


ARTICLE 

Year : 2015  Volume
: 5
 Issue : 1  Page : 4551 

Seismic Behavior of Connections Subjected to Punching Shear in FlatSlab Systems
Saraswati Setia^{1}, Shakti Kalyani^{2}
^{1} Department of Civil Engineering, National Institute of Technology, Kurukshetra, Haryana, India ^{2} Project Associate, IISc, Bangalore, Karnataka, India
Date of Web Publication  16Jan2015 
Correspondence Address: Saraswati Setia Department of Civil Engineering, National Institute of Technology, Kurukshetra, Haryana India
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/09768580.149487
Abstract   
Flatslab structural systems have a large applicability due to their functional and economic advantages. Initially, the reinforced concrete flat slabs had drops and columns with capitals and were considered to be the structures of choice for warehouse construction and heavy loads because shear was not a problem. Flat plates were subsequently developed, with no drops and no column capitals and due to cheaper formwork required, they were popular for residential and office buildings. Flat plate slabs exhibit higher stress at the column connection and are most likely to fail due to punching shear rather than flexural failure. To avoid shear failure, parameters influencing the punching strength need to be clearly investigated by realistic analytical or experimental studies. The present analytical study investigates the influence of some of the parameters governing the behavior of connections under punching shear, which are concrete strength, column aspect ratio, slab thickness and gravity loading. Computer program Structural Analysis Program 2000 V14 is used to model columns and slabs as frame and shell elements, respectively. Parametric studies on aspect ratio and depthtospan ratio have been carried out using displacement control nonlinear static pushover analysis to investigate the influence of these parameters on punching shear capacity of the intermediate and corner column connections, which proved to be the governing criteria to prescribe drift limits for flat plate systems in seismic zones. Keywords: Aspect ratio, depthtospan ratio, flat slab, punching shear, structural analysis program 2000
How to cite this article: Setia S, Kalyani S. Seismic Behavior of Connections Subjected to Punching Shear in FlatSlab Systems. J Eng Technol 2015;5:4551 
1. Introduction   
Reinforced concrete (RC) framed structures that feature slabs supported directly by columns, without the use of beams or girders are referred to as slabcolumn or flat plate framed systems. This type of system offers economic advantages and larger open spaces with reduced storey heights compared to framed systems with beams. In the JohnsonBovey Building in Minneapolis, Minn., the American engineer C.A.P. Turner in the year 1905 employed concrete floor slabs without beams (called flat slabs or flat plates) that used diagonal and orthogonal patterns of reinforcing bars ^{[1],[2]} . This was the beginning of this type of construction. However, the recent and the past failure of flatslab structures have underlined the need for reviewing the current design and construction practices, especially the design of flatslab system under seismic action. In general, the shear strength of connection is governed by the more severe of two mechanisms namely beam action or twoway action. Beamtype or oneway shear failure has the critical section for shear extending across the entire width of the slab. Punching or twoway shear failure involves potential diagonal tension cracks occurring along a truncated cone or pyramid passing through the critical section ^{[3]} . Many flat plate structures have collapsed in the mode of punching failure, especially during earthquakes. In slabcolumn frames located in regions of high seismic risk, the connections must be capable of transferring gravity loads while the structure undergoes earthquakeinduced lateral displacements. These displacements, besides inducing an unbalanced moment, could also translate into large inelastic rotations in the connections, which have the potential to decrease connection punching shear capacity. The detrimental effect of lateral displacements on connection strength may therefore lead to the need for shear reinforcement in slabcolumn connections that otherwise would be capable of resisting the imposed shear stresses.
Thus, punching failure in flat plate system is a major design concern and effective solutions to avoiding punching failure are of great importance. The weakest point in the slab systems is their resistance against punching shear in the vicinity of the supporting column. The flat plates can be designed by any procedure satisfying the criteria of equilibrium and geometrical compatibility. Two design procedures have been prescribed in the Indian Concrete Code (IS 4562000) for their design, namely direct design method and equivalent frame method. Based on extensive parametric study, it is intended to prescribe design guidelines for the safe construction of flat plate structures in strong seismic zones. A typical sixstorey residential type open ground RC flat plate building is considered. The nonlinear static pushover analysis of flat plate building has been performed for which nonlinear model for concrete is taken into account. Out of numerous stressstrain models for confined concrete, Saatcioglu and Razvi model is considered for the present study as the model follows a simple averaging technique to combine the confining pressures in the two orthogonal directions of the rectangular sections. Static pushover analysis is an attempt by the structural engineering profession to evaluate the real strength of the structure and it promises to be a useful and effective tool for performance based design. The process was repeated for various aspect ratios as well as the spandepth ratio and the punching shear stresses are being studied to model curves. Parametric study using nonlinear numerical analysis was performed to investigate the distribution and the strength of the internal forces developing at interior and corner slabcolumn connections.
2. Review of Literature   
A brief review of the literature including instances of past failures owing to earthquakes has been covered under this article.
2.1 Seismic failures of flatslab systems in past earthquakes
The February 2011 Christchurch earthquake saw a pancake collapse of the Smiths City Dundas St. car park due to punching shear failure of the slab column connections has been shown in [Figure 1].  Figure 1: The pancake collapse of the Smiths City Dundas St. car park due to punching shear failure of the slab column connections
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The Northridge Earthquake on January 17, 1994 was the first major earthquake to occur directly beneath a highly urbanized area in Southern California. In [Figure 2], the columns of this structure punched through the concrete slab floor systems, dropping the floors and roof and completely collapsing the interior of the building.  Figure 2: Building collapse in the Northridge Earthquake due to punching of the flat slab
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The Loma Prieta earthquake of October 17, 1989 provided a unique opportunity to understand the actual response of flatslab structures.
Large drift could result in excessive interior damage and may cause failure of the slabcolumn connections due to excessive deformation. During Loma Prieta earthquake lateral drift, which is the critical response parameter resulted in excessive interior damage, increase Pdelta effect and cause failure of slab column connection due to excessive deformation ^{[4]} .
On January 25, 1971, twothirds of a 16story apartment building collapsed while under construction at 2000 Commonwealth Avenue, Boston, Massachusetts [Figure 3]. The failures were punching shear failure in the main roof at column, collapse of the roof slab and the progressive and general collapse of most of the structure.
2.2 Factors influencing the punching shear resistance of flat plate systems
The various factors that govern the punching shear resistance and behavior of flat plate connections are ^{[5],[6],[7],[8],[9],[10],[11],[12],[13],[14],[15]} :
 Compressive strength of concrete
 Percentage flexural reinforcement
 Column aspect ratio
 Size effect
 Gravity load
 Shear reinforcement.
2.3 Nonlinear modeling and nonlinear analysis
Nonlinear modeling is empirical or semiempirical modeling, which takes at least some nonlinearity into account.
The nonlinear model, which is adopted in performing nonlinear analysis for the present work includes stressstrain curves for concrete.
Material nonlinearity coupled with geometric nonlinearity can involve higher level of complexities as well as time constraint and thus the material nonlinearity is taken into account for the present work.
Nonlinear analysis is an elastoplastic analysis method to determine if plastic collapse will occur.
A nonlinear (elastoplastic) analysis assumes the material to be perfectly elastic up to the yield point, providing results identical to a linear solver and post the yield point redistribution of stresses results in the plastic deformation.
2.4 Direct stressstrain model
The shear curve is computed automatically using Structural Analysis Program (SAP) 2000 from the direct stress strain curve.
The stress strain curve for unconfined concrete as adopted by Saatcioglu and Razvi model (1992) ^{[16]} is shown in [Figure 4].
In this model, the concrete is assumed to have equal flexural capacity in both tension and compression. Concrete is strengthened in flexure so that the predominant failure occurs in shear mode.
This dummy model of concrete in shear is based on Saatcioglu and Razvi stressstrain curve.
2.5 Relevance and contributions of the paper
Postearthquake observations and experimental testing have shown that lateral movements induced by earthquake ground motions combined with gravitational pull on slabs can make the connections between slabs and columns susceptible to punching shear failures. Lateral displacement capacity of slabcolumn connections is highly dependent on the level of shear induced by gravity loads. To avoid shear failure parameters influencing the punching strength should be clearly investigated by realistic analytical or experimental studies. Nonlinear parametric study is undertaken for the designed section to find out the influence of various parameters on punching shear capacity.
The present study investigates the influence of parameters governing the behavior of connections under punching shear, which are concrete strength, column aspect ratio, slab thickness and gravity loading. The punching shear behavior of the connection is dependent upon the location of connection in the plateedge, corner or intermediate.
3. Structural Modeling   
Hypothetical six storied"residential type"open ground RC flat plate building is considered [Figure 5]ac. Column size 400 mm × 400 mm and slab (or plate) of overall depth 200 mm is considered. Material properties adopted are as shown in [Table 1].
Total static load on slab:
 9.5 kN/m ^{2} (on floor)
 6.75 kN/m ^{2} (on roof).
3.1 Pushover analysis
Pushover analysis is a stepwise nonlinear static analysis primarily used to monitor the response of a structure at every step. Involves two steps:
 The response is monitored under vertical loads (DL + LL). The structure is slowly displaced in the direction of lateral load.
 Static pushover analysis promises to be a useful and effective tool for monitoring the response of the structure.
Pushover analysis is primarily of two types:
 Force control
This analysis is based on the concept to see up to what level of force the system behaves elastically.
When the structure reaches plastic state, the load carrying capacity of the structure becomes constant.  Displacement control
This analysis is based on the concept to estimate the ductility of the structure.
In the present study, displacement control pushover analysis is performed using an analytical software program SAP 2000 V14 ^{[17]} .
The behavior of punching shear capacity of the platecolumn connection is monitored.
4. Results   
The local and brittle nature of the punching shear leads to failure in the form of crushing of concrete in the column periphery before the steel reinforcement reaches the yield values. Parameters influencing the punching shear strength of flat plate system are concrete strength, flexural reinforcement, column aspect ratio, slab thickness, gravity loading and shear reinforcement. In the present work, the behavior of punching shear strength is investigated considering some parameters namely concrete strength, column aspect ratio, slab thickness and gravity loading. The response of the intermediate floor, i.e., 3 ^{rd} storey is being considered. The results and discussions obtained pertain to flat plate systems only in the vicinity of columns at the corner and intermediate connections of the building. The displacement values (∆) of the building are normalized with respect to the height of the building (H_{b} ). The punching shear capacity of the corresponding column connection (τ) is normalized with respect to the design shear strength of connection (τ_{c} = 0.25 fck 1/2).
4.1 Column aspect ratio
Aspect ratio β = longer dimension of the column/shorter dimension of the column. The aspect ratio is varied only by changing the width of the column for a particular grade of concrete, thickness of the plate and gravity shear ratio. The Analysis has been performed for the various aspect ratios as:
 Column: 400 mm × 400 mm, β = 1
 Column: 400 mm × 350 mm, β = 1.14
 Column: 400 mm × 300 mm, β = 1.33
 Column: 400 mm × 267 mm, β = 1.5
 Column: 400 mm × 200 mm, β = 2.
The shear stress distribution in the flat plate system for the aspect ratio, β = 2 and β = 1.14 is shown in [Figure 6] and [Figure 7] obtained after performing the nonlinear pushover analysis using the computer program SAP 2000. The area of the plate around the corner and edge column positions becomes very critical due to generation of high punching shear stresses. At the corners and edge columns additional torsional moment get generated because of loading on only one side of the connection, which induces significant punching shear stresses in that region. The region around the intermediate columns becomes the least vulnerable because of negligible transfer of unbalanced moment at the connection.  Figure 6: Shear stress distribution in the flat plate system for aspect ratio, β = 2
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 Figure 7: Shear stress distribution in the flat plate system for aspect ratio, β = 1.14
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4.1.1 Intermediate connection with varying aspect ratio
General trend of the graph [Figure 8] depicts that with the increase in the aspect ratio, β the punching shear strength around the flat plate column connection decreases until the peak strength is reached and beyond the peak shear strength, the trend reverses. Beyond peak strength, the shear capacity of the connection having the least aspect ratio falls steeply in comparison to the connection having larger aspect ratios. The peak occurs at higher values of lateral drift with the increase in aspect ratio because the transverse moments are confined to a limited width on either side of the columns due to the reduced column dimension.  Figure 8: Punching shear capacity of flat plate intermediate column connection with varying aspect ratio
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Connections with high aspect ratios (β = 1.5 and 2) appear to be more ductile in comparison to connection with low values of aspect ratios (β = 1 and 1.14). The maximum shear capacity is achieved in a drift range of 2.53.5%. The peak shear strength is found to be of the order of 0.80.9 times of design shear capacity of connection (τ_{c} ). The punching shear capacity varies linearly up to a lateral drift of about 1.5% before the curve goes into the nonlinear zone. The codeprescribed elastic drift limit of 0.4% underestimates the actual behavior because the IS code follows elastic concrete behavior and the additional strength due to material nonlinearity of concrete in resisting punching shear is not taken into account.
4.1.2 Corner connection with varying aspect ratio
The behavior of the corner connection depicts that the trend of the graph [Figure 9] with the low aspect ratios (β = 1, 1.14 and 1.33) falls steeply than high aspect ratios (β = 1.5 and 2). The peak shear strength is found to higher in the case of corner connection in the range of 11.3 times of design shear capacity of connection (τ_{c} ) due to torsional resistance offered by the corner connection. The maximum shear capacity is achieved in a drift range of 22.75%, which is found to higher in the case of intermediate connection. The punching shear capacity is seen to vary linearly up to a lateral drift of about 1% before the curve goes into the nonlinear zone.  Figure 9: Punching shear capacity of flat plate corner column connection with varying aspect ratio
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4.2 Spantodepth ratio
Spantodepth ratio is varied by changing the thickness of the flat plate for the fixed span. Punching shear capacity of the intermediate as well as corner connection is obtained with the varying spantodepth ratio of flat plate for a particular grade of concrete, aspect ratio of the column and gravity shear ratio. For the analysis, various depths to span ratios (d/L) has been taken into consideration are as:
 d /L = 0.15, thickness of plate = 456 mm
 d /L = 0.12, thickness of plate = 365 mm
 d /L = 0.10, thickness of plate = 304 mm
 d /L = 0.08, thickness of plate = 243 mm
 d /L = 0.07, thickness of plate = 212 mm
 d /L = 0.05, thickness of plate = 152 mm
 d /L = 0.03, thickness of plate = 91 mm.
The shear stress distribution in the flat plate system for depth to ratio, d/L = 0.15 and d/L = 0.03 as shown in [Figure 10] and [Figure 11] obtained after performing the nonlinear pushover analysis using the computer program SAP 2000. From the observed behavior, the area of the plate around the corner and edge column positions becomes very critical due to generation of high punching shear stresses. The reason being, at the corners and edge columns additional torsional moment get generated because of loading on only one side of the connection, which induces significant punching shear stresses in that region.  Figure 10: Shear stress distribution in the flat plate system for depthtospan ratio, d/L = 0.15
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 Figure 11: Shear stress distribution in the flat plate system for depthtospan ratio, d/L = 0.03
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4.2.1 Intermediate connection with the spantodepth ratio
Slabs are geometrically similar but due to size effect, i.e., thickness of plate there is a significant effect on the behavior of the system. General trend of the graph [Figure 12] shows that with the increase in the depthtospan ratio (d/L), the shear capacity is increased. With the increased thickness of the flat plate, the level of shear at which the failure occurs diminishes, but the slope for the thinner slabs remains approximately the same. The shear capacity of the connection is found to highest for d/L = 0.15 equal to 1.41τ_{c} with a value of 1.76 N/mm ^{2} and the least was observed for d/L = 0.03 (0.35τ_{c} ) with a value of 0.45 N/mm ^{2} . Beyond the peak shear strength, the trend reverses. The shear capacity of the connection with higher depthtospan ratio (d/L = 0.080.15) fails abruptly with zero post peak shear capacity because the thicker plate has lower rotation capacity, which allows them to fail in a brittle manner.  Figure 12: Punching shear capacity of intermediate plate column connection with varying depthtospan ratio
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Postpeak strength of connections with lower values of the depthtospan ratio (d/L = 0.030.07) is found to degrade gradually and showed significant ultimate shear capacity. The ultimate shear capacity was found to be highest for d/L = 0.05, with a value equal to 0.6τ_{c} . We can define a dimensionless parameter "cdr" as the ratio of (d/L)/0.08 and mathematically, cdr = 12.5 d/L. If cdr < 1, mode of punching shear failure is ductile if cdr = 1, the failure mode can be either of the two and for cdr > 1 the mode of failure is brittle. Connection with high values of d/L fails abruptly while the one with low d/L ratio shows a ductile mode of failure. In thick plates (high d/L ratio), the load transfer takes place predominantly by strut action. This results in very high concentration of stresses at the junction leading to sudden shear failure. While for lower d/L ratios, substantial portion of load from plate to connection gets transferred by flexural action as such ductile failure mode dominates. The lateral drift capacity, ∆max (drift at ultimate failure) showed a decreasing trend up to critical depthtospan ratio (i.e., d/L = 0.08, cdr = 1) with d/L = 0.03, having the highest drift capacity equal to 4%.
Irrespective of the depthtospan ratio, the elastic drift limit (∆elastic) is observed to be around 1% of height of the building (which is nearly twice the drift limit prescribed by IS 18932002).
4.2.2 Corner connection with the spantodepth ratio
The graph [Figure 13] shows a general trend that with the increase in the depthtospan ratio (d/L), the shear capacity is increased.  Figure 13: Punching shear capacity of corner plate column connection with varying depthtospan ratio
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The shear capacity of the corner connection is found to highest for d/L = 0.15 equal to 2.25τ_{c} with a value of 2.8 N/mm ^{2} and the least was observed for d/L = 0.03 (0.62τ_{c} ) with a value of 0.78 N/mm ^{2} , which is observed to be higher than intermediate connection.
Postpeak strength of connections with lower values of the depthtospan ratio (d/L = 0.030.07) is found to degrade gradually and showed significant ultimate shear capacity.
For cdr > 1, the trend of ∆max is almost same with the increase in the value of d/L.
Irrespective of the depthtospan ratio, the elastic drift limit (∆elastic) is observed to be around 1% of height of the building (which is nearly twice the drift limit prescribed by IS 18932002).
5. Conclusions   
Nonlinear analysis of flat plate building was performed to find out the influence of parameters (aspect ratio and spantodepth ratio) on punching shear capacity for the intermediate and corner column connections. Aspect ratio and spantodepth ratio showed significant influence on the punching shear capacity of the flat plate intermediate and corner column connection.
The salient conclusions drawn from the nonlinear analysis are as follows:
 With the increase in aspect ratio, β (longer dimension/shorter dimension) the punching shear strength around the flat plate column connection both for intermediate and corner decreases until the peak shear strength is reached.
 The peak shear strength for intermediate connection is found to be of the order of 0.80.9 times of design shear capacity of connection (τ_{c} ), whereas the peak shear strength in the case of corner connection is found to higher in the range of 11.3 times of design shear capacity of connection (τ_{c} ).
 The increase in the punching shear stresses in the case of corner connection is observed because at the corner columns additional torsional moment gets generated because of loading on only one side of the connection leading to the susceptibility to punching shear failure.
 Intermediate and corner connections with high aspect ratios appear to be more ductile in comparison to connections with low values of aspect ratio because the transverse moments are confined to a limited width on either side of the columns due to the reduced column dimension.
 The shear capacity increased with increasing overall depth by span ratio for both intermediate and corner connection.
 For values of d/L less than 0.08, the punching shear capacity of the connection showed a ductile trend while for d/L values above 0.08, the connection appeared to undergo abrupt failure in shear because the thicker plate has lower rotation capacity, which causes them to fail in brittle manner.
 Thus, it can be observed that the ideal thickness of plate for the flat plate building can be given as the ratio of d/L = 0.08 and thus for a span of 3.0 m thickness of the slab can be 250 mm because for th ratio slower than 0.08 the mode of punching shear failure is ductile and the higher ratios the failure mode is brittle.
 The elastic drift limit (∆elastic) is found to be independent of aspect ratio, spantodepth ratio. For aspect ratio in case of intermediate connection ∆elastic observed is 1.5%, whereas it decreases to 1% in case of corner connection. For spantodepth ratio ∆elastic observed is 1% of the height of the building. Thus, it is found that ∆elastic is independent of the geometry of the connection.
 The code prescribed elastic drift limit of 0.4% underestimates the actual behavior and the reason may be that the IS code follows elastic concrete behavior and as such the additional strength due to material nonlinearity of concrete in resisting punching shear is not taken into account.
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[Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5], [Figure 6], [Figure 7], [Figure 8], [Figure 9], [Figure 10], [Figure 11], [Figure 12], [Figure 13]
[Table 1]
