Tandem bicycle

Design process for a lightweight unisex tandem bike using the finite element analysis (FEA). The problem to solve was whether the bicycle would be able to resist fatigue and its natural frequency. The frame was then modelled using Solidworks which was also used for the fatigue and frequency simulations. To improve the frame there are three iterations each one tested with two materials using mesh refinement.


In order to get an idea of the dimensions of tandem bike frames existing ones were explored. Choosing the tandem bicycle in Figure 1 as inspiration for the final model. First, a base sketch was created to have all the dimensions according to the brief. Hence the centres of the two wheels were 2m apart being 26 inch in diameter and the seats where place 800mm from the surface.


All elements of the frame are assumed to be perfectly rounded tubes with a maximum of 70 mm diameter, all welded together with 10mm fillets. The changes in the properties of the material while welding was not taken into account. The wheels, pedals, seats and handles were not modelled. The surfaces in the model have no imperfection which would not happen in real life. The behaviour of both materials, magnesium and aluminium was assumed to be linear hence a non-linear study is not required. The weight of the users was distributed uniformly which would difficulty happen in reality. The rear wheel bearings were 40 mm in diameter and spaced 150 mm apart from each other and held by bent tubes attached to the main frame in order to leave space for the wheel. The simulations are all tested on the case where both riders would be pedalling in synchronisation.

Boundary conditions and loading

Both rear wheel bearings were set as hinges as there should be rotation happening on the y-axis but no translation on x, y, z-axis. The fork shell was set to a fixed geometry. Hence, the fork shell has 0 degrees of freedom. The bicycle frame must be able to sustain two 100 kg adults. Therefore, two vertical downwards forces of 981 N were set at the two points where the seats would be. Gravity was applied to the simulations. A remote load was set on the crank shell in order to simulate the force from the pedals. This was estimated to a 1000 N, this would happen in the extreme case of the user resting its whole mass on the pedal. To test whether the frame would fail from the loading on the pedals two static simulations were set. The stress was analysed using von Mises criterion, as both aluminium and magnesium are ductile materials. Equivalent stress was needed to compare to the yield strength of the materials to determine if the model would fail.

Frequency and fatigue studies

Bicycle frames are subjected to a reciprocating pedalling load. This produces a cyclic loading event caused by pedalling. These two events were previously simulated using two static studies (one for each side of the bicycle). Hence the importance of undertaking a fatigue study of the model to determine its lifespan. The frame should be able to withstand at least 10 years of cyclic loading (or a million cycles) with no damage. The stress ratio used for the study was R = 0 this is because the force on the pedal is alternating from 0N to 1000N. The loading type chosen was ‘find cycle peaks’ in order to check what would happen in the worst-case scenario, where both pedals would be loaded with 1000N force at the same time. This case is unrealistic as pedals move reciprocally from each other. As mentioned above Von Mises criterion was used to determine the maximum stresses. The Solidworks simulation set R = -1 for the S-N curve which was then changed to the stress ratio of R=0 with a Gerber mean stress correction to find the correct value. On the frequency studies, the forces exerted from the user's weight on the seats was neglected as it does not have any effect on the study. All other fixtures and forces were used on the studies.


1. Modelling in Solidworks.

2. Using finite element analysis to optimize designs.

by Bettina Sosa Rohl/ Design engineer