The Importance of Shear in the Deflection of Bamboo Beams

Abstract

According to the traditional theory of elasticity, the total deflection of a beam occurs due to the combined effect of both the bending moment and the shear force. In isotropic materials such as steel and concrete, the deflection due to shear is usually not taken into account since it represents only 1% of the total deformation approximately. However, in anisotropic materials such as bamboo, the deflection due to shear should be taken into account because it may represent more than 20% of the total deformation of the beam. To better predict the influence of the shear effect on the deflection of bamboo beams, the longitudinal Young ́s modulus and the shear modulus of Guadua angustifolia were determined through the application of repeated three-point bending tests of whole culms and small prismatic elements while aligning their length along the axial direction of the culm. In order to determine the value of the shear modulus, each test was carried out using four different spans. The end results for the culms were: the longitudinal modulus of elasticity E equal to 23525 MPa, and the shear modulus G equal to 298 MPa. Thus, the substantial difference between the Young ́s modulus and the shear modulus confirms the high anisotropy of bamboo, and results indicate that shear deformation should always be included for the calculation of deflections of bamboo structures. Furthermore, the significant differences between these values and those obtained with the small prismatic elements may be attributed to the anisotropy and heterogeneity of the material. However, more tests have to be accomplished to further corroborate these results and find other anisotropic elastic properties of the material.