# Experimental and Numerical Study on Flexural Behavior of a Full-Scale Assembled Integral Two-Way Multi-Ribbed Composite Floor System

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Experimental Investigation

#### 2.1. Material Properties

#### 2.2. Specimen Preparation

#### 2.3. Load Protocol and Sensor Distribution

^{2}and the additional dead load for concrete cement layer and suspended ceiling is calculated as 1.5 kN/m

^{2}. According to the Chinese load code for the design of building structures GB50009-2012 “Load Code for The Design of Building Structures” [29], the live load in residential buildings is 2 kN/m

^{2}. Thus, the maximum area load and the normal service load of the floor system according to GB50009-2012 could be calculated as 1.3 × D

_{load}+ 1.5 × D

_{live}and 1.0 × D

_{load}+ 1.0 × D

_{live}, which equal 10.79 kN/m

^{2}and 7.99 kN/m

^{2}, respectively. Considering the mechanical performance of the floor under 10.79 kN/m

^{2}, where detailed information can be found in Section 3.1, the ultimate area load was enhanced to 16.63 kN/m

^{2}. The overall weight exerted on the floor is 110 tons, which reaches the limits of the laboratory.

^{2}, which was about 10% of the designed bearing load of the floor. The maintained time of each load step was 20 min and the data collection and crack description were carried out after the structural deformation became stable. According to GB/T50152-2012 [29], when the accumulated load reached its self-weight, the structure needed to hold the load for at least 12 h. (3) After the test, the mass blocks on the floor were removed in batches, and the cracking of the concrete on the bottom surface of the floor could be observed after complete unloading.

## 3. Experimental Results

#### 3.1. Experimental Observation

^{2}(the 6th load, accumulated load including its self-weight), a small number of tiny cracks parallel to the direction of the joint appeared on the interface of the new and old concrete. The cracks mainly concentrated in the middle position of the cast-in-situ joints. It is an interesting phenomenon, which will be discussed in the following.

^{2}(the 4th load), the accumulated area load reached 7.89 kN/m

^{2}, which is beyond the service load of GB50010-2010 [24]. There were no cracks and the deflection was only about 2 mm. According to the load protocol, when the additional load reached its self-weight, the experiment was maintained for 24 h. The maximum deflection of the floor increased about 0.5 mm during the maintaining time.

^{2}to 12.38 kN/m

^{2}, the cracks further developed and the number of cracks increased. It was noticed that the cracks did not extend to the joint or the shear keys. Besides that, the distribution of cracks from the 6th load to the 8th load was not symmetrical and not in the sections with maximum movement. Thus, it was predicted that the cracks of the 6th–8th load were mainly caused by initial defects.

^{2}(the 9th load), the accumulated area load exceeded the maximum load of GB50010-2010. The maximum strain of steel rebars was only 450 με and the maximum deflection was 5.32 mm, indicating that the floor did not reach its load-carrying capacity. Thus, additional area load should be exerted to explore its mechanical performance.

^{2}and diagonal cracks appeared in the middle section of the floor. It is worth noting that the diagonal cracks only developed within one single PRBS. With the area load increased, the length and number of diagonal cracks increased rapidly, which was a distinct difference from the cracks that appeared in 6th to 8th load. Some cracks along the shear key of the PRBS appeared during the 11th load, which was a characteristic and typical phenomenon of the innovative floor system. When the 12th load was exerted, a diagonal crack appeared at the intersection of the floor and column, extending from the column to the mid span direction. As the load increased, the width of cracks along the shear key of the PRBS increased.

#### 3.2. Load–Deflection Relationship

^{2}) should be calculated with the long-term effects, and its deflection limit is L

_{0}/300 (L

_{0}is the calculated span of the floor). The maximum deflection was calculated through the displacement sensors D1~D9, as presented in Equation (1).

^{2}, which is its self-weight. Based on this, it can be concluded that the true deflection under normal service load is 2.40 × (7.99/4.49) = 4.27 mm. According to GB50010-2010 [24], the long-term load correction coefficient is 1.856. The calculated long-term load deflection under normal use load is 7.92 mm, which is less than L

_{0}/300 (30.67 mm).

#### 3.3. Stress Distribution

## 4. Finite Element Simulation

^{2}, the finite element method turns out to be a supplementary method.

#### 4.1. Establishment and Meshing of Finite Element Model

#### 4.2. Constitutive Relationship Settings and Element Selection

#### 4.3. Contact and Boundary Conditions

#### 4.4. Load and Analysis Steps

^{2}to fully investigate its nonlinear behaviors. The solver of “static general” in ABAQUS was selected to calculate its numerical results.

#### 4.5. Simulation Results Analysis and Load-Carrying Capacity Calculation

#### 4.5.1. Simulation Results

^{2}(including the self-weight of the floor). The mid span deflection of the floor was 15.91 mm, and the absolute error of the experimental and finite element results was 7.86%.

_{1}is explained as Equation (4) [20], where E

_{0}represents the original undamaged Young’s modulus of concrete, f(ε) is the stress function of a specific node and ${\int}_{0}^{{\epsilon}_{1}}f\left(\epsilon \right)d\epsilon $ stands for the strain energy at the given stress. The range of DAMAGET is within [0,1], indicating the extent of damage of materials. When the concrete works in elastic stage, the strain energy equals $\frac{1}{2}{E}_{0}{{\epsilon}_{1}}^{2}$ and DAMAGET could be calculated as zero. For elements undergoing nonlinear behaviors, the stiffness degrades and the accumulated strain energy is less $\frac{1}{2}{E}_{0}{{\epsilon}_{1}}^{2}$, resulting a larger DAMAGET.

#### 4.5.2. Load-Carrying Capacity Calculation

^{2}. The calculation results of this model are shown in Figure 25 and Figure 26.

#### 4.5.3. Error Discussion

## 5. Conclusions

- (1)
- The assembled integral two-way multi-ribbed composite floor system met the requirements of normal service load and maximum designed load according to GB50010-2010. Under normal use load (7.89 kN/m
^{2}), the long-term deflection of the floor was 7.92 mm, meeting the limit value of deflection L_{0}/300 under normal use limit state. Under the maximum design load of GB50010-2010, the maximum strain of longitudinal rebar at the bottom of the slab was 450 μɛ, indicating that key structural components do not reach the ultimate bearing capacity. - (2)
- The crack mainly concentrated on the joint position and the cracks under 16.63 kN/m
^{2}turned out to be “X-shaped”. At this point, the strain of the longitudinal load-bearing steel bars had not yet yielded, proving that the new floor is of sufficient safety redundancy. - (3)
- The finite element method could serve as an effective tool for studying the ultimate bearing capacity of a new type of assembled integrated bidirectional multi-ribbed composite floor. The absolute error between the experiment and the finite element simulation is less than 10%, and the load-carrying capacity of the floor system is 50.98 kN/m
^{2}.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Ding, D. Calculation of Reinforced Concrete Floor; Press of Science and Technology: Shanghai, China, 1954. (In Chinese) [Google Scholar]
- Safar, A.; Lou, K.B. A study of the action of the beam and beamless (flush) floor slabs of the multistorey buildings. Erciyes Univ. Fen Bilim. Enstitüsü Fen Bilim. Derg.
**2007**, 23, 127–135. [Google Scholar] - Newmark, N.M. Proposed design specifications for two-way floor slabs. J. Proc.
**1950**, 46, 597–607. [Google Scholar] - Nilson, A.H.; Walters, D.B. Deflection of two-way floor systems by the equivalent frame method. J. Proc.
**1975**, 72, 210–218. [Google Scholar] - Idrus, A.B.; Newman, J.B. Construction related factors influencing the choice of concrete floor systems. Constr. Manag. Econ.
**2002**, 20, 13–19. [Google Scholar] [CrossRef] - Hegger, J.; Roggendorf, T.; Teworte, F. FE analyses of shear-loaded hollow-core slabs on different supports. Mag. Concr. Res.
**2010**, 62, 531–541. [Google Scholar] [CrossRef] - Abramski, M.; Schnell, J.; Albert, A.; Pfeffer, K. Experimental and numerical investigation of the bearing behaviour of hollow core slabs. Beton Stahlbetonbau
**2010**, 105, 349–361. [Google Scholar] [CrossRef] - de Lima Araújo, D.; Sales, M.W.R.; Silva, R.P.M.; Antunes, C.D.F.M.; de Araújo Ferreira, M. Shear strength of prestressed 160 mm deep hollow core slabs. Eng. Struct.
**2020**, 218, 110723. [Google Scholar] [CrossRef] - Jiang, Q.; Zhang, K.; Feng, Y.; Chong, X.; Huang, J. Out-of-plane flexural behavior of full precast concrete hollow core slabs with lateral joints. Struct. Concr.
**2020**, 21, 2433–2451. [Google Scholar] [CrossRef] - Xuhong, Z.; Wei, C.; Fangbo, W.; Hailin, H.; Jiyuan, L. Study on stiffness of assembled monolithic concrete hollow floor with two-way ribs. J. Build. Struct.
**2011**, 32, 75. [Google Scholar] - Wang, S.C.; Wang, C.S.; Wang, Q.; Tian, X.F.; Duan, L. Flexural behaviors of full-scale prestressed concrete hollow slab girders with composite strengthening. J. Traffic Transp. Eng.
**2018**, 18, 31–41. [Google Scholar] - Khairussaleh, N.M.; Omar, R.; Aris, S.M.; Nor, M.M.; Saidi, M.M.; Mahari, N.N.M. Flexural Behaviour of the Two-Way Spanning Reinforced Concrete Slab Using Spherical Plastic Bubble Balls. IOP Conf. Ser. Earth Environ. Sci.
**2023**, 1140, 012016. [Google Scholar] [CrossRef] - Morcous, G.; Henin, E.; Fawzy, F.; Lafferty, M.; Tadros, M.K. A new shallow precast/prestressed concrete floor system for multi-story buildings in low seismic zones. Eng. Struct.
**2014**, 60, 287–299. [Google Scholar] [CrossRef] - Huang, Y.; Ma, K.; Zhang, H.; Xiao, J.; Jiang, S. Study and Application of Vierendeel-Sandwich-Plate Floor Framing in Multistoried and Tall Building. J. Build. Struct.
**1997**, 18, 55–64. [Google Scholar] - Pan, Y. Study of Load-bearing Properties of PK Prestressed Composite Slab. Master’s Thesis, University of Hunan, Changsha, China, 2009. (In Chinese). [Google Scholar]
- Niu, W. Experimental and Theoretical Study on Waffle Hollow-Core Composited Floor. Master’s Thesis, University of Hunan, Changsha, China, 2009. (In Chinese). [Google Scholar]
- Pang, R. Research on the Mechanical Property and Seismic Design Method of New Type Precast RC Diaphragms. Master’s Thesis, Southeast University, Nanjing, China. (In Chinese).
- Naito, C.J.; Cao, L.; Peter, W. Precast Concrete Double-tee Connections, Part I: Tension Behavior. PCI J.
**2009**, 54, 49–66. [Google Scholar] [CrossRef] - Spadea, S.; Rossini, M.; Nanni, A. Design analysis and experimental behavior of precast concrete double-tee girders prestressed with carbon-fiber-reinforced polymer strands. PCI J.
**2018**, 63, 72–84. [Google Scholar] [CrossRef] - Gong, L.; Chen, Z.; Feng, Y.; Ruan, S.; Tu, L. Experimental Study on an Innovative Hollow Concrete Floor System Assembled with Precast Panels and Self-Thermal-Insulation Infills. Adv. Civ. Eng.
**2021**, 2021, 6663412. [Google Scholar] [CrossRef] - Fertigteil-Vertrieb, G.; Mannheim, B.-Z. Reinforced Concrete Cellular Plate for One-way and Two-way Stress Directions for High Loads and Large Span. Eng. Des. Broch.
**1965**, 35, 351–354. [Google Scholar] - Fahmy, E.H.; Shaheen, Y.B.I.; Zeid, M.N.A.; Gaafar, H.M. Ferrocement sandwich and hollow core panels for floor construction. Can. J. Civ. Eng.
**2012**, 39, 1297–1310. [Google Scholar] - JGJ/T 268-2012; Technical Specification for Cast-In-Situ Concrete Hollow Floor Structure. China Architecture & Building Press: Beijing, China, 2012.
- GB 50010-2010; Code for Design of Concrete Structures. China Architecture & Building Press: Beijing, China, 2017.
- GB/T 228.1-2010; Metallic Materials–Tensile Testing—Part 1: Method of Test at Room Temperature. Standards Press of China: Beijing, China, 2022.
- GB/T50081-2012; Standards for test methods of mechanical properties on ordinary concrete. China Architecture & Building Press: Beijing, China, 2019.
- JG/T 163-2013; Coupler for Rebar Mechanical Splicing. Standards Press of China: Beijing, China, 2013.
- GB/T 50152-2012; Standard for Test Method of Concrete Structures. China Architecture & Building Press: Beijing, China, 2012.
- GB 50009-2012; Load Code for The Design of Building Structures. China Architecture & Building Press: Beijing, China, 2016.

**Figure 2.**Lightweight infills of the assembled integral two-way multi-ribbed composite floor system.

**Figure 6.**Construction process of the assembled integral two-way multi-ribbed composite floor system. (

**a**) Location of the precast ribbed bottom slab. (

**b**) Insertion of lightweight infills. (

**c**) Coupling the longitudinal rebars and rebar mesh. (

**d**) Casting.

**Figure 14.**Load–deflection relationship of the assembled integral two-way multi-ribbed composite floor.

**Figure 19.**The strain–stress relationship of steel bars [20].

**Figure 20.**Strain–stress relationship of concrete [24].

**Figure 24.**Comparison of load-deflection relationship between experiment and finite element simulation.

**Figure 26.**Comparison of load–deflection relationship between experiment and finite element simulation with a larger area load.

Diameter of Rebar (mm) | Yield Stress (MPa) | Ultimate Stress (MPa) | Young’s Modulus (MPa) |
---|---|---|---|

20 | 420.31 | 620.06 | 217696 |

12 | 451.24 | 616.58 | 209643 |

6 | 436.73 | 580.46 | 213487 |

Position of Concrete | Cubic Compressive Stress (MPa) | Young’s Modulus (MPa) |
---|---|---|

Cast-in-situ section | 36.75 | 30043 |

Precast panels | 39.47 | 29567 |

Coupler for Squeezing Splicing of 20 mm Rebars | Yield Stress (MPa) | Ultimate Stress (MPa) | Young’s Modulus (MPa) |
---|---|---|---|

Tensile strength | 414.57 | 608.02 | 176867 |

Absolute errors compared with rebar (%) | −1.42 | −1.94 | −18.76 |

Load Grade No. | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
---|---|---|---|---|---|---|---|---|---|

Area load (kN/m^{2}) | 0 | 0.85 | 0.85 | 0.85 | 0.85 | 1.09 | 0.85 | 0.85 | 0.85 |

Accumulated area load (kN/m^{2}) | 4.49 | 5.34 | 6.19 | 7.04 | 7.89 | 8.98 | 9.83 | 10.68 | 11.53 |

Maintained time (min) | 20 | 20 | 20 | 20 | 20 | 1440 | 20 | 20 | 20 |

Load grade No. | 9 | 10 | 11 | 12 | 13 | 14 | |||

Area load (kN/m^{2}) | 0.85 | 0.85 | 0.85 | 0.85 | 0.85 | 0.85 | |||

Accumulated area load (kN/m^{2}) | 12.38 | 13.23 | 14.08 | 14.93 | 15.78 | 16.63 | |||

Maintain time (min) | 20 | 20 | 20 | 20 | 20 | 20 |

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**MDPI and ACS Style**

Zeng, X.; Feng, Y.; Ruan, S.; Xu, M.; Gong, L.
Experimental and Numerical Study on Flexural Behavior of a Full-Scale Assembled Integral Two-Way Multi-Ribbed Composite Floor System. *Buildings* **2023**, *13*, 2517.
https://doi.org/10.3390/buildings13102517

**AMA Style**

Zeng X, Feng Y, Ruan S, Xu M, Gong L.
Experimental and Numerical Study on Flexural Behavior of a Full-Scale Assembled Integral Two-Way Multi-Ribbed Composite Floor System. *Buildings*. 2023; 13(10):2517.
https://doi.org/10.3390/buildings13102517

**Chicago/Turabian Style**

Zeng, Xiangqiang, Yan Feng, Sihan Ruan, Ming Xu, and Liang Gong.
2023. "Experimental and Numerical Study on Flexural Behavior of a Full-Scale Assembled Integral Two-Way Multi-Ribbed Composite Floor System" *Buildings* 13, no. 10: 2517.
https://doi.org/10.3390/buildings13102517