How do the thin spokes and rims of bicycle wheels bear the weight of three persons riding on it?

A bicycle wheel has about 40 spokes made of steel rods. These spokes are fixed at the centre on to the hub and at the other end to the rim which itself is a thin steel structure.

The spokes are tightened symmetrically during wheel touring and assume a rigid structure. At any instant of time about 20 spokes are above the horizontal line and about the same number below pointing in nearly equally distributed directions. These two groups of spokes experience the load differently.

A bicycle along with three riders would assumedly weigh about 200kg, a load which gets distributed on to the two wheels. Thus each wheel, in this condition, would carry a load of about 100kg.

The spokes in the vertical position experience higher load than the others. The load is applied at the hub, which results in a tensile loading of the spokes (of the first group) which are above the horizontal line. If these spokes were absent, the load would have been felt by the spokes below; the ones nearly vertical would take the load like a column and the others would experience it as a cantilever. In either case they would buckle or bend under a load technically known as the critical buckling load.

Similarly, it can be seen that even less amount of load would bend the spokes at other angles. This demonstrates that these spokes are not loaded by the weight of 100 kg.

Unlike these ones, the spokes of the first group are loaded in tension. The situation of tensile loading is different from the columnar loading or cantilever loading. The rod under tensile loading would also fail or break when the load exceeds a value known as the ultimate tensile load. For the spokes it turns out to be about 150 kg.

Further, when a cycle is ridden the loading keeps on changing from one spoke to the next and repeats periodically. Thus, no single spoke or no single point in the rim experiences continuous loading, further annulling the propensity to fail.