3.4 Dynamic response of the finite element model

Using the finite element model calibrated and validated, a dynamic response analysis was performed. The maximum reaction force at dropout joint zone was 114 N (Figure 17), the maximum stress was 114.6 MPa at the dropout, and the maximum displacement was 70.6 mm at the seat joint (Figure 18, Table 5). The

Figure 17. Reaction force profile at dropout joint zone.

#### Figure 18.

Results of dynamical analysis simulation.


#### Table 5.

Maximum stress and displacements at control points.

results show that the maximum stress occurs at dropout joints; hereby, this joint requires special attention.

From on the dynamic simulation of bike frame and assuming that the bike travel at 25 km/h, with a rider of 100 kg, and a road with contiguous bumps of 6 cm in height and 34 cm in length. The mechanical response at the intersection between the seat stay and the rear dropout was 114 MPa. Using a rate of application of 1351 cycles/km, 90 km is the distance a rider rides per week. Then, for a year the distance is 4680 km, and assuming a life of the bike of 10 years, the bike works:

Napplied <sup>¼</sup> <sup>4680</sup> kilometer year � ð Þ� <sup>10</sup> years <sup>1351</sup> N kilometer (6)

$$N\_{applied} = 6.3 \times 10^7 \text{ cycles} \tag{7}$$

Using the bamboo fatigue S-N curve reported by Song [24] and the stress profile obtained from the dynamic analysis (Figure 19), a fatigue analysis was performed. The life obtained was 1.7 � 109 cycles, the damage ratio, Napplied/Nallowed = 0.037; this indicates that the bike frame would last 26 times longer than its intended use; then the fatigue life of the frame will be more than 100 years, for these work conditions.

#### 4. Discussion and conclusions

The relatively large scatter obtained for the elastic moduli can be explained by the non-exactly replicated nature of the bamboo material from plant to plant [25]. The differences of Young's moduli between thicker and thinner diameter bamboo

Structural Evaluation of Bamboo Bike Frames: Experimental and Numerical Analysis DOI: http://dx.doi.org/10.5772/intechopen.89858

Figure 19. Stress vs. time profile from dynamical response of the frame.

specimens may be explained by the differences between the compaction of the bamboo structure or the relation between the thickness and diameter of the bamboo samples, depending on the zone of the stem where the specimens were extracted.

In general, bamboo is thicker at the top than at the base of the culms [25]. Comparing the structures for the different diameters, the thinner diameter bamboo (Figure 20) has a structure more compact than the thicker diameter bamboo (Figure 21) and consequently higher Young's modulus [26].

The vascular bundle is a small longitudinal interstice of the bamboo stem (Figures 20 and 21). It affects directly the mechanical properties of the specimen due to these pores that act as stress concentrations. Kanzawa et al. [27] proposed to measure the maximum width and length of the vascular bundles (Figure 22). In this work, an average of 0.45 mm length and 0.38 mm width for thicker bamboo and 0.19 mm length and 0.14 mm width for thinner bamboo. Because the gap in the thinner bamboo is smaller than the thicker bamboo, the Young's modulus in the thinner is going to be higher making it more rigid.

In addition, a dynamic simulation of the bamboo frame was performed to obtain the acting forces at the bike frame and thus the stresses, at the most critical joint entering the rear dropout. With this information, the generic specimen representative of this joint was prepared to generate additional fatigue data to evaluate the useful life of the frame in future works (Figure 23).

Figure 20. Microscopical section view for thinner bamboo specimen (1).

Figure 21. Microscopical section view for thicker bamboo specimen (1).

Finally, a methodology was proposed to evaluate the fatigue life of the bamboo bike frame from the experimental data reported for bamboo samples. However, the results should be taken as an approximation because the fatigue life of the bamboo bike frame has a high dependency on their joints. In this direction and in future works, it is necessary to perform fatigue experiments using the whole bike frame or at least to test the joints separated. This can be explained as there are substantial differences between the fatigue life of base material and the fatigue life of the final product. Also, some technical values of bamboo bike frames were obtained, so that

Figure 22. Vascular bundle scheme in a section view of a bamboo specimen.

Figure 23. Generic specimen representative of the rear dropout joint.

these will allow them to define the technical characteristics of the product and guarantee their operating conditions.
