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## Revista IBRACON de Estruturas e Materiais

##
*versão On-line* ISSN 1983-4195

### Rev. IBRACON Estrut. Mater. vol.7 no.4 São Paulo ago. 2014

#### http://dx.doi.org/10.1590/S1983-41952014000400004

**Two-way ribbed flat slabs with shafts**

**G. M. Mateus ^{I}; A. J. Aguiar^{I};**

**M. P. Ferreira**

^{I}**;**

**D. R. C. Oliveira**

^{I};^{I}Universidade Federal do Pará, Belém, PA,
Brasil: gustavomateus.ac@bol.com.br; ajdeaguiar@gmail.com; mpinaf@ufpa.br; denio@ufpa.br

**ABSTRACT**

The position of pipes and hoses for several installations still deserves special attention from designers mainly when the failure mode can be modified due to changes in behavior. This work compares experimental results of six two-way reinforced concrete ribbed flat slabs with rectangular holes close to the column and without shear reinforcement with the estimates obtained from codes ACI 318 and NBR 6118 equations. All slabs were casted and tested in the Civil Engineering Laboratory of UFPA and had dimensions of 1.800 mm x 1.800 mm x 150 mm and were submitted to central loading applied through 120 mm side square steel plates simulating the columns. EPS was used as inert material and the ribs were spaced 250 mm with 130 mm height and 75 mm average wide. The results showed that the codes’ shear equations estimates agree when the ribs are considered as beam and also for punching shear, but trend to be safer when the slabs present two shafts.

**Keywords**: flat slab, ribbed slab, shaft, holes, shear,
punching.

**1. INTRODUCTION**

The implementation of structural systems with ribbed flat slabs is growing and motivates important questions about their structural response and resistance. Cases in which holes are located in the slab adjacent to the column are of special interest, as concentration of shear stresses are likely to occur, what may reduce significantly the punching resistance of the slab-column connection. According to SOUZA and CUNHA (1998 ) [ 1 ], local failures in the slab-column connection can lead the hole building to ruin through progressive collapse, once punching is a brittle failure mode. In this context, it is important to evaluate the available normative recommendations for the design of this type of slab, since it is known that for specific design situations, as in the case of connections with columns with high rectangularity levels, some codes tend to overestimate the strength of the connection. In practice, this may contribute to major structural accidents such as occurred in July 2013 during the construction of the Rio Poty Shopping in Teresina, where approximately 50% of the structure collapsed and punching shear of the slabs, that had holes adjacent to the columns, was pointed as a possible cause.

This paper presents experimental results of tests in six two-way reinforced concrete ribbed flat slabs. One of the slabs had no holes and served as reference to the other five slabs, which had holes adjacent to the column. Experimental results were compared to normative estimates using recommendations presented by ACI 318 (ACI, 2008) [2] and NBR 6118 (ABNT, 2007) [3]. Slabs were cast without shear reinforcement, thus shear strength is mainly a function of the compressive strength of concrete and of the flexural reinforcement ratio of the slab.

**2. CODE PROVISIONS**

The
codes used in this research estimate the punching shear resistance of slabs
with holes adjacent to the column in a similar way, differing only in the
shape, length and position of the control perimeter. The criteria used to
consider the influence of holes is similar in both ACI 318 and NBR 6118 and
involve the reduction of the control perimeter by limiting its length, removing
the portion of the perimeter between lines that are drawn from the center of
the column to the vertices of the hole. The control perimeter is assumed to be
2·*d* from the column faces in NBR 6118 and 0.5·*d* in ACI 318, where *d* is the effective depth of the slab. Figure 1 shows the control
perimeters and the specific recommendations for slabs with holes presented by
NBR 6118 and ACI 318.

ACI 318 and NBR 6118 recommend that the punching resistance shall be calculated using equations 1 and 2, respectively.

where,

d is
the effective depth of the slab;

f_{c} is the compressive strength of concrete;

r is the
flexural reinforcement ratio;

u is
the length of the control perimeter.

To
check the one-way shear resistance of the slabs two verifications shall be
made. In the first one, the one-way shear resistance shall be checked assuming
that the ribs behave as beams. In the second one, the one-way shear resistance
of the ribs shall be checked as slabs. ACI recommends Equation 1 for the first
case and 50% of the values obtained using Equation 1 for the second situation.
In this procedure, the length of the control perimeter (u) shall be substituted
by the average width of the ribs (b_{w}). The Brazilian code recommends
equations 3 and 4 for these verifications.

The flexural strength of the slabs was estimated according to the yield line theory developed by Johansen (1943) [4].The procedure is to determinate the ultimate moment of resistance per unit width with Equation 5 and, assuming a collapse mechanism characterized by the formation of linear plastic hinges, estimate the ultimate flexural load supported by the slab. The collapse mechanism adopted in this research was the same used by Oliveira (2003) [5] and is shown in Figure 2, yielding Equation 6 to estimate flexural strength of slabs.

Specifically for slab L4, the collapse mechanism used for the other slabs was not optimal, resulting in high values, besides it did not match the experimental observations. In this case, it was used the same method employed for the calculation of beams, and the static scheme assumed the columns as a concentrated load in the middle of a fixed beam with length of 240 mm.

**3. EXPERIMENTAL PROGRAM**

Six reinforced concrete ribbed flat slabs were tested in the laboratory of civil engineering of Federal University of Pará. The slabs were square with sides of 1,800 mm and were 150 mm thick. The main variables were the position and size of the holes. A slab without holes was tested as reference to all others, which had holes adjacent to the column. Figure 3 and Table 1 present the main characteristics of tested slabs.

Figure 4 shows the position of the holes in the vicinity of the columns for all slabs and their control perimeter drawn according the recommendations presented by ACI and NBR 6118.

The number and spacing of flexural rebars was the same for all slabs. The minor differences in the flexural reinforcement ratio () of the slabs, which varied between 0.42% and 0.46% as shown in Table 1, refers to changes in the effective depth of the slabs () after assembling the reinforcement. The values measured of () before casting the slabs ranged from 128 mm to 134 mm. EPS was used as inert material to replace the concrete volume under the cover and between the ribs of the slabs. The slabs were submitted to concentric loading applied through a square steel plate with sides of 120 mm and with thickness of 50 mm. The steel plates were used to simulate the columns and the loading was applied upwards by a hydraulic jack with a capacity of 1,000 kN. Reaction beams were placed over strips of chartered rubbers and the distance between the axes of the reaction rods was 1600 mm. Figure 5 shows the test system.

Rebars were orthogonally placed near the top face of the slabs, with a concrete cover of 10 mm. The ends of the flexural reinforcement and of the rebars placed on the edges of the holes were hooked in order to guarantee their anchorage. Figures 6 and 7 sketches the flexural rebars and the position of strain gauges in steel and in the concrete surface of slabs LR, L1, L2, L3, L4 and L5, respectively.

Strain gauges in the flexural rebars were positioned tangentially to the column, while in the concrete surface they were arranged in both orthogonal directions. Excel Sensores manufactured all gages used in this research. Figure 8 shows the reinforcement positioned on the edges of the holes, fulfilling the recommendations presented in Brazilian code.

**4. RESULTS**

**4.1 Materials
(concrete and steel)**

The
mechanical properties of concrete were obtained with tests following the
recommendations of the NBR 5739 (ABNT, 2007) [6] and NBR 8522 (ABNT, 2008) [7].
These tests were carried on the same day that the slabs were tested. Average
results from tests on three concrete cylinders yielded results of 43** **MPa for the compressive
strength, 2.4 MPa for the tensile strength and 25.6 GPa for the modulus of
elasticity. Tests for characterization of steel were based on the NBR 6892
(ABNT, 2002) [8], and the average results for 3 samples of 8 mm steel bars were
of 553 MPa for the yield stress, corresponding to a strain of 1.95 ‰, and 284
GPa for the modulus of elasticity.

**4.2 Failure load**

Table 2 shows the experimental failure loads and those estimated theoretically using ACI 318 and NBR 6118.

All tested slabs failed by punching after yielding of some of the flexural rebars. The shear resistance of the ribs was not a limitation, unlike predicted by ACI 318 treating them as slab. In this case, the ratio between the experimental and the theoretical failure load by shear on the ribs were approximately 1.4, except for slab L4, which was 0.73. Although the codes agree in their estimates in terms of the one-way shear strength of the ribs (treated as beams), they diverge significantly if the resistance is checked as recommended for slabs, with the Brazilian codes results being around 67% higher than those estimated by ACI.

In terms of the punching shear resistance, except for slab LR, all codes tended to underestimate the experimental results. This was more significant when slabs had two holes or one hole only, but largest than the column. For these cases, the length of the effective control perimeter is smallest if compared to the length of the perimeter of a slab without holes. Reductions reached 72% (L4) for ACI 318 and 50% (L2) in NBR 6118 in the case of slabs with two holes. In the case of slabs with one hole only, reductions were up to 21% for ACI 318 and 12% for NBR 6118.

The flexural resistance estimated for slabs LR, L1, L2, L3 and L5 was in average 25% superior to the ultimate failure load observed on tests. In the case of slab L4, the estimated flexural resistance was slightly lower than the experimental result. In this case, the discrepancy between the observed and the estimated failure load may be related to the fact that flexural cracking can actually favor punching shear failures before the complete formation of the linear plastic hinges mechanism, or even due to the vagueness of the failure mechanism adopted.

**4.3 Cracking**

The cracking pattern of the tested slabs is shown in Figure 9.

For all slabs, cracking initiated and propagated radially toward the hole with a slight reduction in the number of cracks in the region on the back of the holes. In the case of slabs with holes, it was also observed that most of the cracks initiated in the corners of the holes, evidencing the stress concentration in this area, confirming results from finite elements computational analysis.

**4.4 Strains**

Strains on the flexural reinforcement measured on tests indicate a ductile response of all tested slabs, with all installed gauges recording strain values above the yield strain (1.95‰). Figure 10 shows load-strain curves for the flexural rebars in all tests.

The largest flexural strains were observed in slab LR, in which values recorded reached 8.5‰. In the other slabs, flexural tensile strains were between 2.6‰ and 5.2‰, quite above the yield strain. Slab L1, nevertheless, showed a peculiar behavior, presenting the smaller strain increment for loads above 75 kN. It should be emphasized, however, that this behavior does not characterize a flexural failure of this slab, once this response may be restricted to the monitored region, and especially because the slab continued absorbing load increment until it failed by punching shear. Strains in the concrete bottom surface in the vicinities of the column are also shown in Figure 10. In general, the maximum values were around 0.5‰ to 2.0‰, far from the limit of 3.5‰.

**5. CONCLUSIONS**

All slabs failed by punching shear but flexural rebars monitored with strain gauges showed that they yielded before failure. However, it is considered that this may have been restricted to the bars monitored, once that slabs absorbed load increments after yielding of monitored bars, thus the flexural resistance of tested slabs was not reached. ACI failed in predicting the failure mode of 4 of tested slabs, underestimating the resistance of tested slabs, as highlighted previously by other researchers. Unlike ACI, the Brazilian code predicted properly the failure mode of 5 slabs, standard modes of ruin, missing only in the case of the reference slab. In terms of the punching resistance of slabs with holes, both codes are conservative. NBR 6118 underestimated the resistance in tests by 50% while ACI 318 reached 72% in the case of slab L4. In general, except for slab L4, the reduction in the punching resistance due to holes in the tests was significantly lower than expected by codes. In the specific case of L4, the reduction in the resistance was of 48% to a control perimeter 74% lower than the one of the reference slab LR.

**6. ACKNOWLEDGEMENTS**

The authors thank CNPq, CAPES, ITEGAM and IPEAM for financially supporting this and other studies of this nature conducted in the North of Brazil.

**7. REFERENCES**

[01] SOUZA, V. C. M., CUNHA, A. J. P. Lajes em Concreto Armado e Protendido. Rio de Janeiro Ed. UERJ, 1998, 580p. [ Links ]

[02] ACI 318:2008. Building Code Requirements for Structural Concrete. American Concrete Institute, Farmington Hills, Michigan, 2008. [ Links ]

[03] ASSOCIAÇÃO BRASILEIRA DE NORMAS TÉCNICAS. NBR 6118 – Projeto e Execução de Obras de Concreto Armado. Rio de Janeiro, 2007. [ Links ]

[04] JOHANSEN, K. W. Brudlinieteorier (Yield line theories), Copenhagen, Gjellerup, 1943. [ Links ]

[05] OLIVEIRA, D. R. C. Análise Experimental de Lajes Cogumelo de Concreto Armado com Pilares Retangulares. Departamento de Engenharia Civil e Ambiental, Universidade de Brasília, Tese de Doutorado, Brasília, 2003, 214p. [ Links ]

[06] ASSOCIAÇÃO BRASILEIRA DE NORMAS TÉCNICAS. NBR 5739 – Ensaio de compressão de corpos de prova cilíndricos de concreto. Rio de Janeiro, 2007. [ Links ]

[07] ASSOCIAÇÃO BRASILEIRA DE NORMAS TÉCNICAS. NBR 8522 – Concreto – Determinação do módulo de deformação estática e diagrama tensão-deformação – Método de Ensaio. Rio de Janeiro, 2008. [ Links ]

[08] ASSOCIAÇÃO BRASILEIRA DE NORMAS TÉCNICAS. NBR 6892 – Materiais metálicos. Determinação das Propriedades Mecânicas à Tração em Temperatura Ambiente. Rio de Janeiro, 2002. [ Links ]

Received:
30 Oct 2013

Accepted: 25Mar 2014

Available Online: 05 Aug 2014