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SP-297—5 5.1 Modeling Parameters for Reinforced Concrete Slab-Column Connections Amy C. Hufnagel, YeongAe Heo, and Thomas H.-K. Kang Synopsis: Over the past few decades, flat plate concrete building systems have been widely adopted in the United States and other countries because it enables not only to save construction time and cost but also to make better use of interior spaces. However, it has been observed that such buildings whose columns are cast into the concrete flat plate are highly vulnerable to collapse. Such integrated slab-column frames have suffered severe damage or completely collapsed during the past earthquake events. The main failure mode of these structures is punching shear. Although a general guideline for seismic design and a seismic rehabilitation design guideline for both existing and new reinforced concrete frame structures are specified in ACI 318 and ACI 369R, respectively, many uncertainties have still resided in the modeling parameters to accurately predict seismic behavior of the flat plate concrete frame structures. Therefore, a new chart of allowable plastic rotation values for correlating values of gravity shear ratio is presented in this study with the objective of updating the modeling parameters of ACI 369R. The major issues which lead to errors in evaluating flat plate concrete structural behavior under seismic loads are thoroughly investigated. Also, dominant parameters from previous and recent experiments on integrated slab-column connections subjected to seismic loading are utilized to assess the estimation of seismic performance of the flat plate system based on ACI 369R. Consequently, although it is confirmed that there is a trend in correlation between the allowable plastic rotation and gravity shear ratio while almost no correlation is observed with reinforcement ratio, more experimental data are necessary to enhance this correlation study. It is also noticed that the current ACI 369 recommendations for allowable plastic rotation values for slab-column connection under seismic and gravity loading are unconservative. Keywords: reinforced concrete; slab-column connections; modeling; plastic rotation; seismic; evaluation.

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Page 1: Modeling Parameters for Reinforced Concrete Slab-Column ...€¦ · Modeling Parameters for Reinforced Concrete Slab-Column Connections Amy C. Hufnagel, YeongAe Heo, and Thomas H.-K

SP-297—5

5.1

Modeling Parameters for Reinforced Concrete Slab-Column Connections

Amy C. Hufnagel, YeongAe Heo, and Thomas H.-K. Kang Synopsis: Over the past few decades, flat plate concrete building systems have been widely adopted in the United States and other countries because it enables not only to save construction time and cost but also to make better use of interior spaces. However, it has been observed that such buildings whose columns are cast into the concrete flat plate are highly vulnerable to collapse. Such integrated slab-column frames have suffered severe damage or completely collapsed during the past earthquake events. The main failure mode of these structures is punching shear. Although a general guideline for seismic design and a seismic rehabilitation design guideline for both existing and new reinforced concrete frame structures are specified in ACI 318 and ACI 369R, respectively, many uncertainties have still resided in the modeling parameters to accurately predict seismic behavior of the flat plate concrete frame structures. Therefore, a new chart of allowable plastic rotation values for correlating values of gravity shear ratio is presented in this study with the objective of updating the modeling parameters of ACI 369R. The major issues which lead to errors in evaluating flat plate concrete structural behavior under seismic loads are thoroughly investigated. Also, dominant parameters from previous and recent experiments on integrated slab-column connections subjected to seismic loading are utilized to assess the estimation of seismic performance of the flat plate system based on ACI 369R. Consequently, although it is confirmed that there is a trend in correlation between the allowable plastic rotation and gravity shear ratio while almost no correlation is observed with reinforcement ratio, more experimental data are necessary to enhance this correlation study. It is also noticed that the current ACI 369 recommendations for allowable plastic rotation values for slab-column connection under seismic and gravity loading are unconservative. Keywords: reinforced concrete; slab-column connections; modeling; plastic rotation; seismic; evaluation.

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5.2

Amy C. Hufnagel is a Structural Engineer in the Walter P. Moore, Houston. She received her BS and MS from the University of Oklahoma, Norman. Her research interests include the design and analysis of reinforced and prestressed concrete structures. YeongAe Heo, PhD, is a Post-doctoral Researcher in the Department of Architecture and Architectural Engineering, Seoul National University, Korea. She received her BS and MS from Dong-A University, Korea, and her PhD from the University of California at Davis. Her research interests include the seismic evaluation and nonlinear dynamic modeling of reinforced concrete structures. Thomas H.-K. Kang, PhD, PE, FACI, FPTI, is an Associate Professor in the Department of Architecture and Architectural Engineering, Seoul National University, Korea. He received his BS from Seoul National University, Korea, his MS from Michigan State University, and his PhD from the University of California at Los Angeles. His research interests include the design and behavior of reinforced and prestressed concrete structures.

INTRODUCTION

Flat plate concrete building systems consist of monolithically cast slab and column frames, and are widely used with and without shear walls in the United States and other countries for several advantages, including economy and building efficiency. This setup reduces story heights, which allows for lower costs for building material, cladding, electrical and mechanical ductwork, and annual heating and air-conditioning. This lowers both dead loads and lateral loads on the structure. Despite these many advantages, there are also many issues such as complexity in modeling and punching shear failure with flat plate building systems.

Because of the many benefits they provide, there is high motivation for the implementation of flat plate building systems in every type of environment and loading situation. This includes areas of moderate to high seismicity, despite the additional risks of increased lateral loads during earthquake events. Over the years, this has resulted in a high percentage of flat plate buildings that have suffered large amounts of damage or even completely collapsed during past seismic events, like the 1971 San Fernando earthquake, which initially called attention to the weaknesses in flat plate building design. During the 1985 Mexico City earthquake, many non-ductile flat plate slabs suffered severe damage caused by punching shear failure (Figure 1). During this event, 91 buildings completely collapsed, while 44 also suffered severe damage (Robertson and Johnson, 2006). This triggered increased scrutiny into the behavior and the code design methods for these structures in both the United States and Mexico. One source of weakness in these buildings is the slab-column connections and the possibility of punching shear failure, which occurs when the slab area around the column fails and collapses. This failure is caused by excessive shear stress applied to the connection, as well as poor design for lateral loads, including non-ductile connections. It is important that these connections withstand certain levels of lateral drift, while maintaining their gravity load carrying capacity during an earthquake. There is a need to better understand the behavior of slab-column connections in flat plate structures in order to improve design methods, as well as to suggest methods for investigation and retrofit of older buildings in seismic regions.

Figure 1 — Progressive collapse of flat plate buildings in Virginia and Mexico City.

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The purposes of this research are: 1) to investigate several issues with flat plate concrete structures in order to better understand their behavior under gravity and lateral loads; 2) to compile past research and experiments completed on slab-column connections in which specimens were subjected to seismic loading, and record relevant information in a database; and 3) to examine the existing ACI 369 modeling parameters and provide a new chart of modeling parameters of allowable plastic rotation values for correlating values of gravity shear ratio. The research consists of a review of previous large-scale experiments, as well as a series of analyses on the data contained therein, and is concluded by presenting experimentally suggested modeling parameters of allowable plastic rotation for slab-column connections. This study is applicable to both pure flat plate systems and flat plate systems with walls and/or moment frames, though slab-column connections in buildings with walls and/or frames may not be modeled. In such cases, the acceptance criteria of plastic rotation become very important, which will be investigated in depth in the next study of Slab-Column Connections Task Group of ACI Committee 369.

ISSUES IN FLAT PLATE DESIGN AND ACI 369R-11

Complexity in Modeling

Despite the many advantages for flat plate design and construction, the nonlinear behavior of these structures is difficult to predict (Farhey et al., 1993). The complexity of the nonlinear behavior of slab-column connections is the result of several contributing factors. The method of load transfer between the slab and column is complicated and difficult to calculate, because of the combination of torsional and flexural moments and the three-dimensional stress distribution as well as shear forces concentrated on the connection. Several analytical modeling methods have been developed for slab-column frames (e.g., Kang et al., 2009; see Fig. C4.2 of ACI 369R-11). Modeling is especially important in gaining a higher understanding of the complicated behavior of structural components, like slab-column connections. Punching Shear Failure

A major issue in flat plate concrete structures is the possibility of punching shear failure at the slab-column

connections, especially when subjected to cyclic lateral loading combined with gravity loading. This is a result of several contributing factors, and is specifically problematic for those built in the 1950s and 1960s. These older buildings were designed with non-ductile connections to resist gravity loads only, without shear walls or frames to handle the applied lateral loads. The slab-column connection is responsible for transferring the unbalanced moment and the shear forces. If shear stress due to these applied forces and moments surpass the shear capacity of the slab at the face of the column, punching shear failure is a risk.

Another factor contributing to punching shear failure in the design of these older buildings is the lack of continuous bottom reinforcement through the interior columns, which prevents the rebar from developing ultimate strength at the location at the face of the column by acting as “a membrane to suspend the slab following failure of the concrete” (Moehle et al., 1988). This lack of continuity in the connection makes the structure more vulnerable and can lead to sudden punching shear failure or possibly a progressive collapse of the entire building. This collapse may be the result of excessive lateral loading or the redistribution of gravity loads following lateral deformations. When punching shear failure initially takes place, the slab drops and collapses onto the floor below. This, in turn, overloads the floor below, eventually leading to a progressive collapse of the entire building. Punching shear failure can happen for several reasons, including poor construction practices or premature removal of shoring, like the collapse of the Skyline Plaza in Bailey’s Crossroads, Virginia (Figure 1); however, the main focus of this research is the punching shear failure of flat plate systems subjected to lateral loading during seismic events. Even in flat plate buildings that are designed with shear walls, the slab-column connections still need to have the capability of maintaining gravity load carrying capacity under lateral load deformation. In order to prevent punching failure, the connections must be capable of exhibiting ductility in the inelastic range, while still carrying the design loads (Pan and Moehle, 1989). Non-ductile detailing in these connections does not provide enough anchorage between the reinforcement and the concrete at the interior columns, which can cause a sudden brittle pull out and failure (Dovich and Wight, 1996).

As such, several contributing factors aside from overly intensive ground motion may have led to the failure of so many existing flat plate structures. Throughout the years, it is common for the function of certain buildings to change. When these changes call for building modifications, this can sometimes cause an increase in gravity loading that was not considered in the original design (Tian et al., 2008). Any building modifications that cause an increase

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in loading must be accounted for by checking the capacity of the existing structure prior to use. Another source of weakness is that the connections are assumed to take the majority of the shear resistance from the concrete, but damage to the slab during a seismic event may reduce connection strength and shear capacity, thereby significantly overestimating the shear strength of the connection. ACI 369R-11

ACI 369R-11 is the American Concrete Institute’s Guide for Seismic Rehabilitation of Existing Concrete Frame Buildings and Commentary. The guide was based on ASCE/SEI 41-06 and is intended to be used in combination with the code in analyzing the behavior of existing and new concrete elements in buildings subjected to seismic loading. The purpose of ACI 369R-11 is to provide recommendations for acceptance criteria and modeling parameters that are necessary for the linear and nonlinear analysis of concrete components in the seismic rehabilitation design process. This research focuses on Chapter 4, Section 4.4 of the guide, which discusses slab-column moment frames and the analytical processes used in assessment. Section 4.1.3 of ACI 369R-11 defines these frames as monolithically cast concrete structures with slabs, columns, and connections as the main structural framing components, and with non-prestressed or prestressed reinforcement to serve as the primary reinforcement in the slab. General considerations outlined in Section 4.4.1 of ACI 369R-11 state that stiffness, strength, and deformation capacity of the building components should all be represented in analytical models for these frames. This section also warns against the possibility of punching shear failure as a result of a combination of flexural, shear, and torsional transfer at the connections. Section 4.4.3 of ACI 369R-11 outlines the method for determining the flexural strength of a slab to resist moment resulting from lateral deformations using Eq. (1).

nCS gCSM M (1)

where MnCS is the nominal flexural strength of the column strip and MgCS is the column strip moment due to gravity

loads (ACI 369, 2011). This section goes on to describe the possibility of failure for slab-column connections under shear and moment transfer. These connections should be investigated, because of the combined action of torsion, flexure, and shear that all act in the slab at these locations. The current code gives recommendations for modeling parameters a and b in Table 4.9 of ACI 369R-11. These parameters are the allowable inelastic deformations for slab-column frames. In the table, these parameters vary based on the continuity of bottom reinforcement through the interior columns, as well as on the gravity shear ratio. The table contains data for reinforced concrete and post-tensioned concrete slab-column connections; however, this portion of the research focuses solely on reinforced concrete components. Larger allowable deformations are permissible in the event that there is experimental data to support the use of alternative values. Otherwise, slab-column moment frame components that do not meet the acceptance criteria must be rehabilitated as per the Section 3.7 of ACI 369R-11. These suggested seismic rehabilitation methods include deficient component removal and replacement, or modification of the structure in order for the existing portions to meet the criteria.

REVIEW OF PREVIOUS EXPERIMENTS

Reinforced Concrete Slab-Column Connections

A major portion of the research consisted of a review of past studies on interior reinforced concrete slab-column connections subjected to combined lateral and gravity loading. This included individual interior connections, as well as two-bay frames with interior connections. Other qualifications for relevant specimens include absence of shear reinforcement in the slab in the form of either rebar reinforcement, like stirrups, shearbands or headed shear studs, or a shear capital or drop panel.

In these past experiments, reinforced concrete slab-column connections composed of a square or rectangular concrete slab with both an upper and lower column, most commonly measuring half a floor height each, were placed in a tested rig and lateral loading was applied. In most cases, the connections were loaded cyclically and uniaxially, in which a load was applied to one face at the top of the column up to a certain drift ratio, and then the process was reversed in the opposite direction, simulating loads from a seismic event. This uni-directional cycle is typically repeated at increasing levels of drift until failure of the connection. For specimens tested biaxially, force is applied

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5.5

to the column in two principal directions. The order and configuration of the load applications are discussed with each relevant specimen (Hufnagel, 2011).

The critical section perimeter of the interior connection (bo) was determined based on the information in the text or figure of the literature. The critical section perimeter affects the shear capacity of the concrete (Vo) at the connection, which is defined in ACI 369R-11 (and ACI 318-11) and typically determined using Eq. (2).

' '4 (psi) or 0.33 (MPa)o c o c oV f b d f b d (2)

where f’c is the compressive strength of the concrete and d is the effective depth. The shear capacity can then be

compared to the applied gravity shear (Vg) to determine the gravity shear ratio (Vg/Vo). The applied gravity shear was taken from the literature, and should be the value at the peak lateral load so as to determine the most extreme loading case. The gravity shear ratio is thought to significantly affect the overall strength and deformation capacity of the connection.

The top and bottom reinforcement ratios of the slabs were determined at the location at the face of the column using provided rebar layout diagrams for several different slab widths, including c2 + 3h, c2 + 5h, the column strip, and the full width of the slab, where c2 is the column dimension in the direction perpendicular to the lateral loading, and h is the thickness of the slab. The different widths were calculated by the provided dimensions, and the amount of steel was counted for each width. The reinforcement ratios were then calculated using the thickness of the slab.

The moment capacities (Mn) were calculated for the same slab widths as the reinforcement ratios discussed above. The total unbalanced moment capacity of an interior connection was calculated as a combination of the positive and negative moment capacities. The total unbalanced moment capacity for each slab width for the frame members with two exterior connections and one interior connection is doubled, because there are two additional contributing connections. Peak loading values were determined either from the literature or from provided hysteretic curves, and were used to calculate the unbalanced moment. Most of the specimens were tested cyclically in unaxial direction, so the calculations include both a positive and negative unbalanced moment.

Provided hysteretic curves for each specimen were analyzed to collect information on drift capacities. First a backbone curve was established to find the upper bounds of the testing cycles, making it easier to identify the location of the peak load, as well as the drift percentage at that load. Next the unbalanced moment capacities were plotted on the curve and drift percentages were recorded. Then the points at which the loads drop to 95%, 80%, and 20% of the peak loading were determined and plotted on the decreasing portion of the curve (see Figure 2). The corresponding drift values for the points were recorded. These specific values are important in determining the modeling parameter a, a value of plastic deformation from the yielding point, and modeling parameter b, a value of plastic deformation to the point of residual strength. Although not all of the tests were conducted to the point where the hysteretic curves provided information for all of these values, the lower bound values for b were obtained. Some of the specimens showed unreasonable unbalanced moment capacities possibly because of an improper testing setup or data reading, so this drift information could not be collected for those curves. For those specimens that were tested biaxially, the hysteretic curves for each testing direction were analyzed, and the vector drift data was used.

Figure 2 — Selected lateral load vs. drift curves for recently tested slab-column connections (ND4LL – Robertson

and Johnson, 2006; CO – Kang and Wallace, 2008).

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Punching Shear Capacity Each specimen is investigated so as to determine whether or not punching shear failure could be predicted. The

connections are analyzed using the eccentric shear stress model for a slab width of c2 + 5h, the center of the column strip, which should have the highest reinforcement ratio. The nominal moment of the slab over this width is currently the representative recommendation from ACI 369R as to the yield moment of the slab. This width should have the strength to transfer the unbalanced moment by flexure. If the applied shear stress exceeds the nominal shear stress capacity of the concrete, a brittle failure may take place; otherwise, a flexural failure or flexure yielding followed by drift-induced punching failure can be expected (Kang and Wallace, 2006). The eccentric shear stress model was used in order to compare the nominal shear capacity of each connection to the applied shear stresses [Eqs. (3) and (4)].

c uv v (3)

g v u ABu

o c

V M cv

b d J

(4)

where vc is the nominal shear stress capacity provided by the concrete as per ACI 318-11, vu

is the total applied shear stress, Vg is the applied gravity shear, v

is the factor to determine the portion of unbalanced moment transferred by shear, Mu

is the unbalanced moment (M+n_c+5h

+ M–n_c+5h was used for this research), cAB is the

distance between the centroid of the column critical section to the edge of the critical section, and Jc is the property

of the assumed critical section analogous to the polar moment of inertia. ACI 369 Modeling Parameters

From the information collected during the review of previous experiments, the data are analyzed to estimate the approximate value of allowable plastic rotation for each specimen. This includes the determination of the parameters a and b, which, as defined in ACI 369R, are used to measure deformation capacity in component load-deformation curves. These parameters are defined in Figure 3. Current specifications for these modeling parameters can be found in Table 4.9 in ACI 369R-11 (Table 1 of this paper).

Figure 3 — Generalized force-deformation relations for concrete elements or components (ACI 369R-11).

In this paper, the modeling parameters a and b are calculated using Eqs. (5) and (6), respectively; however, the method to determine the yield point should be discussed further in the ACI Committee 369.

0.95_ 5

Peak Mn c h

a

(5)

0.2_ 5

Peak Mn c h

b

(6)

where 0.95Peak and 0.2Peak are the drifts at a 5% drop from the peak (green dots in Figure 2) and at a 80% drop from the peak (purple dots in Figure 2), respectively, and

_ 5M

n c h

is the drift at which the lateral load corresponds to

the sum of M+n_c+5h

and M–n_c+5h during the ascending branch of the backbone curve (blue dots in Figure 2). Here,

M+n_c+5h

and M–n_c+5h are design flexural strengths of the c2 + 5h width for positive and negative bending,

respectively.

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In this paper, these parameters are compared to the reinforcement ratios (ρc+5h) for the width of c2 + 5h, as well as to the gravity shear ratios (Vg/Vo) in order to develop a chart for recommendations to ACI 369R-11.

Table 1 — Modeling parameters and numerical acceptance criteria for nonlinear procedures – Two-way slabs and slab-column connections (ACI 369R-11)

*Values between those listed in the table should be determined by linear interpolation. †Primary and secondary component demands should be within secondary component acceptance criteria where the full backbone curve is explicitly modeled, including strength degradation and residual strength, in accordance with Section 3.4.3.2 of ASCE/SEI 41-06. ‡Where more than Condition i occur for a given component, use the minimum value from Table 4.9 of ACI 369R-11. #Action should be treated as force-controlled

RESULTS FROM REVIEW OF PREVIOUS EXPERIMENTS

Summary of Results from Assessment of Data

A summary of the data recorded in the database during the literature review can be found in Table 2 for the specimens with and without continuous bottom reinforcement. The results for predicted punching shear failure can be found in Table 3. This table includes the values for nominal shear stress capacity (vc) and total applied shear stress (vu_c+5h) calculated as per Eq. (4) and using unbalanced moment values of (M+

n_c+5h + M–

n_c+5h) at an interior connection and M+

n_c+5h or M–

n_c+5h for an exterior connection depending on the direction of slab bending. The width of c2 + 5h was evaluated, because this width typically falls inside the column strip or close to the width of the column strip, and therefore has the highest amount of slab reinforcement. The stress applied at the column is transferred away from the joint as the area weakens, so the region closest to the column is the most crucial. These results do not take into consideration the presence or absence of continuous bottom reinforcement through the column. While many of these specimens seemed to exhibit enough strength to avoid stress-induced punching shear failure, the applied cyclic loading at higher drift levels resulted in drift-induced punching failure anyway, despite the presence of continuity in reinforcement (Kang and Wallace, 2006). While connections are not expected to withstand drift levels beyond a certain level, the maximum allowable inelastic drift needs to be quantified.

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Table 2 — Summary of database for specimens with and without continuous bottom reinforcement

Authors Specimen Loading d

(in.) bo

(in.) Failure Pattern

Vg/Vo Munb

(kip-ft) 0.95Peak

(%) + - + - + -

Pan and Moehle (1992)

: Interior

AP1 Biaxially Cyclic;

Applied to Column

4.1 59.4 Punching

0.37 39.1 36.1 1.6 1.8

AP3 0.18

59.7 56.8 3.6 3.4

AP4 70.1 59.0 3.7 2.5

Robertson and Durrani (1991)

: Frame

2C Cyclic; Applied to

Column 3.6 54.3

Flexure 0.2 99.8 95.3 4 4.3

7L Punching 0.4 63.0 66.0 1.7 1.7

Farhey et al. (1993)

: Interior

3 Cyclic; Applied to

Column 2.8

50.8 One-sided punching

0.2 13.3 13.3 3.7 2.6

4 44.5 0.2 11.1 11.1 2.9 2.6

Robertson et al. (2002) : Interior

1C Cyclic;

Applied to Column

3.7 39.4 Punching 0.15 42.8 37.6 3.5 3.1

Zee and Moehle (1984)

: Interior Interior

Cyclic; Applied to

Column 2.1 29.9 Punching 0.14 7.4 7.4 3.9 4.0

Wey and Durrani (1992)

: Interior SC0

Cyclic; Applied to

Column 3.8 55.1 Punching 0.05 0.06 45.7 45.0 3.6 4.0

Kang and Wallace (2008)

: Interior CO

Cyclic; Applied to

Column 5.1 60.6 Punching 0.3 76.7 60.5 2.9 2.0

Robertson and Johnson (2006)

: Interior†

ND1C

Cyclic; Applied to

Column 3.9 55.7

Flexure/ Punching

0.2 28.8 31.0 5.1 3.3

ND4LL Flexure/ Punching

0.3 31.7 32.5 3.2 3.1

ND5XL Punching 0.4 22.9 23.6 2.0 2.0

ND6HR Punching 0.3 41.3 43.5 3.1 3.2

ND7LR Flexure/ Punching

0.2 19.2 22.1 3.3 3.3

Tian et al. (2008)

: Interior†

L0.5 Cyclic Followed by Monotonic; Applied to

Column

5.0 83.9 Punching 0.2

95.9 99.6 1.6 1.8

LG0.5 90.7 89.2 1.2 1.2

LG1.0 121 117 1.2 1.2

Stark et al. (2005)

: Interior† C-63

Cyclic; Applied to

Column 3.5 61.9 Punching 0.1 30.8 27.7 1.8 2.4

Durrani et al. (1995)

: Frame† DNY_3

Cyclic; Applied to

Column 3.9 55.1 Flexure 0.22 51.6 46.5 3.2 3.5

Luo et al. (1994)

: Interior† II

Cyclic; Applied to

Column 3.9 55.1 Flexure 0.0 28.8 25.8 5.0 5.0

† = without continuous bottom reinforcement; + = positive drift direction; – = negative drift direction bo = perimeter of critical section; d= effective depth of section Vg = applied direct shear; Vo = concrete punching shear capacity [see Eq. (2)]; Munb = measured peak unbalanced moment; 0.95Peak = drift at a 5% drop from the peak; Conversion: 1 in. = 25.4 mm; 1 ft = 305 mm; 1 kip = 4.45 kN.

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5.9

Based on the data and the results in Table 3, the nominal shear stress capacity provided by the concrete (vc) appears to be quite conservative in terms of the stress-induced punching failure (that is, brittle punching shear failure with limited slab bar yielding and ductility); therefore, the nominal stress capacity of 4√f’c (psi) or 0.33√f’c (MPa) is recommended to be increased to some degree [e.g., 5√f’c (psi) or 0.42√f’c (MPa)] for more realistic modeling of stress-induced punching and reasonable seismic evaluation of reinforced concrete interior slab-column connections with typical slab dimension and reinforcement detailing.

Tables 3 and 4 show the calculations for modeling parameters a and b, respectively. The tables provide information for specimens with and without continuous bottom reinforcement. The positive/negative sign represents just the direction of lateral drift. Table 4 includes data for the modeling parameters with respect to gravity shear ratio (Vg/Vo) only, like in the existing Table 4.9 in ACI 369R-11 (or Table 1 of this paper). Note that for interior slab-column connection subassemblies with a pin condition at the column below, story drift due to column elastic bending is typically negligible and no plastic deformation exists in the column (Pan and Moehle, 1992). Thus, the plastic drift is assumed to be equal to the plastic rotation of the slab on either side of an interior slab-column connection. The information shows the relationship between the measured modeling parameter and gravity shear ratio. The values shown in Table 4 are mean values for the specimens with and without continuous bottom reinforcement under variable gravity levels. However, because the data used in this study did not apply to each gravity shear ratio, the data is lacking and should be expanded in future research studies. The relevant data including the mean values are analyzed in this study to choose the best recommendation for each range.

Table 3 — Failure mode and modeling parameters (Gray shades: b is based on the maximum drift during testing)

Authors Specimen / cC v f

Vg/Vo a (%) b (%) Stress-Induced

Punching Expected? / Occurred? v=vc v=vu + - + -

Pan and Moehle (1992)

AP1 4 3.6 0.37 0.8 0.8 0.8 1.9 No / No

AP3 4 2.7 0.18 3 2.9 4.6 3.0 No / No

AP4 4 2.7 0.19 2.7 1.4 4.0 0.9 No / No

Robertson and Durrani (1991)

2C 4 5.6 0.20 3.4 3.4 4.4 4.1 Yes / No

7L 4 6.7 0.40 0.5 0.7 1.8 2.0 Yes / Yes

Farhey et al. (1993) 3 4 3.0 0.20 3.0 2.0 4.4 2.0 No / No

4 4 4.9 0.20 2.2 1.8 4.9 1.8 Yes / No

Robertson et al. (2002) 1C 4 2.4 0.17 2.4 1.9 2.9 2.8 No / No

Zee and Moehle (1984) Interior 4 4.1 0.14 2.9 2.6 2.9 2.6 Yes / No

Wey and Durrani (1992)

SC0 4 2.5

0.05 2.3 2.6 4.2 4.2 No / No

Kang and Wallace (2008)

CO 4 3.1

0.30 2.3 1.2 3.9 3.4 No / No

Robertson and Johnson (2006)

ND1C 4 2.7 0.20 3.5 2.5 7.1 4.4 No / No

ND4LL 4 2.8 0.30 1.9 1.8 3.5 3.4 No / No

ND5XL 4 3.7 0.50 0.6 0.6 0.6 0.6 No / No

ND6HR 4 4.2 0.30 1.1 1.4 3.2 3.3 Yes / No

ND7LR 4 2.5 0.30 2.0 2.2 3.7 3.9 No / No

Tian et al. (2008)

L0.5 4 1.9 0.23 1.3 1.5 1.7 1.7 No / No

LG0.5 4 1.9 0.23 1.0 1.0 1.0 1.0 No / No

LG1.0 4 2.5 0.23 1.0 0.9 1.1 1.0 No / No

Stark et al. (2005) C-63 4 2.5 0.10 0.6 1.0 1.6 2.0 No / No

Durrani et al. (1995) DNY_3 4 4.0 0.22 2.6 2.4 3.7 3.2 Yes / No

Luo et al. (1994) II 4 1.6 0 3.8 3.9 3.8 3.9 No / No

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Table 4 — Comparison of modeling parameters obtained from database to ACI 369R-11

Conditions Modeling Parameters

Plastic Rotation, Radians

x = Vg/Vo Continuity

Reinforcement

a b

ACI 369R-11 Mean Proposed ACI 369R-11 Mean Proposed

0 ≤ x < 0.2

Yes

0.035 0.025 0.025 0.050 0.032 0.035

0.2 ≤ x < 0.4 0.030 0.021 0.020 0.040 0.032 0.03

0.4 ≤ x < 0.6 0.020 0.006 0.015 0.030 0.019 0.025

x ≥ 0.6 0 - - 0 - -

0 ≤ x < 0.2

No

0.025 0.023 0.023 0.025 0.028 0.025

0.2 ≤ x < 0.4 0.020 0.018 0.018 0.020 0.029 0.020

0.4 ≤ x < 0.6 0.010 0.006 0.008 0.010 0.006 0.010

x ≥ 0.6 0 - - 0 - -

Discussion of Results from Assessment of Data

The review of previous experiments on reinforced concrete slab-column connections subjected to lateral loading resulted in a database of test details including dimensions, detailing, and calculated moment strength. This database will be useful as this research continues to expand to include more specimens that are relevant to the study. It also enabled the comparison of several different factors in order to determine which factors may contribute to the punching shear strength and allowable plastic drift capacity for certain connections.

Many comparisons were made between the different variables of interest in this study in order to determine trends in the data (Figures 4 to 7). Both positive and negative story drifts are plotted in Figures 4 to 7. The correlation between gravity shear ratio and allowable plastic drift levels was already known, so it was analyzed in order to provide recommendations for ACI 369R, which are discussed below. Figure 4 shows the relationship between the gravity shear ratio and the measured modeling parameter a. As the applied gravity shear ratio increases, the modeling parameter a tends to decrease for both the specimens with and without continuous bottom reinforcement. Similar comparisons were made for the modeling parameter b. A trend of a positive correlation between gravity shear ratio and the measured modeling parameter b was noticed (Figure 5). The scatter was particularly large for the parameter b. Note that the “maximum” drift value was used to determine b for more than half of the specimens, because the testing was stopped without significant loss of strength in order to avoid the complete collapse of the specimen.

The comparisons also include an analysis between the reinforcement ratios and the modeling parameters, which showed little trend (Figures 6 and 7). Figures 6 and 7 show the modeling parameters with respect to reinforcement ratio (ρc+5h), in order to determine the relationship between allowable plastic drift and the level of reinforcing steel at the face of the interior column. The total reinforcement ratio, top and bottom included, for the slab width of c2 + 5h was used, and the reinforcement ratio is shown as a percentage (%). These figures also have some missing information for lower reinforcement levels, but this is mainly due to minimum code requirements for reinforcement amounts. The critical section area was also compared to the modeling parameters with the thought that larger joint proportions would allow increased levels of plastic deformation; however, no correlation was noted in the data. This may be due to many different variables that are taken into account in testing a slab-column specimen, so the direct comparison of two joints differing only in critical section area was not possible at this time.

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(a) with continuous bottom reinforcement (b) without continuous bottom reinforcement

Figure 4. Gravity shear ratio vs. measured modeling parameter a.

(a) with continuous bottom reinforcement (b) without continuous bottom reinforcement

Figure 5. Gravity shear ratio vs. measured modeling parameter b.

(a) with continuous bottom reinforcement (b) without continuous bottom reinforcement

Figure 6. Reinforcement ratio vs. measured modeling parameter a.

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(a) with continuous bottom reinforcement (b) without continuous bottom reinforcement

Figure 7. Reinforcement ratio vs. measured modeling parameter b.

(a) with continuous bottom reinforcement (b) without continuous bottom reinforcement

Figure 8. Gravity shear ratio vs. proposed modeling parameter a.

(a) with continuous bottom reinforcement (b) without continuous bottom reinforcement

Figure 9. Gravity shear ratio vs. proposed modeling parameter b.

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The majority of the specimens also had continuous bottom reinforcement, which should be used to prevent collapse and improve punching shear capacity (by providing dowel action and connection integrity and by increasing flexural transfer capacity of unbalanced moment). The eccentric shear stress model does not take into account the lack or presence of continuity in bottom reinforcement through the column. This is important, because an insufficient development length may lead to brittle and unexpected failure by pullout of the rebar, which in turn could lead to a progressive collapse of an entire structure. This emphasizes the importance of redundancy in structural design. It is also important to know the varying strength of the slab with increasing flexural transfer widths, in order to better understand the transfer mechanism and failure behavior of a structure. It is important that a slab region around a column has the ability to transfer the load to the column, rather than punch suddenly and catastrophically under load application. ACI 369R recommends the use of a slab width of c2 + 5h for flexural transfer width, unlike ACI 318 where a width of c2 + 3h is specified. This study follows the current recommendation of ACI 369R, because the database suggests that the c2 + 5h width is more reasonable.

Figures 8 and 9 compare the values preliminarily proposed from this research to the current values for the modeling parameters a and b that are recommended in ACI 369R. The values in Figures 8 and 9 and Table 4 are mainly based on the mean values for both specimens with and without continuity in reinforcement, with some engineering judgment applied to address cases where limited data and significant scatter exist (see Figures 4 and 5). The standard deviations of the errors between the experimental values and estimated modeling parameters are also provided (Table 5). The proposed values follow the same basic trends as the current numbers, in that with increasing gravity shear ratio, the modeling parameters decrease. However, due to unconservative estimates of the plastic rotation capacity, smaller values are proposed for both the modeling parameters a and b. The median values are quite close to the mean values (Table 6), so the use of the median would not affect the proposed values for reinforced concrete slab-column connections. For specimens with a gravity shear ratio of 0.6 or greater, ACI 369R typically recommends zero allowable plastic rotation angles for all categories. The research results did not include any specimens that fell in this category, but with such a high amount of gravity loading, it appears that zero would be an appropriate and conservative recommendation. In general, the updated numbers are smaller than those currently recommended, meaning that the ACI 369 recommendations may have areas that are unconservative, and therefore may not be safe for reinforced concrete slab-column connections.

In terms of modeling parameter c, residual strength ratio (see Table 1), at this point no updates are made to the current values. Using the compiled database, acceptance criteria can also be assessed. ASCE/SEI 41-06 provides procedures to define acceptance criteria for the Immediate Occupancy (IO), Life Safety (LS) and Collapse Prevention (CP). For primary members, acceptance criteria for LS and CP are defined as 0.75(a) and the larger of 1.0(a) and 0.75(b), respectively. For secondary members, acceptance criteria for LS and CP are defined as 0.75(b) and 1.0(b), respectively. However, to have the same (or similar) probability of exceeding a modeling parameter a or b for various members/connections that meet acceptance criteria, ACI Committee 369 is proposing a new procedure utilizing specific percentiles. While specific numbers are still being discussed, the same or similar procedure will be applicable to the assessment of slab-column connections’ acceptance criteria. In Table 6, a few selected percentiles are presented to provide a general idea.

Table 5 — Standard deviations of errors between experimental values and estimated modeling parameters (proposed

and ACI 369R-11) for a and b in %

Vg/Vo Continuity

Reinforcement STDa_proposed STDa_ACI369 STDb-proposed STDb_ACI369

0 ≤ x < 0.2

Yes

0.47 1.13 1.07 2.07

0.2 ≤ x < 0.4 0.93 1.30 1.35 1.58

0.4 ≤ x < 0.6 1.17 1.40 0.61 1.10

x ≥ 0.6 - - - -

0 ≤ x < 0.2

No

1.53 1.54 1.09 1.09

0.2 ≤ x < 0.4 0.72 0.76 1.84 1.84

0.4 ≤ x < 0.6 0.20 0.40 0.40 0.40

x ≥ 0.6 - - - -

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Table 6 — Data analysis of modeling parameters of a and b

Vg/Vo Continuity

Reinf. a b Percentile of a Percentile of b

mean median mean median 20th 35th 10th 25th

0 ≤ x < 0.2

Yes

0.025 0.026 0.032 0.030 0.022 0.024 0.024 0.028

0.2 ≤ x < 0.4 0.021 0.021 0.032 0.037 0.011 0.017 0.017 0.019

0.4 ≤ x < 0.6 0.006 0.006 0.019 0.019 0.005 0.006 0.018 0.019

x ≥ 0.6 - - - - - - - -

0 ≤ x < 0.2

No

0.023 0.024 0.028 0.029 0.008 0.011 0.015 0.018

0.2 ≤ x < 0.4 0.018 0.017 0.029 0.033 0.010 0.013 0.010 0.013

0.4 ≤ x < 0.6 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006

x ≥ 0.6 - - - - - - - -

CONCLUSION

The primary purpose of the research was to review the experimental data of previously tested reinforced

concrete slab-column connections and to recommend potential updates to ACI 369R concerning modeling parameters for allowable plastic rotations based on the investigation. The thorough review of previous and recent experiments resulted in a database of useful information, which was used in further calculations and analysis of the punching shear strength of reinforced concrete slab-column connections in flat plate systems. This study showed that the nominal punching shear strength of connections subjected to combined seismic and gravity loading provides a conservative estimate and that conversely the current modeling parameters for plastic deformation outlined in ACI 369R are unconservative. This would help provide more reasonable and safer guidelines for seismic evaluation and rehabilitation, and may work to limit the damage caused to rehabilitated flat plate systems by strong seismic events.

This research was also successful in confirming that flat plate concrete structures without continuous reinforcement are more susceptible to punching shear failure, and therefore have lower recommended allowable plastic deformation values. The modeling parameters correlate with different values of gravity shear ratio and reinforcement ratio; however, the trends suggest that the main variable of interest is the gravity shear ratio. Little trend was noticed in the data between the reinforcement ratio and the modeling parameters. Given that the current ACI 369 recommendations for plastic rotation values for slab-column connections were found to be unconservative, the authors have made preliminary proposals on the values of a and b based on limited experimental data.

This study was especially important in pointing out the lack of information available for this area of research. While many studies have taken place, the large amount of different variables among the specimens allows for less comparable data between the specimens, especially for those without continuity in bottom reinforcement. Although buildings are not designed this way anymore, it is important to determine if those that currently exist with non-ductile connections have the strength to survive a seismic event or if retrofit methods are necessary. Further analysis and specimen testing would be useful in expanding this study to provide more accurate recommendations to ACI 369R.

ACKNOWLEDGEMENTS

Financial support from Seoul National University is greatly appreciated. The authors acknowledge members of

ACI Committee 369 who provided constructive comments during the committee meetings, particularly John Wallace, Ying Tian, Ken Elwood, Wassim Ghannoum, Roberto Stark, Murat Melek, and Mary Beth Hueste.

REFERENCES ACI Committee 318 (2011), Building Code Requirements for Structural Concrete (ACI 318-11) and Commentary,

American Concrete Institute, Farmington Hills, MI.

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