Bamboo is a renewable and environmentally friendly material often used for construction. This study investigates the flexural behavior of bamboo beams through theoretical and finite element (FE) analyses. Considering the material’s nonlinearity, a method of calculating load-deflection curves is proposed and validated via FE analysis. The interfacial slippage dominated by the shear stiffness of the interface between two bamboo poles significantly influences the flexural behavior of double-pole bamboo beams. Thus, the load-deflection curves for different shear stiffnesses can be obtained via theoretical and FE analyses. Subsequently, a novel configuration using diagonal steel bands to avoid slippage is presented. An inclination angle of 45° is suggested to adequately develop the stiffness and bearing capacity of the steel band.

Bamboo is a sustainable material used in the construction of buildings [

For original bamboo beams, the natural shape of the bamboo is maintained; this advantage can be exploited in structures. García-Aladín et al. [

To increase the applicability of original bamboo beams, Tian et al. [

To completely exploit the excellent performance of original bamboo beams, this study investigated the flexural behavior of single-pole and double-pole bamboo beams via theoretical analysis. Simultaneously, the influence of interfacial slippage was analyzed. Then, an effective configuration to avoid slippage without destroying the original bamboo was proposed and validated.

The flexural behavior of bamboo beams is directly related to the constitutive model of bamboo along the grain, as shown in

The strain and stress on the central line of the annulus are adopted to represent the strain and stress at the same polar angle. Thus, the area integral can be simplified as the arc integral in the following deduction.

where

where

When the polar angle

where

where

Considering the deformation relationship over the section yields:

where

The bending moment of the section is expressed as

where the constant coefficient

where

There are also two curvature stages for a double-pole bamboo beam. Owing to the cross-section containing two annuli, the elastic stage can be considered for two cases and the elastic-plastic stage for four. Two polar coordinate systems are separately established for the top and bottom bamboo poles.

The location of the neutral axis differentiates the two cases. The neutral axis is located between the centerlines of the two annuli in Case 1; the neutral axis in Case 2 intersects the centerline of the bottom bamboo pole.

The neutral axis and boundary of the elastic and plastic areas differentiate the four cases.

For a simply supported beam, the bending moment is easily plotted.

where

The elastic stage of a double-pole bamboo beam can be considered for two cases and the elastic-plastic stage for four. For this reason, the first two steps for a double-pole bamboo beam are more complicated. However, the load-deflection curve calculations are the same as for a single-pole bamboo beam. The critical bending moment

The interfacial slippage between two bamboo poles is difficult to avoid; this has not been previously considered in double-pole bamboo beam analyses. The influence of interfacial slippage is analyzed based on the following assumptions: 1) The bamboo materials are linearly elastic. 2) The shear force at the interface is proportional to the slippage. 3) The curvatures and deflections of the two bamboo poles are consistent. 4) The shear deformation is not considered when the plane-section assumption is satisfied.

where

FE analysis was adopted to validate the above analysis.

13 | 12 | 180 | 60 | 0.02 |

During the initial stage, the FE results are consistent with the theoretical results. However, there are some discrepancies in the large deformation stage. The load-deflection curves (referred to as FE-Linear because the FE model is analyzed without considering geometric nonlinearities) almost coincide with the theoretical results, indicating that the discrepancy is caused by geometric nonlinearity. The effect of tapering and joints along the length of the bamboo beam is limited. Considering these two factors improves the similarity between the load-deflection curves and original model.

The theoretical analysis of the interfacial slippage is only suitable for the elastic stage [

The diagonal steel bands should meet the two requirements of stiffness and strength.

where

The steel band cannot be sufficiently broad for the shear deformation to cause uneven stretching. Thus, a steel band width of 20 mm is suggested. The thickness of 2 mm is decided to facilitate fabrication. An ideal elastic-plastic constitutive model is adopted for the following analysis and the yield stress of the steel band is 235 MPa.

The steel band combined with bamboo is also simulated. The FE model is illustrated in

Based on the model FE-0, a double-pole bamboo beam with diagonal steel bands is assembled, as shown in

When the span is 3 m and the spacing is 100 mm, the interfacial slippage can be restrained. Its load-deflection curve is consistent with that of the FE model without slippage. The shear stiffness of the interface per unit length ^{2}, which is greater than that of FE-6.4. As shown in ^{2}, which is close to that of FE-6.4.

Case | ^{2}) |
|||||
---|---|---|---|---|---|---|

3 | FE | 100 | ∞ | ∞ | ∞ | ∞ |

FE-6.4 | 100 | 6.4 | 64 | ∞ | ∞ | |

Steel band-400 | 400 | 10.4 | 26 | 13.4 | 33.5 | |

Steel band-200 | 200 | 52 | 67 | |||

Steel band-100 | 100 | 104 | 134 | |||

4.5 | FE | 150 | ∞ | ∞ | ∞ | ∞ |

FE-6.4 | 150 | 6.4 | 42.7 | ∞ | ∞ | |

Steel band-600 | 600 | 10.4 | 17.3 | 13.4 | 22.3 | |

Steel band-300 | 300 | 34.7 | 44.7 | |||

Steel band-150 | 150 | 69.3 | 89.3 | |||

6 | FE | 200 | ∞ | ∞ | ∞ | ∞ |

FE-6.4 | 200 | 6.4 | 32 | ∞ | ∞ | |

Steel band-800 | 800 | 10.4 | 13 | 13.4 | 16.8 | |

Steel band-400 | 400 | 26 | 33.5 | |||

Steel band-200 | 200 | 52 | 67 |

In this study, the flexural behavior of single-pole and double-pole bamboo beams was investigated via theoretical analysis. Simultaneously, the influence of interfacial slippage was analyzed. Then, an effective configuration to avoid slippage was proposed and validated. The following conclusions can be drawn:

A method for calculating the load-deflection curve is proposed, considering the material’s nonlinearity. FE analysis is conducted to validate the calculation method. The FE results match well with the theoretical results. Moreover, the FE results indicate that the influences of the poles’ natural taper and bamboo joints are limited.

The interfacial slippage between the two bamboo poles is difficult to avoid in double-pole bamboo beams. The shear stiffness of the interface per unit length has a significant influence on the flexural behavior of double-pole bamboo beams. For different shear stiffnesses, the load-deflection curves are obtained via theoretical and FE analyses.

A novel configuration using diagonal steel bands is presented to avoid slippage. Owing to the diagonal arrangement, the tension stiffness of the steel band can be converted to horizontal shear stiffness between the two bamboo poles. An inclination angle of 45° is suggested to adequately develop the stiffness and bearing capacity of the band.