Drift Capacity Models and Shear Strength Degrading Models for

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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 11.12.2.2. 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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