## 1 Introduction

## 2 Experimental Model

### 2.1 Test Materials and Mix Ratio

^{3}and a particle size of 15 mm or less. In addition, ceramsite with a density of 618 kg/m

^{3}, the cylinder strength of 1.8 Mpa, and the particle size of 8 mm–15 mm and a concentrated high-efficiency cement foaming agent were adopted. In this paper, the types of longitudinally stressed steel bars and stirrup steel bars in the specimens are all HRB500 and HPB300, respectively. The mechanical properties of these steel bars are shown in Table 1.

Specimens | f _{y} (MPa) | f _{u} (MPa) | E _{s} (MPa) |
---|---|---|---|

HRB500 | 500 | 630 | 2 × 10 ^{5} |

HPB300 | 300 | 420 | 2 × 10 ^{5} |

^{3}, 1900 kg/m

^{3}, and 2000 kg/m

^{3}respectively. Compared with the density of plain concrete, the density of the two types of lightweight concrete has been reduced by 23.4% and 19.4%, respectively.

Category | Plain concrete Per m ^{3} | Ceramsite concrete Per m ^{3} | Foamed concrete Per m ^{3} |
---|---|---|---|

Cement (kg) | 434.0 (18.1%) | 434.0 (26.1%) | 557.3 (27.9%) |

Mineral powder (kg) | 144.7 (6.0%) | 144.7 (8.7%) | 268.3 (13.4%) |

Sand (kg) | 700.4 (29.2%) | 700.4 (42.2%) | 990.7 (49.5%) |

Water reducing agent (kg) | 15.0 (0.6%) | 15.0 (0.9%) | 18.6 (0.9%) |

Water (kg) | 138.8 (5.8%) | 138.8 (8.4%) | 165.1 (8.3%) |

Gravel (kg) | 967.2 (40.3%) | – | – |

Ceramsite (kg) | – | 228.5 (13.8%) | – |

Foam (L) | – | – | 516 |

### 2.2 Experimental Design

### 2.3 Loading Scheme

## 3 Experimental Phenomena and Results

### 3.1 Experimental Phenomena

### 3.2 Experimental Results

^{3}) is much smaller than that of cement paste (about 1500 kg/m

^{3}), ceramsite tends to float up during concrete solidification, resulting in uneven distribution of ceramsite in concrete. The uneven distribution in concrete, the discreteness of ceramsite strength, and the complexity and randomness of ceramsite interface bonding may lead to the obvious difference of the load deflection data of CC1 and CC2.

## 4 Calculation of Beam Deflection

### 4.1 Basic Assumptions

### 4.2 Bending Analysis and Deflection Calculation of Normal Section

_{c}, the strain at the distance y from the neutral axis of the section can be calculated by the assumption of the flat section as follows:

_{t1}, y

_{t2,}and y

_{p1,}respectively, represent the ordinate of the resultant force of the first-row tensioned steel bars, that of the second-row tensioned steel bars, and that of compressed steel bars.

_{e}of the concrete will change accordingly, which can be determined by Eq. 8. When using the component, the deformation caused by the axial force and the shear force is negligible. Based on the mathematics software matlab for related programming, this paper calculates the theoretical calculation deflection of each beam by adopting the numerical integration method. In order to ensure sufficient accuracy and calculation speed, the integration step length is selected as 2 mm after multiple debugging.

_{p}is the bending moment of section, and \(\rho (M)\) is the corresponding curvature. E is the elastic modulus of reinforced concrete, and I

_{e}is the effective moment of inertia of the section.

## 5 Results and Analysis

### 5.1 Load–deflection Curve Analysis

### 5.2 Bending Stiffness

Plain concrete | Foamed concrete | Ceramsite concrete | |
---|---|---|---|

Deflection limit (mm) | 3.16 | 3.16 | 3.16 |

The corresponding load of deflection limit(kN) | 216.3 | 201.2 | 222.9 |

Bending stiffness (10 ^{6} N·m^{2}) | 6.52 | 5.88 | 6.75 |

Initial bending stiffness (10 ^{6} N·m^{2}) | 6.78 | 6.67 | 7.31 |

Rate of change | 3.83% | 11.84% | 7.70% |

### 5.3 Failure Analysis

Foamed concrete beam | Ceramsite concrete beam | |
---|---|---|

μ _{r} | 1.13 | 0.94 |

Energy absorption ratio | 1.03 | 0.92 |

Failure mode | Service limit | Shear crack |

### 5.4 Displacement Ductility and Energy Absorption

_{r}is further defined as Eq. 11.

_{l}and μ

_{p,}respectively, represent the ductility factor of lightweight concrete beams and that of the plain concrete beams.

_{i}represents the displacement; F

_{i}represents the load (kN) at this displacement (mm); n represents the number of displacement points.