### Load Paths in Structures - 3, Bicycle Example by Kotur Raghavan

An earlier article (https://www.fembestpractices.com/2020/10/load-paths-in-human-body-by-kotur.html ) focused on the load paths in human body for two different cases of loading conditions.

A related article focused on the importance of load path. The components in the load path get stressed. In a human body the stress manifests as ‘pain’.

In the present article we will load path in respect of a commonplace thing, a bicycle.

Fig. 4.1, A Bicycle, Component Parts and Classification.

A typical bicycle is shown in Fig 4.1. Items labelled L are all load bearing parts. They are the seat, the central frame (letter L with yellow fill) along with the wheels (including spokes), the handle and the pedal. Brake cables and chain drive form the functional part. Mud guard and the chain guard are safety features. The parts of the bicycle are assembled in such a way that the functional and safety components do not support load in proper usage.

Fig. 4.2 Load Path

In order to have more clarity on load path, let us consider the example of a Bicycle with a single rider of weight W. Let us also assume that the only load of reckoning is the weight of the rider (W).  We will understand the concept with reference to Fig. 4.2.

There are three locations of physical contact between the rider and the bicycle – the seat, the handle and the pedals and they form the load application points. The total weight of the rider gets applied on to the bike in three parts WS, WH and WP and the sum of them will be equal to W. Their relative proportions depends on the sitting posture and the style of riding. For example, during slow relaxed riding we can expect that most of the weight acts on the seat and WS will be relatively be very high. At higher speeds or while climbing a gradient riders tend to leave seat and thereby apply more load directly on the pedals WS may be zero. Likewise the relative values of reactions RR and RF are also dependent on the posture and riding style.

SIMULATION MODELS

A simple working structural model will be as shown in Fig. 4.3.

Fig. 4.3, Working Structural Analysis Model.

All the load carrying components are included. One-dimensional beam elements will simulate well the structural behaviour of the main frame. Here it is assumed that a single spoke in each wheel transmits the load from the bearings (BF and BR) to the road contact points RF and FF. In reality the wheel assembly is quite complex because of the spokes are in pretension. In any case, the model is realistic up to the bearings BR and BF. One can analyse the bicycle for its structural behaviour using the model shown in Fig. 4.4.

Fig. 4.4 Simpler Structural Model

Here the model is truncated at bearings and the points are constrained. It is to be noted that the reaction forces at bearing locations will be same as those at ground contact points in the first model. Such simplifications are frequently introduced in structural analysis. They call for engineering judgment and a feel for the behaviour of structures.

It will perfectly alright to carry out an independent analysis of the wheel assembly using the reaction forces at BF and BR and support at the ground level.

Key Takeaways:

1.       1.    Further insight into load paths in structures.

2.       An insight into development of simulation models. The importance of engineering judgment is emphasized.

### Comments

1. Sir,
Great and very simplest load transfer schematic.
One query I have.
Load transfer from BR to FR & BF to FF is tensile or compressive load?
Spokes of the wheel takes only tensile load as per the assembly of a typical bicycle.
Thank you.
Thank you.

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