- Open Access

# Strengthening of Cutouts in Existing One-Way Spanning R. C. Flat Slabs Using CFRP Sheets

- Hamdy K. Shehab
^{1}, - Ahmed S. Eisa
^{1}Email author and - Kareem A. El-Awady
^{1}

**11**:186

https://doi.org/10.1007/s40069-017-0186-7

© The Author(s) 2017

**Received: **11 September 2016

**Accepted: **31 January 2017

**Published: **1 June 2017

## Abstract

Openings in slabs are usually required for many different applications such as aeriation ducts and air conditioning. Opening in concrete slabs due to cutouts significantly decrease the member stiffness. There are different techniques to strengthen slabs with opening cutouts. This study presents experimental and numerical investigations on the use of Carbon Fiber Reinforced Polymers (CFRP) as strengthening material to strengthen and restore the load carrying capacity of R.C. slabs after having cutout in the hogging moment region. The experimental program consisted of testing five (oneway spanning R.C. flat slabs) with overhang. All slabs were prismatic, rectangular in cross-section and nominally 2000 mm long, 1000 mm width, and 100 mm thickness with a clear span (distance between supports) of 1200 mm and the overhang length is 700 mm. All slabs were loaded up to 30 kN (45% of ultimate load for reference slab, before yielding of the longitudinal reinforcement), then the load was kept constant during cutting concrete and steel bars (producing cut out). After that operation, slabs were loaded till failure. An analytical study using finite element analysis (FEA) is performed using the commercial software ANSYS. The FEA has been validated and calibrated using the experimental results. The FE model was found to be in a good agreement with the experimental results. The investigated key parameters were slab aspect ratio for the opening ratios of [1:1, 2:1], CFRP layers and the laminates widths, positions for cutouts and the CFRP configurations around cutouts.

## Keywords

## 1 Introduction

Today, the use of carbon fiber reinforced polymers (CFRP) as external reinforcement to strengthen existing slabs due to openings is becoming more popular, partly due to ease of installation and partly due to space saving. In these situations, CFRP sheets are applied to the slab before the opening is made even though CFRP is used for strengthening of openings, very few studies on the structural behavior of slabs with openings have been carried out. Casadei et al. (2003) ANSYS (2011) reported a series of tested one-way slabs with openings strengthened with CFRP. The slabs had openings at the centers and in areas close to the supports. Most of the reported work was related to the strengthening of slab openings at the positive moment regions. It was found that the presence of openings in the negative moment areas usually increases the shear stresses (Casadei et al. 2003). Tan and Zhao (2004) performed a study incorporated strengthened slabs with symmetric and asymmetric openings. The strengthened slabs showed equal or higher capacity of the control slabs with openings. Most of the slabs showed flexural failure mode whereas some of them showed a different failure pattern where the cracks extended from the opening corners. One of the Tan et al. (2004) findings was related to the failure mode dependency on the opening location. Slabs with openings placed in the maximum moment region failed in flexural mode while openings located in the shear region failed in shear mode.

Enochsson et al. (2007) tested two-way slabs strengthened with CFRP and the results showed that the stiffness and ultimate load of the slabs with large opening is higher than the small opening with the same opening locations. Those results could be attributed to the equivalency of larger slabs to hidden beams (Enochsson et al. 2007). Mota and Kamara (2006) presents a particularly detailed review of forming cutouts in two-ways slab systems. A lower-bound analytical model provided herein serves as an alternative form of practical analysis of FRP-strengthened slabs with cutouts. In addition, it considers the FRP effect and associated failure modes. The analytical method is essentially a strip method of analysis, and is based upon the ultimate moment of resistance provided by the slab along critical crack lines in any direction It considers longitudinal and transverse slab behavior, and is found to correlate well with existing and current test data provided certain assumptions are made for the calculation of the sectional strength and position of the critical crack.

Vasquez and Karbhari (2003) showed that the appropriate design of the strengthening measure enables capacity reduced by the presence of the cutout to be regained while mitigating and retarding crack growth. Ultimate failure was through a sequence of cracking and debonding of the FRP composite reinforcing strips with a decrease in load capacity after debonding to the response level of the unstrengthened slab with a cutout after yield of the steel reinforcement. More information about reinforced concrete slabs with cutouts strengthening could be found in Mosallam and Mosalam (2003), Ozgur et al. (2013).

Muhammed (2012), tested eight self-compacting concrete slabs. Results showed that, the use of CFRP strips is more effective than the steel fiber, use of steel fiber increased the load capacity by 26.67 and 9.83% for small and large opening respectively, while CFRP increased the load capacity by 46.67 and 55.7% for small and large opening respectively, CFRP and steel fiber reduced the cracks at the inside faces of the opening while CFRP prevent it at the inside corners of opening. Smith and Kim (2009) reported the results of strengthened one-way slabs with FRP cutouts at their centers. Four slabs with cutouts were tested in addition to two slabs without cutouts. The effect of different load application positions was investigated, in addition to distribution of stresses around the cutout. All FRP-strengthened slabs failed by de-bonding, however, the extent of de-bonding and the ability of the slab to sustain load post-initiation of de-bonding was dependent on the position of the load. The slab in which the line load was located adjacent to the cutout exhibited transverse bending action and as a result was able to withstand more extensive de-bonding prior to loss of load-carrying enhancement from the FRP.

Sorin-Codrut et al. (2015) studied two-way simply supported reinforced concrete slabs subjected to a uniformly distributed load. Slabs with strengthened and non-strengthened openings have been investigated. CFRP sheets have been used for the strengthening. Focusing on examining the structural behavior of two-way RC slabs strengthened with CFRP due to a sawn-up opening, test results clearly showed that the investigated strengthening system can be used to strengthen existing slabs with made openings, and even that the load carrying capacity can be increased when compared to the homogeneous slab, The slabs with the larger openings have a noticeable higher load carrying capacity and a stiffer load–deflection response than the slabs with the smaller openings. In addition to that, it was stated that the ultimate load of strengthened slabs with the cutouts increased by 121%.

The existence of openings in slabs can also degrade the in-plane capacity and stiffness of when they are subjected to in-plane/earthquake loads. Khajehdehia and Panahshahib (2016) conclude that that presence of openings clearly changed the in-plane behavior of RC slabs compared to those of slabs without openings and that this oversimplification in design and analysis of slabs by ignoring the opening effects might lead to erroneous results, Song et al. (2012). Tested three isolated interior flat slab-column connections that include three types of shear reinforcement details; stirrup, shear stud and shear band were tested under reversed cyclic lateral loading to observe the capacity of slab-column connections. The results were applied to the eccentricity shear stress model presented in ACI 318-08. The failure mode was defined by considering the upper limits for punching shear and unbalanced moment. In addition, an intensity factor was proposed for effective widths of slabs that carry an unbalanced moment delivered by bending.

The main aim of this study is to investigate the behavior of reinforced concrete one-way flat slabs with cutouts. The cutouts were made during slab loading which represents slabs under service conditions. The data generated in this paper are mainly came out of testing five slabs experimentally under various key parameters and by using finite element modeling.

## 2 Experimental Program

### 2.1 Description of Tested Slabs

Description of tested specimens.

Group | Specimen | Cutout aspect ratio | Cutout size (mm) | Use of CFRP sheets |
---|---|---|---|---|

Reference | S0 | None | None | None |

1 | S1 | 1:1 | 200 × 200 | None |

S2 | 2:1 | 200 × 400 | None | |

2 | S3 | 1:1 | 200 × 200 | Around cutout at tension surface |

S4 | 2:1 | 200 × 400 | Around cutout at tension surface |

### 2.2 Materials

^{2}at 28-days.

Mechanical properties of steel bars.

Nominal diameter (mm) | Yield load (kN) | Ultimate load (kN) | Yield stress (N/mm | Ultimate tensile strength (N/mm | Ultimate strain (%) |
---|---|---|---|---|---|

10 | 35.5 | 47.8 | 450 | 610 | 16 |

Physical and mechanical properties of Sikawrap Hex^{®}-230C.

Sikawrap Hex | |

Areal weight (±10) | 230 ± 10 (g/m |

Density | 1.76 (g/cm |

Adhesive strength on concrete | 4 (MPa) |

Density | 1.31 (Kg/lit) |

CFRP unidirectional properties | |

Tensile strength of fibers (nominal) | 4300 (MPa) |

Tensile E-modulus of fibers (nominal) | 238,000 (MPa) |

Strain at break of fibers | 1.8 (%) |

Fabric design thickness | 0.13 (mm) |

Tensile strength | 30 (MPa) |

Tensile E-modulus in flexural | 3800 (MPa) |

### 2.3 Sensors and Measurements

### 2.4 Loading Arrangement and Test Procedure

## 3 Experimental Results and Dissusion

### 3.1 Flexural Failure Mode

Ultimate loads and failure modes of tested slabs.

Group | Specimen | Ultimate load (kN) | Failure mode |
---|---|---|---|

Reference | S0 | 67 | Flexure |

1 | S1 | 56 | Flexure |

S2 | 41 | Flexure | |

2 | S3 | 62 | Rupture of CFRP sheets |

S4 | 45 | Rupture of CFRP sheets |

### 3.2 Rupture of CFRP Sheets

Failure mode of the strengthened slabs S3 and S4 was mainly due to the rupture in the CFRP sheets. However, the rupture was preceded by steel yielding. The load carrying capacity at failure was relatively larger for the CFRP strengthened slabs. No significant differences in crack patterns between strengthened and un-strengthened slabs was observed, the extent of cracking from the corners of the cutout to the slab edges become not wider in strengthened slabs.

### 3.3 Behavior of Tested Slabs

Based on the experimental results, the behavior of the tested slabs is discussed in terms of observed crack patterns, ultimate load, measured deflection, and measured strains at different locations along the reinforcing steel bars, concrete surface, and CFRP sheets. The relationships between the applied load, deflection, and the longitudinal strains for concrete, steel, and CFRP of the tested slabs were typical for all tested slabs. Linear behavior followed by a nonlinear Trend and strain hardening and softening until failure. The slope of the first part of the plotted curves (load vs strain) of the tested slabs showed expected behavior until reaching 30 kN (where cutout was made), after that being sharper for un-strengthened slabs, the slope decreases by strengthening the cutouts using CFRP sheets. The reference slab (S0) where no cutout was made showed higher point of initial cracking than the rest of all tested slabs due to the presence of cutout that reduces the slab stiffness.

## 4 Finite Element Analysis

### 4.1 Element Type and Meshing

The properties of the FE elements depend on the element type such as cross-sectional area of beam element is known in ANSYS as real constants. Not all element types require real constants to be defined, and different elements of the same type may have different real constant values. In case of concrete, real constants defined only for SOLID65 element and in the present study the concrete is modeled using discrete reinforcement. Therefore, all real constants which activate the smeared reinforcement are disabled by putting it equal to zero. As there are no reinforcements through the resin, then, the same real constants are specified to the SOLID65 element for resin. In general, crushing stiffness factor (CSTIF) for concrete is set to be 0.1. SOLID185 in form of homogeneous Structural Solid or layered Structural Solid does not require the definition of real constants. LINK180 has real constants; cross sectional area, and added mass (mass/length). Both tension and compression capability is chosen.

### 4.2 Concrete

As shown in Fig. 14, when concrete subjected to compression load, the stress–strain starts linearly in an elastic manner up to about 30 percent of the maximum compressive strength *σ*
_{
cu
}, then, the stress increases gradually up to the maximum compressive strength, and then, the curve descends into a softening region, and eventually crushing failure occurs at an ultimate strain *ε*
_{
cu
}. In tension zone, the stress strain curve is approximately linearly elastic up to the maximum tensile strength. After this point, the concrete cracks and the strength decreases gradually to zero.

Typical shear transfer coefficients range from (0.0 to 1.0), with 0.0 representing a smooth crack (complete loss of shear transfer) and 1.0 representing a rough crack (no loss of shear transfer). This specification may be made for both the closed and open crack. When the element is cracked or crushed, a small amount of stiffness is added to the element for numerical stability. The stiffness multiplier CSTF is used across a cracked face or for a crushed element to be equal to 0.1, ANSYS 2011 (ANSYS 2011). A number of preliminary analyses were attempted in this study with various values for βt and βc within a range between (0.15 to 0.9) and (0.5 to 0.9) respectively. Where βt and βc are shear transfer coefficient for open cracks (βt), and shear transfer coefficient for closed cracks (βc), (ANSYS 2011). For this analysis βt and βc were set to 0.2 and 0.8 respectively, achieving a good converging problem. The uniaxial cracking strength is taken to be equal to the modulus of rupture of concrete. Due to the similarity of resin with concrete in its behavior toward the tensile and compression stress, so SOLID65 solid element with linear and nonlinear properties is used to represent the resin in the present model.

### 4.3 FRP Composites

The FRP composites are anisotropic materials; where the material properties are different in all directions. For the unidirectional lamina, it has three mutually orthogonal planes of material properties, (xy, xz, and yz planes). The xyz coordinate axes are referred to as the principal material coordinates where the x-direction is the same as the fiber direction, and the y and z directions are perpendicular to the x direction. It is a so-called especially orthotropic material. The perpendicular plane of fiber direction can be considered as isotropic material, that’s where; the properties in the y-direction are the same as those in the z-direction. FRP laminates have stress–strain relationships that are roughly linear up to failure. In the nonlinear analysis of the full-scale transverse slabs, no FRP elements show stresses higher than their ultimate strengths. Consequently, in this study it is assumed that the stress strain relationships for the FRP laminates are linearly elastic.

### 4.4 Steel Reinforcement

### 4.5 Loads and Boundary Conditions

## 5 Comparison Between FE and Experimental Results

Comparison between experimental and finite element results.

Group | Specimen | Experimental ultimate load pue (kN) | Finite element ultimate load P | P |
---|---|---|---|---|

Reference | S0 | 67 | 65 | 0.97 |

1 | S1 | 56 | 55.2 | 0.99 |

S2 | 41 | 42 | 1.02 | |

2 | S3 | 62 | 60 | 0.97 |

S4 | 45 | 45.8 | 1.02 |

^{2}as a function of the number of layers. As expected, Increasing the cross sectional area of CFRP by 100%, led to an increase in the ultimate load 0f 14.1% for one layer. Figure 19 shows the effect of number of layers on the ultimate slab load. In general, increasing the number of CFRP layers, has a significant increase in the ultimate load.

Effect of increasing CFRP number of layers and widths on ultimate loads.

Model | Cutout size, mm | No. of layers | Layer width, mm | Area of CFRP layers, mm | Ultimate load (kN) | % increase ultimate load |
---|---|---|---|---|---|---|

S1 | 200 × 200 | – | – | – | 55.2 | – |

S2 | 200 × 400 | – | – | – | 42.0 | – |

S3 | 200 × 200 | 1 | 100 | 13.0 | 60.0 | 8.7 |

150 | 19.5 | 62.4 | 13.0 | |||

200 | 26.0 | 63.0 | 14.1 | |||

2 | 100 | 26.0 | 63.0 | 14.1 | ||

150 | 39.0 | 65.2 | 18.1 | |||

200 | 52.0 | 67.2 | 21.7 | |||

3 | 100 | 39.0 | 64.8 | 17.4 | ||

150 | 58.5 | 69.0 | 25.0 | |||

200 | 78.0 | 71.4 | 29.3 | |||

S4 | 200 × 400 | 1 | 100 | 13.0 | 45.8 | 9.0 |

150 | 19.5 | 47.4 | 12.9 | |||

200 | 26.0 | 48.6 | 15.7 | |||

2 | 100 | 26.0 | 49.2 | 17.1 | ||

150 | 39.0 | 51.6 | 22.9 | |||

200 | 52.0 | 52.8 | 25.7 | |||

3 | 100 | 39.0 | 51.6 | 22.9 | ||

150 | 58.5 | 54.6 | 30.0 | |||

200 | 78.0 | 57.6 | 37.1 | |||

4 | 100 | 52 | 53.4 | 27.1 | ||

150 | 78 | 58.2 | 38.6 | |||

200 | 104.0 | 64.2 | 52.9 | |||

5 | 100 | 65.0 | 56.4 | 34.3 | ||

150 | 97.5 | 63.0 | 50.0 | |||

200 | 130.0 | 69.0 | 64.3 |

### 5.1 Calculations of CFRP Amount Required for Strengthening

*N*) is the number of steel bars which have been cut we can compute the equivalent area of CFRP for each side direction.

For group 1, (N = 1) is the number of steel bars which have been cut (for slab with opening 100 * 100 mm). Substituting into Eq. (3) we can compute the equivalent area of CFR = 33.3 mm^{2}. For group 2 (N = 3) is the number of steel bars which have been cut (for slab with opening 200 * 100 mm). Substituting into Eq. (3) we can compute the equivalent area of CFRP = 100 mm^{2}.

### 5.2 Effect of Cutouts Location

Effect of changing cutouts positions on ultimate load.

Section | Location | Model | Ultimate load, P | P | Moment of resistance M | Ult.Ld. after strengthening, P | % increase ultimate load |
---|---|---|---|---|---|---|---|

1 | At support (M1 = 19.5 kN m) | S0 | 65.0 | 1.00 | 19.0 | Reference | – |

2 | Hogging zone (M2 = 17.9 kN m) | S1 | 55.2 | 0.85 | 16.0 | S3 = 60.0 | 8.7 |

S2 | 42.0 | 0.65 | 11.7 | S4 = 45.8 | 9.0 | ||

3 | Quarter span (M3 = 14.6 kN m) | S1′ | 63.0 | 0.97 | 16.0 | S3′ = 63.6 | 1.0 |

S2′ | 55.0 | 0.85 | 11.7 | S4′ = 59.4 | 8.0 | ||

4 | Mid span (M4 = 11.3 kN m) | S1′′ | 64.2 | 0.99 | 16.0 | S3′′ = 64.8 | 1.0 |

S2′′ | 63.6 | 0.98 | 11.7 | S4′′ = 64.2 | 1.0 |

### 5.3 Effect of Changing of CFRP Configurations Around Cutouts

Effect of changing CFRP sheets configuration around cutouts on ultimate load.

Model | CFRP sheets configuration around cutout | Ultimate load (kN) | % increase ultimate load |
---|---|---|---|

S1 | – | 55.2 | – |

S3 | Parallel to cutout edges | 60.0 | 8.7 |

Inclined 45° at cutout corners | 57.0 | 3.2 | |

S4 | Parallel to cutout edges | 45.8 | 9.0 |

Inclined 45° at cutout corners | 43.4 | 3.3 |

## 6 Conclusions

- 1.
The relationships between the applied load, deflection, and the longitudinal strains for concrete, steel, and CFRP of the tested slabs were typical for all tested slabs, a linear increase behavior followed by a nonlinear behavior until failure has been observed.

- 2.
The slope of the first part of the axial load-strain curves of the tested slabs showed the expected trend and behavior until reaching 30 kN loading (producing cut out), after that the slope became sharper for un-strengthened slabs, the sharpness degree decreased by strengthening the slabs by CFRP sheets.

- 3.
The ultimate loads increased by about 10.7 and 9.7% for slab groups 1 and 2, respectively when slabs strengthened using CFRP sheets and that is due to the confinement stress provided by the CFRP sheets. The deflection decreased by about 23 and 17% for slab groups 1 and 2, respectively when slabs strengthened using CFRP sheets.

- 4.
Reference and un-strengthened slabs had flexural mode failure, where the steel bars reached the ultimate strain at failure load. For strengthened slabs, the rupture of CFRP sheets was the control mode of failure, the CFRP sheets reached the ultimate strain at failure load when the steel bars reached the ultimate strain before failure load due to strengthening technique.

- 5.
The steel bars beside cutout directly had been strained significantly; the strengthened slabs had strained less than the un-strengthened slabs due to the effect of the encirclement by CFRP laminates, whereas transverse CFRP laminates strained proportionally with loading although it was parallel to load line but the practical reason was the diagonal cracks originated from each corner of the cutout.

- 6.
The finite element model results closely agreed with the experimental results; the model overestimates the values of the ultimate loads of the tested slabs by 2–3%.

- 7.
The amount of CFRP used to strengthen slabs was computed under the premise that the loss of steel reinforcement caused by the cutout would be replaced by an equivalent amount of CFRP to restore the load carrying capacity of R.C. slabs after having cutout.

- 8.
To select suitable cutout location in existing R.C. slabs, the moment of resistance should be considered for slab at cutout’s section. The position of the cutout with CFRP strengthening doesn’t provide significant change in load capacity, and finally slabs strengthened with CFRP sheets along the cutout edges give results higher than CFRP sheets at the cutout’s corners with 45° only.

## Declarations

**Open Access**This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

## Authors’ Affiliations

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