Influence of tapered geometry on modal frequencies of bamboo frames

Traditional full-culm bamboo buildings are predominantly found across South America, Africa and Asia, often located in seismically active regions. Despite bamboo's inherently favourable strength-to-weight ratio, which can contribute to good seismic performance, natural bamboo culms can be characterised by significant geometrical variability in their cross-sectional dimensions, causing a non-uniform distribution of the stiffness and mass along the structural element. Nevertheless, common design practice involves modelling bamboo structures with uniform or equivalent uniform culms, determined by using either the average or the smallest cross-section dimensions. This practice can result in a non-conservative design in the case of dynamic response, depending on the computed structural modal frequencies, which differ when using tapered rather than prismatic elements. This study assessed the impact of each geometrical parameter on the transverse vibration properties of bamboo culms through the analytical formulation of a dynamic taper beam of hollow circular section. Parametric modal analyses, considering the natural variation of common bamboo species, were carried out on beam and frame systems. Comparison with the equivalent uniform approach proposed in ISO 22156:2021 highlighted the limiting cases in which the simplified approach could still be applied to the dynamic design of full-culm bamboo structures.