DETERMINATION OF CRITICAL SHEAR, MOMENT, AND DEFORMATION INTERACTIONS FOR RC SLAB-COLUMN

CONNECTIONS

James O. JIRSA1

ABSTRACT

The objective of this project is the determination of critical shear, moment, and deformation interactions at the connections of reinforced concrete slab-column buildings. While considerable research has been conducted to determine shear and moment interactions, little is known about the effect of inelastic deformations due to lateral displacements of the structure on subsequent shear transfer capacity. The consequences of different sequences of load application that produce damage to a level less than failure is generally not understood. For assessment of damaged structures and for design of structures to control damage, the effects of such load sequences must be determined. Buildings that have been subjected to damaging earthquake deformations (even if the damage has not threatened the integrity of the structure during the earthquake) or other disastrous loadings may suffer latent damage that could lead to failure of the connection or progressive collapse of the structure under subsequent post-earthquake loading combinations.

1. BACKGROUND

Flat plate and flat slab floor systems are widely used in residential and commercial buildings. In

the United States, flat plate systems have been an economical form for use in buildings that do

not have to accommodate large gravity loads. The addition of drop panels permits an increase in

the gravity load capacity. In construction, the key feature of these systems is the simplicity of

formwork that leads to speed of construction. For the owners and occupants, the space can be

easily reconfigured to permit a variety of uses. While slab-column floor systems remain a very

economical and popular form for architects and developers, the systems have some inherent

problems that must be considered by the structural engineer.

In buildings that must resist lateral wind or earthquake forces, the column-slab connection is a

very flexible unit. In order to control lateral deformation, separate lateral load-carrying elements

can be provided in the form of perimeter moment-resisting frames, structural walls, or infills.

The problem of deformation control is especially critical where these systems are used in seismic

zones. Many pre 1970’s slab-column systems are located in regions that were once considered to

have “low” seismicity and relied the slab-column connections for providing the necessary lateral

1 Department of Civil Engineering, The University of Texas at Austin, Austin, Texas, 78712 Email: jirsa@uts.cc.utexas.edu

1

capacity. With the modification of seismic hazard maps in recent years, the required lateral

capacity of buildings has increased and deformation control has become an even more critical

requirement. This is especially true in cases where ductile moment-resisting perimeter frames

have been added or where steel braces have been introduced as a rehabilitation measure to

provide added lateral strength and stiffness. Frames or braces added on the exterior faces of the

building do not interfere with the interior floor space or reduce the floor to ceiling clearances.

The cost of rehabilitation can be reduced if modifications to the interior structural systems are

not needed. However, the structures may still experience considerable lateral deformation that

results in damage at slab-column connections. Such damage has been reported following the

recent Nisqually, Washington earthquake (Bartoletti 2002).

The addition of new “column capitals” (shown in Fig. 1) is one approach to strengthening slab-

column connections directly rather than adding new lateral force resisting systems that limit

lateral deformation and “protect” the weak slab-column connections.

a) Strengthening of slab-column connections

b) Reinforcement in new column capital

Fig. 1 Rehabilitation of slab-column floor system (Popovic and Klein 2002)

2

The “Achilles’ heel” of flat plate and flat slab floors is the transfer of shear from the floor to the

columns. Two-way or punching shear capacity is quite low and is a function of the moment

transfer that accompanies shear transfer at the slab-column connection. Strength calculations for

such connections are complex (ACI 318 2002). Computation of shear and moment strength is

further complicated by the amount of inelastic action that occurs at the connection and is the

main reason that deformation control is needed. Moehle (Hwang and Moehle 2000; Pan and

Moehle 1989 and 1992) and Durrani (Robertson and Durrani 1991 and 1992, Durrani, Du, and

Luo 1995; Wey and Durrani 1992) have done extensive research on the interaction of gravity

loads and lateral displacements leading to failure. However, their research does not address the

situation where failure has not occurred under lateral displacements of the structure but enough

damage may have been produced so that subsequent loading with higher gravity loads could be

disastrous. The poor performance of slab-column buildings in the 1985 Mexico City and other

recent earthquakes can be attributed to the inherent weaknesses of the connections. Flexible

floors, connections prone to shear failure, and slender supporting columns create the potential for

failure at many locations in such a system. To correct these deficiencies and to control the

deformations that could trigger loss of shear transfer at the connections, rehabilitation of such

structures usually involves the addition of separate lateral load resisting elements. The cost of

rehabilitation is directly related to the level of lateral capacity required or the maximum

deformation considered acceptable. Since the designer must make calculations of these response

characteristics, accurate simulation of slab-column connection response is critical to the design

of the retrofit system and the associated cost to the owner.

2. SEQUENCE OF DAMAGE

In a building that has been damaged, it is necessary to determine if damage (cracking and

inelastic strains in the reinforcement at or near the slab-column connection) due to lateral

displacements of the structure has reduced the gravity load carrying capacity of the system.

Currently, there are no established procedures or experimental data for determining the gravity

load carrying capacity of a slab-column connection as a function of the degree of damage that

has occurred previously. The lack of technical data is apparent in studying the most recent

document available for seismic rehabilitation—FEMA 356 (FEMA 2000). While the

3

interactions between shear and moment are taken into account in the FEMA provisions for

analysis and acceptance criteria under earthquake actions, the provisions are not applicable for

previous damage or post-earthquake behavior. Likewise, for rehabilitation of existing

undamaged structures or for design of new systems, there is insufficient technical data on which

to base deformation limits for protecting the gravity load capacity of such connections, for

selecting appropriate rehabilitation techniques (the FEMA document is particularly lacking in

this area), or for evaluating the effectiveness of techniques such as those shown in Fig. 1. It

should be noted that if a structure has large gravity loads on the floors, a punching failure might

occur during the earthquake and result in collapse of the entire structure. In a structure that has

suffered a “pancake” failure, it is impossible to determine the triggering failure mechanism but

punching shear is often theorized. Perhaps the most difficult issue to resolve is the capacity

remaining in a complex system when damage has occurred or to determine the lateral force-

lateral deformation relationship for a system where complex interactions between several

different types of actions occur and the controlling mode of failure cannot be well defined

beforehand.

3. ANALOGOUS CASE—COLUMN AXIAL CAPACITY

A comparable situation may help clarify the type of interaction that forms the hypothesis for this

project. Many studies have been conducted defining the shear or flexure-axial load interactions

for columns. Algorithms have been defined to represent those interactions in analyzing the

response of buildings. However, until very recently the effect of lateral column cyclic

deformations on the column capacity under gravity loads was not defined (column stability or

slenderness, P- effects, can be included relatively easily). Recent work at UC Berkeley

(Elwood and Moehle 2001) has provided new insights into column capacity-story drift

relationships. Figure 2 is a sketch of an envelope curve for the axial capacity vs drift relationship

for a column in a structure subjected to cyclic deformations to increasing peak drift levels. The

applied load on the column remains the same but as the lateral deformations (story drift levels)

increase, the axial capacity is reduced because of damage to the hinging region of the column. If

the unsupported length of the column is small (short or captive columns) and shear response

controls, shear damage to the column reduces the axial capacity. At the point where the axial

4

capacity and the applied load intersect, the column would be expected to fail axially. The higher

the level of applied load, the lower will be the drift at which axial failure would be expected.

Columns at the lower levels of the structure would be more vulnerable than those at upper levels

because the applied loads would

generally be a greater fraction of the capacity and the lateral forces (and often drifts) are greater

in lower stories of older existing buildings, especially those with soft first stories. (It is assumed

in this example that the story drift is an indicator of the damage level for either shear or flexural

failure of the column, however, this may not be a satisfactory indicator for use in evaluating a

damaged structure because the peak drift that has occurred may not be readily apparent or easily

determined.)

4. SLAB-COLUMN CONNECTION FAILURES

For slab-column structures the same types of failures are possible, however, it is likely that

punching shear failures will control, especially in flat plates. Figure 3 is a sketch of a slab-

column connection region of a floor slab system. In this case, the lateral deformations of the

structure produce moment and shear on the connection that is superimposed on the moments and

shears from gravity loads on the floors. Flexural cracks will develop on the top surface of the

slab across the negative moment section at the face of the column and on the bottom of the slab

on the opposite face (Fig. 4). The amount of cracking and the positive moment capacity

developed on the opposite face will depend on the amount and location of bottom reinforcement

5

in the slab and the anchorage details of that reinforcement. In older structures, very little bottom

reinforcement was required to extend to the column and it was often only extended a short

distance into the column. Current design codes (ACI 2002) require that some continuous bottom

slab reinforcement be extended through the column to provide a minimum level of structural

integrity in the event a punching shear failure occurs. Regardless of the detail, it is likely that

under reversed cyclic loading, cracking will extend through the depth of the slab with positive

moment cracks joining previously formed negative moment cracks. This region of the slab is

also where the critical punching shear section is located.

6

Typically the punching shear failure starts at the location along the critical section (shown by the

dashed line around the perimeter of the column) where shears from the gravity loads add to

shears from the portion of the slab moment acting on the connection that is considered to be

transferred by shear on the faces of the critical section. Punching shear failure under large

gravity loading is shown in Fig. 5. ACI 318 (2002) and ACI 352 (1997) provide guidance for

considering the effects of simultaneous application of a specified combination of shear and

moment at a slab column connection. However, maximum moment transfer and maximum shear

transfer under gravity loading do not occur simultaneously. The sequence of application of loads

producing damage that does not lead to failure has not been evaluated. It is essential that such

load sequences be considered because buildings that have been subjected to damaging

earthquake deformations (even if the damage has not threatened the integrity of the structure

during the earthquake) may result in latent damage that could lead to failure under subsequent

post-earthquake loading combinations.

5. RESEARCH OBJECTIVES

The experimental work proposed for this project is based on subjecting specimens to separate

loading cases—first producing flexural damage at the slab-column connection due to lateral

displacement of the structure (cyclic loading to simulate earthquake effects) and then subjecting

7

the damaged specimen to loading that maximizes the potential for punching shear (gravity

loading). Cyclic loading is intended to produce damage to the slab-column connection region,

particularly around the critical section for punching shear. The level of damage may be defined

in terms of the lateral drift ratio, the amount of cracking and the crack widths, the extent of

yielding of the reinforcement in the slab at the connection, or other characteristics that will

become apparent during testing. In addition, it is intended to utilize non-destructive techniques to

better quantify the level of damage. The gravity loading will be increased incrementally until a

punching shear failure occurs. The objective of the test program will be to determine the

relationship between punching shear capacity of the slab-column connection as a function of

previous damage to the slab by earthquake actions on the structure (Fig. 6). The information will

be valuable for the following uses:

1) Determining the likelihood of punching shear failures under gravity loading after

damage has occurred due to an earthquake.

2) Development of response characteristics for use in pushover or other seismic analyses

of new or existing structures.

3) Establishing reasonable deformation limits for evaluation and design of rehabilitation

schemes for existing slab-column structures.

4) Evaluating the feasibility of modifications to the slab-column connections (enlarging

column capitals or increasing the shear strength of the slab at critical shear sections)

to improve the load transfer capacity of the existing system.

5.1 Research Program

8

A series of slab-column specimens will be tested to establish the influence of degree of previous

earthquake-related damage on the punching shear capacity of slab-column floor systems under

gravity loads. The key elements of the project are as follows:

1. Determine typical floor details of existing structures in consultation with designers

working on rehabilitation of slab-column structural systems.

2. Conduct analyses of selected floor slab systems to determine the details of test

specimens and to simulate the behavior of the connection region in the complete

structural system.

3. Determine--

a. Degree of damage under earthquake loading as determined through visual

observations, measured local or global deformations, and non-destructive

techniques.

b. Influence of moment transfer in combination with gravity loading (it is

unlikely that gravity loading will ever occur without any moment transfer

because structural systems and loadings are rarely symmetrical)

4. Evaluate effects of--

a. Slab thickness, column or capital size (defines the critical section for punching

shear)

b. Slab reinforcement details at connection

c. Strengthening the connection through the use of column capitals to increase

the critical shear section at the slab-column joint (providing a capital before or

after subjecting the specimen to earthquake loading) or increasing the shear

capacity of the slab using either conventional steel or new CFRP reinforcing

materials.

5. Define the influence of previous damage to the slab by earthquake actions on the

structure on the punching shear capacity of slab-column connections. Crack width,

extent and location of cracks, and residual deformations in the connection region after

the simulated earthquake loading has been completed will provide some quantifiable

measures of response and damage. However, the results of techniques such as SASW

testing should provide the most reliable indication of internal damage to the concrete.

9

6. Develop algorithms for relationships between damage due to lateral deformations and

subsequent load transfer capacity under gravity loads suitable for pushover (or other

analyses) of new, existing, or rehabilitated structures.

5.2 Non-Destructive Techniques

The use of non-destructive techniques is a critical aspect of damage assessment. In previous

research on reinforced concrete shear wall structures under cyclic loads to large deformation

levels at the University of Texas, spectral analysis of surface waves (SASW) testing was used to

assess damage in the walls. The SASW technique will be used to assess the integrity of the

concrete material in the slab-column joint region at various stages of loading and story drift

levels. One difficulty that arises with this technique (and other nondestructive techniques) is that

under cyclic deformations, cracks open and close. Even though the cracking and damage may be

severe at peak deformation in one direction, once the cracks close as loading is reversed, the

SASW results may indicate that the damage is not as severe when the cracks are closed.

However, various reference locations for reading the seismic waves introduced to the slab

(hammer blow to the surface) may permit a more global indication of the total damage to

concrete in the connection region. The ultimate goal in studying this technique would be to

provide a reliable means of assessing damage conditions in the field so that owners and designers

would be able to make rehabilitation or demolition decisions based on quantifiable damage

levels.

6. REFERENCES

ACI Committee 318 (2002), “Building Code Requirements for Structural Concrete (318-02),

American Concrete Institute.

ACI Committee 352 (1997), “Recommendations for Design of Slab-Column Connections in

Monolithic Reinforced Concrete Structures (ACI 352.1R-97),” American Concrete Institute.

Bartoletti, S. (2002), Private Communication regarding damage in flat plate structures in

Nisqually earthquake.

Durrani, A. J., Du, Y., and Luo, Y. H. (1995), “Seismic Resistance of Non-Ductile Slab-Column

Connections in Existing Flat-Slab Buildings, ACI Structural Journal, American Concrete

Institute, July-Aug. 1995, pp 478-487

10

Elwood, K. J., and Moehle, J. P. (2001), “Shake Table Tests on the Gravity Load Collapse of

Reinforced Concrete Frames,” Paper presented at Third US-Japan Workshop on Performance-

Based Earthquake Engineering Methodology for Reinforced Concrete Building Structures,”

Seattle.

FEMA (2000), “Prestandard and Commentary for the Seismic Rehabilitation of Buildings,”,

Federal Emergency Management Agency, FEMA 356.

Hwang, S-J, and Moehle, J. P. (2000), “Vertical and Lateral Load Tests of Nine-Panel Flat-Plate

Frame,” ACI Structural Journal, American Concrete Institute, Jan,-Feb. 2000, pp 193-203

Pan, A. D., and Moehle, J. P. (1989), “Lateral Displacement Ductility of Reinforced Concrete

Flat Plates,” ACI Structural Journal, American Concrete Institute, May-June 1989, pp 250-258

Pan, A. D., and Moehle, J. P. (1992), “An Experimental Study of Slab-Column Connections,”

ACI Structural Journal, American Concrete Institute, Nov.-Dec. 1992, pp 627-638

Popovic, P. L., and Klein, G. J. (2002), “Strengthening with Shear Collars,”Concrete

International, American Concrete Institute, Vol. 24, No. 1, pp 32-36.

Robertson, I. N, and Durrani, A. J. (1991), “Gravity Load Effects on Seismic Behavior of

Exterior Slab-Column Connections,” ACI Structural Journal, American Concrete Institute, May-

June 1991, pp 255-267

Robertson, I. N, and Durrani, A. J. (1992), “Gravity Load Effects on Seismic Behavior of

Interior Slab-Column Connections,” ACI Structural Journal, American Concrete Institute, Jan.-

Feb. 1992, pp 36-45

Wey, E. H., and Durrani, A. J. (1992), Seismic Response of Interior Slab-Column Connections

with Shear Capitals,” ACI Structural Journal, American Concrete Institute, Nov.-Dec. 1992, pp

682-691

7. KEYWORDS

Slab-column connections, shear strength, drift ratio, shear/moment/deformation interaction,

damage level, assessment, rehabilitation.

11