Abstract

Construction of bicycles with bamboo frames has become an alternative to improve the quality of life of some communities, be friendly with the environment and be ecologically sustainable. However, the production of bike frames is made in an artisanal way and there are few antecedents that have proven their reliability. This work presents the evaluation and simulation of the mechanical behavior of bike frames made in bamboo. Three-points bending tests were performed using bamboo bars with similar dimensions to bike frames, and an equivalent elasticity modulus was determined and used as the input datum of a finite element model. A linear model material and beam elements were used to model the bike frame. Tests were performed using bike frames of bamboo applying loads greater than 7000 N, and the displacements were measured. The experimental displacements were used to calibrate the model, which consisted of modifying the rigidity of the connections until the displacements of the model fit near to 90%. The calibrated model was used for a fatigue simulation in order to predict the lifespan of the bike frame. Some technical values of bamboo bike frames were obtained so that these will allow them to define the technical characteristics of the product and guarantee their operating conditions.

Keywords: bicycle, bike frame, bamboo, fatigue, three-point bending tests, finite element analysis

## 1. Introduction

Bicycles offer a cost-effective transportation alternative primarily for lowincome communities [1]. Additionally, bikes have other advantages, such as zero greenhouse gas emissions, low-cost maintenance, quick displacement in high traffic zones, and physical fitness promotion for the users.

Conventional bike frames, using materials, such as steel [2], aluminum [2, 3], carbon fiber [4, 5], and titanium, have been studied via numerical model analyses and experimental tests. The numerical studies generally use the finite element method, and the tests generally obtain the static load carrying capacity; in this direction, the researches' focus has been oriented to improving the relationship between the weight and the strength. However, the new research trends are focused on the replacement of the bike frame material using a low-cost alternative, like

environmentally friendly materials, low weight and very attractive esthetically [6]. In this direction, the bamboo can become a good alternative.

There are more than 1000 species of bamboo around the world of which 70 are abundant in South America and Asia [7]. Bamboo is a natural fiber species that belongs to grass Poaceae family and subfamily Bambusoideae and grows in diverse types of climate. Compared to other trees, the bamboo has significant low density, high strength, and stiffness [8], most high growth rate (30–100 cm per day). Also, the bamboo plays an important environmental role by preventing ground erosion and landslides in mountainous zones and retaining significant amounts of water that restore ground conditions where it grows [9].

Currently, some companies and foundations have been building a bike frame using bamboo [10–12]. Locally, the bike frames are being manufactured using bamboo and their joints with a composite that uses an epoxy matrix reinforced with natural fibers (fique). However, the composite material joints are highly dependent on the geometric and material characteristics; for this reason, the testing of the actual bamboo bike frame is imperative. Some information can be found in the literature about the experimental strength of bamboo bike frame, although some analyses have been made using the finite element method [2, 13–15]. Once experimental data has been obtained, sensitivity and fatigue studies can be performed in order for the useful life of the bamboo bikes to be assessed.

In this direction, this work pretends to estimate the maximum allowable distance traveled by bikes made using bamboo frames. The general structural performance of the bike frames was evaluated under static and dynamic loads using experimental tests and the finite element method. Also, the mechanical strength of the joints was evaluated.

#### 2. Methods and materials

Several steps were defined in order to perform the research (Figure 1). The first step was to determine the experimental properties of bamboo using a three-point bending test, measuring the displacement of some points of the bike under to external load and experimental modal analysis. The next step was to perform a static analysis of the bamboo bike frame using the finite element method. Using the experimental displacements, the finite element model was calibrated (step 3). The model calibrated was validated using the natural frequencies obtained experimentally (step 4). Finally, a fatigue analysis using the finite element method was performed using S-N curves reported and an estimation of the maximum distance that the bike can travel under the load conditions defined.

#### 2.1 Geometry

The bamboo bike frames were made of bamboo tubes joined with a composite material, a resin as a matrix reinforced with fique (Figure 2).

A bamboo frame size M was used to perform the experiments and finite element analysis (Figure 3).

#### 2.2 Experimental tests

#### 2.2.1 Three-point bending tests

Three-point bending tests were performed in order to characterize the structural behavior of bamboo. The load was applied perpendicularly at midspan of a simply

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

supported beam according to ASTM D790-17 standards [16]; from this test Young's modulus was obtained. Bending tests were performed using a universal test machine UTS 200.3. Wood blocks were placed on load application points in order to avoid the load concentration effects (Figure 4).

Sixteen bamboo specimens with two sets of radii were tested, eight samples with 15.5 mm of outer radius and 10.5 of inner radius and another eight samples with

Figure 2. Bamboo bike-frame.

Figure 3. Bamboo bike-frame dimensions (in mm).

10.5 mm of outer radius and 10.25 mm of inner radius, approximately. A monotonically increasing load was applied to bamboo specimens until fracture and load versus displacement curves were obtained. The Young's modulus was calculated as explained below.

The Y displacement of the midspan of the specimen is:

$$Y = \frac{PL^3}{48EI} \tag{1}$$

Knowing the applied load (P) and the displacement (Y), the Young's modulus (E) must be obtained as:

$$E = \frac{PL^3}{48YI} \tag{2}$$

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

#### Figure 4. Setup of three-point bending test.

where L is the distance between supports and I the inertia of the cross section. The inertia can be calculated as:

$$I = \frac{\pi}{64} \left( D\_{outer}^4 - D\_{inner}^4 \right) \tag{3}$$

where Douter is the outer diameter and Dinner is the inner diameter.

#### 2.2.2 Experimental displacements

A universal test machine UTS 200.3 was used to obtain the experimental displacements of the A, B, and C points (Figures 5 and 6). Three load ramps were applied (2000, 3500, and 6500 N) on the seat tube (Figure 7) of the bike frame, and the displacements were measured. The experimental displacements of the bike frame were used to calibrate the numerical model.

#### 2.2.3 Experimental natural frequencies

To validate the finite analysis model of the bike, experimental modal analysis of the frame was performed to obtain their natural frequencies and compare it to the results of the finite element model.

The experimental frequencies were obtained via a mobile application VibSensor [17], loaded on cell phones. The software provides the natural frequency on the system and its direction as responses to impulse loads are induced on the frame by tapping the frame several times at different locations with different intensities. The planes were defined by the phone (Z direction is normal to the screen of the phone).

In order to prove the accuracy of the mobile application, a simple model was used. The simple model consisted of a steel plate. The plate was fixed on both ends and the cell phone placed on the mid-length; then a load was applied to excite the plate, and their experimental natural frequencies were obtained. The first experimental natural frequencies were 19 Hz (Figure 8) and 19.95 Hz from the finite element model (Figure 9). In this direction, the accuracy of the mobile application was near to 5%. For this reason, the results obtained from the mobile application can be considered acceptable, and it can be used to the bamboo bike frame.

Figure 5. Setup to measure the vertical displacement in bottom bracket joint, point A.

Figure 6. Setup to measure the vertical displacement, points B and C.

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

Figure 7. Names of parts and joints of the bike.

Figure 8. Experimental natural frequencies of the plate using Vibsensor software.

A setup was designed to obtain the natural frequencies of the bamboo bike frame (Figure 10). Cell phones were placed on three tubes: seat stay, chain stay, and down tube.

The bike frame was supported simulating the real conditions: the rear dropouts were fixed along x- and y-axes, and the front dropouts were fixed along y-axis and free along x-axis. The bike frame was excited using a load, and the cell phones registered the accelerations from which modal frequencies were processed, via a mobile application VibSensor.

#### 2.3 Finite element model

The finite element analysis was performed using Abaqus 6.14-3 [18]. A static load of 3500 N and a moment of 350,000 N-mm were applied to the frame at the

Figure 9. Natural frequencies of the plate using finite element model.

Figure 10. Setup of modal test.

saddle. The boundary conditions were defined as the rear dropouts were fixed along x- and y-axes, and the front dropouts were fixed along y-axis and free along x-axis (Figure 11). The elastic modulus was taken from the three-point bending tests.

The geometry was represented using straight bars and beam elements. A standard mesh was used in the model with an approximate global size of 60 mm per element. The cross section of each beam elements is shown in Table 1.
