections of the test specimens were determined using two approaches as: (1) the average of the inter-story drift ratios for the stories above and below a connection, and (2) the average of slab rotations on either side of the connection (Figure 4). For the first approach, results are determined from the measured story displacements (e.g., Figure 3), whereas for the second approach, slab rotation (θrot) on either side of a connection was calculated as the sum of the slab elastic (θy) and plastic (θpl) rotations. Elastic rotations were computed based on the calculated slab yield curvature (φy) and stiffness (My/φy) and an assumed inflection point at slab mid-span, whereas plastic rotations were determined by integrating average slab plastic curvatures determined from sensors (LVDTs) mounted on the slab adjacent to the slab-column connections. The displacement readings for each sensor were divided by the sensor gauge length to obtain average strain, and the average curvature was obtained by dividing the average strain readings for sensors on the top and bottom faces of the slab by the distance between the sensors. Results obtained using the two approaches were reasonably close, as shown in Figure 4. Additional details concerning the tests and the data reduction are provided by Kang and Wallace 2005, 2006 and Kang. 0.06 0.06 E C W FL2 RC-FL1SE (Positive RC-FL2NE 0.05 FL1 drift) (Positive 0.05 Slab Rotation at Punching or Drift Ratio at Punching drift) 0.04 N-Frame 0.04 RC-FL1SW t2 t2 (Negative RC-FL2NC t2 t2 RC-FL1NC drift) t1 0.03 t2 t1 0.03 t1 RC-FL2NW t1 t1 t2 (Negative RC-FL1NW RC-FL1NE t1 t2 (Negative t1 drift) 0.02 (Positive t2 0.02 drift) drift) t1 2nd Story Drift Ratio Mean Drift Ratio (at t2 = 12.72 sec) (at t2 = 12.72 sec) 0.01 2nd Story Drift Ratio 0.01 t1= 12.68 sec Mean Drift Ratio (at t1 = 12.68 sec) (at t1 = 12.68 sec) t2= 12.72 sec 0 0 Individual Connections Figure 4. Slab rotation capacity at punching and drift ratio at punching (RC specimen). Drift Capacity at Punching Versus Gravity Shear Ratio Relationships for drift capacity at punching versus gravity shear ratio for slab-column specimens have been derived for reinforced concrete specimens without (e.g., Pan and Moehle) and with stud-rails (Robertson et al., 2002). The results obtained for the shake table tests described herein are compared to results assembled from existing tests of reinforced concrete or post-tensioned slab-column connections (Figures 2 and 5), with and without shear reinforcement, to assess whether existing trends adequately represent the results for the dynamic tests of the RC and PT specimens with shear reinforcement. The data plotted are based on actual material properties and for a capacity reduction factor φ = 1. For RC connections without shear reinforcement (Figure 5), a very clear trend exists, with a drop in the drift capacity at punching as the gravity shear ratio increases. Results for the exterior connections of the RC shake table specimen (Figure 5), which included shear reinforcement, have approximately the same average value and range as prior tests of the interior connections without shear reinforcement, whereas the mean and range for the RC shake table specimen interior connections (Figure 5), which included shear reinforcement, are slightly lower than reported for prior tests. Results for tests of RC slab-column connections with shear reinforcement are plotted in Figure 2(b) and indicate that the drift capacities of isolated specimens tested under quasi-static, cyclic displacement histories are substantially greater where shear reinforcement is used (e.g., Dilger and Brown). However, drift ratios at punching derived from the shake table tests described in this paper are substantially less than those obtained in the prior test programs for quasi-static loadings. Potential reasons for these discrepancies are discussed elsewhere (Kang and Wallace 2006, Kang). Although the drift ratios at punching derived for the RC and PT shake table specimens with shear reinforcement are close to those obtained for the prior test results of the RC and PT connections without shear reinforcement, respectively, the test results indicate that use of slab shear reinforcement substantially reduces the extent of damage (Kang and Wallace 2005, Kang), and in particular, prevents the “dropping” of the slab observed in the test specimens where shear reinforcement is not provided. In addition, the level of strength degradation for the shear- reinforced slab-column connections does not appear to be as drastic as it is for prior tests, particularly for the PT specimen because of the contribution of the unbonded post-tensioning reinforcement to the moment capacity. Based on the shake table test results reported (e.g., Figure 5), the new ACI 318 provisions adopted for “Frame members not proportioned to resist forces induced by earthquake motions” to address the issue of punching of slab-column connections, would not appear to prevent some strength degradation for cases where shear reinforcement is required. However, the degree of strength degradation and damage at the slab-column connections is expected to be substantially reduced relative to expectations for connections without shear reinforcement. 0.09 Experimental Data (θdrift) . 0.08 Analytical Data (θu,model = θyµθ) . Avg .Slab Rotation Capacity (Int.) Best-Fit Line of Avg .Slab Rotation Capacity (Ext.) 0.07 Drift Ratio at Punching Analytical Data Max .Inter-story Ratio at Punching . Min Inter-story Ratio at Punching 0.06 Range of Slab Rotations 0.05 at Punching (RC-Interior) Best-Fit Line of 0.04 Experimental Data 0.03 0.02 Range of Slab Rotations 0.01 at Punching (RC-Exterior) ACI 318-05 Limit 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Gravity Shear Ratio (Vg /φVc), where Vc = (1/3)(f'c)1/2bod Figure 5. Prior data for RC interior connections and test results for RC shake table specimen. Drift Capacity Model and Shear Strength Degrading Model According to the new ACI 318-05 Section 21.11.5 provisions, shear reinforcement is not required if the connection design for the design shear and unbalanced moment transferred under the design displacement satisfies Section 11.12.6 (i.e., no stress-induced failure). As written, the provision does not address the potential shear-strength degradation that occurs for drift-induced punching failures; therefore, punching failures may still occur. To address this issue, available models for shear strength degradation are reviewed and the slab-column test data are used to develop appropriate relationships for both reinforced concrete and post-tensioned concrete slab- column connections. In 1996, Moehle proposed extending the use of a shear strength degrading model to the evaluation of the drift capacity at punching of slab-column connections. In the approach proposed by Moehle, the story drift is assumed equal to the slab rotation, and the slab rotation is determined as θu,model = θy(µθ), where the yield rotation θy is approximated as φy(l1)/6 ≈ l1/(2400h), and µθ is determined from the gravity shear ratio using the shear strength degrading model for the RC bridge columns proposed by Aschheim and Moehle. The model captures the trend observed for tests of 23 isolated RC interior connections and 3 isolated PT interior connections quite well (Moehle). These findings are re-examined based on the availability of new data, as well as the availability of new shear strength degradation models. 0.09 σRes : Stadard Deviation of the Residuals around the Regression Line PT Model (l1/h = 40). 0.08 (Experimental Data) PT Model minus σRes Drift Capacity at Punching Vn Vg RC Model (l1/h = 25) k= 0.07 Vc φVc RC Model minus σRes µδ,1 0.06 1 1 Best-fit Line for Experimental Data of 0.8 0.8 0.05 "PT" Connections without Shear Reinforcement 0.6 m 0.6 0.04 0.4 0.4 0.03 0.2 0.2 0.02 0 0 0.01 0 1 2 3 4 5 ACI 318-05 Limit µθ Ductility 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Gravity Shear Ratio (Vg /φVc) Figure 6. Shear strength degrading model. Figure 7. Drift capacity models for slab-column connections. The shear strength degrading model proposed by Aschheim and Moehle is applied to the slab-column connections. The model uses two parameters, the displacement ductility at which the shear strength begins to degrade (µδ,1) and the rate at which the shear strength degrades (m). Values for these parameters were determined from the existing test data using a least-squares approach, resulting in µδ,1 equal to 1 and m equal to 1/3 for the RC interior connections without shear reinforcement (Figure 6). The model parameters determined for the RC slab-column connections without shear reinforcement are quite similar to those (µδ,1 = 1, m = 1/3.5) used for the model for the RC bridge columns proposed by Aschheim and Moehle, indicating use of the expanded database (from the 23 specimens used by Moehle to the 45 specimens expanded in this paper) and the new shear strength degrading model do not impact significantly the overall trends previously reported. For the RC specimens with shear reinforcement, application of the model to a reduced data set (l1/h > 15) indicated substantial scatter; therefore, reliable results could not be obtained with the model. For PT connections without shear reinforcement, cyclic test results are limited to only eight specimens; however, analysis results for the limited data set indicate the strength degradation trends are similar to those for the RC specimens without shear reinforcement. Therefore, at this time, the relationship for RC specimens is applied to both RC and PT connections. Therefore, for both RC and PT connections, the impact of shear strength degradation for drift-induced punching can be assessed using the proposed model. Using the proposed shear strength degrading model, along with typical slab span-to- thickness ratios for RC (l1/h = 25) and PT (l1/h = 40) construction, alternative relationships for assessing the need for shear reinforcement at slab-column connections for RC and PT construction are developed (e.g., similar to the relation used in ACI 318-05). The (l1/h) ratios and Vg/φVc ratios are used to estimate θy and µθ, respectively, and θu,model = θy(µθ), as discussed previously. Finally, the story drift ratio is assumed to be equal to the story rotation. Results obtained using this approach are presented in Figure 7 and indicate that drift capacities at punching for PT connections are substantially larger than for RC connections, primarily due to greater span-to-thickness ratios for PT connections. Results presented allow shear strength degradation to be incorporated, and also address the differences between RC and PT systems. These findings are useful for both design of new construction (e.g., assessing the potential for punching and the need for shear reinforcement for non-participating systems for deformation compatibility), as well as evaluation of slab-column connections for existing construction (e.g., Kang, Wallace, and Elwood 2006). Conclusions A detailed review of the influence of gravity loads on lateral drift levels at punching were conducted for the two shake table test specimens, as well as for prior tests of 95 reinforced and post-tensioned concrete connections. The shake table test results indicate substantially less drift ratio at punching than for prior tests of isolated connections with shear reinforcement, possibly due to the lower strain demands on the shear reinforcement and the rotation of the slab-column connection due to the apparent loss of interface shear capacity. However, the degree of damage and strength degradation expected for connections with shear reinforcement is substantially less than expected for connections without shear reinforcement. The drift capacity model of the slab-column connections proposed by Moehle was re- examined based on the existing data and available shear strength degrading models. The revised model addresses the impact of shear strength degradation on drift-induced punching and also provides an approach to assess the need for shear reinforcement that differentiates between RC and PT connections; both of these issues are not addressed in ACI 318-05. References ACI 318 Committee, 2002; 2005. Building Code Requirements for Structural Concrete and Commentary (ACI 318-02; ACI 318-05), Farmington Hills. Aschheim, M., and J. P. Moehle, 1992. Shear strength and deformability of RC bridge columns subjected to inelastic cyclic displacements, EERC Report No. UCB/EERC 92/04, Berkeley. Dilger. W. H., and S. J. Brown, 1994. Earthquake resistance of slab column connections, Proceedings, Canadian Society of Civil Engineering Conference, V. 2, Winnipeg, Canada, 388-397. Hawkins, N. M., and D. Mitchell, 1979. Progressive collapse of flat-plate structure, ACI Structural Journal, 76 (7), 775-800. Hawkins, N. M., Mitchell, D., and M. S. Sheu, 1974. Cyclic behavior of six reinforced concrete slab- column specimens transferring moment and shear, Progress Report 1973-74 on NSF Project GI- 38717, Section II, University of Washington, Seattle. Hwang, S. J., and J. P. Moehle, 2000. Vertical and lateral load tests of nine-panel flat-plate frame, ACI Structural Journal, 97 (1), 193-203. Hayes, J. R., Foutch, D. A., and S. L. Wood, 1999. Influence viscoelastic dampers on the seismic response of a lightly reinforced concrete flat slab structure, Earthquake Spectra, 15 (4), 681-710. Hueste, M. B. D., and J. K. Wight, 1999. Nonlinear punching shear failure model for interior slab-column connections, Journal of Structural Engineering, ASCE, 125 (9), 997-1008. Kang, T. H.-K. 2004. Shake table tests and analytical studies of reinforced and post-tensioned concrete flat plate frames, Ph.D. Thesis, University of California, Los Angeles. Kang, T. H.-K., and J. W. Wallace, 2005. Dynamic responses of flat plate systems with shear reinforcement, ACI Structural Journal, 102 (5), 763-773. Kang, T. H.-K., and J. W. Wallace, 2006. Punching of reinforced and post-tensioned concrete slab-column connections, ACI Structural Journal, In-press. Kang, T. H.-K., Wallace. J. W., and K. J. Elwood, 2006. Nonlinear modeling of flat plate systems, Journal of Structural Engineering, ASCE (Submitted for publication). Luo, Y. H., and A. J. Durrani, 1995. Equivalent beam model for flat-slab buildings – part I: interior connections, ACI Structural Journal, 92 (1), 115-124. Megally, S. H, 1998. Punching shear resistance of concrete slabs to gravity and earthquake forces, Ph.D. Thesis, University of Calgary, Calgary, Canada. Megally, S. H., and A. Ghali, 1994. Design considerations for slab-column connections in seismic zones, ACI Structural Journal, 91 (30), 303-314. Moehle, J. P., 1996. Seismic design considerations for flat-plate construction, ACI SP-162: Mete A. Sozen Symposium, Farmington Hills. Moehle, J.P., and J. W. Diebold, 1984. Experimental study of the seismic response of a two-story flat- plate structure, EERC Report No. UCB/EERC 84/08, Berkeley. Pan, A. D., and J. P. Moehle, 1989. Lateral displacement ductility of reinforced concrete flat plates, ACI Structural Journal, 86 (3), 250-258. Pilakoutas, K, and C. Ioannou, 2000. Verification of a novel punching shear reinforcement system of flat slabs, Proceedings, International Workshop on Punching Shear Capacity of RC Slabs, TRITA- BKN Bulletin 57, Royal Institute of Technology, Stockholm, Sweden. Robertson, I. N., and A. J. Durrani, 1990. Seismic response of connections in indeterminate flat-slab subassemblies, Report No.41, Rice University, Houston. Robertson, I. N., Kawai, T., Lee, J., and B. Enomoto, 2002. Cyclic testing of slab-column connections with shear reinforcement, ACI Structural Journal, 99 (5), 605-613. Robertson, I. N., and G. P. Johnson, 2003. Non-ductile slab-column connections subjected to cyclic lateral loading, Proceedings, 13WCEE, Vancouver, Canada (Paper # 143). Qaisrani, A. N. 1993. Interior post-tensioned flat-plate connections subjected to vertical and biaxial loading, Ph.D. Thesis, University of California, Berkeley.
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