how spokes transfers the mass of the wheel to periphery

The spokes of a bicycle wheel are generally “cross-laced” and do not pointdirectly towards the hub as the radius of a circle (when they do, they are called “radially laced”). This is done to allow the wheel to transfer torque from the hub to the rim and vice versa. If the spokes were radial, they would allow the rim to rotate a little in respect to the hub when torque is transfered. For this reason, there can be radial laced wheels at the front of a bike with rim brakes (no torque is transferred from hub to rim) but not on a bike with disc brakes (torque is tranferred fom hub to rim when braking).

The spokes in a spoke wheel are “dished” which means that when looking at the wheel in profile, they do not point straight from the middle of the rim to the middle of the hub, but angle to the outside from the rim towards the hub. This is done to obtain lateral rigidty: if a force acts on the rim from the side, the spokes will prevent the rim from losing its alignment.

We can imagine a very simple wheel with four spokes: one pointing up, one down, one front and one back. All spokes have been pre-tensioned and although such wheel will not be a very solid wheel, it will indeed stay more or less true. When this wheel is loaded with a weight acting on the axle, for example a bicycle with a rider, the weight is tranfered to the ground via the spokes: the top spoke will increase its tension, the bottom spoke will reduce it, while the lateral spokes will simply wait for their turn to be de-tensioned.

When the spokes are diagonal in respect to the vertical, two of them will slightly increase their tension, and two will slightly decrease it. All other positions will show an intermediate behaviour. So, as the wheel turns, the spokes will undergo a cycle of tensioning → de-tensioning at each turn of the wheel. It is very important that the pre-tensioning is sufficient to avoid a cycle of fatigue to occur, which will break the spoke. Where will the spoke break? wherever there is an abrupt change in internal tensions: at the beginning of the threaded part that goes under the nipple, where there is a concentration of tension corresponding to the thread grooves, or at the bend where the spoke is attached to the hub. To increase the robustness of the wheel, often the spokes do not have a bend near the hub. To put the weiight where it is needed, some spokes are thicker at the extremities than at the center.