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Punching of flat slabs with in-plane forces
Engineering Structures 33 (2011) 894–902
Contents lists available at ScienceDirect
Engineering Structures journal homepage: www.elsevier.com/locate/engstruct
Punching of flat slabs with in-plane forces A. Pinho Ramos a,∗ , Válter J.G. Lúcio a , Paul E. Regan b a
Department of Civil Engineering, Faculty of Science and Technology, New University of Lisbon, 2829-516 Caparica, Portugal
b
University of Westminster, London, United Kingdom
article
info
Article history: Received 1 July 2010 Received in revised form 11 October 2010 Accepted 1 December 2010 Available online 19 January 2011 Keywords: Punching Flat slab Concrete Prestress Experimental modelling
abstract The experimental analysis of reduced scale flat slab models under punching, subject to in-plane forces is described and the results are compared with the Eurocode 2 (2004) [1] provisions, the FIP Recommendations for the Design of Post-tensioned Slabs and Foundation Rafts (1998) [2] and ACI 318-08 (2008) [3], to evaluate their validity. The tests presented here consist of two sets of experimental models: Ramos’s tests Ramos (2003) [10] with six reduced scale flat slab specimens and Regan’s tests Regan (1983) [7] that comprised seven experimental specimens. This work aims to improve the understanding of the behaviour of flat slabs under punching load, in order to properly evaluate the effect of the in-plane forces on the punching resistance. © 2010 Elsevier Ltd. All rights reserved.
1. Introduction Flat slab structures are, nowadays, a common structural solution for residential and office buildings. They are an economical structural system, they simplify and speed up site operations, allow easy and flexible space partitioning and reduce the overall height of buildings. Although simple in appearance, the flat slab system presents a complex behaviour, especially in the slab–column connection. The punching resistance is an important subject in the design of concrete flat slabs and frequently is the conditioning factor in choosing its thickness. The punching failure mechanism results from the superposition of shear and flexural stresses near the column and is associated with the formation of a pyramidal plug of concrete which punches through the slab. It is a brittle and local failure mechanism. Despite that it can be the origin of a progressive collapse, and in some cases a global structural collapse. In fact, the loss of a support in a slab–column connection leads to the increase of stresses in the nearby slab–column connections and enhances their probability of failure. Punching of slabs, which are subject to in-plane compression, is a design issue primarily for post-tensioned flat slabs and for bridge decks. In the former the compression results from the prestress, while in the latter it arises from the deck’s action as a compression flange and/or a local compressive membrane action developed due to restraint from the surrounding structure. Where a bridge deck
∗
Corresponding author. Tel.: +351 919 765 727; fax: +351 219 263 377. E-mail address: [email protected] (A. Pinho Ramos).
0141-0296/$ – see front matter © 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.engstruct.2010.12.010
acts as a tension flange a punching load may act simultaneously with an in-plane tension. Relevant code of practice recommendations are written largely in the context of flat slab floors. The approach of Eurocode 2 [1] is however quite general and is to increase the shear resistance of an ordinary rc slab by a fraction of the mean in-plane stress, taken positive for compression and negative for tension. The FIP recommendations [2] use the same control perimeter and almost the same shear resistance for slabs without in-plane forces as EC2, but treat the effect of in-plane compression by the addition of the load at decompression of the slab’s top surface near a column. This involves factors such as the moments due to prestress, which are not considered in EC2. ACI 318-08 [3] is similar to EC2 in considering the increase of shear resistance to be a fraction of the in-plane stress, although the base value for zero in-plane stress is slightly different from that for a rc slab and the control perimeter is closer to the column than in EC2. The fraction of the in-plane stress is considerably higher in ACI 318-08 and, within the stress range treated, the effect of in-plane compression is significantly greater. Although there has been some experimental research on the punching of post-tensioned slabs done by several authors (Scordelis [4], Pralong [5], Shehata [6], Regan [7], Hassanzadeh [8] and Silva [9]), the isolation of the effect of in-plane forces in such tests is difficult because of the simultaneous effects of moments due to prestress, direct support of shear by inclined tendons near columns and other factors. Code treatments of overall resistance differ widely in the evaluations of individual effects. It is also difficult to use the results of research on compressive membrane action, largely because of the complexity in the
A. Pinho Ramos et al. / Engineering Structures 33 (2011) 894–902
Notation b b0 c d fcm fcu fy h M M0 u V
vc0 Veff VRm Vtest V0
σcp ρ
Width of the control perimeter Length of the control perimeter d/2 from the support Side length of column Mean effective depth of bonded flexural reinforcement Mean value of concrete cylinder strength Mean value of concrete cube compressive strength Yield strength of reinforcement Thickness of the slab Total bending moment on the width b Decompression moment Length of the control perimeter 2d from the support Punching force Ultimate shear stress calculated for σcp = 0 Effective failure load Predicted failure load Experimental failure load Decompression punching force Mean in-plane compression stress Bonded lexural reinforcement ratio.
structural behaviour, but also in many cases because of the very small slab thicknesses involved in the tests. The present work reports tests of reinforced concrete flat slabs subject to in-plane forces. It aims to improve the understanding of the behaviour of flat slabs under punching loads, by isolating the effect of one relevant parameter (the in-plane force). Ramos [10] tested six slabs (AR2 to AR7) with variations of the levels of compression force applied in one or both orthogonal directions. Regan [7] conducted seven experimental tests (BD1 to BD8) with different uniaxial in-plane loading (tension and compression). The experimental results are also compared with predictions based on Eurocode 2 [1], the FIP recommendations [2] and ACI 318 [3]. 2. Experimental models The slabs from the AR series (AR2 to AR7) tested were 2300 × 2300 mm2 on plan and 100 mm thick. The vertical punching load was applied by two hydraulic jacks positioned under the laboratory floor (Fig. 1). The load was transferred to eight points on the top of the slab by steel tendons and spreader beams and the slab was supported by a 200 mm2 steel plate at the centre. The bottom and top reinforcement consisted of twelve 6 mm rebars at 200 mm centres and thirty nine 10 mm rebars at 60 mm centres respectively, in both orthogonal directions. The mean effective depth was d = 80 mm and the reinforcement with the greater effective depth was in the E–W direction. Five specimens were made and tested (AR3 to AR7) with inplane forces, and another one (AR2) without in-plane forces to be used as a reference. The in-plane compression forces were applied to the slab edges by hydraulic jacks and external prestressing tendons on steel beams (Fig. 2). The internal in-plane forces were kept constant during the tests by using a load maintainer device connected to the hydraulic jacks. In slabs AR3 and AR4 the inplane forces were applied only in the N–S direction, and in the remaining slabs (AR5, AR6 and AR7) they were applied in both orthogonal directions. After the specimens were compressed the vertical load was incremented until failure, using the two hydraulic jacks positioned under the laboratory floor. During the tests, the total vertical applied load, the actual forces in the prestressing tendons, the strains in some of the top
895
reinforcement rebars and the vertical displacements of the slab at nine points were measured. Slabs from the BD series (BD1 to BD8) were 1500 mm2 and 125 mm thick. They were supported on lines 100 mm from the slab edges either at all four sides or at two opposite sides (Fig. 3). The slabs were subjected to upward concentrated loads at their centres using a hydraulic jack and a 100 mm2 steel plate. The mean effective depth to the flexural reinforcement was 101 mm and the areas of reinforcement were equal in both directions (sixteen 12 mm bars at 87.5 mm centres making a bonded flexural reinforcement ratio of 1.28%). In-plane compression was applied by debonded strands at midheight, which were prestressed immediately prior to testing. In-plane tension was applied via high-yield bars at midheight projecting from the slab edges and anchored 300 mm into the slabs. The in-plane forces acted in one direction only, parallel to the flexural reinforcement with the smaller effective depth (E–W direction). Where the slabs were supported at two opposite sides, these were, with one exception (BD7), the sides parallel to the reinforcement with the smaller effective depth, so that the bars with the larger effective depth were the main steel. In slab BD7 the supports were parallel to the reinforcement with the larger effective depth (E and W edges). To assess the strength of the concrete used in the production of the test specimens, compression tests were conducted on cubes (150 mm3 ) (see Table 1). The reinforcement steel yield strength (fy ) was 639 MPa for 6 mm rebars, 523 MPa for 10 mm rebars and 530 MPa for 12 mm rebars. 3. Test results 3.1. Slabs AR All of the slabs failed by punching and their ultimate loads, including self weight are given in Table 1. In all the slabs the failure surface had the shape of a pyramidal plug of concrete, starting at the bottom of the slab around the column perimeter and arriving to the top surface at a distance about 2d from the column perimeter. In Fig. 4 the top surfaces of the tested slabs after failure can be observed. The slabs were cut transversally after the tests in order to measure the angle between the punching failure surface and the slab plane. On an average that angle was about 30° on the reference slab, and varied between 32° and 35° on the slabs with in-plane compression. In Fig. 5 the punching shear surface of slab AR2 can be seen. Strains of the five top reinforcing bars were measured at a section through the middle of the support and their distributions at various loads are plotted in Fig. 6. In the initial load stages the strains on the top reinforcement bars grew with the increase of the vertical load. As the load approached the punching capacity, widespread cracking near the support caused some irregularities in the strain distributions in several of the slabs. Table 2 gives the average strains obtained for the five bars at three load stages. In general, the presence of the in-plane forces led to smaller strains and an increase of the in-plane forces decreased the average strains. From the five top reinforcing bars with strain gauges glued on it, two of them started to yield on slabs AR2, AR3 and AR4, and one in slab AR7, near failure. None of the reinforcing bars with strain gauges in slabs AR5 and AR6 appeared to yield. The bars that started to yield did it near failure, due to the dowel action effect being mobilized. In all the tests crack development followed a similar pattern. The first cracks to appear were flexural cracks on the top surface around the perimeter of the support. With increase of vertical load, radial cracks started to occur and spread out from the loaded area
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Fig. 1. Arrangement and geometry of the test specimens from the AR series (dimensions in mm).
Fig. 2. System used to apply the in-plane force in slabs from the AR series.
Fig. 3. Arrangement and geometry of the tests specimens from the BD series (dimensions in mm).
towards the slab edges. Subsequently the inclined cracking within the slab thickness that afterwards developed into the punching failure surface, started to be noticed on the top surface. The presence of the in-plane compression forces delayed the beginning of that inclined cracking. This phenomenon started at about 40% of
the experimental failure load in slab AR2 (without compression), and at 60%–70% of the failure load in the other slabs. The vertical deflections of the slabs with in-plane compression were smaller than those in slab AR2, probably due to the delay in the beginning of the cracking, which postponed the stiffness
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Table 1 Comparison between experimental and predicted failure loads. Model
σcp,NS a (MPa)
fcu (MPa)
σcp,EW a (MPa)
Vtest b (kN)
Code
Veff c (kN)
VRm d (kN)
Veff /VRm
258 258 258
270 270 187
0.96 0.96 1.38
AR2
48.9
0
0
258
FIP EC2 ACI 318
AR3
46.8
2.0
0
270
FIP EC2 ACI 318
263 270 270
266 288 186
0.99 0.96 1.45
AR4
53.9
3.1
0
252
FIP EC2 ACI 318
241 252 252
279 312 212
0.86 0.84 1.19
AR5
44.6
2.0
2.0
251
FIP EC2 ACI 318
237 251 251
261 306 210
0.91 0.86 1.20
AR6
46.2
1.9
2.0
250
FIP EC2 ACI 318
237 250 250
265 308 211
0.89 0.85 1.18
AR7
54.8
2.8
2.7
288
FIP EC2 ACI 318
269 288 288
280 340 247
0.96 0.90 1.17
BD1
52.8
7.65
0
293
FIP EC2 ACI 318
226 293 293
276 341 246
0.82 0.86 1.19
BD2
49.0
0
0
268
FIP EC2 ACI 318
268 268 268
269 269 169
0.99 0.99 1.58
BD4
46.0
7.65
0
293
FIP EC2 ACI 318
233 293 293
264 328 236
0.88 0.89 1.24
BD5
41.4
−3.95
0
208
FIP EC2 ACI 318
243 208 208
255 221 87
0.95 0.94 2.38
BD6
43.3
−3.95
0
225
FIP EC2 ACI 318
256 225 225
259 225 90
0.99 1.00 2.49
BD7
44.2
−3.95
0
221
FIP EC2 ACI 318
240 221 221
260 227 92
0.92 0.97 2.40
BD8
44.1
0
0
251
FIP EC2 ACI 318
251 251 251
260 260 161
0.97 0.97 1.56
a b c d
Mean in-plane compression stress. Experimental failure load. Effective punching force: FIP [2]—Veff = Vtest − V0 , EC2 [1] and ACI 318 [3]—Veff = Vtest , where V0 is the decompression punching force. Predicted failure load.
Table 2 Strains on the E–W top reinforcement. Model
AR2 AR3 AR4 AR5 AR6 AR7 a
Mean in-plane compression stress
σcp,NS (MPa)
σcp,EW (MPa)
0 2.0 3.1 2.0 1.9 2.8
0 0 0 2.0 2.0 2.7
Average stains (h) V = 160 kNa
V = 200 kNa
V = 240 kNa
1.5 1.2 1.0 1.0 1.1 0.7
2.0 1.5 1.5 1.4 1.5 1.2
3.3 2.1 2.0 1.8 1.9 1.6
Load stage.
reduction due to cracking (Fig. 7). From the deflected profiles, it can be seen that the deformations of the slabs are approximately rigid body rotations about axes close to the edges of the loaded area (Fig. 8). For this set of tests, the experimental punching loads show no clear tendency of increasing the load capacity when the inplane compression is applied. In a matter of fact some of the test specimens with in-plane compression showed failure loads lower than the reference model down to −3.1% (AR6), and others showed a small increase of the load capacity up to +11.6% (AR7). This could be explained by the inevitable dispersion of experimental results
superposed to the small influence of the compression on the load capacity on this set of experimental specimens. 3.2. Slabs BD All of the tests resulted in punching failures and only slab BD7 with tension parallel to the main span appeared to be close to flexural failure. The tests results are given in Table 1 and show little difference in strength between slabs with supports at two and four edges. The experimental punching loads show the effect from
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Fig. 4. Top surface of tested slabs from the AR series after failure.
Fig. 5. Section of the punching surface of slab AR2.
axial loading, with the compressed slabs giving the highest and the tensioned slabs the lowest punching loads. 4. Comparisons of experimental and predicted punching loads Comparisons are made here between the experimental punching loads of the slabs described above and predictions made by the methods of Eurocode 2—EC2 [1], the FIP recommendations for the Design of Post-Tensioned Slabs and Foundation Rafts [2] and ACI 318-08 [3]. For the calculation of the unfactored resistance using EC2 the following expression was used: VRm = 0.18k(100 ρ fcm )1/3 ud + k1 σcp ud where k
=
1 +
√
(1)
200/d (d in mm); fcm is the concrete
cylinder strength; d is the mean effective depth of the bonded flexural reinforcement = 1/2(dx + dy ); ρ is the bonded flexural √ reinforcement ratio that may be calculated as ρx ρy , with the ρx and ρy being the ratios in orthogonal directions. In each direction the ratio should be calculated for a width equal to the side dimension of the column or loaded area plus 3d to either side of it; u is the length of a control perimeter 2d from a loaded area
(u = 4c + 4π d for a square loaded area of side length c); σcp is the mean in-plane compression stress and is taken as the simple average of the values for the two directions in the case of square supports/loaded areas. The recommended value of k1 is 0.1. The value of k is limited to 2.0 in EC2 but this restriction was neglected. In the FIP recommendations both the in-plane and out-of-plane forces due to prestress are considered on the action side, while the punching resistance is that of a rc slab, as given by Eq. (2): VRm = 0.18k(100ρ fcm )1/3 ud.
(2)
The flexural reinforcement ratio is calculated as for EC2 but taking into account a slab width equal to the side dimension of the column plus 2d to either side of it. This is compared to: Veff = Vtest − V0
(3)
where Vtest is the experimental failure load and V0 is the in-plane compression effect determined as the load that decompresses the top surface of the slab near the support, i.e., produces tensile stresses on the top surface of the slab, in the punching area, equal to the compression stresses caused by the in-plane forces. This decompression punching force may be quantified as a proportion of the punching force as follows: V0 = V
M0 M
(4)
where M0 = σcp bh2 /6 is the decompression moment, h is the thickness of the slab and b is the width of the control perimeter, which is taken as the column dimension plus 4d(b = 2d + c + 2d) for interior columns. The moment M is the total elastic bending
A. Pinho Ramos et al. / Engineering Structures 33 (2011) 894–902
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Fig. 6. Transversal distribution of the strains in the top reinforcement.
Fig. 7. Load versus deflection plots for a point at 1000 mm from the centre of the slab.
moment on the width b, corresponding to the punching force V . For square and circular columns the decompression punching force can be taken as the average of the values for the two directions, but for rectangular columns the FIP recommendations use a weighting factor proportional to the widths of the control perimeter in both directions. If the elastic values are considered V /M is independent of the load. A finite element program was used to find the V /M for these particular slabs, and the results are as follow: AR2 to AR7 − V /M = 7.91 m−1 ; BD1, BD2 and BD5 − V /M = 13.33 m−1 ; BD4, BD6 and BD8 − V /M = 11.94 m−1 ; BD7 − V /M = 7.47 m−1 . According to ACI 318: VRm = (0.29 fcm + 0.3σcp )b0 d
(5)
where b0 is the length of the control perimeter d/2 from the support, b0 = 4(c + d) for a square support, where c is the
width of the column. √ This is valid for b0 /d ≤ 20, beyond which the coefficient of fcm is reduced. σcp is averaged for the two directions, but should not be less than 0.9 MPa nor greater than 3.5 MPa in either direction. Another restriction imposed is that concrete strength should not be considered greater than 35 MPa. These last restrictions were ignored here. Table 1 and Fig. 9 present the results of the comparisons. In the calculations presented the concrete cylinder strength (fcm ) was taken as being 80% of the concrete cube compressive strength (fcu ). At σcp = 0 the calculations for EC2 produce slightly unsafe results with a mean Vtest /VRm of 0.97. This may well be the result of the treatment of the depth factor k. If EC2’s limit k ≤ 2.0 had been applied the predictions would have been 17% lower for the tests in the BD series and 22% for the AR series. For slabs with in-plane compression the predictions obtained by the addition of 0.1 σcp are unsafe and there is no real trend for Vtest to increase with σcp in the
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Fig. 8. Deflected profiles.
A. Pinho Ramos et al. / Engineering Structures 33 (2011) 894–902
901
Fig. 9. Comparisons between predicted and experimental failure loads.
results from the AR series and only a small increase in the BD series for higher values of σcp . However the effects of in-plane tension are well predicted. The chart on the right side with the broken line indicates the predictions with vc0 lowered by limiting k to 2.0. For the FIP recommendations and at σcp = 0 the results are equal to EC2. For slabs with in-plane compression the predictions using the FIP recommendations are slightly better than the ones using EC2, but the calculation involves the extra complexity of assessing the decompression punching force. As for the effects of the in-plane tension the agreement between the predictions and the actual strengths is worse than those obtained with EC2. For ACI 318 the strengths of slabs with σcp = 0 are seriously underestimated and more so for the BD series slabs with the lower ratio c /d. The underestimation increases with in-plane tension but √ reduces with in-plane compression. If the 0.29 fcm in Eq. (5) is √ increased to 0.4 fcm the situation would be as shown by the chart on the right side of Fig. 9 and would be reasonably satisfactory for these tests. This might well not be the case for other values of c /d, ρ and d.
in-plane tension are well predicted. The FIP recommendations present more consistent results but have the complexity of assessing the decompression punching force. The strengths of the slabs predicted using ACI318 are seriously underestimated. For normal flat slab floors with profiled tendons, designed to EC2 or to the FIP recommendations, the relatively small overestimations of the effect of the in-plane components of prestress should be offset by the conservatism in the treatments of the effects of the moments due to prestress. The present work does however show that EC2’s simple addition of 0.1 σcp to the shear resistance can be non-conservative and could potentially lead to unsafe designs, for example where concentrated loads act on compression flanges. However the tested slabs are scaled models, and very thin, so some size effect could be present. More experimental results are needed to allow the development of a general and rational approach to the assessment of the punching resistance of slabs with in-plane forces with and without moments due to prestress.
5. Conclusions
This work received some support from the Fundação para a Ciência e Tecnologia—Ministério da Ciência, Tecnologia e Ensino Superior through Project PTDC/ECM/114492/2009. We would like to thank Concremat for making the slab models in the AR series.
The experimental analysis described shows that the in-plane compression delays the beginning of bending and shear cracking in relation to slabs without in-plane compression. The presence of in-plane compression also causes smaller strains in the slab top reinforcement and smaller transversal deflections. The use of the EC2 formulation to predict the punching resistance of slabs with in-plane compression gives values slightly against safety, and this disagreement increases with the value of the compression stresses, while the punching resistances with
Acknowledgements
References [1] European Committee for Standardization. EN 1992-1-1 Eurocode 2: design of concrete structures—part 1–1: general rules and rules for buildings. CEN; 2004. p. 225. [2] Fédération Internationale de la Précontrainte. Recommendations for the design of post-tensioned slabs and foundation rafts; 1998.
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[3] ACI Committee 318. ACI 318M-08 metric building code requirements for structural concrete & commentary. Farmington Hills: American Concrete Institute; 2008. p. 473. [4] Scordelis AC, Lin TY, May HR. Shearing strength of prestressed lift slabs. ACI J 1958;485–506. [5] Pralong J, Brändli W, Thürlimann B. Durchstanzversuche an stahlbeton-und spannbeton-platten. Bericht no. 7305-3. Zurich: Institut für Baustatik und Konstruktion, ETH; 1979. [6] Shehata IA. Punching of prestressed and non-prestressed reinforced concrete flat slabs. M.Phil. thesis. London: Polytechnic of Central London; 1982. p. 336.
[7] Regan PE. Punching shear in prestressed concrete slab bridges. London: Structures Research Group, Polytechnic of Central London; 1983. [8] Hassanzadeh G, Sundquist H. Influence of post-tensioned reinforcement distribution on design of prestressed reinforcement in column supported flat slabs. In: Proceedings of the international workshop on punching shear capacity of RC slabs. 2000. p. 457–66. [9] Silva RJC, Regan PE, Melo GS. Punching resistances of unbonded posttensioned slabs by decompression methods. Struct Concr 2005;6(1):9–21. [10] Ramos A. Punching in prestressed concrete flat slabs. Ph.D. thesis. Lisbon: Universidade Técnica de Lisboa; 2003.
Contents lists available at ScienceDirect
Engineering Structures journal homepage: www.elsevier.com/locate/engstruct
Punching of flat slabs with in-plane forces A. Pinho Ramos a,∗ , Válter J.G. Lúcio a , Paul E. Regan b a
Department of Civil Engineering, Faculty of Science and Technology, New University of Lisbon, 2829-516 Caparica, Portugal
b
University of Westminster, London, United Kingdom
article
info
Article history: Received 1 July 2010 Received in revised form 11 October 2010 Accepted 1 December 2010 Available online 19 January 2011 Keywords: Punching Flat slab Concrete Prestress Experimental modelling
abstract The experimental analysis of reduced scale flat slab models under punching, subject to in-plane forces is described and the results are compared with the Eurocode 2 (2004) [1] provisions, the FIP Recommendations for the Design of Post-tensioned Slabs and Foundation Rafts (1998) [2] and ACI 318-08 (2008) [3], to evaluate their validity. The tests presented here consist of two sets of experimental models: Ramos’s tests Ramos (2003) [10] with six reduced scale flat slab specimens and Regan’s tests Regan (1983) [7] that comprised seven experimental specimens. This work aims to improve the understanding of the behaviour of flat slabs under punching load, in order to properly evaluate the effect of the in-plane forces on the punching resistance. © 2010 Elsevier Ltd. All rights reserved.
1. Introduction Flat slab structures are, nowadays, a common structural solution for residential and office buildings. They are an economical structural system, they simplify and speed up site operations, allow easy and flexible space partitioning and reduce the overall height of buildings. Although simple in appearance, the flat slab system presents a complex behaviour, especially in the slab–column connection. The punching resistance is an important subject in the design of concrete flat slabs and frequently is the conditioning factor in choosing its thickness. The punching failure mechanism results from the superposition of shear and flexural stresses near the column and is associated with the formation of a pyramidal plug of concrete which punches through the slab. It is a brittle and local failure mechanism. Despite that it can be the origin of a progressive collapse, and in some cases a global structural collapse. In fact, the loss of a support in a slab–column connection leads to the increase of stresses in the nearby slab–column connections and enhances their probability of failure. Punching of slabs, which are subject to in-plane compression, is a design issue primarily for post-tensioned flat slabs and for bridge decks. In the former the compression results from the prestress, while in the latter it arises from the deck’s action as a compression flange and/or a local compressive membrane action developed due to restraint from the surrounding structure. Where a bridge deck
∗
Corresponding author. Tel.: +351 919 765 727; fax: +351 219 263 377. E-mail address: [email protected] (A. Pinho Ramos).
0141-0296/$ – see front matter © 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.engstruct.2010.12.010
acts as a tension flange a punching load may act simultaneously with an in-plane tension. Relevant code of practice recommendations are written largely in the context of flat slab floors. The approach of Eurocode 2 [1] is however quite general and is to increase the shear resistance of an ordinary rc slab by a fraction of the mean in-plane stress, taken positive for compression and negative for tension. The FIP recommendations [2] use the same control perimeter and almost the same shear resistance for slabs without in-plane forces as EC2, but treat the effect of in-plane compression by the addition of the load at decompression of the slab’s top surface near a column. This involves factors such as the moments due to prestress, which are not considered in EC2. ACI 318-08 [3] is similar to EC2 in considering the increase of shear resistance to be a fraction of the in-plane stress, although the base value for zero in-plane stress is slightly different from that for a rc slab and the control perimeter is closer to the column than in EC2. The fraction of the in-plane stress is considerably higher in ACI 318-08 and, within the stress range treated, the effect of in-plane compression is significantly greater. Although there has been some experimental research on the punching of post-tensioned slabs done by several authors (Scordelis [4], Pralong [5], Shehata [6], Regan [7], Hassanzadeh [8] and Silva [9]), the isolation of the effect of in-plane forces in such tests is difficult because of the simultaneous effects of moments due to prestress, direct support of shear by inclined tendons near columns and other factors. Code treatments of overall resistance differ widely in the evaluations of individual effects. It is also difficult to use the results of research on compressive membrane action, largely because of the complexity in the
A. Pinho Ramos et al. / Engineering Structures 33 (2011) 894–902
Notation b b0 c d fcm fcu fy h M M0 u V
vc0 Veff VRm Vtest V0
σcp ρ
Width of the control perimeter Length of the control perimeter d/2 from the support Side length of column Mean effective depth of bonded flexural reinforcement Mean value of concrete cylinder strength Mean value of concrete cube compressive strength Yield strength of reinforcement Thickness of the slab Total bending moment on the width b Decompression moment Length of the control perimeter 2d from the support Punching force Ultimate shear stress calculated for σcp = 0 Effective failure load Predicted failure load Experimental failure load Decompression punching force Mean in-plane compression stress Bonded lexural reinforcement ratio.
structural behaviour, but also in many cases because of the very small slab thicknesses involved in the tests. The present work reports tests of reinforced concrete flat slabs subject to in-plane forces. It aims to improve the understanding of the behaviour of flat slabs under punching loads, by isolating the effect of one relevant parameter (the in-plane force). Ramos [10] tested six slabs (AR2 to AR7) with variations of the levels of compression force applied in one or both orthogonal directions. Regan [7] conducted seven experimental tests (BD1 to BD8) with different uniaxial in-plane loading (tension and compression). The experimental results are also compared with predictions based on Eurocode 2 [1], the FIP recommendations [2] and ACI 318 [3]. 2. Experimental models The slabs from the AR series (AR2 to AR7) tested were 2300 × 2300 mm2 on plan and 100 mm thick. The vertical punching load was applied by two hydraulic jacks positioned under the laboratory floor (Fig. 1). The load was transferred to eight points on the top of the slab by steel tendons and spreader beams and the slab was supported by a 200 mm2 steel plate at the centre. The bottom and top reinforcement consisted of twelve 6 mm rebars at 200 mm centres and thirty nine 10 mm rebars at 60 mm centres respectively, in both orthogonal directions. The mean effective depth was d = 80 mm and the reinforcement with the greater effective depth was in the E–W direction. Five specimens were made and tested (AR3 to AR7) with inplane forces, and another one (AR2) without in-plane forces to be used as a reference. The in-plane compression forces were applied to the slab edges by hydraulic jacks and external prestressing tendons on steel beams (Fig. 2). The internal in-plane forces were kept constant during the tests by using a load maintainer device connected to the hydraulic jacks. In slabs AR3 and AR4 the inplane forces were applied only in the N–S direction, and in the remaining slabs (AR5, AR6 and AR7) they were applied in both orthogonal directions. After the specimens were compressed the vertical load was incremented until failure, using the two hydraulic jacks positioned under the laboratory floor. During the tests, the total vertical applied load, the actual forces in the prestressing tendons, the strains in some of the top
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reinforcement rebars and the vertical displacements of the slab at nine points were measured. Slabs from the BD series (BD1 to BD8) were 1500 mm2 and 125 mm thick. They were supported on lines 100 mm from the slab edges either at all four sides or at two opposite sides (Fig. 3). The slabs were subjected to upward concentrated loads at their centres using a hydraulic jack and a 100 mm2 steel plate. The mean effective depth to the flexural reinforcement was 101 mm and the areas of reinforcement were equal in both directions (sixteen 12 mm bars at 87.5 mm centres making a bonded flexural reinforcement ratio of 1.28%). In-plane compression was applied by debonded strands at midheight, which were prestressed immediately prior to testing. In-plane tension was applied via high-yield bars at midheight projecting from the slab edges and anchored 300 mm into the slabs. The in-plane forces acted in one direction only, parallel to the flexural reinforcement with the smaller effective depth (E–W direction). Where the slabs were supported at two opposite sides, these were, with one exception (BD7), the sides parallel to the reinforcement with the smaller effective depth, so that the bars with the larger effective depth were the main steel. In slab BD7 the supports were parallel to the reinforcement with the larger effective depth (E and W edges). To assess the strength of the concrete used in the production of the test specimens, compression tests were conducted on cubes (150 mm3 ) (see Table 1). The reinforcement steel yield strength (fy ) was 639 MPa for 6 mm rebars, 523 MPa for 10 mm rebars and 530 MPa for 12 mm rebars. 3. Test results 3.1. Slabs AR All of the slabs failed by punching and their ultimate loads, including self weight are given in Table 1. In all the slabs the failure surface had the shape of a pyramidal plug of concrete, starting at the bottom of the slab around the column perimeter and arriving to the top surface at a distance about 2d from the column perimeter. In Fig. 4 the top surfaces of the tested slabs after failure can be observed. The slabs were cut transversally after the tests in order to measure the angle between the punching failure surface and the slab plane. On an average that angle was about 30° on the reference slab, and varied between 32° and 35° on the slabs with in-plane compression. In Fig. 5 the punching shear surface of slab AR2 can be seen. Strains of the five top reinforcing bars were measured at a section through the middle of the support and their distributions at various loads are plotted in Fig. 6. In the initial load stages the strains on the top reinforcement bars grew with the increase of the vertical load. As the load approached the punching capacity, widespread cracking near the support caused some irregularities in the strain distributions in several of the slabs. Table 2 gives the average strains obtained for the five bars at three load stages. In general, the presence of the in-plane forces led to smaller strains and an increase of the in-plane forces decreased the average strains. From the five top reinforcing bars with strain gauges glued on it, two of them started to yield on slabs AR2, AR3 and AR4, and one in slab AR7, near failure. None of the reinforcing bars with strain gauges in slabs AR5 and AR6 appeared to yield. The bars that started to yield did it near failure, due to the dowel action effect being mobilized. In all the tests crack development followed a similar pattern. The first cracks to appear were flexural cracks on the top surface around the perimeter of the support. With increase of vertical load, radial cracks started to occur and spread out from the loaded area
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Fig. 1. Arrangement and geometry of the test specimens from the AR series (dimensions in mm).
Fig. 2. System used to apply the in-plane force in slabs from the AR series.
Fig. 3. Arrangement and geometry of the tests specimens from the BD series (dimensions in mm).
towards the slab edges. Subsequently the inclined cracking within the slab thickness that afterwards developed into the punching failure surface, started to be noticed on the top surface. The presence of the in-plane compression forces delayed the beginning of that inclined cracking. This phenomenon started at about 40% of
the experimental failure load in slab AR2 (without compression), and at 60%–70% of the failure load in the other slabs. The vertical deflections of the slabs with in-plane compression were smaller than those in slab AR2, probably due to the delay in the beginning of the cracking, which postponed the stiffness
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Table 1 Comparison between experimental and predicted failure loads. Model
σcp,NS a (MPa)
fcu (MPa)
σcp,EW a (MPa)
Vtest b (kN)
Code
Veff c (kN)
VRm d (kN)
Veff /VRm
258 258 258
270 270 187
0.96 0.96 1.38
AR2
48.9
0
0
258
FIP EC2 ACI 318
AR3
46.8
2.0
0
270
FIP EC2 ACI 318
263 270 270
266 288 186
0.99 0.96 1.45
AR4
53.9
3.1
0
252
FIP EC2 ACI 318
241 252 252
279 312 212
0.86 0.84 1.19
AR5
44.6
2.0
2.0
251
FIP EC2 ACI 318
237 251 251
261 306 210
0.91 0.86 1.20
AR6
46.2
1.9
2.0
250
FIP EC2 ACI 318
237 250 250
265 308 211
0.89 0.85 1.18
AR7
54.8
2.8
2.7
288
FIP EC2 ACI 318
269 288 288
280 340 247
0.96 0.90 1.17
BD1
52.8
7.65
0
293
FIP EC2 ACI 318
226 293 293
276 341 246
0.82 0.86 1.19
BD2
49.0
0
0
268
FIP EC2 ACI 318
268 268 268
269 269 169
0.99 0.99 1.58
BD4
46.0
7.65
0
293
FIP EC2 ACI 318
233 293 293
264 328 236
0.88 0.89 1.24
BD5
41.4
−3.95
0
208
FIP EC2 ACI 318
243 208 208
255 221 87
0.95 0.94 2.38
BD6
43.3
−3.95
0
225
FIP EC2 ACI 318
256 225 225
259 225 90
0.99 1.00 2.49
BD7
44.2
−3.95
0
221
FIP EC2 ACI 318
240 221 221
260 227 92
0.92 0.97 2.40
BD8
44.1
0
0
251
FIP EC2 ACI 318
251 251 251
260 260 161
0.97 0.97 1.56
a b c d
Mean in-plane compression stress. Experimental failure load. Effective punching force: FIP [2]—Veff = Vtest − V0 , EC2 [1] and ACI 318 [3]—Veff = Vtest , where V0 is the decompression punching force. Predicted failure load.
Table 2 Strains on the E–W top reinforcement. Model
AR2 AR3 AR4 AR5 AR6 AR7 a
Mean in-plane compression stress
σcp,NS (MPa)
σcp,EW (MPa)
0 2.0 3.1 2.0 1.9 2.8
0 0 0 2.0 2.0 2.7
Average stains (h) V = 160 kNa
V = 200 kNa
V = 240 kNa
1.5 1.2 1.0 1.0 1.1 0.7
2.0 1.5 1.5 1.4 1.5 1.2
3.3 2.1 2.0 1.8 1.9 1.6
Load stage.
reduction due to cracking (Fig. 7). From the deflected profiles, it can be seen that the deformations of the slabs are approximately rigid body rotations about axes close to the edges of the loaded area (Fig. 8). For this set of tests, the experimental punching loads show no clear tendency of increasing the load capacity when the inplane compression is applied. In a matter of fact some of the test specimens with in-plane compression showed failure loads lower than the reference model down to −3.1% (AR6), and others showed a small increase of the load capacity up to +11.6% (AR7). This could be explained by the inevitable dispersion of experimental results
superposed to the small influence of the compression on the load capacity on this set of experimental specimens. 3.2. Slabs BD All of the tests resulted in punching failures and only slab BD7 with tension parallel to the main span appeared to be close to flexural failure. The tests results are given in Table 1 and show little difference in strength between slabs with supports at two and four edges. The experimental punching loads show the effect from
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Fig. 4. Top surface of tested slabs from the AR series after failure.
Fig. 5. Section of the punching surface of slab AR2.
axial loading, with the compressed slabs giving the highest and the tensioned slabs the lowest punching loads. 4. Comparisons of experimental and predicted punching loads Comparisons are made here between the experimental punching loads of the slabs described above and predictions made by the methods of Eurocode 2—EC2 [1], the FIP recommendations for the Design of Post-Tensioned Slabs and Foundation Rafts [2] and ACI 318-08 [3]. For the calculation of the unfactored resistance using EC2 the following expression was used: VRm = 0.18k(100 ρ fcm )1/3 ud + k1 σcp ud where k
=
1 +
√
(1)
200/d (d in mm); fcm is the concrete
cylinder strength; d is the mean effective depth of the bonded flexural reinforcement = 1/2(dx + dy ); ρ is the bonded flexural √ reinforcement ratio that may be calculated as ρx ρy , with the ρx and ρy being the ratios in orthogonal directions. In each direction the ratio should be calculated for a width equal to the side dimension of the column or loaded area plus 3d to either side of it; u is the length of a control perimeter 2d from a loaded area
(u = 4c + 4π d for a square loaded area of side length c); σcp is the mean in-plane compression stress and is taken as the simple average of the values for the two directions in the case of square supports/loaded areas. The recommended value of k1 is 0.1. The value of k is limited to 2.0 in EC2 but this restriction was neglected. In the FIP recommendations both the in-plane and out-of-plane forces due to prestress are considered on the action side, while the punching resistance is that of a rc slab, as given by Eq. (2): VRm = 0.18k(100ρ fcm )1/3 ud.
(2)
The flexural reinforcement ratio is calculated as for EC2 but taking into account a slab width equal to the side dimension of the column plus 2d to either side of it. This is compared to: Veff = Vtest − V0
(3)
where Vtest is the experimental failure load and V0 is the in-plane compression effect determined as the load that decompresses the top surface of the slab near the support, i.e., produces tensile stresses on the top surface of the slab, in the punching area, equal to the compression stresses caused by the in-plane forces. This decompression punching force may be quantified as a proportion of the punching force as follows: V0 = V
M0 M
(4)
where M0 = σcp bh2 /6 is the decompression moment, h is the thickness of the slab and b is the width of the control perimeter, which is taken as the column dimension plus 4d(b = 2d + c + 2d) for interior columns. The moment M is the total elastic bending
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Fig. 6. Transversal distribution of the strains in the top reinforcement.
Fig. 7. Load versus deflection plots for a point at 1000 mm from the centre of the slab.
moment on the width b, corresponding to the punching force V . For square and circular columns the decompression punching force can be taken as the average of the values for the two directions, but for rectangular columns the FIP recommendations use a weighting factor proportional to the widths of the control perimeter in both directions. If the elastic values are considered V /M is independent of the load. A finite element program was used to find the V /M for these particular slabs, and the results are as follow: AR2 to AR7 − V /M = 7.91 m−1 ; BD1, BD2 and BD5 − V /M = 13.33 m−1 ; BD4, BD6 and BD8 − V /M = 11.94 m−1 ; BD7 − V /M = 7.47 m−1 . According to ACI 318: VRm = (0.29 fcm + 0.3σcp )b0 d
(5)
where b0 is the length of the control perimeter d/2 from the support, b0 = 4(c + d) for a square support, where c is the
width of the column. √ This is valid for b0 /d ≤ 20, beyond which the coefficient of fcm is reduced. σcp is averaged for the two directions, but should not be less than 0.9 MPa nor greater than 3.5 MPa in either direction. Another restriction imposed is that concrete strength should not be considered greater than 35 MPa. These last restrictions were ignored here. Table 1 and Fig. 9 present the results of the comparisons. In the calculations presented the concrete cylinder strength (fcm ) was taken as being 80% of the concrete cube compressive strength (fcu ). At σcp = 0 the calculations for EC2 produce slightly unsafe results with a mean Vtest /VRm of 0.97. This may well be the result of the treatment of the depth factor k. If EC2’s limit k ≤ 2.0 had been applied the predictions would have been 17% lower for the tests in the BD series and 22% for the AR series. For slabs with in-plane compression the predictions obtained by the addition of 0.1 σcp are unsafe and there is no real trend for Vtest to increase with σcp in the
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Fig. 8. Deflected profiles.
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Fig. 9. Comparisons between predicted and experimental failure loads.
results from the AR series and only a small increase in the BD series for higher values of σcp . However the effects of in-plane tension are well predicted. The chart on the right side with the broken line indicates the predictions with vc0 lowered by limiting k to 2.0. For the FIP recommendations and at σcp = 0 the results are equal to EC2. For slabs with in-plane compression the predictions using the FIP recommendations are slightly better than the ones using EC2, but the calculation involves the extra complexity of assessing the decompression punching force. As for the effects of the in-plane tension the agreement between the predictions and the actual strengths is worse than those obtained with EC2. For ACI 318 the strengths of slabs with σcp = 0 are seriously underestimated and more so for the BD series slabs with the lower ratio c /d. The underestimation increases with in-plane tension but √ reduces with in-plane compression. If the 0.29 fcm in Eq. (5) is √ increased to 0.4 fcm the situation would be as shown by the chart on the right side of Fig. 9 and would be reasonably satisfactory for these tests. This might well not be the case for other values of c /d, ρ and d.
in-plane tension are well predicted. The FIP recommendations present more consistent results but have the complexity of assessing the decompression punching force. The strengths of the slabs predicted using ACI318 are seriously underestimated. For normal flat slab floors with profiled tendons, designed to EC2 or to the FIP recommendations, the relatively small overestimations of the effect of the in-plane components of prestress should be offset by the conservatism in the treatments of the effects of the moments due to prestress. The present work does however show that EC2’s simple addition of 0.1 σcp to the shear resistance can be non-conservative and could potentially lead to unsafe designs, for example where concentrated loads act on compression flanges. However the tested slabs are scaled models, and very thin, so some size effect could be present. More experimental results are needed to allow the development of a general and rational approach to the assessment of the punching resistance of slabs with in-plane forces with and without moments due to prestress.
5. Conclusions
This work received some support from the Fundação para a Ciência e Tecnologia—Ministério da Ciência, Tecnologia e Ensino Superior through Project PTDC/ECM/114492/2009. We would like to thank Concremat for making the slab models in the AR series.
The experimental analysis described shows that the in-plane compression delays the beginning of bending and shear cracking in relation to slabs without in-plane compression. The presence of in-plane compression also causes smaller strains in the slab top reinforcement and smaller transversal deflections. The use of the EC2 formulation to predict the punching resistance of slabs with in-plane compression gives values slightly against safety, and this disagreement increases with the value of the compression stresses, while the punching resistances with
Acknowledgements
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