# Experimental and Numerical Study of Lattice Girder Composite Slabs with Monolithic Joint

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

^{2}in China, 2018. It is also predicted that in the coming 5 years, the usage of precast slabs will expand to 2 billion m

^{2}in China, which will bring about CNY 600 billion to the construction market. According to the construction demands and economic considerations, it is of great interest in studying the experiments and numerical simulations of the precast concrete slabs.

## 2. Experimental Study

#### 2.1. Test Specimen

#### 2.2. Testing Method

^{2}and the bearing capacity limit state is calculated as 16.4 kN/m

^{2}[17]. In order to investigate the ultimate bearing capacity of the composite slab in this study, the maximum value of the uniformly distributed load is chosen as 40 kN/m

^{2}, which is corresponding to 2.5 times of the value of ultimate bearing capacity of the slab. Before the maximum distributed load (40 kN/m

^{2}), the loading procedure (including the weight of the slab and pile loading) is applied progressively by steps, and for each step the load is 2.0 kN/m

^{2}. When the sandbags are piled up, they are distributed evenly to avoid arch effect. It should be noted that for each loading step, sandbags are evenly piled to the slab by forklift. After each loading step, the load should be kept for 15 min until the measured stress, strain and deflection are stable.

#### 2.3. Test Results

^{2}), which satisfy the crack width limit 0.2 mm of the design code [17]. When the slab is loaded to 10 kN/m

^{2}, the first crack appears in the midspan of the precast bottom plank at 45°, which width is recorded as 0.06 mm. After loaded to 10 kN/m

^{2}, the existing cracks in the midspan of the precast bottom plank gradually extend and pass through the monolithic joint. With further increase of load, the cracks in the precast bottom plank continue to increase, and gradually develop towards the direction of 45°. It is also observed that some paralleled cracks developed near the main crack. Finally, when the load reaches 40 kN/m

^{2}, the maximum width of the crack at the precast bottom plank is 0.76 mm, located at the joint, and the maximum width of the crack at the joint is 0.10 mm. Under the maximum loading value of this test is 40 kN/m

^{2}, which is about 2.5 times of the design value of bearing capacity, the crack width of the LGCS does not reach the crack width limit of 1.50 mm corresponding to the bearing capacity limit, and no shear failure is observed near the joint.

^{2}, the deflection increases linearly with the load. The lattice girder slab is a hybrid system and, therefore, its initial stiffness is due to the composite action between the lattice girders, concrete and reinforcement. When cracking in the concrete plank progressively occurs, there is a load redistribution and stiffness degradation. At this stage, the strength of concrete decreases and the stiffness of the slab is primarily provided by the lattice girder and the reinforcement. When loaded to the ultimate state at 40 kN/m

^{2}, the midspan deflection of the bottom slab reaches 24.07 mm, which is about 1/208 of the span of the slab. However, the deflection is far below the limit of the maximum deflection (1/50 of the span of the slab) according to the Code for Design of Concrete Structures (GB50010-2010) [17]. The load–deflection curve of the latticed girder composite slab is depicted in Figure 10. In this figure, W1 curve represents the load–deflection curve of the midspan from measuring point W1 in Figure 7. W2 and W3 curves represent the mean load–deflection curves of W2a and W2b, W3a and W3b, respectively. In this test, the deflections of x direction and y direction are basically the same in the whole process, indicating that the LGCS has compatible deformation capability. Under the uniformly distributed load, the vertical deformation of the slab is similar to that of the traditional concrete two-way slab.

^{2}, which indicates that the slab presents a certain mechanical characteristic of orthogonal anisotropic due to the existence of monolithic joint.

^{2}. After being loaded to 16 kN/m

^{2}, the strains from all measuring points paralleled to joint increases progressively, and their value exceed that of vertical to joint. The maximum strain value appears in the midspan. As for the reinforcement vertical to the joint, similar strain distribution can also be observed. The load–strain curves of the vertical longitudinal reinforcement are more irregular when comparing with that of paralleled longitudinal reinforcement, probably due to the existence of the joint which cuts off the steel bars and brings the discontinuities.

## 3. Numerical Simulation

#### 3.1. Numerical Model

#### 3.2. Simulation Results

## 4. Parametric Study

## 5. Conclusions

^{2}, the deflection increases linearly with the load. When cracking in the concrete plank progressively occurs, there is a load redistribution and stiffness degradation. The final midspan deflection LGCS of the bottom slab is 24.07 mm (about 1/208 of the span) which is far below the limit of the maximum deflection (1/50 of the span of the slab) according to the Code for Design of Concrete Structures (GB50010-2010), under 2.5 times of the bearing capacity limits (40 kN/m

^{2}). It also can be observed by the load–deflection curve that the LGCS has sufficient stiffness and bending resistance. Therefore, the LGCS meets the requirement of existing design code [16,17]. Experimental test data in the presenting paper can be used to determine the load–deflection of the LGCS that can result in significant efficiencies for propping arrangements on site.

^{2}), the final maximum crack appears at the monolithic joint with the value of 0.76 mm which is much bigger than the other areas.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 7.**Arrangement of testing measuring points: (

**a**) Strain measuring points of concrete; (

**b**) Strain measuring points of steel; (

**c**) Deflection measuring point.

**Figure 9.**Cracking distribution of bottom plank at different loading stages: (

**a**) Crack distribution at load q = 10 kN/m

^{2}; (

**b**) Crack distribution at load q = 16 kN/m

^{2}; (

**c**) Crack distribution at load q = 22 kN/m

^{2}; (

**d**) Crack distribution at load q = 28 kN/m

^{2}; (

**e**) Crack distribution at load q = 34 kN/m

^{2}; (

**f**) Crack distribution at load q = 40 kN/m

^{2}.

**Figure 12.**Load–strain curves of reinforcement: (

**a**) Load–strain curves paralleled to the joint; (

**b**) Load–strain curves vertical to the joint.

**Figure 17.**Comparison of experimental and numerical failure modes at concrete bottom plank: (

**a**) Experimental cracking distribution; (

**b**) Tensile damage contour of concrete bottom plank from FE simulation.

Dilation Angle | Eccentricity | ${\mathit{f}}_{{\mathit{b}}_{0}}/{\mathit{f}}_{{\mathit{c}}_{0}}$ | k | Viscosity Parameter |
---|---|---|---|---|

30 | 0.1 | 1.16 | 0.667 | 0.0005 |

Strain/(10^{−6}) | C1 | C2 | C3 | C4 | C5 | C6 |
---|---|---|---|---|---|---|

Experiment | 112 | 81 | 287 | 432 | 656 | 603 |

Simulation | 118 | 80 | 265 | 438 | 653 | 569 |

Error | 5.4% | −1.2% | −7.6% | 1.4% | −0.4% | −5.6% |

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**MDPI and ACS Style**

Zhang, X.; Li, H.; Liang, S.; Zhang, H.
Experimental and Numerical Study of Lattice Girder Composite Slabs with Monolithic Joint. *Crystals* **2021**, *11*, 219.
https://doi.org/10.3390/cryst11020219

**AMA Style**

Zhang X, Li H, Liang S, Zhang H.
Experimental and Numerical Study of Lattice Girder Composite Slabs with Monolithic Joint. *Crystals*. 2021; 11(2):219.
https://doi.org/10.3390/cryst11020219

**Chicago/Turabian Style**

Zhang, Xuefeng, Huiming Li, Shixue Liang, and Hao Zhang.
2021. "Experimental and Numerical Study of Lattice Girder Composite Slabs with Monolithic Joint" *Crystals* 11, no. 2: 219.
https://doi.org/10.3390/cryst11020219